repo
stringlengths 26
115
| file
stringlengths 54
212
| language
stringclasses 2
values | license
stringclasses 16
values | content
stringlengths 19
1.07M
|
|---|---|---|---|---|
https://github.com/daniel-eder/typst-template-jku | https://raw.githubusercontent.com/daniel-eder/typst-template-jku/main/src/template/pages/title.typ | typst | // SPDX-FileCopyrightText: 2023 <NAME>
//
// SPDX-License-Identifier: Apache-2.0
#let title(
title,
subtitle,
author,
department,
first_supervisor,
second_supervisor,
assistant_supervisor,
submission_date,
copyright_year,
thesis_type,
degree,
programme_type,
programme,
) = {
v(0.15fr)
//render title, and slighty smaller the subtitle
align(center)[
#text(2em, weight: 700, title)
#text(1.7em, weight: 400, subtitle)
]
v(1cm)
align(center)[by]
v(1cm)
align(center)[
//now the author
#text(size: 16pt)[#author] \
#v(1.5cm)
//thesis details
#text(size: 15pt)[#thesis_type] \
to confer the academic degree of \
#text(size: 15pt)[#degree] \
in the #programme_type \
#text(size: 15pt)[#programme] \
#v(1cm)
#department \
Johannes Kepler University Linz\
//supervisors
#v(1.5cm)
Supervisor: #first_supervisor \
#{
if(second_supervisor != none){
[Second Supervisor: #second_supervisor \ ]
}
}
#{
if(assistant_supervisor != none){
[Assistant Supervisor: #assistant_supervisor \ ]
}
}
//submission date
#v(1.5cm)
#submission_date
//copyright notice
#v(1cm)
#{
if(copyright_year != none){
[#sym.copyright #author #copyright_year]
}
}
]
} |
|
https://github.com/sitandr/conchord | https://raw.githubusercontent.com/sitandr/conchord/main/examples/tabs.typ | typst | MIT License | #set page(height: auto, width: 60em, margin: 1em)
#import "../lib.typ": tabs, new-chordgen
#let chord = new-chordgen(scale-length: 0.6pt)
#let ending(n) = {
rect(stroke: (left: black, top: black), inset: 0.2em, n + h(3em))
v(0.5em)
}
*This thing doesn't follow musical notation rules, it is used just for demonstration purposes*:
#tabs.new(```
2/4 2/4-3 2/4-2 2/4-3 |
2/4-2 2/4-3 2/4 2/4 2/4 |
2/4-2 p 0/2-3 3/2-2
|:
0/1+0/6 0/1 0/1-3 2/1 | 3/1+3/5-2 3/1 3/1-3 5/1 | 2/1+0/4-2 2/1 0/1-3 3/2-3 | \ \
3/2-2 `5/2-3
p-2
##
chord("022000", name: "Em")
##south
0/2-3 3/2 | | ## [...] ## p-4. | | 7/1-3 0/1-2 p-3 0/1 3/1
##
ending[1.]
##west
|
2/1-3
2/1
3/1 0/1 2/1-2 p-3 0/2-3 3/2-3
##
ending[2.]
##west
|
2/1-2 2/1 0/1-3 3/2 :| 0/6-2 | ^0/6-2 || \
1/1 2/1 2/2 2/2 2/3 2/3 4/4 4/4 4/4 4/4 4/4 4/4 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3 2/3
##
[notice there is no manual break]
##east
| 2/3 2/3 8/3 7/3 6/3 5/3 4/3 2/3 5/3 8/3 9/3 7/3 2/3 | 2/3 2/2 2/3 2/4 |
10/1-3 10/1-3 10/1-3 10/1-4 10/1-4 10/1-4 10/1-4 10/1-5. 10/1-5. 10/1-5 10/1-5 10/1-2 \
1/3bfullr+2/5-2 1/2b1/2-1 2/3v-1
```, eval-scope: (chord: chord, ending: ending)
)
Not a lot customization is available yet, but something is already possible:
#show raw: set text(red.darken(30%), font: "Comic Sans MS")
#tabs.new("0/1+2/5-1 ^0/1+`3/5-2.. 2/3 |: 2/3-1 2/3 2/3 | 3/3 ||",
scale-length: 0.2cm,
one-beat-length: 12,
s-num: 5,
colors: (
lines: gradient.linear(yellow, blue),
bars: green,
connects: red
),
enable-scale: false
)
|
https://github.com/AliothCancer/AppuntiUniversity | https://raw.githubusercontent.com/AliothCancer/AppuntiUniversity/main/ScalettaFisicaTecnica.typ | typst | #import "style.typ": apply_style
#import "custom_functions.typ": def
#let title = align(center)[
#text(
"Formulario di Fisica Tecnica itps",
30pt)
]
#title
#apply_style[
#outline(indent: true)
#pagebreak()
= Trasformazione politropica: Gas perfetto
== Equazione di Stato
== Calore (Q-q)
== Lavoro (W-w)
== Variazione di Entalpia ($Delta$H-$Delta$h)
== Variazione di Entropia ($Delta$S-$Delta$s)
= Cicli a Gas
== Calore
== Lavoro
== Variazione di Entalpia ($Delta$H-$Delta$h)
== Variazione di Entropia ($Delta$S-$Delta$s)
== Efficienza
= Miscela bifasica: Acqua-Vapore
== Calore
== Lavoro
== Variazione di Entalpia ($Delta$H-$Delta$h)
== Variazione di Entropia ($Delta$S-$Delta$s)
= Cicli a Vapore
== Calore
== Lavoro
== Efficienza
= Aria Umida
== Umidità Assoluta
== Umidità Relativa
== Entalpia
== Temperatura di Rugiada
= Trasmissione del calore
== Regime stazionario
== Regime non stazionario
= Scambiatori
== Calore
== Lavoro
== Entropia
== Efficienza
] |
|
https://github.com/tingerrr/subpar | https://raw.githubusercontent.com/tingerrr/subpar/main/test/template.typ | typst | MIT License | // Synopsis:
//
#import "/test/util.typ": *
#import "/src/lib.typ" as subpar
#subpar.grid(
figure(fake-image, caption: [Inner Caption]), <1a>,
figure(fake-image, caption: [Inner Caption]), <1b>,
columns: (1fr, 1fr),
caption: [Super],
label: <1>,
)
|
https://github.com/Lelidle/Q12-cs-scripts | https://raw.githubusercontent.com/Lelidle/Q12-cs-scripts/main/communication.typ | typst | #import "template.typ": *
#import "@preview/tablex:0.0.6": tablex, cellx, rowspanx, colspanx
#import "@preview/bytefield:0.0.2": *
#show: setup
#set enum(numbering: (..args) => strong(numbering("1.", ..args))) // in Aufzählungen Zahlen fett
#set heading (
numbering: "1."
)
#let hm = h(1mm)
#v(1fr)
#align(center)[#text(32pt)[Netzwerkkommunikation \ #align(center)[#image("images/art.png", width: 80%)] ] \ Stable Diffusion Art "Networks"]
#v(1fr)
#pagebreak()
#outline(title: "Inhaltsverzeichnis", indent: auto)
#pagebreak()
#set page(
header: align(right)[
Netzwerkkommunikation Skript 2inf1 \
],
numbering: "1"
)
= Historisches
Das *Internet* entstand primär aus dem 1969 entwickelten ARPANET (Advanced Research Project Agency Networkt) Projekt an dem vier US-Amerikanische Universitäten beteiligt waren, deren Ziel die weitläufige Vernetzung von Rechnern zur gemeinsamen Nutzung von Ressourcen war. Die Idee größere Netzwerke aufzubauen stammte dabei schon aus den Anfängen der 1960er Jahre und viele Gruppen forschten und arbeiteten daran (z.B. auch das US Militär). Dieses Projekt war auch eines der ersten, die das *TCP/IP* Protokoll implementiert haben (#link("https://www.ietf.org/rfc/rfc9293.html")[RFC 9293] - der aktuelle Standard).
In der Folge wurden vor allem weitere Universitäten in Europa und den USA in Netzwerken miteinander verknüpft bis die Technologie so weit ausgereift war, dass es zu einer regelrechten Explosion kam, die dazu führte, dass die meisten technischen Geräte heute miteinander *physikalisch* verbunden sind.
Das *World Wide Web* ist in den 80er Jahren am CERN (Conseil européen pour la recherche nucléaire) entwickelt worden und _nicht_ synonym zum Internet zu verstehen. Spricht man vom Internet, dann ist primär die physikalische Verbindung, d.h. die Hardware der Netzwerke gemeint. Das WWW ist jedoch ein Dienst, d.h. eine Software. Die Grundlage bilden dabei aufeinander verweisende Hypertext-Dokumente, die auf verschiedensten Rechnern abgespeichert sind. Das WWW benutzt also das Internet als Medium, ist jedoch nur einer von vielen Diensten, die das tun. Weitere Beispiele für Dienste sind *E-Mails*, *FTP* (File Transfer Protocol), *HTTP* (Hyper-Text-Transfer-Protocol) oder das *XMPP* (Extensible Messaging and Presence Protocol - für Chat-Anwendungen).
Im Abitur spielt die Netzwerktechnik nur eine sehr untergeordnete Rolle. Dieses Skript ist deswegen deutlich ausführlicher, als es sein müsste, um dennoch einen groben Überblick über die Zusammenhänge zu geben. Im Anhang finden sich einige Abituraufgaben der letzten Jahre.
#pagebreak()
= Wiederholung Bits, Bytes und Hex
In der Informatik werden andere *Stellenwertsysteme* als in der schulüblichen Mathematik verwendet. Während dort das Zehnersystem Einzug gehalten hat ist für Computer das Zweiersystem geeignet (Strom an, Strom aus!).
Das bedeutet konkret: Statt in Zehnerpotenzen zu denken und daraus die Zahlen "zusammenzubauen" wie in der fünften Klasse (z.B. $12985 = 10000 + 2000 + 900 + 80 + 5$) werden *Binärzahlen* aus *Zweierpotenzen* zusammengebaut.
Das erscheint uns auf den ersten Blick merkwürdig - das liegt letztendlich aber nur an der Gewöhnung an das Zehnersystem.
#align(center)[
#tablex(columns: 10, rows: 2, align: center,
colspanx(10)[*Zweierpotenzen für die Umrechnung*],[512],[256],[128],[64],[32],[16],[8],[4],[2],[1]
)]
Wollen wir eine Zahl im Binärsystem darstellen, so sucht man immer die größte Zweierpotenz, die gerade noch in den zu füllenden "Rest" der Zahl hineinpasst und markiert in der Stellenwerttafel dort eine $1$.
Wollen wir beispielsweise $147$ in Binärdarstellung, beginnen wir bei $128 = 2^7$. Damit wissen wir auch, dass die Binärzahl $8$ Zeichen lang ist (wir beginnen bei $2^0=1$!):
$ 1000#hm 0000 $
(Das wäre jetzt nur 128!). Als nächstes betrachten wir den Rest, also $147 - 128 = 19$ Die größte Zweierpotenz, die noch passt ist $16 = 2^4$. Es folgt also eine 1 an fünfter Stelle:
$ 1001#hm 0000 $
Es bleiben $3$, also $2 = 2^1$:
$ 1001#hm 0010 $
Und zuletzt bleibt eine $1 = 2^0$
$ 1001#hm 0011 $
Oder im Zehnersystem ausgeschrieben:
$ 1 dot 128 + 0 dot 64 + 0 dot 32 + 1 dot 16 + 0 dot 8 + 0 dot 4 + 1 dot 2 + 1 dot 1 = 147 $
#hinweis[Die Abstände nach den Viererblöcken wurde nur der besseren Lesbarkeit wegen eingefügt!]
* Weitere Beispiele*
- Binär: $0111#hm 1010$ lässt sich dezimal schreiben als: $ 0 dot 128 + 1 dot 64 + 1 dot 32 + 1 dot 16 + 1 dot 8 + 0 dot 4 + 1 dot 2 +0 dot 1 = 122 $
- Dezimal: $195$ lässt sich umwandeln zu: $ 195 = 1 dot 128 + 1 dot 64 + 0 dot 32 + 0 dot 16 + 0 dot 8 + 0 dot 4 + 1 dot 2 + 1 dot 1 $ und entspricht somit in Binärdarstellung als $1100#hm 0011$
Beschränkt man sich auf Zahlen, die durch 8 Bit (also 1 Byte!) dargestellt werden, dann ist der Zahlenraum also auf die Zahlen von 0 bis 255 beschränkt, da 255 binär $1111#hm 1111$ entspricht.
#hinweis[Ist eine Zahl binär codiert wird häufig die Zeichenkette $0b$ vorangestellt, um zu zeigen, dass es sich um eine Binärzahl handelt, $0\b1011$ ist somit gleichbedeutend mit der Binärzahl $1011$]
<AufgabeBinär>
#task[Wandeln Sie jeweils in Binär bzw. Dezimaldarstellung um.
- $253$
- $1110#h(1mm)0111$
- $187$
- $1011$
- $11#h(1mm)0101#h(1mm)1011$
#link(<LösungBinär>)[Zur Lösung]
]
#v(1cm)
*Hexadezimale Darstellung von Zahlen*
Große 0-1 Folgen sind für Menschen schwer zu lesen. Zum Test - welcher Dezimalzahl entspricht die folgende Binärzahl? $ 01010001101011110000110011101000 $
Es ist natürlich $1370426600$! Um solche $0-1$-Folgen lesbarer zu machen wird häufig die *hexadezimale* Darstellung von Zahlen verwendet, diese verwendet nicht das Zweiersystem, sondern das "Sechzehnersystem". Da wir mit vier Stelle einer Binärzahl gerade 16 Zahlen darstellen können, teilen wir also die obige Zahl in Viererblöcke ein:
$ 0101 #hm 0001 #hm 1010 #hm 1111 #hm 0000 #hm 1100 #hm 1110 hm 1000 $
Jeder dieser Viererblöcke entspricht jetzt einer "Ziffer" im Sechzehnersystem. Da es zu Uneindeutigkeiten kommen würde, wenn man "10" als Ziffer verwendet (Dieses Problem hatte man beim Zweiersystem natürlich nicht) müssen andere Zeichen als "Ziffern" verwendet werden. Man hat sich hier auf die Zeichen a bis f geeinigt, es gilt also:
#table(rows:(auto, auto, auto, auto), columns:(1fr, )*4, inset: 8pt,align: center,
[$(0000)_2 = (0)_16$], [$(0001)_2 = (1)_16$], [$(0010)_2 = (2)_16$], [$(0011)_2 = (3)_16$],[$(0100)_2 = (4)_16$],[$(0101)_2 = (5)_16$],[$(0110)_2 = (6)_16$],[$(0111)_2 = (7)_16$],[$(1000)_2 = (8)_16$],[$(1001)_2 = (9)_16$],[$(1010)_2 = (a)_16$],[$(1011)_2 = (b)_16$],[$(1100)_2 = (c)_16$],[$(1101)_2 = (d)_16$],[$(1110)_2 = (e)_16$],[$(1111)_2 = (f)_16$]
)
Die Klammern zeigen dabei an, wie die Zeichen innerhalb interpretiert werden sollen (das hätte man auch schon bei der Umwandlung vom Binär- ins Dezimalsystem machen können, dort ist die Mehrdeutigkeit aber nicht so dramatisch.)
Die obige Binärzahl enspricht also der folgenden Hex-Zahl:
$ 5 #hm 1 #hm a #hm f #hm 0 #hm c #hm e #hm 8 $
Häufig gruppiert man diese noch zu Zweierpaketen, dann entspricht eine dieser Hex-Gruppen genau einem Byte ($2 dot 4$ Bit!)
$ 51 #hm \af #hm 0c #hm \e8 $
Nochmal veranschaulicht:
$ #text(red)[5]#text(yellow)[1] #hm #text(green)[a]#text(blue)[f] #hm #text(purple)[0]#text(orange)[c] #hm #text(olive)[e]#text(fuchsia)[8] $
$ #text(red)[0101]#hm #text(yellow)[0001] #hm #text(green)[1010]#hm #text(blue)[1111] #hm #text(purple)[0000]#hm #text(orange)[1100] #hm #text(olive)[1110]#hm #text(fuchsia)[1000] $
#hinweis[Ähnlich wie bei der Binärdarstellung wird bei der Hexadezimalen Darstellung häufig die Zeichenkette $0x$ vornangestellt. $0x\f\f11$ ist also die Hexadezimalzahl $\f\f11$]
<AufgabeHexa>
#task[Wandeln Sie jeweils von Binär- in Hexadezimaldarstellung oder umgekehrt um:
- $0110 #hm 0111$
- $\ff #hm \af$
- $1010 #hm 1100 #hm 0001 #hm 1001$
- $0e #hm \c1 #hm 10$
#link(<LösungHexa>)[Zur Lösung]
]
#pagebreak()
== Protokolle
Damit Kommunikation sinnvoll ablaufen kann müssen die "Spielregeln" der Kommunikation eindeutig festgelegt werden, sei es die Wahl der Sprache, das gewählte Kommunikationsmedium oder auch nur die beteiligten Personen bzw. Entitäten. Die Vereinbarungen für die technische Kommunikation sind in *Protokollen* festgehalten.
#hinweis[Dieser Protokollbegriff ist nicht nur auf die Informatik begrenzt, es gibt beispielsweise auch *diplomatische Protokolle*, die den Ablauf von Staatsbesuchen regeln.]
Wir wollen im Folgenden dies unter einem Protokoll verstehen:
#definition[Ein *Protokoll* ist ein Satz von Regeln und Richtlinien für den Austausch von Daten bzw. Informationen zwischen zwei Parteien.
Ein *Netzwerkprotokoll* ist dann ein Kommunikationsprotokoll für den Austausch von Daten zwischen Computern bzw. Prozessen.
]
Es gibt immens viele Protokolle in der technischen Welt, neben den oben bereits erwähnten ließe sich noch eine viel längere Liste ergänzen: *DHCP, DNS, HTTPS, TCP, UDP, IP, SMTP, POP3, IMAP, etc.*
= Das OSI-Modell
Schlägt man ein beliebiges Buch oder einen Text zur Netwerkprogrammierung auf, so ist die Wahrscheinlichkeit auf das OSI-(open Systems Interconnection) Modell zu stoßen sehr groß.
#let cell = rect.with(
inset: 8pt,
fill: rgb("e4e5ea"),
width: 100%,
radius: 6pt
)
#grid(columns:(30%, 70%), rows:(auto,)*7, gutter: 6pt,
cell(fill: rgb(255, 102, 0))[*Anwendungsschicht*], cell(fill: rgb(255, 102, 0))[Alle anwendungsspezifischen Protokolle],
cell(fill: rgb(255, 102, 0))[*Darstellungsschicht*], cell(fill: rgb(255, 102, 0))[Syntax und Semantik der Daten wird geprüft, ggf. Codierung und Datenkompression],
cell(fill: rgb(255, 102, 0))[*Sitzungsschicht*], cell(fill: rgb(255, 102, 0))[Zuständig für Synchronisation, wenn die Benutzer eine gemeinsame Sitzung aufbauen, nur verbindungsorientiert.],
cell(fill: rgb(0, 128, 255))[*Transportschicht*], cell(fill:rgb(0, 128, 255))[Zuständig für die Port-Adressierung, hier kommunizieren zwei Prozesse. Unterteilt den Bitstrom der Sitzung in größere Pakete, Kanal oder Broadcast.],
cell(fill: rgb(251, 255, 0))[*Vermittlungsschicht*], cell(fill: rgb(251, 255, 0))[Zuständig für die IP-Adressierung, Routenwahl, Steuerung bei Staus, Verknüpfung von Teilnetzen.],
cell(fill: rgb(240, 0, 0))[*Sicherungsschicht*], cell(fill:rgb(240, 0, 0))[Zuständig für die Zugriffskontrolle zum Medium, das Verpacken der Daten in Einheiten.],
cell(fill: rgb(240, 0, 0))[*Bitübertragungsschicht*], cell(fill: rgb(240, 0, 0))[Zuständig für die Definition der physikalischen Signale, Anschlüsse, Steuerung der Leitungsaufteilung]
)
Die Farbgebung in obiger Tabelle soll bereits andeuten, dass einige der Schichten für unsere Zwecke zusammenfassbar sind. Wir beschäftigen uns nur mit der:
1. #text(rgb(240, 0, 0))[*Übertragungssschicht*]: Im OSI-Modell die Sicherungs- und Bitübertragungssschicht - hier geht es um die tatsächliche physikalische Verbindung zwischen den Computern bzw. Netzwerken.
2. #text(rgb(255, 200, 0))[*Vermittlungsschicht*]: s.o.
3. #text(rgb(0, 128, 255))[*Transportschicht*]: s.o.
4. #text(rgb(255, 102, 0))[*Anwendungsschicht*]: Hier unterscheiden wir nicht im Detail wie im OSI-Modell, sondern fassen die entsprechenden anwendungsorientierten Aufgaben in einer Schicht zusammen.
Im Abitur beziehen sich fast alle Aufgaben, die zur Netzwerktechnik gestellt werden auf ein Schichtenmodell. Dabei wird allerdings eher selten ein technisches Modell gewählt, sondern eine Analogie (wie das diplomatische Protokoll oben).
Aus diesem Grund folgt hier ein nicht-technisches Beispiel für ein Schichtenmodell, das den Versand eines Pakets von unserem Schulleiter zum Schulleiter des Albert-Einstein-Gymnasiums in München modelliert:
#align(center)[
#image("images/paketversand.png")
]
Die durchgezogenen Pfeile zeigen dabei den physikalischen Datenfluss (hier rot), d.h. in diesem Beispiel das Paket, das durch die verschiedenen Stationen wandert.
#hinweis[Hier haben wir schon den ersten "Pferdefuß" der Analogie, wir werden sehen, dass im technischen Modell die Daten _nicht_ in diesem Sinne durch alle Schichten wandern.]
Für uns interessant sind aber die weiteren Ebenen. Denn auch hier findet Kommunikation statt, die indirekt in den physischen Daten mit eingebettet sind. Das könnte beispielsweise so aussehen:
#align(center)[
#image("images/paketversand_2.png")
]
1. Der Schulleiter wird in aller Regel ein persönliches Anschreiben beigelegt haben, das von seinem Kollegen gelesen wird.
2. Das Sekretariat des WGG muss das Paket addressieren, damit es einerseits von der Post korrekt zugestellt werden kann, andererseits gehen Pakete an Schulen zunächst im Sekretariat ein, d.h. die Weiterleitung an den Schulleiter geschieht durch das Sekretariat des AEG.
3. Die Postfiliale Neumarkt muss das Paket korrekt ettiketieren, damit die Weiterleitung nach München korrekt funktioniert.
Man kann jetzt eine (gewisse) Analogie zwischen diesem Schichtenmodell beim Postversand und der Kommunikation zwischen zwei Computern ziehen.
#align(center)[
#image("images/paketversand_3.png")
]
#pagebreak()
Noch einmal zusammengefasst:
#let cell50 = rect.with(
height: 50pt,
inset: 8pt,
fill: rgb("e4e5ea"),
width: 100%,
radius: 6pt
)
#v(2mm)
#grid(rows: (auto,)*5, columns: (20%, 30%, 50%), gutter: 10pt, cell[*Schicht*], cell[*Post*], cell[*Netzwerk*],
cell50[ \ *Anwendung*],cell50[Informationsaustausch Schulleiter],cell50[anwendungsspezifische Interpretation der übertragenen Daten, Syntaxüberprüfung, ggf. Codierung oder Kompression der Daten],
cell50[ \ *Transport*],cell50[Senden und Empfangen, Adressierung],cell50[Zuverlässiges Senden und Empfangen, Überprüfung auf Vollständigkeit, Unterteilung in Datenpakete, Weitergabe an die richtige Anwendung],
cell50[\ *Vermittlung*], cell50[Weitervermittlung und Wegewahl (Routing)], cell50[Routing innerhalb des Netzwerks, Steuerung bei Staus, Verbindung zu anderen Teilnetzen],
cell50[\ *Übertragung* ], cell50[physikalischer Transport (zumindest den Hauptteil des Weges) des Paketes.], cell50[physikalischer Transport der Daten, Definition der physikalischen Signale, Aufteilung der Leitung, Übergabe der Daten an die Leitung],
)
Es stellt sich die Frage, warum man den Aufwand der Betrachtung der Schichten überhaupt betreibt. Einige Vorteile ergeben sich dadurch offensichtlich:
1. Jede Schicht hat ihre spezielle Aufgabe und agiert *unabhängig* von den anderen Schichten. Die Protokolle der einzelnen Schichten bauen zwar aufeinander auf, können aber dennoch unabhängig voneinander weiterentwickelt werden.
2. Die *Komplexität* der einzelnen Module ist durch die Aufteilung reduziert.
3. Höhere *Flexibilität* für Austausch von Modulen.
4. Leichtere *Handhabbarkeit* durch einfache und sauber definierte Schnittstellen zwischen den Schichten.
Merkt man sich die obigen Fakten ohne weitere Details, so kommt man bei Abituraufgaben schon relativ weit, ein Beispiel aus dem Abitur von 2022, in diesem Fall sogar ein technisches Beispiel:
#align(center)[
#image("images/abi2022.png")
]
Auch im Abitur 2021 lässt sich eine ähnliche Aufgabe finden:
#align(center)[
#image("images/abi2021.png")
]
#pagebreak()
= Übertragungsschicht
Die unterste Schicht beschäftigt sich, wie bereits erwähnt, mit der physikalischen Übertragung der Daten und ist für uns nur von geringem Interesse. Nur ein Aspekt ist von Relevanz:
== Topologie von Rechnernetzen
Geräte können auf verschiedene Arten miteinander verbunden werden, die jeweils verschiedene Vor- und Nachteile haben. Man spricht bei einer "Verbundart" auch von einer *Topologie*.
Im Folgenden werden die einzelnen Topologien jeweils nach den folgenden Kritierien untersucht bzw. bewertet:
1. *Störanfälligkeit*: Wie wirkt sich der Ausfall eines Rechners oder einer Verbindung aus.
2. *Systempflege*: Wie groß ist der Aufwand bei der Fehlersuche oder beim Erweitern.
3. *Kosten*: Wie hoch sind die Kosten für Leitungen oder spezielle Komponenten vergleichsweise.
4. *Übertragungsrate*: hierunter fällt auch die Frage nach möglichen Kollissionen.
*Stern-Topologie*
In der "realen Welt" ist diese Topologie die vorherrschende. Der Name ist im Wesentlichen selbsterklärend, es gibt es einen zentralen Rechner, der in der Mitte sitzt, die anderen werden "sternförmig" darum angeordnet. Das ist natürlich nur eine idealisierte netzwerktechnische Darstellung und stellt nicht notwendigerweise die tatächliche räumliche Positionierung dar.
#align(center)[
#image("images/stern_topologie.png", width:50%)
]
*Analyse*:
1. Der Ausfall des Zentralrechners ist problematisch, der Ausfall aller anderen Rechner dagegen nicht relevant.
2. Sowohl die Fehlersuche als auch die Erweiterung sind problemlos möglich.
3. Der Zentralrechner muss hochwertig sein.
4. Die Übertragungsrate kann, je nach Zentralrechner und Anzahl der Geräte insgesamt sein. Kollisionen können durch eine Steuerung des Zentralrechners aber vermieden werden.
*Bus-Topologie*
Hier sind alle Geräte mit einer zentral verlaufenden Leitung (Bus) verbunden, es gibt in diesem Sinne keine "zentrale" Stelle.
#grid(rows: auto, columns:(50%, 50%),
[#align(center)[
#image("images/bus_topologie.png", width:80%)
\ Bus - Topologie] ], [#align(center)[
#image("images/token_bus_topologie.png", width: 80%)
\ Token -Bus Topologie] ])
1. Der Ausfall des Bus ist problematisch, der Ausfall von Rechnern dagegen nicht.
2. Sowohl die Fehlersuche als auch die Erweiterung sind problemlos möglich.
3. Der Bus muss eine hohe Bandbreite besitzen, ansonsten gibt es keine teuren Komponenten.
4. Die Übertragungsrate hängt (quasi) alleine vom Bus ab. Bei hoher Last lassen sich Kollissionen nicht direkt vermeiden. Es kann der Ansatz eines sogenannten *Token Bus* verwendet werden - dann kann nur derjenige Rechner, der gerade den Token hat Informationen senden.
*Ring-Topologie*
Auch hier ist der Name wieder selbsterklärend.
#grid(rows: auto, columns:(50%, 50%),
[#align(center)[
#image("images/ring_topologie.png", width:80%)
\ Ring - Topologie] ], [#align(center)[
#image("images/token_ring_topologie.png", width: 80%)
\ Token - Ring Topologie] ])
1. Der Ausfall jedes Geräts unterbricht den Ring, führt aber nicht zu einem Totalausfall des Netzes.
2. Der Aufwand bei einer Fehler ist hoch, die Erweiterung geringfügig umständlicher als bei den vorherigen Topologien.
3. Es gibt keine besonders teuren Komponenten.
4. Die Übertragungsrate hängt von der Anzahl der Rechner ab. Kollisionen können analog zum Bus bei hoher Last auftreten und wiederum durch Verwendung eines Token-Rings vermieden werden.
*Direkte Verbindungen (Peer to Peer)*
Bei dieser Bauart ist jeder Rechner mit jedem anderen verbunden.
#align(center)[
#image("images/direkt_topologie.png", width:50%)
]
1. Der Ausfall jedes Geräts ist unproblematisch.
2. Der Aufwand bei der Fehlersuche ist gering, das erweitern dagegen sehr aufwändig.
3. Keine teuren Komponenten, aber sehr viele Leitungen nötig $(~ n^2)$ mit $n$ der Anzahl der Rechner.
4. Die Übertragungsrate ist sehr hoch, Kollisionen sind dagegen selten.
*Kombinationen*
Natürlich sind auch Kombinationen verschiedener Arten von Rechnernetzen möglich!
== Ethernet-Protokoll
Das *Ethernet*-Protokoll operiert eigentlich auf der zweiten Schicht (Sicherungsschicht) des OSI-Modells. Es ist auch den meisten nicht-technisch versierten Personen ein Begriff und bezeichnet einen Standard für die Kommunikation in kabelgebundenen Netzwerken (LAN).
Es verbleibt die Frage, welchen Zweck dieses Protokoll erfüllt. Mit Hilfe des Ethernet-Protokolls können Netzwerkadapter mit ihrer "Umgebung" erst kommunizieren - eine physische Verbindung ist noch nicht ausreichend. Damit sind die Geräte gemeint, die direkt mit diesem (via Kabel) verbunden sind.
Ein Gerät (genauer gesagt seine Netzwerkkarte) hat eine eindeutige *MAC-Adresse* (Media-Access-Control-Address, auch *physische Adresse*) - also die Nummer, die diesem als Identifikator dient.
Ein Ethernet-Paket enthält also zunächst die zugehörige MAC-Adresse des Geräts, zu dem das Paket kommen soll - außerdem die MAC-Adresse des Ursprungsgeräts, sowie einen *EtherType*, das anzeigt, welches Protokoll im Paket enthalten ist. Beispielsweise steht $0\x0800$ der EtherType für das IPv4 Protokoll, $0\x0842$ für das Wake-on-LAN Protokoll, etc. Diese Informationen werden auch als MAC Header bezeichnet.
#align(center)[#image("/images/ethernet_frame.png")]
Danach folgen die eigentlichen Daten, die transportiert werden sollen. Abschließend findet sich noch eine CheckSum, die die Integrität der Daten sicherstellt (sie wird mit dem Cyclic Redundancy Check, kurz CRC berechnet).
#hinweis[Das Ethernet-Protokoll stellt nicht sicher, dass das Paket ankommt, sollte es von einem Geräte unterwegs "fallen gelassen" werden, so erfolgt nicht automatisch ein erneutes Senden.]
Das Ethernet-Protokoll kümmert sich auch nicht weiter um die darauf aufbaueneden Protokolle, d.h. die transportierten Daten sind in keiner Weise in dieses Protokoll mit eingebaut, d.h. die Sicherungsschicht arbeitet autark von den Übrigen.
= Vermittlungsschicht
Im Gegensatz zu früheren direkten Kommunikationsformen ist es - wie bereits erwähnt - nicht mehr ausreichend, dass physikalische Leitungen vorhanden sind.
In früheren Telefonnetzen wurden die Apparate direkt miteinander verbunden ("Ich verbinde.."), um die Kommunikation herzustellen.
Datenpakete müssen heute ihren Weg durch das Netzwerk finden, um zum entsprechenden Ziel zu kommen. Die Wege kurz aufeiander folgender Datenpakete können dabei grundlegend verschieden sein. Hier kommen Begriffe wie die *IP-Adresse*, *Routing* und entsprechende Geräte wie der *Router* ins Spiel.
#merke[Das verschiedene Pakete, die eigentlich zur selben "Sendung" gehören unterschiedliche Routen nehmen bedeutet natürlich auch, dass sie möglicherweise nicht in derselben Reihenfolge ankommen in der sie abgeschickt wurden. Dieses Problem löst das TCP-Protokoll, dazu später mehr.]
== IP-Adressen
*IP(v4)* ist die erste Version des Internet Protocols, das weltweit verbreitet und eingesetzt wurde. Eine solche IP-Adresse besteht aus einer 32-stelligen Binärzahl, die jeweils einem Netzwerkadapter im Internet zugeordnet ist und so eine Identifizierung möglich macht, da sie im betreffenden Netwerk eindeutig ist. Netwerken von z.B. Providern wird dann ein ganzer Block an Adressen zugeordnet (siehe unten).
Für die Weiterleitung von Datenpaketen ist die IP-Adresse geeigneter als die MAC-Adresse, da wir Subnetze zusammenfassen können. Würden nur MAC-Adressen zur Weiterleitung benutzt, so müssten immer alle MAC-Adressen, die erreichbar sind, überall auf dem Weg gespeichert werden. Dies ist mit IP nicht der Fall, da in der Routingtabelle (über die ein Netzwerkgerät i.d.R. verfügt) am Besten passende IP-Adressbereich gesucht wird und das Paket dorthin weitergeleitet wird.
#hinweis[*Für die Experten*:
1. streng genommen erlaubt die Netzwerkadressübersetzung (NAT), dass IP-Adressbereiche mehrfach verwendet werden, da sie "nach außen" hin nur mit der IP-Adresse des Zugangsgeräts (also des Routers) identifiziert werden. Global gesehen ist also auch ein Netzwerkadapter nicht eindeutig mit einer IP-Adresse verknüpft, sondern mit seiner MAC-Adresse.
2. Es gibt zwei weitere Protokolle, die im Detail "vernünftige" Wege durch das Netz finden, nämlich *OSPF* (dieses verwendet auch den Dijkstra Algorithmus! siehe 11.) und *BGP*]
Zur besseren Lesbarkeit wird die Adresse üblicherweise in vier 8-stellige Blöcke aufgeteilt (also in 4 Byte Blöcke) und (für den Menschen) dann in Dezimalschreibweise abgebildet - jeweils durch einen Punkt getrennt.
*Beispiel*
$ 01101100001000010000111100110111 $
$ 01101100#hm 00100001#hm 00001111#hm 00110111 $
$ 108 . 33 . 15 . 55 $
#task(customTitle: "Kurze Denkaufgabe!")[Wie viele solcher IP-Adressen können gebildet werden?]
Es sind natürlich $2^(32)$, also etwa $4,3$ Millarden Adressen.
<AufgabeIP>
#task[Wandeln Sie jeweils von Binär- in Dezimaldarstellung oder umgekehrt um:
- $192.168.3.11$
- $0101#hm 1000 #hm 0110 #hm 0011 #hm 0011 #hm 1111 #hm 1001 #hm 0011 $
#link(<LösungIP>)[Zur Lösung]
]
*IP(v6)* Da die Anzahl der möglichen IPv4-Adressen doch recht klein ist im Vergleich zu der Anzahl an Geräten und Netwerken wurde ein neuer Standard entwickelt. Die Adressen in diesem Standard sind $128$ Bit lang, somit gibt es $2^(128)$ unterschiedliche IPv6-Adressen.
Hier kommt auch die hexadezimale Darstellung ins Spiel, denn die Größe der Zahlen macht es sonst wieder unlesbar. Die Adresse wird also in 8 Blöcke zu je 16 Bit eingeteilt, die wiederum hexadezimal kodiert werden, a.so z.B.:
$ 2600:1\f18:001f:\d\b00:807b:\f1\f4:\d01b:30\b1 $
#hinweis[Ob dieses Format wirklich lesbarer ist oder wirklich sein muss sei einmal dahingestellt..]
Die Tatsache, dass IPv6 Adressen noch nicht "der Standard" ist liegt an zweierlei:
1. Es gab andere technische "Tricks", mit denen die Limitierung von IPv4 abgefedert wurde.
2. Es braucht Zeit, bis sich Dinge durchsetzen, die neu sind. (Es sei nochmal darauf hingewiesen, dass in vielen Betrieben Java 8 der Standard ist z.B.)
== Adressvergabe
IP-Adressblöcke werden an Unternehmen und Organisationen vergegeben, die diese ihrerseits wieder verteilen können.
*Vergebene Adressblöcke*:Findet man z.B. #link("https://ftp.ripe.net/ripe/stats/membership/alloclist.txt")[hier]
Die Einträge sind dabei folgendermaßen zu lesen: *$172.16.58.3\/19$*
Die Zahl 19 bedeutet hier: Für alle Adressen aus dem Adressblock gilt, dass die ersten 19 Bit fest vorgegeben sind (der sogenannte "Netz Anteil") und die restlichen Stellen (also der Anteil des Hosts) verwendet werden kann, d.h. die rot markierten Stellen sind fix:
$ 172.16.58.3 = #text(red)[xxxx #hm xxxx . xxxx #hm xxxx . #hm xxx]"x" #hm "xxxx. xxxx xxxx" $
#task(customTitle: "Kurze Denkaufgabe")[Wie viele Adressen umfasst damit der Adressblock aus dem Beispiel, d.h. wie viele Adressen kann der Kunde hier nutzen]
Da 13 Bit für den Kunden verfügbar sind, kann er $2^(13)$ Adressen verwenden, also alle Adressen von $172.16.58.3$ bis $192.168.127.12$
#hinweis[*Für die Experten*: Streng genommen sind nur $2^13 - 2$ Adressen verwendbar, da es zwei "spezielle" Adressen gibt:
1. Sind alle schwarzen x gleich 0, dann spricht man von der *Network Identifier Adress*, die zur Identifizierung des Netzwerks verwendet wird.
2. Sind alle schwarzen x gleich 1, dann spricht man von der *Broadcast Adress* - Datenpakete, die an diese Adresse gehen werden kopiert und zu allen Adressen im Netzwerk weitergeleitet. ]
Bei der Notation mit dem Slash spricht man auch von der *CIDR*-Notation (Classless Inter-Domain Routing), die das Konzept der #link("https://de.wikipedia.org/wiki/Netzklasse")[Netzklassen] abgelöst hat.
In der #link("https://www.rfc-editor.org/rfc/rfc1918")[RFC 1918] werden außerdem bestimmte Adressblöcke für private Netze festgelt.
#hinweis(customTitle: "Zitat")[The Internet Assigned Numbers Authority (IANA) has reserved the following three blocks of the IP address space for private internets:
1. $10.0.0.0 - 10.255.255.255$ (10/8 prefix)
2. $172.16.0.0 - 172.31.255.255$ (172.16/12 prefix)
3. $192.168.0.0 - 192.168.255.255$ (192.167/16 prefix)
We will refer to the first block as "24-bit block", the second as "20-bit block" and to the third as "16-bit block". Note that (in pre-CIDR notation) the first block is nothing but a single class A network number, while the second block is a set of 16 contiguous class B network numbers and third block is a set of 256 contiguous class C network numbers.
An enterpreise that decides to use IP addresses out of the adress space defined in this document can do so without any coordination with IANA or an Internet registry. The address space can thus beused by many enterprises. Adresses within this private address space will only be unique within the enterprise, or the set of enterprises which choose to cooperate over this space so they may communicate with each other in their own private internet.
]
Nochmals kurz zusammengefasst: die oben erwähnten Bereiche werden *nicht für öffentliche Adressen im Internet vergeben*. Zur öffentlichen Kommunikation wird dem *gesamten Teilnetz* vom Internetprovider eine IP-Adresse aus einem seiner Adressblöcke zugeteilt (siehe NAT weiter oben). Jedes Gerät des Teilnetztes ist nach außen hin dann nur unter dieser Adresse sichtbar (Bei IPv6 ist dies nicht mehr notwendig. Es gibt dort so viele Adressen, dass tatsächlich jedes Gerät (auch auf absehbare Zeit) seine eigene Adresse haben könnte).
*Dynamische Adressierung*: In beiden Fällen (lokal/öffentlich) gibt es sowohl die Möglichkeit, dass man immer die gleiche, also eine feste Adresse hat, als auch die Möglichkeit, dass in gewissen Absständen bzw. bei jedem Beitritt zum Netz eine beliebige verfügbare Adresse zugeteilt wird, also *dynamisch*.
== Routing
Aufgrund der Struktur des Internets verlaufen Wege nicht "direkt", sondern die Kommunikation kann über verschiedenste Geräte verlaufen. Möchte man die *Route* nachverfolgen, kann unter Windows beispielsweise der _tracert_ Befehl verwendet werden. Im folgenden Beispiel wurde
```
tracert wgg-neumarkt.de
```
ausgeführt:
#image("images/routing.png")
Der erste "Hop" ist dabei die hauseigene Fritzbox, die die Verbindung nach außen regelt. Es folgen einige Hops über Zwischenstationen, bis offenbar der Adressbereich der WGG-Homepage erreicht wird (172.16.31.10). Von dort aus ist es dann nur noch ein Sprung bis zur eigentlichen Website.
Im Allgemeinen sind die Strukturen und technischen Details noch wesentlich komplexer. Für uns reicht aber dieser grobe Überblick.
#hinweis[Für Interessierte: der _tracert_ Befehl verwendet das Internet Control Message Protocol ICMP, das zur Fehlersuche und Steuerung in der IP-Welt verwendet wird, da es Metadaten sendet.]
= Transportschicht
An diesem Punkt können wir zwar einen Weg durch unser Netzwerk finden, allerdings müssen wir noch einige Probleme/Fragen lösen:
1. Wie sollen die zu versendenen Daten *aufgeteilt*, d.h *segmentiert* werden?
2. Wie werden *Staus* vermieden?
3. Ist der Verlust einzelner *Datenpakete* in Ordnung?
4. Wie stellen wir sicher, dass die Übertragung *fehlerfrei* abläuft?
Alle diese Fragen werden in der Transportschicht beantwortet. Die beiden wichtigsten Protokolle in diesem Zusammenhang sind *TCP* und *UDP*.
== UDP-Protokoll
Das *User Datagram Protocol* ist vergleichsweise einfach gestrickt, es sendet lediglich die Daten und kümmert sich um nicht viel mehr. *UDP* hat insbesondere einige Eigenschaften, die auf TCP nicht zutreffen:
1. Es ist *verbindungslos* - ein etwas missverständlicher Begriff der aussagt, dass Kommunikation in der "Gegenrichtung" nicht möglich ist (Rundfunk wäre also verbindungslos z.B.).
2. Es ist *nicht-zuverlässig*, d.h es ist nicht sichergestellt, dass die ankommenden Daten vollständig und fehlerfrei sind.
3. Es ist *ungesichert* und *ungeschützt*, d.h. es gibt keine eingebauten Sicherheitsmechanismen, die eine Verfälschung verhindern. (Bei TCP auch nur in Verbindung mit z.B. TLS gegeben, siehe unten).
Diesen Nachteilen stehen einige dadruch entstehende Vorteile gegenüber:
1. TCP hat die obigen Eigenschaften, dadurch wird die Datenlast aber größer, da z.B. Sicherheitsmechanismen durch zusätzliche Daten wie checksums realisiert werden.
2. Die Übertragungsgeschwindigkeit ist deutlich höher.
Der Heder eines UDP-Ports sieht wie folgt aus:
#align(center)[
#image("images/udpheader.png", width:50%)
Quelle: #link("https://www.geeksforgeeks.org/examples-on-udp-header/")[geeksforgeeks]
]
*Zum Port-Begriff*
Da auf jedem Rechner *viele Prozesse* ablaufen, die gegebenenfalls aber alle Datenpakete aus dem Netzwerk beziehen wollen, muss ein Unterscheidungsmerkmal getroffen werden. Dieses Merkmal wird *Port* genannt und entsprechend dieser *Portnummer* werden einkommende Datenpakte eindeutig zugeordnet werden. Die Portnummer ist eine Folge aus 16 Bits.
*Beispiele für übliche Portnummern*
- http: hypertext transfer protocol: 80
- https: hypertext transfer protocol secure: 443
- FTP: file transfer protocol: 21
- POP3: post office protocol 3: 110
- SMTP: Simple mail transfer protocol: 25
#hinweis[UDP und TCP arbeiten voneinander unabhängig, d.h. Ports können von beiden verwendet werden - man kann also eine TCP und eine UDP Anwendung z.B. auf Port 80 lauschen lassen.]
Die Nachteile von UDP scheinen auf den ersten Blick stark zu überwiegen, dennoch nutzen einige Bereiche dieses Protokoll, wenn die Latenz gering sein soll und der Verlust einzelner Pakete nicht so schwer wiegt, Beispiele sind:
1. *Voice over IP*: Anwendungen, die Sprach- oder Videoanrufe aufbauen.
2. *Videostreaming*
3. *Online-Gaming*
== TCP-Protokoll
Das *Transmission Control Protocol* verlangt eine Verbindung zwischen zwei festgelegten Endpunkten (sogenannte *Sockets*) - in der Regel greift TCP dabei auf das IP-Protokoll der Vermittlungsschicht darunter zurück.
Möchte man via TCP eine Verbindung zu einem bestimmten Dienst - also z.B. auf einem Server irgendwo im Internet - aufbauen, dann sind vier Informationen notwendig:
1. Die eigene IP-Adresse, also die der Quelle der Anfrage.
2. Der eigene *Port* (siehe oben).
3. Die IP-Adresse des Ziel-Rechners.
4. Der Port, der auf dem Zielrechner angesteuert werden soll.
Ein typischer Verbindungsaufbau (*Three-Way-Handshake*) sieht dann wie folgt aus:
1. Der Client schickt ein *SYN*-Paket (von engl. synchronize) an den Server.
2. Der Server antwortet - sofern der entsprechende Port geöffnet ist - mit einem *SYN/ACK*-Paket (von engl. acknowledge).
3. Der Client bestätigt den Erhalt dieses Pakets, indem er selbst ein *ACK*-Paket zurücksendet.
Damit ist die Verbindung hergestellt. Ein etwas genaueres Bild der ablaufenden Prozesse bietet das Zustandsdiagramms eines zugehörigen Automaten (aus #link("https://www.ietf.org/rfc/rfc9293.html")[RFC9293]).
Und auch hier gilt noch ein Hinweis, der direkt über dem Diagramm steht:
"NOTA BENE: This diagram is only a summary and must not be taken as the total specification. Many details are not included."
#align(center)[
#image("images/tcpstate.png", width:75%)
]
= Anwendungsschicht
Nachdem nun alle unterliegenden Schritte abgeschlossen sind und eine Verbindung hergestellt wurde, können die Anwendungen die entsprechenden Daten verarbeiten.
== HTTP-Protokoll
Das *Hypertext Transfer Protocol* ist das wohl bekannteste Protokoll, das verwendet wird, um Hypertext-Dokumente (also HTML-Code, üblicherweise) aus dem WWW zu laden und (in der Regel) durch einen Browser darstellen zu lassen.
Ein typischer Ablauf sieht dabei wie folgt aus:
1. Der Nutzer tippt in einen Browser eine *URL* ein (s.u.).
2. Die URL wird mittels des *DNS*-Protokoll (s.u.) in eine IP-Adresse umgesetzt.
3. Zur Verbindung wird das TCP-Protokoll auf Port 80 genutzt und eine HTTP-GET-Anfrage gesendet.
4. Ist die Anfrage in Ordnung, dann folgt eine Antwort mit dem Code "*200*" (OK) und den angeforderten Daten. War mit der Anfrage etwas nicht in Ordnung, so wird in der Regel eine Fehlermeldung zurückgesendet (z.B. das berühmte *404* - nicht gefunden.)
== DNS-Protokoll
Um die Übersetzung von URLS in IP-Adressen möglich zu machen gibt es das *DNS*-Protokoll (Domain Name System). Hierbei handelt es sich um ein globales Netzwerk an Servern, die die "Adressen", die für das Internet relevant sind, speichern und auf Anfrage versenden (z.B. unterhält Google einen DNDS-Server, der unter der IP-Adresse 8.8.8.8 erreichbar ist. Ein weiterer beliebter DNS-Server ist 1.1.1.1 von Cloudflare. Legt man mehr Wert auf Privatsphäre, so empfiehlt sich beispielsweise der DNS Server 9.9.9.9)
Tippt man nun eine URL in die Adresszeile ein, so laufen folgende Schritte ab:
1. Der Browser prüft, ob die Adresse bereits im lokalen *Cache* hinerlegt ist.
2. Falls nein, wird eine Anfrage an den vom Internetanbieter (ISP) bereitgestellten *Router* geschickt - auch dieser hat einen Cache.
3. Falls auch dieser nicht weiterweiß, wird eine Anfrage an den vom ISP verwendeten *DNS-Server* gestellt.
4. Die meisten (üblichen) Seiten sind dort hinterlegt. Falls aber immer noch keine IP-Adresse gefunden werden kann, wird weiter eskaliert - Interessierte können an dieser Stelle weiterrecherchieren!
5. Die Adresse wird zurückgesendet und kann jetzt für einen Verbindungsaufbau verwendet werden.
== URL
Der *Uniform Ressource Locator* ist eine alternative Bezeichnung für bestimmte Internetadressen, damit keine IP-Adressen in den Browser eingegeben werden müssen. Eine URL besteht dabei immer aus einem Schema und einem daraus folgenden schema-spezifischen Anteil.
*Beispiel*:
#align(center)[#text(red)[https]: #text(blue)[\/\/www.wgg-neumarkt.de]]
Das Schema ist dabei das HTTPS-Protokoll, also die (sichere) Anfrage nach einer Website. In Blau stehen dabei der Alias des Namens des Servers, der erreicht werden soll, sowie die Domain.
Auch hier könnte man deutlich tiefer in Details eintauchen, die aus Zeitgründen - und geringer Relevanz für das Abitur - aber entfallen.
= Organisationen
Es gibt mehrere Organisationen, die mit der *"Verwaltung"* des Internets beschäftigt sind:
1. #text(red)[*ICANN*]: Internet Corporation for Assigned Names and Numbers \ Diese Organisation koordiniert die Vergabe von einmaligen Namen und Adressen im Internet. Dazu gehören insbesondere die Koordination des Domain Name Systems und die "IANA-Funktion" (Internet Assigned Names and Numbers).
2. #text(red)[*Réseaux IP Européens Network Coordination Centre*] \ Eine ähnliche Organisation, die aber speziell für Europa, den Nahen Osten und Teile von Zentralasien zuständing ist.
3. #text(red)[*IETF*]: Internet Engineering Task Force \ Hier wird im Wesentlichen die technische Weiterentwicklung des Internets vorangetrieben.
4. #text(red)[*IEEE*]: Ein Berufsverband von Ingenieuren und Technikern, die sich mit der Standardisierung der Netzwerktechnik beschäftigen.
In diesem Sinne keine Organisation, aber #text(red)[*RFC*] Request for Comments sind dennoch unerlässlich: \ In diesem Skript bereits mehrfach erwähnt wurden RFC Memos, die gewisse Standards vorgeben. Diese Standards müssen implementiert bzw. berücksichtigt werden, wenn neue Technologie in den Verbund des Internets aufgenommen werden wollen.
#pagebreak()
= Lösungen
Die Klammerschreibweise zeigt jeweils an, zu welcher Basis die Ziffern interpretiert werden sollen.
- $(253)_10 = (1111#hm 1101)_2$
- $(11100#hm 0111)_2 = (231)_10$
- $(187)_10=(1011#hm 1011)_2$
- Uneindeutige Aufgabenstellung (Genau genommen natürlich überall, aber hier ist es besonders uneindeutig:) Entweder $(1011)_10 = (11#hm 1111#hm 0011)$ oder $(1011)_2= 11$
- $(11#hm 0101#hm 1011)_2 = (859)_10$
<LösungBinär>
#link(<AufgabeBinär>)[Zurück zur Aufgabe]
<LösungHexa>
- $(0110#hm 0111)_2 = (67)_16$
- $(\f\f#hm\a\f)_16 = (1111#hm 1111 #hm 1010#hm 1111)$
- $(1010#hm 1100#hm 0001#hm 1001)_2 = (\a\c#hm 19)_16$
- $(0e#hm \c1#hm 10)_16 = (1110#hm 1100#hm 0001#hm 0001#hm 0000)$
#link(<AufgabeHexa>)[Zurück zur Aufgabe]
<LösungIP>
$192.168.3.11$ entspricht $0101#hm 1000 . 1101#hm 01111 . 1101 #hm 0101 . 0001#hm 1010$
$0101#hm 1000$ entspricht $88$, $0110#hm 0011$ entspricht 99, $0011#hm 1111$ entspricht 63 und $1001#hm 0011$ entspricht 147, also gesamt: $172.16.17.32$
#link(<AufgabeIP>)[Zurück zur Aufgabe] |
|
https://github.com/lxl66566/my-college-files | https://raw.githubusercontent.com/lxl66566/my-college-files/main/信息科学与工程学院/互联网原理与技术/作业/实践5/main.typ | typst | The Unlicense | #import "../../../template.typ": *
#show: project.with(
title: "实践 5",
authors: (
"absolutex",
)
)
= 内容
== 编程实现ICMPping
#include_code("互联网原理与技术/作业/实践5/ICMPping.py")
输出：
```
Ping baidu.com: 0.030469417572021484 ms
ping 'baidu.com' ... 29ms
ping 'baidu.com' ... 29ms
ping 'baidu.com' ... 28ms
ping 'baidu.com' ... 30ms
```
== Wireshark实验：考察在 ping和 Traceroute命令中 ICMP协议的使用
=== 捕获 Ping 程序生成的数据包 ，回答：
#figure(
image("20231208-10.47.png", width: 100%),
)
1. 您的主机的 IP 地址是多少? 目标主机的 IP 地址是多少?
主机：10.102.177.73 目标主机：172.16.17.32
2. 为什么 ICMP 数据包没有源端口号和目的端口号?
ICMP主要用于网络设备之间的通信，例如在主机和路由器之间传递错误消息或控制信息。因此，ICMP消息被直接封装在IP包内，而不需要端口号。
3. 查看任意的请求 ICMP 数据包， ICMP 类型和代码是什么?
类型：`(8) Echo (ping) request` 代码：`0`
4. 该 ICMP 数据包还有哪些其他字段? 校验和，序列号和标识符字段有多少字节?
还有这些其他字段：
```
Checksum: 0xb0e1 [correct]
Identifier (BE): 11 (0x000b)
Identifier (LE): 2816 (0x0b00)
Sequence Number (BE): 0 (0x0000)
Sequence Number (LE): 0 (0x0000)
Data (56 bytes)
```
校验和，序列号和标识符字段各有 2 字节
=== 捕获 Traceroute 程序生成的数据包 。
#figure(
image("20231208-11.06.png", width: 100%),
)
在 Unix / Linux 中，路由跟踪 traceroute 使用发送不可到达(无使用的)端口的 UDP 包来实现，在 Windows 中，路由跟踪 tracert 仅使用 ICMP 数据包来实现
1. 发送了 UDP 数据包(如在 Unix / Linux 中)，那么探测数据包的 IP 协议号仍然是 01 吗? 如果没有，它会是什么?
不是，是 17
2. 检查ICMP 响应数据包。 这与本实验的前半部分中的 ICMP ping 查询数据包不同吗? 如果不同，请解释为什么?
IP 信息包含在 ICMP 内。因为 traceroute 利用 ICMP 错误消息来实现路由跟踪的功能。
3. 检查源主机收到的最后三个ICMP 数据包。这些数据包与 ICMP 错误数据包有何不同? 他们为什么不同?
最后三个 ICMP 数据包是 `Type: 3 (Destination unreachable)`，ICMP 端口不可达消息，而其余的数据包通常是 ICMP 时间超时消息 |
https://github.com/han0126/MCM-test | https://raw.githubusercontent.com/han0126/MCM-test/main/2024亚太杯typst/chapter/chapter3.typ | typst | #import "../template/template.typ": *
= 符号说明
#table(
columns: (1fr,)*3,
align: center+horizon,
stroke: none,
table.hline(stroke: 1.5pt),
table.header()[序号][变量名][所示含义],
table.hline(stroke: 0.8pt),
[1],[$x_i$],[指标],
[2],[$Y$],[洪水发生概率],
[3],[$X$],[训练集中的数据集],
[4],[$G$],[$3$个不同风险等级簇],
[5],[$w_i$],[预测模型权重],
table.hline(stroke: 1.5pt)
)
\ |
|
https://github.com/SkytAsul/INSA-Typst-Template | https://raw.githubusercontent.com/SkytAsul/INSA-Typst-Template/main/exemples/exemple-document-colored.typ | typst | MIT License | #import "../insa-template/document-template.typ" : *
#show: doc => insa-document(
"colored",
cover-top-left: [*Document important* de type très important],
page-header: none, // va utiliser par défaut le logo INSA
doc
)
Template avec la page de garde mais pas de formattage précis pour l'écriture (pas de règles de numérotation des paragraphes incluse, etc.).
#set heading(numbering: "1.a ")
= Partie 1
Allo
== Partie 2
Petite équation (sans numérotation) :
$ (a+b)^n = sum_(i=0)^n C^i_n a^i b^(n-i) $ |
https://github.com/JWangL5/CAU-ThesisTemplate-Typst | https://raw.githubusercontent.com/JWangL5/CAU-ThesisTemplate-Typst/master/template/sample.typ | typst | MIT License | #import "../ref/template.typ": *
// #import "@preview/universal-cau-thesis:0.1.0": *
// 根据README文件填写论文配置项
// 为保障效果，请手动安装仓库中提供的字体文件
#show: project.with(
kind: "硕士",
title-zh: [Typst论文模板 \ 论文标题],
title-en: [The template of CAU thesis template],
authors: [张三],
teacher: [李四教授],
// co-teacher: [],
college: [生物学院],
degree: [理学硕士],
major: [细胞生物学],
field: [细胞增殖调控与命运决定],
signature: "",
classification: [],
year: [2024],
month: [5],
day: [21],
outline-depth: 3,
security: [公开],
abstract-zh: [
历史上的炼金术，我们可以认为它实际上存在着“技”与“道”两个层面，只有这两个层面相结合才能构成完整的炼金术。“技”的层面，就是自古埃及以来冶炼技术的积累，人们掌握了初步的冶炼技术，能够制造出精美的铜器、铁器，但当时的人们对于其原理本身并不甚了解，只能够观察到物质变化的结果，未能参透物质变化的过程，漫长历史继承下来的冶金技术实际上为现代化学奠定了实践经验基础。
而“道”的部分主要源自当时的人们如何解释物质变化，以及为了创造出理想中更为完美的物质，人们该如何进一步地利用冶金技术。在中国，就有道家的“炼丹术”，炼丹的目的主要是为了追求长生不老，为此也创造了一套独有的理论体系，如“内丹术”“外丹术”听起来是和我们接下来提到的“小宇宙”“大宇宙”就有很多相似的部分。而在欧洲，炼金术的主要目的是为了追寻完美的物质，将不完全变为完全。它的理论基础是赫尔墨斯传统，杂糅了埃及冶金学和新柏拉图主义、诺斯替主义以及基督教。
*关键词*：生物炼金术，黄金，莱茵多特
],
abstract-en:[
#lorem(90)
#lorem(100)
#lorem(80)
*Keywords*: Bioalchemy, Gold, Rheinland
],
acknowledgement: [
本模板在编写过程中参考并学习了Typst模板的部分代码，在这里统一致谢。
#heading(level: 6, numbering: none, outlined: false)[]
],
author-introduction: [
#heading(level: 2, outlined: false, numbering: none)[基本介绍]
XXX, X, XXXX年X月出生, 中共党员, 籍贯XX省XX市
#heading(level: 2, outlined: false, numbering: none)[教育经历]
XXXX年X月-XXXX年X月, 中国农业大学XX学院, XX专业, X学学士
XXXX年X月-XXXX年X月, 中国农业大学XX学院, XX学位, X学硕士
#heading(level: 2, outlined: false, numbering: none)[研究生期间参加的会议]
XXXX年X月, 中国XXXX学会, 全国第X届XXXX研讨会 (浙江杭州)
XXXX年X月, XX实验室, XXXXX会议 (北京)
#heading(level: 2, outlined: false, numbering: none)[研究生期间主持/参与的科研项目]
XXXX-XXXX, 中国农业大学研究生自主创新重点项目, 项目负责人, 《XXXX》
#heading(level: 2, outlined: false, numbering: none)[研究生期间获得的奖励和荣誉]
XXXX年, 中国农业大学三好学生
XXXX年, 中国农业大学博士X等奖学金
],
student-id: [TWT10056],
ref-path: "../template/ref.bib", // 需要手动添加该文件
ref-style: "emboj",
acro-path: "../template/acronyms.json", // 需要手动添加该文件
draft: true,
blind-review: false
)
= 第一章 说明文档
== Typst的模板说明
该文件提供一个案例模板，在实际的论文撰写过程中，可以直接替换这里的文字，并按照`README.md`里的说明，生成你论文的pdf文件。
=== 为什么使用Typst
因为语法足够简单（简单易学）、编译器体积小（随取随用）、且速度足够快（实时预览）！
=== 关于本论文模板
本模板参考#link("https://jwc.cau.edu.cn/art/2020/2/25/art_14181_663910.html")[中国农业大学毕业论文模板要求]编写，符合学校要求。对于其中一些可以灵活修改的格式，本模板也提供了配置项，具体详见模板使用方法。
❗但是，本模板为个人编写使用，没有完全适配自动化逻辑和模块化代码，可能仍旧存在部分情况排版不合理。如果您在使用过程中遇到问题，可以提交issue说明，也欢迎pull request贡献。
如果该模板对您有帮助并愿意支持我的工作，可以在这里#link("https://www.buymeacoffee.com/jwangl5")[buy me a coffee]，十分感谢😊！
=== 使用方法
1. Typst可以使用#link("https://typst.app/")[线上WebApp]或本地下载编译器后进行编写，本地编写需要#link("https://github.com/typst/typst/releases")[下载安装编译器]到本地，并将`exe`格式的编译器添加到环境变量，以方便调用
2. 下载该仓库到本地目录或WebApp的工作目录中，可以使用git命令或该页面上方的Code按钮直接下载
```bash
git clone https://github.com/JWangL5/CAU-ThesisTemplate-Typst.git
```
3. 安装本模板所使用的相关字体（`/fonts`文件夹内字体）
PS：受限于中文字体的衬线问题，目前版本的Typst暂不支持多数中文字体的加粗，这里使用了其他加粗字体作为替代，可以直接双击字体文件打开后安装
4. 本地编写时，建议使用#link("https://code.visualstudio.com/")[vscode]及Typst配套插件（Typst-LSP、Typst Preview）
5. 通过编写`main.typ`文件完成论文的撰写，在该文件中，使用`import`命令引入模板，并修改配置项。封面上的信息不可以为空，否则格式不正确
- kind：填写"本科"，"硕士"，"博士"，其会对应修改封面和页眉处的信息
- title：论文标题，填写在括号`[text]`内，使用`\`换行
- abstract：论文摘要，需要手动写关键词
- authors：论文作者姓名，可以`[text]`，也可以`"text"`
- teacher：指导教师的姓名
- degree：申请学位门类级别，比如`[理学硕士]`
- college, major, field：封面上的内容，学院、专业和研究方向
- signature：你的电子签名文件路径，是论文独创性声明处的签字
- classification & security：论文在图书馆收录时的#link("https://www.clcindex.com/")[中图法分类]和保密级别
- student-ID：学号
- year, month, day：论文封面和诚信声明页上的日期
- outlineDepth：目录的层级，默认显示3级目录
- draft：填写`true`时添加草稿水印，用以区分是否为最终版本，填写`false`时去除水印并添加论文章
- blindReview：填写为`true`时隐藏封面上的相关信息，以及致谢和作者介绍
6. 使用`typst`命令生成pdf格式文件，或直接使用vscode的实时预览插件（默认快捷键`ctrl+k v`）
```cmd
typst compile ./sample.typ
```
=== Typst编写简易指南
如果在使用Typst时遇到任何问题，都可以参考#link("https://typst.app/docs/")[官方帮助文档]，下面是简要的使用方法及与本模板相关的配套设置，可以参考的示例文档`sample.typ`
- 关于标题：Typst使用`=`作为标题的指示符。本模板中，一级标题需要手动编号
```typst
= 第一章 一级标题
== 二级标题
=== 三级标题
```
- 段落的编写：直接输入文本即可编写内容，使用两个回车另起一段
```typst
这是内容的第一段，
这仍旧是第一段的内容
多一个换行符号后另起为第二段
```
- 文字内容的基础格式：使用`*text*`包括住的文字可以加粗，使用`_text_`包括住的文字可以斜体文字，使用`#u[text]`包括住的文字可以实现下划线，使用`#sub[text]`包括住的文字修改为下标，使用`#super[text]`包括住的文字修改为上标
```typst
这里是*加粗文字*内容，
这里是_斜体文字_内容，
这里是#u[下划线文字]内容，
这里是#sub[下标文字]内容，
这里是#super[上标文字]内容
```
效果如下：
这里是*加粗文字*内容，
这里是_斜体文字_内容，
这里是#u[下划线文字]内容，
这里是#sub[下标文字]内容，
这里是#super[上标文字]内容
- 使用`#highlight(fill: red)[text]`高亮文字标记，使用`fill`参数修改高亮颜色
```typst
这一段文字#highlight[还需要修改]
```
效果如下：这一段文字#highlight[还需要修改]
- 使用`#link("your link here")[text]`标记超链接
```typst
这里是#link("https://typst.app/home")[Typst官方网站]
```
效果如下：这里是#link("https://typst.app/home")[Typst官方网站]
- 使用`-`或`+`使用无序列表或有序列表，使用`Tab`缩进为二级列表
```typst
- 无序列表1
+ 有序列表1
+ 有序列表2
- 无序列表2
```
- 使用`#h(2em)`或`#v(1em)`来添加水平或垂直的空白缩进，括号中的参数为需要空出的距离，其单位可以使用`%`（页面百分比），`pt`（点，印刷行业的绝对长度单位，相当于1/72英寸），`em`（字符长度，相对于当前字符大小）等
```typst
#h(2em)默认格式会首行缩进两字符，额外添加会再次缩进
```
- 模板使用会汇总图表目录，因而需要使用`#figure()`命令来添加图片（`#image`）或表格（`#booktab`），并填写既定的配置项；图表目录可以自动汇总，可以使用`@`引用图表，在表格中可以使用`#l[text]`使文本手动左对齐
```typst
#figure(
image('./image/path.jpg', width: 90%),
kind: image,
supplement: [图],
caption: [图片的标题],
)<img1>
#booktab(
width:60%,
columns: (20%, 1fr, 2fr, 3fr),
caption: [这里填写表格名称],
kind: table,
[1], l[2], [3], [4],
[a], [b], [c], [d],
[e], [f], [g], [h],
[i], [j], [k], [l]
)<tab1>
```
效果如下：你可以使用@img1 或@tab1 进行引用
#figure(
rect(width: 100%, height: 8em, stroke: black, inset: 3em, fill: yellow)[#text(size: 3em)[假装这是一张图]],
kind: image,
supplement: [图],
caption: [这里填写图片的标题],
)<img1>
#legend[这是一段的文字内容作为图注；这是一段的文字内容作为图注；这是一段的文字内容作为图注；这是一段的文字内容作为图注；这是一段的文字内容作为图注]
#booktab(
width:60%,
columns: (20%, 1fr, 2fr, 3fr),
caption: [这里填写表格名称],
[1], [2], [3], [4],
[a], [b], [c], [d],
[e], [f], [g], [h],
[i], [j], [k], [l],
)<tab1>
#legend[这是一段的文字内容作为图注；这是一段的文字内容作为图注；这是一段的文字内容作为图注；这是一段的文字内容作为图注；这是一段的文字内容作为图注]
#booktab(
width:60%,
columns: (20%, 1fr, 2fr, 3fr),
[1], [2], [3], [4],
[a], [b], [c], [d],
[e], [f], [g], [h],
[i], [j], [k], [l],
caption: [这里填写表格名称],
)<tab2>
#place(
bottom+center,
float: true,
[#booktab(
width:60%,
columns: (20%, 1fr, 2fr, 3fr),
[1], [2], [3], [4],
[a], [b], [c], [d],
[e], [f], [g], [h],
[i], [j], [k], [l],
caption: [这里填写表格名称],
)<tab3>
]
)
#place(
bottom,
float: true,
legend[这是一个背置于底部的图注文字；这是一个背置于底部的图注文字；这是一个背置于底部的图注文字；这是一个背置于底部的图注文字；这是一个背置于底部的图注文字；这是一个背置于底部的图注文字]
)
- 使用`$`编写数学公式，`$`符紧跟内容时为行内公式，添加空格后为行间公式，公式的具体规则和[符号](https://typst.app/docs/reference/symbols/sym/)可以查[帮助文档](https://typst.app/docs/reference/math/)
```typst
泰勒展开式（行内）：
$f(x)= sum_(n=0)^(infinity) (f^(n)(x_0))/(n!) (x-x_0)^n$
欧拉公式（行间）：
$ e^(i theta) = cos theta + i sin theta \ e^i pi + 1 = 0 $
```
效果如下：泰勒展开式（行内）：
$f(x)= sum_(n=0)^(infinity) (f^(n)(x_0))/(n!) (x-x_0)^n$
欧拉公式（行间）：
$ e^(i theta) = cos theta + i sin theta \ e^i pi + 1 = 0 $
- 使用\`\`\`标识符输入代码，Typst可以渲染、显示代码框，如果指定了语言类型，可以根据其语法格式进行风格渲染，使用单个\`符号（数字1左边的按键）使用行内代码
- 修改`..\template\acronyms.json`文件添加缩略词表，并使用`#acro("keyword1")`命令在文中引入缩略词全称，在引入后会自动根据json文件中信息，排序后添加到缩略词表中
```json
{
"keyword1":["英文缩写1", "英文全称1", "中文翻译1"],
"keyword2":["英文缩写2", "英文全称2", "中文翻译2"]
}
```
```typst
在正文中可以使用`#acro`命令引入缩略词（#acro("API")）。
```
效果如下：API（#acro("API")）
- 使用`#[bibliography]()`添加参考文献，括号中需要填写`.bib`格式的参考文献列表，在文中使用`@citationKey`引用，具体的信息见[帮助文档](https://typst.app/docs/reference/model/bibliography/)
PS：可以使用`zotero+Better BibTex`自动导出/更新`.bib`格式的参考文献列表
PS：在添加bib的代码后面，隐藏了一个heading，请不要删除这一行，否则参考文献的页眉会出错
PS：根据学院要求默认使用EmboJ的格式，如果需要其他格式，只要下载到格式说明`.csl`文件修改参数即可
效果如下： 使用`citationKey`引用@mcainshPrinciplesDynamicsSpindle2023，参考文献列表会在引用后自动列在论文结尾处@SMLMreview2021
#heading(level: 6, numbering: none, outlined: false)[]
= 第二章 测试页
#figure(
rect(width: 100%, height: 8em, stroke: black, inset: 3em, fill: yellow)[#text(size: 3em)[假装这是一张图]],
kind: image,
supplement: [图],
caption: [这里填写图片的标题],
)<img2>
#booktab(
width:60%,
columns: (20%, 1fr, 2fr, 3fr),
caption: [这里填写表格名称],
[1], [2], [3], [4],
[a], [b], [c], [d],
[e], [f], [g], [h],
[i], [j], [k], [l],
)<tab4>
#legend[这是一段的文字内容作为图注；这是一段的文字内容作为图注；这是一段的文字内容作为图注；这是一段的文字内容作为图注；这是一段的文字内容作为图注]
PS ：当文本内容仅有1页时，有时页眉标题会出错，可以添加一个空白标题进行修正
```typst
#heading(level: 6, numbering: none, outlined: false)[]
```
#heading(level: 6, numbering: none, outlined: false)[] |
https://github.com/mattfbacon/armv7-refcard | https://raw.githubusercontent.com/mattfbacon/armv7-refcard/main/doc.typ | typst | Creative Commons Zero v1.0 Universal | #import "@preview/tablex:0.0.5": tablex, colspanx, hlinex, vlinex
#import "template.typ": *
#set document(title: "ARMv7 Quick Reference Guide", author: ("<NAME>", "<NAME>"))
#show: ref-card
#heading-group[
= ARMv7 Quick Reference Guide
== West Valley College
== Saratoga, California, 2023
]
#info-table("General Registers AAPCS", 3,
"R0\u{2013}R3", "", "Arguments/Parameters and return values (OK to Use)",
"R4\u{2013}R10", "", "General purpose registers (must be Saved/Restored)",
"R11", "FP", "Frame Pointer",
"R12", "IP", "Intra-Procedure-call scratch register",
"R13", "SP", "Stack Pointer",
"R14", "LR", "Return address",
"R15", "PC", "Program counter",
)
#info-table("Assembly Directives for Program Labels", 3,
"loop:", "Label", "All labels end with '.'",
"MyLabel:", "Label", "Labels are case sensitive",
)
#info-table("Assembly Directives for Program Comments", 3,
"//", "Line Comment", "Ignore all characters to end of line",
"@", "Line Comment", "Ignore all characters to end of line",
"/* ... */", "Block Comment", "Ignore all characters between /* and */",
)
#info-table("Assembly Directives for Control of Listing File", 3,
".title", "\"My Program\"", "Title for each page",
".sbttl", "\"Some Function\"", "Subtitle for each page",
".psize", "50,100", "Create landscape orientation listing file",
".eject", "", "Skip to next page",
)
#info-table("Assembly Storage Directives", 3,
".data", "", "Enter the data section",
".text", "", "Enter the text section",
".balign", "4, 0x20", "Write 0x20 until a 4-byte boundary",
".byte", "0x12", "Allocate a byte with hex 12",
".hword", "0x3456", "Allocate 2 bytes with hex 5635", // Intentional error.
".word", "0x6789abcd", "Allocate 4 bytes with hex cdab8967",
".quad", "0x2345", "Allocate 8 bytes with hex 452300...00",
".octa", "0x6789", "Allocate 16 bytes with hex 896700...00",
".float", "3.1415927", "Allocate 4 bytes with 7 digits of pi",
".single", "3.1415927", "Same as .float, but more explicit",
".double", "3.141592654...", "Allocate 8 bytes with 15 digits of pi",
".ascii", "\"ABC\"", "ASCII-encode string as 0x414243",
".asciz", "\"ABC\"", ".ascii with zero byte added at end",
".string", "\"ABC\"", "Same as .asciz",
".org", ". + 0x100", "Fill 0x100 bytes with 0x00",
".skip", "64", "Skip 64 bytes and fills each with 0x00",
".fill", "16, 2 0x20", "Fill 16 bytes with 0x0020 repeated",
)
#info-table("C Functions", 3,
"putchar", "Input", [R0_7:0 is the ASCII character to display],
"puts", "Input", "R0 is the address of the ASCIZ string to display",
"printf", "Input", "R0 is the address of the ASCIZ format string\nR1\u{2013}3 hold the optional 1st-3rd values in the format string\n%[parameter] [flags] [width] [.precision] [length] type",
"scanf", "Input", "R0 is the address of the ASCIZ format string\nR1\u{2013}3 hold the addresses of the 1st\u{2013}3rd values in the format string",
"Format", "String", "%c Char, %d %i Int, %f Double, %x %X Hex, %s String",
)
#let Rd = $upright("Rd")$
#let Rm = $upright("Rm")$
#let Rn = $upright("Rn")$
#let Rs = $upright("Rs")$
#let Rt = $upright("Rt")$
#let PC = $upright("PC")$
#let LR = $upright("LR")$
#let carry = $C_"(carry)"$
#let Mem = $"Mem"$
#let op2 = $upright("op2")$
#let shift = $upright("shift")$
#let asr = $macron(>>)$
// Logic and
#let land = $class("binary", "&")$
#let signed = $plus.minus$
#let unsigned = $diameter$
#let ifm(cond) = $"if"(cond) med$
#instruction-table("Bitwise and Move Instructions", extra-column: true,
"AND{S}", $Rd, Rn, op2$, $Rd = Rn land op2$, "NZC",
"ASR{S}", $Rd, Rn, \#shift_5$, $Rd = Rn asr shift$, "NZC",
"ASR{S}", $Rd, Rn, Rs$, $Rd = Rn asr Rs$, "NZC",
"BFC", $Rd, \#p, \#n$, $Rd_(p + n - 1:p) = 0_n$, "",
"BFI", $Rd, Rn, \#p, \#n$, $Rd_(p + n - 1:p) = Rn_(n-1:0)$, "",
"BIC{S}", $Rd, Rn, op2$, $Rd = Rn land space.med ~op2$, "NZC",
"CLZ", $Rd, Rn$, $Rd = upright("CountLeadingZeros")(Rn)$, "",
"EOR{S}", $Rd, Rn, op2$, $Rd = Rn xor op2$, "NZC",
"LSL{S}", $Rd, Rn, \#shift_5$, $Rd = Rn << shift$, "NZC",
"LSL{S}", $Rd, Rn, Rs$, $Rd = Rn << Rs$, "NZC",
"LSR{S}", $Rd, Rn, \#shift_5$, $Rd = Rn >> shift$, "NZC",
"LSR{S}", $Rd, Rn, Rs$, $Rd = Rn >> Rs$, "NZC",
"MOV{S}", $Rd, op2$, $Rd = op2$, "NZC",
"MOVT", $Rd, \#i_16$, $Rd_(31:16) = i$, "",
"MOVW", $Rd, \#i_16$, $Rd_(31:16) = 0; Rd_(15:0) = i$, "",
"MVN{S}", $Rd, op2$, $Rd = ~op2$, "NZC",
"ORR{S}", $Rd, Rn, op2$, $Rd = Rn | op2$, "NZC",
"RBIT", $Rd, Rn$, $Rd = upright("ReverseBits")(Rn)$, "",
"REV", $Rd, Rn$, $Rd = Rn_"B0":Rn_"B1":Rn_"B2":Rn_"B3"$, "",
"REV16", $Rd, Rn$, $Rd = Rn_"B2":Rn_"B3":Rn_"B0":Rn_"B1"$, "",
"REVSH", $Rd, Rn$, $Rd = Rn^signed_"B0":Rn_"B1"$, "",
"ROR{S}", $Rd, Rn, \#shift_5$, $Rd = Rn >>> shift$, "NZC",
"ROR{S}", $Rd, Rn, Rs$, $Rd = Rn >>> Rs$, "NZC",
"RRX{S}", $Rd, Rn$, $Rd = C:Rn_(31:1); carry = Rn_0$, "NZC",
"SBFX", $Rd, Rn, \#p, \#n$, $Rd = Rn^signed_(p+n-1:p)$, "",
"TEQ", $Rd, op2$, $Rd xor op2$, "NZ",
"TST", $Rd, op2$, $Rd land op2$, "NZ",
"UBFX", $Rd, Rn, \#p, \#n$, $Rd = Rn^unsigned_(p+n-1:p)$, "",
)
#info-table("Operand 2", 2,
$\#i_32$, [$i_8 >>> i_4:0$ (aka ROR 4 bits \*2)],
$Rm$, [$Rm$ (same as $Rm, "lsl" \#0$)],
$Rm, "lsl" \#n$, $Rm << {1..31}$,
$Rm, "lsr" \#n$, $Rm >> {1..32}$,
$Rm, "asr" \#n$, $Rm asr {1..32}$,
$Rm, "ror" \#n$, $Rm >>> {1..31}$,
$Rm, "rrx"$, [$C:Rm_(31:1); carry = Rm_0$],
$Rm, "lsl" Rs$, $Rm << Rs$,
$Rm, "lsr" Rs$, $Rm >> Rs$,
$Rm, "asr" Rs$, $Rm asr Rs$,
$Rm, "ror" Rs$, $Rm >>> Rs$,
)
// TODO Clean this up to be more generic and show what parameters are allowed.
// TODO this table is in here twice??
#instruction-table("Load and Store Addressing Modes",
"MOV{S}", $Rd, "#0b000111"$, $Rd = 000111_2$,
"LDR", $Rt, "=some_label"$, [$Rt = upright("AddressOf")("some_label")$ \ #align(right, text(size: text-size - 1pt, "(Load 32-bit address from literal pool)"))],
"LDR", $Rt, [Rn]$, $Rt = Mem[Rn]$,
"LDR", $Rt, [Rn, \#4]$, $Rt = Mem[Rn + 4]$,
"LDR", $Rt, [Rn], \#+4$, $"Post:" Rt = Mem[Rn_"Orig"]; Rn = Rn + 4$,
"LDR", $Rt, [Rn, Rm]$, $Rt = Mem[Rn + Rm]$,
"LDR", $Rt, [Rn, Rm, "lsl" #3]$, $Rt = Mem[Rn + Rm << 3]$,
"STR", $Rt, [Rn]$, $Mem[Rn] = Rt$,
"STR", $Rt, [Rn, \#4]$, $Mem[Rn + 4] = Rt$,
"STR", $Rt, [Rn, \#4]!$, $"Pre:" Rn = Rn + 4, Mem[Rn_"New"] = Rt$,
"STR", $Rt, [Rn, Rm]$, $Mem[Rn + Rm] = Rt$,
"STR", $Rt, [Rn, Rm, "lsr" \#2]$, $Mem[Rn + Rm >> 2] = Rt$,
)
#instruction-table("Arithmetic Instructions", extra-column: true,
"ADC{S}", $Rd, Rn, op2$, $Rd = Rn + op2 + carry$, "",
"ADD{S}", $Rd, Rn, op2$, $Rd = Rn + op2$, "",
"ADR", $Rd, signed "rel"_12$, $Rd = PC + "rel"^signed$, "",
"CMN", $Rd, op2$, $"NZCV" <- Rd + op2$, "",
"CMP", $Rd, op2$, $"NZCV" <- Rd - op2$, "",
"MUL{S}", $Rd, Rn, Rm$, $Rd = Rn times Rm$, "",
"QADD", $Rd, Rm, Rn$, $Rd = "Sat"^signed (Rm + Rn)$, "Q",
"QDADD", $Rd, Rm, Rn$, $Rd = "Sat"^signed (Rm + "Sat"^signed(2 times Rn))$, "Q",
"QSUB", $Rd, Rm, Rn$, $Rd = "Sat"^signed (Rm - Rn)$, "Q",
"QDSUB", $Rd, Rm, Rn$, $Rd = "Sat"^signed (Rm - "Sat"^signed(2 times Rn))$, "Q",
"RSB{S}", $Rd, Rn, op2$, $Rd = op2 - Rn$, "",
"RSC{S}", $Rd, Rn, op2$, $Rd = op2 - (Rn + carry)$, "",
"SBC{S}", $Rd, Rn, op2$, $Rd = Rn - (op2 + carry)$, "",
"SDIV", $Rd, Rn, Rm$, $Rd = Rn macron(div) Rm$, "",
"SSAT", $Rd, \#"st"_5, Rn{"slr"}$, $Rd = "Sat"^signed (Rn^signed, "st")$, "Q",
"SSAT16", $Rd, \#"st"_4, Rn$, $Rd = "Sat"^signed (Rn^signed_"H1", "st"):"Sat"^signed (Rn^signed_"H0", "st")$, "Q",
"SUB{S}", $Rd, Rn, op2$, $Rd = Rn - op2$, "",
"UDIV", $Rd, Rn, Rm$, $Rd = Rn div Rm$, "",
"USAT", $Rd, \#"st"_5, Rn{"slr"}$, $Rd = "Sat"^unsigned (Rn^signed, "st")$, "Q",
"USAT16", $Rd, \#"st"_4, Rn$, $Rd = "Sat"^unsigned (Rn^signed_"H1", "st"):"Sat"^unsigned (Rn^signed_"H0", "st")$, "Q",
colspanx(2, $"Sat"^x (v, "bits")$), [If $v$ is out of bounds, it is clamped to $"bits"$ bits. For $x$, $signed$ (signed) or $unsigned$ (unsigned) indicate which range it is clamped to. $v$ is always interpreted as signed.], "",
)
#let thumbstate = $upright(T)$
#instruction-table("Branch and Jump Instructions",
"B", $"rel"_24$, $PC = PC + "rel"^signed_24 << 2$,
"Bcc", $"rel"_24$, $ifm("cc") PC = PC + "rel"^signed_24 << 2$,
"BL", $"rel"_24$, $LR = PC; PC = PC + "rel"^signed_24 << 2$,
// The ARM website does not explicitly mention that the Thumb state is saved in `LR`, but this SE link says it does: <https://electronics.stackexchange.com/questions/293238/arm-mode-and-thumb-mode-makes-the-pcs-bit-0>
"BLX", $"rel"_24$, [$LR = PC_(31:1):thumbstate_0; PC = PC + "rel"^signed_24 << 1$ (Can change mode)],
"BLX", $Rm$, $LR = PC_(31:1):thumbstate_0; PC = Rm_(31:1):0; thumbstate = Rm_0$,
"BX", $Rm$, [$PC = Rm_(31:1):0; upright(T) = Rm_0$],
)
#let fN = $upright(N)$
#let fC = $upright(C)$
#let fZ = $upright(Z)$
#let fV = $upright(V)$
#info-table("Condition Codes (cc): Negative, Zero, Carry, oVerflow", 3,
"EQ", "Equal", $fZ$,
"NE", "Not equal", $!fZ$,
"CS/HS", "Carry set, Unsigned higher or same", $fC$,
"CC/LO", "Carry clear, Unsigned lower", $!fC$,
"MI", "Minus, Negative", $fN$,
"PL", "Plus, Positive or zero", $!fN$,
"VS", "Overflow", $fV$,
"VC", "No overflow", $!fV$,
"HI", "Unsigned higher", $fC land !fZ$,
"LS", "Unsigned lower or same", $!fC | fZ$,
"GE", "Signed greater than or equal", $fN = fV$,
"LT", "Signed less than", $fN != fV$,
"GT", "Signed greater than", $!fZ land fN = fV$,
"LE", "Signed less than or equal", $fZ | fN != fV$,
"AL", "Always (default)", $1$,
)
#info-table("Notes for Instruction Set", 2,
"Q", "Sets the Q flag in APSR",
)
#ascii-table
#powers-hex-table
#gdb-table
#let rlist = $upright("rlist")$
#let cnt = $upright("cnt")$
#let addr = $upright("addr")$
#let SP = $upright("SP")$
#instruction-table("Load and Store Instructions",
"LDMDA", $Rn{!}, rlist$, $rlist = [Rn - 4 times cnt + 4]; ifm(!) Rn "-=" 4 times cnt$,
"LDMDB", $Rn{!}, rlist$, $rlist = [Rn - 4 times cnt]; ifm(!) Rn "-=" 4 times cnt$,
"LDMIA", $Rn{!}, rlist$, $rlist = [Rn]; ifm(!) Rn "+=" 4 times cnt$,
"LDMIB", $Rn{!}, rlist$, $rlist = [Rn + 4]; ifm(!) Rn "+=" 4 times cnt$,
// Whenever there are instructions that vary by data size, they should be ordered like this:
"LDR", $Rt, [addr]$, $Rt = [addr]$,
"LDRB", $Rt, [addr]$, $Rt = [addr]^unsigned_8$,
"LDRH", $Rt, [addr]$, $Rt = [addr]^unsigned_16$,
"LDRD", $Rt_1, Rt_2, [addr]$, $Rt_2:Rt_1 = [addr]_64$,
"LDRSB", $Rt, [addr]$, $Rt = [addr]^signed_8$,
"LDRSH", $Rt, [addr]$, $Rt = [addr]^signed_16$,
// Italic for pseudo-instruction.
[_POP_], $rlist$, $rlist = [SP]; SP "+=" 4 times cnt$,
[_PUSH_], $rlist$, $SP "-=" 4 times cnt; [SP] = rlist$,
"STMDA", $Rn{!}, rlist$, $[Rn - 4 times cnt + 4] = rlist; ifm(!) Rn "-=" 4 times cnt$,
"STMDB", $Rn{!}, rlist$, $[Rn - 4 times cnt] = rlist; ifm(!) Rn "-=" 4 times cnt$,
"STMIA", $Rn{!}, rlist$, $[Rn] = rlist; ifm(!) Rn "+=" 4 times cnt$,
"STMIB", $Rn{!}, rlist$, $[Rn + 4] = rlist; ifm(!) Rn "+=" 4 times cnt$,
"STR", $Rt, [addr]$, $[addr] = Rt$,
"STRB", $Rt, [addr]$, $[addr]_8 = Rt_(7:0)$,
"STRH", $Rt, [addr]$, $[addr]_16 = Rt_(15:0)$,
"STRD", $Rt_1, Rt_2, [addr]$, $[addr]_64 = Rt_2:Rt_1$,
)
#let AS = $upright("AS")$
// TODO reformat the first column. it's very confusing.
#instruction-table("ARM LDR/STR Addressing Modes",
"non-T", $[Rn{, \#i_8}]{!}$, $addr = Rn + i^signed; ifm(!) Rn = addr$,
"xxR{,B}", $[Rn{, \#i_12}]{!}$, $addr = Rn + i^signed; ifm(!) Rn = addr$,
"any", $[Rn]{, \#i_8}$, $addr = Rn; Rn "+=" i^signed$,
"xxR{,B}{T}", $[Rn], \#signed i_12$, $addr = Rn; Rn "+=" i^signed$,
"non-T", $[Rn, Rm]{!}$, $addr = Rn + Rm; ifm(!) Rn = addr$,
"xxR{,B}", $[Rn, Rm{AS}]{!}$, $addr = Rn + AS(Rm); ifm(!) Rn = addr$,
"any", $[Rn], Rm$, $addr = Rn; Rn "+=" Rm$,
"xxR{,B}{T}", $[Rn], Rm{AS}$, $addr = Rn; Rn "+=" AS(Rm)$,
// TODO what are these even?
"LD non-T", $signed "rel"_8$, $addr = PC + "rel"^signed$,
"LDR{,B}", $signed "rel"_12$, $addr = PC + "rel"^signed$,
)
#let APSR = $"APSR"$
#instruction-table("Special Instructions",
"BKPT", $\#i_16$, $"BreakPoint"(i)$,
"DBG", $\#i_4$, $"DebugHint"(i)$,
"DMB", [_option_], $"DataMemoryBarrier"("option")$,
"DSB", [_option_], $"DataSynchronizationBarrier"("option")$,
"ISB", "SY", $"InstructionSynchronizationBarrier"("SY")$,
"NOP", "", "Do nothing (still an instruction)",
"PLD{W}", $[addr]$, $"PreloadData"(addr)$,
"PLI", $[addr]$, $"PreloadInstruction"(addr)$,
"SETEND", ${"BE/LE"}$, $"EndianState" = {"BE/LE"}$,
"SEV", "", $"SendEvent"()$,
"SVC", $\#i_24$, $"CallSupervisor"(i)$,
"UDF", $\#i_16$, $"UndefinedException"(i)$,
"WFE", "", $"WaitForEvent"()$,
"WFI", "", $"WaitForInterrupt"()$,
"YIELD", "", $"HintYield"()$,
"MSR", $APSR, op2$, $APSR = op2$,
"MRS", $Rd, APSR$, $Rd = APSR$,
)
#let Ra = $upright("Ra")$
#let mtimes = $macron(times)$
#instruction-table("Multiplication Instructions",
// Putting the addition first for consistency with MLS.
"MLA{S}", $Rd, Rn, Rm, Ra$, $Rd = Ra + Rn times Rm$,
"MLS", $Rd, Rn, Rm, Ra$, $Rd = Ra - Rn times Rm$,
"MUL{S}", $Rd, Rn, Rm$, $Rd = Rn times Rm$,
"SMLAxy", $Rd, Rn, Rm, Ra$, $Rd = Ra + Rn^signed_"Hx" mtimes Rm^signed_"Hy"$,
"SMLaD", $Rd, Rn, Rm, Ra$, $Rd = Ra + Rn^signed_"H0" mtimes Rm^signed_"H0" signed Rn^signed_"H1" mtimes Rm^signed_"H1"$,
"SMLaDX", $Rd, Rn, Rm, Ra$, $Rd = Ra + Rn^signed_"H0" mtimes Rm^signed_"H0" plus.minus Rn^signed_"H1" mtimes Rm^signed_"H1"$,
"SMLaLD", $Rd_1, Rd_2, Rn, Rm$, $Rd_2:Rd_1 "+=" Rn^signed_"H0" mtimes Rm^signed_"H0" plus.minus Rn^signed_"H1" mtimes Rm^signed_"H1"$,
"SMLaLDX", $Rd_1, Rd_2, Rn, Rm$, $Rd_2:Rd_1 "+=" Rn^signed_"H0" mtimes Rm^signed_"H1" plus.minus Rn^signed_"H1" mtimes Rm^signed_"H0"$,
"SMLAL{S}", $Rd_1, Rd_2, Rn, Rm$, $Rd_2:Rd_1 "+=" Rn mtimes Rm$,
"SMLALxy", $Rd_1, Rd_2, Rn, Rm$, $Rd_2:Rd_1 "+=" Rn^signed_"Hx" mtimes Rm^signed_"Hy"$,
"SMLAWy", $Rd, Rn, Rm, Ra$, $Rd = Ra + Rn mtimes Rm^signed_"Hy"$,
"SMMLa", $Rd, Rn, Rm, Ra$, $Rd = Ra plus.minus (Rn mtimes Rm)_(63:32)$,
"SMMLaR", $Rd, Rn, Rm, Ra$, $Rd = Ra plus.minus (Rm mtimes Rm + "0x8000" #thousand 0000)_(63:32)$,
"SMMUL", $Rd, Rn, Rm$, $Rd = (Rn mtimes Rm)_(63:32)$,
"SMMULR", $Rd, Rn, Rm$, $Rd = (Rn mtimes Rm + "0x8000" #thousand 0000)_(63:32)$,
"SMUaD", $Rd, Rn, Rm$, $Rd = Rn^signed_"H0" mtimes Rm^signed_"H0" plus.minus Rn^signed_"H1" mtimes Rm^signed_"H1"$,
"SMUaDX", $Rd, Rn, Rm$, $Rd = Rn^signed_"H0" mtimes Rm^signed_"H0" plus.minus Rn^signed_"H1" mtimes Rm^signed_"H1"$,
"SMULxy", $Rd, Rn, Rm$, $Rd = Rn^signed_"Hx" mtimes Rm^signed_"Hy"$,
"SMULL", $Rd_1, Rd_2, Rn, Rm$, $Rd_2:Rd_1 = Rn mtimes Rm$,
"SMULL{S}", $Rd_1, Rd_2, Rn, Rm$, $Rd_2:Rd_1 = Rn mtimes Rm$,
"SMULWy", $Rd, Rn, Rm$, $Rd = (Rn mtimes Rm^signed_"Hy")_(47:16)$,
"UMAAL", $Rd_1, Rd_2, Rn, Rm$, $Rd_2:Rd_1 = Rd_1 + Rd_2 + Rn times Rm$,
"UMLAL", $Rd_1, Rd_2, Rn, Rm$, $Rd_2:Rd_1 "+=" Rn times Rm$,
"UMULL", $Rd_1, Rd_2, Rn, Rm$, $Rd_2:Rd_1 = Rn times Rm$,
)
#{
let setmon = $"SetExclusiveMonitor"()$
let pass = $"Pass?"$
let rdpass = $Rd = pass$
instruction-table("Exclusive Load and Store Instructions",
"CLREX", "", "Remove any exclusive monitors",
"LDREX", $Rt, [Rn]$, $Rt = [Rn]; setmon$,
// This is not supported in ARM.
// "LDREX", $Rt, [Rn, \#i_10]$, $Rt = [Rn + i^signed]; setmon$,
"LDREXB", $Rt, [Rn]$, $Rt = [Rn]_(7:0); setmon$,
"LDREXH", $Rt, [Rn]$, $Rt = [Rn]_(15:0); setmon$,
"LDREXD", $Rt_1, Rt_2, [Rn]$, $Rt_2:Rt_1 = [Rn]_(127:0); setmon$,
"STREX", $Rd, Rn, [Rt]$, $ifm(pass) [Rt] = Rn; rdpass$,
"STREX", $Rd, Rn, [Rt, \#i_10]$, $ifm(pass) [Rt] = Rn; rdpass$,
"STREXB", $Rd, Rn, [Rt]$, $ifm(pass) [Rt]_(7:0) = Rn_(7:0); rdpass$,
"STREXH", $Rd, Rn, [Rt]$, $ifm(pass) [Rt]_(15:0) = Rn_(15:0); rdpass$,
"STREXD", $Rd, Rn_1, Rn_2, [Rt]$, $ifm(pass) [Rt]_(127:0) = Rn_2:Rn_1; rdpass$,
)
}
#colbreak(weak: true)
#v(1em) // A slight visual break.
#heading-group[
= ARMv7 Floating Point Instructions
== Quick Reference Guide
]
#let Sd = $"Sd"$
#let Dd = $"Dd"$
#let Sn = $"Sn"$
#let Dn = $"Dn"$
// Perform a value-preserving cast.
#let Cast = $"Cast"$
// Reinterpret the same raw data as a new type.
#let Reinterpret = $"Reinterpret"$
#let imm = $"imm"$
#let FPSCR = $"FPSCR"$
#let nzcv = $"nzcv"$
#instruction-table("Floating-Point Register Transfer Instructions",
"VMOV.F32", $Sd, \#signed imm$, $Sd = signed imm$,
"VMOV.F64", $Sd, \#signed imm$, $Sd = signed imm$, // Intentional error.
"VMOV.F32", $Sd, Sn$, $Sd = Sn$,
"VMOV.F64", $Dd, Dn$, $Dd = Dn$,
"VMOV", $Rd, Sn$, $Rd = Reinterpret(Sn)$,
"VMOV", $Sd, Rn$, $Sd = Reinterpret(Rn)$,
"VMOV", $Dd, Rn_1, Rn_2$, $Dd = Reinterpret(Rn_2:Rn_1)$,
"VMOV", $Rd_1, Rd_2, Dn$, $Rd_2:Rd_1 = Reinterpret(Dn)$,
// TODO What even are these two?
"VMOV{.32}", $"Ddx", Rn$, $Dd_"Wx" = Rn$,
"VMOV{.32}", $Rd, "Dnx"$, $Rd = Dn_"Wx"$,
"VMRS", $Rd, "system-reg"$, $Rd = "system-reg"$,
"VMRS", $"APSR_nzcv", FPSCR$, $"APSR"_nzcv = FPSCR_nzcv$,
"VMSR", $"system-reg", Rn$, $"system-reg" = Rn$,
)
#let fx = $"fx"$
#let fy = $"fy"$
#let fz = $"fz"$
#let fd = $"fd"$
#let fn = $"fn"$
#let dz = $"fz"$
#let Compare = $"Compare"$
#let pmeq = sym.plus.minus + "="
#instruction-table("Floating-Point Instructions",
"VABS.f", $fx, fy$, $fx = |fy|$,
"VADD.f", $fd, fx, fy$, $fd = fx + fy$,
"VCMP{E}.f", $fx, \#0.0$, $FPSCR_nzcv = Compare(fx, 0.0)$,
"VCMP{E}.f", $fx, fy$, $FPSCR_nzcv = Compare(fx, fy)$,
"VCVT.F32.F64", $Sd, Dn$, $Sd = "Float2Float"(Dn)$,
"VCVT.F64.F32", $Dd, Sn$, $Dd = "Float2Float"(Sn)$,
"VCVT.sz.f", $fd, fx, \#i_5$, $fd = "Float2Fixed"(fx, i)$,
"VCVT.f.sz", $fd, fx, \#i_5$, $fd = "Fixed2Float"(fx, i)$,
"VCVT{R}.s32.f", $Sd, fn$, $Sd = "Float2Int"(fn)$,
"VCVT.f.s32", $fd, Sn$, $fd = "Int2Float"(Sn)$,
"VCVTx.F16.F32", $Sd, Sn$, $Sd_"Hx" = "Float2Float"(Sn)$,
"VCVTx.F32.F16", $Sd, Sn$, $Sd = "Float2Float"(Sn_"Hx")$,
"VDIV.f", $fx, fy, dz$, $fx = fy div dz$, // Intentional error.
"VFMa.f", $fx, fy, fz$, $fx pmeq fy times fz$,
"VFMNa.f", $fx, fy, fz$, $fx = -fx plus.minus fy times fz$,
// TODO why is it floored? Seems wrong.
"VMLa.f", $fx, fy, fz$, $fx pmeq floor(fy times fz)$,
"VMUL.f", $fx, fy, fz$, $fx = fy times fz$,
"VNEG.f", $fx, fy$, $fx = -fy$,
"VNMLa.f", $fx, fy, fz$, $fx = -fx plus.minus -floor(fy times fz)$,
"VNMUL.f", $fx, fy, fz$, $fx = -floor(fy times fz)$,
"VSQRT.f", $fx, fy$, $fx = sqrt(fy)$,
"VSUB.f", $fx, fy, fz$, $fx = fy - fz$,
)
#let mx = $"mx"$
#let my = $"my"$
#let rx = $"rx"$
#let ry = $"ry"$
#let dx = $"dx"$
#let dy = $"dy"$
#instruction-table("SIMD Register Transfer Instructions",
"VDUP.z", $mx, ry$, $mx_"z*" = ry_"z"$,
"VDUP.z", $mx, dy[i]$, $mx_"z*" = dy_"zi"$,
"VMOV.z", $dx[i], ry$, $dx_"zi" = ry_"z"$,
// What does "^s" mean?
"VMOV.sz", $rx, dy[i]$, $rx = dy_"zi"^"s"$,
"VMOV", $mx, my$, $mx = my$,
)
#info-table("Floating-Point System Registers", 2,
"FPEXC", "Floating-Point EXception Control",
"FPSCR", "Floating-Point Status and Control Register",
"FPSID", "Floating-Point System ID",
"MVFR{0,1,2}", "Media and VFP feature registers",
)
#{
let bit(..xs) = text(font: monospace, "0x" + chunks(4, left-pad(8, "0", str(xs.pos().map(x => calc.pow(2, x)).sum(), base: 16))).join(thousand))
info-table("Floating-Point Status and Control Register (FPSCR)", 3,
"Name", "Bit", "Meaning",
"IOC", bit(0), "Invalid Operation cumulative exception",
"DZC", bit(1), "Division by Zero cumulative exception",
"OFC", bit(2), "Overflow cumulative exception",
"UFC", bit(3), "Underflow cumulative exception",
"IXC", bit(4), "Inexact cumulative exception",
"IDC", bit(7), "Input Denormal cumulative exception",
"IOE", bit(8), "Invalid Operation exception trap enable",
"DZE", bit(9), "Division by Zero exception trap enable",
"OFE", bit(10), "Overflow exception trap enable",
"UFE", bit(11), "Underflow exception trap enable",
"IXE", bit(12), "Inexact exception trap enable",
"IDE", bit(15), "Input Denormal exception trap enable",
"RMode", bit(23, 22), "Rounding mode (nearest, plus infinity, minus infinity, zero)",
"FZ", bit(24), "Enable Flush-to-zero mode",
"DN", bit(25), "Propagate NaN operands to output",
"AHP", bit(26), "Use alternative half-precision format",
"QC", bit(27), "SIMD saturation occurred",
"V", bit(28), "Overflow condition flag",
"C", bit(29), "Carry condition flag",
"Z", bit(30), "Zero condition flag",
"N", bit(31), "Negative condition flag",
align: (x, y) => if y == 0 { left } else { (left, right, left).at(x) } + horizon,
)
}
#info-table("Floating-Point and SIMD Keys", 2,
"s", "Operation signedness (S or U)",
"z", "Data size (8, 16, or 32)",
"f", "Floating-point size (F32 or F64)",
"sx, dx, qx", "Single-/double-/quadword register",
"fx, fy, fz", "Floating-point register (Sx or Dx depending on data size)",
"mx, my, mz", "SIMD Register (Dx or Qx)",
// TODO floor means round??
$floor(x)$, "Value is rounded",
"{E}", "Any NaN causes an exception",
"{R}", "Use the rounding mode in FPSCR instead of round-to-zero",
)
#info-table("Notes for Floating-Point and SIMD Instructions", 2,
"V3, V4", "Introduced in VFP v3, v4",
"SH, S2", "Introduced in SIMD with half-precision floats, SIMDv2",
"F", "Instruction with data type F32 also exists",
)
#info-table("Keys", 2,
"{S}", "Optional suffix; if present, update NZCV",
"{slr}", "An optional LSL #N or ASR #N",
"op2", "Immediate or shifted register",
"a", [A or S to make $plus.minus$ add or subtract],
"i, j", "Immediate operand, range 0..max or 1..max+1",
"rx, ry, rz, rw", "General registers",
"rlist", "Comma-separated registers within { }",
"{rb}", "Optional rotate by multiple of 8 bits",
"{sl}", "Optional left shift",
"{sr}", "Optional right shift",
"{AS}", [Arm shift or rotate (LSL, ROR, LSR, ASR, RRX). $AS(x)$ uses it.],
$"value"^signed, "value"^unsigned$, "Value is sign/zero extended",
$macron(times), macron(div), macron(>>)$, "Operation is signed",
$C$, "Carry flag as an integer",
)
|
https://github.com/0xpapercut/obsidian-wypst | https://raw.githubusercontent.com/0xpapercut/obsidian-wypst/master/README.md | markdown | MIT License | # Wypst
High quality rendering of [Typst](https://github.com/typst/typst) in Obsidian, powered by [wypst](https://github.com/0xpapercut/wypst).
## Usage
This plugin overrides regular math blocks (`$<...>$` and `$$<...>$$`), so that they're rendered as Typst math.
If this plugin doesn't render the LaTeX code in your vault correctly, you can try out the `fallbackToLatexOnError` experimental setting.
## Compatibility
To maximize compatibility with LaTeX math blocks, the rendering backend switches to MathJax when certain structures like `\begin{environment}<...>\end{environment}` or `\<some-symbol>` are encoutered.
For example, `$pi$` will be rendered using Typst, whereas `$\pi$` will be rendered as regular LaTeX.
In general, expressions in Typst and LaTeX, if equivalent, should render to _exactly_ the same output. If this is not the case, you can report it as an issue.
## Issues
I welcome everyone who encounters a problem to open an issue on [0xpapercut/obsidian-wypst](https://github.com/0xpapercut/obsidian-wypst/issues/new).
|
https://github.com/hewliyang/fyp-typst | https://raw.githubusercontent.com/hewliyang/fyp-typst/main/preliminaries.typ | typst | #import "@preview/showybox:2.0.1": showybox
#set heading(numbering: "1.")
= Preliminaries
This section includes the fundamental concepts and techniques essential for understanding TTS systems and how they can be evaluated, providing a rigorous foundation for subsequent discussions.
== Audio Signals
Audio signals are continuous waveforms that represent variations in sound pressure over time. In digital systems, these signals undergo a process of conversion and processing to enable computational analysis and synthesis.
=== Analog to Digital
The process of converting continuous analog signals to discrete digital representations involves three key steps.
1. *Sampling*
#figure(
image("assets/sampling.svg", width: 100%),
caption: [
Analog to digital sampling from a 5Hz sine wave
],
)
A continuous-time signal $x(t)$ is sampled at discrete time intervals, resulting in a sequence of samples $x[n]$ where $n$ is the sample index. The sampling process can me mathematically represented as
$
x[n] = x(n\T)
$
Additionally,
- $T$ is the sampling period
- $f_s = 1/T$ is the sampling rate, which is defined as the number of samples taken per second.
- $x[n]$ is the amplitude of the signal $x(t)$ at time t=$n\T$
A larger $f_s$ preserves more detail of the original signal which may be helpful for accurately reconstructing the original signal in certain applications such as high fidelity audio streaming, but imposes a computational and storage penalty.
For example, at a sampling rate $f_s$ of 48,000 kHz, a mere 10-second audio clip would result in a vector of size $10 times 48,000$ samples, ie: shape `(1, 480_000)` or `(480_000,)`
On the other hand, a smaller sampling rate may lose important details in the original signal, especially if the sampling rate drops below the *Nyquist* rate, which can negatively impact downstream performance.
In general, most TTS datasets such as in @tab-tts-datasets such as Gigaspeech @GigaSpeech2021
are typically resampled to 16kHz, which strikes a good balance between detail and computational efficiency.
Additionally, a raw discretized waveform, even at this sampling rate is still unsuitable for sequence modelling due to the high temporal resolution. Instead, the waveform is typically converted into an intermediary representation, such as a spectrogram which is temporally more compact.
2. *Quantization*:
The amptitude for each sample is approximated to a finite set of values. For a $b$-bit quantizer, the quantization levels are typically
$
Q = {-1 + (2k) / (2^b - 1)}:k=0,1,...,2^b-1
$
Similar to sampling frequency, a higher bit depth $b$ allows for a more accurate recording of the true amplitude of the sound wave, with similar trade offs in storage and computation.
For example, a 16-bit quantization would provide 65,536 bins, or a range of [-32768, 32768]. Evidently, there will be some information loss due to quantization to some extent depending on the choice of $b$.
As machine learning models typically operates in floating point operations, this range can be normalized to $[-1, 1]$ at the precision level of choice.
In audio processing libraries such as `librosa` and `torchaudio`, the default data type assigned when reading in audio files is a `float32` which is equivalent to a bit depth of 24.
#showybox(
title: [Documentation for `librosa.load()` method],
frame: (
border-color: blue,
title-color: blue.lighten(30%),
body-color: blue.lighten(95%),
footer-color: blue.lighten(80%),
),
footer: "Method signature extracted from documentation version 0.10.2 (Sept 2024)",
)[
```
librosa.load(path, *, sr=22050, mono=True, offset=0.0, duration=None, dtype=<class 'numpy.float32'>, res_type='soxr_hq')
```
]
3. *Nyquist-Shannon Sampling Theorem*:
To accurately represent a signal with a maximum frequency component of $f_{max}$, the Nyquist-Shannon Sampling Theorem states that the sampling rate $f_s = 1 / T$ must satisfy $f_s >= 2f_{max}$
As the maximum audible frequency by humans are $<=$ 8 kHz, sampling speech at 16kHz is the minimum $f_s$ that satisfies the theorem, and hence is a typical choice for tasks such as TTS and ASR
To summarize, the result of the Analog to Digital conversion process is simply a 1D vector of shape $[1, t times f_s]$, where $t$ is the length of a signal in seconds with values that can be integers or floats.
=== Fourier Transform
The *Fourier Transform* is used to decompose a continuous signal such as an audio signal into its constituent frequencies. It is defined as:
$
X(f) = integral_(-infinity)^infinity x(t) exp{-i 2 pi} upright(d)t
$<eq-fourier-transform>
Where:
- $t$ is time
- $f$ is frequency
- $x(t)$ is the input signal in the time domain (amplitude vs time)
- $X(f)$ is the complex valued frequency domain representation of the signal (amplitude vs frequency)
In audio processing, the frequency domain representation of audio signals is often more informative compared to it's time domain counterpart for identifying types of sounds in a signal.
As we have established above, in digital signal processing we work with *discrete* signals. Similarly, the *Discrete Fourier Transform (DFT)* is defined as:
$
X[k] = sum_(n=0)^(N-1)x[n] dot exp{-i 2 pi k / N n}
$
for $k=0,1,..., N-1$ where:
- $x[n]$ is the discrete input signal of sample $n$
- $X[k]$ is the $k$-th frequency component of the DFT
- $N$ is the total number of samples
Notably, a key property of fourier transformers is that they are invertible, and hence can be used for instance in removing unwanted frequencies in audio by flattening peaks in $X[k]$, then applying the inverse CFT or DFT to obtain a cleaned signal x[n].
Additionally, as the transforms produce complex values and since in the audio domain we generally are only concerned with power of signals, it is not uncommon to only consider the absolute values i.e. $abs(x[n])$.
=== Fast Fourier Transform (FFT)
#grid(
columns: 2,
figure(
caption: "Sum of 2 sine waves at different frequencies",
kind: image,
[#image("assets/simple-wave.svg")],
),
figure(
caption: "Resulting FFT of Figure 2",
kind: image,
[#image("assets/simple-wave-fft.svg")],
),
)
The FFT is an efficient implementation of the DFT, and is commonly implemented in mathematical and signal processing libraries like `numpy`, `scipy`, `librosa` and `torchaudio` as a manifestation of the works of @cooley1965algorithm.
The time complexity of the proposed algorithm is $O(n log N)$, while a brute force approach would require $O(N^2)$.
=== Short Time Fourier Transform (STFT) <section-stft>
While the FFT is powerful, it's limitation is that it assumes the signal is stationary, i.e. the frequency content does not change over time. However, it is obvious that many real-world signals like speech are in fact non-stationary.
The STFT addresses this by applying the FFT to short segments of the signal over time. It can be expressed mathematically as:
$
"STFT"{x[n]}(m,k) = sum_(n=-infinity)^infinity x[n]w[n-m] exp{-i 2 pi k / N n}
$
where
- $x[n]$ is the input signal
- $w[n]$ is the window function
- $m$ is the time index of the window
- $k$ is the frequency index
In practice,
1. The signal is divided into shorter segments which are often overlapping using a window function, in order to avoid losing information at the edges
2. FFT is applied to each segment
3. The results are concatenated to create a time-frequency representation
When using a library such as `librosa`, the primary parameters that one should pay attention to is:
- `n_fft`: number of samples per window, i.e. size of the window
- `hop_length`: number of samples to skip until the next window, i.e. the higher the value, the lower the overlap between windows and vice versa
The resulting vector or tensor, i.e. the linear spectrogram takes the shape
$
["n_fft" / 2 + 1, floor((T dot f_s - "n_fft") / "hop_length") + 1]
$ <eq-spectrogram-shape>
where the first dimension corresponds to the frequency bins while the second correspond to the time frames. The magnitude of each element in the spectrogram i.e. `spectrogram[t][f]` corresponds to the amplitude of the frequency $f$ at time $t$.
#figure(
caption: "STFT of a sample from LibriSpeech",
kind: image,
[#image("assets/linear-spectrogram.svg")],
) <image-linear-spectrogram-speech>
#figure(
caption: "STFT of an instrument (trumpet)",
kind: image,
[#image("assets/linear-spectrogram-trumpet.svg")],
) <image-linear-spectrogram-instrument>
@image-linear-spectrogram-speech and @image-linear-spectrogram-instrument illustrates the interpretable nature of spectrograms, as the difference between human speech and music instruments can be easily differentiated compared to more primitive forms such as the discrete waveform.
== Representations of Discrete Audio Signals
In deep learning for audio processing, the choice of input representation can signifcantly impact model performance and efficiency. In @section-stft, we have explored a method of representing raw discrete waveforms as spectrograms using the STFT.
Indeed, this is a valid format for further processing by battle tested techniques from adjacent fields such as Convolutional Neural Networks (CNN) in computer vision. In addition, as the STFT is a non-lossy operation, enabling the resulting spectrogram can be easily inverted via the inverse STFT back to a waveform, without requiring the use of a vocoder.
However, in practice, both raw waveforms and linear spectrograms are rarely used for tasks such as TTS due to
1. High dimensionality on the frequency scale - requires more compute and memory for processing
2. Perceptual misalignment with the human auditory system - humans are more perceptive to differences lower frequencies compared to higher frequencies.
Mel-spectrograms address both of these issues, but it's transformaton operation is lossy and hence requires the use of a vocoder to invert the mel-spectrogram back into an audible waveform. Despite this, they are widely used across many of the earlier prominent works such as Tacotron @wang2017tacotronendtoendspeechsynthesis. VITS @kim2021conditionalvariationalautoencoderadversarial utilises both linear spectrograms as input to a posterior encoder, but uses mel-spectrograms for computing the reconstruction loss during training.
WaveNet @oord2016wavenetgenerativemodelraw and achieved success utilizing raw waveforms while modern language model inspired causal decoders such as @betker2023betterspeechsynthesisscaling rely on discrete audio tokens, which are learnt representations from a VQVAE.
=== Mel Spectrograms
Mel spectrograms are a popular representation that captures both time and frequency information, tailored to human auditory perception. The difference between a linear spectrogram and mel spectrograms are simply a projection of the frequency dimension onto the mel scale.
The mel scale is designed to better represent how humans perceive frequency differences. Chiefly:
- Humans are more sensitive to small changes in pitch at lower frequencies than at higher frequencies.
- THe mel scale is approximately linear below 1000Hz and logarithmic above 1000Hz.
The conversion from Hz to mel is given by:
$
m = 2595 log_10 (1 + f / 700)
$
where $m$ is the mel scale value and $f$ is the frequency in Hz.
Transforming a discrete waveform into a mel-spectrogram entails largely the same recipe as the STFT, with a few extra steps which are applying a mel filterbank, then logarithmic scaling.
Mathematically,
$
"S"_"mel" = log(M dot.c abs("STFT(x)")^2)
$ <eqn-mel-transform>
where $M$ is the transformation matrix and $x$ is the discrete input signal.
#figure(
caption: "Visualization of triangular mel filter banks",
kind: image,
[#image("assets/mel-filter-banks.svg", height: 200pt)],
) <image-mel-filterbanks>
The operation in @eqn-mel-transform can be thought of as multiple 1D convolutions on the linear spectrogram, where each filter bank represented by the different colors corresponds to one convolution kernel. Equivalently, each kernel would be represented as a row of the transformation matrix $M$.
Let us denote the number of filter banks or the number of bands as $n_"mels"$. Also recall @eq-spectrogram-shape. The resulting shape of the mel spectrogram is now:
$
[n_"mels", floor((T dot f_s - "n_fft") / "hop_length") + 1]
$
such that the frequency spectrum has been quantized to a chosen $n_"mels"$.
The choice of $n_"mels"$ is depends on the use case. For example both @wang2017tacotronendtoendspeechsynthesis and @kim2021conditionalvariationalautoencoderadversarial both choose a value of 80 bands for training Tacotron and VITS respectively.
Also recall @image-linear-spectrogram-instrument. Applying the mel-scale transform with $n_"mels"=128$, we get
#figure(
caption: [Mel scale spectrogram of @image-linear-spectrogram-instrument],
kind: image,
[#image("assets/mel-spectrogram.svg")],
)
=== Mel Frequency Cepstral Coefficients (MFCC)
MFCCs are a compact representation of the spectral envelope of a signal and is also widely used in speech and music processing tasks. MFCCs build upon the mel spectrogram representation, applying additional transformations in order to capture the most salient features of the signal.
The process of computing MFCCs involves:
1. Applying the Discrete Cosine Transform (DCT) to the log mel spectrogram
2. Keep only the first N coefficients, which is typically 13-20 for speech applications
$
"MFCC" = "DCT"("S"_"mel")[:N]
$
The DCT can be thought of as a way to seperate the overall shape of the spectrum which is captured by lower order coefficients from the fine details, which are captured by the higher order coefficients.
In the context of evaluation, MFCCs can be used to compute the Mel Cepstral Distortion metric (MCD), which is a pairwise metric measuring the spectral difference between two signals. Concretely,
$
"MCD" = (10 / ln(10)) sqrt(2 sum_(n=1)^N (c_n - c'_n)^2)
$
where $c_n$ and $c'_n$ are the $n^("th")$ coefficients of the natural and synthesized speech respectively. The lower the MCD, the higher their spectral similarity.
=== Discrete Audio Tokens
Taking a language modelling approach for speech generation was first introduced in Tortoise @betker2023betterspeechsynthesisscaling, who indentified the opportunity to leverage the same recipe detailed in the original DALLE-1 paper by @ramesh2021zeroshottexttoimagegeneration.
More specifically, Betker firstly trained a VQVAE to learn latent, discrete representations of speech signals via a mel spectrogram reconstruction loss, producing an intermediate representation which he described as MEL tokens.
==== VQVAE
The VQVAE architecture consists of three main components which are analogous to the original paper by @oord2018neuraldiscreterepresentationlearning:
#figure(
caption: "Original figure describing VQ-VAE from 2017 DeepMind paper altered with inputs as spectrograms instead of images",
kind: image,
[#image("assets/vqvae.png")],
)
1. An encoder that maps the input signal (mel spectrogram) to a latest space
2. A vector quantization layer that discretizes the continuous latent representations using *codebooks*.
3. A decoder that reconstructs the audio from the quantized representations.
A codebook is a finite set of learned vector embeddings. During the forward pass, each latent vector produced by the encoder is replaced by it's nearest neighbour in the codebook, i.e. for an input latent $z_(e(x)) in RR^n$ produced by the encoder network:
$
q(z_e (x)) = op("arg min", limits: #true)_(k) ||z_e (x) - e_k||_2
$
where $e_k in RR^n$ are the codebook entries, $n$ is the embedding dimension of the codes, while $k$ is the codebook size. A larger codebook allows for finer representation of the audio signal but increases computational complexity. For completeness, it is worth to note that in @betker2023betterspeechsynthesisscaling,
- $k = 8192$
- $n = 256$
==== Autoregressive Prior
Secondly, an autoregressive decoder, specifically GPT-2 @radford2019language was trained using the next token prediction objective on these MEL tokens conditioned on text token labels.
$
P(x_1, ..., x_T | y_1, ..., y_Q) = product_(t=1)^T P(x_t | x_1, ..., x_(t-1), y_1, ... y_Q)
$
During inference, regular text tokens $y_i$ are passed to the AR decoder as inputs, and MEL tokens $x_i$ are sampled as outputs before being passed to the decoder and subsequently vocoder to be transformed into an audible waveform.
This approach allows the model to generate each token conditioned on all previously generated tokens, capturing long-range dependencies in the audio signal. Indeed, the benchmarks indicate superior consistency and prosody and cadence compared to non-autoregressive models such as VITS.
Since then, there has been no shortage of similar systems such as AudioLM @borsos2023audiolmlanguagemodelingapproach, Base TTS @łajszczak2024basettslessonsbuilding, VALL-E @wang2023neuralcodeclanguagemodels, and XTTS by @casanova2024xttsmassivelymultilingualzeroshot which each has tricks of it's own but operates on the same foundations.
The mental model of such models are simple and proven to work at scale from the adjacent field of language modelling, but suffer from runtime & compute penalties due to the need for autoregressive decoding. Namely, it is slow and memory requirements scale with the input length at both training and inference time.
Additionally, recent discrete neural audio codecs such as Encodec @défossez2022highfidelityneuralaudio have shown state of the art results in the audio compression-decompression space even in the out of domain cases by employing the same latent space quantization techniques. In fact, the codes generated by these models can be used off the shelf as audio tokens directly for causal modelling which is demonstrated by @wang2023neuralcodeclanguagemodels in VALL-E. This is to say, the weights of the codec model can be frozen during training.
#figure(
caption: "Architecture of VALL-E",
kind: image,
[#image("assets/vall-e.png", height: 200pt)],
)
At the same time, no bespoke decoder or vocoder networks is required to invert the tokens back to a waveform. Simply passing the sampled codes back into the frozen Encodec decoder reconstructs the waveform.
On the other hand, systems such as VALL-E suffer from content inaccuracies and high word error rates (WER). This phenomenon is in part, due to the fact that acoustic codecs are designed primarily for audio compression and the latents prioritize capturing acoustic fidelity over semantic richness as suggested by @ye2024codecdoesmatterexploring. The authors demonstrated that self-supervised features, such as those extracted by HuBERT @hsu2021hubertselfsupervisedspeechrepresentation can augment the codec latents with a richer semantic representation, leading to better performance.
== Evaluating TTS Systems
TTS systems are judged by their ability to produce accurate, natural-sounding and intelligible speech. These systems can be assessed using both subjective and objective methods.
Studies have shown however that objective metrics tend to not correlate well @vasilijevic2011perceptual with human perception, which necessitates the need for subjective, listening tests typically using volunteers (paid or unpaid).
Subjective tests require a human in the loop, meaning it is time-consuming, error prone and expensive. It is also not feasible to scale evaluation efforts for multi-system use cases. Additionally, it cannot be used during training to validate the real-time performance of systems while training @TTS-scores.
=== Absolute vs Relative Evaluations
*Absolute* evaluations, or reference-free evaluations access the performance of a TTS system on a fixed scale, independent of other systems or comparisons. They provide a direct evaluation of the model's quality, usually on predefined scales. They are used when evaluating systems in isolation, and when comparisons are not possible.
Examples of absolute evaluations include
- Mean Opinion Scores (MOS)
- Multiple Stimuli with Hidden Reference and Anchor (MUSHRA)
- Mel-Cepstral Distortion (MCD)
- Word Error Rate (WER)
These metrics are easy to interpret and are a direct measurement of performance, but can be influenced by listeners bias.
*Relative* evaluations compare the performance of one TTS system against the ground truths, i.e. a held-out test set or against other systems, focusing on preference and ranking rather than independent scores. It is used when the goal is to determine which system is better in a pairwise or multi-system comparison.
Common relative evaluations in TTS include:
- ABX tests: double blind trials to determine a perceptible difference between two signals
- Preference tests: participants are asked to compare samples $> 2$ samples and choose the highest performing sample (such as most natural) without any explicit scoring
- Spectral reconstruction error/loss: where $k=1$ corresponds to Mean Absolute Error (MAE) and $k=2$ corresponds to Mean Squared Error.
$
L_"recon" = "MAE" = ||x_"mel" - hat(x)_"mel"||_k
$
A holistic evaluation set up typically uses a combination of subjective and objective metrics in order to provide a comprehensive understanding of the system's performance.
=== Subjective Evaluation
Subjective Evaluation involves human listeners assessing the quality of synthesized speech. These evaluations can focus on attributes such as naturalness, intelligibility or preference.
==== Mean Opinion Score (MOS)
MOS is a widely-used subjective metric where human listeners rate the quality of speech on a fixed Likert scale, typically from 1 to 5 where 1 is "bad" and 5 is "excellent". MOS is actually a subset of a classification of Absolute Category Rating (ACR) tests used historically in the telecommunications industry for assessing transmission quality @5946971.
Recommended experimental setups are inscribed in the ITU-T P.800 standard @ITU1996.
The MOS is computed as the average of all ratings.
$
"MOS" = 1 / N sum_(i=1)^N r_i
$
where $r_i$ is the rating provided by the $i^"th"$ listener and $N$ is the total number of listeners.
#figure(
caption: "Example of a MOS scoring rubric for naturalness",
kind: table,
[#table(
columns: 2,
[Rating], [Quality],
[5], [Excellent],
[4], [Good],
[3], [Fair],
[2], [Poor],
[1], [Bad],
)],
)
MOS can be used to evaluate multiple dimensions of speech and not just naturalness including intelligibility, speaker similarity, typically denoted by adding a prefix or suffix such as $"S-MOS"$ or $"MOS-N"$ for example.
==== Multiple Stimuli Hidden Reference and Anchor (MUSHRA)
MUSHRA is a more rigorous subjective testing methodology compared to MOS, which also originates from evaluating lossy-compression in the telecommunications industry, described by ITU-R BS.1534-1 @itu_bs1534-3_2015. Listeners are presented with multiple stimuli, including a hidden reference and low quality anchor, and are instead asked to rate samples on a more fine-grained scale from 0 to 100.
In the context of TTS evaluations, the lower and upper anchor references are typically not used in order to save costs, while achieving a higher overall listening time per test such as in BASE TTS @łajszczak2024basettslessonsbuilding.
==== Analysis for statistical significance
Firstly, both MOS and MUSHRA requires careful execution of the experimental setup in order to ensure statistically significant results.
As recruiting a large number of volunteers in reality can be costly and time consuming, works such as @5946971 introduce toolkits for conducting such tests on crowdsourcing platforms such as Amazon's Mechanical Turk platform.
Secondly, the relevant statistical tests must be done after conducting said listenings tests. Typically, the Students t-test is applicable when comparing pairwise systems such as synthesized vs ground-truth or ANOVA for multi-system comparisons.
Correlation metrics such as Pearsons correlation coefficient (PCC) or Spearman's rank correlation coefficient (SPCC) are also typically computed to measure the perceived correlation compared to ground truths.
When reporting MOS and MUSHRA, it is also standard practice to report a confidence interval, i.e. $hat(u) plus.minus t sqrt("var"(hat(u))) $, where $hat(u)$ is the observed metric and $t$ is the correct percentile from the t-distribution.
==== ELO
The ELO rating system, originating from chess can be adapted for pairwise comparisons in TTS evaluation. In this context, listeners compare pairs of speech outputs, and systems receive ELO ratings based on the outcome of these comparisons.
In particular, assume a system $A$ with rating $E_A$ competes against system $B$ with rating $E_B$. Then, the expected score for system A is:
$
E_A = 1 / (1 + 10^((E_B-E_A) / 400) )
$
If system $A$ wins, it's new rating is:
$
R'_A = R_A + K * (S_A-E_A)
$
where
$
S_A := cases(
1 wide& "A wins",
0.5 wide& "draw",
0 wide& "otherwise",
)
$
An example of such as system is #link("https://huggingface.co/spaces/TTS-AGI/TTS-Arena")[TTS Arena] @tts-arena hosted on the HuggingFace platform, where members of the public are prompted to do pairwise comparisons based on naturalness of the randomly generated samples.
As of the time of writing, $binom(14,2)$ possible combinations of systems are available for comparison including proprietary systems like ElevenLabs.
=== Objective Metrics
Objective metrics rely on automated methods to evaluate TTS systems. These metrics compare are mainly reference dependent, comparing synthesized speech against a ground truth.
==== Word Error Rate (WER)
WER is a common objective metric to evaluate the intelligibility of synthesized speech by measuring how well an ASR system transcribes it.
Mathematically, it is defined as:
$
"WER" = (S + D + I) / N
$
Where:
- $S$ is the number of substitutions
- $D$ is the number of deletions,
- $I$ is the number of insertions
- $N$ is the total number of words in the reference transcript
WER is widely used due to it's simplicity, and the exceptional quality of recent ASR models like Whisper @radford2022robustspeechrecognitionlargescale.
==== Character Error Rate (CER)
CER is defined identically to WER, except at the character level instead of the world level. It is used when detecting small mistakes, particularly in languages with complex orthographies are critical.
==== Signal-to-Noise Ratio (SNR)
SNR is a basic metric that measures the ratio between the desired speech signal and background noise. Higher SNR indicates clearer and more intelligible speech. SNR can be used to identify generated noise in synthetic speech.
The SNR is computed as
$
"SNR" = 10log_(10) (P_"signal" / P_"noise")
$
where $P$ represents power of the speech and noise signal respectively.
==== Perceptual Evaluation of Speech Quality (PESQ)
PESQ attempts to predict the quality of speech as perceived by human listeners, i.e. tries to mimic MOS. It compares synthesized speech with a reference signal and evaluates the perceptual quality and was standarzied in ITU-T P.862 @itu_pesq_p862_2001.
PESQ is a model-based metric, but does not actually have any learnable parameters and hence is still considered an objective metric. However, it is important to note that PESQ was originally designed to measure degradations in telecommunication transmissions, and hence may not generalize well for TTS prediction tasks.
The metric ranges from -0.5 to 4.5. A Python implementation of PESQ is made available by @miao_wang_2022_6549559.
==== Short-Term Objective Intelligibility (STOI)
STOI is yet another object measure used to predict the intelligibility of speech in noisy environments. It compares short-term temporal envelopes of the synthesized and reference speech signals, and provides a score between 0 and 1. A higher STOI indicates higher intelligibility.
$
"STOI" = 1 / K sum_(k=1)^K "corr"(x_k,y_k)
$
where $x_k$ and $y_k$ are the time frames of the reference and synthesized signals respectively.
=== Survey of the latest TTS papers
For completeness, the following table enumerates the different types of metrics used in leading TTS architectures by their respective authors, showing the variance in testing rigour across the field.
#show figure: set block(breakable: true)
#figure(
caption: [Evaluation Metrics Across TTS Systems],
kind: table,
[
#set text(size: 10pt)
#show table.cell.where(y: 0): strong
#table(
columns: 3,
stroke: 0.5pt,
[System], [Metric], [Description],
table.cell(
stroke: (bottom: 0pt),
[FastSpeech 2],
),
[Mean Opinion Score (MOS)],
[Overall quality assessment of synthesized speech compared to ground truth],
table.cell(
stroke: (bottom: 0pt),
[@ren2022fastspeech2fasthighquality],
), [Comparative MOS (CMOS)], [Relative naturalness comparison with other systems],
table.cell(
stroke: (bottom: 0pt),
[],
),
[Statistical Measures (σ, γ, K)],
[Analysis of pitch accuracy using standard deviation, skewness, and kurtosis],
[], [DTW Distance], [Similarity measurement between synthesized and ground truth pitch contours],
table.cell(
stroke: (bottom: 0pt),
[StyleTTS 2],
), [MOS-N], [Assessment of speech naturalness/human-likeness],
table.cell(
stroke: (bottom: 0pt),
[@li2023styletts2humanleveltexttospeech],
), [MOS-S], [Similarity evaluation for multi-speaker models],
table.cell(
stroke: (bottom: 0pt),
[],
), [CMOS-N], [Comparative naturalness assessment between different configurations],
table.cell(
stroke: (bottom: 0pt),
[],
), [MCD & MCD-SL], [Mel-cepstral distortion measurement, with and without speech length weighting],
table.cell(
stroke: (bottom: 0pt),
[],
), [F0 RMSE], [Accuracy of pitch prediction],
table.cell(
stroke: (bottom: 0pt),
[],
), [DUR MAD], [Accuracy of phoneme duration prediction],
table.cell(
stroke: (bottom: 0pt),
[],
), [WER], [Speech recognition accuracy/intelligibility],
table.cell(
stroke: (bottom: 0pt),
[],
), [CV (dur/f0)], [Diversity assessment through duration and pitch variation],
[], [RTF], [Speed of synthesis relative to real-time],
table.cell(
stroke: (bottom: 0pt),
[Voicebox],
), [WER], [Speech correctness and intelligibility measurement],
table.cell(
stroke: (bottom: 0pt),
[@le2023voiceboxtextguidedmultilingualuniversal],
), [QMOS], [Subjective audio quality assessment],
table.cell(stroke: (bottom: 0pt), []), [SMOS], [Speaker and style similarity evaluation],
table.cell(stroke: (bottom: 0pt), []), [MS-MAE/MS-Corr], [Phoneme duration prediction accuracy and correlation],
table.cell(stroke: (bottom: 0pt), []), [FDD/FSD], [Quality and diversity assessment of duration/speech samples],
[], [SIM-r/SIM-o], [Audio similarity evaluation using WavLM-TDCNN],
table.cell(
stroke: (bottom: 0pt),
[NaturalSpeech 3],
), [SIM-O/SIM-R], [Speaker similarity assessment with original/reconstructed prompts],
table.cell(
stroke: (bottom: 0pt),
[@ju2024naturalspeech3zeroshotspeech],
), [UTMOS], [Objective substitute for MOS evaluation],
table.cell(stroke: (bottom: 0pt), []), [WER], [Speech intelligibility measurement],
table.cell(stroke: (bottom: 0pt), []), [MCD & MCD-Acc], [Prosodic similarity and emotion accuracy assessment],
table.cell(stroke: (bottom: 0pt), []), [CMOS/SMOS], [Comparative naturalness and similarity evaluation],
table.cell(stroke: (bottom: 0pt), []), [PESQ/STOI], [Perceptual quality and intelligibility measurement],
[], [MSTFT], [Spectral distance measurement],
table.cell(stroke: (bottom: 0pt), [CLaM TTS]), [CER/WER], [Character and word-level transcription accuracy],
table.cell(
stroke: (bottom: 0pt),
[@kim2024clamttsimprovingneuralcodec],
), [SIM-o/SIM-r], [Speaker similarity using WavLM-TDCNN embeddings],
table.cell(stroke: (bottom: 0pt), []), [QMOS/SMOS], [Quality and similarity assessment],
table.cell(stroke: (bottom: 0pt), []), [CMOS], [Comparative quality evaluation],
[], [PESQ/ViSQOL], [Objective speech quality metrics],
table.cell(stroke: (bottom: 0pt), [XTTS]), [CER], [Pronunciation accuracy assessment],
table.cell(
stroke: (bottom: 0pt),
[@casanova2024xttsmassivelymultilingualzeroshot],
), [UTMOS], [Predicted naturalness score],
table.cell(stroke: (bottom: 0pt), []), [SECS], [Speaker similarity using ECAPA2 embeddings],
[], [CMOS/SMOS], [Comparative naturalness and speaker similarity evaluation],
table.cell(stroke: (bottom: 0pt), [BASE TTS]), [MUSHRA], [Quality comparison on 0-100 scale],
table.cell(
stroke: (bottom: 0pt),
[@łajszczak2024basettslessonsbuilding],
), [Expert Evaluation], [Assessment of handling complex linguistic features],
table.cell(stroke: (bottom: 0pt), []), [WER], [Speech intelligibility measurement],
[], [SIM], [Speaker similarity evaluation],
)
],
) |
|
https://github.com/derwind/mathlog-docs | https://raw.githubusercontent.com/derwind/mathlog-docs/main/articles/measure-curve-length.typ | typst | #import "../style/mathlog_style.typ": *
= 曲線の長さはどこで測られているか？
== 概要
普通の Euclid 空間で曲線の長さを測る時、特に深く意識はしないことだが、もうちょっと高尚に多様体目線で見た時には、どこで長さが測られていると思えるのか気になったので少しまとめてみたい。
== 簡単な例 1
平面の中の原点 $(0, 0) in RR^2$ から点 $(x, y) in RR^2$ への距離を測りたい時、いわゆるピタゴラスの定理により、長さは $sqrt(x^2 + y^2)$ となるであろう。この $(x, y)$ が原点に限りなく近い時、これを $(Delta x, Delta y)$ とでも書くことにすると長さは $sqrt((Delta x)^2 + (Delta y)^2)$ になるだろう。 \
覚えていないが、たぶん中学の数学の範囲だったと思う。
#figure(
image("measure-curve-length/pythagoras.png", width: 50%),
caption: [ピタゴラスの定理]
)
== 簡単な例 2
次に平面の中の適当に滑らかな曲線 $gamma(dot) in RR^2$ について考えてみたい。$t in [0, 1]$ というパラメータを用いて
$
gamma(t) = (x(t), y(t))
$
と書かれているとする。$gamma(0)$ が始点 $P$ で、$gamma(1)$ が終点 $Q$ とする。長さを測るためには素朴に折れ線近似を考えよう。
十分に大きな $n in NN$ をとって、$t_i = i/n$ として $P = gamma(0), Q = gamma(1)$ となるような点列 $P = P_0, P_1, dots, P_n = Q$ を考える。この点列を結ぶ線分の長さを考えると、これは $n$ 本の線分の長さの和になる。$i = 0, 1, dots, n-1$ に対して、$P_i$ と $P_{i+1}$ を結ぶ線分の長さは $sqrt((x((i+1)/n) - x(i/n))^2 + (y((i+1)/n) - y(i/n))^2)$ である。これを $n$ 本の線分について足し合わせると、$n$ 本の線分の長さの和が得られる。$n$ を無限大に近づけると、この和は $gamma$ の長さに収束するだろう。（と、Copilot が勝手に文章を書いてくれたが、悪くなさそうなのでそのまま採用した）
この線分の長さの総和は $Delta x_i = x((i+1)/n) - x(i/n)$, $Delta y_i = y((i+1)/n) - y(i/n)$, $Delta t = frac(1, n)$ と書くことにすると、
$
&sum_(i=0)^(n-1) sqrt((x((i+1)/n) - x(i/n))^2 + (y((i+1)/n)- y(i/n))^2) \
= &sum_(i=0)^(n-1) sqrt(Delta x_i^2 + Delta y_i^2) \
= &sum_(i=0)^(n-1) sqrt((frac(Delta x_i, Delta t))^2 + (frac(Delta y_i, Delta t))^2) Delta t \
-> &integral_0^1 sqrt(x'(t)^2 + y'(t)^2) d t
$
となって、ピタゴラスの定理に極小の距離の和が積分の形になる。たぶん高校の数学の範囲だったと思う。この極限値を曲線 $gamma$ の長さ $L$ と呼んだであろう。
#figure(
image("measure-curve-length/polyline.png", width: 50%),
caption: [折れ線近似]
)
さて、$gamma'(t) = (x'(t), y'(t))$ と書くことにすると、ちょっとカッコをつけて
$
L = integral_0^1 ||gamma'(t)|| d t
$
となる。ここで $||dot||$ は気取って書くと Euclid ノルムというやつになる。
== 無限小のベクトルはどこにいる？
ここで、*$gamma'$ はどこにいるのか？* ということについて考えたい。
結局、オチとしては「接空間にいるので～」ということになって以下は大変つまらない内容である。ただ、普通にはどう考えても平面上の無限小のベクトルでしょとしか思えないが、一方で無限小のベクトルは厳密には書けないので、書けない以上は普通には存在していないとも言えるわけではある。
突如多様体 $M$ について考えよう。多様体は位相空間であって、局所的に Euclid 空間と同相であるようなものであった。Möbius の帯のようなものを考えると、局所的には 2 次元平面だが、全体としては「うむむ？」という形状なので、全体としては Euclid 空間には一致しない。
#thm(title: "Whitney の埋め込み定理")[
*性質の良い* $m$ 次元の多様体は $RR^(2m + 1)$ に埋め込める。
]
という定理があるようで（ Ref. [M] 定理 13.13）、これを考えると大体の多様体は Euclid 空間の図形のような気もするし、Möbius の帯も紙工作できることから分かるように、3 次元空間、特に $RR^(2 times 2 + 1) = RR^5$ に埋め込めている。
とは言え、性質の良い場合の話なので、何でもかんでも Euclid 空間の中で考えるのも宜しくない（よく分からないという場合もあるだろうし）。ということで、多様体論は多様体の中で考えるのが基本であるだろう。
== 接空間
多様体の接空間という概念がある。多様体 $M$ の点 $p in M$ に対して、$p$ に “接する” ベクトルの集合を $T_p M$ と書く。これは $p$ に接するベクトルの集合である。多様体 $M$ が $m$ 次元であるとすると、$T_p M$ は $p$ に “接する” $m$ 次元のベクトル空間になる。$T_p M$ の元を接ベクトルと呼ぶ。（と、再び Copilot が勝手に文章を書いてくれたが、悪くなさそうなのでそのまま採用した）
#figure(
image("measure-curve-length/tangent_space.png", width: 50%),
caption: [接空間]
)
先の曲線を 1 次元多様体と思うと、典型的には赤線のようなものを「接空間」のイメージ図とするのであろうが、あまりこのイメージが良くないこともあるし、「接束」を考える時に絵的にイマイチだと思うが、「長さ」の話をする時はこれでも良さそうなので、これにしておく。
さて、この曲線を多様体と思いたい。記号を流用して
$
M: [0, 1] tilde.eq gamma (subset RR^2)
$
でほぼほぼ自明な局所座標が入った多様体と考えられるだろう。素朴な曲線論のイメージを可視化したような図にしたが、この図からしても接ベクトルは多様体 $M$ の外にいってしまっていて、接空間 $T_p M$ に入っていそうである。曲線論の話を思い出すとこの接ベクトルを無限小の長さにした時に、その長さを測りたい。それを各点 $p in M$ で足し合わせると、多様体上の曲線の長さも測れるのではないかということになるだろう。
== 計量テンソル
突然難しそうなキーワードが出て来る。曲線の長さを測りたいというお話だったので、実は今まで考えていた多様体 $M$ は Riemann 多様体で、Riemann 計量というものが入っていますと思うことにする。Riemann 計量とは接空間 $T_p M$ の *内積* である。ベクトル空間のベクトルの長さを測るなら内積だということである。$p in M$ ごとに $T_p M$ に定まるこの内積 $g_p$ は
$
g_p: T_p M times T_p M -> RR
$
という双線型写像であるが、多重線型代数の用語を用いてちょっとカッコイイ書き方をすると、
$
[T_p M times T_p M -> RR] = (T_p M times T_p M)^* tilde.eq T_p M^* times.circle T_p M^*
$
となってしまい、「$g_p in T_p M^* times.circle T_p M^*$ なので、2 階共変テンソルですね」みたいなとんでもないことになってしまう。が、居場所を「近所の宿泊施設」と呼ぶか「ホテルニューグランド」と呼ぶかの違いくらいだと思う。2 階共変テンソルとかどうでも良くて、単に内積である。$g_p$ を内積らしくするために $angle.l dot, dot angle.r_p$ と書くことにすると、$xi in T_p M$ に対してノルム
$
||xi||_p = sqrt(angle.l xi\, xi angle.r_p)
$
を導入できる。後は、何かしらの形で積分が定まれば多様体上の曲線の長さを測ることができるだろう。
#figure(
image("measure-curve-length/measure_tangent_vector.png", width: 50%),
caption: [無限小の接ベクトルの長さを測る]
)
と言うことで、曲線を外側の空間を使って折れ線近似をして長さを測っているつもりが、気が付いたら接空間の中でベクトルの長さを測っていたのである。
== 故郷の Euclid 空間に帰ってくる
多様体の話になったので何か特別な話をしている感じがするが、Euclid 空間もまた多様体として考えられるので、ここまでの話はすべて Euclid 空間にも適用できる。ではこの観点で見るとどうなるか？
#figure(
image("measure-curve-length/euclid_space.png", width: 50%),
caption: [Euclid 空間における曲線の長さ]
)
少し見やすくするために $M = RR$ を曲げているが、Euclid 空間の各点で自身と見分けのつかない空間が接空間としてべたっと貼りついていると考えることができるのである。実は我々は Euclid 空間の中で曲線の長さを測っていると思っていたら、いつの間にか *透明なフィルムのように貼りついた平らな接空間の上で無限小のベクトルの長さを測って足し合わせていた* というのである。
== まとめ
この記事はただの冗談である。途中で触れた「Whitney の埋め込み定理」によって、普通のシチュエーションならちょっと次元は高まるが Euclid 空間の中の図形として具現化されているはずである。なので、素直に多様体の外の領域を活用して折れ線近似で長さを測っていると思えば良いのではないだろうか。
あと、ここでも Copilot が総括してくれたが、そのお気持ちは狙いとちょっと違ったので棄却して、自分で書いた。
== 参考文献
[M] 多様体の基礎
|
|
https://github.com/mem-courses/linear-algebra | https://raw.githubusercontent.com/mem-courses/linear-algebra/main/homework/linear-algebra-homework2.typ | typst | #import "../template.typ": *
#show: project.with(
title: "Linear Algebra Homework #2",
authors: (
(name: "<NAME> (#95)", email: "<EMAIL>", phone: "3230104585"),
),
date: "September 25, 2023",
)
= P35 习题二 2 #ac
#prob[
设 $n-$ 排列 $i_1 i_2 dots.c i_(n-1) i_n$ 的逆序对数为 $k$，求排列 $i_n i_(n-1) dots.c i_2 i_1$ 的逆序对数
]
根据定义，新排列的逆序对数即原排列的“顺序对”数，为 $display(1/2 n(n-1) - k)
$．
= P35 习题二 5(1) #ac
#prob[
确定 $7$ 阶行列式 $|a_(i j)|$ 中该项的符号：$ a_12 a_21 a_34 a_45 a_53 a_66 a_77 $
]
统计排列 $2145367$ 中的逆序对个数．共 $(2,1) (4,3) (5,3)$ 这三个．故该项的符号为 $-$．
= P35 习题二 6(1) #ac
#prob[
用定义计算行列式的值：
#set math.mat(delim: "|")
$ mat(
0,1,0,dots.c,0;
0,0,2,dots.c,0;
dots.v,dots.v,dots.v,,dots.v;
0,0,0,dots.c,n-1;
n,0,0,dots.c,0;
) $
]
注意到仅该项非零：
$ a_12 a_23 a_34 dots.c a_((n-1)n) a_(n 1) $
故
$ |bold(A)| = (-1)^(n-1) n! $
= P35 习题二 6(2) #ac
#prob[
用定义计算行列式的值：
#set math.mat(delim: "|")
$ mat(
a_1, a_2, a_3, a_4, a_5;
b_1, b_2, b_3, b_4, b_5;
c_1, c_2, 0, 0, 0;
d_1, d_2, 0, 0, 0;
e_1, e_2, 0, 0, 0;
) $
]
$ |bold(A)|=(-1)^tau(i_1i_2i_3i_4i_5) a_i_1 b_i_2 c_i_3 d_i_4 e_i_5 $
根据鸽巢原理 $i_3,i_4,i_5$ 中至少有一个数不等于 $1$ 或 $2$，即 $c_i_3, d_i_4, e_i_5$ 中至少有一个为 $0$．所以，$ |bold(A)| = 0 $
= P35 习题二 8(4) #ac
#prob[
利用行列式的性质计算行列式的值：
#set math.mat(delim: "|")
$ mat(
a^2, (a+1)^2, (a+2)^2, (a+3)^2;
b^2, (b+1)^2, (b+2)^2, (b+3)^2;
c^2, (c+1)^2, (c+2)^2, (c+3)^2;
d^2, (d+1)^2, (d+2)^2, (d+3)^2;
) $
]
#set math.mat(delim: "|")
$ |bold(A)| = mat(
a^2, 2a+1, 4a+4, 6a+9;
b^2, 2b+1, 4b+4, 6b+9;
c^2, 2c+1, 4c+4, 6c+9;
d^2, 2d+1, 4d+4, 6d+9;
) = mat(
a^2, 2a+1, 2, 6;
b^2, 2b+1, 2, 6;
c^2, 2c+1, 2, 6;
d^2, 2d+1, 2, 6;
) = 0 $
= P35 习题二 8(5) #ac
#prob[
利用行列式的性质计算行列式的值：
#set math.mat(delim: "|")
$ mat(
1,-1,dots.c,-1,-1;
1,1,dots.c,-1,-1;
dots.v,dots.v,,dots.v,dots.v;
1,1,dots.c,1,-1;
1,1,dots.c,1,1
)_n quad (n>1) $
]
#set math.mat(delim: "|")
$ |bold(A)| = mat(
1,-2,-2,dots.c,-2,-2;
1,0,-2,dots.c,-2,-2;
1,0,0,dots.c,-2,-2;
dots.v,dots.v,dots.v,,dots.v,dots.v;
1,0,0,dots.c,0,-2;
1,0,0,dots.c,0,0;
)_n = (-1)^(n-1) mat(
-2,-2,dots.c,-2,-2,1;
0,-2,dots.c,-2,-2,1;
0,0,dots.c,-2,-2,1;
dots.v,dots.v,,dots.v,dots.v,dots.v;
0,0,dots.c,0,-2,1;
0,0,dots.c,0,0,1;
)_n = 2^(n-1) quad (n>1) $
= P36 习题二 8(6) #ac
#prob[
利用行列式的性质计算行列式的值：
#set math.mat(delim: "|")
$ mat(
a_1,-a_1,0,dots.c,0,0;
0,a_2,-a_2,dots.c,0,0;
dots.v,dots.v,dots.v,,dots.v,dots.v;
0,0,0,dots.c,a_n,-a_n;
b,b,b,dots.c,b,b;
) $
]
#set math.mat(delim: "|")
$ |bold(A)| = mat(
a_1,0,0,dots.c,0,0;
0,a_2,0,dots.c,0,0;
0,0,a_3,dots.c,0,0;
dots.v,dots.v,dots.v,,dots.v,dots.v;
0,0,0,dots.c,a_n,0;
b,2b,3b,dots.c,n b,(n+1)b;
) = (n+1) b dot product_(i=1)^n a_i $
= P36 习题二 9(1) #ac
#prob[
证明等式成立：
#set math.mat(delim: "|")
$ mat(
a_1+k b_1,b_1+c_1,c_1;
a_2+k b_2,b_2+c_2,c_2;
a_3+k b_3,b_3+c_3,c_3;
) = mat(
a_1,b_1,c_1;
a_2,b_2,c_2;
a_3,b_3,c_3;
) $
]
#set math.mat(delim: "|")
$ mat(
a_1+k b_1,b_1+c_1,c_1;
a_2+k b_2,b_2+c_2,c_2;
a_3+k b_3,b_3+c_3,c_3;
) = mat(
a_1+k b_1,b_1,c_1;
a_2+k b_2,b_2,c_2;
a_3+k b_3,b_3,c_3;
) = mat(
a_1,b_1,c_1;
a_2,b_2,c_2;
a_3,b_3,c_3;
) $
原命题得证．
= P36 习题二 9(2) #ac
#prob[
证明等式成立：
#set math.mat(delim: "|")
$ mat(
a_1-b_1,a_1-b_2,dots.c,a_1-b_n;
a_2-b_1,a_2-b_2,dots.c,a_2-b_n;
dots.v,dots.v,,dots.v;
a_n-b_1,a_n-b_2,dots.c,a_n-b_n;
) = 0 $
]
$ mat(
a_1-b_1,a_1-b_2,dots.c,a_1-b_n;
a_2-b_1,a_2-b_2,dots.c,a_2-b_n;
dots.v,dots.v,,dots.v;
a_n-b_1,a_n-b_2,dots.c,a_n-b_n;
) = mat(
a_1-b_1,b_1-b_2,dots.c,b_1-b_n;
a_2-b_1,b_1-b_2,dots.c,b_1-b_n;
dots.v,dots.v,,dots.v;
a_n-b_1,b_1-b_2,dots.c,b_1-b_n;
) = 0 $
原命题得证．
= P40 补充题二 1 #ac
#prob[
试证明在所有的 $n-$ 排列中，奇排列和偶排列的个数相等，并求出奇（偶）排列的个数．
]
定义一个 $n-$ 排列到 $n-$ 排列的映射 $f(i_1i_2i_3 dots.c i_n) = i_2i_1i_3 dots.c i_n$．
1. 排列 $i_1i_2i_3 dots.c i_n$ 与排列 $i_2i_1i_3 dots.c i_n$ 的奇偶性相反．
证明：其余 $n-2$ 个数内部和开头两个数与这 $n-2$ 个数的逆序对数不变，
- 如果 $i_1>i_2$，则交换后逆序对个数减少一
- 如果 $i_1<i_2$，则交换后逆序对个数增加一
可见逆序对个数的奇偶性恰好发生改变．
2. 可以将所有 $n!$ 个排列所组成的二元组 $(x,f(x))$ 恰能找到
#info[也可以参照课件里证法．]
= P40 补充题二 2 #ac
#prob[
试证明：如果数域 $PP$ 上的 $n$ 阶方阵 $bold(A)$ 的元素全为 $2$ 或 $-2$，那么 $2^(2n-1)$ 整除 $|bold(A)|$．
]
将第 $2$ 到 $n$ 行减去第 $1$ 行，则每个位置上的数要么为 $4$，要么为 $0$，要么为 $-4$．
根据行列式的定义，考察新矩阵行列式的每一项：
$
(-1)^tau(i_1i_2 dots.c i_n)a_(1,i_1)a_(2,i_2) dots.c a_(n,i_n)
$
其中 $a_(1,i_1) in {-2,2}$，故 $2 | a_(1,i_1)$．
对于 $k>1$，有 $a_(k,i_k) in {-4,0,4}$，故 $4 | a_(k,i_k)$．
可得每一项都是 $2 dot 4^(n-1) = 2^(2n-1)$ 的倍数，故 $2^(2n-1)$ 整除 $|bold(A)|$． |
|
https://github.com/kdog3682/mathematical | https://raw.githubusercontent.com/kdog3682/mathematical/main/0.1.0/src/demos/proportion-table.typ | typst | #import "@local/typkit:0.1.0": *
#let proportion-table(a, b, count: auto, headers: none) = {
let get(x, n) = {
if is-number(x) {
return $#{x * n}$
} else {
let (c, d) = x.split("/").map(int)
return [$#{n * c}/#d$]
}
}
let callback(n) = {
return (get(a, n), get(b, n))
}
if count == auto {
count = int(if is-str-frac(a) { a.at(0) } else { b.at(0) })
count = if is-str-frac(a) {
a.split("/").map(int).at(1)
} else {
b.split("/").map(int).at(1)
}
assert(is-number(count), message: "count is required")
}
let items = range(1, count + 1).map(callback)
if headers == none {
headers = ()
} else {
// HELPME: how to do table.headers?
// headers = headers.map((x) => table.header(HELPME))
}
x-table(..headers, ..items, dir: "H")
}
// #svg-test(
// proportion-table("1/8", 9),
// proportion-table("1/8", "1/5"),
// proportion-table(6, "1/5"),
// )
|
|
https://github.com/Myriad-Dreamin/typst.ts | https://raw.githubusercontent.com/Myriad-Dreamin/typst.ts/main/packages/typst.node/npm/linux-arm64-gnu/README.md | markdown | Apache License 2.0 | # `@myriaddreamin/typst-ts-node-compiler-linux-arm64-gnu`
This is the **aarch64-unknown-linux-gnu** binary for `@myriaddreamin/typst-ts-node-compiler`
|
https://github.com/typst/packages | https://raw.githubusercontent.com/typst/packages/main/packages/preview/quill/0.2.0/src/decorations.typ | typst | Apache License 2.0 | #import "gates.typ": *
// align: "left" (for rstick) or "right" (for lstick)
// brace: auto, none, "{", "}", "|", "[", ...
#let lrstick(content, n, align, brace, label) = gate(
content,
draw-function: draw-functions.draw-lrstick.with(align: align),
size-hint: layout.lrstick-size-hint,
box: false,
floating: true,
multi: if n == 1 { none } else {
(
target: none,
num-qubits: n,
wire-count: 0,
label: label,
size-all-wires: if n > 1 { none } else { false }
)},
data: (
brace: brace,
align: align,
),
label: label
)
/// Basic command for labelling a wire at the start.
/// - content (content): Label to display, e.g., `$|0〉$`.
/// - n (content): How many wires the `lstick` should span.
/// - brace (auto, none, string): If `brace` is `auto`, then a default `{` brace
/// is shown only if `n > 1`. A brace is always shown when
/// explicitly given, e.g., `"}"`, `"["` or `"|"`. No brace is shown for
/// `brace: none`
/// - label (array, string, content, dictionary): One or more labels to add to the gate.
/// See @@gate(). .
#let lstick(content, n: 1, brace: auto, label: none) = lrstick(content, n, "right", brace, label)
/// Basic command for labelling a wire at the end.
/// - content (content): Label to display, e.g., `$|0〉$`.
/// - n (content): How many wires the `rstick` should span.
/// - brace (auto, none, string): If `brace` is `auto`, then a default `}` brace
/// is shown only if `n > 1`. A brace is always shown when
/// explicitly given, e.g., `"}"`, `"["` or `"|"`. No brace is shown for
/// `brace: none`.
/// - label (array, string, content, dictionary): One or more labels to add to the gate.
/// See @@gate().
#let rstick(content, n: 1, brace: auto, label: none) = lrstick(content, n, "left", brace, label)
/// Create a midstick, i.e., a mid-circuit text.
/// - content (content): Label to display, e.g., `$|0〉$`.
/// - label (array, string, content, dictionary): One or more labels to add to the gate.
#let midstick(content, label: none) = gate(content, draw-function: draw-functions.draw-unboxed-gate, label: label)
/// Creates a symbol similar to `\qwbundle` on `quantikz`. Annotates a wire to
/// be a bundle of quantum or classical wires.
/// - label (integer, content):
#let nwire(label) = gate([#label], draw-function: draw-functions.draw-nwire, box: false)
/// Set current wire mode (0: none, 1 wire: quantum, 2 wires: classical, more
/// are possible) and optionally the stroke style.
///
/// The wire style is reset for each row.
///
/// - wire-count (integer): Number of wires to display.
/// - stroke (none, stroke): When given, the stroke is applied to the wire.
/// Otherwise the current stroke is kept.
/// - wire-distance (length): Distance between wires.
#let setwire(wire-count, stroke: none, wire-distance: 1pt) = (
qc-instr: "setwire",
wire-count: wire-count,
stroke: stroke,
wire-distance: wire-distance
)
/// Highlight a group of circuit elements by drawing a rectangular box around
/// them.
///
/// - wires (integer): Number of wires to include.
/// - steps (integer): Number of columns to include.
/// - padding (length, dictionary): Padding of rectangle. May be one length
/// for all sides or a dictionary with the keys `left`, `right`, `top`,
/// `bottom` and `default`. Not all keys need to be specified. The value
/// for `default` is used for the omitted sides or `0pt` if no `default`
/// is given.
/// - stroke (stroke): Stroke for rectangle.
/// - fill (color): Fill color for rectangle.
/// - radius (length, dictionary): Corner radius for rectangle.
/// - label (array, string, content, dictionary): One or more labels to add to the
/// group. See @@gate().
#let gategroup(
wires,
steps,
padding: 0pt,
stroke: .7pt,
fill: none,
radius: 0pt,
label: none
) = (
qc-instr: "gategroup",
wires: wires,
steps: steps,
padding: process-args.process-padding-arg(padding),
style: (fill: fill, stroke: stroke, radius: radius),
labels: process-args.process-label-arg(label, default-pos: top)
)
/// Slice the circuit vertically, showing a separation line between columns.
///
/// - n (integer): Number of wires to slice.
/// - stroke (stroke): Line style for the slice.
/// - label (array, string, content, dictionary): One or more labels to add to the
/// slice. See @@gate().
#let slice(
n: 0,
stroke: (paint: red, thickness: .7pt, dash: "dashed"),
label: none
) = (
qc-instr: "slice",
wires: n,
style: (stroke: stroke),
labels: process-args.process-label-arg(label, default-pos: top)
)
/// Lower-level interface to the cell coordinates to create an arbitrary
/// annotatation by passing a custom function.
///
/// This function is passed the coordinates of the specified cell rows
/// and columns.
///
/// - columns (integer, array): Column indices for which to obtain coordinates.
/// - rows (integer, array): Row indices for which to obtain coordinates.
/// - callback (function): Function to call with the obtained coordinates. The
/// signature should be with signature `(col-coords, row-coords) => {}`.
/// This function is expected to display the content to draw in absolute
/// coordinates within the circuit.
#let annotate(
columns,
rows,
callback
) = (
qc-instr: "annotate",
rows: rows,
columns: columns,
callback: callback
)
|
https://github.com/jamesrswift/pixel-pipeline | https://raw.githubusercontent.com/jamesrswift/pixel-pipeline/main/src/math/complex.typ | typst | The Unlicense | /// Returns the real part of a complex number.
/// - V (complex): A complex number.
/// -> float
#let re(V) = V.at(0)
/// Returns the imaginary part of a complex number.
/// - V (complex): A complex number.
/// -> float
#let im(V) = V.at(1)
/// Multiplies two complex numbers together and returns the result $V W$.
/// - V (complex): The complex number on the left hand side.
/// - W (complex): The complex number on the right hand side.
#let mul(V, W) = (re(V) * re(W) - im(V) * im(W), im(V) * re(W) + re(V) * im(W))
/// Calculates the conjugate of a complex number.
/// - V (complex): A complex number.
/// -> complex
#let conj(V) = (re(V),-im(V))
// TODO: check what "in R^2" means.
/// Calculates the dot product of two complex numbers in R^2 $V \cdot W$.
/// - V (complex): The complex number on the left hand side.
/// - W (complex): The complex number on the right hand side.
/// -> float
#let dot(V,W) = re(mul(V,conj(W)))
/// Calculates the squared normal of a complex number.
/// - V (complex): The complex number.
/// -> float
#let normsq(V) = dot(V,V)
/// Calculates the normal of a complex number
/// - V (complex): The complex number.
/// -> float
#let norm(V) = calc.sqrt(normsq(V))
/// Multiplies a complex number by a scale factor.
/// - V (complex): The complex number to scale.
/// - t (float): The scale factor.
/// -> complex
#let scale(V,t) = mul(V,(t,0))
/// Returns a unit vector in the direction of a complex number.
/// - V (complex): The complex number.
/// -> vector
#let unit(V) = scale(V, 1/norm(V))
/// Inverts a complex number.
/// - V (complex): The complex number
/// -> complex
#let inv(V) = scale(conj(V), 1/normsq(V))
/// Divides two complex numbers.
/// - V (complex): The complex number of the numerator.
/// - W (complex): The complex number of the denominator.
/// -> complex
#let div(V,W) = mul(V,inv(W))
/// Adds two complex numbers together.
/// - V (complex): The complex number on the left hand side.
/// - W (complex): The complex number on the right hand side.
/// -> complex
#let add(V,W) = (re(V) + re(W),im(V) + im(W))
/// Subtracts two complex numbers together.
/// - V (complex): The complex number on the left hand side.
/// - W (complex): The complex number on the right hand side.
/// -> complex
#let sub(V,W) = (re(V) - re(W),im(V) - im(W))
/// Calculates the argument of a complex number.
/// - V (complex): The complex number.
#let arg(V) = calc.atan2(..V) / 1rad
/// Get the signed angle of two complex numbers from V to W.
/// - V (complex): A complex number.
/// - W (complex): A complex number.
#let ang(V,W) = arg(div(W,V))
// exp(i*a)
#let expi(a) = (calc.cos(a),calc.sin(a))
// Rotate by angle a
#let rot(v,a) = mul(v,expi(a)) |
https://github.com/dismint/docmint | https://raw.githubusercontent.com/dismint/docmint/main/biology/lec8.typ | typst | #import "template.typ": *
#show: template.with(
title: "Lecture 8",
subtitle: "7.016"
)
= Repair Mechanisms
Deamination of 5-methylcytosine leads to a replication error because now it has the properties of thymine, meaning it will be incorrectly paired with guanine. Thus when this bad half becomes a template for replication, it will result in an incorrect duplication of the original DNA.
DNA glycosylase works to automatically solve this problem by getting rid of the "thymine", after which the endonuclease severs the backbone allowing for the repair.
Sometimes thymine dimers can be formed when they covalently bond with each other (by UV light).
If both sides are damaged, you need to use the homologous chromosome in a homologous repair - this happens from intense procedures such as x-rays or other forms of radiation.
= RNA Polymerase
RNA polymerase synthesizes RNA from a DNA template. Notably, it does *not* require a primer.
General transcription factors load RNA polymerase near the transcription start site. These are loaded by the TATA box upstream of the starting location. There are also enhancers upstream that allow tissue-specific expression in a modular way.
|
|
https://github.com/typst/packages | https://raw.githubusercontent.com/typst/packages/main/packages/preview/gentle-clues/0.7.0/README.md | markdown | Apache License 2.0 | # gentle-clues
Simple admonitions for typst. Add predefined or define your own.
Inspired from [mdbook-admonish](https://tommilligan.github.io/mdbook-admonish/).
## Usage
Import the package
```typst
#import "@preview/gentle-clues:0.7.0": *
```
if needed you can change the default settings.
[See the docs.pdf for all options](https://github.com/jomaway/typst-admonish/blob/main/docs.pdf)
### Use predefined clues
```typst
// info clue
#info[ This is the info clue ... ]
// or a tip
#tip(title: "Best tip ever")[Check out this cool package]
```
Overview of the predefined clues:
`abstract`, `info`, `question`, `memo`, `task`, `idea`, `tip`, `quote`, `success`, `warning`, `error`, `example`.
#### Language support
This package does use [linguify](https://github.com/jomaway/typst-linguify) to support multiple languages.
**Header titles:**
The language of the header titles is detected automatically from the `context text.lang`.
Currently the following languages are supported: "en", "de", "es", "fr".
If an unsupported language is set it will fallback to english as default.
Feel free to open a PR with your language added to the `lang.toml` file.
### Define your own clue
But it is very easy to define your own.
```typst
// Define a clue called ghost
#let ghost(title: "Buuuuuuh", icon: emoji.ghost , ..args) = clue(
accent-color: purple,
title: title,
icon: icon,
..args
)
// Use it
#ghost[Huuuuuuh.]
```
The icon can be an `emoji`, `symbol` or `.svg`-file.
## License
[MIT License](LICENSE)
## Changelog
[See CHANGELOG.md](CHANGELOG.md)
|
https://github.com/kotfind/hse-se-2-notes | https://raw.githubusercontent.com/kotfind/hse-se-2-notes/master/android/lectures/2024-09-14.typ | typst | = Введение
Сайт: `https://makse.site/GA/`
Препод: <NAME>
Экзамен --- 7 более сложный задач
Способы разработки под Андроид:
- Нативный (мы)
- Гибридный
- Веб приложение
Дедлайн --- конец третьего модуля (до "экзамена")
Сдача заданий в Zoom-е
Первая пара --- лекция
Вторая пара --- сдача заданий
За четкое следование методичке ставится 8. 10 ставится за дополнительные фичи.
|
|
https://github.com/Enter-tainer/typstyle | https://raw.githubusercontent.com/Enter-tainer/typstyle/master/tests/assets/book.typ | typst | Apache License 2.0 |
// #import "@preview/book:0.2.2": *
#show: book
#book-meta(
title: "typst-book",
description: "typst-book Documentation",
repository: "https://github.com/Myriad-Dreamin/typst-book",
repository-edit: "https://github.com/Myriad-Dreamin/typst-book/edit/main/github-pages/docs/{path}",
authors: ("Myriad-Dreamin", "7mile"),
language: "en",
summary: [ // begin of summary
#prefix-chapter("introduction.typ")[Introduction]
= User Guide
- #chapter("guide/installation.typ", section: "1")[Installation]
- #chapter("guide/get-started.typ", section: "2")[Get Started]
- #chapter("guide/faq.typ", section: "3")[Frequently Asked Questions]
- #chapter(none, section: "4")[Further reading]
= Reference Guide
- #chapter("cli/main.typ", section: "5")[Command Line Tool]
- #chapter("cli/init.typ", section: "5.1")[init]
- #chapter("cli/build.typ", section: "5.2")[build]
- #chapter("cli/serve.typ", section: "5.3")[serve]
- #chapter("cli/clean.typ", section: "5.4")[clean]
- #chapter("cli/completions.typ", section: "5.5")[completions]
- #chapter("format/main.typ", section: "6")[Format]
- #chapter("format/book.typ", section: "6.1")[book.typ]
- #chapter("format/book-meta.typ", section: "6.1.1")[Book Metadata]
- #chapter(none, section: "6.1.1.1")[Draft chapter]
// - #chapter(none, section: "6.1.1.2")[chapter with - markers]
// - #chapter(none, "= Introduction", section: "6.1.1.2")
// - #chapter(none, section: "6.1.1.2")[#text("= Introduction")]
- #chapter("format/build-meta.typ", section: "6.1.2")[Build Metadata]
- #chapter("format/theme.typ", section: "6.2")[Theme]
- #chapter(none, section: "6.3")[Typst Support]
- #chapter(none, section: "7")[For developers]
- #chapter(none, section: "7.1")[Typst-side APIs]
- #chapter(none, section: "7.2")[typst-book CLI Internals]
- #chapter(none, section: "7.3")[Alternative Backends]
// end of summary
]
)
#build-meta(
dest-dir: "../dist",
)
#get-book-meta()
// re-export page template
#import "/contrib/typst/gh-pages.typ": project
#let book-page = project
|
https://github.com/7sDream/fonts-and-layout-zhCN | https://raw.githubusercontent.com/7sDream/fonts-and-layout-zhCN/master/template/util.typ | typst | Other | #import "@preview/book:0.2.5": target
#let is-pdf-target = () => "realpdf" in sys.inputs
#let is-web-target = () => not is-pdf-target()
#let __build-selector(elem, start, end) = {
let select = selector(elem)
if start != none {
select = select.after(start, inclusive: false)
}
if end != none {
select = select.before(end, inclusive: false)
}
return select
}
#let query-first(elem, start, end, kind: none) = {
let items = query(
__build-selector(elem, start, end),
start,
)
if elem != metadata or kind == none {
return items.at(0, default: none)
}
for meta in items {
let data = meta.value
if data.kind == kind {
return data
}
}
return none
}
#let query-last(elem, start, end, kind: none) = {
let items = query(
__build-selector(elem, start, end),
end,
)
if elem != metadata or kind == none {
return if items.len() > 0 { items.last() } else { none }
}
while items.len() > 0 {
let data = items.pop().value
if data.kind == kind {
return data
}
}
return none
}
#let to-string-zero-padding(num, length, base: 10) = {
assert(type(num) == int)
let s = str(num, base: base)
let count = length - s.len()
if count > 0 {
s = "0" * count + s
}
return s
}
|
https://github.com/jneug/typst-ccicons | https://raw.githubusercontent.com/jneug/typst-ccicons/main/src/ccicons.typ | typst | MIT License | #import "utils.typ": ccicon, cc-url, cc-is-valid, _cc-colorize
// Logos
#let ccLogo = ccicon("logo")
#let cc = ccicon("cc")
// Icons
#let ccAttribution = ccicon("by")
#let ccShareAlike = ccicon("sa")
#let ccNoDerivatives = ccicon("nd")
#let ccNonCommercial = ccicon("nc")
#let ccNonCommercialEU = ccicon("nceu")
#let ccNonCommercialJP = ccicon("ncjp")
#let ccZero = ccicon("zero")
#let ccPublicDomain = ccicon("pd")
#let ccSampling = ccicon("sampling")
#let ccSamplingPlus = ccicon("sampling.plus")
#let ccRemix = ccicon("remix")
#let ccShare = ccicon("share")
#let cc-by = ccicon("cc-by")
#let cc-by-sa = ccicon("cc-by-sa")
#let cc-by-nd = ccicon("cc-by-nd")
#let cc-by-nc = ccicon("cc-by-nc")
#let cc-by-nc-sa = ccicon("cc-by-nc-sa")
#let cc-by-nc-sa-eu = ccicon("cc-by-nceu-sa")
#let cc-by-nc-sa-jp = ccicon("cc-by-ncjp-sa")
#let cc-by-nc-nd = ccicon("cc-by-nc-nd")
#let cc-by-nc-nd-eu = ccicon("cc-by-nceu-nd")
#let cc-by-nc-nd-jp = ccicon("cc-by-ncjp-nd")
#let cc-zero = ccicon("zero")
#let cc-pd = ccicon("pd")
// Badges
#let cc-by-badge = ccicon("by", format: "badge")
#let cc-by-sa-badge = ccicon("cc-by-sa", format: "badge")
#let cc-by-nd-badge = ccicon("cc-by-nd", format: "badge")
#let cc-by-nc-badge = ccicon("cc-by-nc", format: "badge")
#let cc-by-nc-sa-badge = ccicon("cc-by-nc-sa", format: "badge")
#let cc-by-nc-nd-badge = ccicon("cc-by-nc-nd", format: "badge")
#let cc-zero-badge = ccicon("zero", format: "badge")
#let cc-pd-badge = ccicon("pd", format: "badge")
// Shields
#let cc-by-shield = ccicon("by", format: "shield")
#let cc-by-sa-shield = ccicon("cc-by-sa", format: "shield")
#let cc-by-nd-shield = ccicon("cc-by-nd", format: "shield")
#let cc-by-nc-shield = ccicon("cc-by-nc", format: "shield")
#let cc-by-nc-sa-shield = ccicon("cc-by-nc-sa", format: "shield")
#let cc-by-nc-nd-shield = ccicon("cc-by-nc-nd", format: "shield")
#let cc-zero-shield = ccicon("zero", format: "shield")
#let cc-pd-shield = ccicon("pd", format: "shield")
|
https://github.com/0xPARC/0xparc-intro-book | https://raw.githubusercontent.com/0xPARC/0xparc-intro-book/main/summer-notes-evan/src/0813-evan-talk.typ | typst | #import "@local/evan:1.0.0":*
= Evan's talk (delivered August 19)
== Overview
Brian asked me to give a math-for-engineers talk on why polynomials
keep on reappearing over and over in cryptography.
I'm going to try my best, but this is going to be really a math philosophy talk.
I don't know if I'm able to give _the_ reason why polynomials, because that's above my pay-grade,
so I'm content to try to explain _one_ reason why polynomials appear.
The overall assertion is the following pseudo-theorem.
#proposition[
Whenever you are trying to do linear algebra,
the "best" choice of coefficients are given by polynomials.
]
To try to stake this claim, I'm going to do a dive into one particular protocol,
Shamir secret-sharing.
I'm going to phrase it entirely in terms of linear algebra at first,
and then show how polynomials arise "organically" as the best fit by several criteria.
== Secret-sharing
Let's say we want to do a $2$-of-$N$ secret sharing scheme,
which means we give each of $N$ people a secret share
such that any two of them can reconstruct the secret, but no single one of them.
The typical way to do this is to let $x$ be a number corresponding to the secret
and $y$ a random "noise" number.
Then
- Send person 1 the value of $x+y$
- Send person 2 the value of $2x+y$
- ...
- Send person $N$ the value of $N x+ y$.
Then each individual person has no information,
but any two can solve a two-variable system of equations to extract $x$.
For example, if person $8$ is told that $8x + y = 12245$
while person $9$ is told that $9x + y = 13112$,
then each of them alone doesn't know anything about $x$,
but together they can solve to get $(x,y) = (867, 5309)$.
What if you want to do $3$-of-$N$?
If you want to keep buying the linear algebra idea,
then the general principle is that we want to choose some functions $f$, $g$, $h$ such that
- Send person 1 the value of $f(1) x + g(1) y + h(1) z$
- Send person 2 the value of $f(2) x + g(2) y + h(2) z$
- ...
- Send person $N$ the value of $f(N) x + g(N) y + h(N) z$.
In the two-variable example, we just used $f(n) = n$ and $g(n) = 1$.
For three functions, what would we pick?
Well, let's first make a wish-list of properties that we would want to satisfy:
1. For every three indices $1 <= a < b < c <= N$, we want there to be a unique $(x,y,z)$
solution to the linear algebra task
$
f(a) x + g(a) y + h(a) z &= 0 \
f(b) x + g(b) y + h(b) z &= 0 \
f(c) x + g(c) y + h(c) z &= 0.
$
This is equivalent to
$ det M_(a,b,c) != 0 " where "
M_(a,b,c) = mat(f(a), g(a), h(a); f(b), g(b), h(b); f(c), g(c), h(c)). $
2. Ideally, for practical reasons, we'd like $f$, $g$, $h$ to not grow too quickly
and be pretty easy to calculate.
3. Ideally, for practical reasons, we'd like inverting $M_(a,b,c)^(-1)$ to be
easy to implement.
That is, actually solving the system shouldn't be too expensive.
Now, the thing I want to communicate is that the first property is "easy" to satisfy,
in the sense that I pull random numbers out of a hat,
the chance that the determinant happens to be zero is vanishingly small.
The issue with random garbage is that the second and third properties become harder to check,
and anyway we want a deterministic promise that $det M_(a,b,c) != 0$, not just a "probably".
== Vandermonde determinant
Up until now I've made no mention of polynomials yet, and that's on purpose,
because my thesis is that even in pure linear-algebra contexts
there are good reasons to want polynomials.
Now we'll bring them in.
If you know how Shamir's secret-sharing works already, you know what the functions
$f$, $g$, $h$ should be: it uses $f(n) = n^2$, $g(n) = n$, $h(n) = 1$.
To convince you there is something special about this choice,
let me show you a magic trick, which is how you can calculate the determinant
$ det mat(a^2, a, 1; b^2, b, 1; c^2, c, 1) $
completely in your head.
The idea is that this determinant has got to vanish when $a=b$,
because then the first two rows of the matrix will coincide.
Therefore, the determinant is a multiple of $a-b$.
For the same reason, it must be a multiple of $a-c$ and $b-c$.
In other words, the determinant should be a multiple of $(a-b)(a-c)(b-c)$.
However, the determinant is also a polynomial of degree $2+1+0=3$.
So there's no more "room" left for any additional factors!
In other words, the determinant _has_ to be equal to
$lambda (a-b)(a-c)(b-c)$ for some constant $lambda$.
And so all you need to is look at any particular monomial to determine $lambda$;
for example, if you look at the determinant you can see a $+a^2b$ on the diagonal,
which isn't cancelled out by anything else,
while $(a-b)(a-c)(b-c)$ also has an $+a^2b$ term, ergo $lambda = 1$.
In summary, we have the following result:
#theorem[Vandermonde determinant][
We have
$
det M_(a,b,c) = det mat(a^2, a, 1; b^2, b, 1; c^2, c, 1)
= (a-b)(a-c)(b-c)
$
The obvious generalization to more than three variables (with the same proof)
is also valid, e.g.
$
det mat(
a^3, a^2, a, 1;
b^3, b^2, b, 1;
c^3, c^2, c, 1;
d^3, d^2, d, 1
)
= (a-b)(a-c)(a-d)(b-c)(b-d)(c-d).
$
]
This theorem provides an affirmative answer to the first criteria,
and gives a reason to believe this is "pretty good" for the second criteria.
The point is that $M_(a,b,c)$ is _always_ going to equal zero if any of the variables are equal.
That means we expect $det M_(a,b,c)$ will always at least have to be "divisible" by
$(a-b)(a-c)(b-c)$, depending on what you mean by "divisible".
The fact that the Vandermonde determinant has no additional "garbage" factors means,
philosophically, we can't compress the sizes of $f$, $g$, $h$ in a meaningful further way.
== Lagrange interpolation
What about the last criteria --- actually solving the system quickly?
Let's specialize again to three-variables,
and in fact let's specialize to $a=2$, $b=3$, $c=5$ so we have fewer symbols.
That means we'd like to rapidly solve equations of the form
$
4x + 2y + z &= lambda_2 \
9x + 3y + z &= lambda_3 \
25x + 5y + z &= lambda_5.
$
=== The case where just one $lambda_*$ is zero
Linear algebra means that it suffices to do the case where all but
one of the $lambda_*$'s is zero.
Let's try $lambda_2 = 1$, $lambda_3 = lambda_5 = 0$, that is:
$
4x + 2y + z &= 1 \
9x + 3y + z &= 0 \
25x + 5y + z &= 0.
$
I'm going to show you yet another magic trick:
how you can solve for $(x,y,z)$ in your head, too.
The idea is to consider the polynomial whose roots are $3$ and $5$, namely
$ P(n) = (n-3)(n-5) = n^2 - 8 n + 15. $
Now the trick is that this polynomial has $P(3) = P(5) = 0$ by definition,
and so $(x,y,z) = (1, -8, 15)$ will actually satisfy the second two equations! Indeed,
$
9(1) + 3(-8) + (15) &= 0 \
25(1) + 5(-8) + (15) &= 0.
$
But it doesn't satisfy the first equation, because $P(2) = (2-3)(2-5) = 3$ instead of $1$.
But that's no problem, because you can just scale by a factor of $3$:
so the answer is
$ (x,y,z) = (1/3, (-8)/3, 15/3). $
So in fact, solving the system of equations when all but one $lambda$ is zero
is really equivalent to just expanding the polynomial whose roots are the other $n-1$ numbers,
and then adding a scaling factor to get the last equation right.
And then solving a general system can be done by adding them all together.
=== A full general example
Let's put some flesh on this example by doing it fully explicitly for some numbers.
$
4x + 2y + z &= 42 \
9x + 3y + z &= 1337 \
25x + 5y + z &= 2024.
$
We first solve the three "basic" systems using the procedure we described earlier
$
cases(
4x + 2y + z = 1,
9x + 3y + z = 0,
25x + 5y + z = 0,
reverse: #true
) &=> arrow(v_2) = (1/3, (-8)/3, 15/3) " since " (n-3)(n-5) = n^2-8n+15 \
cases(
4x + 2y + z = 0,
9x + 3y + z = 1,
25x + 5y + z = 0,
reverse: #true
) &=> arrow(v_3) = (1/(-2), (-7)/(-2), 10/(-2)) " since " (n-2)(n-5) = n^2-7n+10 \
cases(
4x + 2y + z = 0,
9x + 3y + z = 0,
25x + 5y + z = 1,
reverse: #true
) &=> arrow(v_5) = (1/6, (-5)/6, 6/6) " since " (n-2)(n-3) = n^2-5n+6 \
$
Again, to reiterate,
the numerators are the coefficients you get when you expand a quadratic polynomial,
and the denominator is the scaling factor you throw in to make sure the last equation
comes out to $1$ (by plugging in the final input into the polyonmial).
Then the answer to the general system will just be
$
& 42 arrow(v_2)
+ 1337 arrow(v_3)
+ 2024 arrow(v_5) \
&=
(
42/3 + 1337/(-2) + 2024/6,
(42 dot -8)/3 + (1337 dot -7)/(-2) + (2024 dot -5)/6,
(42 dot 15)/3 + (1337 dot 10)/(-2) + (2024 dot 6)/6
) \
&=
(-1903/6, 17285/6, -4451).
$
This process, which works equally well in any number of variables,
is known in mathematics as
#link("https://en.wikipedia.org/wiki/Lagrange_polynomial")[Lagrange interpolation].
== Afterthought: random challenges
You might remember the following fundamental theorem about polynomials:
#theorem[
A polynomial of degree $n$ has at most $n$ roots.
]
Fun fact: this theorem is secretly a _linear algebra_ fact, too.
In fact, we've basically already proven this, and I'll just point it out.
Suppose $P(T) = x T^2 + y T + z$ is a quadratic polynomial,
and $P$ has three roots $P(2) = P(3) = P(5) = 0$.
The claim is that $P$ must then be the zero polynomial.
If you actually plug in the numbers, this just saying
$ 4x+2y+z = 9x+3y+z = 25x+5y+z = 0 $
has only the solution $(x,y,z) = (0,0,0)$,
which is what we showed earlier by calculating the determinant $M_(2,3,5) = (2-3)(2-5)(3-5) != 0$.
As a consequence, we get the following corollary.
#corollary[
Whenever $P$ and $Q$ are two _different_ polynomials of degree at most $d$,
then there will be at most $d$ points at which they give different outputs,
because $P-Q$ is a nonzero polynomial of degree at most $d$, and hence has at most $d$ roots.
]
This key fact is used in a lot of cryptographic protocols,
where whenever a prover wants to show two polynomials $P$ and $Q$ are equal to each other,
it's enough for them to receive a random challenge $lambda$ and show $P(lambda) = Q(lambda)$.
This works because if $P != Q$, a cheating prover would be exposed unless the verifier
was so unlucky they picked one of the $d$ roots of $P-Q$.
As long as the verifier has a lot of numbers to pick from (often $2^256$), this is vanishingly small.
And so the same linear algebra idea that let us do
Lagrange interpolation is also quietly pulling the strings
behind all the "random-challenge" protocols that show up ubiquitously.
|
|
https://github.com/thuvasooriya/thuvasooriya | https://raw.githubusercontent.com/thuvasooriya/thuvasooriya/main/cv-readme.md | markdown | # setup guide to use the cv template
if you have just command runner and typst cli installed all you have to do is,
```bash
just cv
```
|
|
https://github.com/1216892614/learn-category | https://raw.githubusercontent.com/1216892614/learn-category/main/lib.typ | typst | #import "@preview/commute:0.2.0": node, arr, commutative-diagram
#import "@preview/bob-draw:0.1.0": render
// The project function defines how your document looks.
// It takes your content and some metadata and formats it.
// Go ahead and customize it to your liking!
#let project(
title: "",
authors: (),
date: none,
logo: none,
body,
) = {
// Set the document's basic properties.
set document(author: authors.map(a => a.name), title: title)
set page(
margin: (left: 25mm, right: 25mm, top: 25mm, bottom: 20mm),
numbering: "1",
number-align: start,
)
// Save heading and body font families in variables.
let body-font = "Sarasa Mono SC"
let sans-font = "更紗黑體 CL"
// Set body font family.
set text(font: body-font, lang: "zh")
show heading: set text(font: sans-font)
set heading(numbering: "1.1")
// Set run-in subheadings, starting at level 3.
show heading: it => {
if it.level > 2 {
parbreak()
text(11pt, style: "italic", weight: "regular", it.body + ".")
} else {
it
}
}
show raw: it => {
set text(font: ("Fira Code", "等距更紗黑體 Slab CL"))
stack(dir: ttb, ..it.lines)
}
show raw.line: it => {
box(
width: 100%,
height: 1.75em,
inset: 0.25em,
fill: rgb(0 ,0 ,0, 10),
align(horizon, stack(
dir: ltr,
box(width: 15pt)[#it.number],
it.body,
))
)
}
// Title page.
// The page can contain a logo if you pass one with `logo: "logo.png"`.
v(0.6fr)
if logo != none {
align(right, image(logo, width: 26%))
}
v(9.6fr)
text(1.1em, date)
v(1.2em, weak: true)
text(font: sans-font, 2em, weight: 700, title)
// Author information.
pad(
top: 0.7em,
right: 20%,
grid(
columns: (1fr,) * calc.min(3, authors.len()),
gutter: 1em,
..authors.map(author => align(start)[
*#author.name* \
#author.email
]),
),
)
v(2.4fr)
pagebreak()
// Table of contents.
outline(depth: 3, indent: true)
pagebreak()
// Main body.
set par(justify: true)
body
}
|
|
https://github.com/Krsnik/typst-nix | https://raw.githubusercontent.com/Krsnik/typst-nix/main/templates/example/src/example2/main.typ | typst | #import "@example/test1:0.1.0": test as test1
#import "@example/test2:0.1.0": test as test2
#import "@preview/polylux:0.3.1": *
#test1
#test2
#polylux-slide[
#align(horizon + center)[
= Very minimalist slides
A lazy author
July 23, 2023
]
]
|
|
https://github.com/drupol/master-thesis | https://raw.githubusercontent.com/drupol/master-thesis/main/src/thesis/theme/abstract.typ | typst | Other | #import "common/metadata.typ": *
#let abstract(title: "Abstract", body) = {
pagebreak(weak: true)
heading(level: 1, title, outlined: false)
body
}
|
https://github.com/Yzx7/public_study_files | https://raw.githubusercontent.com/Yzx7/public_study_files/main/Monografía FIEE/readme.md | markdown | Plantilla para crear monografías estilo cybertesis.unmsm.edu.pe, hecha en typst
<img src="https://raw.githubusercontent.com/Yzx7/public_study_files/refs/heads/main/Monograf%C3%ADa%20FIEE/Captura%20de%20pantalla%202024-09-28%20220009.png" alt="preview" />
|
|
https://github.com/AsiSkarp/grotesk-cv | https://raw.githubusercontent.com/AsiSkarp/grotesk-cv/main/src/template/cv.typ | typst | The Unlicense | #let metadata = toml("info.toml")
#import metadata.import.path: cv
#let photo = image("./img/" + metadata.personal.profile_image)
#let import-sections(
sections,
) = {
for section in sections {
include {
"content/" + section + ".typ"
}
}
}
#let left-pane = (
"profile",
"experience",
"education",
)
#let right-pane = (
"skills",
"languages",
"other_experience",
"references",
)
#show: cv.with(
metadata,
photo: photo,
use-photo: true,
left-pane: import-sections(left-pane),
right-pane: import-sections(right-pane),
left-pane-proportion: eval(metadata.layout.left_pane_width),
)
|
https://github.com/elenev/elenev.github.io | https://raw.githubusercontent.com/elenev/elenev.github.io/main/cv/main.typ | typst | #let cvdata = yaml("cv.yml")
#let personal = cvdata.identity
#set page(
"us-letter",
margin: (left: 1in, right: 1in, top: 1in, bottom: 1in),
header: context
if here().page() == 1 {
} else {
grid(
columns: (2fr, 2fr),
rows: auto,
align: (left, right),
[#personal.name],
[#counter(page).display("1",both: false)]
)
}
)
#set text(font: "EB Garamond", size: 11pt)
#show link: underline
#show heading.where(
level: 1
): it => [
#set align(center)
#set text(26pt, weight: "semibold")
#block(smallcaps(it.body))
]
#show heading.where(
level: 2
): it => [
#set text(11pt, weight: "regular")
#block(smallcaps(it.body))
]
#let toplevel_block(header, contents) = {
block(
grid(
columns: (16%, 1fr),
gutter: 12pt,
[== #header],
[#contents]
),
spacing: 20pt
)
}
#let jobtitle(title) = [- #title]
#let nonblank(dict, field) = {
field in dict.keys() and dict.at(field) != ""
}
#let employer_block(institution, location, positions) = {
grid(
columns: (60%, 1fr),
rows: auto,
gutter: 6pt,
align: (left, right),
[#institution],
[#location],
..for (title, dates) in positions {
(jobtitle(title), dates)
}
)
}
#let my_paper(d) = {
block([
*#d.title* \
#d.coauthors
#if nonblank(d,"journal") [
\
_#d.journal _
#if nonblank(d,"biblio") [
, #d.biblio
]
]
])
}
#let remove_repeated_dates(entries, datefield: "year") = {
let sort_by(x) = x.at(datefield)
entries = entries.sorted(key: sort_by).rev()
let current_year = 0
for (i,entry) in entries.enumerate() {
if entry.at(datefield) == current_year {
// do not print the year
entries.at(i).at(datefield) = ""
}
current_year = entry.at(datefield)
}
entries
}
#let grant_text(grant) = [
#grant.name
#if "amount" in grant.keys() and grant.amount != "" [ (#grant.amount)]
#if "corecipients" in grant.keys() and grant.corecipients != "" [
\
#h(1em) with #grant.corecipients
]
\
]
#let grants_block(grants) = {
grid(
columns: (80%, 1fr),
rows: auto,
gutter: 6pt,
align: (left, right),
..for (..other, year) in grants {
(grant_text(other), year)
}
)
}
#let teaching_block(d) = {
[
#grid(
columns: (80%, 1fr),
rows: auto,
gutter: 6pt,
align: (left, right),
[#d.institution],
[#d.dates],
..for (title, role, level) in d.courses {
([ - #title (*#role*, #level)], "")
}
)
]
}
#let presentations_block(paper_title, presentations) = block[
*#paper_title*
#grid(
columns: (70%, 15%, 1fr),
rows: auto,
gutter: 6pt,
align: (left, left, right),
..for p in presentations {
let descr = ""
if nonblank(p,"coauthor") {descr = descr + "*"}
descr = descr + p.venue + ", " + p.location
(descr, p.type, p.date)
}
)
]
#let unbreaking(..args) = args.pos().map(grid.cell.with(breakable: false))
#let discussions_block(discussions) = {
set grid.cell(breakable: false)
grid(
columns: (80%, 1fr),
rows: auto,
gutter: 10pt,
align: (left, right),
..for d in discussions {
let dstr = [#d.title, by #d.authors\
_#d.venue, #d.location _]
(dstr, d.date)
}
)
}
#let service_block(type, entries) = block[
#type \
_#entries.join("; ")_
]
#let advising_block(header, advisees) = [
*#header*:
#grid(
columns: (85%, 1fr),
rows: auto,
gutter: 10pt,
align: (left, right),
..for a in advisees {
let astr = [
#a.name, "#a.title" \
#h(1em) Placement: #a.placement.role, #a.placement.institution, #a.placement.location
]
(astr, a.date)
}
)
]
#let two_column_block(array_of_dicts, sep: " ") = grid(
columns: (80%, 1fr),
rows: auto,
gutter: 6pt,
align: (left, right),
..for d in array_of_dicts {
let v = d.values()
let date = v.pop()
(v.join(sep), date)
}
)
// Name
= #personal.name
#line(length: 100%)
// Contact Info
#grid(
columns: (60%, 1fr),
[#personal.address.join("\n") \
#personal.phone \
#link("mailto:" + personal.email) ],
align(right)[
#link(personal.website) \
#for (url, network) in personal.profiles [
#link(url)[#network] \
]
]
)
// Academic Positions
#toplevel_block("Academic Positions",
for (institution, location, positions) in cvdata.academic-positions {
employer_block(institution, location, positions)
}
)
#toplevel_block("Education",
for (institution, location, degrees) in cvdata.education {
employer_block(institution, location, degrees)
})
#toplevel_block("Research Interests", [Macro Finance: financial intermediation, monetary policy, real estate])
#toplevel_block("Peer-Reviewed Publications",
for p in cvdata.publications {
my_paper(p)
}
)
#toplevel_block("Working Papers", for p in cvdata.working-papers {
if nonblank(p,"status") {p.journal = p.status}
my_paper(p)
})
#toplevel_block("Works in Progress", for p in cvdata.works-in-progress {
my_paper(p)
})
#toplevel_block("Grants", grants_block(remove_repeated_dates(cvdata.grants))
)
#toplevel_block("Awards, Honors, and Fellowships",
for g in cvdata.awards {
grant_text(g)
}
)
#toplevel_block("Teaching Experience",
for t in cvdata.teaching {
teaching_block(t)
}
)
#toplevel_block("Presentations", [
Including scheduled. Conference presentations by co-authors marked with a \*.
#for p in cvdata.presentations {
presentations_block(p.paper, p.talks)
}
])
#toplevel_block("Conference Discussions",
discussions_block(remove_repeated_dates(cvdata.discussions, datefield: "date"))
)
#toplevel_block("Professional Service",
for s in cvdata.professional-service {
service_block(s.title, s.items)
}
)
#toplevel_block("Doctoral Advising",
for d in cvdata.advising {
advising_block(d.institution,
remove_repeated_dates(d.advisees, datefield: "date"))
}
)
#toplevel_block("University Service",[
#two_column_block(cvdata.university-service)
])
#toplevel_block("Memberships",[
#cvdata.memberships.join(", ")
])
#toplevel_block("Other Employment",[
#two_column_block(cvdata.other-employment, sep: ", ")
])
#toplevel_block("Personal",cvdata.personal.join("\n")) |
|
https://github.com/nathanielknight/tsot | https://raw.githubusercontent.com/nathanielknight/tsot/main/src/utils_playbook.typ | typst | #import("util.typst")
#set text(font: "Fantasque Sans Mono")
#let inset = 9pt
#let text_np = t => text(font: "National Park", t)
#let inline_header = hdr => text(font: "National Park", weight: "bold", hdr)
#let name(nm) = {
block(
above: 0%,
below: 8mm,
smallcaps(text(font: "National Park", size: 8mm, weight: "bold")[#nm])
)
}
#let pitch(body) = {
text(size: 9pt, style: "italic", body)
}
#let nameAndTraits(directives) = {
grid(
columns: (1fr, 3fr),
rows: auto,
inset: inset,
stroke: 0.14mm + black,
grid.cell(rowspan: 2,
[
#inline_header("Directives")
#directives
]
),
inline_header("Name"),
inline_header("Traits"),
)
}
#let moves(prelude: [], encounter: [], struggle: []) = [
#set text(size: 10pt)
#set par(linebreaks: "optimized")
#grid(
columns: (2fr, 2fr, 2fr, 2fr),
rows: auto,
inset: inset,
stroke: 0.14mm + gray,
[],
grid.cell(colspan: 3, inline_header("Moves")),
// Prelude
[
#inline_header("Prelude")
- Choose and make moves until you have none left, or until it makes sense to move to the Encounter Phase.
],
grid.cell(
colspan: 3,
util.checklist(prelude)
),
// Encounter
grid.cell(rowspan: 2)[
#inline_header("Encounter")
- Roll the crew's dice pool, reduced by Tension.
- For negative dice, roll extra and take lowest.
- Each player takes one die and makes a move based on its value.
],
[#util.dicier[1 2 3]],
[#util.dicier[4 5]],
[#util.dicier[6]],
util.checklist(encounter.miss),
util.checklist(encounter.partial),
util.checklist(encounter.hit),
// Struggle
[#inline_header("Struggle")
When rolling Escape or Calamity, fill
- 1 on #util.dicier[1 2 3]
- 2 on #util.dicier[4 5]
- 3 on #util.dicier[6]
- 5 on #util.dicier[6 6]
],
grid.cell(colspan: 3, util.checklist(struggle))
)
]
#let development(milestones) = align(bottom)[
#rect(
width: 100%,
stroke: 0.14mm + black,
inset: 7pt,
)[
When your scene does one of the following, cross it off.
#milestones
When you've crossed off at least three items, you may alter or remove one of your Directives.
]
]
|
|
https://github.com/sitandr/typst-examples-book | https://raw.githubusercontent.com/sitandr/typst-examples-book/main/src/snippets/math/operations.md | markdown | MIT License | # Operations
## Fractions
```typ
$
p/q, p slash q, p\/q
$
```
### Slightly moved:
```typ
#let mfrac(a, b) = move(a, dy: -0.2em) + "/" + move(b, dy: 0.2em, dx: -0.1em)
$A\/B, #mfrac($A$, $B$)$,
```
### Large fractions
```typ
#let dfrac(a, b) = $display(frac(#a, #b))$
$(x + y)/(1/x + 1/y) quad (x + y)/(dfrac(1,x) + dfrac(1, y))$
```
|
https://github.com/tingerrr/chiral-thesis-fhe | https://raw.githubusercontent.com/tingerrr/chiral-thesis-fhe/main/src/lib.typ | typst | #import "prelude.typ"
#import "core.typ"
#import "utils.typ"
|
|
https://github.com/EpicEricEE/typst-plugins | https://raw.githubusercontent.com/EpicEricEE/typst-plugins/master/united/src/number.typ | typst | // Regex pattern for a number with plus/minus uncertainty.
//
// Returns the following captures:
// - 0: The value.
// - 1: The upper error.
// - 2: The lower error.
// - 3: The combined error.
// - 4: The exponent.
#let number-pattern-plusminus = regex({
"^" // Start of string
"([\+-]?\d+\.?\d*)?" // Value (optional)
"(?:" // Uncertainty (start)
"(?:\+(\d+\.?\d*)-(\d+\.?\d*))" // > Upper and lower
"|" // > or
"(?:(?:±|\+-|-\+)(\d+\.?\d*))" // > Combined
")?" // Uncertainty (end) (optional)
"(?:[eE]([-\+]?\d+))?" // Exponent (optional)
"$" // End of string
})
// Regex pattern for a number with last-digits uncertainty.
//
// Returns the following captures:
// - 0: The value.
// - 1: The uncertainty.
// - 2: The exponent.
#let number-pattern-parentheses = regex({
"^" // Start of string
"([\+-]?\d+\.?\d*)" // Value
"(?:\((\d+)\))?" // Uncertainty
"(?:[eE]([-\+]?\d+))?" // Exponent (optional)
"$" // End of string
})
// Parse a number string.
//
// Parameters:
// - value: String with the number.
//
// Returns:
// - value: String with the number.
// - exponent: String with the exponent.
// - upper: String with the upper error.
// - lower: String with the lower error.
#let parse-number(value) = {
if type(value) == dictionary {
// ! Necessary for `format-range` to work.
return value
}
value = value.replace(",", ".").replace(" ", "")
let match = value.match(number-pattern-plusminus)
if match == none {
match = value.match(number-pattern-parentheses)
}
assert.ne(match, none, message: "invalid number: " + value)
let (value, ..rest, exponent) = match.captures
// Strip leading plus signs.
if value != none {
value = value.trim("+", at: start)
}
if exponent != none {
exponent = exponent.trim("+", at: start)
}
let (upper, lower) = if rest.len() == 3 {
// Plus/minus uncertainty.
let (upper, lower, combined) = rest
if combined != none {
(combined, combined)
} else {
(upper, lower)
}
} else {
// Parentheses uncertainty.
let error = rest.first()
let len = value.replace(".", "").len()
if error.len() < len {
error = "0" * (len - error.len()) + error
}
let decimal-pos = value.position(".")
if decimal-pos != none {
decimal-pos = value.len() - decimal-pos - 1 // Position from end
error = error.slice(0, -decimal-pos) + "." + error.slice(-decimal-pos)
}
error = error.replace(regex("^0+(\d+)"), m => m.captures.first())
(error, error)
}
(
value: value,
exponent: exponent,
upper: upper,
lower: lower
)
}
// Format a float (or integer).
//
// Parameters:
// - value: The float to format.
// - decimal-sep: The decimal separator.
// - group-sep: The separator between digit groups.
#let format-float(
value,
decimal-sep: ".",
group-sep: math.thin,
) = {
value = str(value)
let split = value.split(".")
let int-part = split.at(0)
let dec-part = split.at(1, default: none)
let result = []
// Append integer part.
let digits = int-part.clusters()
result += if digits.len() < 5 or group-sep == none {
digits.join()
} else {
digits.remove(0)
for (i, digit) in digits.enumerate() {
if calc.rem(digits.len() - i, 3) == 0 {
[#group-sep]
}
digit
}
}
// Append decimal part.
if dec-part != none {
result += decimal-sep
let digits = dec-part.clusters()
result += if digits.len() < 5 or group-sep == none {
digits.join()
} else {
for (i, digit) in digits.enumerate() {
if i not in (0, digits.len() - 1) and calc.rem(i, 3) == 0 {
[#group-sep]
}
digit
}
}
}
show ",": math.class.with("normal") // Remove space after comma.
show "-": math.minus // Show proper minus sign instead of hyphen.
result
}
// Format a number.
//
// Parameters:
// - string: The string containing the number.
// - product: The symbol to use for the exponent product.
// - uncertainty: How to display uncertainties.
// - decimal-sep: The decimal separator.
// - group-sep: The separator between digit groups.
// - follows-unit: Whether this number is followed by a unit.
#let format-number(
string,
product: math.dot,
uncertainty: "plusminus",
decimal-sep: ".",
group-sep: math.thin,
follows-unit: false
) = {
assert(
uncertainty in ("plusminus", "parentheses"),
message: "invalid uncertainty mode: " + uncertainty
)
let (value, exponent, lower, upper) = parse-number(string)
if exponent == "0" { exponent = none }
let format-float = format-float.with(
decimal-sep: decimal-sep,
group-sep: group-sep
)
let result = []
// Append main value.
let uncertain = upper != none or lower != none
if value != none {
// Don't show value if it is 1 and there is an exponent.
if value != "1" or uncertain or exponent == none {
result += format-float(value)
}
}
// Append uncertainties.
if upper != none and lower not in (none, upper) {
// Always use plus/minus if uncertainties are different.
result = math.attach(
result,
tr: math.plus + format-float(upper),
br: math.minus + format-float(lower)
)
} else if upper != none or lower != none {
let error = if upper != none { upper } else { lower }
result += if uncertainty == "plusminus" {
math.plus.minus + format-float(error)
} else {
// Pad with zeros to match lengths of decimals.
let decimal-len = value.rev().position(".")
let error-decimal-len = error.rev().position(".")
if decimal-len == none { decimal-len = 0 }
if error-decimal-len == none { error-decimal-len = 0 }
if decimal-len < error-decimal-len {
if decimal-len == 0 [#decimal-sep]
"0" * (error-decimal-len - decimal-len)
} else if error-decimal-len < decimal-len {
error += "0" * (decimal-len - error-decimal-len)
}
math.lr[(#error.replace(".", "").trim("0", at: start))]
}
}
// Wrap in brackets if necessary.
let uncertain = upper != none or lower != none
let plusminus = uncertainty == "plusminus" or upper != lower
let exponent-product = value != none and exponent != none
let parentheses = uncertain and plusminus and (follows-unit or exponent-product)
if parentheses {
result = math.lr[(#result)]
}
// Append exponent.
if exponent != none {
if value != none {
// Same as above, don't show product if only the exponent is left.
if value != "1" or uncertain or exponent == none {
result += product
}
}
result += math.attach([10], tr: format-float(exponent))
}
result
}
// Format a range.
//
// Parameters:
// - lower: The string containing the lower bound.
// - upper: The string containing the upper bound.
// - product: The symbol to use for the exponent product.
// - uncertainty: How to display uncertainties.
// - decimal-sep: The decimal separator.
// - group-sep: The separator between digit groups.
// - delim: Symbol between the numbers.
// - delim-space: Space between the numbers and the delimiter.
// - follows-unit: Whether this range is followed by a unit.
#let format-range(
lower,
upper,
product: math.dot,
uncertainty: "plusminus",
decimal-sep: ".",
group-sep: math.thin,
delim: "to",
delim-space: math.space,
follows-unit: false,
) = {
let lower = parse-number(lower)
let upper = parse-number(upper)
let format-float = format-float.with(
decimal-sep: decimal-sep,
group-sep: group-sep
)
let format-number = format-number.with(
product: product,
uncertainty: uncertainty,
decimal-sep: decimal-sep,
group-sep: group-sep
)
let common-exponent = {
if lower.exponent == upper.exponent and lower.exponent != none {
format-float(lower.exponent)
// Remove exponent from numbers.
lower.exponent = none
upper.exponent = none
}
}
let result = []
// Append numbers and delimiter.
// ! `format-number` takes a string, but these numbers are already parsed.
// ! This is why `parse-number` includes a short-circuit for dictionaries.
result += format-number(lower)
result += [#delim-space] + math.upright(delim) + [#delim-space]
result += format-number(upper)
// Wrap in brackets if necessary.
let parantheses = follows-unit or common-exponent != none
if parantheses {
result = math.lr[(#result)]
}
// Append common exponent.
if common-exponent != none {
result += product + math.attach([10], tr: common-exponent)
}
result
}
|
|
https://github.com/jgm/typst-hs | https://raw.githubusercontent.com/jgm/typst-hs/main/test/typ/compiler/let-05.typ | typst | Other | // Ref: false
// Destructuring with multiple placeholders.
#let (a, _, c, _) = (1, 2, 3, 4)
#test(a, 1)
#test(c, 3)
|
https://github.com/typst/packages | https://raw.githubusercontent.com/typst/packages/main/packages/preview/cetz/0.0.2/lib/chart.typ | typst | Apache License 2.0 | // CeTZ Library for drawing charts
#import "axes.typ"
#import "palette.typ"
#import "../draw.typ"
// Styles
#let barchart-default-style = (
axes: (tick: (length: 0))
)
#let columnchart-default-style = (
axes: (tick: (length: 0))
)
#let radarchart-default-style = (
grid: (stroke: (paint: gray, dash: "dashed")),
mark: (size: .075, stroke: none, fill: black),
label-padding: .1,
)
// Valid bar- and columnchart modes
#let barchart-modes = (
"basic", "clustered", "stacked", "stacked100"
)
// Functions for max value calculation
#let barchart-max-value-fn = (
basic: (data, value-key) => {
calc.max(0, ..data.map(t => t.at(value-key)))
},
clustered: (data, value-key) => {
calc.max(0, ..data.map(t => calc.max(
..value-key.map(k => t.at(k)))))
},
stacked: (data, value-key) => {
calc.max(0, ..data.map(t =>
value-key.map(k => t.at(k)).sum()))
},
stacked100: (..) => {
100
}
)
/// Draw a bar chart. A bar chart is a chart that represents data with
/// rectangular bars that grow from left to right, proportional to the values
/// they represent. For examples see @barchart-examples.
///
/// *Style root*: `barchart`.
///
/// - data (array): Array of data rows. A row can be of type array or
/// dictionary, with `label-key` and `value-key` being
/// the keys to access a rows label and value(s).
///
/// *Example*
/// ```typc
/// (([A], 1), ([B], 2), ([C], 3),)
/// ```
/// - label-key (int,string): Key to access the label of a data row.
/// This key is used as argument to the
/// rows `.at(..)` function.
/// - value-key (int,string): Key(s) to access value(s) of data row.
/// These keys are used as argument to the
/// rows `.at(..)` function.
/// - mode (string): Chart mode:
/// - `"basic"` -- Single bar per data row
/// - `"clustered"` -- Group of bars per data row
/// - `"stacked"` -- Stacked bars per data row
/// - `"stacked100"` -- Stacked bars per data row relative
/// to the sum of the row
/// - size (array): Chart size as width and height tuple in canvas unist;
/// height can be set to `auto`.
/// - bar-width (float): Size of a bar in relation to the charts height.
/// - bar-style (style,function): Style or function (idx => style) to use for
/// each bar, accepts a palette function.
/// - x-tick-step (float): Step size of x axis ticks
/// - x-ticks (array): List of tick values or value/label tuples
///
/// *Example*
///
/// `(1, 5, 10)` or `((1, [One]), (2, [Two]), (10, [Ten]))`
/// - x-unit (content,auto): Tick suffix added to each tick label
/// - x-label (content,none): X axis label
/// - y-label (content,none): Y axis label
#let barchart(data,
label-key: 0,
value-key: 1,
mode: "basic",
size: (1, auto),
bar-width: .8,
bar-style: palette.red,
x-tick-step: auto,
x-ticks: (),
x-unit: auto,
x-label: none,
y-label: none,
) = {
import draw: *
assert(mode in barchart-modes,
message: "Invalid barchart mode")
assert(type(label-key) in ("integer", "string"))
if mode == "basic" {
assert(type(value-key) in ("integer", "string"))
} else {
assert(type(value-key) in ("array"))
}
if size.at(1) == auto {
size.at(1) = (data.len() + 1)
}
let max-value = (barchart-max-value-fn.at(mode))(data, value-key)
let y-tic-list = data.enumerate().map(((i, t)) => {
(i, t.at(label-key))
})
let x-unit = x-unit
if x-unit == auto {
x-unit = if mode == "stacked100" {[%]} else []
}
let x = axes.axis(min: 0, max: max-value,
label: x-label,
ticks: (grid: true, step: x-tick-step,
minor-step: none,
unit: x-unit, decimals: 1,
list: x-ticks))
let y = axes.axis(min: data.len(), max: -1,
label: y-label,
ticks: (grid: true,
step: none,
minor-step: none,
list: y-tic-list))
let basic-draw-bar(idx, y, item, ..style) = {
rect((0, y - bar-width / 2),
(rel: (item.at(value-key), bar-width)),
..bar-style(idx))
}
let clustered-draw-bar(idx, y, item, ..style) = {
let y-offset = bar-width / 2
let sub-values = value-key.map(k => item.at(k))
let bar-width = bar-width / sub-values.len()
for (sub-idx, sub) in sub-values.enumerate() {
rect((0, y - y-offset + sub-idx * bar-width),
(rel: (sub, bar-width)),
..bar-style(sub-idx))
}
}
let stacked-draw-bar(idx, y, item, ..style) = {
let sub-values = value-key.map(k => item.at(k))
move-to((0, y))
let sum = 0
for (sub-idx, sub) in sub-values.enumerate() {
move-to((sum, y))
rect((sum, y - bar-width / 2),
(rel: (sub, bar-width)),
..bar-style(sub-idx))
sum += sub
}
}
let stacked100-draw-bar(idx, y, item, ..style) = {
let sum = value-key.map(k => item.at(k)).sum()
for k in value-key {
item.at(k) *= 100 / sum
}
stacked-draw-bar(idx, y, item, ..style)
}
let draw-data = (
if mode == "basic" {basic-draw-bar} else
if mode == "clustered" {clustered-draw-bar} else
if mode == "stacked" {stacked-draw-bar} else
if mode == "stacked100" {stacked100-draw-bar}
)
group(ctx => {
let style = util.merge-dictionary(barchart-default-style,
styles.resolve(ctx.style, (:), root: "barchart"))
axes.scientific(size: size,
left: y,
right: none,
bottom: x,
top: none,
frame: "set",
..style.axes)
if data.len() > 0 {
if type(bar-style) != "function" { bar-style = ((i) => bar-style) }
axes.axis-viewport(size, x, y, {
for (i, row) in data.enumerate() {
draw-data(i, y.min - i - 1, row)
}
})
}
})
}
/// Draw a column chart. A bar chart is a chart that represents data with
/// rectangular bars that grow from bottom to top, proportional to the values
/// they represent. For examples see @columnchart-examples.
///
/// *Style root*: `columnchart`.
///
/// - data (array): Array of data rows. A row can be of type array or
/// dictionary, with `label-key` and `value-key` being
/// the keys to access a rows label and value(s).
///
/// *Example*
/// ```typc
/// (([A], 1), ([B], 2), ([C], 3),)
/// ```
/// - label-key (int,string): Key to access the label of a data row.
/// This key is used as argument to the
/// rows `.at(..)` function.
/// - value-key (int,string): Key(s) to access value(s) of data row.
/// These keys are used as argument to the
/// rows `.at(..)` function.
/// - mode (string): Chart mode:
/// - `"basic"` -- Single bar per data row
/// - `"clustered"` -- Group of bars per data row
/// - `"stacked"` -- Stacked bars per data row
/// - `"stacked100"` -- Stacked bars per data row relative
/// to the sum of the row
/// - size (array): Chart size as width and height tuple in canvas unist;
/// width can be set to `auto`.
/// - bar-width (float): Size of a bar in relation to the charts height.
/// - bar-style (style,function): Style or function (idx => style) to use for
/// each bar, accepts a palette function.
/// - y-tick-step (float): Step size of y axis ticks
/// - y-ticks (array): List of tick values or value/label tuples
///
/// *Example*
///
/// `(1, 5, 10)` or `((1, [One]), (2, [Two]), (10, [Ten]))`
/// - y-unit (content,auto): Tick suffix added to each tick label
/// - y-label (content,none): Y axis label
/// - x-label (content,none): x axis label
#let columnchart(data,
label-key: 0,
value-key: 1,
mode: "basic",
size: (auto, 1),
bar-width: .8,
bar-style: palette.red,
x-label: none,
y-tick-step: auto,
y-ticks: (),
y-unit: auto,
y-label: none,
) = {
import draw: *
assert(mode in barchart-modes,
message: "Invalid columnchart mode")
assert(type(label-key) in ("integer", "string"))
if mode == "basic" {
assert(type(value-key) in ("integer", "string"))
} else {
assert(type(value-key) in ("array"))
}
if size.at(0) == auto {
size.at(0) = (data.len() + 1)
}
let max-value = (barchart-max-value-fn.at(mode))(data, value-key)
let x-tic-list = data.enumerate().map(((i, t)) => {
(i, t.at(label-key))
})
let y-unit = y-unit
if y-unit == auto {
y-unit = if mode == "stacked100" {[%]} else []
}
let x = axes.axis(min: -1, max: data.len(),
label: x-label,
ticks: (grid: true,
step: none,
minor-step: none,
list: x-tic-list))
let y = axes.axis(min: 0, max: max-value,
label: y-label,
ticks: (grid: true, step: y-tick-step,
minor-step: none,
unit: y-unit, decimals: 1,
list: y-ticks))
let basic-draw-bar(idx, x, item, ..style) = {
rect((x - bar-width / 2, 0),
(rel: (bar-width, item.at(value-key))),
..bar-style(idx))
}
let clustered-draw-bar(idx, x, item, ..style) = {
let x-offset = bar-width / 2
let sub-values = value-key.map(k => item.at(k))
let bar-width = bar-width / sub-values.len()
for (sub-idx, sub) in sub-values.enumerate() {
rect((x - x-offset + sub-idx * bar-width, 0),
(rel: (bar-width, sub)),
..bar-style(sub-idx))
}
}
let stacked-draw-bar(idx, x, item, ..style) = {
let sub-values = value-key.map(k => item.at(k))
move-to((x, 0))
let sum = 0
for (sub-idx, sub) in sub-values.enumerate() {
move-to((x, sum))
rect((x - bar-width / 2, sum),
(rel: (bar-width, sub)),
..bar-style(sub-idx))
sum += sub
}
}
let stacked100-draw-bar(idx, x, item, ..style) = {
let sum = value-key.map(k => item.at(k)).sum()
for k in value-key {
item.at(k) *= 100 / sum
}
stacked-draw-bar(idx, x, item, ..style)
}
let draw-data = (
if mode == "basic" {basic-draw-bar} else
if mode == "clustered" {clustered-draw-bar} else
if mode == "stacked" {stacked-draw-bar} else
if mode == "stacked100" {stacked100-draw-bar}
)
group(ctx => {
let style = util.merge-dictionary(columnchart-default-style,
styles.resolve(ctx.style, (:), root: "columnchart"))
axes.scientific(size: size,
left: y,
right: none,
bottom: x,
top: none,
frame: "set",
..style.axes)
if data.len() > 0 {
if type(bar-style) != "function" { bar-style = ((i) => bar-style) }
axes.axis-viewport(size, x, y, {
for (i, row) in data.enumerate() {
draw-data(i, i, row)
}
})
}
})
}
|
https://github.com/Luv-Ray/Resume-template | https://raw.githubusercontent.com/Luv-Ray/Resume-template/main/README.md | markdown | # Resume template
A resume template written in typst, designed for zh_CN.
## How to use
Create a project on [typst.app](https://typst.app/), then copy and paste everything in `main.typ` and `template.typ`, and all done!
Online [preview](https://typst.app/project/rOKiFS0kMTLBWEmtIVLckq). (The first compilation may be a bit slow, but afterwards it will be an incremental compilation where you see the results immediately.）
## Showcases
|
|
https://github.com/DaavidT/CV-2023 | https://raw.githubusercontent.com/DaavidT/CV-2023/main/modules/education.typ | typst | Apache License 2.0 | #import "../brilliant-CV/template.typ": *
#cvSection("Educación")
#cvEntry(
title: [Ing. en Sistemas Computacionales],
society: [Universidad Tecnológica de México],
date: [2020 - 2023],
location: [MX],
logo: "../src/logos/unitec.jpg",
description: list(
[Seminario de Titulación: Analítica e inteligencia de negocios],
[Cursos: Gestión de base de datos #hBar() Analítica Web #hBar() Redes de área local]
)
)
|
https://github.com/Isaac-Fate/math | https://raw.githubusercontent.com/Isaac-Fate/math/main/complex-analysis/complex-analysis.typ | typst | #import "@local/booxtyp:0.0.1": *
#show: book
#cover(
[Complex Analysis],
image("figures/forest.jpg"),
authors: ("<NAME>",),
bar-color: rgb(67, 118, 108),
)
#preface(
)[
This is a notebook for self-studying complex analysis. I mainly follow the
structure of the book _Complex Analysis_ by Stein and Shakarchi
@steinComplexAnalysis2003.
]
#outline()
= Set Theory
== Preimages
Let $f: X -> Y$ be a function between two sets. The #index[preimage] of a subset $S subset.eq Y$ under $f$,
written $f^(-1)(S)$, is defined by
$
f^(-1)(S) := {x in X | f(x) in S}
$
In other words,
$
x in f^(-1)(S) <==> f(x) in S
$
#proposition[
Let $f: X -> Y$ be a function. We have the following properties:
+ $f^(-1)(emptyset) = emptyset$ and $f^(-1)(Y) = X$.
+ $f^(-1)(sect.big_alpha S_alpha) = sect.big_alpha f^(-1)(S_alpha)$.
+ $f^(-1)(S^complement) = (f^(-1)(S))^complement$.
+ $f^(-1)(S_1 without S_2) = f^(-1)(S_1) without f^(-1)(S_2)$.
+ $f^(-1)(union.big_alpha S_alpha) = union.big_alpha f^(-1)(S_alpha)$.
+ $f^(-1)(union.sq.big_alpha S_alpha) = union.sq.big_alpha f^(-1)(S_alpha)$.
]
#proof[
We prove each property separately.
*Proof of 1:* The first property is evident.
*Proof of 2:* We have
$
x in f^(-1)(sect.big_alpha S_alpha) &<==> f(x) in sect.big_alpha S_alpha\
&<==> f(x) in S_alpha, space forall alpha in I \
&<==> x in f^(-1)(S_alpha), space forall alpha in I\
&<==> x in sect.big_alpha f^(-1)(S_alpha)
$
*Proof of 3:* We have
$
x in f^(-1)(S^complement) &<==> f(x) in S^complement\
&<==> f(x) in.not S\
&<==> x in.not f^(-1)(S)\
&<==> x in (f^(-1)(S))^complement
$
*Proof of 4:* By applying the second and third property, we have
$
f^(-1)(S_1 without S_2) &= f^(-1)(S_1 sect S_2^complement) \
&= f^(-1)(S_1) sect f^(-1)(S_2^complement)
&"by the second property" \
&= f^(-1)(S_1) sect (f^(-1)(S_2))^complement
&"by the third property" \
&= f^(-1)(S_1) without f^(-1)(S_2)
$
*Proof of 5:* Again, we can prove this by applying the second and third
property:
$
f^(-1)(union.big_alpha S_alpha) &= f^(-1)(sect.big_alpha (S_alpha^complement))^complement\
&= (f^(-1)(sect.big_alpha S_alpha^complement))^complement
&"by the third property"\
&= (sect.big_alpha f^(-1)(S_alpha^complement))^complement
&"by the second property"\
&= union.big_alpha (f^(-1)(S_alpha^complement))^complement \
&= union.big_alpha f^(-1)(S_alpha)
&"by the third property"
$
*Proof of 6:* This is proved by the first, second and fifth property.
]
= Point-Set Topology
The knowledge from topology is too important to be neglected. Before we start to
study complex analysis, we shall first introduce some basic concepts in
topology.
== Topology
Topology is the collection of all open subsets in a set.
#definition[
A #index[topology] on a set $X$ is a collection $cal(T)$ of subsets of $X$ having
the following properties:
+ $emptyset, X in cal(T)$.
+ $cal(T)$ is closed under arbitrary unions, i.e., $U_alpha in cal(T) space forall alpha in I ==> union.big_(alpha in I) U_alpha in cal(T)$.
+ $cal(T)$ is closed under finite intersections, i.e., $U_1, U_2 in cal(T) ==> U_1 sect U_2 in cal(T)$.
]
A set for which a topology has been specified is called a #index(entry: [topological spaces])[topological space],
and is denoted by $(X, cal(T))$. If the topology is clear from the context, we
simply write $X$ instead of $(X, cal(T))$.
#example[
The only topology on the empty set $emptyset$ is the singleton $cal(T) = {emptyset}$.
]
#example[
For a set $X$, the topology containing only $emptyset$ and $X$ is called the #index[trivial topology].
]
#example[
The power set $cal(P)(X)$ of a set $X$ is a topology on $X$, and is referred to
as the #index[discrete topology].
]
== Continuous Functions
#definition[
Let $f: X -> Y$ be a function between two topological spaces. We say $f$ is
continuous if for any open set $U subset.eq Y$, its preimage $f^(-1)(U)$ is also
open in $X$.
]
== Compact Spaces
A collection $cal(A) = {A_alpha | alpha in I}$ of subsets in $X$ is said to #index(entry: [covering of a topological space])[cover] $X$,
or to be a #index(entry: [covering of a topological space])[covering] or $X$, if
the union $union.big_(alpha in I) A_alpha$ equals $X$.
And a #index(entry: [subcovering of a topological space])[subcovering] $cal(A)'$ of $cal(A)$ is
a subcollection of $cal(A)$ that also covers $X$.
#definition[
A topological space $X$ is #index(entry: [compact topological spaces])[compact] if
every open covering of $X$ has a finite subcovering. Formally, if
$
X = union.big_(alpha in I) U_alpha
$
where each $U_alpha$ is open in $X$, then there exist $alpha_1, ..., alpha_k in I$ such
that
$
X = union.big_(j=1)^k U_(alpha_j)
$
]
If $Y$ is a subspace of $X$, to check whether $Y$ is compact, it is usually more
convenient to consider the subsets in $X$ rather than those in $Y$.
A collection $cal(A) = {A_alpha | alpha in I}$ of subsets in $X$ is said to
cover subspace $Y$ if $Y subset.eq union.big_(alpha in I) A_alpha$.
The following proposition states that a subspace $Y$ of $X$ is compact if and
only if any open covering of $Y$ in $X$ has a finite subcovering.
#proposition[
Let $Y$ be a subspace of $X$. Then $Y$ is compact if and only if every open
covering of $Y$ in $X$ has a finite subcovering.
]
#proof[
We prove each direction separately.
*Proof of $==>$:* Suppose $Y$ is compact. Let ${U_alpha | alpha in I}$ be an
open covering of $Y$ in $X$. Let $V_alpha = U_alpha sect Y, space alpha in I$.
Note that $V_alpha$ is open in $Y$. Then, due to the compactness of $Y$, there
exists a finite subset $J$ of the index set $I$, i.e., $J subset.eq I$ and $abs(J) < oo$,
such that
$
Y = union.big_(alpha in J) V_(alpha) = union.big_(alpha in J) (U_alpha sect Y) subset.eq union.big_(alpha in J) U_alpha
$
This shows that ${U_alpha | alpha in J}$ is a finite subcovering of $Y$.
*Proof of $<==$:* Suppose
$
Y = union.big_(alpha in I) V_alpha
$
where each $V_alpha$ is open in $Y$. There exists $U_alpha$ open in $X$ such
that $V_alpha = U_alpha sect Y$. Then, we have
$
Y = union.big_(alpha in I) V_alpha = union.big_(alpha in I) (U_alpha sect Y) subset.eq union.big_(alpha in I) U_alpha
$
By the given condition, there exists a finite subcovering ${U_alpha | alpha in J}$ of $Y$.
Consequently, $Y subset.eq union.big_(alpha in J) U_alpha$. It then follows that
$
Y = (union.big_(alpha in J) U_(alpha)) sect Y = union.big_(alpha in J) (U_alpha sect Y)
= union.big_(alpha in J) V_alpha
$
This proves that ${V_alpha | alpha in J}$ is a finite subcovering of $Y$, and
hence $Y$ is compact.
]
#theorem[
Let $X$ be a compact space. If subset $K subset.eq X$ is closed in $X$, then $K$ is
also compact.
]<thm:3>
Continuous functions preserve compactness.
#theorem[
Let $f: X -> Y$ be a continuous function between two topological spaces. If
$X$ is compact, then $f(X)$ is also compact.
]
#proof[
Let ${V_alpha | alpha in I}$ be an open covering of $f(X)$ in $Y$. Then, we have $f(X) subset.eq union.big_(alpha in I) V_alpha$.
It follows that $X subset.eq union.big_(alpha in I) f^(-1)(V_alpha)$. Note that ${f^(-1)(V_alpha) | alpha in I}$ is
an open covering of $X$. Because $X$ is compact, there exists a finite
subcovering ${f^(-1)(V_alpha) | alpha in J}$ of $X$. Then, the image $f(X)$ can
be covered by ${V_alpha | alpha in J}$ of $f(X)$. This proves that $f(X)$ is
compact.
]
The preimage of a compact set under a continuous function is not necessarily
compact.
#example[
Consider the identity map $id: (a, b] -> RR$. It is continuous. But the preimage $id^(-1)([a, b]) = (a, b]$ is
not compact.
]
There is a criterion for a space to be compact formulated in terms of closed
sets instead of open sets.
A collection $cal(C) = {C_alpha | alpha in I}$ of closed subsets in $X$ is said
to have the #index(entry: [finite intersection property])[finite intersection property] if
every finite intersection is nonempty, i.e.,
$
J subset.eq I "and" abs(J) < oo ==> sect.big_(alpha in J) C_alpha != emptyset
$
#theorem[
A topological space $X$ is compact if and only if every collection $cal(C) = {C_alpha | alpha in I}$ of
closed subsets in $X$ that has the finite intersection property also has a
nonempty intersection, i.e., $sect_(alpha in I) C_alpha != emptyset$.
]<thm:4>
#corollary[
Let $X$ be a compact Hausdorff metric space. If ${C_n}$ is a sequence of
nonempty closed subsets such that
$
C_1 supset.eq C_2 supset.eq dots.c supset.eq C_n supset.eq ...
$
and $lim_(n -> oo) diam(C_n) = 0$, then they intersect at exactly one point:
$
sect.big_(n = 1)^oo C_n = {x_0}
$
]<cor:1>
== Connected Spaces
#definition[
Let $X$ be a topological space. A #index(entry: [separation of topological spaces])[separation] of $X$ is
a pair of open subsets $U$ and $V$ such that
+ $U != emptyset$ and $V != emptyset$,
+ $U sect V = emptyset$, and
+ $X = U union V$.
The last two conditions are equivalent to saying that $X$ is contained in the
disjoint union of $U$ and $V$, i.e., $X subset.eq U union.sq V$.
If such a separation exists, we say $X$ is #index(entry: [disconnected topological spaces])[disconnected].
Otherwise, we say $X$ is #index(entry: [connected topological spaces])[connected].
]
#example[
The empty set $emptyset$ and the entire space $X$ are connected.
]
The following proposition gives a useful characterization of connectedness of a
topological subspace.
#proposition[
Let $Y subset.eq X$ be a topological subspace of $X$. Then $Y$ is disconnected
if and only if there exist two open sets $U, V$ in $X$ such that
+ $U sect Y != emptyset$ and $V sect Y != emptyset$,
+ $U sect V = emptyset$, and
+ $Y subset.eq U union V$.
]
Continuous functions preserve connectedness.
#theorem[
Let $f: X -> Y$ be a continuous function between two topological spaces. If
$X$ is connected, then $f(X)$ is also connected.
]
#proof[
Suppose $f(X) subset.eq V_1 union.sq V_2$ where $V_1$ and $V_2$ are open in $Y$ and $V_1 sect f(X) != emptyset$.
We want to show that $V_2 sect f(X) = emptyset$. Taking the preimage, we have
$
X subset.eq f^(-1)(V_1 union.sq V_2) = f^(-1)(V_1) union.sq f^(-1)(V_2)
$
Since $f$ is continuous, $f^(-1)(V_1)$ and $f^(-1)(V_2)$ are open in $X$.
Moreover, $f^(-1)(V_1) != emptyset$ since $V_1 sect f(X) != emptyset$. Because $X$ is
connected, we must have $f^(-1)(V_2) = emptyset$. This implies $V_2 sect f(X) = emptyset$ as
desired.
]
#definition[
A topological space $X$ is #index(entry: [path-connected topological spaces])[path-connected] if
for any two points $x, y in X$, there exists a continuous function $p: [0, 1] -> X$ such
that $p(0) = x$ and $p(1) = y$.
]
#example[
The famous #index(entry: [topologist's sine curve])[topologist's sine curve] is
a connected but not path-connected topological space. It is the closure $overline(S)$ of
the set
$
S := { (x, sin 1/x) mid(|) x > 0 }
$
One can show that
$
overline(S) = { (x, sin 1/x) mid(|) x > 0 } union { (0, y) | y in [-1, 1] }
$
Its graph is shown in @fig:4.
#figure(image("./figures/topologist-sine-curve.svg", width: 60%), caption: [
The topologist's sine curve.
])<fig:4>
]
= Complex Numbers and the Complex Plane
== Algebraic Operations
#definition[
The set of #index(entry: [complex number])[complex numbers], denoted by $CC$, is
a field $(RR^2, +, dot)$
where the addition and multiplication are defined as follows:
$
(x_1, y_1) + (x_2, y_2) &= (x_1 + x_2, y_1 + y_2) \
(x_1, y_1) dot (x_2, y_2) &= (x_1 x_2 - y_1 y_2, x_1 y_2 + x_2 y_1)
$<eq:1>
]
Specially, we call $(0, 1) in CC$ the #index[imaginary unit], and denote it by $i$.
Just like representing a vector in $RR^2$ by its components, we can write a
complex number $z$ as
$ z = (x, y) = x (1, 0) + y (0, 1) $
By neglecting the _real unit_ $(1, 0)$ and substitute $i$ for $(0, 1)$, we
obtain the simplified notation
$ z = x + i y $
Moreover, it is evident that
$ i^2 = i dot i &= (0, 1) dot (0, 1) quad & \
&= (-1, 0) &"multiplication rule" \
&= -1 $
Then, with this formula $i^2 = -1$, equations in @eq:1, which are now reduced to
$
(x_1 + i y_1) + (x_2 + i y_2) &= (x_1 + x_2) + i (y_1 + y_2) \
(x_1 + i y_1) (x_2 + i y_2) &= (x_1 x_2 - y_1 y_2) + i (x_1 y_2 + x_2 y_1)
$
can be easily verified by straightforward calculation.
In $RR^2$, the length of a vector $(x, y)$ is defined as $sqrt(x^2 + y^2)$.
Similarly, we define the #index[modulus] or #index[absolute value] of a complex
number $z = x + i y$ as $|z| := sqrt(x^2 + y^2)$, which measure the length or
the magnitude of $z$.
The #index[complex conjugate] of $z = x + i y$ is defined by
$ overline(z) := x - i y $
== Smooth Curves
Using a set of points of describe a curve may not be sufficient because we also
need the direction of a curve at each point. To solve this problem, we think of
a curve as a trajectory of some particle. The position of this particle at time $t$ is
given by a function $z(t)$.
A #index[parameterized curve] is a function
$
z: RR supset.eq [a, b] -> CC
$
We say curve $gamma$ is traced out by $z(t)$. It is the set $gamma = z([a, b])$.
A complex-valued function $f: [a, b] -> CC$ is differentiable at a point $x in (a, b)$ if
both the real and imaginary parts of $f$ are differentiable at $x$, and its
derivative is given by
$
f'(x) = [Re(f)]'(x) + i [Im(f)]'(x)
$
The one-sided derivatives are defined similarly.
When we are going to study complex integration, we shall always be interested in #index[smooth curves].
A curve $z: [a, b] -> CC$ is said to be smooth if
+ $z'(t)$ exists and is continuous on $[a, b]$, and
+ $z'(t) != 0$ for all $t in [a, b]$, which means it never vanishes.
#note[
The derivative $z'$ of a smooth curve $z$ is necessarily finite at the two
endpoints since it is continuous throughout $[a, b]$. We also say $gamma$ is
continuously differentiable on $[a, b]$.
]
#exercise[
Show that
+ the curve $z_1(t) = t^3 cos 1/t + i t^3 sin 1/t$ is smooth,
+ but $z_2(t) = t^2 cos 1/t + i t^2 sin 1/t$ is not
where $t in [0, b]$ in both cases.
]
#solution[
We first show that $z_1$ is smooth. It is clear $z_1$ is differentiable in the
open interval $(0, b)$
with derivative
$
z'_1 (t) = 3 t^2 cos 1/t + t sin 1/t + i (3 t^2 sin 1/t - t cos 1/t),
quad t in (0, b)
$<eq:3>
And $z'_1(t)$ is continuous in $(0, b)$. The problem is whether $z'_1(t)$ exists
at the endpoints $t = 0$ and $t = b$. (Well, we can immediately see that $z'_1(b)$ exists
by considering a slightly larger domain $[0, b + delta]$ for some $delta > 0$.)
When checking the existence of $z'_1(0)$, one may suggest to use the definition
of derivative, which is absolutely correct. However, if we know the limit of $gamma'(t)$ exists
at an endpoint, then the (one-sided) derivative must also exist there and equal
to the limit. See @prop:1 for a proof of this fact. From @eq:3, we note that
$
lim_(t -> 0) z'_1(t) = 0 quad
"and" quad lim_(t -> b) z'_1(t) "also exists"
$
Therefore, $z'_1(t)$ indeed exists on $[0, b]$ and is continuous, which
satisfies the first condition of smooth curves.
We also need to show that $z'_1(t) != 0$ for all $t in (0, b)$. The equation $z'_1(t) = 0$ yields
$
cases(3 t^2 cos 1/t + t sin 1/t = 0, 3 t^2 sin 1/t - t cos 1/t = 0)
$<eq:4>
Multiplying the second equation by $3t$, we obtain
$
cases(3 t^2 cos 1/t + t sin 1/t = 0, 9 t^3 sin 1/t - 3t^2 cos 1/t = 0)
$
Adding these two equations to eliminate $3t^2 cos 1/t$, we get
$
t (9t^2 + 1) sin 1/t = 0
$
Since $t > 0$, we must have $sin 1/t = 0$. But then by plugging $sin 1/t = 0$ into
the @eq:4, we have $cos 1/t = 0$, which leads to a contradiction because $sin 1/t$ and $cos 1/t$ cannot
be zero simultaneously. This shows @eq:4 has no solution, and hence $z'_1(t) != 0$ for
all $t in (0, b)$. In conclusion, $z_1$ is smooth.
Now, we show that $z_2$ is not a smooth curve. In the open interval $(0, b)$, we
have
$
z'_2(t) = 2t cos 1/t + sin 1/t + i (2t sin 1/t - cos 1/t)
$
Though the derivative of $z_2$ exists at $t = 0$ (one can show by definition
that $z'_2(0) = 0$), it is not continuous there.
]
@fig:1 depicts the two curves $z_1$ and $z_2$. They look similar to each other
and are smooth in most part. The only problematic point is $t = 0$ for $z_2$.
#figure(
image("figures/two-spirals.svg", width: 60%),
caption: [
Left: $z_1(t) = t^3 cos 1/t + i t^3 sin 1/t$ is smooth. Right: $z_2(t) = t^2 cos 1/t + i t^2 sin 1/t$ is
not.
],
)<fig:1>
#proposition[
Let $f: [a, b] -> RR$ be a continuous function whose derivative $f'$ exists in $(a, b)$.
If the limit of $f'$ exists at $a$, then $f'$ also exists at $a$ and
$ f'_+(a) = lim_(x -> a^+) f'(x) $
An analogous statement holds for the left-hand derivative at $b$.
]<prop:1>
#proof[
Suppose $lim_(x -> a^+) f'(x) = L$. Let $epsilon > 0$ be an arbitrary positive
number. Then there exists $delta > 0$ such that
$ 0 < x - a < delta ==> |f'(x) - L| < epsilon $<eq:2>
Let a number $h$ be such that $0 < h < delta$. By the Mean Value Theorem, we
have
$
(f(a + h) - f(a) ) / h = f'(xi)
quad "for some" xi in (a, a + h)
$
It then follows that
$
abs((f(a + h) - f(a) ) / h - L) = abs(f'(xi) - L) < epsilon
$
where the last inequality is due to @eq:2 since $0 < xi - a < h < delta$. This
proves that $f$ is differentiable at $a$ and $f'_+(a) = L$.
]
A curve may have multiple parameterizations. For example, $z(t) = t + i t, t in [0, 1]$
and $w(s) = 1/2 s+ i 1/2 s, s in [0, 2]$ both trace out the same straight line.
But they vary in speed. How can we define the equivalence of two parameterized
curves?
Imagine two particles $P$ and $Q$ are traveling along the same curve $gamma$ in
two different ways $z(t), t in [a, b]$ and $w(s), s in [c, d]$, respectively.
suppose $Q$ spent time $s$ and arrived at $z = z(t)$ (for the $n$-th time). Then
for $P$ to arrive at the same point $z = w(s)$ (for the $n$-th time), the time
it will take, $t$, is certain and hence uniquely determined by $s$. This gives
rise to a function $t = g(s)$.
Moreover, if we think of the previous process in the opposite way, that is,
determined how much time $Q$ will take to arrive at $P$'s position, then we find
that $g$ must be a bijection.
And as particle $P$ spends more time traveling, the spent time of $Q$ must also
increase, which means $g$ is a increasing function.
#definition[
Let $z: [a, b] -> CC$ and $w: [c, d] -> CC$ be two parameterized curves. We say $z(t)$ and $w(s)$ are #index(entry: [equivalent parameterizations])[equivalent] via $g$ if
there exists a bijection $g: [c, d] <-> [a, b]$ such that
+ $g$ is increasing,
+ and $z((g(s))) = w(s)$ for all $s in [c, d]$.
We also say that $z(t)$ and $w(s)$ are two #index[reparametrization] of each
other.
]
A simple observation is that such function $g$ is continuous. See @prop:2.
#proposition[
If $f: [c, d] -> [a, b]$ is a monotonic surjective function, then $f$ is
continuous.
]<prop:2>
#proof[
Without loss of generality, we assume $f$ is increasing. Choose a point $x_0 in [c, d]$.
In what follows, we only consider $x_0 in (c, d)$ since the proofs for $x_0 = c$ and $x_0 = d$ are
similar. Let $epsilon > 0$ be sufficiently small so that $f(x_0) plus.minus epsilon in [a, b]$.
Since $f$ is surjective, there exist $x_1, x_2 in [c, d]$ such that $f(x_1) = f(x_0) - epsilon$ and $f(x_2) = f(x_0) + epsilon$.
Note that $x_1 < x_0 < x_2$. Let $delta = min(x_0 - x_1, x_2 - x_0)$. Then for
any $x in [c, d]$ such that $|x - x_0| < delta$, we have
$x_1 < x < x_2$. It then follows that
$
f(x_0) - epsilon = f(x_1) <= f(x) <= f(x_2) = f(x_0) + epsilon
$
since $f$ is increasing. This proves that $f$ is continuous at $x_0$.
]
If $z(t)$ and $w(s)$ are smooth curves, and they are equivalent via $g$, then
apart from continuity, $g$ must enjoy some other nice properties.
== Topology on the Complex Plane
The #index[open disk] of radius $r$ centered at $z_0$ is the set
$
D(z_0, r) := { z in CC | |z - z_0| < r }
$
The #index[closed disk] of radius $r$ centered at $z_0$ is the set
$
overline(D)(z_0, r) := { z in CC | |z - z_0| <= r }
$
The complex plane $CC$ is endowed with the #index[Euclidean topology]. A subset $Omega$ in $CC$ is
open if and only if for every point $z in Omega$, there exists an open disk $D(z, r) subset.eq Omega$ for
some $r > 0$.
In complex analysis, because we will define the integration of a complex
function along a curve, we are especially interested in the sets in which every
two points can be joined by a curve.
We say a set $S subset.eq CC$ is #index(entry: [curve-connected sets in $CC$])[curve-connected] if
any two points in $S$ can be joined by a piecewise smooth curve in $S$. Note
that this is not a common term. We introduce it to be concise in the following
discussion.
Recall that a curve is a piecewise continuously differentiable function.
Therefore, a path-connected set may not be good enough at a first glance since a
path $p$ is only continuous. However, we shall see in the next theorem that if
an open set $Omega subset.eq CC$ is path-connected, then it is also
curve-connected. And in fact, we only need to assume $Omega$ is connected
because all these three conditions about connectedness are equivalent.
#theorem[
Let $Omega in CC$ be an open set. Then the following statements are equivalent:
+ $Omega$ is connected.
+ $Omega$ is path-connected.
+ $Omega$ is curve-connected.
]<thm:8>
#proof[
We prove 1 $==>$ 3 $==>$ 2 $==>$ 1.
*Proof of 1 $==>$ 3:* Suppose $Omega$ is connected. Fix a point $z_0 in Omega$.
Let $U$ be the set of all points in $Omega$ that can be joined to $z_0$ by a
curve, i.e.,
$
U = {z in Omega mid(|) "There exits a piecewise smooth" gamma: [a, b] -> Omega "from" z_0 "to" z}
$
And let $V = Omega - U$, which means $V$ is the set of all points in $Omega$ that
cannot be joined to $z_0$ by a curve. Clearly $U$ and $V$ are disjoint. We now
claim that $U$ and $V$ are open sets.
To see $U$ is open, let $z in U$. Because $Omega$ is open, there exists an open
disk $D(z, r) subset.eq Omega$. We want to show it is also contained in $U$,
i.e., $D(z, r) subset.eq U$. Pick any point $w in D(z, r)$. We need to show $w in U$,
which means we need to find a curve from $z_0$ to $w$. Since $z in U$, there
exists a curve $alpha$ from $z_0$ to $z$. Then, we can join $z$ and $w$ by a
line segment $beta$. After that, we can travel from $z_0$ to $w$ by first
passing through $alpha$ and then $beta$, which gives us a curve $gamma$ from $z_0$ to $w$.
See @fig:3 for an illustration.
#figure(
image("./figures/piecewise-smooth-curve-from-z0-to-w.svg", width: 60%),
caption: [
Construction of a piecewise smooth curve from $z_0$ to $w$.
],
)<fig:3>
Formally, $beta: [0, 1] -> Omega$ is given by
$
beta(t) = (1 - t) z + t w, quad t in [0, 1]
$
We claim
+ $beta$ is well-defined, and
+ $beta$ is a smooth curve.
By the well-definedness, we mean $beta(t)$ is always in $Omega$ for all $t in [0, 1]$.
To see this, we consider the distance from $beta(t)$ to $z$:
$
abs(beta(t) - z) &= abs((1 - t) z + t w - z) quad& \
&= abs(t (w - z)) \
&= t abs(w - z) &"since" t >= 0\
&< t r & "since" w in D(z, r)\
&<= r & "since" t <= 1
$
Hence, $beta(t) in D(z, r), space forall t in [0, 1]$, which is indeed
well-defined. Our second claim that $beta$ is smooth is evident since $beta'$ exists,
and it is continuous and never vanishes.
Let $gamma = alpha * beta$. Clearly, $gamma$ is a piecewise smooth curve from $z_0$ to $w$ since $alpha$ is
piecewise smooth and $beta$ is smooth. Therefore, by the definition of $U$, we
have $w in U$. Because $w in D(z, r)$ is arbitrarily chosen, it follows that $D(z, r) subset.eq U$,
which further implies that $U$ is open.
Now, we show that $V$ is also open. Let $z in V$. There exists an open disk $D(z, r) subset.eq Omega$ since $Omega$ is
open. We want to show $D(z, r) subset.eq V$, that is, to show there is no curve
from $z_0$ to $w$ for any $w in D(z, r)$. Assume that there exits a piecewise
smooth curve $gamma$ from $z_0$ to $w$. By applying the same argument as above
when we proved $U$ is open, we can construct a (smooth) line segment $beta$ from $z$ to $w$.
Now, let $alpha$ be the curve obtained by joining $gamma$ and $beta^-$, i.e., $alpha = gamma * beta^-$.
Then, one can show that $alpha$ is a piecewise smooth curve from $z_0$ to $z$ using
the a similar argument we did before. This leads to a contradiction since there
cannot be a curve from $z_0$ to $z$ be the definition of $V$. Therefore, our
assumption that there exists a curve from $z_0$ to $w$ is false, and hence $w in V$,
which further implies that $D(z, r) subset.eq V$. This proves $V$ is open.
So far, we have shown that both $U$ and $V$ are open and $Omega = U union.sq V$.
We also note that $U != emptyset$ since $z_0 in U$. This is because that the
constant function $gamma: t |-> z_0$ is a smooth curve from $z_0$ to $z_0$. Now,
because $Omega$ is connected, by definition, we must have $V = emptyset$.
equivalently, $Omega = U$, which means $Omega$ every point in $Omega$ can be
joined to $z_0$ by a curve.
*Proof of 3 $==>$ 2:* The proof of this direction is trivial since loosely
speaking, every curve is a path. Let $z, w in Omega$. There exists a curve $gamma: [a, b] -> Omega$ from $z$ to $w$.
Let $p: [0, 1] -> Omega$ be given by
$
p(t) = gamma((1-t)a + t b), quad t in [0, 1]
$
Note that $p$ is continuous since both $gamma$ and $t |-> (1-t) a + t b$ are
continuous. Notice also that $t(0) = z$ and $t(1) = w$. Therefore, $p$ is indeed
a path from $z$ to $w$. Hence, $Omega$ is path-connected.
*Proof of 2 $==>$ 1:* Finally,we need to show $Omega$ is connected given that it
is path-connected. We shall prove by contradiction. Assume on the contrary that $Omega$ is
not connected. Then, there exist two nonempty open sets $U, V subset.eq CC$ such
that $Omega = U union.sq V$. Suppose $z in U$ and $w in V$. There exists a path $p: [0, 1] -> Omega$ from $z$ to $w$.
Let
$
t^* = sup { t in [0, 1] mid(|) p(s) in U, space forall s in [0, t]}
$<eq:9>
Note that $t^*$ exists since $[0, 1]$ is bounded above. Consider the point $p(t^*)$.
Loosely speaking, $p(t^*)$ is somewhat the point that separates $U$ and $V$. We
now show $p(t^*)$ cannot be either in $U$ or $V$ to reach a contradiction.
Suppose first $p(t^*) in U$. Then, there exists an open disk $D(p(t^*), epsilon) subset.eq U$ for
some $r > 0$ since $U$ is open. Note that the preimage $p^(-1)[D(p(t^*, epsilon))]$ must
be open in $[0, 1]$ because $p$ is continuous. But
$
p^(-1)[D(p(t^*, epsilon))] = [0, t^*]
$
due to the definition of $t^*$. This implies that $t^* = 1$. Then, $p(t) in U, space forall t in [0, 1]$,
which leads to a contradiction since $p(1) = w in V$ and $U sect V = emptyset$.
We have seen $p(t^*) in.not U $. Then, we must have $p(t^*) in V$. Because $V$ open,
there exists an open disk $D(p(t^*), epsilon) subset.eq V$. Since $p$ is
continuous, there exists $delta > 0$ such that
$
p(t) in D(p(t^*), epsilon) subset.eq V quad forall t in (t^* - delta, t^* + delta)
$
In particular, $p(t^* - delta/2) in V$. This contradicts @eq:9.
Therefore, $p(t^*) in.not U$ and $p(t^*) in.not V$, which contradicts $Omega = U union.sq V$.
In conclusion, $Omega$ is connected.
]
= Complex Functions
== Limits and Continuity
If $f$ is a real-valued continuous function defined on a closed interval $[a, b]$,
then we know $f$ attains its maximum and minimum values there. Since we cannot
compare complex numbers, we we cannot define the maximum and minimum values of a
complex functions. But we can instead consider the modulus. Then an analogous
result for complex functions holds, which says the modulus $|f|$ attains its
maximum and minimum values on a compact set $K subset.eq CC$.
In the following, we will prove a slightly more general result.
#theorem[
Let $K$ be a compact topological space. If $f: K -> RR$ is continuous, then $f$ attains
its maximum and minimum values on $K$.
]<thm:5>
#proof[
We will only prove that $f$ attains its maximum value on $K$. The proof for the
minimum value of $f$ is similar. The general idea is as follows. We will first
show that $f$ is bounded on $K$, and hence it has a supremum $M$. And then we
will show that $f$ may take the value $M$.
*Proof of $f$ Being Bounded:* Consider a collection of open intervals in $RR$:
$
V_x = (f(x) - epsilon, f(x) + epsilon), quad x in K
$
where $epsilon > 0$ is a fixed positive number. Because $f$ is continuous, the
preimage $f^(-1)(V_x)$ is open in $K$. And we note that ${f^(-1)(V_x) | x in K}$ forms
an open cover for $K$. Then because $K$ is compact, there exists a finite
subcovering, say ${f^(-1)(V_(x_j)) | j=1,...,k}$. We have
$
& K subset.eq union.big_(j=1)^k f^(-1)(V_(x_j)) \
==> & x in union.big_(j=1)^k f^(-1)(V_(x_j)) quad forall x in K\
==> & f(x) in union.big_(j=1)^k V_(x_j) quad forall x in K\
==> & min_(1 <= j <= m) f(x_j) - epsilon < f(x) < max_(1 <= j <= m) f(x_j) + epsilon quad forall x in K
$
This shows that $f$ is bounded on $K$.
*Proof of That $f$ May Attain Its Supremum:* Since the range $f(K)$ is bounded
above, there exists a supremum $M$. We now show that $f(x_0) = M$ for some $x_0 in K$.
Consider a sequence of closed intervals in $RR$:
$
I_n = [M - 1/n, M], quad n in ZZ^+
$
The preimage $f^(-1)(I_n)$ is closed in $K$ since $f$ is continuous. Note that
$
f^(-1)(I_1) supset.eq f^(-1)(I_2) supset.eq dots.c supset.eq f^(-1)(I_n) supset.eq ...
$
And each of them is nonempty since $M$ is the supremum of $f(K)$, which means
there always exists some $x_n in K$ such that $f(x_n) > M - 1/n$. Therefore, by
@thm:4, the intersection of all theses closed preimages is nonempty. In other
words, there exists at least one $x_0 in X$ such that
$
x_0 in sect.big_(n=1)^oo f^(-1)(I_n)
$
Then, the value $f(x_0)$ satisfies
$
M - 1/n <= f(x_0) <= M quad forall n in ZZ^+
$
This implies $f(x_0) = M$. Therefore, $M$ is indeed the maximum value of $f$ on $K$.
]
== Holomorphic Functions
#definition[
Let $f: Omega -> CC$ be a function defined on an open set $Omega subset.eq CC$.
We say $f$ is #index(entry: [complex differentiable functions])[complex differentiable] at $z in Omega$ if
the quotient
$
(f(z + h) - f(z)) / h
$
converges when $h -> 0$. Its limit is denoted by $f'(z)$ and called the
derivative of $f$ at $z$. We write
$
f'(z) = lim_(h -> 0) (f(z + h) - f(z)) / h
$
We say $f$ is #index(entry: [holomorphic functions])[holomorphic] in an open set $Omega$ if $f$ is
complex differentiable at every point of $Omega$. And we say $f$ is holomorphic
at a point $z$ if if is holomorphic in a neighborhood of $z$.
]
#note[
It should be emphasized that $f$ being holomorphic at a point $z$ is not the
same as $f$ being complex differentiable at $z$.
]
#example[
Function $f(z) = abs(z)^2, space z in CC$ is complex differentiable at $z = 0$.
But it is not holomorphic at $z = 0$.
To see $f$ is complex differentiable at $z = 0$, we have
$
(f(h) - f(0)) / h
= (abs(h)^2 - 0) / h
= (h overline(h)) / h
= overline(h)
$
It is cleat that $overline(h) -> 0$ as $h -> 0$. Therefore, $f'(0) = 0$.
Now, we show that $f$ is not holomorphic at $z = 0$.
]
Recall in real analysis, we introduced the concept of infinite derivatives to
handle the problems of vertical tangent lines
@apostolMathematicalAnalysisModern1974.
For example, as illustrated in @fig:2, the function $f(x) = root(3, x), space x in [-1, 1]$ has
a vertical tangent line at $x = 0$. It is by definition not differentiable at $x = 0$.
And hence a lot of theorems do not apply to $f(x) = root(3, x)$ if we assume
functions must be differentiable in some open interval. For instance, we cannot
apply the Mean Value Theorem to $f(x) = root(3, x)$ on $[-1, 1]$ if the
assumption of the theorem requires that $f$ must be differentiable on $(-1, 1)$.
By allowing infinite derivatives, and modifying the assumptions of being
differentiable to the existence of finite or infinite derivatives, we can solve
this problem.
However, in complex analysis usually we shall not consider infinite complex
derivatives.
#figure(image("./figures/cubic-root-function.svg", width: 60%), caption: [
Cubic root function $f(x) = root(3, x), space x in [-1, 1]$
and its vertical tangent line at $x=0$.
])<fig:2>
We say $f$ is #index(entry: [holomorphic functions in open sets])[holomorphic in]
an open set $Omega$ if $f$ is holomorphic at every point of $Omega$. Let $E$ be
a closed subset of $CC$. We say $f$ is #index(entry: [holomorphic functions on closed sets])[holomorphic on] $E$ if $f$ is
holomorphic in an open set containing $E$. Finally, if $f$ is holomorphic on $CC$,
we say $f$ is #index(entry: [entire functions])[entire].
#example[
The simplest example of a holomorphic function is the constant function $f(z) = c$.
Its derivative is $f'(z) = 0$.
]
#example[
The function $f(z) = z$ is entire. Its derivative is $f'(z) = 1$.
]
#example[
The real and image parts of a complex function $f(z) = z$:
+ $Re(z)$
+ $Im(z)$
are not holomorphic at any point.
To see $Re(z)$ is not holomorphic, we approach to $z = x + i y, space x, y in RR$ from
the real and imaginary axes, respectively. Approaching from the real axis, we
have
$
lim_(u -> 0) (Re(z + u) - Re(z)) / u
= lim_(u -> 0) (Re(x + i y + u) - Re(x + i y)) / u
= lim_(u -> 0) (x + u - x) / u = 1
$
and from the imaginary axis, we have
$
lim_(v -> 0) (Re(z + i v) - Re(z)) / (i v)
= lim_(v -> 0) (Re(x + i y + i v) - Re(x + i y)) / (i v)
= lim_(v -> 0) (x - x) / (i v) = 0
$<eq:5>
where $u, v in RR$. Since the two limits are different, $Re(z)$ is not
holomorphic at $z$.
#note[
In @eq:5, referring to the definition, we really should let $i v -> 0$. But in
this case, $i v -> 0$ is equivalent to $v -> 0$.
]
A similar argument shows that $Im(z)$ is not holomorphic either.
]
#example[
The complex conjugate function $f(z) = overline(z)$ is not holomorphic at any
point. This is because we can write the real and imaginary parts of $z$ as
$
Re(z) = (z + overline(z)) / 2 quad "and" quad Im(z) = (z - overline(z)) / (2 i)
$
If the conjugate $f(z) = overline(z)$ were to be holomorphic, then the real and
imaginary parts would also be holomorphic due to @prop:3. But we have shown in
the previous example that the real and imaginary parts of $z$ are not
holomorphic. Therefore, $f(z) = overline(z)$ is not holomorphic.
]
#proposition[
If $f$ and $g$ are holomorphic in an open set $Omega$, then:
+ $f + g$ is holomorphic in $Omega$ and $(f + g)' = f' + g'$.
+ $f dot g$ is holomorphic in $Omega$ and $(f dot g)' = f' g + f g'$.
+ If $g(z_0) != 0$, then $f/g$ is holomorphic at $z_0$ and
$
(f / g)'(z_0) = (f'(z_0) g(z_0) - f(z_0) g'(z_0)) / g(z_0)^2
$
]<prop:3>
#theorem(
title: [Chain Rule],
)[
Let $Omega, U subset.eq CC$ be open subsets. If $f: Omega -> U$ and $g: U -> CC$ are
holomorphic, then the composite function $g compose f$ is also holomorphic in $Omega$ and
its derivative is given by
$
(g compose f)'(z) = g'(f(z)) f'(z), quad z in Omega
$
]
== Power Series
Recall in real analysis, we defined the number $e$ as
$
e := sum_(n=0)^oo 1 / n!
$
and the exponential function $exp: RR -> RR$ as the power series
$
exp(x) := sum_(n=0)^oo x^n / n!, quad x in RR
$<eq:8>
Then, we showed an important property:
$
exp(x + y) = exp(x) exp(y), space forall x, y in RR
$<eq:6>
By applying @eq:6, it is easy to prove
+ $exp(n) = e^n, space forall n in NN$
+ $exp(1/n) = root(n, e) space forall n in NN$, which is proven by showing $(exp(1/n))^n = e$
It then follows that $exp(x)$ agrees with $e^x$ for every rational number $x in QQ$.
This tells us that we can extend the exponents of $e$ to real numbers:
$
e^x := exp(x), quad x in RR
$
Now, we can take one step further and extend the exponents of $e$ to complex
numbers. Define
$
exp(z) := sum_(n=0)^oo z^n / n!, quad z in CC
$<eq:7>
When $z in RR$, @eq:7 reduces to @eq:8.
== Contour Integration
Think about how to integrate a complex-valued function $f$ of a real variable $x$ on
a closed interval $[a, b]$. Naturally, the result should be a complex number
whose real part is the integral of $Re(f)$ and imaginary part is the integral of $Im(f)$.
#definition[
Let $f: [a, b] -> CC$ be a complex valued function. Suppose that $Re(f)$ and $Im(f)$ are
both integrable on $[a, b]$. We define the #index[complex integral] of $f$ on $[a, b]$ by
$
integral_a^b f(x) dif x := integral_a^b Re[f(x)] dif x + i integral_a^b Im[f(x)] dif x
$<eq:10>
]<def:1>
#theorem(
title: [Change of Variables],
)[
Suppose $g: [c, d] -> RR$ has a continuous derivative $g'$ on $[c, d]$. Let $f$ be
a real-valued continuous function on $g([c, d])$. Let $F$ be defined by
$
F(x) = integral_(g(c))^x f(t) dif t, quad x in g([c, d])
$
Then, for each $x in [c, d]$, the integral $integral_c^x f(g(t)) g'(t) dif t$ exists
and has value $F(g(x))$, i.e.,
$
integral_c^x f(g(t)) g'(t) dif t = F(g(x)) quad forall x in [c, d]
$<eq:12>
In particular, putting $x = d$ in @eq:12, we obtain the change of variables
formula:
$
integral_(g(c))^g(d) f(x) dif x = integral_c^d f(g(t)) g'(t) dif t
$
]<thm:1>
#theorem(
title: [Change of Variables for Complex-Valued Functions],
)[
Suppose $g: [c, d] -> RR$ has a continuous derivative $g'$ on $[c, d]$. Let $f$ be
a complex-valued continuous function on $g([c, d])$. Let $F$ be defined by
$
F(t) = integral_(g(c))^t f(x) dif x, quad t in g([c, d])
$
Then, for each $s in [c, d]$, the integral $integral_c^s f(g(x)) g'(x) dif x$ exists
and has value $F(g(s))$, i.e.,
$
F(g(s)) = integral_c^s f(g(x)) g'(x) dif x quad forall s in [c, d]
$<eq:13>
In particular, putting $s = d$ in @eq:13, we obtain the change of variables
formula:
$
integral_(g(c))^g(d) f(t) dif t = integral_c^d f(g(s)) g'(s) dif s
$
]<thm:2>
#proof[
By @def:1, we have
$
Re[F(t)] = integral_(g(c))^t Re[f(x)] dif x quad "and" quad
Im[F(t)] = integral_(g(c))^t Im[f(x)] dif x quad forall t in [c, d]
$
Apply @thm:1 to both $Re(f)$ and $Im(f)$, we have
$
Re[F(g(s))] &= integral_c^s Re[f(g(x))] g'(x) dif x quad forall s in [c, d] \
Im[F(g(s))] &= integral_c^s Im[f(g(x))] g'(x) dif x quad forall s in [c, d]
$
This yields @eq:13. The change of variables formula follows from @eq:13.
]
Thanks to the parameterizations of curves, we can reduce the complex integral of
a general complex function along a curve to the one like @eq:10.
#definition[
Let $gamma$ be a smooth curve parameterized by $z: [a, b] -> CC$, and $f$ a
continuous function on $gamma$. Then the #index(
entry: [complex integral of a function along a curve],
)[complex integral of $f$ along $gamma$] or the #index[contour integral] is
defined by
$
integral_gamma f(z) dif z := integral_a^b f(z(t)) z'(t) dif t
$<eq:11>
]
Recall for the same curve $gamma$, there may be multiple different but
equivalent parameterizations. And hence for different parameterizations, we have
different expressions on the right-hand side of @eq:11. However, we shall see
that the complex integral of a function along a curve is independent of the
parameterization, which means the integral is indeed well-defined.
Suppose $z: [a, b] -> CC$ and $w: [c, d] -> CC$ are two parameterizations of the
same curve $gamma$, and they are equivalent via $g: [c, d] -> [a, b]$. We need
to show
$
integral_a^b f(z(t)) z'(t) dif t = integral_c^d f(w(s)) w'(s) dif s
$
Since $g$ has a continuous derivate on $[c, d]$, we may apply @thm:2. We have
$
integral_a^b f(z(t)) z'(t) dif t &= integral_g(c)^g(d) f(z(t)) z'(t) dif t \
&= integral_c^d f(z(g(s))) z'(g(s)) g'(s) dif s \
&= integral_c^d f(z(g(s))) dif / (dif s)[z(g(s))] dif s \
&= integral_c^d f(w(s)) dif / (dif s) w(s) dif s \
&= integral_c^d f(w(s)) w'(s) dif s
$
This proves $integral_gamma f(z) dif z$ is independent of parameterizations.
If $gamma$ is a piecewise smooth curve, then the integral of $f$ along $gamma$ is
defined by the sum of the integrals of $f$ along each smooth piece of $gamma$.
Formally, suppose $gamma = gamma_1 * dots.c * gamma_n$ where each $gamma_j$ is
smooth. Then define
$
integral_gamma f(z) dif z := sum_(j=1)^n integral_(gamma_j) f(z) dif z
$
The length of a smooth curve $gamma = z(t), space t in [a, b]$ is defined by
$
len(gamma) := integral_a^b abs(z'(t)) dif t
$<eq:14>
#note[
The integral in @eq:14 exists because $abs(z'(t))$ is continuous on $[a, b]$.
The definition of length of a curve does not even require the knowledge of
complex integrals since $abs(z'(t))$ is a real-valued function. And one should
verify that @eq:14 is also independent of parameterizations.
]
Of course, the length of a piecewise smooth curve is defined by the sum of the
length of each smooth piece.
#proposition[
Complex integrals of continuous functions along curves satisfy the following
properties:
+ If $alpha, beta in CC$, then
$
integral_gamma (alpha f(z) + beta g(z)) dif z = alpha integral_gamma f(z) dif z + beta integral_gamma g(z) dif z
$
+ Let $gamma^-$ be the curve of $gamma$ with reverse orientation. Then
$
integral_(gamma^-) f(z) dif z = - integral_gamma f(z) dif z
$
]
#proof[
We prove each property as follows.
*Proof of 1:* The first property is proved by applying the linearity of
integrals of the real and imaginary parts of $f$ on each smooth piece of $gamma$.
*Proof of 2:* It suffices to prove for the case that $gamma$ is smooth. Let $gamma = z(t), space t in [a, b]$.
Then $gamma^- = z(b + a - s), space s in [a, b]$. We have
$
integral_(gamma^-) f(z) dif z &= integral_a^b f(z(b+a-s)) 1 / (dif s) [z(b+a-s)] dif s \
&= integral_a^b f(z(b+a-s)) (-1) z'(b+a-s) dif s \
&= - integral_a^b f(z(b+a-s)) z'(b+a-s) dif s \
&"Apply change of variables" t = g(s) = b+a-s \
&= - integral_b^a f(z(t)) z'(t) dot (-1) dif t quad "Note" a "and" b "are switched"\
&= - integral_a^b f(z(t)) z'(t) dif t \
&= - integral_gamma f(z) dif z
$
]
In many proofs, it is useful to find an upper bound for the quantity $abs(integral_gamma f(z) dif z)$.
Intuitively, it should be bounded by the maximum value of $abs(f(z))$ on $gamma$ times
the length of $gamma$.
#proposition(
title: [ML Inequality],
)[
Let $f$ be a continuous function defined on a curve $gamma$. Then
$
abs(integral_gamma f(z) dif z) <= max_(z in gamma) abs(f(z)) len(gamma)
$<eq:16>
]
Inequality @eq:16 is known as the #index(entry: [ML inequality])[ML inequality],
in which _M_ and _L_ stand for the _Maximum_ _Modulus_ of $f$ on $gamma$ and the _Length_ of $gamma$,
respectively.
#proof[
We will first prove the proposition for the case that $gamma$ is smooth, and
then extend it to the case that $gamma$ is piecewise smooth.
*Proof for the Smooth Curves:*
Assume $gamma$ is smooth. Let $gamma = z(t), space t in [a, b]$. Then we have
$
abs(integral_gamma f(z) dif z) &= abs(integral_a^b f(z(t)) z'(t) dif t) \
&<= integral_a^b abs(f(z(t))) abs(z'(t)) dif t
$<eq:15>
Because and $abs(f(z(t)))$ a real-valued continuous function on $[a, b]$ and $[a, b]$ is
compact, by @thm:5, $abs(f(z(t)))$ attains its maximum value $M = max_(t in [a, b]) abs(f(z(t)))$ on $[a, b]$.
Applying the same argument to $abs(f(z))$ on $gamma$, we find that $abs(f(z))$ attains
its maximum value $M' = max_(z in gamma) abs(f(z))$ on $gamma$. In fact, $M = M'$.
Then the right-hand side of @eq:15 can be further bounded by
$
integral_a^b abs(f(z(t))) abs(z'(t)) dif t &<= integral_a^b M abs(z'(t)) dif t \
&= M integral_a^b abs(z'(t)) dif t \
&= M len(gamma)
&"by definition of length of a curve"
$
This proves the proposition for smooth curves.
*Proof for the Piecewise Smooth Curves:* Suppose $gamma = gamma_1 + dots.c + gamma_n$ where
each $gamma_j$ is smooth. Then
$
abs(integral_gamma f(z) dif z) &= abs(integral_(gamma_1 + dots.c + gamma_n) f(z) dif z) \
&= abs(integral_(gamma_1) f(z) dif z + dots.c + integral_(gamma_n) f(z) dif z) \
&<= abs(integral_(gamma_1) f(z) dif z) + dots.c + abs(integral_(gamma_n) f(z) dif z) \
&"Apply the ML inequality to each smooth piece" \
&<= max_(z in gamma_1) abs(f(z)) len(gamma_1) + dots.c + max_(z in gamma_n) abs(f(z)) len(gamma_n) \
&"Pick the greatest value among all max's"\
&= max_(z in gamma) abs(f(z)) (len(gamma_1) + dots.c + len(gamma_n) )\
&= max_(z in gamma) abs(f(z)) len(gamma)
$
]
A #index[primitive] for $f$ in an open set $Omega$ is a function $F$ such that $F$ is
holomorphic in $Omega$ and $F'(z) = f(z) space forall z in Omega$. This term is
an analogy to the antiderivative for real functions.
#theorem(
title: [Second Fundamental Theorem of Calculus],
)[
Suppose $f: [a, b] -> RR$ is Riemann integrable on $[a, b]$. Let function $F$ be
defined on $[a, b]$ such that its derivate $F'$ exists in $(a, b)$ and
$
F'(x) = f(x) quad forall x in (a, b)
$
Moreover, we assume at the endpoints $a$ and $b$, the one-sided derivatives of $F$, $F(a+)$ and $F(b-)$,
both exist (as finite numbers). Then we have
$
integral_a^b f(x) dif x = F(b-) - F(a+)
$<eq:18>
]<thm:6>
Equation @eq:18 might not be the one the reader might be familiar with. The
usual one is
$
integral_a^b f(x) dif x = F(b) - F(a)
$
We will use the following example to show why we need to consider the one-sided
limits of $F$.
#example[
Let
$
f(x) = cases(2x sin(1/x) - cos(1/x) quad &x != 0, 0 &x = 0) space, quad x in [0, 2/pi]
$
and
$
F(x) = cases(x^2 sin(1/x) quad &x != 0, c &x = 0) space, quad x in [0, 2/pi]
$
where $c$ is some constant. Note that $F'(x) = f(x) space forall x in (0, 2/pi)$.
Hence, by @thm:6, we have
$
integral_0^(2/pi) f(x) dif x = F(2/pi-) - F(0+) = F(2/pi) - F(0+) = 4/pi^2 - 0 = 4/pi^2
$
In fact, the value $F(0) = c$ does not affect the integral since in the
computation, we used the right-hand limit $F(0+)$ instead of $F(0)$.
]
#theorem(
title: [Second Fundamental Theorem of Calculus for Contour Integration],
)[
Suppose $f: Omega -> CC$ is continuous and has a primitive $F$ in $Omega$. Let $gamma$ be
a curve in $Omega$ that starts at $z_0$ and ends at $z_1$. Then
$
integral_gamma f(z) dif z = F(z_1) - F(z_0)
$
]<thm:7>
#proof[
As usual, we first prove the theorem assuming $gamma$ is smooth, and then extend
it piecewise smooth curves.
*Proof for the Smooth Curves:* Let $gamma = z(t), space t in [a, b]$. The
function $F(z(t))$ has a derivate on $[a, b]$ by the chain rule since $z$ is
differentiable on $[a, b]$, and $F$ is holomorphic ar each point $z(t)$.
Moreover, the derivative of $F(z(t))$ is given by
$
dif / (dif t) F(z(t)) = F'(z(t)) z'(t) = f(z(t)) z'(t)
$<eq:17>
Note that $f(z(t)) z'(t)$ is continuous on $[a, b]$. Consequently, both its real
and imaginary parts are also continuous, and hence Riemann integrable on $[a, b]$.
Notice also that since the functions involved in @eq:17 are functions of a real
variable $t$, we have
$
Re[f(z(t)) z'(t)] &= Re[ dif / (dif t) F(z(t)) ] = dif / (dif t) Re[F(z(t))]\
Im[f(z(t)) z'(t)] &= Im[ dif / (dif t) F(z(t)) ] = dif / (dif t) Im[F(z(t))]
$
Then, we may apply @thm:6 to both $Re[f(z(t)) z'(t)]$ and $Im[f(z(t)) z'(t)]$:
$
integral_a^b Re[f(z(t)) z'(t)] dif t &= Re[F(z(b))] - Re[F(z(a))]
= Re[F(z_1) - F(z_0)] \
integral_a^b Im[f(z(t)) z'(t)] dif t &= Im[F(z(b))] - Im[F(z(a))]
= Im[F(z_1) - F(z_0)]
$
Adding the two equations above, we obtain
$
integral_gamma f(z) dif z = integral_a^b f(z(t)) z'(t) dif t = F(z_1) - F(z_0)
$
*Proof for the Piecewise Smooth Curves:* Suppose $gamma = gamma_1 + dots.c + gamma_n$ where
each $gamma_j$ is smooth, and $gamma_j$ starts at $w_(j-1)$ and ends at $w_j$ ($w_0 = z_0$ and $w_n = z_1$).
Then
$
integral_gamma f(z) dif z &= integral_(gamma_1) f(z) dif z + dots.c + integral_(gamma_n) f(z) dif z \
&"Apply this theorem to each smooth piece" \
&= sum_(j=1)^n (F(w_j) - F(w_(j-1))) \
&= F(w_n) - F(w_0)\
&= F(z_1) - F(z_0)
$
]
An immediate consequence of @thm:7 is that if $gamma$ is a closed curve, then
the contour integral will be zero.
#corollary[
Let $f: Omega -> CC$ be a continuous function that has a primitive $F$ in $Omega$.
If a curve $gamma$ in $Omega$ is closed, then
$
integral_gamma f(z) dif z = 0
$
]<cor:2>
#proof[
Let $gamma$ be parameterized by $z: [a, b] -> CC$ ($z(a) = z(b)$). (Note that $z(t)$ is
not necessarily continuously differentiable on $[a, b]$ since $gamma$ may be
only piecewise smooth.) We can split $gamma$ into two pieces. Let $alpha = z(t), space t in [a, (a+b)/2]$ and $beta = z(t), space t in [(a+b)/2, b]$.
Suppose $z_0 = z(a) = z(b)$ and $z_1 = z((a+b)/2)$. We have $gamma = alpha + beta$.
Note that curves $alpha$ and $beta^-$ both start at $z_0$ and end at $z_1$.
Therefore, by @thm:7, we have
$
integral_gamma f(z) dif z &= integral_alpha f(z) dif z + integral_beta f(z) dif z \
&= integral_alpha f(z) dif z - integral_(beta^-) f(z) dif z \
&= (F(z_1) - F(z_0)) - (F(z_1) - F(z_0)) \
&= 0
$
]
#corollary[
If $f$ is holomorphic in a connected open set $Omega$ and $f' = 0$, then $f$ is
constant.
]<cor:5>
#proof[
Pick a point $z_0 in Omega$. Because $Omega$ is connected, by @thm:8, there
exits a curve $gamma$ from $z_0$ to $z$ for any $z in Omega$. Since $f' = 0$ is
continuous, and $f$ is its primitive, @thm:7 is applicable. Integrating $f'$ along $gamma$,
we have
$
integral_gamma f'(z) dif z = f(z) - f(z_0)
$
Meanwhile,
$
integral_gamma f'(z) dif z = integral_a^b f'(z) z'(t) dif t
= integral_a^b 0 dot z'(t) dif t
= 0
$
Therefore, $f(z) = f(z_0)$ for all $z in Omega$. This proves $f$ is constant.
]
= Cauchy's Theorem and Its Applications
== Goursat's Theorem
Recall in previous chapter, we have seen in @cor:2 that if $f$ has a primitive
in an open set containing a closed curve $gamma$, then
$
integral_gamma f(z) dif z = 0
$
Now, assuming $f$ is holomorphic, we want to show that $f$ has a primitive in
some open set, and hence conclude that the integral of $f$ along any closed
curve in that open set is zero. We shall start from #index[Goursat's theorem].
#theorem(
title: [Goursat's Theorem],
)[
Let $Omega subset.eq CC$ be a open set and $T subset.eq Omega$ a triangle whose
interior is also contained in $Omega$. If $f$ is holomorphic in $Omega$, then
$
integral_T f(z) dif z = 0
$
]<thm:9>
We could state and prove Goursat's Theorem considering the counter integral
along a rectangle. But we will see in @cor:3 that the rectangle version is an
immediate corollary of this triangle version since we can divide a rectangle
into two triangles.
#proof[
Let $T^(0)$ denote the original triangle $T$, and let $d_0$ and $p_0$ denote the
diameter and perimeter of $T^(0)$, respectively. We will divide this triangle
into four smaller triangles, $T^(1)_1$, $T^(1)_2$, $T^(1)_3$, and $T^(1)_4$.
This is done by bisecting each side of $T^(0)$, and then connecting the
midpoints. The construction is illustrated in @fig:5.
#figure(
image("./figures/dividing-into-4-triangles.svg", width: 60%),
caption: [Dividing triangle $T$ into four smaller triangles.],
)<fig:5>
Note that each small triangle $T^(1)_j$ is positively oriented and has half the
diameter and half the perimeter of $T^(0)$, i.e, $d_1 = 1/2 d_0$ and $p_1 = 1/2 p_0$.
More importantly, we have
$
integral_(T^(0)) f(z) dif z = sum_(j=1)^4 integral_(T^(1)_j) f(z) dif z
$<eq:19>
In the big picture, we want to estimate an upper bound of the modulus of the
contour integral on the left-hand side of @eq:19. And then we will show that
that upper bound will tend to zero. Taking the modulus on both sides of @eq:19,
we have
$
abs(integral_(T^(0)) f(z) dif z) = abs(sum_(j=1)^4 integral_(T^(1)_j) f(z) dif z)
<= sum_(j=1)^4 abs(integral_(T^(1)_j) f(z) dif z)
<= 4 abs(integral_(T^(1)_(j_1)) f(z) dif z)
$
where $abs(integral_(T^(1)_(j_1)) f(z) dif z)$ is the maximum value among all
four moduli of integrals.
Now, we can further divide the triangle $T^(1)_(j_1)$ in a similar fashion to
obtain four even smaller triangles, and then further bound the value of $abs(integral_(T^(1)_(j_1)) f(z) dif z)$.
Repeat this process for $n$ times, we will have a sequence of triangles, ${T^n_(j_n)}$ with
$
d_n = 1 / 2^n d_0 quad "and" quad p_n = 1 / 2^n p_0 quad forall n in ZZ^+
$
And we have the following inequality:
$
abs(integral_(T^(0)) f(z) dif z) <= 4^n abs(integral_(T^n_(j_n)) f(z) dif z)
$<eq:20>
We want to show that the right-hand side of @eq:20 tends to zero as $n -> oo$.
#note[
It is appealing to apply the ML inequality directly to $integral_(T^n_(j_n)) f(z) dif z$.
Though the length of the triangle tends to zero, it is still $1/2^n p_0$, which
is not enough to cancel $4^n$ on the right-hand side of @eq:20. Hence, we need
to further exploit the fact that $f$ is holomorphic by estimating $f(z)$ about
some point $z_0$.
]
Let $cal(T)^n$ denote solid the union of the triangle $T^n$ and its interior. In
other words, it is the solid triangle. Clearly we have
$
cal(T^0) supset.eq cal(T^1) supset.eq dots.c supset.eq cal(T^n) supset.eq dots.c
$
and the diameter $diam cal(T)^n = diam T^n = d_n$ tends to zero as $n -> oo$ since $d_n = 1 / 2^n d_0$.
Therefore, by @cor:1, these solid triangles intersect at a single point, say $z_0$,
i.e, $sect.big_(n=0)^oo cal(T^n) = {z_0}$.
We now estimate $f(z)$ about point $z_0$. Because $f$ is holomorphic at $z_0$,
we can write
$
f(z) = f(z_0) + f'(z_0) (z - z_0) + psi(z) (z - z_0), quad z != z_0
$<eq:21>
where $psi(z)$ is a continuous function, and
$
lim_(z -> z_0) psi(z) = 0
$
Observe the right-hand side of @eq:21. We note that the function defined by the
sum of the first two term
$
g(z) = f(z_0) + f'(z_0) (z - z_0)
$
has a primitive
$
G(z) = f(z_0) (z - z_0) + 1/2 f'(z_0) (z - z_0)^2
$
Therefore, by @thm:7, the contour integral of $g$ along the triangle $T^n_(j_n)$ is
zero. It then follows that
$
integral_(T^n_(j_n)) f(z_0) dif z &= integral_(T^n_(j_n)) f(z_0) + f'(z_0) (z - z_0) + psi(z) (z - z_0) dif z \
&= integral_(T^n_(j_n)) f(z_0) + f'(z_0) (z - z_0) dif z + integral_(T^n_(j_n)) psi(z) (z - z_0) dif z \
&= integral_(T^n_(j_n)) psi(z) (z - z_0) dif z \
$<eq:22>
Applying the ML inequality to the last integral, we have
$
abs(integral_(T^n_(j_n)) psi(z) (z - z_0) dif z)
&<= max_(z in T^n_(j_n)) abs(psi(z)(z - z_0)) p_n \
&"Note that" abs(z - z_0) <= d_n space forall z in T^n_(j_n) \
&<= max_(z in T^n_(j_n)) abs(psi(z)) d_n p_n \
&"To ease the notation, let" epsilon_n = max_(z in T^n_(j_n)) abs(psi(z)) \
&= epsilon_n d_n p_n \
&= 1/4^n epsilon_n d_0 p_0
$<eq:23>
Combining @eq:20, @eq:22, and @eq:23, we have
$
abs(integral_(T) f(z) dif z) <= 4^n abs(integral_(T^n_(j_n)) f(z) dif z) <= epsilon_n d_0 p_0
$<eq:24>
Since $psi(z) -> 0$ as $z -> z_0$, we have $epsilon_n -> 0$ as $n -> oo$. Let $n -> oo$ at
both sides of @eq:24, we have $integral_(T) f(z) dif z = 0$. This completes the
proof.
]
#corollary[
If $f$ is holomorphic in an open set $Omega$ containing a rectangle $R$ and its
interior, then
$
integral_R f(z) dif z = 0
$
]<cor:3>
#proof[
We can split the rectangle $R$ into two triangles $T_1$ and $T_2$ by drawing a
diagonal. See @fig:6 for the illustration.
#figure(
image("./figures/dividing-a-rectangle-into-2-triangles.svg", width: 60%),
caption: [Dividing rectangle $R$ into two triangles.],
)<fig:6>
Then applying @thm:9 to each triangle, we have
$
integral_R f(z) dif z = integral_(T_1) f(z) dif z + integral_(T_2) f(z) dif z = 0
$
]
== Local Existence of Primitives and Cauchy's Theorem in a Disk
#theorem[
If $f$ is holomorphic in an open disk $D subset.eq CC$, then $f$ has a primitive
there.
]
#proof[
Without loss of generality, we may assume the disk $D$ is centered at the
origin. If it is centered at $z_0$, we can translate the disk to the origin and
define $tilde(f)(z) = f(z + z_0)$. Then we find a primitive for $tilde(f)$, say $tilde(F)$.
The primitive for $f$ is then given by $F(z) = tilde(F)(z - z_0)$.
Assume $D$ is centered at the origin, we are going to construct a primitive $F$ for $f$ in $D$ using
a contour integral. For any point $z in D$, curve $gamma_z$ is taken to be the
horizontal line segment from $0$ to $Re z$ followed by the vertical segment from $Re z$ to $z$.
Note that $gamma_z$ is indeed contained in $D$. Let function $F$ be defined by
$
F(z) = integral_(gamma_z) f(w) dif w
$
We will show $F$ is indeed a primitive for $f$ in $D$. Hence, we need to
estimate the quotient $(F(z+h) - F(z)) / h$ when $h -> 0$.
This invites us to consider the contour integral of $f$ along curve $gamma_(z_h) - gamma_z$.
As illustrated in @fig:7, by adding a rectangle and a triangle without change
the value of the contour integral due to @thm:9 and cor:3, one may verify that
$
F(z+h) - F(z)
= integral_(gamma_(z+h) - gamma_z) f(w) dif w
= integral_eta f(w) dif w
$<eq:25>
where $eta$ is the line segment from $z$ to $z+h$.
#figure(
image("./figures/adding-a-rectangle-and-a-triangle.svg", width: 60%),
caption: [
Construction of curve $eta$ by adding a rectangle and a triangle to the curve $gamma_(z+h) - gamma_z$.
],
)<fig:7>
Now, we are going to estimate $f(w)$ about the point $z$. Because $f$ is
continuous, we can write
$
f(w) = f(z) + psi(w), quad w in D without {z}
$
where $psi(w)$ is continuous and
$
lim_(w -> z) psi(w) = 0
$
#note[
Estimating $f(w)$ about $z$ using the derivate of $f$ at $z$, like what we did
in the proof of @thm:9, may be an overkill. It suffices to estimate $f(w)$ by
exploiting the continuity of $f$. We have already used the fact that $f$ is
holomorphic to construct the curve $eta$ by applying the Goursat's theorem.
]
It then follows that
$
integral_eta f(w) dif w
&= integral_eta f(z) + psi(w) dif w \
&= f(z) integral_eta 1 dif w + integral_eta psi(w) dif w \
&= f(z) h + integral_eta psi(w) dif w
$<eq:26>
Combining @eq:25 and @eq:26, we have
$
abs((F(z+h) - F(z)) / h - f(z))
&= 1 / abs(h) abs(integral_eta psi(w) dif w)\
&"Apply the ML inequality"\
&<= 1 / abs(h) max_(w in eta) abs(psi(w)) abs(h)\
&= max_(w in eta) abs(psi(w))
$<eq:27>
As $h -> 0$, we have $w -> z$ and hence $psi(w) -> 0$. Therefore, the limit of
the right-hand side of @eq:27 is $0$ as $h -> 0$. This proves $F'(z) = f(z)$.
]
#exercise[
Show that the values of the #index[Fresnel integrals] are given by
$
integral_0^oo sin x^2 dif x = integral_0^oo cos x^2 dif x = sqrt(2pi) / 4
$<eq:54>
]
#solution[
Let $f(z) = e^(-z^2)$. Consider the contour shown in @fig:10. By Cauchy's
Theorem, the integrals of $f$ along $ell_1 + gamma$ and $ell_2$ should be equal,
i.e.,
$
integral_(ell_1) f(z) dif z + integral_(gamma) f(z) dif z = integral_(ell_2) f(z) dif z
$<eq:49>
#figure(
image("./figures/contour-for-fresnel-integrals.svg", width: 60%),
caption: [
$ell_1 + gamma + ell_2^-$ is a sector, which is $1/8$ of a circle. We further
divide the curve $gamma$ into two pieces, $tilde(gamma)$ and $gamma_epsilon$.
$tilde(gamma)$ is the major piece while $gamma_epsilon$ is the minor one with
length $epsilon = pi / sqrt(R)$.
],
)<fig:10>
*On Curve $ell_1$:* The values of the Fresnel integrals are primarily
contributed by the integral along this curve. Let $ell_1$ be parameterized by $z(t) = t, space t in [0, R]$.
We have
$
integral_(ell_1) f(z) dif z
= integral_0^R e^(-t^2) dif t
$
As $R -> oo$, the right-hand side becomes the famous Gaussian integral
(actually, half of the Gaussian integral). We have
$
lim_(R -> oo) integral_(ell_1) f(z) dif z
= integral_0^oo e^(-t^2) dif t = sqrt(pi) / 2
$<eq:50>
*On Curve $ell_2$:* Let $ell_2$ be parameterized by $z(t) = t e^(i pi/4), space t in [0, R]$.
We have
$
integral_(ell_2) f(z) dif z
&= integral_0^R e^(-t^2 e^(i pi/2)) e^(i pi / 4) dif t\
&= e^(i pi/4) integral_0^R e^(-i t^2) dif t\
&= e^(i pi/4)( integral_0^R cos t^2 dif t + i integral_0^R sin t^2 dif t)\
&= (1/sqrt(2) + i/sqrt(2))( integral_0^R cos t^2 dif t + i integral_0^R sin t^2 dif t)\
&= 1/sqrt(2)(integral_0^R cos t^2 dif t - integral_0^R sin t^2 dif t) + i/sqrt(2) (integral_0^R cos t^2 dif t + integral_0^R sin t^2 dif t)
$<eq:51>
Next, we will show the contour integral along $gamma$ is zero when $R -> oo$. We
will show this using the ML inequality.
*On Curve $tilde(gamma)$:* On this major piece $tilde(gamma)$ of $gamma$, we
will show the M (the maximum modulus in the context of ML inequality) will
decays to $0$ as $R -> oo$. And the rate of decay is so fact that even though
the length L will tend to infinitely, M will cancel its increase.
For a point $z in tilde(gamma)$, write $z = R cos theta + i R sin theta$, the
modulus of $f$ is then given by
$
abs(f(z)) &= abs(e^(-z^2))\
&= abs(e^(-R^2(cos^2 theta - sin^2 theta)) e^(-i 2R^2 cos theta sin theta))\
&"The modulus of a pure imaginary number is zero"\
&= e^(-R^2(cos^2 theta - sin^2 theta))\
&= e^(-R^2 cos 2 theta)\
$
Because $0 <= theta <= pi/4 - pi / (R sqrt(R))$, the maximum modulus is taken
when $theta =pi/4 - pi / (R sqrt(R)) $:
$
abs(f(z)) <= e^(-R^2 sin (2pi) / (R sqrt(R))) quad forall z in tilde(gamma)
$
#note[
The length of $tilde(gamma)$ is
$
len(tilde(gamma)) = (pi R) / 4 - pi / sqrt(R) = O(R)
$
We need to find a way to cancel $O(R)$. First, note that the variable of the
sine function tends to zero as $R -> 0$. We need to use the limit
$
lim_(x -> 0) (sin x) / x = 1
$
to control the sine term. Then we will use the series expansion of $e^x$ to
generate a term with sufficient power of $R$ to cancel $O(R)$.
]
Next, we will further estimate the right-hand side. We have
$
e^(-R^2 sin pi / (R sqrt(R)))
&= e^(-2pi sqrt(R) dot (R sqrt(R))/(2pi) sin (2pi)/ (R sqrt(R)))\
&"To ease the notation, write" g(R) = 2pi sqrt(R) dot (R sqrt(R))/(2pi) sin (2pi)/ (R sqrt(R))\
&"Note" g(R) > 0 "when" R "is sufficiently large"\
&= e^(-g(R))\
&<= 1 / (1 + g(R) + 1/2 g^2(R) + 1/6 g^3(R))\
&<=1 / (1/6 g^3(R))
$<eq:46>
Since the term $(R sqrt(R))/(2pi) sin (2pi)/ (R sqrt(R)) -> 1$ in $g(R)$ as $R -> oo$,
we can conclude form @eq:46 that
$
abs(f(z)) <= e^(-R^2 sin pi / (R sqrt(R))) = O(1 / (R sqrt(R)))
$<eq:47>
On the other hand the length of $tilde(gamma)$ is
$
len(tilde(gamma)) = (pi R) / 4 - pi / sqrt(R) = O(R)
$<eq:48>
Combining @eq:46 and @eq:48, the ML inequality yields
$
abs(integral_tilde(gamma) f(z) dif z)
<= max_(z in tilde(gamma)) abs(f(z)) len(tilde(gamma))
= O(1 / (R sqrt(R))) O(R)
= O(1 / sqrt(R))
$
Therefore,
$
lim_(R -> oo) integral_tilde(gamma) f(z) dif z = 0
$<eq:52>
*On Curve $gamma_epsilon$:* Along this curve, we will show M is actually bounded
by $1$ and the length of $gamma_epsilon$ will tend to zero as $R -> oo$.
Similarly, the modulus of $f$ is given by
$
abs(f(z)) = e^(-z^2) = e^(-R^2 cos 2 theta), quad pi/4 - pi/(R sqrt(R)) <= theta <= pi / 4
$
Since $e^(-R^2 cos 2 theta)$ is a decreasing function, we have
$
abs(f(z)) <= 1 quad forall z in gamma_epsilon
$
The length of $gamma_epsilon$ is simply given by
$
len(gamma_epsilon) = pi / sqrt(R)
$
Therefore, by applying the ML inequality, we have
$
abs(integral_(gamma_epsilon) f(z) dif z) <= max_(z in gamma_epsilon) abs(f(z)) len(gamma_epsilon)
= 1 dot pi / sqrt(R)
$
Letting $R -> oo$, it follows that
$
lim_(R -> oo) integral_(gamma_epsilon) f(z) dif z = 0
$<eq:53>
Finally, combining @eq:49, @eq:50, @eq:51, @eq:52 and @eq:53 together, we find
the the Fresnel integrals indeed exist (the limits exist as $R -> oo$), and are
given by @eq:54.
]
== Cauchy's Integral Formulas
#theorem[
Let $D$ be an open disk, and $Omega$ an open set containing $overline(D)$. If $f$ is
holomorphic in $Omega$. Then for any point $z in D$, we have
$
f(z) = 1 / (2 pi i) integral_C f(zeta) / (zeta - z) dif zeta
$<eq:35>
where $C = diff D$ is the positively oriented circle boundary of $D$.
]<thm:10>
#proof[
We will consider the contour integrals of the integrand
$
g(zeta) = f(zeta) / (zeta - z), quad zeta in Omega without {z}
$
Consider the $Gamma_(delta, epsilon)$ be a keyhole contour illustrated in
@fig:8. Here $delta$ denotes width of the corridor and $epsilon$ is the radius
of the small arc $gamma_epsilon$ centered at $z$. The outer arc is denoted by $gamma$ and
the two line segments forming the corridor are denoted by $ell_1$ and $ell_2$.
Cauchy's Theorem tells us the counter integral along $Gamma_(delta, epsilon)$ is
zero, i.e.,
$
integral_gamma g(zeta) dif zeta
+ integral_(gamma_epsilon) g(zeta) dif zeta
+ integral_(ell_1) g(zeta) dif zeta
+ integral_(ell_2) g(zeta) dif zeta
= 0
$<eq:28>
#figure(image(
"./figures/keyhole-for-proving-the-cauchy-integral-formula.svg",
width: 60%,
), caption: [The keyhole contour $Gamma_(delta, epsilon)$.])<fig:8>
As $delta -> 0$, the corridor gets narrower and narrower, the integrals along $ell_1$ and $ell_2$ will
cancel each other. To see this, consider the illustration in @fig:9.
#figure(
image(
"./figures/adding-a-quadrilateral-to-two-line-segments.svg",
width: 60%,
),
caption: [By adding a quadrilateral to the two line segments, the sum of the contour
integrals along $ell_1$ and $ell_2$ is equivalently transformed to the sum of
contour integrals along $ell_3$ and $ell_4$. As $delta -> 0$, both lengths of $ell_3$ and $ell_4$ tend
to zero, and hence the contour integrals along them will also vanish by the ML
inequality.],
)<fig:9>
Meanwhile, as $delta -> 0$, the contour integrals along arcs will tend to the
integrals along the circles, i.e., $integral_(gamma) g(zeta) dif zeta -> integral_C g(zeta) dif zeta$ and $integral_(gamma_epsilon) g(zeta) dif zeta -> integral_(C_epsilon) g(zeta)dif zeta$.
Hence, letting $delta -> 0$, @eq:28 becomes
$
integral_C g(zeta) dif zeta + integral_(C_epsilon) g(zeta) dif zeta = 0
$<eq:29>
We now study the contour integral on $C_epsilon$. Note that
$
g(zeta) = f(zeta) / (zeta - z)
= (f(zeta) - f(z)) / (zeta - z) + f(z) / (zeta - z)
$<eq:31>
We claim that the first term on the right-hand side of the above equation is
bounded. This is because we may estimate $f(zeta)$ about point $z$ by (since $f$ is
holomorphic):
$
f(zeta) = f(z) + f'(z) (zeta - z) + psi(zeta) (zeta - z)
$<eq:30>
where $psi(zeta) -> 0$ as $zeta -> z$. Rearranging the terms in @eq:20, we have
$
(f(zeta) - f(z)) / (zeta - z) = f'(z) + psi(zeta)
$
Therefore, the modulus of the quotient $abs((f(zeta) - f(z)) / (zeta - z))$ is
bounded in a neighborhood of $z$. It then follows that
$
lim_(epsilon -> 0) integral_(C_epsilon) (f(zeta) - f(z)) / (zeta - z) dif zeta = 0
$<eq:32>
by applying the ML inequality. Reviewing @eq:31, we shall turn our attention to
the function $f(z) / (zeta - z)$ on $C_epsilon$. Let $C_epsilon^-$ be
parametrized by $zeta(t) = z + epsilon e^(i t), space t in [0, 2 pi]$. Then
$
integral_(C_epsilon) f(z) / (zeta - z) dif zeta
&= -integral_(C_epsilon^-) f(z) / (zeta - z) dif zeta\
&= -integral_0^(2 pi) f(z) / (epsilon e^(i t)) epsilon i e^(i t) dif t\
&= -f(z) integral_0^(2 pi) i dif t\
&= -2 pi i f(z)
$<eq:33>
which is in fact independent of $epsilon$. Therefore, as $epsilon -> 0$,
combining @eq:31, @eq:32, and @eq:33, we have
$
lim_(epsilon -> 0) integral_(C_epsilon) g(zeta) dif zeta = -2 pi i f(z)
$<eq:34>
Finally, combining @eq:29 and @eq:34, we have
$
integral_C g(zeta) dif zeta - 2 pi i f(z) = 0
$
which is exactly the Cauchy's integral formula @eq:35.
]
If we consider a rectangular keyhole instead of a circular one, then applying a
similar argument as in the proof of @thm:10, we will find that the function
value every point inside the rectangle can be evaluated by the contour integral
along the rectangle boundary:
$
f(z) = 1 / (2 pi i) integral_(R) f(zeta) / (zeta - z) dif zeta
$
#corollary[
Let $f$ be a holomorphic function in an open set $Omega$ containing a closed
disk $overline(D)$. Then $f$ is infinitely differentiable in $D$, and the $n$-th
derivative of $f$ at $z in D$ is given by
$
f^((n))(z) = n! / (2 pi i) integral_C f(zeta) / (zeta - z)^(n+1) dif zeta
$<eq:36>
where $C = diff D$ is the positively oriented circle boundary of $D$.
]
#note[
Of course, $f$ is in fact infinitely differentiable in $Omega$ since for any
point $z in Omega$, we can find a closed disk $overline(D)(z, r)$ centered at $z$ and
contained in $Omega$.
]
#proof[
We shall prove by induction.
*Base Case:* If $n = 0$, then this corollary is exactly @thm:10.
*Inductive Step:* Suppose the corollary holds for $n = k - 1$. We shall show it
holds for $n = k$. Let $z in D$. To show the $k$-th derivate of $f$ exits at $z$,
we consider the quotient
$
(f^((k-1))(z + h) - f^((k-1))(z)) / h
= (k-1) / (2 pi i) integral_C f(zeta) / h (1 / (zeta - z - h)^(k) - 1 / (zeta - z)^(k)) dif zeta
$<eq:37>
To simply the difference of the two terms in the integrand, we recall a useful
formula:
$
A^k - B^k
= (A - B) sum_(j=0)^(k-1) A^(k-1-j) B^j
= (A - B) (A^(k-1) + A^(k-2) B + dots.c + B^(k-1))
$<eq:38>
Substituting $A = 1 / (zeta - z - h)$ and $B = 1 / (zeta - z)$ in @eq:38, we
have
$
1 / (zeta - z - h)^k - 1 / (zeta - z)^k
&= (1 / (zeta - z - h) - 1 / (zeta - z)) sum_(j=0)^(k-1) 1 / (zeta - z - h)^(k-1-j) 1 / (zeta - z)^j\
&= h / ((zeta - z - h) (zeta - z)) sum_(j=0)^(k-1) 1 / (zeta - z - h)^(k-1-j) 1 / (zeta - z)^j
$<eq:39>
Plugging the right-hand sided of @eq:39 into the integral of @eq:37, we obtain
$
(f^((k-1))(z + h) - f^((k-1))(z)) / h
= 1 / (2 pi i) integral_C f(zeta) sum_(j=0)^(k-1) 1 / (zeta - z - h)^(k-1-j) 1 / (zeta - z)^j dif zeta
$<eq:40>
Letting $h -> 0$ on both sides of @eq:40, we see that limit of the quotient
indeed exists and
$
f^((k))(z)
&= (k-1)! / (2 pi i) integral_C f(zeta) / (zeta - z)^2 sum_(j=0)^(k-1) 1 / (zeta - z)^(k-1-j) 1 / (zeta - z)^j dif zeta\
&= (k-1)! / (2 pi i) integral_C f(zeta) / (zeta - z)^2 sum_(j=0)^(k-1) 1 / (zeta - z)^(k-1) \
&= (k-1)! / (2 pi i) integral_C f(zeta) / (zeta - z)^2 dot k / (zeta - z)^(k-1) \
&= k! / (2 pi i) integral_C f(zeta) / (zeta - z)^(k+1) dif zeta
$
This completes the proof.
]
Next, we will show that a holomorphic function is in fact analytic, and it is
given by its Taylor series.
But before, we present the theorem and its proof, we need to first review the
concepts of uniform convergence and term-by-term differentiation. What we aim to
achieve is that one can interchange the order of contour integration and sum of
complex functions under some conditions:
$
integral_gamma sum_(n=0)^oo f_n (z) dif z = sum_(n=0)^oo integral_gamma f_n (z) dif z
$
Recall that we can integrate a uniformly convergent series of real functions
term by term.
#theorem[
Suppose the series $sum f_n$ converges uniformly to $f$ on $[a, b]$ where each $f_n$ is
real-valued and is Riemann integrable on $[a, b]$. Then
+ $f$ is also Riemann integrable on $[a, b]$,
+ the series of functions $sum integral_a^x f_n (t) dif t$ (regarded as functions
of $x$) converges uniformly to $integral_a^x f(t) dif t$ on $[a, b]$, i.e.,
$
integral_a^x sum_(n=0)^oo f_n (t) dif t
= sum_(n=0)^oo integral_a^x f_n (t) dif t
$<eq:42>
Specially,letting $x = b$ in @eq:42, we have
$
integral_a^b sum_(n=0)^oo f_n (x) dif x
= sum_(n=0)^oo integral_a^b f_n (x) dif x
$
]
In the next lemma, we want to show that if we multiply a bounded function $g$ to
each term $f_n$ of a uniformly convergent series , then the series $sum f_n g$ also
converges uniformly.
The reason why we care about this result is that we are going to study the
series
$
sum_(n=0)^oo f_n (z(t)) z'(t)
$
where $sum f_n$ converges uniformly and we know $z'(t)$ is bounded.
#lemma[
Let $sum f_n$ be a series of complex-valued uniformly convergent series on $S subset.eq CC$.
If $g$ is a bounded function on $S$, then the series $sum f_n g$ converges
uniformly to $f g$ on $S$ where $f = sum f_n$.
]<lem:2>
#proof[
Suppose $abs(g(z)) <= M, space forall z in S$ where $M > 0$. Let $epsilon > 0$ be
arbitrary. Because $sum f_n$ converges uniformly to $f$ on $S$, there exists an
integer $N$ such that
$
abs(sum_(n=0)^m f_n (z) - f(z)) < epsilon / M quad forall z in S, forall m >= N
$
Multiplying both sides of the above inequality by the modulus of $g(z)$ yields
$
abs(sum_(n=0)^m f_n (z) g(z) - f(z) g(z)) < abs(g(z)) epsilon / M <= M dot epsilon / M = epsilon quad forall z in S, forall m >= N
$
This implies that $sum f_n g$ converges uniformly to $f g$ on $S$.
]
#corollary[
Suppose a series of complex-valued functions $sum f_n$ converges to $f$ uniformly
convergent on a piecewise smooth curve $gamma subset.eq CC$. Let $gamma$ be
parametrized by $z(t), space t in [a, b]$. Then the series $sum f(z(t)) z'(t)$ converges
uniformly to $f(t) z'(t)$ on $[a, b]$, i.e.,
$
sum_(n=0)^oo f_n (z(t)) z'(t) = f(t) z'(t)
$
]
#lemma[
Suppose a series of continuous complex-valued functions $sum f_n$ converges to $f$ uniformly
convergent on a piecewise smooth curve $gamma subset.eq CC$. Then
$
integral_gamma sum_(n=0)^oo f_n (z) dif z = sum_(n=0)^oo integral_gamma f_n (z) dif z
$
]<lem:1>
Finally, we are ready to prove that holomorphic functions are analytic.
#theorem[
Suppose $f$ is holomorphic in an open set $Omega$, and $D$ is an open disk
centered at $z_0$ whose closure is contained in $Omega$. Then $f$ has a power
series expansion at $z_0$:
$
f(z) = sum_(n=0)^oo (f^((n))(z_0)) / n! (z - z_0)^n quad forall z in D
$<eq:45>
]
#proof[
Applying Cauchy's integral formula to $f(z)$, we have
$
f(z) = 1 / (2 pi i) integral_C f(zeta) / (zeta - z) dif zeta
$<eq:43>
where $C = diff D$.
#note[
The highlight of the proof is to expand the integrand $f(zeta) / (zeta - z)$ as
a geometric series so that the infinite sum $sum$ may appear. And then we may
interchange the order of integration and summation.
]
The integrand can be written as
$
f(zeta) / (zeta - z) &= f(zeta) / (zeta - z_0) dot 1 / (1 - (z - z_0) / (zeta - z_0))\
&"Note that" 1 / (1 - (z - z_0) / (zeta - z_0)) "is the sum of a geometric series"\
&= f(zeta) / (zeta - z_0) sum_(n=0)^oo ((z - z_0) / (zeta - z_0))^n\
&= sum_(n=0)^oo f(zeta) / (zeta - z_0)^(n+1) dot (z - z_0)^n
$<eq:44>
Combining @eq:43 and @eq:44, we have
$
f(z)
= 1 / (2 pi i) integral_C sum_(n=0)^oo f(zeta) / (zeta - z_0)^(n+1) dot (z - z_0)^n dif zeta
$
#note[
We claim $f(zeta) / (zeta - z_0)^(n+1) dot (z - z_0)^n$ (a function of $zeta$)
converges uniformly on $C$. To see this, we may apply @lem:2 to argue that
because the series $sum (z - z_0)^n / (zeta - z_0)^(n+1)$ converges uniformly
(since it is a geometric series) and $f(zeta)$ is bounded on $C$ (since it is
continuous and $C$ is compact), the product $f(zeta) / (zeta - z_0)^(n+1) dot (z - z_0)^n$ also
converges uniformly on $C$.
]
Because $f(zeta) / (zeta - z_0)^(n+1) dot (z - z_0)^n$ converges uniformly on
the circle $C$, we may move the contour integration into the sum by @lem:1. We
have
$
f(z)
&= 1 / (2 pi i) sum_(n=0)^oo integral_C f(zeta) / (zeta - z_0)^(n+1) dot (z - z_0)^n dif zeta\
&"Transform the expression to conform to Cauchy's integral formula"\
&= sum_(n=0)^oo n! / (2 pi i) integral_C f(zeta) / (zeta - z_0)^(n+1) dif zeta dot (z - z_0)^n / n!\
&"Apply the Cauchy's integral formula"\
&= sum_(n=0)^oo f^((n)) (z_0) dot (z - z_0)^n / n!
$
]
A simple observation is that the power series in @eq:45 at $z$ will converge as
long as we can find a closed disk $overline(D)$ centered at $z_0$ that contains
this point $z$.
Using the Cauchy's integral formula @eq:36, we can easily approximate an upper
bound of the modulus of $n$-th derivative of a holomorphic function at a point
in a disk by @eq:41. It is known as the #index[Cauchy's inequality].
#corollary(
title: [Cauchy's Inequality],
)[
Let $D$ be an open disk centered at $z_0$ with radius $R$. If $f$ is holomorphic
in an open set containing $overline(D)$, then the $n$-th derivative of $f$ at $z_0$ is
bounded by
$
abs(f^((n))(z_0)) <= (n! norm(f)_C) / R^n
$<eq:41>
where $norm(f)_C = max_(z in C) abs(f(z))$ and $C = diff D$.
]<cor:4>
#proof[
Using the Cauchy's integral formula @eq:36, we have
$
abs(f^((n))(z_0))
&= abs(n! / (2 pi i) integral_C f(zeta) / (zeta - z_0)^(n+1) dif zeta)\
&= n! / (2 pi) abs(integral_C f(zeta) / (zeta - z_0)^(n+1) dif zeta)\
&<= n! / (2 pi) max_(zeta in C) abs(f(zeta)) / abs(zeta - z_0)^(n+1) dot 2pi R\
&"Note that" abs(zeta - z_0) = R space forall zeta in C\
&= (n! norm(f)_C) / R^n
$
]
Observe @eq:41. Let $n$ be fixed. As the radius $R$ becomes larger and larger,
the denominator on the right-hand side will tend to infinity. And if $f$ is
bounded globally, then $norm(f)_C$ is bounded, which implies the quotient on the
right-hand side will tend to zero. Then this inequality tells us that the
derivate of $f$ of any order vanishes if $f$ is defined and holomorphic on the
entire complex plane and is bounded. In particular the first order derivate $f'$ is
constantly zero, which means $f$ is in fact just a constant function. This
result is known as the #index[Liouville's theorem].
#theorem(title: [Liouville's Theorem])[
If $f$ is entire and bounded, then $f$ is constant.
]<thm:11>
#proof[
Suppose $abs(f(z)) < M space forall z in CC$ for some $M > 0$. For any disk
centered at the origin with radius $R$, applying Cauchy's inequality in @cor:4,
we have
$
abs(f'(z)) <= (norm(f)_C) / R < M / R quad forall R > 0
$
Letting $R -> oo$, we have $f'(z) = 0$. This implies $f$ is constant by @cor:5.
]
As an application of Liouville's theorem, we can provide a simple and elegant
proof of the #index[fundamental theorem of algebra].
#theorem(
title: [Fundamental Theorem of Algebra],
)[
Every polynomial with degree greater than $0$ with complex coefficients has a
root in $CC$.
]
#proof[
Let polynomial $p(z)$ be given by
$
p(z) = a_n z^n + dots.c a_1 z + a_0
$
where $n >= 1$ and $a_n != 0$. We shall prove by contradiction. Assume $p(z)$ has
no roots in $CC$. Then the reciprocal $1 / p(z)$ is defined on the entire
complex plane. Moreover, the derivate of $1 / p(z)$ clearly exists everywhere.
Therefore, $1 / p(z)$ is entire. We will use Liouville's theorem to establish a
contradiction. To do so, we are going $1 / p(z)$ is bounded.
We have
$
p(z) / z^n = a_n + a_(n-1) / z + dots.c + a_1 / z^(n-1) + a_0 / z^n
$
Note that when $abs(z) -> oo$, the modulus of the quotient $p(z) / z^n$ will
tend to $abs(a_n)$. This implies that there exists $R > 0$ such that
$
abs(p(z) / z^n) > abs(a_n) / 2
$<eq:55>
whenever $abs(z) > R$. Rearranging @eq:55, we have
$
abs(1 / p(z)) < 2 / abs(a_n) dot 1 / abs(z)^n < 2 / (abs(a_n) R^n) quad "if" abs(z) > R
$
The above inequality shows $1 / p(z)$ is bounded outside the disk $D$ centered
at $0$ with radius $R$.
For points inside the closed disk $overline(D)$, since function $abs(1 / p(z))$ is
continuous and $overline(D)$ is compact, $abs(1 / p(z))$ attains its maximum $M$ on $overline(D)$.
Therefore, we see that $1 / p(z)$ is indeed bounded on entire complex plane $CC$.
By Liouville's theorem @thm:11, $1 / p(z)$ is constant, which leads to a
contradiction since polynomials with degree greater than $0$ are non-constant.
#note[
The last assertion that polynomials with degree greater than $0$ are
non-constant seem evident. But the reader should still prove it. See @prop:4.
And the proof is not that trivial.
]
]
#proposition[
Polynomials with degree greater than $0$ are non-constant.
]<prop:4>
#proof[
To prove polynomial $p(z)$ is non-constant, we show that its derivative $p'(z)$ is
nonzero. And we will prove this by induction. Let hypothesis $P(n)$ be that the
polynomial
$
p(z) = a_n z^n + dots.c + a_1 z + a_0, quad a_n != 0
$
is nonzero for all nonnegative integer $n in NN$.
*Base Case:* If $n = 0$, then $p(z) = a_0 != 0$.
*Inductive Step:* Suppose $P(k)$ holds, we need to show $P(k+1)$ also holds. Let
$
p(z) = a_(k+1) z^(k+1) + dots.c + a_1 z + a_0, quad a_(k+1) != 0
$
Its derivative is
$
p'(z) = (k+1) a_(k+1) z^k + dots.c + 2a_2 z + a_1
$
Clearly, $p'(z)$ is a polynomial with degree $k$. Therefore, by the hypothesis $P(k)$, $p'(z)$ is
nonzero. This implies that $p(z)$ is non-constant. Specially, $p(z)$ is nonzero,
which shows $P(k+1)$ also holds.
Now, for any polynomial $p(z)$ with degree $n >= 1$ we have shown its derivate $p'(z)$,
which is a polynomial with degree greater than $0$ is a nonzero function.
Therefore, $p(z)$ is non-constant.
]
// References
#bibliography("complex-analysis.bib", title: "References")
// Indices
#index-page() |
|
https://github.com/zomvie-break/cv-typst | https://raw.githubusercontent.com/zomvie-break/cv-typst/main/modules/education.typ | typst | Apache License 2.0 | #import "../brilliant-CV/template.typ": *
#cvSection("Education")
#cvEntry(
title: [Bachelors of Science in Engineering],
society: [Technical University of Denmark, DTU],
date: [2017 - 2019],
location: [Denmark],
logo: "../src/logos/dtu.png",
description: list(
[Thesis: Alternatives in coping with surplus renewable energy based on the case study of Ndeda mini-grid in Kenya.],
[Courses: Mathematical Modeling #hBar() Introduction to Numerical Algorithms]
),
tags: ("Python", "Data Analysis", "Data Visualization")
)
#cvEntry(
title: [Bachelors of Science in Physics Engineering \*\*],
society: [Instituto Tecnológico y de Estudios Superiores de Monterrey, ITESM],
date: [2014 - 2016],
location: [Mexico],
logo: "../src/logos/itesm.png",
description: list(
[\*\* Completed 16 courses towards earning the degree.],
[Courses: Problem solving with Programming #hBar() Linear Algebra]
)
) |
https://github.com/MuShann/typst-graph | https://raw.githubusercontent.com/MuShann/typst-graph/main/calculate.typ | typst | // Set number precision
#let precise(data, prec: 5) = {
if type(data) == "angle" {return data/180deg*calc.pi}
let prec = calc.pow(10, prec)
data = calc.round(data*prec)/prec
if data < calc.round(1.63312395319537*prec)/prec*calc.pow(10, 16) {return data}
else {return calc.inf}
}
// Calculate function dictionary
#let calc_cases = (
"sin": calc.sin,
"cos": calc.cos,
"tan": calc.tan,
"ln": calc.ln,
"lg": calc.log,
"arcsin": calc.asin,
"arccos": calc.acos,
"arctan": calc.atan,
)
// Operators set
#let opers = ([+], [−], [∗], [⋅], [×], [ ])
// Calculate partial expressions
#let parse_calc_part(parse, math, var, val) = {
if type(math) == "array" {
let now_oper = math.at(0)
let now_val = (parse.calc_math)(parse, math.at(1), var, val)
if now_oper.has("text") {
return precise((calc_cases.at(now_oper.text))(now_val))
}
else {
return precise(calc.log(now_val, base: float(now_oper.b.text)))
}
}
else if math.has("t") {
let base = (parse.calc_math)(parse, math.base, var, val)
let index = (parse.calc_math)(parse, math.t, var, val)
return precise(calc.pow(base, index))
}
else if math.has("denom") {
let num = (parse.calc_math)(parse, math.num, var, val)
let denom = (parse.calc_math)(parse, math.denom, var, val)
return precise(num/denom)
}
else if math.has("radicand") {
let radicand = (parse.calc_math)(parse, math.radicand, var, val)
if math.has("index") {
let index = (parse.calc_math)(parse, math.index, var, val)
return precise(calc.pow(radicand, 1/index))
}
else {return precise(calc.sqrt(radicand))}
}
else if math == [e] {
return calc.e
}
else if math == [#var] {
return val
}
else if math.has("text") {
return int(math.text)
}
}
// Calculate expression
#let parse_calc_math(parse, math, var, val) = {
if math.has("body") and math.body.has("children") or math.has("children") {
let children = none
if math.has("children") {children = math.children}
else {children = math.body.children}
children = children.filter(x => x!=[(] and x!=[)])
let len = children.len()
let part_str = ()
for index in range(len) {
if children.at(index) in opers {continue}
if children.at(index).has("limits") or children.at(index).has("b") {
let next = none
for j in range(index+1, len) {
if children.at(j) == [ ] {continue}
next = children.at(j)
children.at(j) = [ ]
break
}
part_str.push(str((parse.calc_part)(parse, (children.at(index), next), var, val)))
}
else {part_str.push(str((parse.calc_math)(parse, children.at(index), var, val)))}
}
for (index, child) in children.filter(x => x != [ ]).enumerate() {
if child == [+] {part_str.insert(index, "+")}
else if child == [−] {part_str.insert(index, "-")}
else if child == [∗] or child == [⋅] or child == [×] {part_str.insert(index, "*")}
}
return eval(part_str.join())
}
else if math.has("body") {
return (parse.calc_part)(parse, math.body, var, val)
}
else {
return (parse.calc_part)(parse, math, var, val)
}
}
// Process tool
#let parse = (
calc_part: parse_calc_part,
calc_math: parse_calc_math
)
// Calculation program entry
#let calc_math(math, var, val) = {
parse_calc_math(parse, math, var, val)
}
|
|
https://github.com/Myriad-Dreamin/typst.ts | https://raw.githubusercontent.com/Myriad-Dreamin/typst.ts/main/fuzzers/corpora/visualize/gradient-repeat_00.typ | typst | Apache License 2.0 |
#import "/contrib/templates/std-tests/preset.typ": *
#show: test-page
#rect(
height: 40pt,
width: 100%,
fill: gradient.linear(..color.map.inferno).repeat(2, mirror: true)
)
|
https://github.com/7sDream/fonts-and-layout-zhCN | https://raw.githubusercontent.com/7sDream/fonts-and-layout-zhCN/master/chapters/02-concepts/dimension/kerns-2.typ | typst | Other | #import "/lib/draw.typ": *
#import "/lib/glossary.typ": tr
#import "/template/lang.typ": armenian
#import "kerns-1.typ": start, end, base, lt, rb, bbox1-lt, bbox1-rb, bbox-calc, line-color, down
#let lt2 = (rb.at(0) - 40, lt.at(1))
#let rb2 = (rb.at(0) + 330, rb.at(1))
#let (bbox2-lt, bbox2-rb) = bbox-calc(lt2, rb2, (30, 48, 20, down))
#let graph = with-unit((ux, uy) => {
// mesh(start, end, (100, 100), stroke: 1 * ux + gray)
rect(
lt, end: rb,
stroke: 6 * ux + red,
)
rect(
lt2, end: rb2,
stroke: stroke(
paint: green,
thickness: 6 * ux,
dash: (10 * ux, 2 * ux),
),
)
let line-stroke = 4 * ux + line-color
segment(
(0, base.at(1)), (end.at(0), base.at(1)),
stroke: line-stroke,
)
txt([#tr[baseline]], (0, base.at(1)), size: 48 * ux, anchor: "lb", dy: 8)
rect(bbox1-lt, end: bbox1-rb, stroke: line-stroke)
rect(bbox2-lt, end: bbox2-rb, stroke: (
paint: line-color,
thickness: line-stroke.thickness,
dash: (10 * ux, 2 * ux),
))
txt(armenian[Ր], base, size: 635 * ux, anchor: "lb", dx: 15)
txt(armenian[ձ], (lt2.at(0), base.at(1)), size: 635 * ux, anchor: "lb", dx: 0)
let arrow-y = rb.at(1) - 20
arrow((rb.at(0), arrow-y), (lt2.at(0), arrow-y), head-scale: 3, stroke: line-stroke)
txt([
#tr[kern] -140 单位
], ((rb.at(0) + lt2.at(0)) / 2, arrow-y),
anchor: "ct", dy: -25, size: 48 * ux,
)
})
#canvas(end, start: start, width: 50%, graph)
|
https://github.com/Enter-tainer/typstyle | https://raw.githubusercontent.com/Enter-tainer/typstyle/master/tests/assets/unit/comment/comment-in-func-call.typ | typst | Apache License 2.0 | #let f(a, b, c: none) = {
[#a]
}
#f(1, 2, c: 3)
#f[a][b]
#f(1, /* actually, b is ignored*/ 0, c: /* actually, c is ignored */ 0)
#set text(
size: 10pt,
fallback: false,
// lang: "de",
) |
https://github.com/raygo0312/Typst_template | https://raw.githubusercontent.com/raygo0312/Typst_template/main/template-document.typ | typst | #import "template-common.typ": *
#let font-size = 11pt
#let jarticle(
titlepage: false, // make a title page
title: "", // document title
office: "", // author's office
author: "", // author's name
date: false, // insert today's date
column: false,
it,
) = {
set document(
title: title,
author: author,
date: datetime.today()
)
// set the fonts for text
set text(
font: font-serif,
size: font-size,
)
// make a title
set page(numbering: "1") if not titlepage
align(center)[
#if titlepage {
v(100pt)
text(
size: 25pt,
font: font-sans,
)[
#title
]
v(100pt)
text(
size: 16pt,
)[
#office\
#author
]
v(100pt)
if date [
#text(
size: 16pt,
)[
#datetime.today().year()年#datetime.today().month()月#datetime.today().day()日
]
]
pagebreak()
} else {
text(
size: 17pt,
font: font-sans,
)[
#title
]
v(0.5em)
text(size: font-size)[
#if office != "" [
#office\
]
#author
]
parbreak()
if date [
#text(
size: font-size,
)[
#datetime.today().year()年#datetime.today().month()月#datetime.today().day()日
]
]
v(1em)
}
]
set page(numbering: "1") if titlepage
if titlepage {
counter(page).update(1)
}
// // section settings
set heading(numbering: "1.1")
show heading: it => {
set text(
font: font-sans,
weight: "regular",
)
v(font-size)
set par(first-line-indent: 0em)
counter(heading).display(
it.numbering
)
h(1em)
it.body
v(font-size)
}
// paragraph settings
set par(
leading: 0.8em,
first-line-indent: 1em,
justify: true,
)
show: it => {
if column {
columns(2)[#it]
} else {
it
}
}
show: it => common-style(it)
it
} |
|
https://github.com/esafwan/typst_doc | https://raw.githubusercontent.com/esafwan/typst_doc/main/README.md | markdown | MIT License | ## Typst Doc
Create better PDFs with Typst, a markup-based typesetting system as powerful as LaTeX but easier.
#### License
mit |
https://github.com/polarkac/MTG-Stories | https://raw.githubusercontent.com/polarkac/MTG-Stories/master/README.md | markdown | # MTG Stories
This is an archive of MTG stories publicly available on Wizard of the Coast website and compiled into PDF version. Images are also available either in PDF or as a separate files.
Stories are sorted into folder `stories` by set name and in published order.
Stories from Magic 2013 to Modern Masters 2015 are sorted with https://mtg.fandom.com/wiki/Magic_Story.
Stories from Magic Origins to March of the Machine: The Aftermath are sorted with https://mtglore.com/story-timeline-published-order/.
Stories from Wilds of Eldraine going forward sorted with https://mtgstory.com
To download and compile I wrote a small Python script, which is not part this repository.
If you want to download all the PDFs or complete stories in one big file (with or without images), use https://github.com/polarkac/MTG-Stories/releases
If you want to compile all stories into one big PDF yourself, use Typst source file `COMPLETE_STORIES.typ`.
# List of sets (in published order)
- Magic 2013
- Return to Ravnica
- Gatecrash
- Dragon's Maze
- Modern Masters
- Magic 2014
- Theros
- Commander (2013 Edition)
- Born of the Gods
- Duel Decks: Jace vs. Vraska
- Journey info Nyx
- Conspiracy
- Magic 2015
- Khans of Tarkir
- Commander (2014 Edition)
- Fate Reforged
- Dragons of Tarkir
- Modern Masters 2015
- Magic Origins
- Prologue to Battle for Zendikar
- Battle for Zendikar
- Commander (2015 Edition)
- Oath of the Gatewatch
- Shadows Over Innistrad
- Eternal Masters
- Eldritch Moon
- Conspiracy: Take the Crown
- Kaladesh
- Aether Revolt
- Amonkhet
- Hour of Devastation
- Ixalan
- Rivals of Ixalan
- Dominaria
- Core 2019
- Guilds of Ravnica
- Ravnica Allegiance
- War of the Spark
- Throne of Eldraine
- Theros: Beyond Death
- Ikoria: Lair of Behemoths
- Zendikar Rising
- Kaldheim
- Strixhaven: School of Mages
- Innistrad: Midnight Hunt
- Innistrad: Crimson Vow
- Kamigawa: Neon Dynasty
- Streets of New Capenna
- Pride Across the Multiverse
- Dominaria United
- The Brothers’ War
- Phyrexia: All Will Be One
- March of the Machine
- March of the Machine: The Aftermath
- Wilds of Eldraine
- Lost Caverns of Ixalan
- Murders at Karlov Manor
- Outlaws of Thunder Junction
- Bloomburrow
- Duskmourn: House of Horror
# Typst
I used [Typst](https://typst.app/) as typesetting system (modern version of LaTeX). Every story has source file `.typ` which can be used to compile your own PDF.
You can use web app - though I do not know how to work with own packages in web app - or better to use CLI version of Typst which you can download from https://github.com/typst/typst
Folder `typst_packages` has a small package `mtgstory` under `local` namespace which is used as base setting for all the stories. If you want to use it, you have to put it in your Typst package directory:
Windows: `%APPDATA/typst/packages/`
Linux: `~/.local/share/typst/packages/`
More info can be found https://github.com/typst/packages#local-packages
# Contribution
If you find any mistake or you want to contribute, feel free to send a pull request. You can also contact me at <EMAIL>.
|
|
https://github.com/cwreed/cv | https://raw.githubusercontent.com/cwreed/cv/main/src/utils.typ | typst | #import "metadata.typ": choiceColor
#let hBar() = [
#h(5pt) | #h(5pt)
]
#let autoImport(file) = {
include { "modules/" + file + ".typ" }
}
#let to-string(content) = {
if content.has("text") {
content.text
} else if content.has("children") {
content.children.map(to-string).join("")
} else if content.has("body") {
to-string(content.body)
} else if content == [ ] {
" "
}
}
#let fontList = ("Lato")
#let headerFont = ("Lato")
#let colors = (
sky: rgb("#7ca1bf"),
sage: rgb("#688567"),
clay: rgb("#ad6a55"),
flax: rgb("#dbbc74"),
)
#let regularColors = (
subtlegray: rgb("#ededee"),
lightgray: rgb("#343a40"),
darkgray: rgb("#212529"),
)
#let beforeSectionSkip = 1pt
#let beforeEntrySkip = 1pt
#let beforeEntryDescriptionSkip = 1pt
#let headerFirstNameStyle(str) = {
text(
font: headerFont,
size: 32pt,
weight: "light",
fill: regularColors.darkgray,
str,
)
}
#let headerLastNameStyle(str) = { text(font: headerFont, size: 32pt, weight: "regular", str) }
#let headerInfoStyle(str, accentColor) = { text(size: 10pt, fill: accentColor, str) }
#let headerQuoteStyle(str, accentColor) = { text(size: 10pt, weight: "medium", style: "italic", fill: accentColor, str) }
#let sectionTitleStyle(str, color: black) = { text(size: 16pt, font: fontList, weight: "bold", fill: color, str) }
#let entryA1Style(content) = {
text(size: 10pt, weight: "bold", content)
}
#let entryA2Style(str, accentColor) = {
align(
right,
text(weight: "medium", fill: accentColor, style: "oblique", str),
)
}
#let entryB1Style(str, accentColor) = { text(size: 8pt, fill: accentColor, weight: "medium", smallcaps(str)) }
#let entryB2Style(str) = {
align(
right,
text(size: 8pt, weight: "medium", fill: gray, style: "oblique", str),
)
}
#let entryDescriptionStyle(str) = {
text(fill: regularColors.lightgray, {
v(beforeEntryDescriptionSkip)
str
})
}
#let entryTagStyle(str) = { align(center, text(size: 8pt, weight: "regular", str)) }
#let entryTagListStyle(tags) = {
for tag in tags {
box(
inset: (x: 0.25em),
outset: (y: 0.25em),
fill: regularColors.subtlegray,
radius: 3pt,
entryTagStyle(tag),
)
h(5pt)
}
}
#let skillTypeStyle(str) = {
align(left, text(size: 10pt, weight: "bold", str))
}
#let skillInfoStyle(str) = { text(str) }
#let honorDateStyle(str) = {
align(right, text(str))
}
#let honorTitleStyle(str) = { text(weight: "bold", str) }
#let honorIssuerStyle(str) = { text(str) }
#let honorLocationStyle(str, accentColor) = {
align(
right,
text(weight: "medium", fill: accentColor, style: "oblique", str),
)
}
#let publicationStyle(str, firstName, lastName) = {
// Bold any instances of my name in the bibliography
let nameVersions = (
firstName + " " + lastName,
lastName + ", " + firstName.first() + ".",
firstName.first() + ". " + lastName,
)
show regex("(" + nameVersions.join("|") + ")"): it => text(weight: "bold", it)
text(str)
}
#let footerStyle(str) = { text(size: 8pt, fill: rgb("#999999"), smallcaps(str)) }
#let letterHeaderNameStyle(str, accentColor) = { text(fill: accentColor, weight: "bold", str) }
#let letterHeaderAddressStyle(str) = { text(fill: gray, size: 0.9em, smallcaps(str)) }
#let letterDateStyle(str) = { text(size: 0.9em, style: "italic", str) }
#let letterSubjectStyle(str, accentColor) = { text(fill: accentColor, weight: "bold", underline(str)) } |
|
https://github.com/EpicEricEE/typst-plugins | https://raw.githubusercontent.com/EpicEricEE/typst-plugins/master/equate/README.md | markdown | # equate
A package for improved layout of equations and mathematical expressions.
> [!WARNING]
> This repository has been archived. The package has been moved to the [EpicEricEE/typst-equate](https://github.com/EpicEricEE/typst-equate) repository.
When applied, this package will split up multi-line block equations into multiple elements, so that each line can be assigned a separate number. By default, the equation counter is incremented for each line, but this behavior can be changed by setting the `sub-numbering` argument to `true`. In this case, the equation counter will only be incremented once for the entire block, and each line will be assigned a sub-number like `1a`, `2.1`, or similar, depending on the set equation numbering. You can also set the `number-mode` argument to `"label"` to only number labelled lines. If a label is only applied to the full equation, all lines will be numbered.
This splitting also makes it possible to spread equations over page boundaries while keeping alignment in place, which can be useful for long derivations or proofs. This can be configured by the `breakable` parameter of the `equate` function, or by setting the `breakable` parameter of `block` for equations via a show-set rule. Additionally, the alignment of the equation number is improved, so that it always matches the baseline of the equation.
If you want to create a "standard" equation with a single equation number centered across all lines, you can attach the `<equate:revoke>` label to the equation. This will disable the effect of this package for the current equation.
## Usage
The package comes with a single `equate` function that is supposed to be used as a template. It takes two optional arguments for customization:
| Argument | Type | Description | Default |
| --------------- | ------------------- | ---------------------------------------------------------- | -------- |
| `breakable` | `boolean`, `auto` | Whether to allow the equation to break across pages. | `auto` |
| `sub-numbering` | `boolean` | Whether to assign sub-numbers to each line of an equation. | `false` |
| `number-mode` | `"line"`, `"label"` | Whether to number all lines or only those with a label. | `"line"` |
To reference a specific line of an equation, include the label at the end of the line, like in the following example:
```typ
#import "@preview/equate:0.2.0": equate
#show: equate.with(breakable: true, sub-numbering: true)
#set math.equation(numbering: "(1.1)")
The dot product of two vectors $arrow(a)$ and $arrow(b)$ can
be calculated as shown in @dot-product.
$
angle.l a, b angle.r &= arrow(a) dot arrow(b) \
&= a_1 b_1 + a_2 b_2 + ... a_n b_n \
&= sum_(i=1)^n a_i b_i. #<sum>
$ <dot-product>
The sum notation in @sum is a useful way to express the dot
product of two vectors.
```
### Local Usage
If you only want to use the package features on selected equations, you can also apply the `equate` function directly to the equation. This will override the default behavior for the current equation only. Note, that this will require you to use the `equate` function as a show rule for references, as shown in the following example:
```typ
#import "@preview/equate:0.2.0": equate
// Allow references to a line of the equation.
#show ref: equate
#set math.equation(numbering: "(1.1)", supplement: "Eq.")
#equate($
E &= m c^2 #<short> \
&= sqrt(p^2 c^2 + m^2 c^4) #<long>
$)
While @short is the famous equation by Einstein, @long is a
more general form of the energy-momentum relation.
```
As an alternative to the show rule, it is also possible to manually wrap each reference in an `equate` function, though this is less convenient and more prone to mistakes.
|
|
https://github.com/TypstApp-team/typst | https://raw.githubusercontent.com/TypstApp-team/typst/master/tests/typ/math/matrix-alignment.typ | typst | Apache License 2.0 | // Test matrix alignment math.
---
// Test alternating alignment in a vector.
$ vec(
"a" & "a a a" & "a a",
"a a" & "a a" & "a",
"a a a" & "a" & "a a a",
) $
---
// Test alternating explicit alignment in a matrix.
$ mat(
"a" & "a a a" & "a a";
"a a" & "a a" & "a";
"a a a" & "a" & "a a a";
) $
---
// Test alignment in a matrix.
$ mat(
"a", "a a a", "a a";
"a a", "a a", "a";
"a a a", "a", "a a a";
) $
---
// Test explicit left alignment in a matrix.
$ mat(
&"a", &"a a a", &"a a";
&"a a", &"a a", &"a";
&"a a a", &"a", &"a a a";
) $
---
// Test explicit right alignment in a matrix.
$ mat(
"a"&, "a a a"&, "a a"&;
"a a"&, "a a"&, "a"&;
"a a a"&, "a"&, "a a a"&;
) $
---
// Test #460 equations.
#let stop = {
math.class("punctuation",$.$)
}
$ mat(&a+b,c;&d, e) $
$ mat(&a+b&,c;&d&, e) $
$ mat(&&&a+b,c;&&&d, e) $
$ mat(stop &a+b&stop,c;...stop stop&d&...stop stop, e) $
---
// Test #454 equations.
$ mat(-1, 1, 1; 1, -1, 1; 1, 1, -1) $
$ mat(-1&, 1&, 1&; 1&, -1&, 1&; 1&, 1&, -1&) $
$ mat(-1&, 1&, 1&; 1, -1, 1; 1, 1, -1) $
$ mat(&-1, &1, &1; 1, -1, 1; 1, 1, -1) $
|
https://github.com/sses7757/sustech-graduated-thesis | https://raw.githubusercontent.com/sses7757/sustech-graduated-thesis/main/sustech-graduated-thesis/utils/state-notations.typ | typst | Apache License 2.0 | #import "style.typ": 字体
#let print-notations(abbr, name-en, name-cn) = {
if abbr == none {
none
} else {
([#abbr], [#name-cn（#name-en）])
}
}
#let smart-abbr(name-en, name-cn, abbr) = {
if abbr == none or abbr != auto {
abbr
} else {
let words = name-en.split(regex("[ \-]"))
let uppercase-count = words.map(w => w.matches(regex("[A-Z]")).len()).sum(default: 0)
if uppercase-count <= 1 {
words.map(w => upper(w.at(0))).sum(default: "")
} else {
words.map(w => w.matches(regex("[A-Z]")).map(m => m.text).sum(default: "")).sum(default: "")
}
}
}
#let notations = state("notations", (:))
#let notation-prefix = "no:"
#let notation-full-suffix = "-full"
// 创建或访问术语
// ### 参数
// - name-en: 英文名称
// - name-cn: 中文名称
// - abbr: 缩写，默认值为从name-en自动生成
// - full: 访问全称（true）或缩写（false）或无缩写全称（none）
// - args: 键值等内容
// ### 使用
// ```typst
// 创建：#notation("en", name-en: "English Name", name-cn: "中文名称", abbr: "EngN")
// 访问缩写：#notation("en")
// 创建无键值术语：#notation("", name-en: "English Name", name-cn: "中文名称")
// 或#notation("", "English Name", "中文名称")
// 或#notation("中文名称", "English Name") // 2个参数时顺序可互换
// ```
#let notation(..args, name-en: none, name-cn: none, abbr: auto, full: false) = {
assert(args.pos().all(x => type(x) == str) and args.named().values().all(x => type(x) == str), message: "all arguments must be string")
assert(args.pos().len() <= 3 and args.pos().len() >= 1, message: "invalid number of positional argument(s)")
// check named args
let _ = if "name-en" in args.named() {
name-en = if name-en == none {args.named().at("name-en")} else {name-en}
}
let _ = if "name-cn" in args.named() {
name-cn = if name-cn == none {args.named().at("name-cn")} else {name-cn}
}
// check positional args
let k = args.pos().at(0)
let _ = if args.pos().len() == 1 {
} else if args.pos().len() == 2 {
if args.pos().at(0).contains(regex("\p{script=Han}")) {
name-cn = if name-cn == none {args.pos().at(0)} else {name-cn}
name-en = if name-en == none {args.pos().at(1)} else {name-en}
} else {
name-cn = if name-cn == none {args.pos().at(1)} else {name-cn}
name-en = if name-en == none {args.pos().at(0)} else {name-en}
}
k = ""
} else {
if args.pos().at(1).contains(regex("\p{script=Han}")) {
name-cn = if name-cn == none {args.pos().at(1)} else {name-cn}
name-en = if name-en == none {args.pos().at(2)} else {name-en}
} else {
name-cn = if name-cn == none {args.pos().at(2)} else {name-cn}
name-en = if name-en == none {args.pos().at(1)} else {name-en}
}
k = args.pos().at(0)
}
// evalueate
let key = lower(k)
let c = context (
if key not in notations.get() {
if name-en == none or name-cn == none {
panic("Notation key \"" + key + "\" not found! Must provide name.")
}
let name = name-en
if name-en.matches(regex("[A-Z]")).len() == 0 {
name = name-en.split(" ").map(w => upper(w.at(0)) + w.slice(1)).join(" ")
name = name.split("-").map(w => upper(w.at(0)) + w.slice(1)).join("-")
}
if key == "" {
[#text(font: 字体.楷体, name-cn)（#name]
} else {
let value = (smart-abbr(name-en, name-cn, abbr), name, name-cn)
let ttt = notations.update(n => {
n.insert(key, value)
n
}
)
[#text(font: 字体.楷体, value.at(2))（#value.at(1)，#value.at(0)#ttt]
}
} else {
let value = notations.get().at(key)
if full == true {
[#text(font: 字体.楷体, value.at(2))（#value.at(1)，#value.at(0)]
} else if full == false {
[#value.at(0)]
} else {
[#text(font: 字体.楷体, value.at(2))（#value.at(1)]
}
}
)
if full == none or full or name-en != none {c + "）"} else {c}
} |
https://github.com/mattyoung101/uqthesis_eecs_hons | https://raw.githubusercontent.com/mattyoung101/uqthesis_eecs_hons/master/pages/bibliography.typ | typst | ISC License | = Bibliography
#bibliography("../thesis.bib", title: none, style: "institute-of-electrical-and-electronics-engineers")
|
https://github.com/liuguangxi/fractusist | https://raw.githubusercontent.com/liuguangxi/fractusist/main/tests/test-sierpinski-square-curve.typ | typst | MIT License | #set document(date: none)
#import "/src/lib.typ": *
#set page(margin: 1cm)
= n = 1
#align(center)[
#sierpinski-square-curve(1, step-size: 40)
]
= n = 2
#align(center)[
#sierpinski-square-curve(2, step-size: 15, fill-style: gray, stroke-style: none)
]
= n = 3
#align(center)[
#sierpinski-square-curve(3, step-size: 8, fill-style: silver, stroke-style: stroke(paint: orange, thickness: 3pt, cap: "round", join: "round"))
]
#pagebreak(weak: true)
= n = 4
#align(center)[
#sierpinski-square-curve(4, step-size: 4, fill-style: gradient.radial((orange, 0%), (silver, 100%), focal-center: (30%, 30%)), stroke-style: stroke(paint: gradient.linear(..color.map.crest, angle: 45deg), thickness: 2pt))
]
= n = 5
#align(center)[
#sierpinski-square-curve(5, step-size: 3, fill-style: gradient.linear(..color.map.crest, angle: 45deg), stroke-style: none)
]
#pagebreak(weak: true)
|
https://github.com/jgm/typst-hs | https://raw.githubusercontent.com/jgm/typst-hs/main/test/typ/text/tracking-spacing-00.typ | typst | Other | // Test tracking.
#set text(tracking: -0.01em)
I saw Zoe yӛsterday, on the tram.
|
https://github.com/oliver-ni/resume | https://raw.githubusercontent.com/oliver-ni/resume/main/main.typ | typst | MIT License | #import "template.typ": *
#show: project
#let title_items = (
sys.inputs.at("phone", default: none),
link("mailto:<EMAIL>"),
link("https://linkedin.com/in/oliverni")[#fab("linkedin") oliverni],
link("https://github.com/oliver-ni")[#fab("github") oliver-ni],
)
// Title row.
#align(center)[
#block(text(weight: 700, size: 1.5em)[<NAME>])
#title_items.filter(x => x != none).join([#h(0.5em)•#h(0.5em)])
]
= Education
#entry[
== University of California, Berkeley
Electrical Engineering and Computer Sciences, B.S. \
Mathematics, B.A.
][
*Expected Graduation:* May 2026 \
*Grade:* 4.0/4.0 \
\* currently taking course
]
*Relevant Coursework:*
Data Structures
· Computer Architecture
· Operating Systems
· Graphics\*
· Structure & Interpretation of Computer Programs
· Discrete Mathematics & Probability Theory
· Linear Algebra
· Abstract Algebra
· Real Analysis
· Category Theory\*
// #h(1fr) \* currently taking course
= Experience
#entry[
== Pokétwo
_Creator, Lead Developer_
][May 2020 -- Present]
- Created Pokémon-themed game chatbot enabling *5 million users* across *1 million communities* to connect online.
- Managed distributed Linux server cluster handling *10,000+ requests per second* with Kubernetes, RabbitMQ, gRPC, and Redis.
- Optimized MongoDB database to efficiently accommodate complex queries across 1.7 billion documents.
#entry[
== Apple
_Hardware Technology Intern_
][June -- August 2023]
- Accelerated wireless simulation workflow by building unified internal platform for data processing and visualization.
- Designed and implemented specialized query language using *parsing expression grammars* and executed them in *ClickHouse*.
#entry[
== UC Berkeley AUTOLab
_Undergraduate Researcher, Systems Administrator_
][August 2023 -- Present]
- Managed GPU compute cluster and desktop workstations for *30+ researchers* in robotics, computer vision, and machine learning.
- Deployed centralized authentication server supporting LDAP, enabling single sign-on across all lab workstations and servers.
- Automated deployment and configuration of new workstations with Ansible, reducing setup time from hours to minutes.
#entry[
== UC Berkeley Open Computing Facility
_Site Manager_
][July 2023 -- Present]
- Administered Linux infrastructure serving *petabytes of data* annually for *80,000+ students and faculty* as technical lead.
- Architected and built new bare-metal Kubernetes infrastructure, directing migration of *40+ services* from legacy systems.
- Developed bespoke Infrastructure-as-Code tool to declaratively automate continuous building and deployment on the new cluster.
// #entry[
// == Apple Pi Learning
// _Deep Learning Course Instructor_
// ][June -- September 2020]
// - Prepared and taught 12-week course on Deep Learning fundamentals (linear algebra and calculus for feed-forward NNs).
// - Guided students to create their own projects using deep learning models to classify images.
// #entry[
// == Project Code Foundation
// _President, Instructor_
// ][April 2018 -- June 2022]
// - Directed 2 middle school hackathons (200+ concurrent participants each) with workshops on Python, Unity, Swift, and AI.
// - Oversaw 30+ free online programming classes taught to *1,100+ youth* total; personally wrote and taught 6 six-week courses.
// #entry[
// == Lynbrook High School
// _Teaching Assistant, AP Computer Science A_
// ][August 2021 -- June 2022]
// - Modernized assignment download and submission for *180+ students* by designing and developing VS Code autograder system.
// // - Enabled CS department to migrate curriculum from older Eclipse IDE for smoother learning experience.
// - Taught students Java, data structures (BSTs, heaps, hash tables), and algorithms (searching, sorting, graph traversals).
= Projects
#entry[
== ContestDojo
_TypeScript · React · Next.js · Remix · Firebase_
][February 2021 -- Present]
- Built online math competition platform hosting over *11,000+ students* in the *Stanford* and *Berkeley* Math Tournaments.
- Designed atomic grading system enabling *1,000+ tests* to be graded in parallel within 20 minutes, reducing manpower by 95%.
// - Designed and implemented atomic grading system enabling *1,000+ tests* to be graded in parallel within minutes.
// - Reduced required manpower to grade tests by *95%* while simultaneously enabling more flexible answer formats.
// - Empowered independent student groups around the world to run their own math tournaments, inspired by SMT and BMT.
#entry[
== Lynbrook Mobile App
_Python · Django · PostgreSQL · TypeScript · React Native_
][September 2019 -- June 2022]
- Developed cross-platform iOS and Android app enabling *1,400+ students* to keep up with news from the school and their clubs.
- Automated attendance tracking for *20+ clubs*, unifying dozens of Google forms and eliminating hours of manual work per week.
// - Trained team of *5* other students in React & React Native to continue improving the app after my own graduation.
= Technical Skills
#let TeX = style(styles => {
set text(font: "New Computer Modern")
let e = measure("E", styles)
let T = "T"
let E = text(1em, baseline: e.height * 0.31, "E")
let X = "X"
box(T + h(-0.15em) + E + h(-0.125em) + X)
})
#let LaTeX = style(styles => {
set text(font: "New Computer Modern")
let a-size = 0.66em
let l = measure("L", styles)
let a = measure(text(a-size, "A"), styles)
let L = "L"
let A = box(scale(x: 105%, text(a-size, baseline: a.height - l.height, "A")))
box(L + h(-a.width * 0.67) + A + h(-a.width * 0.25) + TeX)
})
*Programming Languages:* Python · JavaScript · TypeScript · Rust · Elixir/OTP · C · Java · SQL
*Infrastructure and Tools:* Docker · Kubernetes · Nix · NixOS · Ansible · #LaTeX · Typst · Linux · Git · GitHub Actions
*Web Frameworks:* React · React Native · Next.js · Remix · Svelte · SvelteKit · Vue.js · Django · Flask · Starlette · Phoenix
*Other Technologies:* NumPy · PyTorch · Pandas · gRPC · PostgreSQL · MongoDB · Redis · Prometheus · Grafana
= Honors & Awards
#let award(title, description) = entry(
below: 1em,
[=== #title],
description
)
#award(
"USA Computing Olympiad, Platinum Contestant",
"Top ~500 pre-college students in US (2022)"
)
#award(
"Advent of Code, Global Rank 17",
"17/225,000+ (2023) · 29/250,000+ (2022) · 34/175,000+ (2020)"
)
#award(
"American Invitational Mathematics Examination, Qualifier",
"Top 5% of AMC 12 participants (2019, 2021, 2022)"
)
#award(
"USA Physics Olympiad, Semifinalist",
"Top ~400 pre-college students in US (2020, 2022)"
)
#award(
"<NAME>",
"Developed extensive leadership and planning skills through my 8-year scouting journey."
)
|
https://github.com/Area-53-Robotics/53E-Notebook-Over-Under-2023-2024 | https://raw.githubusercontent.com/Area-53-Robotics/53E-Notebook-Over-Under-2023-2024/giga-notebook/entries/management-road-to-states/entry.typ | typst | Creative Commons Attribution Share Alike 4.0 International | #import "/packages.typ": notebookinator
#import notebookinator: *
#import themes.radial.components: *
#show: create-body-entry.with(
title: "Management: Road to States",
type: "management",
date: datetime(year: 2024, month: 2, day: 11),
author: "<NAME>",
witness: "Violet Ridge",
)
We have a limited amount of time before states, so we need to plan out the
timeline we want to follow in 4 weeks we have leading up to it.
= Priorities
Based on what we've seen at the three consecutive tournaments we've been to,
performance during the autonomous period and driver experience are much more
important than the build of the robot.
We decided that the issues on the intake were the highest priority subsystem
that needed repairing, so we allocated a week to redesign and build it. This is
by far our most used subsystem, so we need to make sure that it works 100% of
the time.
Any remaining time would be allocated to driver and autonomous practice.
= Gantt Chart
We've created a Gantt chart to visualize what we've planned:
#gantt-chart(
start: datetime(year: 2024, month: 2, day: 10),
end: datetime(year: 2024, month: 3, day: 2),
date-interval: 7,
tasks: (
("Intake Rebuild", (0, 1)),
("Autonomous Skills", (1, 4)),
("Driver Practice", (1, 4)),
),
goals: (("State Championship", 4),),
)
|
https://github.com/Bit-Part-Young/report-template-MMMS-typst | https://raw.githubusercontent.com/Bit-Part-Young/report-template-MMMS-typst/main/template.typ | typst | #import "@preview/codly:0.2.1": *
#import "@preview/tablex:0.0.8": tablex, hlinex
#import "@preview/tablem:0.1.0": tablem
#import "@preview/outrageous:0.1.0"
#import "@preview/cuti:0.2.1": show-cn-fakebold
// reference: https://github.com/lucifer1004/pkuthss-typst/blob/main/template.typ
#let 字号 = (
初号: 42pt,
小初: 36pt,
一号: 26pt,
小一: 24pt,
二号: 22pt,
小二: 18pt,
三号: 16pt,
小三: 15pt,
四号: 14pt,
中四: 13pt,
小四: 12pt,
五号: 10.5pt,
小五: 9pt,
六号: 7.5pt,
小六: 6.5pt,
七号: 5.5pt,
小七: 5pt,
)
#let 字体 = (
仿宋: ("Times New Roman", "FangSong"),
宋体: ("Times New Roman", "SimSun"),
黑体: ("Times New Roman", "SimHei"),
楷体: ("Times New Roman", "KaiTi"),
代码: ("New Computer Modern Mono", "Times New Roman", "SimSun"),
得意黑: ("Smiley Sans",),
)
// 封面设置
#let CoverInfo(
ClassName: "",
ReportName: "",
Name: "",
StudentID: "",
School: "",
) = {
set text(font: 字体.宋体)
set page(numbering: none)
set align(center)
figure(
image(
"assets/Icons/banner_zh_sjtu.png",
width: 75%,
)
)
v(-2em)
figure(
image(
"assets/Icons/banner_eng_sjtu.png",
width: 75%,
)
)
v(-1.5em)
figure(
image(
"assets/Icons/badge_sjtu.png",
width: 30%,
)
)
v(2em)
par(
text(
font: 字体.黑体,
size: 字号.二号,
weight: "bold",
[#ClassName] + "\n",
)
)
par(
text(
font: 字体.黑体,
size: 字号.三号,
weight: "bold",
"实验报告 - " + [#ReportName],
)
)
v(4em)
let info-key(key) = {
rect(
width: 100%,
stroke: none,
text(
font: 字体.黑体,
size: 字号.四号,
weight: "bold",
strong(key)
),
)
}
let table-stroke = 0.5pt
let info-value(value) = {
rect(
width: 100%,
stroke: (bottom: table-stroke + black),
text(
font: 字体.黑体,
size: 字号.四号,
bottom-edge: "descender",
value,
),
)
}
grid(
columns: (80pt, 160pt),
row-gutter: 1em,
column-gutter: 3pt,
info-key(text("姓") + h(2em) + text("名：")), info-value[#Name],
info-key(text("学") + h(2em) + text("号：")), info-value[#StudentID],
info-key(text("学") + h(2em) + text("院：")), info-value[#School],
)
v(8em)
text(
font: 字体.黑体,
size: 字号.三号,
weight: "bold",
datetime.today().display("[year]年[month]月[day]日"),
)
pagebreak(weak: true)
}
// 目录设置
#let ChineseOutline() = {
set text(font: 字体.宋体, size: 字号.小四)
show: show-cn-fakebold
set align(center)
set page(numbering: "I")
counter(page).update(1)
set par(
justify: true,
first-line-indent: 2em,
)
// 一级目录字体、间距设置
show outline.entry.where(
level: 1
): it => {
set text(size: 字号.中四)
v(2pt)
strong(it)
}
// outrageous 目录设置
show outline.entry: outrageous.show-entry.with(
..outrageous.presets.typst,
fill: (none, auto),
)
outline(
title: text("目录"),
indent: 1em,
)
pagebreak(weak: true)
}
// 报告模板
#let ReportTemplate(
ClassName: "",
ReportName: "",
Name: "",
StudentID: "",
School: "",
body
) = {
/* ################### 封面设置 ###################### */
CoverInfo(
ClassName: ClassName,
ReportName: ReportName,
Name: Name,
StudentID: StudentID,
School: School,
)
/* ################### 目录设置 ###################### */
ChineseOutline()
/* ################### 正文设置 ###################### */
// 字体设置
show: show-cn-fakebold
set text(font: 字体.宋体, size: 字号.小四)
// 数学公式标号格式: (章节.数字)
set math.equation(numbering: num =>
"(" + str(counter(heading).get().first()) + "." + str(num) + ")")
// 标题编号
set heading(numbering: "1.1.1.1.")
set page(
// 页眉设置
header: context {
set text(font: 字体.宋体, size: 字号.小五)
set par(leading: 12pt)
show par: set block(spacing: 0pt)
v(-6pt)
line(length: 100%, stroke: 2.2416pt)
v(-8pt)
line(length: 100%, stroke: 0.7472pt)
v(12pt)
},
// 页脚设置
footer: context {
set align(center)
set text(size: 字号.小五)
counter(page).display()
}
)
set par(
first-line-indent: 2em,
justify: true,
)
// 解决标题后首段无法正确缩进问题
// 在标题后面添加空白段 使得首段不再是首段
show heading: it => {
it
par(leading: 1.5em)[#text(size:0.0em)[#h(0.0em)]]
}
counter(page).update(1)
body
}
// 编程语言图标
#let icon(codepoint) = {
box(
height: 0.8em,
baseline: 0.05em,
image(codepoint)
)
h(0.1em)
}
// 三线表
#let three-line-table = tablem.with(
render: (columns: auto, ..args) => {
tablex(
columns: columns,
auto-lines: false,
align: center + horizon,
hlinex(y: 0),
hlinex(y: 1),
..args,
hlinex(),
)
}
)
|
|
https://github.com/Besthope-Official/backend | https://raw.githubusercontent.com/Besthope-Official/backend/master/camp/qa/slim.typ | typst | #import "@preview/cuti:0.2.1": show-cn-fakebold
#show: show-cn-fakebold
#let title = [2024奇点后端部面试]
#set text(font: ("Source Han Serif SC"))
#set page(
header: align(right + horizon, title),
background: image("backend_logo_opacity_0.25.png", fit: "cover", width: 30%),
numbering: "1",
number-align: right,
)
#align(center, text(20pt)[
*#title*
])
#show link: underline
= 面试题
== 背景
后端的一大任务是将数据*持久化存储*，换句话说，就是将数据存储到*数据库*，以文件的形式存放到服务器的*硬盘*上。
例如，为了存放用户数据，会对“用户”这个概念进行*抽象*，即，用 `user` 的数据结构来记录用户的关键信息，如手机号、用户名、密码等。
在关系型数据库中，我们会用*表格*来存放数据，表中的每一*列*（字段）代表数据的某个属性，每一*行*则代表一个数据记录。每个表都应当有*主键*，作为一条数据的唯一标识，如学生学号。*关系*则用来表示数据对象之间的关联，如：学生和课程之间是多对多关系。
== 任务
设计微信红包的*数据库表结构*，并绘制一张实体关系图。
== 要求
*红包*能够作为*消息*出现在*群聊*中，可以被*用户*发出和接收，可以查看*用户领取的状态*。
*Bonus*：针对红包发放这样的*高并发场景*，在数据库*选用*和*设计*上，你可以做出哪些性能方面的优化？
== 提示
实体关系图可以参考下面这张图绘制：
- 用矩形表示实体、椭圆形表示属性、菱形表示关系。
- 在表示关系的连线上，1:N 表示一对多关系，M:N 表示多对多关系。
- 文字下方加下划线表示作为主键的属性。
#figure(image("example.jpg", height: 35%), caption: "选课系统的数据库表ER图例")
== 绘图区
```
Happy hacking :)
```
|
|
https://github.com/The-Notebookinator/notebookinator | https://raw.githubusercontent.com/The-Notebookinator/notebookinator/main/docs/src/installation.md | markdown | The Unlicense | # Installation
```admonish warning
This installation process is temporary, as we wait for Typst to overhaul its
process for packaging templates and packages.
```
## Devcontainer / Codespaces
The easiest way to use the Notebookinator is to use our devcontainer/codespace. This will automatically install all of the needed dependencies inside of a Docker container. We recommend using our [quick start template](https://github.com/The-Notebookinator/quick-start-template) for the best experience.
```admonish warning
While this approach is easier, you may encounter some performance issues as your notebook increases in size.
```
The only thing you'll need in preparation is a [GitHub](https://github.com/) account (only if using Codespaces) and [VSCode](https://code.visualstudio.com/) installed. Once you do that, just follow the instructions in the [README](https://github.com/The-Notebookinator/quick-start-template).
## Local Installation
This installation process is a little harder, and requires more software to be manually installed on your computer.
Make sure you have the following software installed:
- [Typst](https://github.com/typst/typst?tab=readme-ov-file#installation)
- [Git](https://git-scm.com/downloads)
- [VSCode](https://code.visualstudio.com/)
Once you've installed everything, run the following commands:
```admonish info
If you're running this on Windows, you'll need to run these commands in a sh
shell, like git-bash or the shell packaged with Cygwin or GitHub Desktop.
```
```bash
git clone --depth 1 --branch 1.0.1 https://github.com/The-Notebookinator/notebookinator
./notebookinator/scripts/package @local
rm -rf notebookinator
```
Once you do that you should be good to go!
|
https://github.com/TypstApp-team/TypstApp | https://raw.githubusercontent.com/TypstApp-team/TypstApp/main/README.md | markdown | # Typst App
iOS app for editing & viewing typst docs.
## Development
### Setup
* xcode tools: `xcode-select --install`
* rust toolchains: `curl https://sh.rustup.rs -sSf | sh`
* targets: `rustup target add aarch64-apple-ios aarch64-apple-ios-sim`
* cargo-lipo: `cargo install cargo-lipo`
> credit: https://mozilla.github.io/firefox-browser-architecture/experiments/2017-09-06-rust-on-ios.html
## Compile
Debug (for simulator)
```bash
cd typst
cargo lipo --release --targets aarch64-apple-ios-sim
```
|
|
https://github.com/fenjalien/metro | https://raw.githubusercontent.com/fenjalien/metro/main/tests/num/output-decimal-marker/test.typ | typst | Apache License 2.0 | #import "/src/lib.typ": num, metro-setup
#set page(width: auto, height: auto)
#num[1.23]
#num(output-decimal-marker: ",")[1.23] |
https://github.com/a-mhamdi/graduation-report | https://raw.githubusercontent.com/a-mhamdi/graduation-report/main/Typst/fr-Rapport/chaps/chpt3.typ | typst | MIT License | /* --------------------------------- DO NOT EDIT -------------------------------- */
#import "../Class.typ": *
#show: report.with(isAbstract: false)
#set page(header: none)
#figure(chap(chap3, numbering: "1."), kind: "chapter", supplement: "Chapitre") <chp:chap3> // Chapter 3
#set page(header: smallcaps(title) + h(1fr) + emph(chap3) + line(length: 100%))
#set heading(outlined: true, numbering: "1.")
/* ------------------------------------------------------------------------------ */
== Introduction
#lorem(32)
== Section 1
#lorem(16)
=== Sous-section 1.1
#lorem(64)
=== Sous-section 1.2
#lorem(64)
== Section 2
#lorem(16)
=== Sous-section 2.1
#lorem(64)
=== Sous-section 2.2
#lorem(64)
/* --- FIGURE --- */
#figure(
image("images/typst.svg", width: 10%),
caption: "Logo de Typst",
) <fig:typst-logo>
@fig:typst-logo affiche le logo de `Typst`.
/* --- TABLE --- */
#figure(
table(
columns: (auto, auto, auto),
[a], [b], [c], [$a$], [$b$], [$c$],
),
caption: "Une table",
) <tab:une-table>
@tab:une-table montre un tableau.
== Conclusion
#lorem(32)
|
https://github.com/zenor0/FZU-report-typst-template | https://raw.githubusercontent.com/zenor0/FZU-report-typst-template/main/examples/example.typ | typst | MIT License | #import "@local/fzu-report:0.1.0": report-conf, thanks, appendix
#import "@preview/sourcerer:0.2.1": code
#import "@preview/lovelace:0.2.0": *
#import "@preview/gentle-clues:0.8.0": *
#show: doc => report-conf(
studentID: "xxxxxx",
author: "xxxxxx",
school: "xxxxxx",
major: "xxxxxx",
advisor: "xxxxxx",
thesisname: "示例实验报告",
date: datetime(year: 2024, month: 5, day: 28),
outlinedepth: 4,
cnabstract: [你有这么高速运转的机械进入中国，记住我给出的原理，小的时候。就是研发人，就研发这个东西的一个原理是阴间证权管，你知道为什么会有生灵给他运转，先（仙）位。还有、还有专门饲养这个，为什么地下产这种东西，他管着、他是五世同堂旗下子孙。你以为我在给你闹着玩呢，你不、你不、你不警察吗，黄龙江一派全部带蓝牙，黄龙江、我告诉你，在阴间是、是那个化名、化名，我小舅，亲小舅，张学兰的那个、那个嫡子、嫡孙。咋的你跟王守义玩呢，她是我儿子，她都管我叫太祖奶奶。爱因斯节叶赫那拉，我是施瓦辛格。我告诉你，他不听命于杜康。我跟你说句根儿上的事，你不刑警队的吗？他不听命于杜康。为什么，他是韩国人，他属于合、合作方，合伙人，自己有自己的政权，但是你进入亚洲了，这、这块牡丹江号称小联合国，你触犯了军权就可以抓他！但是你们为了什么，你是为了碎银几两啊，还是限制你的数字啊，还是你兵搁不了，你没有主权。你这兵不硬啊，你理论不强，你都说不明白。你人情世故，你为了几个数字导致你的方向啊。因为什么这块有交警队的人，才说这话的，你天天交警队、交警队的，你、你、你干什么工作了你？你这军情我分析的，我控股人。到时候你张口了管我要军费的时候挺牛逼的。没有定向资金你们，你们的资金全是佣金，就是你那水平，你这活你给我干完了，有这个有这笔钱，不干完没有。这就是连我都是的，我的账号运转是完成阴间的事，生灵，你们的生灵怎么的，嫁接我，养的野门子，改变生理，那你上监狱，那问我这话我也不能告诉你啊。
],
cnkeywords: ("高速运转", "机械"),
enabstract: [#lorem(100)],
enkeywords: ("Keywords1", "Keywords2"),
show-code-language: true,
show-code-icon: true,
doc,
)
#show: setup-lovelace
// 自定义枚举和列表的缩进, 默认为 1em
#set enum(indent: 1em)
#set list(indent: 1em)
= 基本功能
本模板提供了一些基本功能，包括：
1. 封面
2. 摘要
3. 目录
4. 正文
5. 代码块
6. 数学公式
7. 交叉引用
8. 图表 & 脚注
9. 信息块
10. 伪代码块
11. 参考文献说明
12. 附录
13. 致谢
= 一级标题
== 二级标题
=== 三级标题
===== 四级标题
====== 五级标题
默认最高层级为五级标题，如果需要更多层级，请修改模板的 `outlinedepth` 参数。
= 图表 & 脚注
但是如果你想要给插入的图片自动编号, 请使用 `figure` 指令，例如：
#figure(
image("./assets/fzu_logo.svg", width: 100pt),
caption: "福州大学校徽"
)<fig1>
这样将图片作为`figure`插入图片就会自动居中，并且带有图片描述。图片描述使用 `caption` 参数指定#footnote[你发现了吗? 上面这一段的首行缩进消失了. 这是 typst在排版CJK字符时的一个问题. 你需要手动的在没有缩进的地方加上 h(2em) 来解决这个问题.]。
你还可以以同样的方式插入表格，例如：
#figure(
table(
columns: (auto, auto, auto),
stroke: none,
table.hline(),
table.header([姓名], [年龄], [性别]),
table.hline(stroke: 0.5pt),
[张三], [18], [男],
[李四], [19], [女],
[王五], [20], [男],
table.hline(),
),
caption: [三线表示例]
)<fig2>
// #figure(
// table(
// header: ["姓名", "年龄", "性别"],
// ),
// caption: "学生信息表"
// )
= 代码块
本模板提供了两种样式的代码块。
1. `code` 是一个简单的代码块，例如：
#code(
```python
print("Hello, World!")
print("Hello, World!")
print("Hello, World!")
print("Hello, World!")
print("Hello, World!")
```
)
1. 使用`typst`默认的代码块样式，例如：
```python
print("Hello, World!")
print("Hello, World!")
print("Hello, World!")
print("Hello, World!")
print("Hello, World!")
```
#h(2em)代码块右上角会显示代码块的语言，如果不需要显示语言或不需要显示图表，请你将模板参数中的 `show-code-language` 或 `show-code-icon` 设置为 `false`#footnote[像这段一样! 你的首行缩进就回来了.]。
= 数学公式
数学公式使用`$`包裹，例如：$E=m c^2$. 这是一个行间公式。
如果在`$`与公式之间加上空格，那么公式将会被居中显示, 并且被自动编号：
$ E = m c^2 $
$ E = m c^2 $
$ E = m c^2 $
= 交叉引用
<tag>
你可以使用`<>`来创建标签，然后使用`@`来引用标签。例如：
这是一个小节的引用 @tag, 图片的引用 @fig1, 表格的引用 @fig2。
= 信息块
信息块是一个可以包含任意内容的块。例如：
#info[
这是一个信息块，可以包含任意内容。
]
#warning(
title: [标题也是可以自定义的哈]
)[
这是一个警告块，可以包含任意内容。
]
= 伪代码块
#algorithm(
caption: [计算GOTO函数的算法],
pseudocode(
no-number,
[*input: * 项目集 I, 文法符号 X],
no-number, [*output: * 新的项目集 J],
[function GOTO(I, X):], ind,
[J ← ∅], ind,
[*for* each 项目 [A → α•Xβ, a] in I:], ind,
[newItem ← [A → αX•β, a]], ded,
[将 newItem 添加到 J], ded,
ded,
[计算 CLOSURE(J)], ded,
[*return* J],
)
)
= 参考文献说明
参考文献的引用在模板的 `doc` 参数中指定。例如：
== 为了参考文献而加的章节
参考文献需要使用 bib 格式的引用文献表，再在正文中通过 `@labelname` 方式引用。
这里有一段话 @kopka2004guide，引用多个会自动合并 @kopka2004guide @wang2010guide 。
为了生成中英文双语的参考文献表，本模板实验性地引入了 `bilingual-bibliography` 。有关该功能的详细信息，请访问 https://github.com/nju-lug/modern-nju-thesis/issues/3 。如果出现参考文献显示不正常的情况，请前往 https://github.com/csimide/SEU-Typst-Template/issues/1 反馈。
模板提供了 `bilingual-bib` 参数，用于控制是否使用 `bilingual-bibliography`。当 `bilingual-bib` 参数设置为 `true` 时，模板会使用 `bilingual-bibliography` 渲染。
本模板附带的 `gb-t-7714-2015-numeric-seu.csl` 是“修复”部分 bug 的 CSL 文件。该格式和东大格式不完全吻合，但比自带的 `gb7714-2015` 稍微符合一些。
参考文献过后，会自动进入使用 A B C 排序的附录部分。
如果不需要插入参考文献，但是需要进入附录部分，请使用 `#appendix()` ，后续会自动进入附录部分。
#bibliography(
"ref.bib", // 替换为自己的bib路径
style: "gb-t-7714-2015-numeric-seu-bachelor.csl"
)
= 这里是附录内容
== 附录测试1
在参考文献之后的章节会自动编为附录。同样，图表等要素在此都会使用 A B C 序号。例如：
$ a^2 + b^2 = c^2 $ <ss1>
#figure(
[（假装这里是表格内容）],
caption: [附录中的一个表格],
kind: table,
)
#thanks[
学位论文正文和附录之后，一般应放置致谢（后记或说明），主要感谢指导老师和对论文工作有直接贡献和帮助的人士和单位。致谢言语应谦虚诚恳，实事求是。字数一般不超过1000个汉字。
“致谢”用三号黑体加粗居中，两字之间空4个半角空格。致谢内容为小四号宋体，1.5倍行距。
若需要渲染致谢，请用 `#thanks[内容]`。
]
|
https://github.com/schmidma/typst-workshop | https://raw.githubusercontent.com/schmidma/typst-workshop/main/examples/04-newlines.typ | typst | Creative Commons Zero v1.0 Universal | You can break \
line anywhere you \
want using the \\ symbol. |
https://github.com/Complex2-Liu/macmo | https://raw.githubusercontent.com/Complex2-Liu/macmo/main/contests/2023/content/problem-03.typ | typst | #import "../lib/math.typ": problem, solution, note, ans
#import "../lib/utils.typ": hphantom
#problem[
若 $x, y, z$ 为正实数满足 $tan^(-1)(x) + tan^(-1)(y) + tan^(-1)(z) = pi$, 则
$ 1 / (x y) + 1 / (y z) + 1 / (z x) = underline(hphantom("ANSWER")). $
]
#solution[
$tan$ 的和角公式告诉我们 $tan^(-1)(x) + tan^(-1)(y) = tan^(-1)((x + y) / (1 - x y))$,
进一步得到 $ tan^(-1)(x) + tan^(-1)(y) + tan^(-1)(z) = tan^(-1)((x + y + z - x y z)
/ (1 - x y - y z - z x)). $ 所以 $x + y + z = x y z$, 从而
$1 / (x y) + 1 / (y z) + 1 / (z x) = ans(1.)$
]
/* vim: set ft=typst: */
|
|
https://github.com/kiwiyou/algorithm-lecture | https://raw.githubusercontent.com/kiwiyou/algorithm-lecture/main/advanced/03-graph-dp.typ | typst | #import "@preview/cetz:0.1.2"
#import "@preview/algorithmic:0.1.0"
#import "../slide.typ"
#show: slide.style
#show link: slide.link
#show footnote.entry: slide.footnote
#let algorithm(..args) = text(
font: ("linux libertine", "Pretendard"),
size: 17pt,
)[#algorithmic.algorithm(..args)]
#let func(body) = text(font: ("linux libertine", "Pretendard"))[#smallcaps[#body]]
#align(horizon + center)[
= 알고리즘 중급 세미나
03: 그래프에서의 다이나믹 프로그래밍
#text(size: 0.8em)[
연세대학교 전우제#super[kiwiyou] \
2023.12.08.r1
]
]
#slide.slide[방향 비순환 그래프][
- 방향이 있고#super[Directed], 순환이 없는#super[Acyclic] 그래프
- 순서 관계를 일반화한 것?
#align(center + horizon)[
#text(size: 20pt)[
#cetz.canvas({
import cetz.draw: *
let r = 0.75cm
set-style(
content: (
frame: "circle",
padding: 0.2,
),
circle: (
radius: r
),
line: (
mark: (
end: ">",
size: 0.2,
fill: black,
)
),
)
let connect(a, b) = line((a + ".center", r, b + ".center"), (b + ".center", r, a + ".center"))
group({
content((0, 0), [A], name: "A")
content((3, 0), [B], name: "B")
content((6, 0), [C], name: "C")
content((9, 0), [D], name: "D")
content((0, -2), [E], name: "E")
content((9, -2), [F], name: "F")
connect("A", "B")
connect("B", "C")
connect("C", "D")
connect("E", "B")
connect("C", "F")
connect("B", "F")
}, name: "O")
content((rel: (0, -0.5), to: "O.bottom"), [DAG의 예], frame: none)
group({
set-origin((12, 0))
content((0, 0), [A], name: "A")
content((3, 0), [B], name: "B")
content((6, 0), [C], name: "C")
content((9, 0), [D], name: "D")
content((0, -2), [E], name: "E")
content((9, -2), [F], name: "F")
connect("A", "B")
connect("B", "C")
connect("C", "D")
connect("E", "B")
connect("B", "F")
connect("F", "E")
let mid = ("E.center", 0.5, "F.center")
set-style(
line: (
mark: (
end: none
),
stroke: (
paint: red,
thickness: 0.1cm,
),
),
)
line((rel: (-0.2, -0.2), to: mid), (rel: (0.2, 0.2), to: mid))
line((rel: (-0.2, 0.2), to: mid), (rel: (0.2, -0.2), to: mid))
}, name: "X")
content((rel: (0, -0.5), to: "X.bottom"), [DAG가 아닌 예], frame: none)
})
]
]
]
#slide.slide[위상 정렬][
- 정점을 순서대로 나열하는 방법
- 순서가 정의되지 않은 두 정점의 경우 어떤 순서라도 가능
#align(center + horizon)[
#text(size: 20pt)[
#cetz.canvas({
import cetz.draw: *
let r = 0.75cm
set-style(
content: (
frame: "circle",
padding: 0.2,
),
circle: (
radius: r
),
line: (
mark: (
end: ">",
size: 0.2,
fill: black,
)
),
)
let connect(a, b) = line((a + ".center", r, b + ".center"), (b + ".center", r, a + ".center"))
group({
content((0, 0), [A], name: "A")
content((3, 0), [B], name: "B")
content((6, 0), [C], name: "C")
content((9, 0), [D], name: "D")
content((0, -2), [E], name: "E")
content((9, -2), [F], name: "F")
connect("A", "B")
connect("B", "C")
connect("C", "D")
connect("E", "B")
connect("C", "F")
connect("B", "F")
}, name: "g")
group(anchor: "top-right", {
set-origin((rel: (0, -2), to: "g.bottom"))
content((-6, 0), [A], name: "A")
content((-4, 0), [E], name: "E")
content((-2, 0), [B], name: "B")
content((0, 0), [C], name: "C")
content((2, 0), [D], name: "D")
content((4, 0), [F], name: "F")
connect("A", "E")
connect("E", "B")
connect("B", "C")
connect("C", "D")
connect("D", "F")
}, name: "s1")
group(anchor: "top-left", {
set-origin((rel: (0, -2), to: "g.bottom"))
content((-4, 0), [A], name: "A")
content((-2, 0), [B], name: "B")
content((0, 0), [C], name: "C")
content((2, 0), [E], name: "E")
content((4, 0), [F], name: "F")
content((6, 0), [D], name: "D")
connect("A", "B")
connect("B", "C")
connect("C", "E")
connect("E", "F")
connect("F", "D")
}, name: "s2")
set-style(
line: (
mark: (
end: ">"
)
)
)
line((rel: (-5, -0.5), to: "g.bottom"), (rel: (0, 0.5), to: "s1.top"))
line((rel: (5, -0.5), to: "g.bottom"), (rel: (0, 0.5), to: "s2.top"))
})
]
]
#pagebreak()
- 진입 차수#super([indegree]): 정점을 가리키는 화살표의 개수
- 진입 차수가 0인 정점을 아무거나 방문
- 정점을 방문할 때마다 그 정점에서 출발하는 화살표를 모두 제거
- 큐와 스택 모두 이용 가능
#pagebreak()
#algorithm({
import algorithmic: *
Function("Topological-Sort", args: ($V$, $E$), {
Assign[$"indegree"[u]$][$0$]
For(
cond: [$(u, v)$ *in* $E$],
Assign[$"indegree"[v]$][$"indegree"[v] + 1$]
)
Assign[$Q$][${}$]
For(
cond: [$u$ *in* $V$],
If(
cond: $"indegree"[u] = 0$,
State[*add* $u$ to $Q$]
)
)
Assign[$"order"$][${}$]
While(
cond: [$Q$ is not empty],
{
State[*pop* $u$ from $Q$]
State[*append* $u$ to $"order"$]
For(
cond: [$(u, v)$ *in* $E$],
{
Assign[$"indegree"[v]$][$"indegree"[v] - 1$]
If(
cond: $"indegree"[v] = 0$,
State[*add* $u$ to $Q$]
)
}
)
}
)
Return[$"order"$]
})
})
]
#slide.slide[DAG에서의 다이나믹 프로그래밍][
- 위상 정렬 후 bottom-up으로 접근하면 1차원 다이나믹 프로그래밍과 동일
- 간선을 역방향으로 놓은 후 DFS
- 동일 정점을 여러 번 방문하지 않도록 주의
- 간선이 모두 부모 방향인 트리는 DAG
]
#slide.slide[과제][
- #slide.problem("25168", "게으른 아리를 위한 접종 계획")
- #slide.problem("24526", "전화 돌리기")
- #slide.problem("26159", "트리와 수열")
] |
|
https://github.com/MaxAtoms/T-705-ASDS | https://raw.githubusercontent.com/MaxAtoms/T-705-ASDS/main/content/week5.typ | typst | #import "../template.typ": example, exercise
#import "../boxes.typ": definition
#import "../tags.typ": week, barron
== Continous Distributions
#exercise("4.1")[
Lifetime in years has density
$ f(x) = lr("{", size: #350%) #stack($k/x^4, x gt.eq 1$, 1em, $0, x < 1$) $
Find $k$, the cdf and $P(X>2)$
a) As f is a density we know
$
1 &= integral_(-oo)^(oo) f(x) dif x = integral_1^(oo) k/x^4 = k dot.op [ -1/3x^(-3)]_1^(oo) \
&= k dot.op (0-(-1/3*1^(-3))) = k/3 <=> k=3
$
b) Find cdf
$
F(x) &= integral_(-oo)^(x) f(t) dif t = integral_1^(x) 3/t^4 dif t = [-t^(-3)]_1^x \
&= -x^(-3)-(-1) = 1-x^(-3)
$
$
F(x) = lr("{", size: #350%) #stack($1-x^(-3), x gt.eq 1$, 1em, $0, x<1$)
$
c)
$
P(X>2) = 1-P(X lt.eq 2) = 1-F(2) = 1-(1-2^(-3)) = 2^(-3) = 1/8
$
]
#pagebreak()
#exercise("4.5")[
$X$ and $Y$ have the joint density
$ f(x,y)=C(x^2+y), -1<x<1, 0<y<1 $
a) Find C
$
1 &= integral_(-oo)^(oo) integral_(-oo)^(oo) C(x^2+y) dif y dif x = integral_(-1)^1 integral_0^1 C(x^2+y) dif y dif x \
&= integral_(-1)^1 [ C(x^2y+1/2 y^2) ]_(y=0)^(y=1) dif x = integral_(-1)^1 C(x^2 + 1/2) dif x \
&= C[1/3 x^3 + 1/2x]_(-1)^1 = C(1/3+1/2-(-1/3-1/2)) = 5/3 C => C=3/5
$
b) Marginal densities
$
f_X (x) = integral_0^1 f(x,y) dif y = 3/5 integral_0^1 (x^2 + y) dif y = 3/5 [x^2 y + 1/2 y^2]_0^1 = 3/5 (x^2+1/2)
$
$
f_Y (y) &= integral_(-1)^1 f(x,y) dif x = 3/5 integral_(-1)^1 (x^2+y) dif x = 3/5 [1/3 x^3 + y x]_(-1)^1 \
&= 3/5 (1/3+y-(-1/3-y)) = 3/5 (2/3+2y) = 2/5 + 6/5y
$
c)
$
P(X<0.6) &= integral_0^0.6 f_Y (y) dif y = integral_0^0.6 2/5 + 6/5 y dif y \
&= [2/5 y + 6/10 y^2]_0^0.6 = 2/5 dot.op 3/5 + 6/10 dot.op (3/5)^2
$
$
P(X<0.6|X<0.5) &= frac(P(Y<0.6 sect X <0.5), P(X<0.5)) \
&= frac(integral_0^0.6 integral_0^0.5 f(x,y) dif x dif y, integral_(-1)^0.5 f_X (x) dif x)
$
Bonus: Find the expected value of $X$
$
E(X) &= integral_(-oo)^(oo) x f_X (x) dif x \
&= integral_(-1)^1 x dot.op 3/5 (x^2 + 1/2) dif x = 3/5 integral_(-1)^1 x^3 + 1/2 x dif x \
&= 3/5 [1/4 x^4 + 1/4 x^2]_(-1)^1 = 3/5 (1/4 + 1/4 - (1/4 + 1/4)) = 0
$
]
#pagebreak()
== Parameter Estimation
#week("5")
#barron("9.1")
#definition[
An estimator $accent(Theta,hat)$ is #underline([unbiased]) for a parameter $Theta$ if $E(accent(Theta,hat)) = Theta #h(.2em) forall #h(.2em) Theta$
]
We can measure the bias of an estimator:
$ text("Bias")(accent(Theta,hat)) = E(accent(Theta,hat) - Theta) $
#example[
Sample mean is an unbiased estimator of the population mean:
$ E(accent(X,macron))
&= E(frac(X_1+dots+X_n,n)) \
&= frac(E(X_1)+dots+E(X_n),n) \
&= frac(mu+dots+mu,n) = frac(n dot.op mu,n) = mu
$
]
We estimate parameters of distributions using samples:
- method of moments (MoM)
- method of maximum likelihood (ML)
#definition[
The k-th #underline([population moment]) is $mu_k = E(X^k)$.
The k-th #underline([sample moment]) is $m_k = 1/n sum_(i=1)^n X^k$.
This estimates $mu_k$ from the sample $(X_1,...,X_n)$.
We see that the first sample moment is the sample mean $accent(X,macron)$.
]
#definition[
For $k gt.eq 2$, the k-th #underline([population central moment]) is $mu'_k = E(X - mu_1)^k$.
The k-th #underline([sample central moment]) $m'_k = 1/n sum_(i=1)^n (X_i - accent(X,macron))^k$ estimates $mu'_k$ from the sample $(X_1,...,X_n)$.
]
#pagebreak()
=== Method of Moments
#week("5")
#barron("9.1.1")
Given a sample we know it comes from some family of distributions ${F(Theta)}$.
Use the MoM to choose the member of the family who has properties that are closest to our data.
$
y_1 &= m_1 \
y_2 &= m_2 \
&dots.h \
y_k &= m_k \
$
To estimate k parameters we equate the first k population moments with the corresponding sample moments.
#example[
Poisson Distribution: Estimate $lambda$ with MoM
For the poisson distribution we know:
$ mu_1 = E(X) = lambda $
We calculate the first sample moment:
$ m_1 = 1/n sum X_i = accent(X,macron) $
We must solve the system of equations
$ mu_1 = m_1 <=> lambda = accent(X,macron) => accent(lambda,hat) = accent(X,macron) $
]
#example[
Gamma distribution
This distribution has two parameters $alpha$ and $lambda$.
We have a sample which we can use to estimate $alpha$ and $lambda$.
First we find the sample moments:
$
m_1 &= accent(X,macron) = 48.2333 \
m_2 &= 1/n sum_(i=1)^n (X_i - accent(X,macron))^2 = 679.7122
$
We know for the gamma distribution:
$
mu_1 &= E(X) = alpha / lambda \
mu_2 &= text("Var")(X) = alpha / lambda^2
$
We need to solve:
$
mu_1 = m_1 &<=> alpha / lambda = accent(X,macron) \
mu_2 = m_2 &<=> alpha / lambda^2 = m'_2
$
#pagebreak()
We see that:
$
lambda accent(X,macron) = alpha = lambda^2 m'_2 <=> lambda = accent(X,macron)/m'_2
$
$
accent(lambda,hat) &= m_1/m'_2 = accent(X,hat) / m'_2 = 48.2333/679.7122 = 0.0710 \
accent(alpha,hat) &= accent(lambda,hat) m_1
= accent(lambda,hat) accent(X,macron)
= 0.0710 dot.op 48 2333 = 3.4227
$
The estimates are:
$
accent(alpha,hat) &= accent(lambda,hat) dot.op m_1 = m_1^2/m'_2 \
accent(lambda,hat) &= m_1 / m'_2
$
]
|
|
https://github.com/Myriad-Dreamin/typst.ts | https://raw.githubusercontent.com/Myriad-Dreamin/typst.ts/main/fuzzers/corpora/text/numbers_05.typ | typst | Apache License 2.0 |
#import "/contrib/templates/std-tests/preset.typ": *
#show: test-page
// Test the `repr` function with integers.
#repr(12) \
#repr(1234567890) \
#repr(0123456789) \
#repr(0) \
#repr(-0) \
#repr(-1) \
#repr(-9876543210) \
#repr(-0987654321) \
#repr(4 - 8)
|
https://github.com/posit-dev/bcorp-report | https://raw.githubusercontent.com/posit-dev/bcorp-report/main/pbc-report.typ | typst | // Some definitions presupposed by pandoc's typst output.
#let blockquote(body) = [
#set text( size: 0.92em )
#block(inset: (left: 1.5em, top: 0.2em, bottom: 0.2em))[#body]
]
#let horizontalrule = [
#line(start: (25%,0%), end: (75%,0%))
]
#let endnote(num, contents) = [
#stack(dir: ltr, spacing: 3pt, super[#num], contents)
]
#show terms: it => {
it.children
.map(child => [
#strong[#child.term]
#block(inset: (left: 1.5em, top: -0.4em))[#child.description]
])
.join()
}
// Some quarto-specific definitions.
#show raw.where(block: true): block.with(
fill: luma(230),
width: 100%,
inset: 8pt,
radius: 2pt
)
#let block_with_new_content(old_block, new_content) = {
let d = (:)
let fields = old_block.fields()
fields.remove("body")
if fields.at("below", default: none) != none {
// TODO: this is a hack because below is a "synthesized element"
// according to the experts in the typst discord...
fields.below = fields.below.amount
}
return block.with(..fields)(new_content)
}
#let empty(v) = {
if type(v) == "string" {
// two dollar signs here because we're technically inside
// a Pandoc template :grimace:
v.matches(regex("^\\s*$")).at(0, default: none) != none
} else if type(v) == "content" {
if v.at("text", default: none) != none {
return empty(v.text)
}
for child in v.at("children", default: ()) {
if not empty(child) {
return false
}
}
return true
}
}
// Subfloats
// This is a technique that we adapted from https://github.com/tingerrr/subpar/
#let quartosubfloatcounter = counter("quartosubfloatcounter")
#let quarto_super(
kind: str,
caption: none,
label: none,
supplement: str,
position: none,
subrefnumbering: "1a",
subcapnumbering: "(a)",
body,
) = {
context {
let figcounter = counter(figure.where(kind: kind))
let n-super = figcounter.get().first() + 1
set figure.caption(position: position)
[#figure(
kind: kind,
supplement: supplement,
caption: caption,
{
show figure.where(kind: kind): set figure(numbering: _ => numbering(subrefnumbering, n-super, quartosubfloatcounter.get().first() + 1))
show figure.where(kind: kind): set figure.caption(position: position)
show figure: it => {
let num = numbering(subcapnumbering, n-super, quartosubfloatcounter.get().first() + 1)
show figure.caption: it => {
num.slice(2) // I don't understand why the numbering contains output that it really shouldn't, but this fixes it shrug?
[ ]
it.body
}
quartosubfloatcounter.step()
it
counter(figure.where(kind: it.kind)).update(n => n - 1)
}
quartosubfloatcounter.update(0)
body
}
)#label]
}
}
// callout rendering
// this is a figure show rule because callouts are crossreferenceable
#show figure: it => {
if type(it.kind) != "string" {
return it
}
let kind_match = it.kind.matches(regex("^quarto-callout-(.*)")).at(0, default: none)
if kind_match == none {
return it
}
let kind = kind_match.captures.at(0, default: "other")
kind = upper(kind.first()) + kind.slice(1)
// now we pull apart the callout and reassemble it with the crossref name and counter
// when we cleanup pandoc's emitted code to avoid spaces this will have to change
let old_callout = it.body.children.at(1).body.children.at(1)
let old_title_block = old_callout.body.children.at(0)
let old_title = old_title_block.body.body.children.at(2)
// TODO use custom separator if available
let new_title = if empty(old_title) {
[#kind #it.counter.display()]
} else {
[#kind #it.counter.display(): #old_title]
}
let new_title_block = block_with_new_content(
old_title_block,
block_with_new_content(
old_title_block.body,
old_title_block.body.body.children.at(0) +
old_title_block.body.body.children.at(1) +
new_title))
block_with_new_content(old_callout,
new_title_block +
old_callout.body.children.at(1))
}
// 2023-10-09: #fa-icon("fa-info") is not working, so we'll eval "#fa-info()" instead
#let callout(body: [], title: "Callout", background_color: rgb("#dddddd"), icon: none, icon_color: black) = {
block(
breakable: false,
fill: background_color,
stroke: (paint: icon_color, thickness: 0.5pt, cap: "round"),
width: 100%,
radius: 2pt,
block(
inset: 1pt,
width: 100%,
below: 0pt,
block(
fill: background_color,
width: 100%,
inset: 8pt)[#text(icon_color, weight: 900)[#icon] #title]) +
block(
inset: 1pt,
width: 100%,
block(fill: white, width: 100%, inset: 8pt, body)))
}
#let posit_colors = (
blue: rgb("#447099"),
grey: rgb("#404041"),
dark_blue_3: rgb("#17212B"),
light_blue_1: rgb("#D1DBE5"),
light_blue_2: rgb("#A2B8CB")
)
#let hex_background={
image("assets/images/hexes-8.5x11-#17212B.png", height: 100%, fit: "cover")
}
// Pages with a blue background
#let page_blue(content)={
set page(background: hex_background)
set text(fill: posit_colors.light_blue_1)
show link: set text(fill: posit_colors.light_blue_2)
show heading: set text(fill: posit_colors.light_blue_2)
show heading.where(level: 1): it => {
pagebreak()
it
}
content
}
#let col-2(content)={
columns(2, gutter: 3em, content)
}
// Custom title page
#let title_page(title, subtitle)={
page(margin: 0in,
background: image("assets/images/09.17.23PositDayOne2.jpg", height: 100%, fit: "cover"))[
#set text(fill: white)
#place(center + horizon, dy: -2.5in)[
#set align(center + horizon)
#block(width: 100%, fill: posit_colors.dark_blue_3, outset: 5em)[
#text(weight: "light", size: 36pt, title)
#text(weight: "bold", size: 24pt, subtitle)
]
]
#place(center + bottom, dy: -36pt)[
#block(height: 36pt)[
#box(height: 24pt, baseline: -6pt, image("assets/images/posit-logo-white-TM.svg"))
#box(inset: (x: 12pt), line(length: 100%, angle: 90deg, stroke: 0.5pt + white))
#box(image("assets/images/B-Corp-Logo-White-RGB.png"))
]
]
]
}
#let back_page(repo: none, content)={
page_blue()[
#set page(background: hex_background, numbering: none)
#set text(fill: white)
#show link: set text(fill: white)
#show par: set block(spacing: 0.5em)
#place(bottom + center)[
#block(height: 48pt)[
#box(height: 36pt, baseline: -8pt, image("assets/images/posit-logo-white-TM.svg"))
#box(inset: (x: 24pt), line(length: 100%, angle: 90deg, stroke: 0.5pt + white))
#box(image("assets/images/B-Corp-Logo-White-RGB.png"))
]
The open source data science company
#text(size: 24pt, link("http://posit.co/")[posit.co])
#v(2em)
#set text(size: 10pt)
#(content)
Published with #box(height: 12pt, baseline: 20% , image("assets/images/quarto-logo-trademark-white.svg"))
#if repo != none {
[Source code available at #link(repo)]
}
]
]
}
// Page with image in header
#let page_banner(image_paths: none, image_height: 100%, image_location: right + horizon, fill: posit_colors.light_blue_1, content)={
set page(
margin: (top: 2in),
header: [
#set text(fill: white)
#block(width: 100%, height: 100%, outset: (x: 1.25in), inset: (y: 2em), fill: fill)[
#if (image_paths != none){
set image(height: image_height)
place(image_location, stack(dir: ltr, ..image_paths.map(image)))
}
]
]
)
content
}
#let posit(
title: none,
subtitle: none,
margin: (x: 1.25in, y: 1.25in),
paper: "us-letter",
lang: "en",
region: "US",
font: (),
fontsize: 10pt,
doc,
) = {
set page(
paper: paper,
margin: margin,
numbering: none,
)
set text(lang: lang,
region: region,
font: font,
size: fontsize,
fill: posit_colors.grey)
set par(
leading: 0.8em
)
set table(
align: left,
inset: 7pt,
stroke: (x: none, y: 0.5pt)
)
if title != none {
title_page(title, subtitle)
}
show heading.where(level: 1): set text(weight: "light", size: 24pt)
show heading.where(level: 1): set block(width: 100%, below: 1em)
show heading.where(level: 2): it => {
set block(below: 1.5em)
upper(it)
}
show link: underline
show link: set underline(stroke: 1pt, offset: 2pt)
show link: set text(fill: posit_colors.blue)
block(above: 0em, below: 2em)[
#outline(
indent: 1.5em
);
]
set page(numbering: "1")
doc
}
#show: doc => posit(
title: [Posit Benefit Corporation],
subtitle: [2024 Annual Report],
font: ("Open Sans",),
doc,
)
#page_blue()[
#counter(page).update(1)
= A Message from our CEO
<a-message-from-our-ceo>
#col-2()[
Posit aims to create free and open-source software for data science, scientific research, and technical communication in a sustainable way, because it benefits everyone when the essential tools to produce and consume knowledge are available to all, regardless of economic means.
We believe corporations should fulfill a purposeful benefit to the public and be run for the benefit of all stakeholders including employees, customers, and the larger community.
As a Delaware Public Benefit Corporation (PBC) and a Certified B Corporation®, Posit’s open-source mission and commitment to a beneficial public purpose are codified in our charter, requiring our corporate decisions to balance the interests of the community, customers, employees, and shareholders.
B Corps#super[TM] meet the highest verified standards of social and environmental performance, transparency, and accountability. Posit measures its public benefit by utilizing the non-profit B Lab®’s "Impact Assessment", a rigorous assessment of a company’s impact on its workers, customers, community, and environment.
#colbreak()
In 2019, Posit (then RStudio) met the B Corporation certification requirements set by the B Lab. In 2023, our certification was renewed, and we are proud to share that our B Lab Impact Assessment score rose from 86.1 to 92.5 with this renewal. The B Lab certification process uses credible, comprehensive, transparent, and independent standards to measure social and environmental performance. Details of these assessments can be found on our #link("https://www.bcorporation.net/en-us/find-a-b-corp/company/rstudio/")[B Lab company page];.
To fulfill its beneficial purposes, Posit intends to remain an independent company over the long term. With the support of our customers, employees, and the community, we remain excited to contribute useful solutions to the important problems of knowledge they face.
#place(right, dy: 3em)[
#emph[<NAME>] \
CEO, Posit PBC
]
]
]
= Introduction
<introduction>
#col-2()[
Posit’s mission is to create free and open-source software for data science, scientific research, and technical communication. We do this to enhance the production and consumption of knowledge by everyone, regardless of economic means, and to facilitate collaboration and reproducible research, both of which are critical to the integrity and efficacy of work in science, education, government, and industry.
In addition to our open source products, Posit produces a modular platform of commercial software products that enable teams to adopt R, Python, and other open-source data science software at scale. Posit also offers online services that make it easier to learn and use data science tools over the web.
Together, Posit’s open-source software and commercial software form a virtuous cycle. In most companies, a "customer" is someone who pays you. For us, the definition of a customer must include the open source community, with whom we exchange the currencies of attention, respect, and love. When we deliver value to our open source users, they will likely bring our software into their professional environments, which opens up the possibility of commercial partnerships. To keep this cycle flowing, our open source developers must know and care about the integrations with proprietary solutions that matter to our enterprise customers. #colbreak() It also means that Posit’s commercial teams consistently provide value to individuals who may never directly spend a dollar with us.
Posit’s approach is not typical. Traditionally, scientific and technical computing companies create exclusively proprietary software. While it can provide a robust foundation for investing in product development, proprietary software can also create excessive dependency that is not good for data science practitioners and the community. In contrast, Posit provides core productivity tools, packages, protocols, and file formats as open-source software so customers aren’t overly dependent on a single software vendor. Additionally, while our commercial products enhance the development and use of our open-source software, they are not fundamentally required for those without the need or the ability to pay for them.
As of May 2024, Posit is spending \~38% of its engineering resources on open-source software development, and is leading contributions to over 350 open-source projects. Posit-led projects targeted a broad range of areas including the RStudio IDE; infrastructure libraries for R and Python; numerous packages and tools to streamline data manipulation, exploration and visualization, modeling, and machine learning; and integration with external data sources. Posit also sponsors or contributes to many open-source and community projects led by others, including NumFOCUS, the R Consortium, the Python Software Foundation, DuckDB, Pandoc, pyodide, and ProseMirror, as well as dozens of smaller projects via the Open Source Collective or directly on Github. Additional information about our products and company contributions for the past two years can be found in our #link("https://posit.co/blog/2023-posit-year-in-review/")["Year In Review" blog posts];.
#colbreak()
Today, millions of people download and use Posit open-source products in their daily lives. Additionally, more than 10,000 customers that purchase our professional products help us sustain and grow our mission. It is inspiring to help so many people participate in global economies that increasingly reward data literacy, and know that our tools help produce insights essential to navigating our complex world.
]
#place(bottom, dy: 1.25in,
align(center,
image("assets/images/1-1547.jpg",
width: 100% + 2.5in, fit: "cover")
)
)
#pagebreak()
= Posit’s Charter and Statement of Public Benefit
<posits-charter-and-statement-of-public-benefit>
#col-2()[
== Posit’s Charter
<posits-charter>
We want Posit to serve a meaningful public purpose, and we run the company for the benefit of our customers, employees, and the community at large. That’s why we’re organized as a Public Benefit Corporation (PBC).
What makes a PBC different from other types of corporations?
#quote(block: true)[
#emph["A 'public benefit corporation' is a for-profit corporation organized under and subject to the requirements of this chapter that is intended to produce a public benefit or public benefits and to operate in a responsible and sustainable manner."] — #link("https://delcode.delaware.gov/title8/c001/sc15/")[Delaware Public Benefit Corporations Law]
]
As a PBC and Certified B Corporation, we must meet the highest verified standards of social and environmental performance, transparency, and accountability. Our directors and officers have a fiduciary responsibility to address social, economic, and environmental needs while still overseeing our business goals.
#colbreak()
== Posit’s Statement of Public Benefit
<posits-statement-of-public-benefit>
Creation of free and open source software for data science, scientific research, and technical communication:
#quote(block: true)[
1) To enhance the production and consumption of knowledge by everyone, regardless of economic means.
2) To facilitate collaboration and reproducible research, both of which are critical for ensuring the integrity and efficacy of scientific work.
]
]
#pagebreak()
== Our primary obligations as a PBC and Certified B Corporation
<our-primary-obligations-as-a-pbc-and-certified-b-corporation>
#col-2()[
=== Public Benefit Corporation
<public-benefit-corporation>
#emph[How we built our company charter]
- The board of directors shall manage or direct the business and affairs of the public benefit corporation in a manner that balances the pecuniary interests of the stockholders, the best interests of those materially affected by the corporation’s conduct, and the specific public benefit or public benefits identified in its certificate of incorporation.
- A public benefit corporation shall no less than biennially provide its stockholders with a statement as to the corporation’s promotion of the public benefit or public benefits identified in the certificate of incorporation and of the best interests of those materially affected by the corporation’s conduct.
#colbreak()
=== Certified B Corp
<certified-b-corp>
#emph[How we hold ourselves accountable to our charter]
- Demonstrate high social and environmental performance by achieving a B Lab Impact Assessment score of 80 or above and passing the risk review.
- Make a legal commitment by changing our corporate governance structure to be accountable to all stakeholders, not just shareholders, and achieve benefit corporation status if available in our jurisdiction.
- Exhibit transparency by allowing information about our performance measured against B Lab’s standards to be publicly available on our B Corp profile on B Lab’s website.
]
#pagebreak()
= Posit’s Open Source Development Projects
<posits-open-source-development-projects>
#col-2()[
Before the company re-branded in 2022, Posit (then RStudio) was often thought of as an "R company" in the data community because of its dedication to developing and maintaining some of the most used R libraries in the world. However, Posit has always been better described as a #emph[scientific software] company. Supporting Python (via the #link("https://github.com/rstudio/reticulate")[reticulate] package, RStudio language support), working with relational databases and data platforms such as Apache Spark (a cross-platform data frame compatibility via #link("https://github.com/apache/arrow")[feather/Apache Arrow];), and much more mean that we’ve never been solely an "R company".
#colbreak()
Since the 2021 PBC report, Posit has released several new packages in the Python and R ecosystems and continues to maintain and grow the libraries previously developed. The following subsections highlight selected Posit software projects of interest to the broad data science community. Where metrics are published, please note these represent a #emph[lower bound] on the actual number, as it is difficult-to-impossible to account for every install and usage in the world.
]
#place(bottom, dy: 1.25in,
align(center,
image("assets/images/2-0616.jpg",
width: 100% + 2.5in, fit: "cover")
)
)
#pagebreak()
#page_banner(
image_paths:("assets/images/quarto-logo-dark.svg",),
image_height:50%,
[
== Quarto
<quarto>
#col-2()[
In July 2022, #link("https://posit.co/blog/announcing-quarto-a-new-scientific-and-technical-publishing-system/")[Posit announced] the #link("https://quarto.org/")[Quarto] project, an open-source scientific and technical publishing system as a successor to the #link("https://rmarkdown.rstudio.com/")[R Markdown] library. While Quarto incorporates the lessons learned from over 10 years of developing R Markdown into an entirely new project, it’s likely still quite familiar to users of R Markdown as they share two core dependencies: Knitr and Pandoc. In fact, despite the fact that Quarto does some things differently, most existing R Markdown documents can be rendered unmodified using Quarto.
#colbreak()
Quarto allows users to choose from multiple computational engines (Knitr, Jupyter, and Observable), which makes it easy to use Quarto with R, Python, Julia, JavaScript and many other languages. It also allows users to author documents as plain text markdown or Jupyter Notebooks, and publish to numerous outputs such as HTML, PDF, MS Word, ePub and more. Finally, the community has already extended Quarto , as shown by the #link("https://machow.github.io/quartodoc/get-started/overview.html")[quartodoc] project for developing API documentation.
There are 5 full time equivalent (FTE) employees developing open-source Quarto products as of May 2024.
]
#box(image("pbc-report_files/figure-typst/quarto-1.svg"))
])
#page_banner(
image_paths:("assets/images/shiny-logo.png",),
image_height:50%,
[
== Shiny
<shiny>
#col-2()[
Shiny has been a mainstay in the R community since its launch in 2012, providing a web application framework that makes it easy to tell data stories in interactive point-and-click web applications. In April 2023, Posit released the Python version of Shiny, bringing the same great reactive programming model and modular design to the PyData ecosystem.
#colbreak()
Shiny applications can be shared with others via an open-source #link("https://posit.co/products/open-source/shinyserver/")[Shiny Server];, the hosted #link("http://shinyapps.io")[shinyapps.io] service, or with #link("https://posit.co/products/enterprise/connect/")[Posit Connect];. Shiny and related packages include shiny (#link("https://shiny.posit.co/py/")[Python];, #link("https://shiny.posit.co/r/getstarted")[R];), #link("https://rstudio.github.io/bslib/")[bslib];, #link("https://rstudio.github.io/shinytest/")[shinytest];, #link("https://rstudio.github.io/shinyloadtest/")[shinyloadtest];, #link("https://rstudio.github.io/shinydashboard/")[shinydashboard];, #link("https://rstudio.github.io/leaflet/")[leaflet];, and #link("https://rstudio.github.io/crosstalk/")[crosstalk];.
There are 5 FTE Posit employees developing the open-source Shiny and Shiny Server products as of May 2024.
]
#box(image("pbc-report_files/figure-typst/shiny-1.svg"))
#block[
#box(image("pbc-report_files/figure-typst/shiny-2.svg"))
]
])
#pagebreak()
#page_banner(
image_paths:("assets/images/hexes/gt.svg",),
[
== gt / Great Tables
<gt-great-tables>
#col-2()[
When presenting an analysis, a table can often convey the results more concisely than the most beautiful and interactive of charts. However, the experience of creating and displaying tables in R and Python has been mixed, especially when you want to display something beyond a plain data frame representation.
#colbreak()
To that end, the #link("https://gt.rstudio.com/")[gt] and #link("https://posit-dev.github.io/great-tables/articles/intro.html")[Great Tables] packages have defined a "grammar of tables" to solve this problem (in R and Python, respectively), analogous to the "grammar of graphics" for specifying charts.
As of May 2024, there is 1 FTE Posit employee developing gt / Great Tables open-source packages.
]
#box(image("pbc-report_files/figure-typst/gt-1.svg"))
#block[
#box(image("pbc-report_files/figure-typst/gt-2.svg"))
]
])
#page_banner(
image_paths:("assets/images/hexes/vetiver.svg",),
[
== Vetiver
<vetiver>
#col-2()[
#link("https://vetiver.posit.co/")[Vetiver] solves the issues around versioning, sharing, deploying and monitoring predictive models served via APIs. Available for both R and Python, vetiver is extensible via generics that support many common types of models. #colbreak() Vetiver also provides the "model cards" functionality, which can help to generate documentation by extracting some information about the generated model.
]
#box(image("pbc-report_files/figure-typst/vetiver-1.svg"))
#block[
#box(image("pbc-report_files/figure-typst/vetiver-2.svg"))
]
])
#page_banner(
[
== Posit Public Package Manager
<posit-public-package-manager>
#col-2()[
WIth the ubiquity of open source software in our daily lives, one area that most people don’t think about is 'How do you distribute that software quickly and securely to the end user?'. To that end, Posit created #link("https://posit.co/products/enterprise/package-manager/")[Posit Package Manager];, which gives companies a means for providing curated repositories, repository snapshots for better reproducibility, the ability to air-gap the repository for enhanced security and much more.
#colbreak()
As part of our commitment to improving the quality and availability of open source software for all, Posit hosts a public instance of Posit Package Manager called #link("https://packagemanager.posit.co/client/#/")[Posit Public Package Manager] that mirrors CRAN, PyPI and Bioconductor. This mirror served nearly 40 million downloads per month in Q1 2024.
]
#v(6em)
#place(right, dy: -3em, image("assets/images/hexes/webr.svg", height: 5em))
== webR
<webr>
#col-2()[
#link("https://docs.r-wasm.org/webr/latest/")[WebR] has the ambitious goal of bringing the R language to the browser, removing the need for a backend server for computation. It also allows for computation to be done on the client machine, supporting use cases that are infeasible or undesirable for using server-side processing (such as not wanting to send personal data over the internet). #colbreak() Also, by making the most of the user’s device capabilities, webR can improve performance and lower app hosting costs.
There is 1 FTE Posit employee developing webR open-source products as of May 2024.
]
])
#page_banner(
image_paths:("assets/images/hexes/plotnine.png",),
[
== Plotnine
<plotnine>
#col-2()[
#link("https://plotnine.org/")[Plotnine] is an implementation of the grammar of graphics in Python, heavily influenced by ggplot2 in R. Built upon the ubiquitous #link("https://matplotlib.org/")[matplotlib] plotting library, #colbreak() custom (and otherwise complex) plots are easy to reason about and build incrementally, while the simple plots remain simple to create.
]
#box(image("pbc-report_files/figure-typst/plotnine-1.svg"))
])
#page_banner(
image_paths:("assets/images/hexes/siuba.svg",),
[
== Siuba
<siuba>
#col-2()[
#link("https://siuba.org/")[Siuba] is a port of dplyr and other R libraries. It’s aim is to make data science faster through a consistent interface of verbs for working with real-world data: filter, arrange, select, mutate and summarize. #colbreak() Siuba supports several backends including pandas, #link("https://duckdb.org/")[DuckDB] and SQL, providing a "write once, run many" freedom for your analytics code.
]
#box(image("pbc-report_files/figure-typst/siuba-1.svg"))
])
#page_banner(
image_paths:("assets/images/hexes/RStudio.svg",),
[
== RStudio Integrated Development Environment
<rstudio-integrated-development-environment>
#col-2()[
#link("https://posit.co/products/open-source/rstudio/")[RStudio] is a multi-language IDE designed for Data Science with R and Python. It augments the standard code console with an editor that can display Notebooks, launch apps, highlight code syntax, spot code errors, and directly execute code. Built into the IDE are tools for debugging, plotting, browsing files, and managing project histories and workspaces. Together these tools make data scientists and developers much more efficient.
#colbreak()
There are 5 FTE Posit employees developing the RStudio IDE open-source desktop and server products as of May 2024.
]
#box(image("pbc-report_files/figure-typst/rstudio-1.svg"))
])
#page_banner(
image_paths:("assets/images/hexes/tidyverse.svg", ),
[
== Tidyverse
<tidyverse>
#col-2()[
The #link("https://www.tidyverse.org/")[tidyverse] is an opinionated collection of R packages designed for data science. All packages share an underlying design philosophy, grammar and data structures.
The tidyverse consists of nine core packages (including ggplot2, tidyr and readr) and 31 packages overall.
#colbreak()
There are 9 FTE Posit employees developing Tidyverse and related open-source products as of May 2024.
]
#box(image("pbc-report_files/figure-typst/tidyverse-1.svg"))
])
#page_banner(
image_paths:("assets/images/hexes/tidymodels.svg", ),
[
== Tidymodels
<tidymodels>
#col-2()[
#link("https://www.tidymodels.org/")[Tidymodels] is a cohesive collection of packages that perform tasks relevant to statistical modeling and machine learning. Tidymodels packages share a common syntax and design philosophy, and are designed to work seamlessly with Tidyverse packages.
#colbreak()
There are currently 42 tidymodels packages on CRAN. Popular tidymodels packages include parsnip, rsample, recipes, tune and yardstick.
There are 3 FTE Posit employees developing Tidymodels and related open-source products as of May 2024.
]
#box(image("pbc-report_files/figure-typst/tidymodels-1.svg"))
])
#page_banner(
image_paths:("assets/images/hexes/sparklyr.svg", "assets/images/hexes/reticulate.svg", "assets/images/hexes/tensorflow.svg"),
[
== Connectivity Packages
<connectivity-packages>
#col-2()[
Posit increases the efficiency of customers by making open-source packages that connect data scientists to spreadsheets, databases, distributed storage frameworks for big data, machine learning platforms, and the programming environments of other languages, like python.
#colbreak()
Connectivity packages include: #link("https://spark.posit.co/")[sparklyr];, #link("https://tensorflow.rstudio.com/")[tensorflow for R];, #link("https://keras.posit.co/")[keras];, #link("https://solutions.posit.co/connections/db/r-packages/odbc/")[odbc];, and #link("https://rstudio.github.io/reticulate/")[reticulate];.
There are 3 FTE Posit employees creating connectivity-related open-source packages as of May 2024.
]
#box(image("pbc-report_files/figure-typst/connectivity-1.svg"))
])
#page_banner(
image_paths:("assets/images/hexes/devtools.svg","assets/images/hexes/usethis.svg", "assets/images/hexes/roxygen2.svg", "assets/images/hexes/testthat.svg", "assets/images/hexes/pkgdown.svg"),
[
== R Infrastructure Tools (r-lib)
<r-infrastructure-tools-r-lib>
#col-2()[
R-lib is a large collection of R packages that make it easier to build, find, and use effective tools for data analysis.
#colbreak()
There are currently 114 R-lib packages. Popular packages include #link("https://devtools.r-lib.org/")[devtools];, #link("https://testthat.r-lib.org/")[testthat];, #link("https://roxygen2.r-lib.org/")[roxygen2];, #link("https://pkgdown.r-lib.org/")[pkgdown] and #link("https://usethis.r-lib.org/")[usethis];.
]
#box(image("pbc-report_files/figure-typst/rlibs-1.svg"))
])
#page_banner(
fill:posit_colors.blue,
image_paths:("assets/images/BLab_B_Impact_Assessment-white.png",),
image_height:75%,
[
= B Lab® Impact Assessment Results
<b-lab-impact-assessment-results>
#col-2()[
The BLab Impact Assessment is composed of questions in five Impact Areas: Governance, Workers, Community, Environment, and Customers. Posit’s assessment results are available to the public #link("https://www.bcorporation.net/en-us/find-a-b-corp/company/rstudio/")[here];. We completed our first Impact Assessment in 2019 and earned an overall score of #strong[86.1.] We are proud to report that our latest score from our recertification process in 2023, is #strong[92.5];. To put this in context, the threshold for B Lab certification is a score of 80 or higher, and the median score for ordinary businesses who take the assessment is 50.9. Posit seeks to continually improve our internal governance, increase our workforce diversity and employee development efforts, expand our stewardship of the environment, deepen our engagement in our communities, and better serve our customers so that our public benefit will continue to improve each year.
#colbreak()
In our initial assessment, we received high marks for incorporating as a benefit corporation, the health, wellness, safety, and financial security of our employees, and for educating and serving customers. We identified formal goal setting, career development, diversity, equity & inclusion, civic engagement & giving, and air & climate as areas for improvement.
]
])
== Summary of Score Improvements Since 2019
<summary-of-score-improvements-since-2019>
The B Lab’s Impact assessment standards have evolved since 2019 (we are now on version 6 of the assessment). New questions were added, and thresholds for performance were raised in other cases. Of the scored questions we responded to in our most recent assessment, 38 were unchanged from 2019, 71 were modified from 2019 wording, and 22 were brand new questions. On the unchanged or modified questions, we have gained points in the areas listed below.
#figure(
align(center)[#table(
columns: (25%, 35%, 40%),
align: (left,left,left,),
table.header(table.cell(align: left)[#strong[Impact Area];], table.cell(align: left)[#strong[Topic];], table.cell(align: left)[#strong[% Achievement Gain since 2019];],),
table.hline(),
table.cell(align: left, rowspan: 2)[Community], table.cell(align: left)[Civic Engagement & Giving], table.cell(align: left)[39%],
table.cell(align: left)[Diversity, Equity, & Inclusion], table.cell(align: left)[60%],
table.cell(align: left)[Customers], table.cell(align: left)[Customer Stewardship], table.cell(align: left)[28%],
table.cell(align: left)[Environment], table.cell(align: left)[Air & Climate], table.cell(align: left)[75%],
table.cell(align: left)[Governance], table.cell(align: left)[Ethics & Transparency], table.cell(align: left)[37%],
table.cell(align: left, rowspan: 3)[Workers], table.cell(align: left)[Career Development], table.cell(align: left)[62%],
table.cell(align: left)[Engagement & Satisfaction], table.cell(align: left)[50%],
table.cell(align: left)[Financial Security], table.cell(align: left)[58%],
)]
, kind: table
)
#v(1em)
#col-2()[
== Community
<community>
=== Civic Engagement and Giving
<civic-engagement-and-giving>
In addition to the open-source software we make freely available, and the open source data science package development produced by Posit engineers, Posit recognizes the importance of contributing financially to other valuable open-source and community initiatives. To date, Posit has given over \$1.9M to projects led by others. Current commitments include contributing to NumFOCUS, the R Consortium, the R Foundation, DuckDB, the Eclipse Foundation, and the authors and maintainers of several other open-source projects.
Posit’s financial support also extends beyond the world of open source data science. Since 2020, Posit and its employees have given over \$60k to over 135 nonprofits. Our donations reach a range of community-based causes, including organizations dedicated to racial equality, equal justice, LGBTQ+ support, and access to education. Alongside our donations to open source software development, this pool of charitable contributions contributes to the important work many are doing to increase the accessibility of data science for all. Our scoring in this area of the B Lab assessment has increased by 39.5% since 2019.
=== Diversity, Equity, and Inclusion
<diversity-equity-and-inclusion>
Since our initial B Lab assessment in 2019, Posit has continued to focus on increasing the strength of our team by utilizing talent practices that encourage diverse people to apply, join, and thrive at Posit. Specific changes made in recent years include the formation of a diversity, equity, inclusion, and accessibility council (DEIA Council), as well as the sponsoring of employee resource groups (ERG’s). We report our progress on our diversity metrics, as defined in the B Lab Assessment, in each quarter’s board meeting. We also pay close attention to issues of equity in compensation, hiring and interviewing, and employee experience. Our efforts to date have yielded increases in the percentages of women and those with minority racial or ethnic identities in both management and the employee population as a whole – and our recent assessment results reflect these gains.
== Customers
<customers>
We have made meaningful improvements in our care for customers in the past few years – particularly in our standards for managing customer data and privacy. Since 2019, we have formalized our approach to data privacy and compliance – we now conduct thorough internal and external audits and train all employees on the essentials of guarding customer data. These changes have increased our assessment performance by 28% since 2019.
== Environment
<environment>
We are happy to share that our assessment scores for Air and Climate impacts have improved by 75% since 2019. In November 2020, Posit achieved carbon neutrality by purchasing carbon offsets that counter the environmental impact of business travel (primarily for our annual conference and internal meetings). As a remote-first organization, we do not generate meaningful greenhouse gas emissions outside of air travel. By offsetting this impact through the funding of reforestation work in both South America and closer to home in Massachusetts, we hope to neutralize Posit’s potential damage to our planet.
== Governance
<governance>
A company’s positive governance impact is measured by the extent to which the company is accountable to stakeholders, and the extent to which its decision-making is transparent to all constituents. In 2019, RStudio scored 16.1 points out of a possible 21.9+ points in the Governance Impact Area, including 10 points awarded for the specific legal structures we have established as a Benefit Corporation that preserve our mission and consider our stakeholders regardless of company ownership.
In our latest assessment, our governance score improved by 37% via improvements in ethics and transparency areas, including anti-corruption and code of ethics training for employees, and more rigorous financial controls and financial transparency with employees. Looking ahead, we plan to incorporate more social and community benefit metrics in our corporate reporting, including board meeting updates, so that all of our stakeholders are aware of our ongoing progress and can help support our success.
== Workers
<workers>
We have made significant strides in our Worker assessment category since 2019, with scores increasing by 50% or more in areas such as career development, engagement and satisfaction, and financial security for our employees. #colbreak() Investments in employee career development include in-house management training programs, tooling and education to support constructive feedback, and documentation of job levels, pay ranges, and career paths within our major functions. In 2021, we initiated an annual organizational health survey, which allows us to collect and respond to employee feedback. We have also augmented our benefits to include a "lifestyle savings account" (LSA) funded by Posit that each individual can choose to apply to home office, professional development, wellness, or financial health expenses as they see fit. All together, we are working to continuously improve the value offered to our workers as our company grows.
]
#place(bottom, dy: 1.25in,
align(center,
image("assets/images/Conf-2023-Crowd.jpg",
width: 100% + 2.5in, fit: "cover")
)
)
#back_page(repo: "https://github.com/posit-dev/bcorp-report/")[
]
|
|
https://github.com/tomeichlersmith/zen-zine | https://raw.githubusercontent.com/tomeichlersmith/zen-zine/main/README.md | markdown | MIT License | # zen-zine
Excellently type-set a cute little zine about your favorite topic!
Providing your eight pages in order will produce a US-Letter page with
the content in a layout ready to be folded into a zine! The content is
wrapped before movement so that padding and alignment are respected.
Here is the template and its preview:
```typst
#import "@preview/zen-zine:0.1.0": zine
#set document(author: "Tom", title: "Zen Zine Example")
#set text(font: "Linux Libertine", lang: "en")
#let my_eight_pages = (
range(8).map(
number => [
#pad(2em, text(10em, align(center, str(number))))
]
)
)
// provide your content pages in order and they
// are placed into the zine template positions.
// the content is wrapped before movement so that
// padding and alignment are respected.
#zine(
// draw_border: true,
// zine_page_margin: 8pt,
// digital: false
contents: my_eight_pages
)
```
## Improvement Ideas
Roughly in order of priority.
- Write documentation and generate a manual
- Deduce `page` properties so that user can change the page they wish to use.
- Make sure the page is `flipped` and deduce the zine page width and height
from the full page width and height (and the zine margin)
- I'm currently struggling with finding out the page properties (what's the `#get` equivalent to `#set`?)
- Add other zine sizes (there is a 16 page one I believe?)
- ~~Digital mode where zine pages are separate pages (of the same size) rather than 'sub pages' of a printer page~~
- [cc323123](https://github.com/tomeichlersmith/zen-zine/commit/cc323123592d6a9203a96c7652e939d07f35ffbb)
- Figure out how syntax to enable `#show.zine(config)` syntax like other templates
- [can "unpack" argument sinks `..sink` with `sink.pos()` to get an array of positional arguments](https://typst.app/docs/reference/foundations/arguments/)
- still trying to figure out how to _provide_ an array of zine content pages in this syntactical style
- Tweak margins to optimize for folding
- Zines have 3 borders - cut, outer fold, inner fold - we can squeeze the inner folds to expand the outer folds so that there is more tolerance on the folds and text wrapping around the outside is less likely
- 🤯give user acces to two next pages next to each other (in final zine) so they can decide how to handle an inner fold🤯
|
https://github.com/Le-foucheur/Typst-VarTable | https://raw.githubusercontent.com/Le-foucheur/Typst-VarTable/main/examples/hyperbolicFuntion.typ | typst | MIT License | #set page(width: auto, height: auto, margin: 5pt)
#import "../tabvar.typ": tabvar
#tabvar(
init: (
variable: $x$,
label: (
([sign of $f’$], "Sign"),
([variation of $f$], "Variation"),
),
),
domain: ($ -oo $, $ 0 $, $ +oo $),
content: (
($+$, ("||", $+$)),
(
(center, $0$),
(bottom, top, "||", $ -oo $, $ +oo $),
(center, $ 0 $),
),
),
) |
https://github.com/duskmoon314/typst-fontawesome | https://raw.githubusercontent.com/duskmoon314/typst-fontawesome/main/lib-gen.typ | typst | MIT License | #import "lib-impl.typ": fa-icon
// Generated icon list of Font Aewsome 6.6.0
#let fa-icon-map = (
"0": "\u{30}",
"00": "\u{e467}",
"1": "\u{31}",
"2": "\u{32}",
"3": "\u{33}",
"360-degrees": "\u{e2dc}",
"4": "\u{34}",
"42-group": "\u{e080}",
"innosoft": "\u{e080}",
"5": "\u{35}",
"500px": "\u{f26e}",
"6": "\u{36}",
"7": "\u{37}",
"8": "\u{38}",
"9": "\u{39}",
"a": "\u{41}",
"abacus": "\u{f640}",
"accent-grave": "\u{60}",
"accessible-icon": "\u{f368}",
"accusoft": "\u{f369}",
"acorn": "\u{f6ae}",
"address-book": "\u{f2b9}",
"contact-book": "\u{f2b9}",
"address-card": "\u{f2bb}",
"contact-card": "\u{f2bb}",
"vcard": "\u{f2bb}",
"adn": "\u{f170}",
"adversal": "\u{f36a}",
"affiliatetheme": "\u{f36b}",
"airbnb": "\u{f834}",
"air-conditioner": "\u{f8f4}",
"airplay": "\u{e089}",
"alarm-clock": "\u{f34e}",
"alarm-exclamation": "\u{f843}",
"alarm-plus": "\u{f844}",
"alarm-snooze": "\u{f845}",
"album": "\u{f89f}",
"album-circle-plus": "\u{e48c}",
"album-circle-user": "\u{e48d}",
"album-collection": "\u{f8a0}",
"album-collection-circle-plus": "\u{e48e}",
"album-collection-circle-user": "\u{e48f}",
"algolia": "\u{f36c}",
"alicorn": "\u{f6b0}",
"alien": "\u{f8f5}",
"alien-8bit": "\u{f8f6}",
"alien-monster": "\u{f8f6}",
"align-center": "\u{f037}",
"align-justify": "\u{f039}",
"align-left": "\u{f036}",
"align-right": "\u{f038}",
"align-slash": "\u{f846}",
"alipay": "\u{f642}",
"alt": "\u{e08a}",
"amazon": "\u{f270}",
"amazon-pay": "\u{f42c}",
"amilia": "\u{f36d}",
"ampersand": "\u{26}",
"amp-guitar": "\u{f8a1}",
"anchor": "\u{f13d}",
"anchor-circle-check": "\u{e4aa}",
"anchor-circle-exclamation": "\u{e4ab}",
"anchor-circle-xmark": "\u{e4ac}",
"anchor-lock": "\u{e4ad}",
"android": "\u{f17b}",
"angel": "\u{f779}",
"angellist": "\u{f209}",
"angle": "\u{e08c}",
"angle-90": "\u{e08d}",
"angle-down": "\u{f107}",
"angle-left": "\u{f104}",
"angle-right": "\u{f105}",
"angles-down": "\u{f103}",
"angle-double-down": "\u{f103}",
"angles-left": "\u{f100}",
"angle-double-left": "\u{f100}",
"angles-right": "\u{f101}",
"angle-double-right": "\u{f101}",
"angles-up": "\u{f102}",
"angle-double-up": "\u{f102}",
"angles-up-down": "\u{e60d}",
"angle-up": "\u{f106}",
"angrycreative": "\u{f36e}",
"angular": "\u{f420}",
"ankh": "\u{f644}",
"ant": "\u{e680}",
"apartment": "\u{e468}",
"aperture": "\u{e2df}",
"apostrophe": "\u{27}",
"apper": "\u{f371}",
"apple": "\u{f179}",
"apple-core": "\u{e08f}",
"apple-pay": "\u{f415}",
"apple-whole": "\u{f5d1}",
"apple-alt": "\u{f5d1}",
"app-store": "\u{f36f}",
"app-store-ios": "\u{f370}",
"archway": "\u{f557}",
"arrow-down": "\u{f063}",
"arrow-down-1-9": "\u{f162}",
"sort-numeric-asc": "\u{f162}",
"sort-numeric-down": "\u{f162}",
"arrow-down-9-1": "\u{f886}",
"sort-numeric-desc": "\u{f886}",
"sort-numeric-down-alt": "\u{f886}",
"arrow-down-arrow-up": "\u{f883}",
"sort-alt": "\u{f883}",
"arrow-down-a-z": "\u{f15d}",
"sort-alpha-asc": "\u{f15d}",
"sort-alpha-down": "\u{f15d}",
"arrow-down-big-small": "\u{f88c}",
"sort-size-down": "\u{f88c}",
"arrow-down-from-arc": "\u{e614}",
"arrow-down-from-bracket": "\u{e667}",
"arrow-down-from-dotted-line": "\u{e090}",
"arrow-down-from-line": "\u{f345}",
"arrow-from-top": "\u{f345}",
"arrow-down-left": "\u{e091}",
"arrow-down-left-and-arrow-up-right-to-center": "\u{e092}",
"arrow-down-long": "\u{f175}",
"long-arrow-down": "\u{f175}",
"arrow-down-right": "\u{e093}",
"arrow-down-short-wide": "\u{f884}",
"sort-amount-desc": "\u{f884}",
"sort-amount-down-alt": "\u{f884}",
"arrow-down-small-big": "\u{f88d}",
"sort-size-down-alt": "\u{f88d}",
"arrow-down-square-triangle": "\u{f889}",
"sort-shapes-down-alt": "\u{f889}",
"arrow-down-to-arc": "\u{e4ae}",
"arrow-down-to-bracket": "\u{e094}",
"arrow-down-to-dotted-line": "\u{e095}",
"arrow-down-to-line": "\u{f33d}",
"arrow-to-bottom": "\u{f33d}",
"arrow-down-to-square": "\u{e096}",
"arrow-down-triangle-square": "\u{f888}",
"sort-shapes-down": "\u{f888}",
"arrow-down-up-across-line": "\u{e4af}",
"arrow-down-up-lock": "\u{e4b0}",
"arrow-down-wide-short": "\u{f160}",
"sort-amount-asc": "\u{f160}",
"sort-amount-down": "\u{f160}",
"arrow-down-z-a": "\u{f881}",
"sort-alpha-desc": "\u{f881}",
"sort-alpha-down-alt": "\u{f881}",
"arrow-left": "\u{f060}",
"arrow-left-from-arc": "\u{e615}",
"arrow-left-from-bracket": "\u{e668}",
"arrow-left-from-line": "\u{f344}",
"arrow-from-right": "\u{f344}",
"arrow-left-long": "\u{f177}",
"long-arrow-left": "\u{f177}",
"arrow-left-long-to-line": "\u{e3d4}",
"arrow-left-to-arc": "\u{e616}",
"arrow-left-to-bracket": "\u{e669}",
"arrow-left-to-line": "\u{f33e}",
"arrow-to-left": "\u{f33e}",
"arrow-pointer": "\u{f245}",
"mouse-pointer": "\u{f245}",
"arrow-progress": "\u{e5df}",
"arrow-right": "\u{f061}",
"arrow-right-arrow-left": "\u{f0ec}",
"exchange": "\u{f0ec}",
"arrow-right-from-arc": "\u{e4b1}",
"arrow-right-from-bracket": "\u{f08b}",
"sign-out": "\u{f08b}",
"arrow-right-from-line": "\u{f343}",
"arrow-from-left": "\u{f343}",
"arrow-right-long": "\u{f178}",
"long-arrow-right": "\u{f178}",
"arrow-right-long-to-line": "\u{e3d5}",
"arrow-right-to-arc": "\u{e4b2}",
"arrow-right-to-bracket": "\u{f090}",
"sign-in": "\u{f090}",
"arrow-right-to-city": "\u{e4b3}",
"arrow-right-to-line": "\u{f340}",
"arrow-to-right": "\u{f340}",
"arrow-rotate-left": "\u{f0e2}",
"arrow-left-rotate": "\u{f0e2}",
"arrow-rotate-back": "\u{f0e2}",
"arrow-rotate-backward": "\u{f0e2}",
"undo": "\u{f0e2}",
"arrow-rotate-right": "\u{f01e}",
"arrow-right-rotate": "\u{f01e}",
"arrow-rotate-forward": "\u{f01e}",
"redo": "\u{f01e}",
"arrows-cross": "\u{e0a2}",
"arrows-down-to-line": "\u{e4b8}",
"arrows-down-to-people": "\u{e4b9}",
"arrows-from-dotted-line": "\u{e0a3}",
"arrows-from-line": "\u{e0a4}",
"arrows-left-right": "\u{f07e}",
"arrows-h": "\u{f07e}",
"arrows-left-right-to-line": "\u{e4ba}",
"arrows-maximize": "\u{f31d}",
"expand-arrows": "\u{f31d}",
"arrows-minimize": "\u{e0a5}",
"compress-arrows": "\u{e0a5}",
"arrows-repeat": "\u{f364}",
"repeat-alt": "\u{f364}",
"arrows-repeat-1": "\u{f366}",
"repeat-1-alt": "\u{f366}",
"arrows-retweet": "\u{f361}",
"retweet-alt": "\u{f361}",
"arrows-rotate": "\u{f021}",
"refresh": "\u{f021}",
"sync": "\u{f021}",
"arrows-rotate-reverse": "\u{e630}",
"arrows-spin": "\u{e4bb}",
"arrows-split-up-and-left": "\u{e4bc}",
"arrows-to-circle": "\u{e4bd}",
"arrows-to-dot": "\u{e4be}",
"arrows-to-dotted-line": "\u{e0a6}",
"arrows-to-eye": "\u{e4bf}",
"arrows-to-line": "\u{e0a7}",
"arrows-turn-right": "\u{e4c0}",
"arrows-turn-to-dots": "\u{e4c1}",
"arrows-up-down": "\u{f07d}",
"arrows-v": "\u{f07d}",
"arrows-up-down-left-right": "\u{f047}",
"arrows": "\u{f047}",
"arrows-up-to-line": "\u{e4c2}",
"arrow-trend-down": "\u{e097}",
"arrow-trend-up": "\u{e098}",
"arrow-turn-down": "\u{f149}",
"level-down": "\u{f149}",
"arrow-turn-down-left": "\u{e2e1}",
"arrow-turn-down-right": "\u{e3d6}",
"arrow-turn-left": "\u{e632}",
"arrow-turn-left-down": "\u{e633}",
"arrow-turn-left-up": "\u{e634}",
"arrow-turn-right": "\u{e635}",
"arrow-turn-up": "\u{f148}",
"level-up": "\u{f148}",
"arrow-up": "\u{f062}",
"arrow-up-1-9": "\u{f163}",
"sort-numeric-up": "\u{f163}",
"arrow-up-9-1": "\u{f887}",
"sort-numeric-up-alt": "\u{f887}",
"arrow-up-arrow-down": "\u{e099}",
"sort-up-down": "\u{e099}",
"arrow-up-a-z": "\u{f15e}",
"sort-alpha-up": "\u{f15e}",
"arrow-up-big-small": "\u{f88e}",
"sort-size-up": "\u{f88e}",
"arrow-up-from-arc": "\u{e4b4}",
"arrow-up-from-bracket": "\u{e09a}",
"arrow-up-from-dotted-line": "\u{e09b}",
"arrow-up-from-ground-water": "\u{e4b5}",
"arrow-up-from-line": "\u{f342}",
"arrow-from-bottom": "\u{f342}",
"arrow-up-from-square": "\u{e09c}",
"arrow-up-from-water-pump": "\u{e4b6}",
"arrow-up-left": "\u{e09d}",
"arrow-up-left-from-circle": "\u{e09e}",
"arrow-up-long": "\u{f176}",
"long-arrow-up": "\u{f176}",
"arrow-up-right": "\u{e09f}",
"arrow-up-right-and-arrow-down-left-from-center": "\u{e0a0}",
"arrow-up-right-dots": "\u{e4b7}",
"arrow-up-right-from-square": "\u{f08e}",
"external-link": "\u{f08e}",
"arrow-up-short-wide": "\u{f885}",
"sort-amount-up-alt": "\u{f885}",
"arrow-up-small-big": "\u{f88f}",
"sort-size-up-alt": "\u{f88f}",
"arrow-up-square-triangle": "\u{f88b}",
"sort-shapes-up-alt": "\u{f88b}",
"arrow-up-to-arc": "\u{e617}",
"arrow-up-to-bracket": "\u{e66a}",
"arrow-up-to-dotted-line": "\u{e0a1}",
"arrow-up-to-line": "\u{f341}",
"arrow-to-top": "\u{f341}",
"arrow-up-triangle-square": "\u{f88a}",
"sort-shapes-up": "\u{f88a}",
"arrow-up-wide-short": "\u{f161}",
"sort-amount-up": "\u{f161}",
"arrow-up-z-a": "\u{f882}",
"sort-alpha-up-alt": "\u{f882}",
"artstation": "\u{f77a}",
"asterisk": "\u{2a}",
"asymmetrik": "\u{f372}",
"at": "\u{40}",
"atlassian": "\u{f77b}",
"atom": "\u{f5d2}",
"atom-simple": "\u{f5d3}",
"atom-alt": "\u{f5d3}",
"audible": "\u{f373}",
"audio-description": "\u{f29e}",
"audio-description-slash": "\u{e0a8}",
"austral-sign": "\u{e0a9}",
"autoprefixer": "\u{f41c}",
"avianex": "\u{f374}",
"aviato": "\u{f421}",
"avocado": "\u{e0aa}",
"award": "\u{f559}",
"award-simple": "\u{e0ab}",
"aws": "\u{f375}",
"axe": "\u{f6b2}",
"axe-battle": "\u{f6b3}",
"b": "\u{42}",
"baby": "\u{f77c}",
"baby-carriage": "\u{f77d}",
"carriage-baby": "\u{f77d}",
"backpack": "\u{f5d4}",
"backward": "\u{f04a}",
"backward-fast": "\u{f049}",
"fast-backward": "\u{f049}",
"backward-step": "\u{f048}",
"step-backward": "\u{f048}",
"bacon": "\u{f7e5}",
"bacteria": "\u{e059}",
"bacterium": "\u{e05a}",
"badge": "\u{f335}",
"badge-check": "\u{f336}",
"badge-dollar": "\u{f645}",
"badge-percent": "\u{f646}",
"badger-honey": "\u{f6b4}",
"badge-sheriff": "\u{f8a2}",
"badminton": "\u{e33a}",
"bagel": "\u{e3d7}",
"bag-seedling": "\u{e5f2}",
"bag-shopping": "\u{f290}",
"shopping-bag": "\u{f290}",
"bag-shopping-minus": "\u{e650}",
"bag-shopping-plus": "\u{e651}",
"bags-shopping": "\u{f847}",
"baguette": "\u{e3d8}",
"bahai": "\u{f666}",
"haykal": "\u{f666}",
"baht-sign": "\u{e0ac}",
"balloon": "\u{e2e3}",
"balloons": "\u{e2e4}",
"ballot": "\u{f732}",
"ballot-check": "\u{f733}",
"ball-pile": "\u{f77e}",
"ban": "\u{f05e}",
"cancel": "\u{f05e}",
"banana": "\u{e2e5}",
"ban-bug": "\u{f7f9}",
"debug": "\u{f7f9}",
"bandage": "\u{f462}",
"band-aid": "\u{f462}",
"bandcamp": "\u{f2d5}",
"bangladeshi-taka-sign": "\u{e2e6}",
"banjo": "\u{f8a3}",
"ban-parking": "\u{f616}",
"parking-circle-slash": "\u{f616}",
"ban-smoking": "\u{f54d}",
"smoking-ban": "\u{f54d}",
"barcode": "\u{f02a}",
"barcode-read": "\u{f464}",
"barcode-scan": "\u{f465}",
"bars": "\u{f0c9}",
"navicon": "\u{f0c9}",
"bars-filter": "\u{e0ad}",
"bars-progress": "\u{f828}",
"tasks-alt": "\u{f828}",
"bars-sort": "\u{e0ae}",
"bars-staggered": "\u{f550}",
"reorder": "\u{f550}",
"stream": "\u{f550}",
"baseball": "\u{f433}",
"baseball-ball": "\u{f433}",
"baseball-bat-ball": "\u{f432}",
"basketball": "\u{f434}",
"basketball-ball": "\u{f434}",
"basketball-hoop": "\u{f435}",
"basket-shopping": "\u{f291}",
"shopping-basket": "\u{f291}",
"basket-shopping-minus": "\u{e652}",
"basket-shopping-plus": "\u{e653}",
"basket-shopping-simple": "\u{e0af}",
"shopping-basket-alt": "\u{e0af}",
"bat": "\u{f6b5}",
"bath": "\u{f2cd}",
"bathtub": "\u{f2cd}",
"battery-bolt": "\u{f376}",
"battery-empty": "\u{f244}",
"battery-0": "\u{f244}",
"battery-exclamation": "\u{e0b0}",
"battery-full": "\u{f240}",
"battery": "\u{f240}",
"battery-5": "\u{f240}",
"battery-half": "\u{f242}",
"battery-3": "\u{f242}",
"battery-low": "\u{e0b1}",
"battery-1": "\u{e0b1}",
"battery-quarter": "\u{f243}",
"battery-2": "\u{f243}",
"battery-slash": "\u{f377}",
"battery-three-quarters": "\u{f241}",
"battery-4": "\u{f241}",
"battle-net": "\u{f835}",
"bed": "\u{f236}",
"bed-bunk": "\u{f8f8}",
"bed-empty": "\u{f8f9}",
"bed-front": "\u{f8f7}",
"bed-alt": "\u{f8f7}",
"bed-pulse": "\u{f487}",
"procedures": "\u{f487}",
"bee": "\u{e0b2}",
"beer-mug": "\u{e0b3}",
"beer-foam": "\u{e0b3}",
"beer-mug-empty": "\u{f0fc}",
"beer": "\u{f0fc}",
"behance": "\u{f1b4}",
"bell": "\u{f0f3}",
"bell-concierge": "\u{f562}",
"concierge-bell": "\u{f562}",
"bell-exclamation": "\u{f848}",
"bell-on": "\u{f8fa}",
"bell-plus": "\u{f849}",
"bell-ring": "\u{e62c}",
"bells": "\u{f77f}",
"bell-school": "\u{f5d5}",
"bell-school-slash": "\u{f5d6}",
"bell-slash": "\u{f1f6}",
"bench-tree": "\u{e2e7}",
"bezier-curve": "\u{f55b}",
"bicycle": "\u{f206}",
"bilibili": "\u{e3d9}",
"billboard": "\u{e5cd}",
"bimobject": "\u{f378}",
"binary": "\u{e33b}",
"binary-circle-check": "\u{e33c}",
"binary-lock": "\u{e33d}",
"binary-slash": "\u{e33e}",
"bin-bottles": "\u{e5f5}",
"bin-bottles-recycle": "\u{e5f6}",
"binoculars": "\u{f1e5}",
"bin-recycle": "\u{e5f7}",
"biohazard": "\u{f780}",
"bird": "\u{e469}",
"bitbucket": "\u{f171}",
"bitcoin": "\u{f379}",
"bitcoin-sign": "\u{e0b4}",
"bity": "\u{f37a}",
"blackberry": "\u{f37b}",
"black-tie": "\u{f27e}",
"blanket": "\u{f498}",
"blanket-fire": "\u{e3da}",
"blender": "\u{f517}",
"blender-phone": "\u{f6b6}",
"blinds": "\u{f8fb}",
"blinds-open": "\u{f8fc}",
"blinds-raised": "\u{f8fd}",
"block": "\u{e46a}",
"block-brick": "\u{e3db}",
"wall-brick": "\u{e3db}",
"block-brick-fire": "\u{e3dc}",
"firewall": "\u{e3dc}",
"block-question": "\u{e3dd}",
"block-quote": "\u{e0b5}",
"blog": "\u{f781}",
"blogger": "\u{f37c}",
"blogger-b": "\u{f37d}",
"blueberries": "\u{e2e8}",
"bluesky": "\u{e671}",
"bluetooth": "\u{f293}",
"bluetooth-b": "\u{f294}",
"bold": "\u{f032}",
"bolt": "\u{f0e7}",
"zap": "\u{f0e7}",
"bolt-auto": "\u{e0b6}",
"bolt-lightning": "\u{e0b7}",
"bolt-slash": "\u{e0b8}",
"bomb": "\u{f1e2}",
"bone": "\u{f5d7}",
"bone-break": "\u{f5d8}",
"bong": "\u{f55c}",
"book": "\u{f02d}",
"book-arrow-right": "\u{e0b9}",
"book-arrow-up": "\u{e0ba}",
"book-atlas": "\u{f558}",
"atlas": "\u{f558}",
"book-bible": "\u{f647}",
"bible": "\u{f647}",
"book-blank": "\u{f5d9}",
"book-alt": "\u{f5d9}",
"book-bookmark": "\u{e0bb}",
"book-circle-arrow-right": "\u{e0bc}",
"book-circle-arrow-up": "\u{e0bd}",
"book-copy": "\u{e0be}",
"book-font": "\u{e0bf}",
"book-heart": "\u{f499}",
"book-journal-whills": "\u{f66a}",
"journal-whills": "\u{f66a}",
"bookmark": "\u{f02e}",
"bookmark-slash": "\u{e0c2}",
"book-medical": "\u{f7e6}",
"book-open": "\u{f518}",
"book-open-cover": "\u{e0c0}",
"book-open-alt": "\u{e0c0}",
"book-open-reader": "\u{f5da}",
"book-reader": "\u{f5da}",
"book-quran": "\u{f687}",
"quran": "\u{f687}",
"books": "\u{f5db}",
"book-section": "\u{e0c1}",
"book-law": "\u{e0c1}",
"book-skull": "\u{f6b7}",
"book-dead": "\u{f6b7}",
"books-medical": "\u{f7e8}",
"book-sparkles": "\u{f6b8}",
"book-spells": "\u{f6b8}",
"book-tanakh": "\u{f827}",
"tanakh": "\u{f827}",
"book-user": "\u{f7e7}",
"boombox": "\u{f8a5}",
"boot": "\u{f782}",
"booth-curtain": "\u{f734}",
"boot-heeled": "\u{e33f}",
"bootstrap": "\u{f836}",
"border-all": "\u{f84c}",
"border-bottom": "\u{f84d}",
"border-bottom-right": "\u{f854}",
"border-style-alt": "\u{f854}",
"border-center-h": "\u{f89c}",
"border-center-v": "\u{f89d}",
"border-inner": "\u{f84e}",
"border-left": "\u{f84f}",
"border-none": "\u{f850}",
"border-outer": "\u{f851}",
"border-right": "\u{f852}",
"border-top": "\u{f855}",
"border-top-left": "\u{f853}",
"border-style": "\u{f853}",
"bore-hole": "\u{e4c3}",
"bots": "\u{e340}",
"bottle-baby": "\u{e673}",
"bottle-droplet": "\u{e4c4}",
"bottle-water": "\u{e4c5}",
"bow-arrow": "\u{f6b9}",
"bowl-chopsticks": "\u{e2e9}",
"bowl-chopsticks-noodles": "\u{e2ea}",
"bowl-food": "\u{e4c6}",
"bowl-hot": "\u{f823}",
"soup": "\u{f823}",
"bowling-ball": "\u{f436}",
"bowling-ball-pin": "\u{e0c3}",
"bowling-pins": "\u{f437}",
"bowl-rice": "\u{e2eb}",
"bowl-scoop": "\u{e3de}",
"bowl-shaved-ice": "\u{e3de}",
"bowl-scoops": "\u{e3df}",
"bowl-soft-serve": "\u{e46b}",
"bowl-spoon": "\u{e3e0}",
"box": "\u{f466}",
"box-archive": "\u{f187}",
"archive": "\u{f187}",
"box-ballot": "\u{f735}",
"box-check": "\u{f467}",
"box-circle-check": "\u{e0c4}",
"box-dollar": "\u{f4a0}",
"box-usd": "\u{f4a0}",
"boxes-packing": "\u{e4c7}",
"boxes-stacked": "\u{f468}",
"boxes": "\u{f468}",
"boxes-alt": "\u{f468}",
"box-heart": "\u{f49d}",
"boxing-glove": "\u{f438}",
"glove-boxing": "\u{f438}",
"box-open": "\u{f49e}",
"box-open-full": "\u{f49c}",
"box-full": "\u{f49c}",
"box-taped": "\u{f49a}",
"box-alt": "\u{f49a}",
"box-tissue": "\u{e05b}",
"bracket-curly": "\u{7b}",
"bracket-curly-left": "\u{7b}",
"bracket-curly-right": "\u{7d}",
"bracket-round": "\u{28}",
"parenthesis": "\u{28}",
"bracket-round-right": "\u{29}",
"brackets-curly": "\u{f7ea}",
"bracket-square": "\u{5b}",
"bracket": "\u{5b}",
"bracket-left": "\u{5b}",
"bracket-square-right": "\u{5d}",
"brackets-round": "\u{e0c5}",
"parentheses": "\u{e0c5}",
"brackets-square": "\u{f7e9}",
"brackets": "\u{f7e9}",
"braille": "\u{f2a1}",
"brain": "\u{f5dc}",
"brain-arrow-curved-right": "\u{f677}",
"mind-share": "\u{f677}",
"brain-circuit": "\u{e0c6}",
"brake-warning": "\u{e0c7}",
"brave": "\u{e63c}",
"brave-reverse": "\u{e63d}",
"brazilian-real-sign": "\u{e46c}",
"bread-loaf": "\u{f7eb}",
"bread-slice": "\u{f7ec}",
"bread-slice-butter": "\u{e3e1}",
"bridge": "\u{e4c8}",
"bridge-circle-check": "\u{e4c9}",
"bridge-circle-exclamation": "\u{e4ca}",
"bridge-circle-xmark": "\u{e4cb}",
"bridge-lock": "\u{e4cc}",
"bridge-suspension": "\u{e4cd}",
"bridge-water": "\u{e4ce}",
"briefcase": "\u{f0b1}",
"briefcase-arrow-right": "\u{e2f2}",
"briefcase-blank": "\u{e0c8}",
"briefcase-medical": "\u{f469}",
"brightness": "\u{e0c9}",
"brightness-low": "\u{e0ca}",
"bring-forward": "\u{f856}",
"bring-front": "\u{f857}",
"broccoli": "\u{e3e2}",
"broom": "\u{f51a}",
"broom-ball": "\u{f458}",
"quidditch": "\u{f458}",
"quidditch-broom-ball": "\u{f458}",
"broom-wide": "\u{e5d1}",
"browser": "\u{f37e}",
"browsers": "\u{e0cb}",
"brush": "\u{f55d}",
"btc": "\u{f15a}",
"bucket": "\u{e4cf}",
"buffer": "\u{f837}",
"bug": "\u{f188}",
"bugs": "\u{e4d0}",
"bug-slash": "\u{e490}",
"building": "\u{f1ad}",
"building-circle-arrow-right": "\u{e4d1}",
"building-circle-check": "\u{e4d2}",
"building-circle-exclamation": "\u{e4d3}",
"building-circle-xmark": "\u{e4d4}",
"building-columns": "\u{f19c}",
"bank": "\u{f19c}",
"institution": "\u{f19c}",
"museum": "\u{f19c}",
"university": "\u{f19c}",
"building-flag": "\u{e4d5}",
"building-lock": "\u{e4d6}",
"building-magnifying-glass": "\u{e61c}",
"building-memo": "\u{e61e}",
"building-ngo": "\u{e4d7}",
"buildings": "\u{e0cc}",
"building-shield": "\u{e4d8}",
"building-un": "\u{e4d9}",
"building-user": "\u{e4da}",
"building-wheat": "\u{e4db}",
"bulldozer": "\u{e655}",
"bullhorn": "\u{f0a1}",
"bullseye": "\u{f140}",
"bullseye-arrow": "\u{f648}",
"bullseye-pointer": "\u{f649}",
"buoy": "\u{e5b5}",
"buoy-mooring": "\u{e5b6}",
"burger": "\u{f805}",
"hamburger": "\u{f805}",
"burger-cheese": "\u{f7f1}",
"cheeseburger": "\u{f7f1}",
"burger-fries": "\u{e0cd}",
"burger-glass": "\u{e0ce}",
"burger-lettuce": "\u{e3e3}",
"burger-soda": "\u{f858}",
"buromobelexperte": "\u{f37f}",
"burrito": "\u{f7ed}",
"burst": "\u{e4dc}",
"bus": "\u{f207}",
"business-time": "\u{f64a}",
"briefcase-clock": "\u{f64a}",
"bus-school": "\u{f5dd}",
"bus-simple": "\u{f55e}",
"bus-alt": "\u{f55e}",
"butter": "\u{e3e4}",
"buy-n-large": "\u{f8a6}",
"buysellads": "\u{f20d}",
"c": "\u{43}",
"cabin": "\u{e46d}",
"cabinet-filing": "\u{f64b}",
"cable-car": "\u{f7da}",
"tram": "\u{f7da}",
"cactus": "\u{f8a7}",
"caduceus": "\u{e681}",
"cake-candles": "\u{f1fd}",
"birthday-cake": "\u{f1fd}",
"cake": "\u{f1fd}",
"cake-slice": "\u{e3e5}",
"shortcake": "\u{e3e5}",
"calculator": "\u{f1ec}",
"calculator-simple": "\u{f64c}",
"calculator-alt": "\u{f64c}",
"calendar": "\u{f133}",
"calendar-arrow-down": "\u{e0d0}",
"calendar-download": "\u{e0d0}",
"calendar-arrow-up": "\u{e0d1}",
"calendar-upload": "\u{e0d1}",
"calendar-check": "\u{f274}",
"calendar-circle-exclamation": "\u{e46e}",
"calendar-circle-minus": "\u{e46f}",
"calendar-circle-plus": "\u{e470}",
"calendar-circle-user": "\u{e471}",
"calendar-clock": "\u{e0d2}",
"calendar-time": "\u{e0d2}",
"calendar-day": "\u{f783}",
"calendar-days": "\u{f073}",
"calendar-alt": "\u{f073}",
"calendar-exclamation": "\u{f334}",
"calendar-heart": "\u{e0d3}",
"calendar-image": "\u{e0d4}",
"calendar-lines": "\u{e0d5}",
"calendar-note": "\u{e0d5}",
"calendar-lines-pen": "\u{e472}",
"calendar-minus": "\u{f272}",
"calendar-pen": "\u{f333}",
"calendar-edit": "\u{f333}",
"calendar-plus": "\u{f271}",
"calendar-range": "\u{e0d6}",
"calendars": "\u{e0d7}",
"calendar-star": "\u{f736}",
"calendar-users": "\u{e5e2}",
"calendar-week": "\u{f784}",
"calendar-xmark": "\u{f273}",
"calendar-times": "\u{f273}",
"camcorder": "\u{f8a8}",
"video-handheld": "\u{f8a8}",
"camera": "\u{f030}",
"camera-alt": "\u{f030}",
"camera-cctv": "\u{f8ac}",
"cctv": "\u{f8ac}",
"camera-movie": "\u{f8a9}",
"camera-polaroid": "\u{f8aa}",
"camera-retro": "\u{f083}",
"camera-rotate": "\u{e0d8}",
"camera-security": "\u{f8fe}",
"camera-home": "\u{f8fe}",
"camera-slash": "\u{e0d9}",
"camera-viewfinder": "\u{e0da}",
"screenshot": "\u{e0da}",
"camera-web": "\u{f832}",
"webcam": "\u{f832}",
"camera-web-slash": "\u{f833}",
"webcam-slash": "\u{f833}",
"campfire": "\u{f6ba}",
"campground": "\u{f6bb}",
"canadian-maple-leaf": "\u{f785}",
"candle-holder": "\u{f6bc}",
"candy": "\u{e3e7}",
"candy-bar": "\u{e3e8}",
"chocolate-bar": "\u{e3e8}",
"candy-cane": "\u{f786}",
"candy-corn": "\u{f6bd}",
"can-food": "\u{e3e6}",
"cannabis": "\u{f55f}",
"cannon": "\u{e642}",
"capsules": "\u{f46b}",
"car": "\u{f1b9}",
"automobile": "\u{f1b9}",
"caravan": "\u{f8ff}",
"caravan-simple": "\u{e000}",
"caravan-alt": "\u{e000}",
"car-battery": "\u{f5df}",
"battery-car": "\u{f5df}",
"car-bolt": "\u{e341}",
"car-building": "\u{f859}",
"car-bump": "\u{f5e0}",
"car-burst": "\u{f5e1}",
"car-crash": "\u{f5e1}",
"car-bus": "\u{f85a}",
"car-circle-bolt": "\u{e342}",
"card-club": "\u{e3e9}",
"card-diamond": "\u{e3ea}",
"card-heart": "\u{e3eb}",
"cards": "\u{e3ed}",
"cards-blank": "\u{e4df}",
"card-spade": "\u{e3ec}",
"caret-down": "\u{f0d7}",
"caret-left": "\u{f0d9}",
"caret-right": "\u{f0da}",
"caret-up": "\u{f0d8}",
"car-garage": "\u{f5e2}",
"car-mirrors": "\u{e343}",
"car-on": "\u{e4dd}",
"car-rear": "\u{f5de}",
"car-alt": "\u{f5de}",
"carrot": "\u{f787}",
"cars": "\u{f85b}",
"car-side": "\u{f5e4}",
"car-side-bolt": "\u{e344}",
"cart-arrow-down": "\u{f218}",
"cart-arrow-up": "\u{e3ee}",
"cart-circle-arrow-down": "\u{e3ef}",
"cart-circle-arrow-up": "\u{e3f0}",
"cart-circle-check": "\u{e3f1}",
"cart-circle-exclamation": "\u{e3f2}",
"cart-circle-plus": "\u{e3f3}",
"cart-circle-xmark": "\u{e3f4}",
"cart-flatbed": "\u{f474}",
"dolly-flatbed": "\u{f474}",
"cart-flatbed-boxes": "\u{f475}",
"dolly-flatbed-alt": "\u{f475}",
"cart-flatbed-empty": "\u{f476}",
"dolly-flatbed-empty": "\u{f476}",
"cart-flatbed-suitcase": "\u{f59d}",
"luggage-cart": "\u{f59d}",
"car-tilt": "\u{f5e5}",
"cart-minus": "\u{e0db}",
"cart-plus": "\u{f217}",
"cart-shopping": "\u{f07a}",
"shopping-cart": "\u{f07a}",
"cart-shopping-fast": "\u{e0dc}",
"car-tunnel": "\u{e4de}",
"cart-xmark": "\u{e0dd}",
"car-wash": "\u{f5e6}",
"car-wrench": "\u{f5e3}",
"car-mechanic": "\u{f5e3}",
"cash-register": "\u{f788}",
"cassette-betamax": "\u{f8a4}",
"betamax": "\u{f8a4}",
"cassette-tape": "\u{f8ab}",
"cassette-vhs": "\u{f8ec}",
"vhs": "\u{f8ec}",
"castle": "\u{e0de}",
"cat": "\u{f6be}",
"cat-space": "\u{e001}",
"cauldron": "\u{f6bf}",
"cc-amazon-pay": "\u{f42d}",
"cc-amex": "\u{f1f3}",
"cc-apple-pay": "\u{f416}",
"cc-diners-club": "\u{f24c}",
"cc-discover": "\u{f1f2}",
"cc-jcb": "\u{f24b}",
"cc-mastercard": "\u{f1f1}",
"cc-paypal": "\u{f1f4}",
"cc-stripe": "\u{f1f5}",
"cc-visa": "\u{f1f0}",
"cedi-sign": "\u{e0df}",
"centercode": "\u{f380}",
"centos": "\u{f789}",
"cent-sign": "\u{e3f5}",
"certificate": "\u{f0a3}",
"chair": "\u{f6c0}",
"chair-office": "\u{f6c1}",
"chalkboard": "\u{f51b}",
"blackboard": "\u{f51b}",
"chalkboard-user": "\u{f51c}",
"chalkboard-teacher": "\u{f51c}",
"champagne-glass": "\u{f79e}",
"glass-champagne": "\u{f79e}",
"champagne-glasses": "\u{f79f}",
"glass-cheers": "\u{f79f}",
"charging-station": "\u{f5e7}",
"chart-area": "\u{f1fe}",
"area-chart": "\u{f1fe}",
"chart-bar": "\u{f080}",
"bar-chart": "\u{f080}",
"chart-bullet": "\u{e0e1}",
"chart-candlestick": "\u{e0e2}",
"chart-column": "\u{e0e3}",
"chart-gantt": "\u{e0e4}",
"chart-kanban": "\u{e64f}",
"chart-line": "\u{f201}",
"line-chart": "\u{f201}",
"chart-line-down": "\u{f64d}",
"chart-line-up": "\u{e0e5}",
"chart-line-up-down": "\u{e5d7}",
"chart-mixed": "\u{f643}",
"analytics": "\u{f643}",
"chart-mixed-up-circle-currency": "\u{e5d8}",
"chart-mixed-up-circle-dollar": "\u{e5d9}",
"chart-network": "\u{f78a}",
"chart-pie": "\u{f200}",
"pie-chart": "\u{f200}",
"chart-pie-simple": "\u{f64e}",
"chart-pie-alt": "\u{f64e}",
"chart-pie-simple-circle-currency": "\u{e604}",
"chart-pie-simple-circle-dollar": "\u{e605}",
"chart-pyramid": "\u{e0e6}",
"chart-radar": "\u{e0e7}",
"chart-scatter": "\u{f7ee}",
"chart-scatter-3d": "\u{e0e8}",
"chart-scatter-bubble": "\u{e0e9}",
"chart-simple": "\u{e473}",
"chart-simple-horizontal": "\u{e474}",
"chart-tree-map": "\u{e0ea}",
"chart-user": "\u{f6a3}",
"user-chart": "\u{f6a3}",
"chart-waterfall": "\u{e0eb}",
"check": "\u{f00c}",
"check-double": "\u{f560}",
"check-to-slot": "\u{f772}",
"vote-yea": "\u{f772}",
"cheese": "\u{f7ef}",
"cheese-swiss": "\u{f7f0}",
"cherries": "\u{e0ec}",
"chess": "\u{f439}",
"chess-bishop": "\u{f43a}",
"chess-bishop-piece": "\u{f43b}",
"chess-bishop-alt": "\u{f43b}",
"chess-board": "\u{f43c}",
"chess-clock": "\u{f43d}",
"chess-clock-flip": "\u{f43e}",
"chess-clock-alt": "\u{f43e}",
"chess-king": "\u{f43f}",
"chess-king-piece": "\u{f440}",
"chess-king-alt": "\u{f440}",
"chess-knight": "\u{f441}",
"chess-knight-piece": "\u{f442}",
"chess-knight-alt": "\u{f442}",
"chess-pawn": "\u{f443}",
"chess-pawn-piece": "\u{f444}",
"chess-pawn-alt": "\u{f444}",
"chess-queen": "\u{f445}",
"chess-queen-piece": "\u{f446}",
"chess-queen-alt": "\u{f446}",
"chess-rook": "\u{f447}",
"chess-rook-piece": "\u{f448}",
"chess-rook-alt": "\u{f448}",
"chestnut": "\u{e3f6}",
"chevron-down": "\u{f078}",
"chevron-left": "\u{f053}",
"chevron-right": "\u{f054}",
"chevrons-down": "\u{f322}",
"chevron-double-down": "\u{f322}",
"chevrons-left": "\u{f323}",
"chevron-double-left": "\u{f323}",
"chevrons-right": "\u{f324}",
"chevron-double-right": "\u{f324}",
"chevrons-up": "\u{f325}",
"chevron-double-up": "\u{f325}",
"chevron-up": "\u{f077}",
"chf-sign": "\u{e602}",
"child": "\u{f1ae}",
"child-combatant": "\u{e4e0}",
"child-rifle": "\u{e4e0}",
"child-dress": "\u{e59c}",
"child-reaching": "\u{e59d}",
"children": "\u{e4e1}",
"chimney": "\u{f78b}",
"chopsticks": "\u{e3f7}",
"chrome": "\u{f268}",
"chromecast": "\u{f838}",
"church": "\u{f51d}",
"circle": "\u{f111}",
"circle-0": "\u{e0ed}",
"circle-1": "\u{e0ee}",
"circle-2": "\u{e0ef}",
"circle-3": "\u{e0f0}",
"circle-4": "\u{e0f1}",
"circle-5": "\u{e0f2}",
"circle-6": "\u{e0f3}",
"circle-7": "\u{e0f4}",
"circle-8": "\u{e0f5}",
"circle-9": "\u{e0f6}",
"circle-a": "\u{e0f7}",
"circle-ampersand": "\u{e0f8}",
"circle-arrow-down": "\u{f0ab}",
"arrow-circle-down": "\u{f0ab}",
"circle-arrow-down-left": "\u{e0f9}",
"circle-arrow-down-right": "\u{e0fa}",
"circle-arrow-left": "\u{f0a8}",
"arrow-circle-left": "\u{f0a8}",
"circle-arrow-right": "\u{f0a9}",
"arrow-circle-right": "\u{f0a9}",
"circle-arrow-up": "\u{f0aa}",
"arrow-circle-up": "\u{f0aa}",
"circle-arrow-up-left": "\u{e0fb}",
"circle-arrow-up-right": "\u{e0fc}",
"circle-b": "\u{e0fd}",
"circle-bolt": "\u{e0fe}",
"circle-bookmark": "\u{e100}",
"bookmark-circle": "\u{e100}",
"circle-book-open": "\u{e0ff}",
"book-circle": "\u{e0ff}",
"circle-c": "\u{e101}",
"circle-calendar": "\u{e102}",
"calendar-circle": "\u{e102}",
"circle-camera": "\u{e103}",
"camera-circle": "\u{e103}",
"circle-caret-down": "\u{f32d}",
"caret-circle-down": "\u{f32d}",
"circle-caret-left": "\u{f32e}",
"caret-circle-left": "\u{f32e}",
"circle-caret-right": "\u{f330}",
"caret-circle-right": "\u{f330}",
"circle-caret-up": "\u{f331}",
"caret-circle-up": "\u{f331}",
"circle-check": "\u{f058}",
"check-circle": "\u{f058}",
"circle-chevron-down": "\u{f13a}",
"chevron-circle-down": "\u{f13a}",
"circle-chevron-left": "\u{f137}",
"chevron-circle-left": "\u{f137}",
"circle-chevron-right": "\u{f138}",
"chevron-circle-right": "\u{f138}",
"circle-chevron-up": "\u{f139}",
"chevron-circle-up": "\u{f139}",
"circle-d": "\u{e104}",
"circle-dashed": "\u{e105}",
"circle-divide": "\u{e106}",
"circle-dollar": "\u{f2e8}",
"dollar-circle": "\u{f2e8}",
"usd-circle": "\u{f2e8}",
"circle-dollar-to-slot": "\u{f4b9}",
"donate": "\u{f4b9}",
"circle-dot": "\u{f192}",
"dot-circle": "\u{f192}",
"circle-down": "\u{f358}",
"arrow-alt-circle-down": "\u{f358}",
"circle-down-left": "\u{e107}",
"circle-down-right": "\u{e108}",
"circle-e": "\u{e109}",
"circle-ellipsis": "\u{e10a}",
"circle-ellipsis-vertical": "\u{e10b}",
"circle-envelope": "\u{e10c}",
"envelope-circle": "\u{e10c}",
"circle-euro": "\u{e5ce}",
"circle-exclamation": "\u{f06a}",
"exclamation-circle": "\u{f06a}",
"circle-exclamation-check": "\u{e10d}",
"circle-f": "\u{e10e}",
"circle-g": "\u{e10f}",
"circle-gf": "\u{e67f}",
"circle-h": "\u{f47e}",
"hospital-symbol": "\u{f47e}",
"circle-half": "\u{e110}",
"circle-half-stroke": "\u{f042}",
"adjust": "\u{f042}",
"circle-heart": "\u{f4c7}",
"heart-circle": "\u{f4c7}",
"circle-i": "\u{e111}",
"circle-info": "\u{f05a}",
"info-circle": "\u{f05a}",
"circle-j": "\u{e112}",
"circle-k": "\u{e113}",
"circle-l": "\u{e114}",
"circle-left": "\u{f359}",
"arrow-alt-circle-left": "\u{f359}",
"circle-location-arrow": "\u{f602}",
"location-circle": "\u{f602}",
"circle-m": "\u{e115}",
"circle-microphone": "\u{e116}",
"microphone-circle": "\u{e116}",
"circle-microphone-lines": "\u{e117}",
"microphone-circle-alt": "\u{e117}",
"circle-minus": "\u{f056}",
"minus-circle": "\u{f056}",
"circle-n": "\u{e118}",
"circle-nodes": "\u{e4e2}",
"circle-notch": "\u{f1ce}",
"circle-o": "\u{e119}",
"circle-p": "\u{e11a}",
"circle-parking": "\u{f615}",
"parking-circle": "\u{f615}",
"circle-pause": "\u{f28b}",
"pause-circle": "\u{f28b}",
"circle-phone": "\u{e11b}",
"phone-circle": "\u{e11b}",
"circle-phone-flip": "\u{e11c}",
"phone-circle-alt": "\u{e11c}",
"circle-phone-hangup": "\u{e11d}",
"phone-circle-down": "\u{e11d}",
"circle-play": "\u{f144}",
"play-circle": "\u{f144}",
"circle-plus": "\u{f055}",
"plus-circle": "\u{f055}",
"circle-q": "\u{e11e}",
"circle-quarter": "\u{e11f}",
"circle-quarters": "\u{e3f8}",
"circle-quarter-stroke": "\u{e5d3}",
"circle-question": "\u{f059}",
"question-circle": "\u{f059}",
"circle-r": "\u{e120}",
"circle-radiation": "\u{f7ba}",
"radiation-alt": "\u{f7ba}",
"circle-right": "\u{f35a}",
"arrow-alt-circle-right": "\u{f35a}",
"circle-s": "\u{e121}",
"circle-small": "\u{e122}",
"circle-sort": "\u{e030}",
"sort-circle": "\u{e030}",
"circle-sort-down": "\u{e031}",
"sort-circle-down": "\u{e031}",
"circle-sort-up": "\u{e032}",
"sort-circle-up": "\u{e032}",
"circles-overlap": "\u{e600}",
"circle-star": "\u{e123}",
"star-circle": "\u{e123}",
"circle-sterling": "\u{e5cf}",
"circle-stop": "\u{f28d}",
"stop-circle": "\u{f28d}",
"circle-t": "\u{e124}",
"circle-three-quarters": "\u{e125}",
"circle-three-quarters-stroke": "\u{e5d4}",
"circle-trash": "\u{e126}",
"trash-circle": "\u{e126}",
"circle-u": "\u{e127}",
"circle-up": "\u{f35b}",
"arrow-alt-circle-up": "\u{f35b}",
"circle-up-left": "\u{e128}",
"circle-up-right": "\u{e129}",
"circle-user": "\u{f2bd}",
"user-circle": "\u{f2bd}",
"circle-v": "\u{e12a}",
"circle-video": "\u{e12b}",
"video-circle": "\u{e12b}",
"circle-w": "\u{e12c}",
"circle-waveform-lines": "\u{e12d}",
"waveform-circle": "\u{e12d}",
"circle-wifi": "\u{e67d}",
"circle-wifi-circle-wifi": "\u{e67e}",
"circle-wifi-group": "\u{e67e}",
"circle-x": "\u{e12e}",
"circle-xmark": "\u{f057}",
"times-circle": "\u{f057}",
"xmark-circle": "\u{f057}",
"circle-y": "\u{e12f}",
"circle-yen": "\u{e5d0}",
"circle-z": "\u{e130}",
"citrus": "\u{e2f4}",
"citrus-slice": "\u{e2f5}",
"city": "\u{f64f}",
"clapperboard": "\u{e131}",
"clapperboard-play": "\u{e132}",
"clarinet": "\u{f8ad}",
"claw-marks": "\u{f6c2}",
"clipboard": "\u{f328}",
"clipboard-check": "\u{f46c}",
"clipboard-list": "\u{f46d}",
"clipboard-list-check": "\u{f737}",
"clipboard-medical": "\u{e133}",
"clipboard-prescription": "\u{f5e8}",
"clipboard-question": "\u{e4e3}",
"clipboard-user": "\u{f7f3}",
"clock": "\u{f017}",
"clock-four": "\u{f017}",
"clock-desk": "\u{e134}",
"clock-eight": "\u{e345}",
"clock-eight-thirty": "\u{e346}",
"clock-eleven": "\u{e347}",
"clock-eleven-thirty": "\u{e348}",
"clock-five": "\u{e349}",
"clock-five-thirty": "\u{e34a}",
"clock-four-thirty": "\u{e34b}",
"clock-nine": "\u{e34c}",
"clock-nine-thirty": "\u{e34d}",
"clock-one": "\u{e34e}",
"clock-one-thirty": "\u{e34f}",
"clock-rotate-left": "\u{f1da}",
"history": "\u{f1da}",
"clock-seven": "\u{e350}",
"clock-seven-thirty": "\u{e351}",
"clock-six": "\u{e352}",
"clock-six-thirty": "\u{e353}",
"clock-ten": "\u{e354}",
"clock-ten-thirty": "\u{e355}",
"clock-three": "\u{e356}",
"clock-three-thirty": "\u{e357}",
"clock-twelve": "\u{e358}",
"clock-twelve-thirty": "\u{e359}",
"clock-two": "\u{e35a}",
"clock-two-thirty": "\u{e35b}",
"clone": "\u{f24d}",
"closed-captioning": "\u{f20a}",
"closed-captioning-slash": "\u{e135}",
"clothes-hanger": "\u{e136}",
"cloud": "\u{f0c2}",
"cloud-arrow-down": "\u{f0ed}",
"cloud-download": "\u{f0ed}",
"cloud-download-alt": "\u{f0ed}",
"cloud-arrow-up": "\u{f0ee}",
"cloud-upload": "\u{f0ee}",
"cloud-upload-alt": "\u{f0ee}",
"cloud-binary": "\u{e601}",
"cloud-bolt": "\u{f76c}",
"thunderstorm": "\u{f76c}",
"cloud-bolt-moon": "\u{f76d}",
"thunderstorm-moon": "\u{f76d}",
"cloud-bolt-sun": "\u{f76e}",
"thunderstorm-sun": "\u{f76e}",
"cloud-check": "\u{e35c}",
"cloud-drizzle": "\u{f738}",
"cloud-exclamation": "\u{e491}",
"cloudflare": "\u{e07d}",
"cloud-fog": "\u{f74e}",
"fog": "\u{f74e}",
"cloud-hail": "\u{f739}",
"cloud-hail-mixed": "\u{f73a}",
"cloud-meatball": "\u{f73b}",
"cloud-minus": "\u{e35d}",
"cloud-moon": "\u{f6c3}",
"cloud-moon-rain": "\u{f73c}",
"cloud-music": "\u{f8ae}",
"cloud-plus": "\u{e35e}",
"cloud-question": "\u{e492}",
"cloud-rain": "\u{f73d}",
"cloud-rainbow": "\u{f73e}",
"clouds": "\u{f744}",
"cloudscale": "\u{f383}",
"cloud-showers": "\u{f73f}",
"cloud-showers-heavy": "\u{f740}",
"cloud-showers-water": "\u{e4e4}",
"cloud-slash": "\u{e137}",
"cloud-sleet": "\u{f741}",
"cloudsmith": "\u{f384}",
"clouds-moon": "\u{f745}",
"cloud-snow": "\u{f742}",
"clouds-sun": "\u{f746}",
"cloud-sun": "\u{f6c4}",
"cloud-sun-rain": "\u{f743}",
"cloudversify": "\u{f385}",
"cloud-word": "\u{e138}",
"cloud-xmark": "\u{e35f}",
"clover": "\u{e139}",
"club": "\u{f327}",
"cmplid": "\u{e360}",
"coconut": "\u{e2f6}",
"code": "\u{f121}",
"code-branch": "\u{f126}",
"code-commit": "\u{f386}",
"code-compare": "\u{e13a}",
"code-fork": "\u{e13b}",
"code-merge": "\u{f387}",
"codepen": "\u{f1cb}",
"code-pull-request": "\u{e13c}",
"code-pull-request-closed": "\u{e3f9}",
"code-pull-request-draft": "\u{e3fa}",
"code-simple": "\u{e13d}",
"codiepie": "\u{f284}",
"coffee-bean": "\u{e13e}",
"coffee-beans": "\u{e13f}",
"coffee-pot": "\u{e002}",
"coffin": "\u{f6c6}",
"coffin-cross": "\u{e051}",
"coin": "\u{f85c}",
"coin-blank": "\u{e3fb}",
"coin-front": "\u{e3fc}",
"coins": "\u{f51e}",
"coin-vertical": "\u{e3fd}",
"colon": "\u{3a}",
"colon-sign": "\u{e140}",
"columns-3": "\u{e361}",
"comet": "\u{e003}",
"comma": "\u{2c}",
"command": "\u{e142}",
"comment": "\u{f075}",
"comment-arrow-down": "\u{e143}",
"comment-arrow-up": "\u{e144}",
"comment-arrow-up-right": "\u{e145}",
"comment-captions": "\u{e146}",
"comment-check": "\u{f4ac}",
"comment-code": "\u{e147}",
"comment-dollar": "\u{f651}",
"comment-dots": "\u{f4ad}",
"commenting": "\u{f4ad}",
"comment-exclamation": "\u{f4af}",
"comment-heart": "\u{e5c8}",
"comment-image": "\u{e148}",
"comment-lines": "\u{f4b0}",
"comment-medical": "\u{f7f5}",
"comment-middle": "\u{e149}",
"comment-middle-top": "\u{e14a}",
"comment-minus": "\u{f4b1}",
"comment-music": "\u{f8b0}",
"comment-pen": "\u{f4ae}",
"comment-edit": "\u{f4ae}",
"comment-plus": "\u{f4b2}",
"comment-question": "\u{e14b}",
"comment-quote": "\u{e14c}",
"comments": "\u{f086}",
"comments-dollar": "\u{f653}",
"comment-slash": "\u{f4b3}",
"comment-smile": "\u{f4b4}",
"comment-sms": "\u{f7cd}",
"sms": "\u{f7cd}",
"comments-question": "\u{e14e}",
"comments-question-check": "\u{e14f}",
"comment-text": "\u{e14d}",
"comment-xmark": "\u{f4b5}",
"comment-times": "\u{f4b5}",
"compact-disc": "\u{f51f}",
"compass": "\u{f14e}",
"compass-drafting": "\u{f568}",
"drafting-compass": "\u{f568}",
"compass-slash": "\u{f5e9}",
"compress": "\u{f066}",
"compress-wide": "\u{f326}",
"computer": "\u{e4e5}",
"computer-classic": "\u{f8b1}",
"computer-mouse": "\u{f8cc}",
"mouse": "\u{f8cc}",
"computer-mouse-scrollwheel": "\u{f8cd}",
"mouse-alt": "\u{f8cd}",
"computer-speaker": "\u{f8b2}",
"confluence": "\u{f78d}",
"connectdevelop": "\u{f20e}",
"container-storage": "\u{f4b7}",
"contao": "\u{f26d}",
"conveyor-belt": "\u{f46e}",
"conveyor-belt-arm": "\u{e5f8}",
"conveyor-belt-boxes": "\u{f46f}",
"conveyor-belt-alt": "\u{f46f}",
"conveyor-belt-empty": "\u{e150}",
"cookie": "\u{f563}",
"cookie-bite": "\u{f564}",
"copy": "\u{f0c5}",
"copyright": "\u{f1f9}",
"corn": "\u{f6c7}",
"corner": "\u{e3fe}",
"cotton-bureau": "\u{f89e}",
"couch": "\u{f4b8}",
"court-sport": "\u{e643}",
"cow": "\u{f6c8}",
"cowbell": "\u{f8b3}",
"cowbell-circle-plus": "\u{f8b4}",
"cowbell-more": "\u{f8b4}",
"cpanel": "\u{f388}",
"crab": "\u{e3ff}",
"crate-apple": "\u{f6b1}",
"apple-crate": "\u{f6b1}",
"crate-empty": "\u{e151}",
"creative-commons": "\u{f25e}",
"creative-commons-by": "\u{f4e7}",
"creative-commons-nc": "\u{f4e8}",
"creative-commons-nc-eu": "\u{f4e9}",
"creative-commons-nc-jp": "\u{f4ea}",
"creative-commons-nd": "\u{f4eb}",
"creative-commons-pd": "\u{f4ec}",
"creative-commons-pd-alt": "\u{f4ed}",
"creative-commons-remix": "\u{f4ee}",
"creative-commons-sa": "\u{f4ef}",
"creative-commons-sampling": "\u{f4f0}",
"creative-commons-sampling-plus": "\u{f4f1}",
"creative-commons-share": "\u{f4f2}",
"creative-commons-zero": "\u{f4f3}",
"credit-card": "\u{f09d}",
"credit-card-alt": "\u{f09d}",
"credit-card-blank": "\u{f389}",
"credit-card-front": "\u{f38a}",
"cricket-bat-ball": "\u{f449}",
"cricket": "\u{f449}",
"critical-role": "\u{f6c9}",
"croissant": "\u{f7f6}",
"crop": "\u{f125}",
"crop-simple": "\u{f565}",
"crop-alt": "\u{f565}",
"cross": "\u{f654}",
"crosshairs": "\u{f05b}",
"crosshairs-simple": "\u{e59f}",
"crow": "\u{f520}",
"crown": "\u{f521}",
"crutch": "\u{f7f7}",
"crutches": "\u{f7f8}",
"cruzeiro-sign": "\u{e152}",
"crystal-ball": "\u{e362}",
"css3": "\u{f13c}",
"css3-alt": "\u{f38b}",
"cube": "\u{f1b2}",
"cubes": "\u{f1b3}",
"cubes-stacked": "\u{e4e6}",
"cucumber": "\u{e401}",
"cupcake": "\u{e402}",
"cup-straw": "\u{e363}",
"cup-straw-swoosh": "\u{e364}",
"cup-togo": "\u{f6c5}",
"coffee-togo": "\u{f6c5}",
"curling-stone": "\u{f44a}",
"curling": "\u{f44a}",
"custard": "\u{e403}",
"cuttlefish": "\u{f38c}",
"d": "\u{44}",
"dagger": "\u{f6cb}",
"dailymotion": "\u{e052}",
"d-and-d": "\u{f38d}",
"d-and-d-beyond": "\u{f6ca}",
"dart-lang": "\u{e693}",
"dash": "\u{e404}",
"minus-large": "\u{e404}",
"dashcube": "\u{f210}",
"database": "\u{f1c0}",
"debian": "\u{e60b}",
"deer": "\u{f78e}",
"deer-rudolph": "\u{f78f}",
"deezer": "\u{e077}",
"delete-left": "\u{f55a}",
"backspace": "\u{f55a}",
"delete-right": "\u{e154}",
"delicious": "\u{f1a5}",
"democrat": "\u{f747}",
"deploydog": "\u{f38e}",
"deskpro": "\u{f38f}",
"desktop": "\u{f390}",
"desktop-alt": "\u{f390}",
"desktop-arrow-down": "\u{e155}",
"dev": "\u{f6cc}",
"deviantart": "\u{f1bd}",
"dharmachakra": "\u{f655}",
"dhl": "\u{f790}",
"diagram-cells": "\u{e475}",
"diagram-lean-canvas": "\u{e156}",
"diagram-nested": "\u{e157}",
"diagram-next": "\u{e476}",
"diagram-predecessor": "\u{e477}",
"diagram-previous": "\u{e478}",
"diagram-project": "\u{f542}",
"project-diagram": "\u{f542}",
"diagram-sankey": "\u{e158}",
"diagram-subtask": "\u{e479}",
"diagram-successor": "\u{e47a}",
"diagram-venn": "\u{e15a}",
"dial": "\u{e15b}",
"dial-med-high": "\u{e15b}",
"dial-high": "\u{e15c}",
"dial-low": "\u{e15d}",
"dial-max": "\u{e15e}",
"dial-med": "\u{e15f}",
"dial-med-low": "\u{e160}",
"dial-min": "\u{e161}",
"dial-off": "\u{e162}",
"diamond": "\u{f219}",
"diamond-exclamation": "\u{e405}",
"diamond-half": "\u{e5b7}",
"diamond-half-stroke": "\u{e5b8}",
"diamonds-4": "\u{e68b}",
"diamond-turn-right": "\u{f5eb}",
"directions": "\u{f5eb}",
"diaspora": "\u{f791}",
"dice": "\u{f522}",
"dice-d10": "\u{f6cd}",
"dice-d12": "\u{f6ce}",
"dice-d20": "\u{f6cf}",
"dice-d4": "\u{f6d0}",
"dice-d6": "\u{f6d1}",
"dice-d8": "\u{f6d2}",
"dice-five": "\u{f523}",
"dice-four": "\u{f524}",
"dice-one": "\u{f525}",
"dice-six": "\u{f526}",
"dice-three": "\u{f527}",
"dice-two": "\u{f528}",
"digg": "\u{f1a6}",
"digital-ocean": "\u{f391}",
"dinosaur": "\u{e5fe}",
"diploma": "\u{f5ea}",
"scroll-ribbon": "\u{f5ea}",
"disc-drive": "\u{f8b5}",
"discord": "\u{f392}",
"discourse": "\u{f393}",
"disease": "\u{f7fa}",
"display": "\u{e163}",
"display-arrow-down": "\u{e164}",
"display-chart-up": "\u{e5e3}",
"display-chart-up-circle-currency": "\u{e5e5}",
"display-chart-up-circle-dollar": "\u{e5e6}",
"display-code": "\u{e165}",
"desktop-code": "\u{e165}",
"display-medical": "\u{e166}",
"desktop-medical": "\u{e166}",
"display-slash": "\u{e2fa}",
"desktop-slash": "\u{e2fa}",
"distribute-spacing-horizontal": "\u{e365}",
"distribute-spacing-vertical": "\u{e366}",
"ditto": "\u{22}",
"divide": "\u{f529}",
"dna": "\u{f471}",
"dochub": "\u{f394}",
"docker": "\u{f395}",
"dog": "\u{f6d3}",
"dog-leashed": "\u{f6d4}",
"dollar-sign": "\u{24}",
"dollar": "\u{24}",
"usd": "\u{24}",
"dolly": "\u{f472}",
"dolly-box": "\u{f472}",
"dolly-empty": "\u{f473}",
"dolphin": "\u{e168}",
"dong-sign": "\u{e169}",
"do-not-enter": "\u{f5ec}",
"donut": "\u{e406}",
"doughnut": "\u{e406}",
"door-closed": "\u{f52a}",
"door-open": "\u{f52b}",
"dove": "\u{f4ba}",
"down": "\u{f354}",
"arrow-alt-down": "\u{f354}",
"down-from-bracket": "\u{e66b}",
"down-from-dotted-line": "\u{e407}",
"down-from-line": "\u{f349}",
"arrow-alt-from-top": "\u{f349}",
"down-left": "\u{e16a}",
"down-left-and-up-right-to-center": "\u{f422}",
"compress-alt": "\u{f422}",
"download": "\u{f019}",
"down-long": "\u{f309}",
"long-arrow-alt-down": "\u{f309}",
"down-right": "\u{e16b}",
"down-to-bracket": "\u{e4e7}",
"down-to-dotted-line": "\u{e408}",
"down-to-line": "\u{f34a}",
"arrow-alt-to-bottom": "\u{f34a}",
"draft2digital": "\u{f396}",
"dragon": "\u{f6d5}",
"draw-circle": "\u{f5ed}",
"draw-polygon": "\u{f5ee}",
"draw-square": "\u{f5ef}",
"dreidel": "\u{f792}",
"dribbble": "\u{f17d}",
"drone": "\u{f85f}",
"drone-front": "\u{f860}",
"drone-alt": "\u{f860}",
"dropbox": "\u{f16b}",
"droplet": "\u{f043}",
"tint": "\u{f043}",
"droplet-degree": "\u{f748}",
"dewpoint": "\u{f748}",
"droplet-percent": "\u{f750}",
"humidity": "\u{f750}",
"droplet-slash": "\u{f5c7}",
"tint-slash": "\u{f5c7}",
"drum": "\u{f569}",
"drum-steelpan": "\u{f56a}",
"drumstick": "\u{f6d6}",
"drumstick-bite": "\u{f6d7}",
"drupal": "\u{f1a9}",
"dryer": "\u{f861}",
"dryer-heat": "\u{f862}",
"dryer-alt": "\u{f862}",
"duck": "\u{f6d8}",
"dumbbell": "\u{f44b}",
"dumpster": "\u{f793}",
"dumpster-fire": "\u{f794}",
"dungeon": "\u{f6d9}",
"dyalog": "\u{f399}",
"e": "\u{45}",
"ear": "\u{f5f0}",
"ear-deaf": "\u{f2a4}",
"deaf": "\u{f2a4}",
"deafness": "\u{f2a4}",
"hard-of-hearing": "\u{f2a4}",
"ear-listen": "\u{f2a2}",
"assistive-listening-systems": "\u{f2a2}",
"earlybirds": "\u{f39a}",
"ear-muffs": "\u{f795}",
"earth-africa": "\u{f57c}",
"globe-africa": "\u{f57c}",
"earth-americas": "\u{f57d}",
"earth": "\u{f57d}",
"earth-america": "\u{f57d}",
"globe-americas": "\u{f57d}",
"earth-asia": "\u{f57e}",
"globe-asia": "\u{f57e}",
"earth-europe": "\u{f7a2}",
"globe-europe": "\u{f7a2}",
"earth-oceania": "\u{e47b}",
"globe-oceania": "\u{e47b}",
"ebay": "\u{f4f4}",
"eclipse": "\u{f749}",
"edge": "\u{f282}",
"edge-legacy": "\u{e078}",
"egg": "\u{f7fb}",
"egg-fried": "\u{f7fc}",
"eggplant": "\u{e16c}",
"eject": "\u{f052}",
"elementor": "\u{f430}",
"elephant": "\u{f6da}",
"elevator": "\u{e16d}",
"ellipsis": "\u{f141}",
"ellipsis-h": "\u{f141}",
"ellipsis-stroke": "\u{f39b}",
"ellipsis-h-alt": "\u{f39b}",
"ellipsis-stroke-vertical": "\u{f39c}",
"ellipsis-v-alt": "\u{f39c}",
"ellipsis-vertical": "\u{f142}",
"ellipsis-v": "\u{f142}",
"ello": "\u{f5f1}",
"ember": "\u{f423}",
"empire": "\u{f1d1}",
"empty-set": "\u{f656}",
"engine": "\u{e16e}",
"engine-warning": "\u{f5f2}",
"engine-exclamation": "\u{f5f2}",
"envelope": "\u{f0e0}",
"envelope-circle-check": "\u{e4e8}",
"envelope-dot": "\u{e16f}",
"envelope-badge": "\u{e16f}",
"envelope-open": "\u{f2b6}",
"envelope-open-dollar": "\u{f657}",
"envelope-open-text": "\u{f658}",
"envelopes": "\u{e170}",
"envelopes-bulk": "\u{f674}",
"mail-bulk": "\u{f674}",
"envira": "\u{f299}",
"equals": "\u{3d}",
"eraser": "\u{f12d}",
"erlang": "\u{f39d}",
"escalator": "\u{e171}",
"ethereum": "\u{f42e}",
"ethernet": "\u{f796}",
"etsy": "\u{f2d7}",
"euro-sign": "\u{f153}",
"eur": "\u{f153}",
"euro": "\u{f153}",
"evernote": "\u{f839}",
"excavator": "\u{e656}",
"exclamation": "\u{21}",
"expand": "\u{f065}",
"expand-wide": "\u{f320}",
"expeditedssl": "\u{f23e}",
"explosion": "\u{e4e9}",
"eye": "\u{f06e}",
"eye-dropper": "\u{f1fb}",
"eye-dropper-empty": "\u{f1fb}",
"eyedropper": "\u{f1fb}",
"eye-dropper-full": "\u{e172}",
"eye-dropper-half": "\u{e173}",
"eye-evil": "\u{f6db}",
"eye-low-vision": "\u{f2a8}",
"low-vision": "\u{f2a8}",
"eyes": "\u{e367}",
"eye-slash": "\u{f070}",
"f": "\u{46}",
"face-angry": "\u{f556}",
"angry": "\u{f556}",
"face-angry-horns": "\u{e368}",
"face-anguished": "\u{e369}",
"face-anxious-sweat": "\u{e36a}",
"face-astonished": "\u{e36b}",
"face-awesome": "\u{e409}",
"gave-dandy": "\u{e409}",
"face-beam-hand-over-mouth": "\u{e47c}",
"facebook": "\u{f09a}",
"facebook-f": "\u{f39e}",
"facebook-messenger": "\u{f39f}",
"face-clouds": "\u{e47d}",
"face-confounded": "\u{e36c}",
"face-confused": "\u{e36d}",
"face-cowboy-hat": "\u{e36e}",
"face-diagonal-mouth": "\u{e47e}",
"face-disappointed": "\u{e36f}",
"face-disguise": "\u{e370}",
"face-dizzy": "\u{f567}",
"dizzy": "\u{f567}",
"face-dotted": "\u{e47f}",
"face-downcast-sweat": "\u{e371}",
"face-drooling": "\u{e372}",
"face-exhaling": "\u{e480}",
"face-explode": "\u{e2fe}",
"exploding-head": "\u{e2fe}",
"face-expressionless": "\u{e373}",
"face-eyes-xmarks": "\u{e374}",
"face-fearful": "\u{e375}",
"face-flushed": "\u{f579}",
"flushed": "\u{f579}",
"face-frown": "\u{f119}",
"frown": "\u{f119}",
"face-frown-open": "\u{f57a}",
"frown-open": "\u{f57a}",
"face-frown-slight": "\u{e376}",
"face-glasses": "\u{e377}",
"face-grimace": "\u{f57f}",
"grimace": "\u{f57f}",
"face-grin": "\u{f580}",
"grin": "\u{f580}",
"face-grin-beam": "\u{f582}",
"grin-beam": "\u{f582}",
"face-grin-beam-sweat": "\u{f583}",
"grin-beam-sweat": "\u{f583}",
"face-grin-hearts": "\u{f584}",
"grin-hearts": "\u{f584}",
"face-grin-squint": "\u{f585}",
"grin-squint": "\u{f585}",
"face-grin-squint-tears": "\u{f586}",
"grin-squint-tears": "\u{f586}",
"face-grin-stars": "\u{f587}",
"grin-stars": "\u{f587}",
"face-grin-tears": "\u{f588}",
"grin-tears": "\u{f588}",
"face-grin-tongue": "\u{f589}",
"grin-tongue": "\u{f589}",
"face-grin-tongue-squint": "\u{f58a}",
"grin-tongue-squint": "\u{f58a}",
"face-grin-tongue-wink": "\u{f58b}",
"grin-tongue-wink": "\u{f58b}",
"face-grin-wide": "\u{f581}",
"grin-alt": "\u{f581}",
"face-grin-wink": "\u{f58c}",
"grin-wink": "\u{f58c}",
"face-hand-over-mouth": "\u{e378}",
"face-hand-peeking": "\u{e481}",
"face-hand-yawn": "\u{e379}",
"face-head-bandage": "\u{e37a}",
"face-holding-back-tears": "\u{e482}",
"face-hushed": "\u{e37b}",
"face-icicles": "\u{e37c}",
"face-kiss": "\u{f596}",
"kiss": "\u{f596}",
"face-kiss-beam": "\u{f597}",
"kiss-beam": "\u{f597}",
"face-kiss-closed-eyes": "\u{e37d}",
"face-kiss-wink-heart": "\u{f598}",
"kiss-wink-heart": "\u{f598}",
"face-laugh": "\u{f599}",
"laugh": "\u{f599}",
"face-laugh-beam": "\u{f59a}",
"laugh-beam": "\u{f59a}",
"face-laugh-squint": "\u{f59b}",
"laugh-squint": "\u{f59b}",
"face-laugh-wink": "\u{f59c}",
"laugh-wink": "\u{f59c}",
"face-lying": "\u{e37e}",
"face-mask": "\u{e37f}",
"face-meh": "\u{f11a}",
"meh": "\u{f11a}",
"face-meh-blank": "\u{f5a4}",
"meh-blank": "\u{f5a4}",
"face-melting": "\u{e483}",
"face-monocle": "\u{e380}",
"face-nauseated": "\u{e381}",
"face-nose-steam": "\u{e382}",
"face-party": "\u{e383}",
"face-pensive": "\u{e384}",
"face-persevering": "\u{e385}",
"face-pleading": "\u{e386}",
"face-pouting": "\u{e387}",
"face-raised-eyebrow": "\u{e388}",
"face-relieved": "\u{e389}",
"face-rolling-eyes": "\u{f5a5}",
"meh-rolling-eyes": "\u{f5a5}",
"face-sad-cry": "\u{f5b3}",
"sad-cry": "\u{f5b3}",
"face-sad-sweat": "\u{e38a}",
"face-sad-tear": "\u{f5b4}",
"sad-tear": "\u{f5b4}",
"face-saluting": "\u{e484}",
"face-scream": "\u{e38b}",
"face-shush": "\u{e38c}",
"face-sleeping": "\u{e38d}",
"face-sleepy": "\u{e38e}",
"face-smile": "\u{f118}",
"smile": "\u{f118}",
"face-smile-beam": "\u{f5b8}",
"smile-beam": "\u{f5b8}",
"face-smile-halo": "\u{e38f}",
"face-smile-hearts": "\u{e390}",
"face-smile-horns": "\u{e391}",
"face-smile-plus": "\u{f5b9}",
"smile-plus": "\u{f5b9}",
"face-smile-relaxed": "\u{e392}",
"face-smile-tear": "\u{e393}",
"face-smile-tongue": "\u{e394}",
"face-smile-upside-down": "\u{e395}",
"face-smile-wink": "\u{f4da}",
"smile-wink": "\u{f4da}",
"face-smiling-hands": "\u{e396}",
"face-smirking": "\u{e397}",
"face-spiral-eyes": "\u{e485}",
"face-sunglasses": "\u{e398}",
"face-surprise": "\u{f5c2}",
"surprise": "\u{f5c2}",
"face-swear": "\u{e399}",
"face-thermometer": "\u{e39a}",
"face-thinking": "\u{e39b}",
"face-tired": "\u{f5c8}",
"tired": "\u{f5c8}",
"face-tissue": "\u{e39c}",
"face-tongue-money": "\u{e39d}",
"face-tongue-sweat": "\u{e39e}",
"face-unamused": "\u{e39f}",
"face-viewfinder": "\u{e2ff}",
"face-vomit": "\u{e3a0}",
"face-weary": "\u{e3a1}",
"face-woozy": "\u{e3a2}",
"face-worried": "\u{e3a3}",
"face-zany": "\u{e3a4}",
"face-zipper": "\u{e3a5}",
"falafel": "\u{e40a}",
"family": "\u{e300}",
"family-dress": "\u{e301}",
"family-pants": "\u{e302}",
"fan": "\u{f863}",
"fan-table": "\u{e004}",
"fantasy-flight-games": "\u{f6dc}",
"farm": "\u{f864}",
"barn-silo": "\u{f864}",
"faucet": "\u{e005}",
"faucet-drip": "\u{e006}",
"fax": "\u{f1ac}",
"feather": "\u{f52d}",
"feather-pointed": "\u{f56b}",
"feather-alt": "\u{f56b}",
"fedex": "\u{f797}",
"fedora": "\u{f798}",
"fence": "\u{e303}",
"ferris-wheel": "\u{e174}",
"ferry": "\u{e4ea}",
"field-hockey-stick-ball": "\u{f44c}",
"field-hockey": "\u{f44c}",
"figma": "\u{f799}",
"file": "\u{f15b}",
"file-arrow-down": "\u{f56d}",
"file-download": "\u{f56d}",
"file-arrow-up": "\u{f574}",
"file-upload": "\u{f574}",
"file-audio": "\u{f1c7}",
"file-binary": "\u{e175}",
"file-cad": "\u{e672}",
"file-certificate": "\u{f5f3}",
"file-award": "\u{f5f3}",
"file-chart-column": "\u{f659}",
"file-chart-line": "\u{f659}",
"file-chart-pie": "\u{f65a}",
"file-check": "\u{f316}",
"file-circle-check": "\u{e5a0}",
"file-circle-exclamation": "\u{e4eb}",
"file-circle-info": "\u{e493}",
"file-circle-minus": "\u{e4ed}",
"file-circle-plus": "\u{e494}",
"file-circle-question": "\u{e4ef}",
"file-circle-xmark": "\u{e5a1}",
"file-code": "\u{f1c9}",
"file-contract": "\u{f56c}",
"file-csv": "\u{f6dd}",
"file-dashed-line": "\u{f877}",
"page-break": "\u{f877}",
"file-doc": "\u{e5ed}",
"file-eps": "\u{e644}",
"file-excel": "\u{f1c3}",
"file-exclamation": "\u{f31a}",
"file-export": "\u{f56e}",
"arrow-right-from-file": "\u{f56e}",
"file-gif": "\u{e645}",
"file-heart": "\u{e176}",
"file-image": "\u{f1c5}",
"file-import": "\u{f56f}",
"arrow-right-to-file": "\u{f56f}",
"file-invoice": "\u{f570}",
"file-invoice-dollar": "\u{f571}",
"file-jpg": "\u{e646}",
"file-lines": "\u{f15c}",
"file-alt": "\u{f15c}",
"file-text": "\u{f15c}",
"file-lock": "\u{e3a6}",
"file-magnifying-glass": "\u{f865}",
"file-search": "\u{f865}",
"file-medical": "\u{f477}",
"file-minus": "\u{f318}",
"file-mov": "\u{e647}",
"file-mp3": "\u{e648}",
"file-mp4": "\u{e649}",
"file-music": "\u{f8b6}",
"file-pdf": "\u{f1c1}",
"file-pen": "\u{f31c}",
"file-edit": "\u{f31c}",
"file-plus": "\u{f319}",
"file-plus-minus": "\u{e177}",
"file-png": "\u{e666}",
"file-powerpoint": "\u{f1c4}",
"file-ppt": "\u{e64a}",
"file-prescription": "\u{f572}",
"files": "\u{e178}",
"file-shield": "\u{e4f0}",
"file-signature": "\u{f573}",
"file-slash": "\u{e3a7}",
"files-medical": "\u{f7fd}",
"file-spreadsheet": "\u{f65b}",
"file-svg": "\u{e64b}",
"file-user": "\u{f65c}",
"file-vector": "\u{e64c}",
"file-video": "\u{f1c8}",
"file-waveform": "\u{f478}",
"file-medical-alt": "\u{f478}",
"file-word": "\u{f1c2}",
"file-xls": "\u{e64d}",
"file-xmark": "\u{f317}",
"file-times": "\u{f317}",
"file-xml": "\u{e654}",
"file-zip": "\u{e5ee}",
"file-zipper": "\u{f1c6}",
"file-archive": "\u{f1c6}",
"fill": "\u{f575}",
"fill-drip": "\u{f576}",
"film": "\u{f008}",
"film-canister": "\u{f8b7}",
"film-cannister": "\u{f8b7}",
"films": "\u{e17a}",
"film-simple": "\u{f3a0}",
"film-alt": "\u{f3a0}",
"film-slash": "\u{e179}",
"filter": "\u{f0b0}",
"filter-circle-dollar": "\u{f662}",
"funnel-dollar": "\u{f662}",
"filter-circle-xmark": "\u{e17b}",
"filter-list": "\u{e17c}",
"filters": "\u{e17e}",
"filter-slash": "\u{e17d}",
"fingerprint": "\u{f577}",
"fire": "\u{f06d}",
"fire-burner": "\u{e4f1}",
"fire-extinguisher": "\u{f134}",
"fire-flame": "\u{f6df}",
"flame": "\u{f6df}",
"fire-flame-curved": "\u{f7e4}",
"fire-alt": "\u{f7e4}",
"fire-flame-simple": "\u{f46a}",
"burn": "\u{f46a}",
"firefox": "\u{f269}",
"firefox-browser": "\u{e007}",
"fire-hydrant": "\u{e17f}",
"fireplace": "\u{f79a}",
"fire-smoke": "\u{f74b}",
"firstdraft": "\u{f3a1}",
"first-order": "\u{f2b0}",
"first-order-alt": "\u{f50a}",
"fish": "\u{f578}",
"fish-bones": "\u{e304}",
"fish-cooked": "\u{f7fe}",
"fish-fins": "\u{e4f2}",
"fishing-rod": "\u{e3a8}",
"flag": "\u{f024}",
"flag-checkered": "\u{f11e}",
"flag-pennant": "\u{f456}",
"pennant": "\u{f456}",
"flag-swallowtail": "\u{f74c}",
"flag-alt": "\u{f74c}",
"flag-usa": "\u{f74d}",
"flashlight": "\u{f8b8}",
"flask": "\u{f0c3}",
"flask-gear": "\u{e5f1}",
"flask-round-poison": "\u{f6e0}",
"flask-poison": "\u{f6e0}",
"flask-round-potion": "\u{f6e1}",
"flask-potion": "\u{f6e1}",
"flask-vial": "\u{e4f3}",
"flatbread": "\u{e40b}",
"flatbread-stuffed": "\u{e40c}",
"flickr": "\u{f16e}",
"flipboard": "\u{f44d}",
"floppy-disk": "\u{f0c7}",
"save": "\u{f0c7}",
"floppy-disk-circle-arrow-right": "\u{e180}",
"save-circle-arrow-right": "\u{e180}",
"floppy-disk-circle-xmark": "\u{e181}",
"floppy-disk-times": "\u{e181}",
"save-circle-xmark": "\u{e181}",
"save-times": "\u{e181}",
"floppy-disk-pen": "\u{e182}",
"floppy-disks": "\u{e183}",
"florin-sign": "\u{e184}",
"flower": "\u{f7ff}",
"flower-daffodil": "\u{f800}",
"flower-tulip": "\u{f801}",
"flute": "\u{f8b9}",
"flutter": "\u{e694}",
"flux-capacitor": "\u{f8ba}",
"fly": "\u{f417}",
"flying-disc": "\u{e3a9}",
"folder": "\u{f07b}",
"folder-blank": "\u{f07b}",
"folder-arrow-down": "\u{e053}",
"folder-download": "\u{e053}",
"folder-arrow-up": "\u{e054}",
"folder-upload": "\u{e054}",
"folder-bookmark": "\u{e186}",
"folder-check": "\u{e64e}",
"folder-closed": "\u{e185}",
"folder-gear": "\u{e187}",
"folder-cog": "\u{e187}",
"folder-grid": "\u{e188}",
"folder-heart": "\u{e189}",
"folder-image": "\u{e18a}",
"folder-magnifying-glass": "\u{e18b}",
"folder-search": "\u{e18b}",
"folder-medical": "\u{e18c}",
"folder-minus": "\u{f65d}",
"folder-music": "\u{e18d}",
"folder-open": "\u{f07c}",
"folder-plus": "\u{f65e}",
"folders": "\u{f660}",
"folder-tree": "\u{f802}",
"folder-user": "\u{e18e}",
"folder-xmark": "\u{f65f}",
"folder-times": "\u{f65f}",
"fondue-pot": "\u{e40d}",
"font": "\u{f031}",
"font-awesome": "\u{f2b4}",
"font-awesome-flag": "\u{f2b4}",
"font-awesome-logo-full": "\u{f2b4}",
"font-case": "\u{f866}",
"fonticons": "\u{f280}",
"fonticons-fi": "\u{f3a2}",
"football": "\u{f44e}",
"football-ball": "\u{f44e}",
"football-helmet": "\u{f44f}",
"fork": "\u{f2e3}",
"utensil-fork": "\u{f2e3}",
"fork-knife": "\u{f2e6}",
"utensils-alt": "\u{f2e6}",
"forklift": "\u{f47a}",
"fort": "\u{e486}",
"fort-awesome": "\u{f286}",
"fort-awesome-alt": "\u{f3a3}",
"forumbee": "\u{f211}",
"forward": "\u{f04e}",
"forward-fast": "\u{f050}",
"fast-forward": "\u{f050}",
"forward-step": "\u{f051}",
"step-forward": "\u{f051}",
"foursquare": "\u{f180}",
"frame": "\u{e495}",
"franc-sign": "\u{e18f}",
"freebsd": "\u{f3a4}",
"free-code-camp": "\u{f2c5}",
"french-fries": "\u{f803}",
"frog": "\u{f52e}",
"fulcrum": "\u{f50b}",
"function": "\u{f661}",
"futbol": "\u{f1e3}",
"futbol-ball": "\u{f1e3}",
"soccer-ball": "\u{f1e3}",
"g": "\u{47}",
"galactic-republic": "\u{f50c}",
"galactic-senate": "\u{f50d}",
"galaxy": "\u{e008}",
"gallery-thumbnails": "\u{e3aa}",
"game-board": "\u{f867}",
"game-board-simple": "\u{f868}",
"game-board-alt": "\u{f868}",
"game-console-handheld": "\u{f8bb}",
"game-console-handheld-crank": "\u{e5b9}",
"gamepad": "\u{f11b}",
"gamepad-modern": "\u{e5a2}",
"gamepad-alt": "\u{e5a2}",
"garage": "\u{e009}",
"garage-car": "\u{e00a}",
"garage-open": "\u{e00b}",
"garlic": "\u{e40e}",
"gas-pump": "\u{f52f}",
"gas-pump-slash": "\u{f5f4}",
"gauge": "\u{f624}",
"dashboard": "\u{f624}",
"gauge-med": "\u{f624}",
"tachometer-alt-average": "\u{f624}",
"gauge-circle-bolt": "\u{e496}",
"gauge-circle-minus": "\u{e497}",
"gauge-circle-plus": "\u{e498}",
"gauge-high": "\u{f625}",
"tachometer-alt": "\u{f625}",
"tachometer-alt-fast": "\u{f625}",
"gauge-low": "\u{f627}",
"tachometer-alt-slow": "\u{f627}",
"gauge-max": "\u{f626}",
"tachometer-alt-fastest": "\u{f626}",
"gauge-min": "\u{f628}",
"tachometer-alt-slowest": "\u{f628}",
"gauge-simple": "\u{f629}",
"gauge-simple-med": "\u{f629}",
"tachometer-average": "\u{f629}",
"gauge-simple-high": "\u{f62a}",
"tachometer": "\u{f62a}",
"tachometer-fast": "\u{f62a}",
"gauge-simple-low": "\u{f62c}",
"tachometer-slow": "\u{f62c}",
"gauge-simple-max": "\u{f62b}",
"tachometer-fastest": "\u{f62b}",
"gauge-simple-min": "\u{f62d}",
"tachometer-slowest": "\u{f62d}",
"gavel": "\u{f0e3}",
"legal": "\u{f0e3}",
"gear": "\u{f013}",
"cog": "\u{f013}",
"gear-code": "\u{e5e8}",
"gear-complex": "\u{e5e9}",
"gear-complex-code": "\u{e5eb}",
"gears": "\u{f085}",
"cogs": "\u{f085}",
"gem": "\u{f3a5}",
"genderless": "\u{f22d}",
"get-pocket": "\u{f265}",
"gg": "\u{f260}",
"gg-circle": "\u{f261}",
"ghost": "\u{f6e2}",
"gif": "\u{e190}",
"gift": "\u{f06b}",
"gift-card": "\u{f663}",
"gifts": "\u{f79c}",
"gingerbread-man": "\u{f79d}",
"git": "\u{f1d3}",
"git-alt": "\u{f841}",
"github": "\u{f09b}",
"github-alt": "\u{f113}",
"gitkraken": "\u{f3a6}",
"gitlab": "\u{f296}",
"gitter": "\u{f426}",
"glass": "\u{f804}",
"glass-citrus": "\u{f869}",
"glass-empty": "\u{e191}",
"glasses": "\u{f530}",
"glasses-round": "\u{f5f5}",
"glasses-alt": "\u{f5f5}",
"glass-half": "\u{e192}",
"glass-half-empty": "\u{e192}",
"glass-half-full": "\u{e192}",
"glass-water": "\u{e4f4}",
"glass-water-droplet": "\u{e4f5}",
"glide": "\u{f2a5}",
"glide-g": "\u{f2a6}",
"globe": "\u{f0ac}",
"globe-pointer": "\u{e60e}",
"globe-snow": "\u{f7a3}",
"globe-stand": "\u{f5f6}",
"globe-wifi": "\u{e685}",
"goal-net": "\u{e3ab}",
"gofore": "\u{f3a7}",
"golang": "\u{e40f}",
"golf-ball-tee": "\u{f450}",
"golf-ball": "\u{f450}",
"golf-club": "\u{f451}",
"golf-flag-hole": "\u{e3ac}",
"goodreads": "\u{f3a8}",
"goodreads-g": "\u{f3a9}",
"google": "\u{f1a0}",
"google-drive": "\u{f3aa}",
"google-pay": "\u{e079}",
"google-play": "\u{f3ab}",
"google-plus": "\u{f2b3}",
"google-plus-g": "\u{f0d5}",
"google-scholar": "\u{e63b}",
"google-wallet": "\u{f1ee}",
"gopuram": "\u{f664}",
"graduation-cap": "\u{f19d}",
"mortar-board": "\u{f19d}",
"gramophone": "\u{f8bd}",
"grapes": "\u{e306}",
"grate": "\u{e193}",
"grate-droplet": "\u{e194}",
"gratipay": "\u{f184}",
"grav": "\u{f2d6}",
"greater-than": "\u{3e}",
"greater-than-equal": "\u{f532}",
"grid": "\u{e195}",
"grid-3": "\u{e195}",
"grid-2": "\u{e196}",
"grid-2-plus": "\u{e197}",
"grid-4": "\u{e198}",
"grid-5": "\u{e199}",
"grid-dividers": "\u{e3ad}",
"grid-horizontal": "\u{e307}",
"grid-round": "\u{e5da}",
"grid-round-2": "\u{e5db}",
"grid-round-2-plus": "\u{e5dc}",
"grid-round-4": "\u{e5dd}",
"grid-round-5": "\u{e5de}",
"grill": "\u{e5a3}",
"grill-fire": "\u{e5a4}",
"grill-hot": "\u{e5a5}",
"grip": "\u{f58d}",
"grip-horizontal": "\u{f58d}",
"grip-dots": "\u{e410}",
"grip-dots-vertical": "\u{e411}",
"gripfire": "\u{f3ac}",
"grip-lines": "\u{f7a4}",
"grip-lines-vertical": "\u{f7a5}",
"grip-vertical": "\u{f58e}",
"group-arrows-rotate": "\u{e4f6}",
"grunt": "\u{f3ad}",
"guarani-sign": "\u{e19a}",
"guilded": "\u{e07e}",
"guitar": "\u{f7a6}",
"guitar-electric": "\u{f8be}",
"guitars": "\u{f8bf}",
"gulp": "\u{f3ae}",
"gun": "\u{e19b}",
"gun-slash": "\u{e19c}",
"gun-squirt": "\u{e19d}",
"h": "\u{48}",
"h1": "\u{f313}",
"h2": "\u{f314}",
"h3": "\u{f315}",
"h4": "\u{f86a}",
"h5": "\u{e412}",
"h6": "\u{e413}",
"hacker-news": "\u{f1d4}",
"hackerrank": "\u{f5f7}",
"hammer": "\u{f6e3}",
"hammer-brush": "\u{e620}",
"hammer-crash": "\u{e414}",
"hammer-war": "\u{f6e4}",
"hamsa": "\u{f665}",
"hand": "\u{f256}",
"hand-paper": "\u{f256}",
"hand-back-fist": "\u{f255}",
"hand-rock": "\u{f255}",
"hand-back-point-down": "\u{e19e}",
"hand-back-point-left": "\u{e19f}",
"hand-back-point-ribbon": "\u{e1a0}",
"hand-back-point-right": "\u{e1a1}",
"hand-back-point-up": "\u{e1a2}",
"handcuffs": "\u{e4f8}",
"hand-dots": "\u{f461}",
"allergies": "\u{f461}",
"hand-fingers-crossed": "\u{e1a3}",
"hand-fist": "\u{f6de}",
"fist-raised": "\u{f6de}",
"hand-heart": "\u{f4bc}",
"hand-holding": "\u{f4bd}",
"hand-holding-box": "\u{f47b}",
"hand-holding-circle-dollar": "\u{e621}",
"hand-holding-dollar": "\u{f4c0}",
"hand-holding-usd": "\u{f4c0}",
"hand-holding-droplet": "\u{f4c1}",
"hand-holding-water": "\u{f4c1}",
"hand-holding-hand": "\u{e4f7}",
"hand-holding-heart": "\u{f4be}",
"hand-holding-magic": "\u{f6e5}",
"hand-holding-medical": "\u{e05c}",
"hand-holding-seedling": "\u{f4bf}",
"hand-holding-skull": "\u{e1a4}",
"hand-horns": "\u{e1a9}",
"hand-lizard": "\u{f258}",
"hand-love": "\u{e1a5}",
"hand-middle-finger": "\u{f806}",
"hand-peace": "\u{f25b}",
"hand-point-down": "\u{f0a7}",
"hand-pointer": "\u{f25a}",
"hand-point-left": "\u{f0a5}",
"hand-point-ribbon": "\u{e1a6}",
"hand-point-right": "\u{f0a4}",
"hand-point-up": "\u{f0a6}",
"hands": "\u{f2a7}",
"sign-language": "\u{f2a7}",
"signing": "\u{f2a7}",
"hands-asl-interpreting": "\u{f2a3}",
"american-sign-language-interpreting": "\u{f2a3}",
"asl-interpreting": "\u{f2a3}",
"hands-american-sign-language-interpreting": "\u{f2a3}",
"hands-bound": "\u{e4f9}",
"hands-bubbles": "\u{e05e}",
"hands-wash": "\u{e05e}",
"hand-scissors": "\u{f257}",
"hands-clapping": "\u{e1a8}",
"handshake": "\u{f2b5}",
"handshake-angle": "\u{f4c4}",
"hands-helping": "\u{f4c4}",
"handshake-simple": "\u{f4c6}",
"handshake-alt": "\u{f4c6}",
"handshake-simple-slash": "\u{e05f}",
"handshake-alt-slash": "\u{e05f}",
"handshake-slash": "\u{e060}",
"hands-holding": "\u{f4c2}",
"hands-holding-child": "\u{e4fa}",
"hands-holding-circle": "\u{e4fb}",
"hands-holding-diamond": "\u{f47c}",
"hand-receiving": "\u{f47c}",
"hands-holding-dollar": "\u{f4c5}",
"hands-usd": "\u{f4c5}",
"hands-holding-heart": "\u{f4c3}",
"hands-heart": "\u{f4c3}",
"hand-sparkles": "\u{e05d}",
"hand-spock": "\u{f259}",
"hands-praying": "\u{f684}",
"praying-hands": "\u{f684}",
"hand-wave": "\u{e1a7}",
"hanukiah": "\u{f6e6}",
"hard-drive": "\u{f0a0}",
"hdd": "\u{f0a0}",
"hashnode": "\u{e499}",
"hashtag": "\u{23}",
"hashtag-lock": "\u{e415}",
"hat-beach": "\u{e606}",
"hat-chef": "\u{f86b}",
"hat-cowboy": "\u{f8c0}",
"hat-cowboy-side": "\u{f8c1}",
"hat-santa": "\u{f7a7}",
"hat-winter": "\u{f7a8}",
"hat-witch": "\u{f6e7}",
"hat-wizard": "\u{f6e8}",
"heading": "\u{f1dc}",
"header": "\u{f1dc}",
"headphones": "\u{f025}",
"headphones-simple": "\u{f58f}",
"headphones-alt": "\u{f58f}",
"headset": "\u{f590}",
"head-side": "\u{f6e9}",
"head-side-brain": "\u{f808}",
"head-side-cough": "\u{e061}",
"head-side-cough-slash": "\u{e062}",
"head-side-gear": "\u{e611}",
"head-side-goggles": "\u{f6ea}",
"head-vr": "\u{f6ea}",
"head-side-headphones": "\u{f8c2}",
"head-side-heart": "\u{e1aa}",
"head-side-mask": "\u{e063}",
"head-side-medical": "\u{f809}",
"head-side-virus": "\u{e064}",
"heart": "\u{f004}",
"heart-circle-bolt": "\u{e4fc}",
"heart-circle-check": "\u{e4fd}",
"heart-circle-exclamation": "\u{e4fe}",
"heart-circle-minus": "\u{e4ff}",
"heart-circle-plus": "\u{e500}",
"heart-circle-xmark": "\u{e501}",
"heart-crack": "\u{f7a9}",
"heart-broken": "\u{f7a9}",
"heart-half": "\u{e1ab}",
"heart-half-stroke": "\u{e1ac}",
"heart-half-alt": "\u{e1ac}",
"heart-pulse": "\u{f21e}",
"heartbeat": "\u{f21e}",
"heat": "\u{e00c}",
"helicopter": "\u{f533}",
"helicopter-symbol": "\u{e502}",
"helmet-battle": "\u{f6eb}",
"helmet-safety": "\u{f807}",
"hard-hat": "\u{f807}",
"hat-hard": "\u{f807}",
"helmet-un": "\u{e503}",
"hexagon": "\u{f312}",
"hexagon-check": "\u{e416}",
"hexagon-divide": "\u{e1ad}",
"hexagon-exclamation": "\u{e417}",
"hexagon-image": "\u{e504}",
"hexagon-minus": "\u{f307}",
"minus-hexagon": "\u{f307}",
"hexagon-plus": "\u{f300}",
"plus-hexagon": "\u{f300}",
"hexagon-vertical-nft": "\u{e505}",
"hexagon-vertical-nft-slanted": "\u{e506}",
"hexagon-xmark": "\u{f2ee}",
"times-hexagon": "\u{f2ee}",
"xmark-hexagon": "\u{f2ee}",
"high-definition": "\u{e1ae}",
"rectangle-hd": "\u{e1ae}",
"highlighter": "\u{f591}",
"highlighter-line": "\u{e1af}",
"hill-avalanche": "\u{e507}",
"hill-rockslide": "\u{e508}",
"hippo": "\u{f6ed}",
"hips": "\u{f452}",
"hire-a-helper": "\u{f3b0}",
"hive": "\u{e07f}",
"hockey-mask": "\u{f6ee}",
"hockey-puck": "\u{f453}",
"hockey-stick-puck": "\u{e3ae}",
"hockey-sticks": "\u{f454}",
"holly-berry": "\u{f7aa}",
"honey-pot": "\u{e418}",
"hood-cloak": "\u{f6ef}",
"hooli": "\u{f427}",
"horizontal-rule": "\u{f86c}",
"hornbill": "\u{f592}",
"horse": "\u{f6f0}",
"horse-head": "\u{f7ab}",
"horse-saddle": "\u{f8c3}",
"hose": "\u{e419}",
"hose-reel": "\u{e41a}",
"hospital": "\u{f0f8}",
"hospital-alt": "\u{f0f8}",
"hospital-wide": "\u{f0f8}",
"hospitals": "\u{f80e}",
"hospital-user": "\u{f80d}",
"hotdog": "\u{f80f}",
"hotel": "\u{f594}",
"hotjar": "\u{f3b1}",
"hot-tub-person": "\u{f593}",
"hot-tub": "\u{f593}",
"hourglass": "\u{f254}",
"hourglass-empty": "\u{f254}",
"hourglass-clock": "\u{e41b}",
"hourglass-end": "\u{f253}",
"hourglass-3": "\u{f253}",
"hourglass-half": "\u{f252}",
"hourglass-2": "\u{f252}",
"hourglass-start": "\u{f251}",
"hourglass-1": "\u{f251}",
"house": "\u{f015}",
"home": "\u{f015}",
"home-alt": "\u{f015}",
"home-lg-alt": "\u{f015}",
"house-blank": "\u{e487}",
"home-blank": "\u{e487}",
"house-building": "\u{e1b1}",
"house-chimney": "\u{e3af}",
"home-lg": "\u{e3af}",
"house-chimney-blank": "\u{e3b0}",
"house-chimney-crack": "\u{f6f1}",
"house-damage": "\u{f6f1}",
"house-chimney-heart": "\u{e1b2}",
"house-chimney-medical": "\u{f7f2}",
"clinic-medical": "\u{f7f2}",
"house-chimney-user": "\u{e065}",
"house-chimney-window": "\u{e00d}",
"house-circle-check": "\u{e509}",
"house-circle-exclamation": "\u{e50a}",
"house-circle-xmark": "\u{e50b}",
"house-crack": "\u{e3b1}",
"house-day": "\u{e00e}",
"house-fire": "\u{e50c}",
"house-flag": "\u{e50d}",
"house-flood-water": "\u{e50e}",
"house-flood-water-circle-arrow-right": "\u{e50f}",
"house-heart": "\u{f4c9}",
"home-heart": "\u{f4c9}",
"house-laptop": "\u{e066}",
"laptop-house": "\u{e066}",
"house-lock": "\u{e510}",
"house-medical": "\u{e3b2}",
"house-medical-circle-check": "\u{e511}",
"house-medical-circle-exclamation": "\u{e512}",
"house-medical-circle-xmark": "\u{e513}",
"house-medical-flag": "\u{e514}",
"house-night": "\u{e010}",
"house-person-leave": "\u{e00f}",
"house-leave": "\u{e00f}",
"house-person-depart": "\u{e00f}",
"house-person-return": "\u{e011}",
"house-person-arrive": "\u{e011}",
"house-return": "\u{e011}",
"house-signal": "\u{e012}",
"house-tree": "\u{e1b3}",
"house-tsunami": "\u{e515}",
"house-turret": "\u{e1b4}",
"house-user": "\u{e1b0}",
"home-user": "\u{e1b0}",
"house-water": "\u{f74f}",
"house-flood": "\u{f74f}",
"house-window": "\u{e3b3}",
"houzz": "\u{f27c}",
"hryvnia-sign": "\u{f6f2}",
"hryvnia": "\u{f6f2}",
"html5": "\u{f13b}",
"hubspot": "\u{f3b2}",
"hundred-points": "\u{e41c}",
"100": "\u{e41c}",
"hurricane": "\u{f751}",
"hydra": "\u{e686}",
"hyphen": "\u{2d}",
"i": "\u{49}",
"ice-cream": "\u{f810}",
"ice-skate": "\u{f7ac}",
"icicles": "\u{f7ad}",
"icons": "\u{f86d}",
"heart-music-camera-bolt": "\u{f86d}",
"i-cursor": "\u{f246}",
"id-badge": "\u{f2c1}",
"id-card": "\u{f2c2}",
"drivers-license": "\u{f2c2}",
"id-card-clip": "\u{f47f}",
"id-card-alt": "\u{f47f}",
"ideal": "\u{e013}",
"igloo": "\u{f7ae}",
"image": "\u{f03e}",
"image-landscape": "\u{e1b5}",
"landscape": "\u{e1b5}",
"image-polaroid": "\u{f8c4}",
"image-polaroid-user": "\u{e1b6}",
"image-portrait": "\u{f3e0}",
"portrait": "\u{f3e0}",
"images": "\u{f302}",
"image-slash": "\u{e1b7}",
"images-user": "\u{e1b9}",
"image-user": "\u{e1b8}",
"imdb": "\u{f2d8}",
"inbox": "\u{f01c}",
"inboxes": "\u{e1bb}",
"inbox-full": "\u{e1ba}",
"inbox-in": "\u{f310}",
"inbox-arrow-down": "\u{f310}",
"inbox-out": "\u{f311}",
"inbox-arrow-up": "\u{f311}",
"indent": "\u{f03c}",
"indian-rupee-sign": "\u{e1bc}",
"indian-rupee": "\u{e1bc}",
"inr": "\u{e1bc}",
"industry": "\u{f275}",
"industry-windows": "\u{f3b3}",
"industry-alt": "\u{f3b3}",
"infinity": "\u{f534}",
"info": "\u{f129}",
"inhaler": "\u{f5f9}",
"input-numeric": "\u{e1bd}",
"input-pipe": "\u{e1be}",
"input-text": "\u{e1bf}",
"instagram": "\u{f16d}",
"instalod": "\u{e081}",
"integral": "\u{f667}",
"intercom": "\u{f7af}",
"internet-explorer": "\u{f26b}",
"interrobang": "\u{e5ba}",
"intersection": "\u{f668}",
"invision": "\u{f7b0}",
"ioxhost": "\u{f208}",
"island-tropical": "\u{f811}",
"island-tree-palm": "\u{f811}",
"italic": "\u{f033}",
"itch-io": "\u{f83a}",
"itunes": "\u{f3b4}",
"itunes-note": "\u{f3b5}",
"j": "\u{4a}",
"jack-o-lantern": "\u{f30e}",
"jar": "\u{e516}",
"jar-wheat": "\u{e517}",
"java": "\u{f4e4}",
"jedi": "\u{f669}",
"jedi-order": "\u{f50e}",
"jenkins": "\u{f3b6}",
"jet-fighter": "\u{f0fb}",
"fighter-jet": "\u{f0fb}",
"jet-fighter-up": "\u{e518}",
"jira": "\u{f7b1}",
"joget": "\u{f3b7}",
"joint": "\u{f595}",
"joomla": "\u{f1aa}",
"joystick": "\u{f8c5}",
"js": "\u{f3b8}",
"jsfiddle": "\u{f1cc}",
"jug": "\u{f8c6}",
"jug-bottle": "\u{e5fb}",
"jug-detergent": "\u{e519}",
"jxl": "\u{e67b}",
"k": "\u{4b}",
"kaaba": "\u{f66b}",
"kaggle": "\u{f5fa}",
"kazoo": "\u{f8c7}",
"kerning": "\u{f86f}",
"key": "\u{f084}",
"keybase": "\u{f4f5}",
"keyboard": "\u{f11c}",
"keyboard-brightness": "\u{e1c0}",
"keyboard-brightness-low": "\u{e1c1}",
"keyboard-down": "\u{e1c2}",
"keyboard-left": "\u{e1c3}",
"keycdn": "\u{f3ba}",
"keynote": "\u{f66c}",
"key-skeleton": "\u{f6f3}",
"key-skeleton-left-right": "\u{e3b4}",
"khanda": "\u{f66d}",
"kickstarter": "\u{f3bb}",
"square-kickstarter": "\u{f3bb}",
"kickstarter-k": "\u{f3bc}",
"kidneys": "\u{f5fb}",
"kip-sign": "\u{e1c4}",
"kitchen-set": "\u{e51a}",
"kite": "\u{f6f4}",
"kit-medical": "\u{f479}",
"first-aid": "\u{f479}",
"kiwi-bird": "\u{f535}",
"kiwi-fruit": "\u{e30c}",
"knife": "\u{f2e4}",
"utensil-knife": "\u{f2e4}",
"knife-kitchen": "\u{f6f5}",
"korvue": "\u{f42f}",
"l": "\u{4c}",
"lacrosse-stick": "\u{e3b5}",
"lacrosse-stick-ball": "\u{e3b6}",
"lambda": "\u{f66e}",
"lamp": "\u{f4ca}",
"lamp-desk": "\u{e014}",
"lamp-floor": "\u{e015}",
"lamp-street": "\u{e1c5}",
"landmark": "\u{f66f}",
"landmark-dome": "\u{f752}",
"landmark-alt": "\u{f752}",
"landmark-flag": "\u{e51c}",
"landmark-magnifying-glass": "\u{e622}",
"land-mine-on": "\u{e51b}",
"language": "\u{f1ab}",
"laptop": "\u{f109}",
"laptop-arrow-down": "\u{e1c6}",
"laptop-binary": "\u{e5e7}",
"laptop-code": "\u{f5fc}",
"laptop-file": "\u{e51d}",
"laptop-medical": "\u{f812}",
"laptop-mobile": "\u{f87a}",
"phone-laptop": "\u{f87a}",
"laptop-slash": "\u{e1c7}",
"laravel": "\u{f3bd}",
"lari-sign": "\u{e1c8}",
"lasso": "\u{f8c8}",
"lasso-sparkles": "\u{e1c9}",
"lastfm": "\u{f202}",
"layer-group": "\u{f5fd}",
"layer-minus": "\u{f5fe}",
"layer-group-minus": "\u{f5fe}",
"layer-plus": "\u{f5ff}",
"layer-group-plus": "\u{f5ff}",
"leaf": "\u{f06c}",
"leaf-heart": "\u{f4cb}",
"leaf-maple": "\u{f6f6}",
"leaf-oak": "\u{f6f7}",
"leafy-green": "\u{e41d}",
"leanpub": "\u{f212}",
"left": "\u{f355}",
"arrow-alt-left": "\u{f355}",
"left-from-bracket": "\u{e66c}",
"left-from-line": "\u{f348}",
"arrow-alt-from-right": "\u{f348}",
"left-long": "\u{f30a}",
"long-arrow-alt-left": "\u{f30a}",
"left-long-to-line": "\u{e41e}",
"left-right": "\u{f337}",
"arrows-alt-h": "\u{f337}",
"left-to-bracket": "\u{e66d}",
"left-to-line": "\u{f34b}",
"arrow-alt-to-left": "\u{f34b}",
"lemon": "\u{f094}",
"less": "\u{f41d}",
"less-than": "\u{3c}",
"less-than-equal": "\u{f537}",
"letterboxd": "\u{e62d}",
"life-ring": "\u{f1cd}",
"lightbulb": "\u{f0eb}",
"lightbulb-cfl": "\u{e5a6}",
"lightbulb-cfl-on": "\u{e5a7}",
"lightbulb-dollar": "\u{f670}",
"lightbulb-exclamation": "\u{f671}",
"lightbulb-exclamation-on": "\u{e1ca}",
"lightbulb-gear": "\u{e5fd}",
"lightbulb-message": "\u{e687}",
"lightbulb-on": "\u{f672}",
"lightbulb-slash": "\u{f673}",
"light-ceiling": "\u{e016}",
"light-emergency": "\u{e41f}",
"light-emergency-on": "\u{e420}",
"lighthouse": "\u{e612}",
"lights-holiday": "\u{f7b2}",
"light-switch": "\u{e017}",
"light-switch-off": "\u{e018}",
"light-switch-on": "\u{e019}",
"line": "\u{f3c0}",
"line-columns": "\u{f870}",
"line-height": "\u{f871}",
"lines-leaning": "\u{e51e}",
"link": "\u{f0c1}",
"chain": "\u{f0c1}",
"linkedin": "\u{f08c}",
"linkedin-in": "\u{f0e1}",
"link-horizontal": "\u{e1cb}",
"chain-horizontal": "\u{e1cb}",
"link-horizontal-slash": "\u{e1cc}",
"chain-horizontal-slash": "\u{e1cc}",
"link-simple": "\u{e1cd}",
"link-simple-slash": "\u{e1ce}",
"link-slash": "\u{f127}",
"chain-broken": "\u{f127}",
"chain-slash": "\u{f127}",
"unlink": "\u{f127}",
"linode": "\u{f2b8}",
"linux": "\u{f17c}",
"lips": "\u{f600}",
"lira-sign": "\u{f195}",
"list": "\u{f03a}",
"list-squares": "\u{f03a}",
"list-check": "\u{f0ae}",
"tasks": "\u{f0ae}",
"list-dropdown": "\u{e1cf}",
"list-music": "\u{f8c9}",
"list-ol": "\u{f0cb}",
"list-1-2": "\u{f0cb}",
"list-numeric": "\u{f0cb}",
"list-radio": "\u{e1d0}",
"list-timeline": "\u{e1d1}",
"list-tree": "\u{e1d2}",
"list-ul": "\u{f0ca}",
"list-dots": "\u{f0ca}",
"litecoin-sign": "\u{e1d3}",
"loader": "\u{e1d4}",
"lobster": "\u{e421}",
"location-arrow": "\u{f124}",
"location-arrow-up": "\u{e63a}",
"location-check": "\u{f606}",
"map-marker-check": "\u{f606}",
"location-crosshairs": "\u{f601}",
"location": "\u{f601}",
"location-crosshairs-slash": "\u{f603}",
"location-slash": "\u{f603}",
"location-dot": "\u{f3c5}",
"map-marker-alt": "\u{f3c5}",
"location-dot-slash": "\u{f605}",
"map-marker-alt-slash": "\u{f605}",
"location-exclamation": "\u{f608}",
"map-marker-exclamation": "\u{f608}",
"location-minus": "\u{f609}",
"map-marker-minus": "\u{f609}",
"location-pen": "\u{f607}",
"map-marker-edit": "\u{f607}",
"location-pin": "\u{f041}",
"map-marker": "\u{f041}",
"location-pin-lock": "\u{e51f}",
"location-pin-slash": "\u{f60c}",
"map-marker-slash": "\u{f60c}",
"location-plus": "\u{f60a}",
"map-marker-plus": "\u{f60a}",
"location-question": "\u{f60b}",
"map-marker-question": "\u{f60b}",
"location-smile": "\u{f60d}",
"map-marker-smile": "\u{f60d}",
"location-xmark": "\u{f60e}",
"map-marker-times": "\u{f60e}",
"map-marker-xmark": "\u{f60e}",
"lock": "\u{f023}",
"lock-a": "\u{e422}",
"lock-hashtag": "\u{e423}",
"lock-keyhole": "\u{f30d}",
"lock-alt": "\u{f30d}",
"lock-keyhole-open": "\u{f3c2}",
"lock-open-alt": "\u{f3c2}",
"lock-open": "\u{f3c1}",
"locust": "\u{e520}",
"lollipop": "\u{e424}",
"lollypop": "\u{e424}",
"loveseat": "\u{f4cc}",
"couch-small": "\u{f4cc}",
"luchador-mask": "\u{f455}",
"luchador": "\u{f455}",
"mask-luchador": "\u{f455}",
"lungs": "\u{f604}",
"lungs-virus": "\u{e067}",
"lyft": "\u{f3c3}",
"m": "\u{4d}",
"mace": "\u{f6f8}",
"magento": "\u{f3c4}",
"magnet": "\u{f076}",
"magnifying-glass": "\u{f002}",
"search": "\u{f002}",
"magnifying-glass-arrow-right": "\u{e521}",
"magnifying-glass-arrows-rotate": "\u{e65e}",
"magnifying-glass-chart": "\u{e522}",
"magnifying-glass-dollar": "\u{f688}",
"search-dollar": "\u{f688}",
"magnifying-glass-location": "\u{f689}",
"search-location": "\u{f689}",
"magnifying-glass-minus": "\u{f010}",
"search-minus": "\u{f010}",
"magnifying-glass-music": "\u{e65f}",
"magnifying-glass-play": "\u{e660}",
"magnifying-glass-plus": "\u{f00e}",
"search-plus": "\u{f00e}",
"magnifying-glass-waveform": "\u{e661}",
"mailbox": "\u{f813}",
"mailbox-flag-up": "\u{e5bb}",
"mailchimp": "\u{f59e}",
"manat-sign": "\u{e1d5}",
"mandalorian": "\u{f50f}",
"mandolin": "\u{f6f9}",
"mango": "\u{e30f}",
"manhole": "\u{e1d6}",
"map": "\u{f279}",
"map-location": "\u{f59f}",
"map-marked": "\u{f59f}",
"map-location-dot": "\u{f5a0}",
"map-marked-alt": "\u{f5a0}",
"map-pin": "\u{f276}",
"markdown": "\u{f60f}",
"marker": "\u{f5a1}",
"mars": "\u{f222}",
"mars-and-venus": "\u{f224}",
"mars-and-venus-burst": "\u{e523}",
"mars-double": "\u{f227}",
"mars-stroke": "\u{f229}",
"mars-stroke-right": "\u{f22b}",
"mars-stroke-h": "\u{f22b}",
"mars-stroke-up": "\u{f22a}",
"mars-stroke-v": "\u{f22a}",
"martini-glass": "\u{f57b}",
"glass-martini-alt": "\u{f57b}",
"martini-glass-citrus": "\u{f561}",
"cocktail": "\u{f561}",
"martini-glass-empty": "\u{f000}",
"glass-martini": "\u{f000}",
"mask": "\u{f6fa}",
"mask-face": "\u{e1d7}",
"mask-snorkel": "\u{e3b7}",
"masks-theater": "\u{f630}",
"theater-masks": "\u{f630}",
"mask-ventilator": "\u{e524}",
"mastodon": "\u{f4f6}",
"mattress-pillow": "\u{e525}",
"maxcdn": "\u{f136}",
"maximize": "\u{f31e}",
"expand-arrows-alt": "\u{f31e}",
"mdb": "\u{f8ca}",
"meat": "\u{f814}",
"medal": "\u{f5a2}",
"medapps": "\u{f3c6}",
"medium": "\u{f23a}",
"medium-m": "\u{f23a}",
"medrt": "\u{f3c8}",
"meetup": "\u{f2e0}",
"megaphone": "\u{f675}",
"megaport": "\u{f5a3}",
"melon": "\u{e310}",
"melon-slice": "\u{e311}",
"memo": "\u{e1d8}",
"memo-circle-check": "\u{e1d9}",
"memo-circle-info": "\u{e49a}",
"memo-pad": "\u{e1da}",
"memory": "\u{f538}",
"mendeley": "\u{f7b3}",
"menorah": "\u{f676}",
"mercury": "\u{f223}",
"merge": "\u{e526}",
"message": "\u{f27a}",
"comment-alt": "\u{f27a}",
"message-arrow-down": "\u{e1db}",
"comment-alt-arrow-down": "\u{e1db}",
"message-arrow-up": "\u{e1dc}",
"comment-alt-arrow-up": "\u{e1dc}",
"message-arrow-up-right": "\u{e1dd}",
"message-bot": "\u{e3b8}",
"message-captions": "\u{e1de}",
"comment-alt-captions": "\u{e1de}",
"message-check": "\u{f4a2}",
"comment-alt-check": "\u{f4a2}",
"message-code": "\u{e1df}",
"message-dollar": "\u{f650}",
"comment-alt-dollar": "\u{f650}",
"message-dots": "\u{f4a3}",
"comment-alt-dots": "\u{f4a3}",
"messaging": "\u{f4a3}",
"message-exclamation": "\u{f4a5}",
"comment-alt-exclamation": "\u{f4a5}",
"message-heart": "\u{e5c9}",
"message-image": "\u{e1e0}",
"comment-alt-image": "\u{e1e0}",
"message-lines": "\u{f4a6}",
"comment-alt-lines": "\u{f4a6}",
"message-medical": "\u{f7f4}",
"comment-alt-medical": "\u{f7f4}",
"message-middle": "\u{e1e1}",
"comment-middle-alt": "\u{e1e1}",
"message-middle-top": "\u{e1e2}",
"comment-middle-top-alt": "\u{e1e2}",
"message-minus": "\u{f4a7}",
"comment-alt-minus": "\u{f4a7}",
"message-music": "\u{f8af}",
"comment-alt-music": "\u{f8af}",
"message-pen": "\u{f4a4}",
"comment-alt-edit": "\u{f4a4}",
"message-edit": "\u{f4a4}",
"message-plus": "\u{f4a8}",
"comment-alt-plus": "\u{f4a8}",
"message-question": "\u{e1e3}",
"message-quote": "\u{e1e4}",
"comment-alt-quote": "\u{e1e4}",
"messages": "\u{f4b6}",
"comments-alt": "\u{f4b6}",
"messages-dollar": "\u{f652}",
"comments-alt-dollar": "\u{f652}",
"message-slash": "\u{f4a9}",
"comment-alt-slash": "\u{f4a9}",
"message-smile": "\u{f4aa}",
"comment-alt-smile": "\u{f4aa}",
"message-sms": "\u{e1e5}",
"messages-question": "\u{e1e7}",
"message-text": "\u{e1e6}",
"comment-alt-text": "\u{e1e6}",
"message-xmark": "\u{f4ab}",
"comment-alt-times": "\u{f4ab}",
"message-times": "\u{f4ab}",
"meta": "\u{e49b}",
"meteor": "\u{f753}",
"meter": "\u{e1e8}",
"meter-bolt": "\u{e1e9}",
"meter-droplet": "\u{e1ea}",
"meter-fire": "\u{e1eb}",
"microblog": "\u{e01a}",
"microchip": "\u{f2db}",
"microchip-ai": "\u{e1ec}",
"microphone": "\u{f130}",
"microphone-lines": "\u{f3c9}",
"microphone-alt": "\u{f3c9}",
"microphone-lines-slash": "\u{f539}",
"microphone-alt-slash": "\u{f539}",
"microphone-slash": "\u{f131}",
"microphone-stand": "\u{f8cb}",
"microscope": "\u{f610}",
"microsoft": "\u{f3ca}",
"microwave": "\u{e01b}",
"mill-sign": "\u{e1ed}",
"minimize": "\u{f78c}",
"compress-arrows-alt": "\u{f78c}",
"mintbit": "\u{e62f}",
"minus": "\u{f068}",
"subtract": "\u{f068}",
"mistletoe": "\u{f7b4}",
"mitten": "\u{f7b5}",
"mix": "\u{f3cb}",
"mixcloud": "\u{f289}",
"mixer": "\u{e056}",
"mizuni": "\u{f3cc}",
"mobile": "\u{f3ce}",
"mobile-android": "\u{f3ce}",
"mobile-phone": "\u{f3ce}",
"mobile-button": "\u{f10b}",
"mobile-notch": "\u{e1ee}",
"mobile-iphone": "\u{e1ee}",
"mobile-retro": "\u{e527}",
"mobile-screen": "\u{f3cf}",
"mobile-android-alt": "\u{f3cf}",
"mobile-screen-button": "\u{f3cd}",
"mobile-alt": "\u{f3cd}",
"mobile-signal": "\u{e1ef}",
"mobile-signal-out": "\u{e1f0}",
"modx": "\u{f285}",
"monero": "\u{f3d0}",
"money-bill": "\u{f0d6}",
"money-bill-1": "\u{f3d1}",
"money-bill-alt": "\u{f3d1}",
"money-bill-1-wave": "\u{f53b}",
"money-bill-wave-alt": "\u{f53b}",
"money-bills": "\u{e1f3}",
"money-bill-simple": "\u{e1f1}",
"money-bill-simple-wave": "\u{e1f2}",
"money-bills-simple": "\u{e1f4}",
"money-bills-alt": "\u{e1f4}",
"money-bill-transfer": "\u{e528}",
"money-bill-trend-up": "\u{e529}",
"money-bill-wave": "\u{f53a}",
"money-bill-wheat": "\u{e52a}",
"money-check": "\u{f53c}",
"money-check-dollar": "\u{f53d}",
"money-check-alt": "\u{f53d}",
"money-check-dollar-pen": "\u{f873}",
"money-check-edit-alt": "\u{f873}",
"money-check-pen": "\u{f872}",
"money-check-edit": "\u{f872}",
"money-from-bracket": "\u{e312}",
"money-simple-from-bracket": "\u{e313}",
"monitor-waveform": "\u{f611}",
"monitor-heart-rate": "\u{f611}",
"monkey": "\u{f6fb}",
"monument": "\u{f5a6}",
"moon": "\u{f186}",
"moon-cloud": "\u{f754}",
"moon-over-sun": "\u{f74a}",
"eclipse-alt": "\u{f74a}",
"moon-stars": "\u{f755}",
"moped": "\u{e3b9}",
"mortar-pestle": "\u{f5a7}",
"mosque": "\u{f678}",
"mosquito": "\u{e52b}",
"mosquito-net": "\u{e52c}",
"motorcycle": "\u{f21c}",
"mound": "\u{e52d}",
"mountain": "\u{f6fc}",
"mountain-city": "\u{e52e}",
"mountains": "\u{f6fd}",
"mountain-sun": "\u{e52f}",
"mouse-field": "\u{e5a8}",
"mp3-player": "\u{f8ce}",
"mug": "\u{f874}",
"mug-hot": "\u{f7b6}",
"mug-marshmallows": "\u{f7b7}",
"mug-saucer": "\u{f0f4}",
"coffee": "\u{f0f4}",
"mug-tea": "\u{f875}",
"mug-tea-saucer": "\u{e1f5}",
"mushroom": "\u{e425}",
"music": "\u{f001}",
"music-magnifying-glass": "\u{e662}",
"music-note": "\u{f8cf}",
"music-alt": "\u{f8cf}",
"music-note-slash": "\u{f8d0}",
"music-alt-slash": "\u{f8d0}",
"music-slash": "\u{f8d1}",
"mustache": "\u{e5bc}",
"n": "\u{4e}",
"naira-sign": "\u{e1f6}",
"napster": "\u{f3d2}",
"narwhal": "\u{f6fe}",
"neos": "\u{f612}",
"nesting-dolls": "\u{e3ba}",
"network-wired": "\u{f6ff}",
"neuter": "\u{f22c}",
"newspaper": "\u{f1ea}",
"nfc": "\u{e1f7}",
"nfc-directional": "\u{e530}",
"nfc-lock": "\u{e1f8}",
"nfc-magnifying-glass": "\u{e1f9}",
"nfc-pen": "\u{e1fa}",
"nfc-signal": "\u{e1fb}",
"nfc-slash": "\u{e1fc}",
"nfc-symbol": "\u{e531}",
"nfc-trash": "\u{e1fd}",
"nimblr": "\u{f5a8}",
"node": "\u{f419}",
"node-js": "\u{f3d3}",
"nose": "\u{e5bd}",
"notdef": "\u{e1fe}",
"note": "\u{e1ff}",
"notebook": "\u{e201}",
"note-medical": "\u{e200}",
"not-equal": "\u{f53e}",
"notes": "\u{e202}",
"notes-medical": "\u{f481}",
"note-sticky": "\u{f249}",
"sticky-note": "\u{f249}",
"npm": "\u{f3d4}",
"ns8": "\u{f3d5}",
"nutritionix": "\u{f3d6}",
"o": "\u{4f}",
"object-exclude": "\u{e49c}",
"object-group": "\u{f247}",
"object-intersect": "\u{e49d}",
"objects-align-bottom": "\u{e3bb}",
"objects-align-center-horizontal": "\u{e3bc}",
"objects-align-center-vertical": "\u{e3bd}",
"objects-align-left": "\u{e3be}",
"objects-align-right": "\u{e3bf}",
"objects-align-top": "\u{e3c0}",
"objects-column": "\u{e3c1}",
"object-subtract": "\u{e49e}",
"object-ungroup": "\u{f248}",
"object-union": "\u{e49f}",
"octagon": "\u{f306}",
"octagon-check": "\u{e426}",
"octagon-divide": "\u{e203}",
"octagon-exclamation": "\u{e204}",
"octagon-minus": "\u{f308}",
"minus-octagon": "\u{f308}",
"octagon-plus": "\u{f301}",
"plus-octagon": "\u{f301}",
"octagon-xmark": "\u{f2f0}",
"times-octagon": "\u{f2f0}",
"xmark-octagon": "\u{f2f0}",
"octopus": "\u{e688}",
"octopus-deploy": "\u{e082}",
"odnoklassniki": "\u{f263}",
"odysee": "\u{e5c6}",
"oil-can": "\u{f613}",
"oil-can-drip": "\u{e205}",
"oil-temperature": "\u{f614}",
"oil-temp": "\u{f614}",
"oil-well": "\u{e532}",
"old-republic": "\u{f510}",
"olive": "\u{e316}",
"olive-branch": "\u{e317}",
"om": "\u{f679}",
"omega": "\u{f67a}",
"onion": "\u{e427}",
"opencart": "\u{f23d}",
"openid": "\u{f19b}",
"opensuse": "\u{e62b}",
"opera": "\u{f26a}",
"optin-monster": "\u{f23c}",
"option": "\u{e318}",
"orcid": "\u{f8d2}",
"ornament": "\u{f7b8}",
"osi": "\u{f41a}",
"otter": "\u{f700}",
"outdent": "\u{f03b}",
"dedent": "\u{f03b}",
"outlet": "\u{e01c}",
"oven": "\u{e01d}",
"overline": "\u{f876}",
"p": "\u{50}",
"padlet": "\u{e4a0}",
"page": "\u{e428}",
"page4": "\u{f3d7}",
"page-caret-down": "\u{e429}",
"file-caret-down": "\u{e429}",
"page-caret-up": "\u{e42a}",
"file-caret-up": "\u{e42a}",
"pagelines": "\u{f18c}",
"pager": "\u{f815}",
"paintbrush": "\u{f1fc}",
"paint-brush": "\u{f1fc}",
"paintbrush-fine": "\u{f5a9}",
"paint-brush-alt": "\u{f5a9}",
"paint-brush-fine": "\u{f5a9}",
"paintbrush-alt": "\u{f5a9}",
"paintbrush-pencil": "\u{e206}",
"paint-roller": "\u{f5aa}",
"palette": "\u{f53f}",
"palfed": "\u{f3d8}",
"pallet": "\u{f482}",
"pallet-box": "\u{e208}",
"pallet-boxes": "\u{f483}",
"palette-boxes": "\u{f483}",
"pallet-alt": "\u{f483}",
"pancakes": "\u{e42d}",
"panel-ews": "\u{e42e}",
"panel-fire": "\u{e42f}",
"pan-food": "\u{e42b}",
"pan-frying": "\u{e42c}",
"panorama": "\u{e209}",
"paperclip": "\u{f0c6}",
"paperclip-vertical": "\u{e3c2}",
"paper-plane": "\u{f1d8}",
"paper-plane-top": "\u{e20a}",
"paper-plane-alt": "\u{e20a}",
"send": "\u{e20a}",
"parachute-box": "\u{f4cd}",
"paragraph": "\u{f1dd}",
"paragraph-left": "\u{f878}",
"paragraph-rtl": "\u{f878}",
"party-bell": "\u{e31a}",
"party-horn": "\u{e31b}",
"passport": "\u{f5ab}",
"paste": "\u{f0ea}",
"file-clipboard": "\u{f0ea}",
"patreon": "\u{f3d9}",
"pause": "\u{f04c}",
"paw": "\u{f1b0}",
"paw-claws": "\u{f702}",
"paw-simple": "\u{f701}",
"paw-alt": "\u{f701}",
"paypal": "\u{f1ed}",
"peace": "\u{f67c}",
"peach": "\u{e20b}",
"peanut": "\u{e430}",
"peanuts": "\u{e431}",
"peapod": "\u{e31c}",
"pear": "\u{e20c}",
"pedestal": "\u{e20d}",
"pegasus": "\u{f703}",
"pen": "\u{f304}",
"pencil": "\u{f303}",
"pencil-alt": "\u{f303}",
"pencil-mechanical": "\u{e5ca}",
"pencil-slash": "\u{e215}",
"pen-circle": "\u{e20e}",
"pen-clip": "\u{f305}",
"pen-alt": "\u{f305}",
"pen-clip-slash": "\u{e20f}",
"pen-alt-slash": "\u{e20f}",
"pen-fancy": "\u{f5ac}",
"pen-fancy-slash": "\u{e210}",
"pen-field": "\u{e211}",
"pen-line": "\u{e212}",
"pen-nib": "\u{f5ad}",
"pen-nib-slash": "\u{e4a1}",
"pen-paintbrush": "\u{f618}",
"pencil-paintbrush": "\u{f618}",
"pen-ruler": "\u{f5ae}",
"pencil-ruler": "\u{f5ae}",
"pen-slash": "\u{e213}",
"pen-swirl": "\u{e214}",
"pen-to-square": "\u{f044}",
"edit": "\u{f044}",
"people": "\u{e216}",
"people-arrows": "\u{e068}",
"people-arrows-left-right": "\u{e068}",
"people-carry-box": "\u{f4ce}",
"people-carry": "\u{f4ce}",
"people-dress": "\u{e217}",
"people-dress-simple": "\u{e218}",
"people-group": "\u{e533}",
"people-line": "\u{e534}",
"people-pants": "\u{e219}",
"people-pants-simple": "\u{e21a}",
"people-pulling": "\u{e535}",
"people-robbery": "\u{e536}",
"people-roof": "\u{e537}",
"people-simple": "\u{e21b}",
"pepper": "\u{e432}",
"pepper-hot": "\u{f816}",
"perbyte": "\u{e083}",
"percent": "\u{25}",
"percentage": "\u{25}",
"period": "\u{2e}",
"periscope": "\u{f3da}",
"person": "\u{f183}",
"male": "\u{f183}",
"person-arrow-down-to-line": "\u{e538}",
"person-arrow-up-from-line": "\u{e539}",
"person-biking": "\u{f84a}",
"biking": "\u{f84a}",
"person-biking-mountain": "\u{f84b}",
"biking-mountain": "\u{f84b}",
"person-booth": "\u{f756}",
"person-breastfeeding": "\u{e53a}",
"person-burst": "\u{e53b}",
"person-cane": "\u{e53c}",
"person-carry-box": "\u{f4cf}",
"person-carry": "\u{f4cf}",
"person-chalkboard": "\u{e53d}",
"person-circle-check": "\u{e53e}",
"person-circle-exclamation": "\u{e53f}",
"person-circle-minus": "\u{e540}",
"person-circle-plus": "\u{e541}",
"person-circle-question": "\u{e542}",
"person-circle-xmark": "\u{e543}",
"person-digging": "\u{f85e}",
"digging": "\u{f85e}",
"person-dolly": "\u{f4d0}",
"person-dolly-empty": "\u{f4d1}",
"person-dots-from-line": "\u{f470}",
"diagnoses": "\u{f470}",
"person-dress": "\u{f182}",
"female": "\u{f182}",
"person-dress-burst": "\u{e544}",
"person-dress-fairy": "\u{e607}",
"person-dress-simple": "\u{e21c}",
"person-drowning": "\u{e545}",
"person-fairy": "\u{e608}",
"person-falling": "\u{e546}",
"person-falling-burst": "\u{e547}",
"person-from-portal": "\u{e023}",
"portal-exit": "\u{e023}",
"person-half-dress": "\u{e548}",
"person-harassing": "\u{e549}",
"person-hiking": "\u{f6ec}",
"hiking": "\u{f6ec}",
"person-military-pointing": "\u{e54a}",
"person-military-rifle": "\u{e54b}",
"person-military-to-person": "\u{e54c}",
"person-pinball": "\u{e21d}",
"person-praying": "\u{f683}",
"pray": "\u{f683}",
"person-pregnant": "\u{e31e}",
"person-rays": "\u{e54d}",
"person-rifle": "\u{e54e}",
"person-running": "\u{f70c}",
"running": "\u{f70c}",
"person-running-fast": "\u{e5ff}",
"person-seat": "\u{e21e}",
"person-seat-reclined": "\u{e21f}",
"person-shelter": "\u{e54f}",
"person-sign": "\u{f757}",
"person-simple": "\u{e220}",
"person-skating": "\u{f7c5}",
"skating": "\u{f7c5}",
"person-skiing": "\u{f7c9}",
"skiing": "\u{f7c9}",
"person-skiing-nordic": "\u{f7ca}",
"skiing-nordic": "\u{f7ca}",
"person-ski-jumping": "\u{f7c7}",
"ski-jump": "\u{f7c7}",
"person-ski-lift": "\u{f7c8}",
"ski-lift": "\u{f7c8}",
"person-sledding": "\u{f7cb}",
"sledding": "\u{f7cb}",
"person-snowboarding": "\u{f7ce}",
"snowboarding": "\u{f7ce}",
"person-snowmobiling": "\u{f7d1}",
"snowmobile": "\u{f7d1}",
"person-swimming": "\u{f5c4}",
"swimmer": "\u{f5c4}",
"person-through-window": "\u{e5a9}",
"person-to-door": "\u{e433}",
"person-to-portal": "\u{e022}",
"portal-enter": "\u{e022}",
"person-walking": "\u{f554}",
"walking": "\u{f554}",
"person-walking-arrow-loop-left": "\u{e551}",
"person-walking-arrow-right": "\u{e552}",
"person-walking-dashed-line-arrow-right": "\u{e553}",
"person-walking-luggage": "\u{e554}",
"person-walking-with-cane": "\u{f29d}",
"blind": "\u{f29d}",
"peseta-sign": "\u{e221}",
"peso-sign": "\u{e222}",
"phabricator": "\u{f3db}",
"phoenix-framework": "\u{f3dc}",
"phoenix-squadron": "\u{f511}",
"phone": "\u{f095}",
"phone-arrow-down-left": "\u{e223}",
"phone-arrow-down": "\u{e223}",
"phone-incoming": "\u{e223}",
"phone-arrow-right": "\u{e5be}",
"phone-arrow-up-right": "\u{e224}",
"phone-arrow-up": "\u{e224}",
"phone-outgoing": "\u{e224}",
"phone-flip": "\u{f879}",
"phone-alt": "\u{f879}",
"phone-hangup": "\u{e225}",
"phone-intercom": "\u{e434}",
"phone-missed": "\u{e226}",
"phone-office": "\u{f67d}",
"phone-plus": "\u{f4d2}",
"phone-rotary": "\u{f8d3}",
"phone-slash": "\u{f3dd}",
"phone-volume": "\u{f2a0}",
"volume-control-phone": "\u{f2a0}",
"phone-xmark": "\u{e227}",
"photo-film": "\u{f87c}",
"photo-video": "\u{f87c}",
"photo-film-music": "\u{e228}",
"php": "\u{f457}",
"pi": "\u{f67e}",
"piano": "\u{f8d4}",
"piano-keyboard": "\u{f8d5}",
"pickaxe": "\u{e5bf}",
"pickleball": "\u{e435}",
"pie": "\u{f705}",
"pied-piper": "\u{f2ae}",
"pied-piper-alt": "\u{f1a8}",
"pied-piper-hat": "\u{f4e5}",
"pied-piper-pp": "\u{f1a7}",
"pig": "\u{f706}",
"piggy-bank": "\u{f4d3}",
"pills": "\u{f484}",
"pinata": "\u{e3c3}",
"pinball": "\u{e229}",
"pineapple": "\u{e31f}",
"pinterest": "\u{f0d2}",
"pinterest-p": "\u{f231}",
"pipe": "\u{7c}",
"pipe-circle-check": "\u{e436}",
"pipe-collar": "\u{e437}",
"pipe-section": "\u{e438}",
"pipe-smoking": "\u{e3c4}",
"pipe-valve": "\u{e439}",
"pix": "\u{e43a}",
"pixiv": "\u{e640}",
"pizza": "\u{f817}",
"pizza-slice": "\u{f818}",
"place-of-worship": "\u{f67f}",
"plane": "\u{f072}",
"plane-arrival": "\u{f5af}",
"plane-circle-check": "\u{e555}",
"plane-circle-exclamation": "\u{e556}",
"plane-circle-xmark": "\u{e557}",
"plane-departure": "\u{f5b0}",
"plane-engines": "\u{f3de}",
"plane-alt": "\u{f3de}",
"plane-lock": "\u{e558}",
"plane-prop": "\u{e22b}",
"plane-slash": "\u{e069}",
"plane-tail": "\u{e22c}",
"planet-moon": "\u{e01f}",
"planet-ringed": "\u{e020}",
"plane-up": "\u{e22d}",
"plane-up-slash": "\u{e22e}",
"plant-wilt": "\u{e5aa}",
"plate-utensils": "\u{e43b}",
"plate-wheat": "\u{e55a}",
"play": "\u{f04b}",
"play-pause": "\u{e22f}",
"playstation": "\u{f3df}",
"plug": "\u{f1e6}",
"plug-circle-bolt": "\u{e55b}",
"plug-circle-check": "\u{e55c}",
"plug-circle-exclamation": "\u{e55d}",
"plug-circle-minus": "\u{e55e}",
"plug-circle-plus": "\u{e55f}",
"plug-circle-xmark": "\u{e560}",
"plus": "\u{2b}",
"add": "\u{2b}",
"plus-large": "\u{e59e}",
"plus-minus": "\u{e43c}",
"podcast": "\u{f2ce}",
"podium": "\u{f680}",
"podium-star": "\u{f758}",
"police-box": "\u{e021}",
"poll-people": "\u{f759}",
"pompebled": "\u{e43d}",
"poo": "\u{f2fe}",
"pool-8-ball": "\u{e3c5}",
"poop": "\u{f619}",
"poo-storm": "\u{f75a}",
"poo-bolt": "\u{f75a}",
"popcorn": "\u{f819}",
"popsicle": "\u{e43e}",
"potato": "\u{e440}",
"pot-food": "\u{e43f}",
"power-off": "\u{f011}",
"prescription": "\u{f5b1}",
"prescription-bottle": "\u{f485}",
"prescription-bottle-medical": "\u{f486}",
"prescription-bottle-alt": "\u{f486}",
"prescription-bottle-pill": "\u{e5c0}",
"presentation-screen": "\u{f685}",
"presentation": "\u{f685}",
"pretzel": "\u{e441}",
"print": "\u{f02f}",
"print-magnifying-glass": "\u{f81a}",
"print-search": "\u{f81a}",
"print-slash": "\u{f686}",
"product-hunt": "\u{f288}",
"projector": "\u{f8d6}",
"pump": "\u{e442}",
"pumpkin": "\u{f707}",
"pump-medical": "\u{e06a}",
"pump-soap": "\u{e06b}",
"pushed": "\u{f3e1}",
"puzzle": "\u{e443}",
"puzzle-piece": "\u{f12e}",
"puzzle-piece-simple": "\u{e231}",
"puzzle-piece-alt": "\u{e231}",
"python": "\u{f3e2}",
"q": "\u{51}",
"qq": "\u{f1d6}",
"qrcode": "\u{f029}",
"question": "\u{3f}",
"quinscape": "\u{f459}",
"quora": "\u{f2c4}",
"quote-left": "\u{f10d}",
"quote-left-alt": "\u{f10d}",
"quote-right": "\u{f10e}",
"quote-right-alt": "\u{f10e}",
"quotes": "\u{e234}",
"r": "\u{52}",
"rabbit": "\u{f708}",
"rabbit-running": "\u{f709}",
"rabbit-fast": "\u{f709}",
"raccoon": "\u{e613}",
"racquet": "\u{f45a}",
"radar": "\u{e024}",
"radiation": "\u{f7b9}",
"radio": "\u{f8d7}",
"radio-tuner": "\u{f8d8}",
"radio-alt": "\u{f8d8}",
"rainbow": "\u{f75b}",
"raindrops": "\u{f75c}",
"ram": "\u{f70a}",
"ramp-loading": "\u{f4d4}",
"ranking-star": "\u{e561}",
"raspberry-pi": "\u{f7bb}",
"ravelry": "\u{f2d9}",
"raygun": "\u{e025}",
"react": "\u{f41b}",
"reacteurope": "\u{f75d}",
"readme": "\u{f4d5}",
"rebel": "\u{f1d0}",
"receipt": "\u{f543}",
"record-vinyl": "\u{f8d9}",
"rectangle": "\u{f2fa}",
"rectangle-landscape": "\u{f2fa}",
"rectangle-ad": "\u{f641}",
"ad": "\u{f641}",
"rectangle-barcode": "\u{f463}",
"barcode-alt": "\u{f463}",
"rectangle-code": "\u{e322}",
"rectangle-history": "\u{e4a2}",
"rectangle-history-circle-plus": "\u{e4a3}",
"rectangle-history-circle-user": "\u{e4a4}",
"rectangle-list": "\u{f022}",
"list-alt": "\u{f022}",
"rectangle-pro": "\u{e235}",
"pro": "\u{e235}",
"rectangles-mixed": "\u{e323}",
"rectangle-terminal": "\u{e236}",
"rectangle-vertical": "\u{f2fb}",
"rectangle-portrait": "\u{f2fb}",
"rectangle-vertical-history": "\u{e237}",
"rectangle-wide": "\u{f2fc}",
"rectangle-xmark": "\u{f410}",
"rectangle-times": "\u{f410}",
"times-rectangle": "\u{f410}",
"window-close": "\u{f410}",
"recycle": "\u{f1b8}",
"reddit": "\u{f1a1}",
"reddit-alien": "\u{f281}",
"redhat": "\u{f7bc}",
"red-river": "\u{f3e3}",
"reel": "\u{e238}",
"reflect-both": "\u{e66f}",
"reflect-horizontal": "\u{e664}",
"reflect-vertical": "\u{e665}",
"refrigerator": "\u{e026}",
"registered": "\u{f25d}",
"renren": "\u{f18b}",
"repeat": "\u{f363}",
"repeat-1": "\u{f365}",
"reply": "\u{f3e5}",
"mail-reply": "\u{f3e5}",
"reply-all": "\u{f122}",
"mail-reply-all": "\u{f122}",
"reply-clock": "\u{e239}",
"reply-time": "\u{e239}",
"replyd": "\u{f3e6}",
"republican": "\u{f75e}",
"researchgate": "\u{f4f8}",
"resolving": "\u{f3e7}",
"restroom": "\u{f7bd}",
"restroom-simple": "\u{e23a}",
"retweet": "\u{f079}",
"rev": "\u{f5b2}",
"rhombus": "\u{e23b}",
"ribbon": "\u{f4d6}",
"right": "\u{f356}",
"arrow-alt-right": "\u{f356}",
"right-from-bracket": "\u{f2f5}",
"sign-out-alt": "\u{f2f5}",
"right-from-line": "\u{f347}",
"arrow-alt-from-left": "\u{f347}",
"right-left": "\u{f362}",
"exchange-alt": "\u{f362}",
"right-left-large": "\u{e5e1}",
"right-long": "\u{f30b}",
"long-arrow-alt-right": "\u{f30b}",
"right-long-to-line": "\u{e444}",
"right-to-bracket": "\u{f2f6}",
"sign-in-alt": "\u{f2f6}",
"right-to-line": "\u{f34c}",
"arrow-alt-to-right": "\u{f34c}",
"ring": "\u{f70b}",
"ring-diamond": "\u{e5ab}",
"rings-wedding": "\u{f81b}",
"road": "\u{f018}",
"road-barrier": "\u{e562}",
"road-bridge": "\u{e563}",
"road-circle-check": "\u{e564}",
"road-circle-exclamation": "\u{e565}",
"road-circle-xmark": "\u{e566}",
"road-lock": "\u{e567}",
"road-spikes": "\u{e568}",
"robot": "\u{f544}",
"robot-astromech": "\u{e2d2}",
"rocket": "\u{f135}",
"rocketchat": "\u{f3e8}",
"rocket-launch": "\u{e027}",
"rockrms": "\u{f3e9}",
"roller-coaster": "\u{e324}",
"rotate": "\u{f2f1}",
"sync-alt": "\u{f2f1}",
"rotate-exclamation": "\u{e23c}",
"rotate-left": "\u{f2ea}",
"rotate-back": "\u{f2ea}",
"rotate-backward": "\u{f2ea}",
"undo-alt": "\u{f2ea}",
"rotate-reverse": "\u{e631}",
"rotate-right": "\u{f2f9}",
"redo-alt": "\u{f2f9}",
"rotate-forward": "\u{f2f9}",
"route": "\u{f4d7}",
"route-highway": "\u{f61a}",
"route-interstate": "\u{f61b}",
"router": "\u{f8da}",
"r-project": "\u{f4f7}",
"rss": "\u{f09e}",
"feed": "\u{f09e}",
"ruble-sign": "\u{f158}",
"rouble": "\u{f158}",
"rub": "\u{f158}",
"ruble": "\u{f158}",
"rug": "\u{e569}",
"rugby-ball": "\u{e3c6}",
"ruler": "\u{f545}",
"ruler-combined": "\u{f546}",
"ruler-horizontal": "\u{f547}",
"ruler-triangle": "\u{f61c}",
"ruler-vertical": "\u{f548}",
"rupee-sign": "\u{f156}",
"rupee": "\u{f156}",
"rupiah-sign": "\u{e23d}",
"rust": "\u{e07a}",
"rv": "\u{f7be}",
"s": "\u{53}",
"sack": "\u{f81c}",
"sack-dollar": "\u{f81d}",
"sack-xmark": "\u{e56a}",
"safari": "\u{f267}",
"sailboat": "\u{e445}",
"salad": "\u{f81e}",
"bowl-salad": "\u{f81e}",
"salesforce": "\u{f83b}",
"salt-shaker": "\u{e446}",
"sandwich": "\u{f81f}",
"sass": "\u{f41e}",
"satellite": "\u{f7bf}",
"satellite-dish": "\u{f7c0}",
"sausage": "\u{f820}",
"saxophone": "\u{f8dc}",
"saxophone-fire": "\u{f8db}",
"sax-hot": "\u{f8db}",
"scale-balanced": "\u{f24e}",
"balance-scale": "\u{f24e}",
"scale-unbalanced": "\u{f515}",
"balance-scale-left": "\u{f515}",
"scale-unbalanced-flip": "\u{f516}",
"balance-scale-right": "\u{f516}",
"scalpel": "\u{f61d}",
"scalpel-line-dashed": "\u{f61e}",
"scalpel-path": "\u{f61e}",
"scanner-gun": "\u{f488}",
"scanner": "\u{f488}",
"scanner-image": "\u{f8f3}",
"scanner-keyboard": "\u{f489}",
"scanner-touchscreen": "\u{f48a}",
"scarecrow": "\u{f70d}",
"scarf": "\u{f7c1}",
"schlix": "\u{f3ea}",
"school": "\u{f549}",
"school-circle-check": "\u{e56b}",
"school-circle-exclamation": "\u{e56c}",
"school-circle-xmark": "\u{e56d}",
"school-flag": "\u{e56e}",
"school-lock": "\u{e56f}",
"scissors": "\u{f0c4}",
"cut": "\u{f0c4}",
"screencast": "\u{e23e}",
"screenpal": "\u{e570}",
"screen-users": "\u{f63d}",
"users-class": "\u{f63d}",
"screwdriver": "\u{f54a}",
"screwdriver-wrench": "\u{f7d9}",
"tools": "\u{f7d9}",
"scribble": "\u{e23f}",
"scribd": "\u{f28a}",
"scroll": "\u{f70e}",
"scroll-old": "\u{f70f}",
"scroll-torah": "\u{f6a0}",
"torah": "\u{f6a0}",
"scrubber": "\u{f2f8}",
"scythe": "\u{f710}",
"sd-card": "\u{f7c2}",
"sd-cards": "\u{e240}",
"seal": "\u{e241}",
"seal-exclamation": "\u{e242}",
"seal-question": "\u{e243}",
"searchengin": "\u{f3eb}",
"seat-airline": "\u{e244}",
"section": "\u{e447}",
"seedling": "\u{f4d8}",
"sprout": "\u{f4d8}",
"sellcast": "\u{f2da}",
"sellsy": "\u{f213}",
"semicolon": "\u{3b}",
"send-back": "\u{f87e}",
"send-backward": "\u{f87f}",
"sensor": "\u{e028}",
"sensor-cloud": "\u{e02c}",
"sensor-smoke": "\u{e02c}",
"sensor-fire": "\u{e02a}",
"sensor-on": "\u{e02b}",
"sensor-triangle-exclamation": "\u{e029}",
"sensor-alert": "\u{e029}",
"server": "\u{f233}",
"servicestack": "\u{f3ec}",
"shapes": "\u{f61f}",
"triangle-circle-square": "\u{f61f}",
"share": "\u{f064}",
"mail-forward": "\u{f064}",
"share-all": "\u{f367}",
"share-from-square": "\u{f14d}",
"share-square": "\u{f14d}",
"share-nodes": "\u{f1e0}",
"share-alt": "\u{f1e0}",
"sheep": "\u{f711}",
"sheet-plastic": "\u{e571}",
"shekel-sign": "\u{f20b}",
"ils": "\u{f20b}",
"shekel": "\u{f20b}",
"sheqel": "\u{f20b}",
"sheqel-sign": "\u{f20b}",
"shelves": "\u{f480}",
"inventory": "\u{f480}",
"shelves-empty": "\u{e246}",
"shield": "\u{f132}",
"shield-blank": "\u{f132}",
"shield-cat": "\u{e572}",
"shield-check": "\u{f2f7}",
"shield-cross": "\u{f712}",
"shield-dog": "\u{e573}",
"shield-exclamation": "\u{e247}",
"shield-halved": "\u{f3ed}",
"shield-alt": "\u{f3ed}",
"shield-heart": "\u{e574}",
"shield-keyhole": "\u{e248}",
"shield-minus": "\u{e249}",
"shield-plus": "\u{e24a}",
"shield-quartered": "\u{e575}",
"shield-slash": "\u{e24b}",
"shield-virus": "\u{e06c}",
"shield-xmark": "\u{e24c}",
"shield-times": "\u{e24c}",
"ship": "\u{f21a}",
"shirt": "\u{f553}",
"t-shirt": "\u{f553}",
"tshirt": "\u{f553}",
"shirt-long-sleeve": "\u{e3c7}",
"shirt-running": "\u{e3c8}",
"shirtsinbulk": "\u{f214}",
"shirt-tank-top": "\u{e3c9}",
"shish-kebab": "\u{f821}",
"shoelace": "\u{e60c}",
"shoe-prints": "\u{f54b}",
"shop": "\u{f54f}",
"store-alt": "\u{f54f}",
"shopify": "\u{e057}",
"shop-lock": "\u{e4a5}",
"shop-slash": "\u{e070}",
"store-alt-slash": "\u{e070}",
"shopware": "\u{f5b5}",
"shovel": "\u{f713}",
"shovel-snow": "\u{f7c3}",
"shower": "\u{f2cc}",
"shower-down": "\u{e24d}",
"shower-alt": "\u{e24d}",
"shredder": "\u{f68a}",
"shrimp": "\u{e448}",
"shuffle": "\u{f074}",
"random": "\u{f074}",
"shutters": "\u{e449}",
"shuttlecock": "\u{f45b}",
"shuttle-space": "\u{f197}",
"space-shuttle": "\u{f197}",
"sickle": "\u{f822}",
"sidebar": "\u{e24e}",
"sidebar-flip": "\u{e24f}",
"sigma": "\u{f68b}",
"signal": "\u{f012}",
"signal-5": "\u{f012}",
"signal-perfect": "\u{f012}",
"signal-bars": "\u{f690}",
"signal-alt": "\u{f690}",
"signal-alt-4": "\u{f690}",
"signal-bars-strong": "\u{f690}",
"signal-bars-fair": "\u{f692}",
"signal-alt-2": "\u{f692}",
"signal-bars-good": "\u{f693}",
"signal-alt-3": "\u{f693}",
"signal-bars-slash": "\u{f694}",
"signal-alt-slash": "\u{f694}",
"signal-bars-weak": "\u{f691}",
"signal-alt-1": "\u{f691}",
"signal-fair": "\u{f68d}",
"signal-2": "\u{f68d}",
"signal-good": "\u{f68e}",
"signal-3": "\u{f68e}",
"signal-messenger": "\u{e663}",
"signal-slash": "\u{f695}",
"signal-stream": "\u{f8dd}",
"signal-stream-slash": "\u{e250}",
"signal-strong": "\u{f68f}",
"signal-4": "\u{f68f}",
"signal-weak": "\u{f68c}",
"signal-1": "\u{f68c}",
"signature": "\u{f5b7}",
"signature-lock": "\u{e3ca}",
"signature-slash": "\u{e3cb}",
"sign-hanging": "\u{f4d9}",
"sign": "\u{f4d9}",
"sign-post": "\u{e624}",
"sign-posts": "\u{e625}",
"sign-posts-wrench": "\u{e626}",
"signs-post": "\u{f277}",
"map-signs": "\u{f277}",
"sim-card": "\u{f7c4}",
"sim-cards": "\u{e251}",
"simplybuilt": "\u{f215}",
"sink": "\u{e06d}",
"siren": "\u{e02d}",
"siren-on": "\u{e02e}",
"sistrix": "\u{f3ee}",
"sitemap": "\u{f0e8}",
"sith": "\u{f512}",
"sitrox": "\u{e44a}",
"skeleton": "\u{f620}",
"skeleton-ribs": "\u{e5cb}",
"sketch": "\u{f7c6}",
"ski-boot": "\u{e3cc}",
"ski-boot-ski": "\u{e3cd}",
"skull": "\u{f54c}",
"skull-cow": "\u{f8de}",
"skull-crossbones": "\u{f714}",
"skyatlas": "\u{f216}",
"skype": "\u{f17e}",
"slack": "\u{f198}",
"slack-hash": "\u{f198}",
"slash": "\u{f715}",
"slash-back": "\u{5c}",
"slash-forward": "\u{2f}",
"sleigh": "\u{f7cc}",
"slider": "\u{e252}",
"sliders": "\u{f1de}",
"sliders-h": "\u{f1de}",
"sliders-simple": "\u{e253}",
"sliders-up": "\u{f3f1}",
"sliders-v": "\u{f3f1}",
"slideshare": "\u{f1e7}",
"slot-machine": "\u{e3ce}",
"smog": "\u{f75f}",
"smoke": "\u{f760}",
"smoking": "\u{f48d}",
"snake": "\u{f716}",
"snapchat": "\u{f2ab}",
"snapchat-ghost": "\u{f2ab}",
"snooze": "\u{f880}",
"zzz": "\u{f880}",
"snow-blowing": "\u{f761}",
"snowflake": "\u{f2dc}",
"snowflake-droplets": "\u{e5c1}",
"snowflakes": "\u{f7cf}",
"snowman": "\u{f7d0}",
"snowman-head": "\u{f79b}",
"frosty-head": "\u{f79b}",
"snowplow": "\u{f7d2}",
"soap": "\u{e06e}",
"socks": "\u{f696}",
"soft-serve": "\u{e400}",
"creemee": "\u{e400}",
"solar-panel": "\u{f5ba}",
"solar-system": "\u{e02f}",
"sort": "\u{f0dc}",
"unsorted": "\u{f0dc}",
"sort-down": "\u{f0dd}",
"sort-desc": "\u{f0dd}",
"sort-up": "\u{f0de}",
"sort-asc": "\u{f0de}",
"soundcloud": "\u{f1be}",
"sourcetree": "\u{f7d3}",
"spa": "\u{f5bb}",
"space-awesome": "\u{e5ac}",
"space-station-moon": "\u{e033}",
"space-station-moon-construction": "\u{e034}",
"space-station-moon-alt": "\u{e034}",
"spade": "\u{f2f4}",
"spaghetti-monster-flying": "\u{f67b}",
"pastafarianism": "\u{f67b}",
"sparkle": "\u{e5d6}",
"sparkles": "\u{f890}",
"speakap": "\u{f3f3}",
"speaker": "\u{f8df}",
"speaker-deck": "\u{f83c}",
"speakers": "\u{f8e0}",
"spell-check": "\u{f891}",
"spider": "\u{f717}",
"spider-black-widow": "\u{f718}",
"spider-web": "\u{f719}",
"spinner": "\u{f110}",
"spinner-scale": "\u{e62a}",
"spinner-third": "\u{f3f4}",
"split": "\u{e254}",
"splotch": "\u{f5bc}",
"spoon": "\u{f2e5}",
"utensil-spoon": "\u{f2e5}",
"sportsball": "\u{e44b}",
"spotify": "\u{f1bc}",
"spray-can": "\u{f5bd}",
"spray-can-sparkles": "\u{f5d0}",
"air-freshener": "\u{f5d0}",
"sprinkler": "\u{e035}",
"sprinkler-ceiling": "\u{e44c}",
"square": "\u{f0c8}",
"square-0": "\u{e255}",
"square-1": "\u{e256}",
"square-2": "\u{e257}",
"square-3": "\u{e258}",
"square-4": "\u{e259}",
"square-5": "\u{e25a}",
"square-6": "\u{e25b}",
"square-7": "\u{e25c}",
"square-8": "\u{e25d}",
"square-9": "\u{e25e}",
"square-a": "\u{e25f}",
"square-a-lock": "\u{e44d}",
"square-ampersand": "\u{e260}",
"square-arrow-down": "\u{f339}",
"arrow-square-down": "\u{f339}",
"square-arrow-down-left": "\u{e261}",
"square-arrow-down-right": "\u{e262}",
"square-arrow-left": "\u{f33a}",
"arrow-square-left": "\u{f33a}",
"square-arrow-right": "\u{f33b}",
"arrow-square-right": "\u{f33b}",
"square-arrow-up": "\u{f33c}",
"arrow-square-up": "\u{f33c}",
"square-arrow-up-left": "\u{e263}",
"square-arrow-up-right": "\u{f14c}",
"external-link-square": "\u{f14c}",
"square-b": "\u{e264}",
"square-behance": "\u{f1b5}",
"behance-square": "\u{f1b5}",
"square-bolt": "\u{e265}",
"square-c": "\u{e266}",
"square-caret-down": "\u{f150}",
"caret-square-down": "\u{f150}",
"square-caret-left": "\u{f191}",
"caret-square-left": "\u{f191}",
"square-caret-right": "\u{f152}",
"caret-square-right": "\u{f152}",
"square-caret-up": "\u{f151}",
"caret-square-up": "\u{f151}",
"square-check": "\u{f14a}",
"check-square": "\u{f14a}",
"square-chevron-down": "\u{f329}",
"chevron-square-down": "\u{f329}",
"square-chevron-left": "\u{f32a}",
"chevron-square-left": "\u{f32a}",
"square-chevron-right": "\u{f32b}",
"chevron-square-right": "\u{f32b}",
"square-chevron-up": "\u{f32c}",
"chevron-square-up": "\u{f32c}",
"square-code": "\u{e267}",
"square-d": "\u{e268}",
"square-dashed": "\u{e269}",
"square-dashed-circle-plus": "\u{e5c2}",
"square-divide": "\u{e26a}",
"square-dollar": "\u{f2e9}",
"dollar-square": "\u{f2e9}",
"usd-square": "\u{f2e9}",
"square-down": "\u{f350}",
"arrow-alt-square-down": "\u{f350}",
"square-down-left": "\u{e26b}",
"square-down-right": "\u{e26c}",
"square-dribbble": "\u{f397}",
"dribbble-square": "\u{f397}",
"square-e": "\u{e26d}",
"square-ellipsis": "\u{e26e}",
"square-ellipsis-vertical": "\u{e26f}",
"square-envelope": "\u{f199}",
"envelope-square": "\u{f199}",
"square-exclamation": "\u{f321}",
"exclamation-square": "\u{f321}",
"square-f": "\u{e270}",
"square-facebook": "\u{f082}",
"facebook-square": "\u{f082}",
"square-font-awesome": "\u{e5ad}",
"square-font-awesome-stroke": "\u{f35c}",
"font-awesome-alt": "\u{f35c}",
"square-fragile": "\u{f49b}",
"box-fragile": "\u{f49b}",
"square-wine-glass-crack": "\u{f49b}",
"square-full": "\u{f45c}",
"square-g": "\u{e271}",
"square-git": "\u{f1d2}",
"git-square": "\u{f1d2}",
"square-github": "\u{f092}",
"github-square": "\u{f092}",
"square-gitlab": "\u{e5ae}",
"gitlab-square": "\u{e5ae}",
"square-google-plus": "\u{f0d4}",
"google-plus-square": "\u{f0d4}",
"square-h": "\u{f0fd}",
"h-square": "\u{f0fd}",
"square-hacker-news": "\u{f3af}",
"hacker-news-square": "\u{f3af}",
"square-heart": "\u{f4c8}",
"heart-square": "\u{f4c8}",
"square-i": "\u{e272}",
"square-info": "\u{f30f}",
"info-square": "\u{f30f}",
"square-instagram": "\u{e055}",
"instagram-square": "\u{e055}",
"square-j": "\u{e273}",
"square-js": "\u{f3b9}",
"js-square": "\u{f3b9}",
"square-k": "\u{e274}",
"square-kanban": "\u{e488}",
"square-l": "\u{e275}",
"square-lastfm": "\u{f203}",
"lastfm-square": "\u{f203}",
"square-left": "\u{f351}",
"arrow-alt-square-left": "\u{f351}",
"square-letterboxd": "\u{e62e}",
"square-list": "\u{e489}",
"square-m": "\u{e276}",
"square-minus": "\u{f146}",
"minus-square": "\u{f146}",
"square-n": "\u{e277}",
"square-nfi": "\u{e576}",
"square-o": "\u{e278}",
"square-odnoklassniki": "\u{f264}",
"odnoklassniki-square": "\u{f264}",
"square-p": "\u{e279}",
"square-parking": "\u{f540}",
"parking": "\u{f540}",
"square-parking-slash": "\u{f617}",
"parking-slash": "\u{f617}",
"square-pen": "\u{f14b}",
"pen-square": "\u{f14b}",
"pencil-square": "\u{f14b}",
"square-person-confined": "\u{e577}",
"square-phone": "\u{f098}",
"phone-square": "\u{f098}",
"square-phone-flip": "\u{f87b}",
"phone-square-alt": "\u{f87b}",
"square-phone-hangup": "\u{e27a}",
"phone-square-down": "\u{e27a}",
"square-pied-piper": "\u{e01e}",
"pied-piper-square": "\u{e01e}",
"square-pinterest": "\u{f0d3}",
"pinterest-square": "\u{f0d3}",
"square-plus": "\u{f0fe}",
"plus-square": "\u{f0fe}",
"square-poll-horizontal": "\u{f682}",
"poll-h": "\u{f682}",
"square-poll-vertical": "\u{f681}",
"poll": "\u{f681}",
"square-q": "\u{e27b}",
"square-quarters": "\u{e44e}",
"square-question": "\u{f2fd}",
"question-square": "\u{f2fd}",
"square-quote": "\u{e329}",
"square-r": "\u{e27c}",
"square-reddit": "\u{f1a2}",
"reddit-square": "\u{f1a2}",
"square-right": "\u{f352}",
"arrow-alt-square-right": "\u{f352}",
"square-ring": "\u{e44f}",
"square-root": "\u{f697}",
"square-root-variable": "\u{f698}",
"square-root-alt": "\u{f698}",
"square-rss": "\u{f143}",
"rss-square": "\u{f143}",
"square-s": "\u{e27d}",
"square-share-nodes": "\u{f1e1}",
"share-alt-square": "\u{f1e1}",
"square-sliders": "\u{f3f0}",
"sliders-h-square": "\u{f3f0}",
"square-sliders-vertical": "\u{f3f2}",
"sliders-v-square": "\u{f3f2}",
"square-small": "\u{e27e}",
"square-snapchat": "\u{f2ad}",
"snapchat-square": "\u{f2ad}",
"squarespace": "\u{f5be}",
"square-star": "\u{e27f}",
"square-steam": "\u{f1b7}",
"steam-square": "\u{f1b7}",
"square-t": "\u{e280}",
"square-terminal": "\u{e32a}",
"square-this-way-up": "\u{f49f}",
"box-up": "\u{f49f}",
"square-threads": "\u{e619}",
"square-tumblr": "\u{f174}",
"tumblr-square": "\u{f174}",
"square-twitter": "\u{f081}",
"twitter-square": "\u{f081}",
"square-u": "\u{e281}",
"square-up": "\u{f353}",
"arrow-alt-square-up": "\u{f353}",
"square-up-left": "\u{e282}",
"square-up-right": "\u{f360}",
"external-link-square-alt": "\u{f360}",
"square-upwork": "\u{e67c}",
"square-user": "\u{e283}",
"square-v": "\u{e284}",
"square-viadeo": "\u{f2aa}",
"viadeo-square": "\u{f2aa}",
"square-vimeo": "\u{f194}",
"vimeo-square": "\u{f194}",
"square-virus": "\u{e578}",
"square-w": "\u{e285}",
"square-web-awesome": "\u{e683}",
"square-web-awesome-stroke": "\u{e684}",
"square-whatsapp": "\u{f40c}",
"whatsapp-square": "\u{f40c}",
"square-x": "\u{e286}",
"square-xing": "\u{f169}",
"xing-square": "\u{f169}",
"square-xmark": "\u{f2d3}",
"times-square": "\u{f2d3}",
"xmark-square": "\u{f2d3}",
"square-x-twitter": "\u{e61a}",
"square-y": "\u{e287}",
"square-youtube": "\u{f431}",
"youtube-square": "\u{f431}",
"square-z": "\u{e288}",
"squid": "\u{e450}",
"squirrel": "\u{f71a}",
"stack-exchange": "\u{f18d}",
"stack-overflow": "\u{f16c}",
"stackpath": "\u{f842}",
"staff": "\u{f71b}",
"staff-snake": "\u{e579}",
"rod-asclepius": "\u{e579}",
"rod-snake": "\u{e579}",
"staff-aesculapius": "\u{e579}",
"stairs": "\u{e289}",
"stamp": "\u{f5bf}",
"standard-definition": "\u{e28a}",
"rectangle-sd": "\u{e28a}",
"stapler": "\u{e5af}",
"star": "\u{f005}",
"star-and-crescent": "\u{f699}",
"star-christmas": "\u{f7d4}",
"star-exclamation": "\u{f2f3}",
"starfighter": "\u{e037}",
"starfighter-twin-ion-engine": "\u{e038}",
"starfighter-alt": "\u{e038}",
"starfighter-twin-ion-engine-advanced": "\u{e28e}",
"starfighter-alt-advanced": "\u{e28e}",
"star-half": "\u{f089}",
"star-half-stroke": "\u{f5c0}",
"star-half-alt": "\u{f5c0}",
"star-of-david": "\u{f69a}",
"star-of-life": "\u{f621}",
"stars": "\u{f762}",
"star-sharp": "\u{e28b}",
"star-sharp-half": "\u{e28c}",
"star-sharp-half-stroke": "\u{e28d}",
"star-sharp-half-alt": "\u{e28d}",
"starship": "\u{e039}",
"starship-freighter": "\u{e03a}",
"star-shooting": "\u{e036}",
"staylinked": "\u{f3f5}",
"steak": "\u{f824}",
"steam": "\u{f1b6}",
"steam-symbol": "\u{f3f6}",
"steering-wheel": "\u{f622}",
"sterling-sign": "\u{f154}",
"gbp": "\u{f154}",
"pound-sign": "\u{f154}",
"stethoscope": "\u{f0f1}",
"sticker-mule": "\u{f3f7}",
"stocking": "\u{f7d5}",
"stomach": "\u{f623}",
"stop": "\u{f04d}",
"stopwatch": "\u{f2f2}",
"stopwatch-20": "\u{e06f}",
"store": "\u{f54e}",
"store-lock": "\u{e4a6}",
"store-slash": "\u{e071}",
"strava": "\u{f428}",
"strawberry": "\u{e32b}",
"street-view": "\u{f21d}",
"stretcher": "\u{f825}",
"strikethrough": "\u{f0cc}",
"stripe": "\u{f429}",
"stripe-s": "\u{f42a}",
"stroopwafel": "\u{f551}",
"stubber": "\u{e5c7}",
"studiovinari": "\u{f3f8}",
"stumbleupon": "\u{f1a4}",
"stumbleupon-circle": "\u{f1a3}",
"subscript": "\u{f12c}",
"subtitles": "\u{e60f}",
"subtitles-slash": "\u{e610}",
"suitcase": "\u{f0f2}",
"suitcase-medical": "\u{f0fa}",
"medkit": "\u{f0fa}",
"suitcase-rolling": "\u{f5c1}",
"sun": "\u{f185}",
"sun-bright": "\u{e28f}",
"sun-alt": "\u{e28f}",
"sun-cloud": "\u{f763}",
"sun-dust": "\u{f764}",
"sunglasses": "\u{f892}",
"sun-haze": "\u{f765}",
"sun-plant-wilt": "\u{e57a}",
"sunrise": "\u{f766}",
"sunset": "\u{f767}",
"superpowers": "\u{f2dd}",
"superscript": "\u{f12b}",
"supple": "\u{f3f9}",
"suse": "\u{f7d6}",
"sushi": "\u{e48a}",
"nigiri": "\u{e48a}",
"sushi-roll": "\u{e48b}",
"maki-roll": "\u{e48b}",
"makizushi": "\u{e48b}",
"swap": "\u{e609}",
"swap-arrows": "\u{e60a}",
"swatchbook": "\u{f5c3}",
"swift": "\u{f8e1}",
"sword": "\u{f71c}",
"sword-laser": "\u{e03b}",
"sword-laser-alt": "\u{e03c}",
"swords": "\u{f71d}",
"swords-laser": "\u{e03d}",
"symbols": "\u{f86e}",
"icons-alt": "\u{f86e}",
"symfony": "\u{f83d}",
"synagogue": "\u{f69b}",
"syringe": "\u{f48e}",
"t": "\u{54}",
"table": "\u{f0ce}",
"table-cells": "\u{f00a}",
"th": "\u{f00a}",
"table-cells-column-lock": "\u{e678}",
"table-cells-column-unlock": "\u{e690}",
"table-cells-large": "\u{f009}",
"th-large": "\u{f009}",
"table-cells-lock": "\u{e679}",
"table-cells-row-lock": "\u{e67a}",
"table-cells-row-unlock": "\u{e691}",
"table-cells-unlock": "\u{e692}",
"table-columns": "\u{f0db}",
"columns": "\u{f0db}",
"table-layout": "\u{e290}",
"table-list": "\u{f00b}",
"th-list": "\u{f00b}",
"table-picnic": "\u{e32d}",
"table-pivot": "\u{e291}",
"table-rows": "\u{e292}",
"rows": "\u{e292}",
"tablet": "\u{f3fb}",
"tablet-android": "\u{f3fb}",
"tablet-button": "\u{f10a}",
"table-tennis-paddle-ball": "\u{f45d}",
"ping-pong-paddle-ball": "\u{f45d}",
"table-tennis": "\u{f45d}",
"table-tree": "\u{e293}",
"tablet-rugged": "\u{f48f}",
"tablets": "\u{f490}",
"tablet-screen": "\u{f3fc}",
"tablet-android-alt": "\u{f3fc}",
"tablet-screen-button": "\u{f3fa}",
"tablet-alt": "\u{f3fa}",
"tachograph-digital": "\u{f566}",
"digital-tachograph": "\u{f566}",
"taco": "\u{f826}",
"tag": "\u{f02b}",
"tags": "\u{f02c}",
"tally": "\u{f69c}",
"tally-5": "\u{f69c}",
"tally-1": "\u{e294}",
"tally-2": "\u{e295}",
"tally-3": "\u{e296}",
"tally-4": "\u{e297}",
"tamale": "\u{e451}",
"tank-water": "\u{e452}",
"tape": "\u{f4db}",
"tarp": "\u{e57b}",
"tarp-droplet": "\u{e57c}",
"taxi": "\u{f1ba}",
"cab": "\u{f1ba}",
"taxi-bus": "\u{e298}",
"teamspeak": "\u{f4f9}",
"teddy-bear": "\u{e3cf}",
"teeth": "\u{f62e}",
"teeth-open": "\u{f62f}",
"telegram": "\u{f2c6}",
"telegram-plane": "\u{f2c6}",
"telescope": "\u{e03e}",
"temperature-arrow-down": "\u{e03f}",
"temperature-down": "\u{e03f}",
"temperature-arrow-up": "\u{e040}",
"temperature-up": "\u{e040}",
"temperature-empty": "\u{f2cb}",
"temperature-0": "\u{f2cb}",
"thermometer-0": "\u{f2cb}",
"thermometer-empty": "\u{f2cb}",
"temperature-full": "\u{f2c7}",
"temperature-4": "\u{f2c7}",
"thermometer-4": "\u{f2c7}",
"thermometer-full": "\u{f2c7}",
"temperature-half": "\u{f2c9}",
"temperature-2": "\u{f2c9}",
"thermometer-2": "\u{f2c9}",
"thermometer-half": "\u{f2c9}",
"temperature-high": "\u{f769}",
"temperature-list": "\u{e299}",
"temperature-low": "\u{f76b}",
"temperature-quarter": "\u{f2ca}",
"temperature-1": "\u{f2ca}",
"thermometer-1": "\u{f2ca}",
"thermometer-quarter": "\u{f2ca}",
"temperature-snow": "\u{f768}",
"temperature-frigid": "\u{f768}",
"temperature-sun": "\u{f76a}",
"temperature-hot": "\u{f76a}",
"temperature-three-quarters": "\u{f2c8}",
"temperature-3": "\u{f2c8}",
"thermometer-3": "\u{f2c8}",
"thermometer-three-quarters": "\u{f2c8}",
"tencent-weibo": "\u{f1d5}",
"tenge-sign": "\u{f7d7}",
"tenge": "\u{f7d7}",
"tennis-ball": "\u{f45e}",
"tent": "\u{e57d}",
"tent-arrow-down-to-line": "\u{e57e}",
"tent-arrow-left-right": "\u{e57f}",
"tent-arrows-down": "\u{e581}",
"tent-arrow-turn-left": "\u{e580}",
"tent-double-peak": "\u{e627}",
"tents": "\u{e582}",
"terminal": "\u{f120}",
"text": "\u{f893}",
"text-height": "\u{f034}",
"text-size": "\u{f894}",
"text-slash": "\u{f87d}",
"remove-format": "\u{f87d}",
"text-width": "\u{f035}",
"themeco": "\u{f5c6}",
"themeisle": "\u{f2b2}",
"the-red-yeti": "\u{f69d}",
"thermometer": "\u{f491}",
"theta": "\u{f69e}",
"think-peaks": "\u{f731}",
"thought-bubble": "\u{e32e}",
"threads": "\u{e618}",
"thumbs-down": "\u{f165}",
"thumbs-up": "\u{f164}",
"thumbtack": "\u{f08d}",
"thumb-tack": "\u{f08d}",
"thumbtack-slash": "\u{e68f}",
"thumb-tack-slash": "\u{e68f}",
"tick": "\u{e32f}",
"ticket": "\u{f145}",
"ticket-airline": "\u{e29a}",
"ticket-perforated-plane": "\u{e29a}",
"ticket-plane": "\u{e29a}",
"ticket-perforated": "\u{e63e}",
"tickets": "\u{e658}",
"tickets-airline": "\u{e29b}",
"tickets-perforated-plane": "\u{e29b}",
"tickets-plane": "\u{e29b}",
"ticket-simple": "\u{f3ff}",
"ticket-alt": "\u{f3ff}",
"tickets-perforated": "\u{e63f}",
"tickets-simple": "\u{e659}",
"tiktok": "\u{e07b}",
"tilde": "\u{7e}",
"timeline": "\u{e29c}",
"timeline-arrow": "\u{e29d}",
"timer": "\u{e29e}",
"tire": "\u{f631}",
"tire-flat": "\u{f632}",
"tire-pressure-warning": "\u{f633}",
"tire-rugged": "\u{f634}",
"toggle-large-off": "\u{e5b0}",
"toggle-large-on": "\u{e5b1}",
"toggle-off": "\u{f204}",
"toggle-on": "\u{f205}",
"toilet": "\u{f7d8}",
"toilet-paper": "\u{f71e}",
"toilet-paper-blank": "\u{f71f}",
"toilet-paper-alt": "\u{f71f}",
"toilet-paper-blank-under": "\u{e29f}",
"toilet-paper-reverse-alt": "\u{e29f}",
"toilet-paper-check": "\u{e5b2}",
"toilet-paper-slash": "\u{e072}",
"toilet-paper-under": "\u{e2a0}",
"toilet-paper-reverse": "\u{e2a0}",
"toilet-paper-under-slash": "\u{e2a1}",
"toilet-paper-reverse-slash": "\u{e2a1}",
"toilet-paper-xmark": "\u{e5b3}",
"toilet-portable": "\u{e583}",
"toilets-portable": "\u{e584}",
"tomato": "\u{e330}",
"tombstone": "\u{f720}",
"tombstone-blank": "\u{f721}",
"tombstone-alt": "\u{f721}",
"toolbox": "\u{f552}",
"tooth": "\u{f5c9}",
"toothbrush": "\u{f635}",
"torii-gate": "\u{f6a1}",
"tornado": "\u{f76f}",
"tower-broadcast": "\u{f519}",
"broadcast-tower": "\u{f519}",
"tower-cell": "\u{e585}",
"tower-control": "\u{e2a2}",
"tower-observation": "\u{e586}",
"tractor": "\u{f722}",
"trade-federation": "\u{f513}",
"trademark": "\u{f25c}",
"traffic-cone": "\u{f636}",
"traffic-light": "\u{f637}",
"traffic-light-go": "\u{f638}",
"traffic-light-slow": "\u{f639}",
"traffic-light-stop": "\u{f63a}",
"trailer": "\u{e041}",
"train": "\u{f238}",
"train-subway": "\u{f239}",
"subway": "\u{f239}",
"train-subway-tunnel": "\u{e2a3}",
"subway-tunnel": "\u{e2a3}",
"train-track": "\u{e453}",
"train-tram": "\u{e5b4}",
"train-tunnel": "\u{e454}",
"transformer-bolt": "\u{e2a4}",
"transgender": "\u{f225}",
"transgender-alt": "\u{f225}",
"transporter": "\u{e042}",
"transporter-1": "\u{e043}",
"transporter-2": "\u{e044}",
"transporter-3": "\u{e045}",
"transporter-4": "\u{e2a5}",
"transporter-5": "\u{e2a6}",
"transporter-6": "\u{e2a7}",
"transporter-7": "\u{e2a8}",
"transporter-empty": "\u{e046}",
"trash": "\u{f1f8}",
"trash-arrow-up": "\u{f829}",
"trash-restore": "\u{f829}",
"trash-can": "\u{f2ed}",
"trash-alt": "\u{f2ed}",
"trash-can-arrow-up": "\u{f82a}",
"trash-restore-alt": "\u{f82a}",
"trash-can-check": "\u{e2a9}",
"trash-can-clock": "\u{e2aa}",
"trash-can-list": "\u{e2ab}",
"trash-can-plus": "\u{e2ac}",
"trash-can-slash": "\u{e2ad}",
"trash-alt-slash": "\u{e2ad}",
"trash-can-undo": "\u{f896}",
"trash-can-arrow-turn-left": "\u{f896}",
"trash-undo-alt": "\u{f896}",
"trash-can-xmark": "\u{e2ae}",
"trash-check": "\u{e2af}",
"trash-clock": "\u{e2b0}",
"trash-list": "\u{e2b1}",
"trash-plus": "\u{e2b2}",
"trash-slash": "\u{e2b3}",
"trash-undo": "\u{f895}",
"trash-arrow-turn-left": "\u{f895}",
"trash-xmark": "\u{e2b4}",
"treasure-chest": "\u{f723}",
"tree": "\u{f1bb}",
"tree-christmas": "\u{f7db}",
"tree-city": "\u{e587}",
"tree-deciduous": "\u{f400}",
"tree-alt": "\u{f400}",
"tree-decorated": "\u{f7dc}",
"tree-large": "\u{f7dd}",
"tree-palm": "\u{f82b}",
"trees": "\u{f724}",
"trello": "\u{f181}",
"t-rex": "\u{e629}",
"triangle": "\u{f2ec}",
"triangle-exclamation": "\u{f071}",
"exclamation-triangle": "\u{f071}",
"warning": "\u{f071}",
"triangle-instrument": "\u{f8e2}",
"triangle-music": "\u{f8e2}",
"triangle-person-digging": "\u{f85d}",
"construction": "\u{f85d}",
"tricycle": "\u{e5c3}",
"tricycle-adult": "\u{e5c4}",
"trillium": "\u{e588}",
"trophy": "\u{f091}",
"trophy-star": "\u{f2eb}",
"trophy-alt": "\u{f2eb}",
"trowel": "\u{e589}",
"trowel-bricks": "\u{e58a}",
"truck": "\u{f0d1}",
"truck-arrow-right": "\u{e58b}",
"truck-bolt": "\u{e3d0}",
"truck-clock": "\u{f48c}",
"shipping-timed": "\u{f48c}",
"truck-container": "\u{f4dc}",
"truck-container-empty": "\u{e2b5}",
"truck-droplet": "\u{e58c}",
"truck-fast": "\u{f48b}",
"shipping-fast": "\u{f48b}",
"truck-field": "\u{e58d}",
"truck-field-un": "\u{e58e}",
"truck-fire": "\u{e65a}",
"truck-flatbed": "\u{e2b6}",
"truck-front": "\u{e2b7}",
"truck-ladder": "\u{e657}",
"truck-medical": "\u{f0f9}",
"ambulance": "\u{f0f9}",
"truck-monster": "\u{f63b}",
"truck-moving": "\u{f4df}",
"truck-pickup": "\u{f63c}",
"truck-plane": "\u{e58f}",
"truck-plow": "\u{f7de}",
"truck-ramp": "\u{f4e0}",
"truck-ramp-box": "\u{f4de}",
"truck-loading": "\u{f4de}",
"truck-ramp-couch": "\u{f4dd}",
"truck-couch": "\u{f4dd}",
"truck-tow": "\u{e2b8}",
"truck-utensils": "\u{e628}",
"trumpet": "\u{f8e3}",
"tty": "\u{f1e4}",
"teletype": "\u{f1e4}",
"tty-answer": "\u{e2b9}",
"teletype-answer": "\u{e2b9}",
"tugrik-sign": "\u{e2ba}",
"tumblr": "\u{f173}",
"turkey": "\u{f725}",
"turkish-lira-sign": "\u{e2bb}",
"try": "\u{e2bb}",
"turkish-lira": "\u{e2bb}",
"turn-down": "\u{f3be}",
"level-down-alt": "\u{f3be}",
"turn-down-left": "\u{e331}",
"turn-down-right": "\u{e455}",
"turn-left": "\u{e636}",
"turn-left-down": "\u{e637}",
"turn-left-up": "\u{e638}",
"turn-right": "\u{e639}",
"turntable": "\u{f8e4}",
"turn-up": "\u{f3bf}",
"level-up-alt": "\u{f3bf}",
"turtle": "\u{f726}",
"tv": "\u{f26c}",
"television": "\u{f26c}",
"tv-alt": "\u{f26c}",
"tv-music": "\u{f8e6}",
"tv-retro": "\u{f401}",
"twitch": "\u{f1e8}",
"twitter": "\u{f099}",
"typewriter": "\u{f8e7}",
"typo3": "\u{f42b}",
"u": "\u{55}",
"uber": "\u{f402}",
"ubuntu": "\u{f7df}",
"ufo": "\u{e047}",
"ufo-beam": "\u{e048}",
"uikit": "\u{f403}",
"umbraco": "\u{f8e8}",
"umbrella": "\u{f0e9}",
"umbrella-beach": "\u{f5ca}",
"umbrella-simple": "\u{e2bc}",
"umbrella-alt": "\u{e2bc}",
"uncharted": "\u{e084}",
"underline": "\u{f0cd}",
"unicorn": "\u{f727}",
"uniform-martial-arts": "\u{e3d1}",
"union": "\u{f6a2}",
"uniregistry": "\u{f404}",
"unity": "\u{e049}",
"universal-access": "\u{f29a}",
"unlock": "\u{f09c}",
"unlock-keyhole": "\u{f13e}",
"unlock-alt": "\u{f13e}",
"unsplash": "\u{e07c}",
"untappd": "\u{f405}",
"up": "\u{f357}",
"arrow-alt-up": "\u{f357}",
"up-down": "\u{f338}",
"arrows-alt-v": "\u{f338}",
"up-down-left-right": "\u{f0b2}",
"arrows-alt": "\u{f0b2}",
"up-from-bracket": "\u{e590}",
"up-from-dotted-line": "\u{e456}",
"up-from-line": "\u{f346}",
"arrow-alt-from-bottom": "\u{f346}",
"up-left": "\u{e2bd}",
"upload": "\u{f093}",
"up-long": "\u{f30c}",
"long-arrow-alt-up": "\u{f30c}",
"up-right": "\u{e2be}",
"up-right-and-down-left-from-center": "\u{f424}",
"expand-alt": "\u{f424}",
"up-right-from-square": "\u{f35d}",
"external-link-alt": "\u{f35d}",
"ups": "\u{f7e0}",
"up-to-bracket": "\u{e66e}",
"up-to-dotted-line": "\u{e457}",
"up-to-line": "\u{f34d}",
"arrow-alt-to-top": "\u{f34d}",
"upwork": "\u{e641}",
"usb": "\u{f287}",
"usb-drive": "\u{f8e9}",
"user": "\u{f007}",
"user-alien": "\u{e04a}",
"user-astronaut": "\u{f4fb}",
"user-beard-bolt": "\u{e689}",
"user-bounty-hunter": "\u{e2bf}",
"user-check": "\u{f4fc}",
"user-chef": "\u{e3d2}",
"user-clock": "\u{f4fd}",
"user-cowboy": "\u{f8ea}",
"user-crown": "\u{f6a4}",
"user-doctor": "\u{f0f0}",
"user-md": "\u{f0f0}",
"user-doctor-hair": "\u{e458}",
"user-doctor-hair-long": "\u{e459}",
"user-doctor-message": "\u{f82e}",
"user-md-chat": "\u{f82e}",
"user-gear": "\u{f4fe}",
"user-cog": "\u{f4fe}",
"user-graduate": "\u{f501}",
"user-group": "\u{f500}",
"user-friends": "\u{f500}",
"user-group-crown": "\u{f6a5}",
"users-crown": "\u{f6a5}",
"user-group-simple": "\u{e603}",
"user-hair": "\u{e45a}",
"user-hair-buns": "\u{e3d3}",
"user-hair-long": "\u{e45b}",
"user-hair-mullet": "\u{e45c}",
"business-front": "\u{e45c}",
"party-back": "\u{e45c}",
"trian-balbot": "\u{e45c}",
"user-headset": "\u{f82d}",
"user-helmet-safety": "\u{f82c}",
"user-construction": "\u{f82c}",
"user-hard-hat": "\u{f82c}",
"user-hoodie": "\u{e68a}",
"user-injured": "\u{f728}",
"user-large": "\u{f406}",
"user-alt": "\u{f406}",
"user-large-slash": "\u{f4fa}",
"user-alt-slash": "\u{f4fa}",
"user-lock": "\u{f502}",
"user-magnifying-glass": "\u{e5c5}",
"user-minus": "\u{f503}",
"user-music": "\u{f8eb}",
"user-ninja": "\u{f504}",
"user-nurse": "\u{f82f}",
"user-nurse-hair": "\u{e45d}",
"user-nurse-hair-long": "\u{e45e}",
"user-pen": "\u{f4ff}",
"user-edit": "\u{f4ff}",
"user-pilot": "\u{e2c0}",
"user-pilot-tie": "\u{e2c1}",
"user-plus": "\u{f234}",
"user-police": "\u{e333}",
"user-police-tie": "\u{e334}",
"user-robot": "\u{e04b}",
"user-robot-xmarks": "\u{e4a7}",
"users": "\u{f0c0}",
"users-between-lines": "\u{e591}",
"user-secret": "\u{f21b}",
"users-gear": "\u{f509}",
"users-cog": "\u{f509}",
"user-shakespeare": "\u{e2c2}",
"user-shield": "\u{f505}",
"user-slash": "\u{f506}",
"users-line": "\u{e592}",
"users-medical": "\u{f830}",
"users-rays": "\u{e593}",
"users-rectangle": "\u{e594}",
"users-slash": "\u{e073}",
"users-viewfinder": "\u{e595}",
"user-tag": "\u{f507}",
"user-tie": "\u{f508}",
"user-tie-hair": "\u{e45f}",
"user-tie-hair-long": "\u{e460}",
"user-unlock": "\u{e058}",
"user-visor": "\u{e04c}",
"user-vneck": "\u{e461}",
"user-vneck-hair": "\u{e462}",
"user-vneck-hair-long": "\u{e463}",
"user-xmark": "\u{f235}",
"user-times": "\u{f235}",
"usps": "\u{f7e1}",
"ussunnah": "\u{f407}",
"utensils": "\u{f2e7}",
"cutlery": "\u{f2e7}",
"utensils-slash": "\u{e464}",
"utility-pole": "\u{e2c3}",
"utility-pole-double": "\u{e2c4}",
"v": "\u{56}",
"vaadin": "\u{f408}",
"vacuum": "\u{e04d}",
"vacuum-robot": "\u{e04e}",
"value-absolute": "\u{f6a6}",
"van-shuttle": "\u{f5b6}",
"shuttle-van": "\u{f5b6}",
"vault": "\u{e2c5}",
"vector-circle": "\u{e2c6}",
"vector-polygon": "\u{e2c7}",
"vector-square": "\u{f5cb}",
"vent-damper": "\u{e465}",
"venus": "\u{f221}",
"venus-double": "\u{f226}",
"venus-mars": "\u{f228}",
"vest": "\u{e085}",
"vest-patches": "\u{e086}",
"viacoin": "\u{f237}",
"viadeo": "\u{f2a9}",
"vial": "\u{f492}",
"vial-circle-check": "\u{e596}",
"vials": "\u{f493}",
"vial-virus": "\u{e597}",
"viber": "\u{f409}",
"video": "\u{f03d}",
"video-camera": "\u{f03d}",
"video-arrow-down-left": "\u{e2c8}",
"video-arrow-up-right": "\u{e2c9}",
"video-plus": "\u{f4e1}",
"video-slash": "\u{f4e2}",
"vihara": "\u{f6a7}",
"vimeo": "\u{f40a}",
"vimeo-v": "\u{f27d}",
"vine": "\u{f1ca}",
"violin": "\u{f8ed}",
"virus": "\u{e074}",
"virus-covid": "\u{e4a8}",
"virus-covid-slash": "\u{e4a9}",
"viruses": "\u{e076}",
"virus-slash": "\u{e075}",
"vk": "\u{f189}",
"vnv": "\u{f40b}",
"voicemail": "\u{f897}",
"volcano": "\u{f770}",
"volleyball": "\u{f45f}",
"volleyball-ball": "\u{f45f}",
"volume": "\u{f6a8}",
"volume-medium": "\u{f6a8}",
"volume-high": "\u{f028}",
"volume-up": "\u{f028}",
"volume-low": "\u{f027}",
"volume-down": "\u{f027}",
"volume-off": "\u{f026}",
"volume-slash": "\u{f2e2}",
"volume-xmark": "\u{f6a9}",
"volume-mute": "\u{f6a9}",
"volume-times": "\u{f6a9}",
"vr-cardboard": "\u{f729}",
"vuejs": "\u{f41f}",
"w": "\u{57}",
"waffle": "\u{e466}",
"wagon-covered": "\u{f8ee}",
"walker": "\u{f831}",
"walkie-talkie": "\u{f8ef}",
"wallet": "\u{f555}",
"wand": "\u{f72a}",
"wand-magic": "\u{f0d0}",
"magic": "\u{f0d0}",
"wand-magic-sparkles": "\u{e2ca}",
"magic-wand-sparkles": "\u{e2ca}",
"wand-sparkles": "\u{f72b}",
"warehouse": "\u{f494}",
"warehouse-full": "\u{f495}",
"warehouse-alt": "\u{f495}",
"washing-machine": "\u{f898}",
"washer": "\u{f898}",
"watch": "\u{f2e1}",
"watch-apple": "\u{e2cb}",
"watch-calculator": "\u{f8f0}",
"watch-fitness": "\u{f63e}",
"watchman-monitoring": "\u{e087}",
"watch-smart": "\u{e2cc}",
"water": "\u{f773}",
"water-arrow-down": "\u{f774}",
"water-lower": "\u{f774}",
"water-arrow-up": "\u{f775}",
"water-rise": "\u{f775}",
"water-ladder": "\u{f5c5}",
"ladder-water": "\u{f5c5}",
"swimming-pool": "\u{f5c5}",
"watermelon-slice": "\u{e337}",
"wave": "\u{e65b}",
"waveform": "\u{f8f1}",
"waveform-lines": "\u{f8f2}",
"waveform-path": "\u{f8f2}",
"wave-pulse": "\u{f5f8}",
"heart-rate": "\u{f5f8}",
"wave-sine": "\u{f899}",
"wave-square": "\u{f83e}",
"waves-sine": "\u{e65d}",
"wave-triangle": "\u{f89a}",
"waze": "\u{f83f}",
"web-awesome": "\u{e682}",
"webflow": "\u{e65c}",
"webhook": "\u{e5d5}",
"weebly": "\u{f5cc}",
"weibo": "\u{f18a}",
"weight-hanging": "\u{f5cd}",
"weight-scale": "\u{f496}",
"weight": "\u{f496}",
"weixin": "\u{f1d7}",
"whale": "\u{f72c}",
"whatsapp": "\u{f232}",
"wheat": "\u{f72d}",
"wheat-awn": "\u{e2cd}",
"wheat-alt": "\u{e2cd}",
"wheat-awn-circle-exclamation": "\u{e598}",
"wheat-awn-slash": "\u{e338}",
"wheat-slash": "\u{e339}",
"wheelchair": "\u{f193}",
"wheelchair-move": "\u{e2ce}",
"wheelchair-alt": "\u{e2ce}",
"whiskey-glass": "\u{f7a0}",
"glass-whiskey": "\u{f7a0}",
"whiskey-glass-ice": "\u{f7a1}",
"glass-whiskey-rocks": "\u{f7a1}",
"whistle": "\u{f460}",
"whmcs": "\u{f40d}",
"wifi": "\u{f1eb}",
"wifi-3": "\u{f1eb}",
"wifi-strong": "\u{f1eb}",
"wifi-exclamation": "\u{e2cf}",
"wifi-fair": "\u{f6ab}",
"wifi-2": "\u{f6ab}",
"wifi-slash": "\u{f6ac}",
"wifi-weak": "\u{f6aa}",
"wifi-1": "\u{f6aa}",
"wikipedia-w": "\u{f266}",
"wind": "\u{f72e}",
"window": "\u{f40e}",
"window-flip": "\u{f40f}",
"window-alt": "\u{f40f}",
"window-frame": "\u{e04f}",
"window-frame-open": "\u{e050}",
"window-maximize": "\u{f2d0}",
"window-minimize": "\u{f2d1}",
"window-restore": "\u{f2d2}",
"windows": "\u{f17a}",
"windsock": "\u{f777}",
"wind-turbine": "\u{f89b}",
"wind-warning": "\u{f776}",
"wind-circle-exclamation": "\u{f776}",
"wine-bottle": "\u{f72f}",
"wine-glass": "\u{f4e3}",
"wine-glass-crack": "\u{f4bb}",
"fragile": "\u{f4bb}",
"wine-glass-empty": "\u{f5ce}",
"wine-glass-alt": "\u{f5ce}",
"wirsindhandwerk": "\u{e2d0}",
"wsh": "\u{e2d0}",
"wix": "\u{f5cf}",
"wizards-of-the-coast": "\u{f730}",
"wodu": "\u{e088}",
"wolf-pack-battalion": "\u{f514}",
"won-sign": "\u{f159}",
"krw": "\u{f159}",
"won": "\u{f159}",
"wordpress": "\u{f19a}",
"wordpress-simple": "\u{f411}",
"worm": "\u{e599}",
"wpbeginner": "\u{f297}",
"wpexplorer": "\u{f2de}",
"wpforms": "\u{f298}",
"wpressr": "\u{f3e4}",
"rendact": "\u{f3e4}",
"wreath": "\u{f7e2}",
"wreath-laurel": "\u{e5d2}",
"wrench": "\u{f0ad}",
"wrench-simple": "\u{e2d1}",
"x": "\u{58}",
"xbox": "\u{f412}",
"xing": "\u{f168}",
"xmark": "\u{f00d}",
"close": "\u{f00d}",
"multiply": "\u{f00d}",
"remove": "\u{f00d}",
"times": "\u{f00d}",
"xmark-large": "\u{e59b}",
"xmarks-lines": "\u{e59a}",
"xmark-to-slot": "\u{f771}",
"times-to-slot": "\u{f771}",
"vote-nay": "\u{f771}",
"x-ray": "\u{f497}",
"x-twitter": "\u{e61b}",
"y": "\u{59}",
"yahoo": "\u{f19e}",
"yammer": "\u{f840}",
"yandex": "\u{f413}",
"yandex-international": "\u{f414}",
"yarn": "\u{f7e3}",
"y-combinator": "\u{f23b}",
"yelp": "\u{f1e9}",
"yen-sign": "\u{f157}",
"cny": "\u{f157}",
"jpy": "\u{f157}",
"rmb": "\u{f157}",
"yen": "\u{f157}",
"yin-yang": "\u{f6ad}",
"yoast": "\u{f2b1}",
"youtube": "\u{f167}",
"z": "\u{5a}",
"zhihu": "\u{f63f}",
)
#let fa-0 = fa-icon.with("\u{30}")
#let fa-00 = fa-icon.with("\u{e467}")
#let fa-1 = fa-icon.with("\u{31}")
#let fa-2 = fa-icon.with("\u{32}")
#let fa-3 = fa-icon.with("\u{33}")
#let fa-360-degrees = fa-icon.with("\u{e2dc}")
#let fa-4 = fa-icon.with("\u{34}")
#let fa-42-group = fa-icon.with("\u{e080}")
#let fa-innosoft = fa-icon.with("\u{e080}")
#let fa-5 = fa-icon.with("\u{35}")
#let fa-500px = fa-icon.with("\u{f26e}")
#let fa-6 = fa-icon.with("\u{36}")
#let fa-7 = fa-icon.with("\u{37}")
#let fa-8 = fa-icon.with("\u{38}")
#let fa-9 = fa-icon.with("\u{39}")
#let fa-a = fa-icon.with("\u{41}")
#let fa-abacus = fa-icon.with("\u{f640}")
#let fa-accent-grave = fa-icon.with("\u{60}")
#let fa-accessible-icon = fa-icon.with("\u{f368}")
#let fa-accusoft = fa-icon.with("\u{f369}")
#let fa-acorn = fa-icon.with("\u{f6ae}")
#let fa-address-book = fa-icon.with("\u{f2b9}")
#let fa-contact-book = fa-icon.with("\u{f2b9}")
#let fa-address-card = fa-icon.with("\u{f2bb}")
#let fa-contact-card = fa-icon.with("\u{f2bb}")
#let fa-vcard = fa-icon.with("\u{f2bb}")
#let fa-adn = fa-icon.with("\u{f170}")
#let fa-adversal = fa-icon.with("\u{f36a}")
#let fa-affiliatetheme = fa-icon.with("\u{f36b}")
#let fa-airbnb = fa-icon.with("\u{f834}")
#let fa-air-conditioner = fa-icon.with("\u{f8f4}")
#let fa-airplay = fa-icon.with("\u{e089}")
#let fa-alarm-clock = fa-icon.with("\u{f34e}")
#let fa-alarm-exclamation = fa-icon.with("\u{f843}")
#let fa-alarm-plus = fa-icon.with("\u{f844}")
#let fa-alarm-snooze = fa-icon.with("\u{f845}")
#let fa-album = fa-icon.with("\u{f89f}")
#let fa-album-circle-plus = fa-icon.with("\u{e48c}")
#let fa-album-circle-user = fa-icon.with("\u{e48d}")
#let fa-album-collection = fa-icon.with("\u{f8a0}")
#let fa-album-collection-circle-plus = fa-icon.with("\u{e48e}")
#let fa-album-collection-circle-user = fa-icon.with("\u{e48f}")
#let fa-algolia = fa-icon.with("\u{f36c}")
#let fa-alicorn = fa-icon.with("\u{f6b0}")
#let fa-alien = fa-icon.with("\u{f8f5}")
#let fa-alien-8bit = fa-icon.with("\u{f8f6}")
#let fa-alien-monster = fa-icon.with("\u{f8f6}")
#let fa-align-center = fa-icon.with("\u{f037}")
#let fa-align-justify = fa-icon.with("\u{f039}")
#let fa-align-left = fa-icon.with("\u{f036}")
#let fa-align-right = fa-icon.with("\u{f038}")
#let fa-align-slash = fa-icon.with("\u{f846}")
#let fa-alipay = fa-icon.with("\u{f642}")
#let fa-alt = fa-icon.with("\u{e08a}")
#let fa-amazon = fa-icon.with("\u{f270}")
#let fa-amazon-pay = fa-icon.with("\u{f42c}")
#let fa-amilia = fa-icon.with("\u{f36d}")
#let fa-ampersand = fa-icon.with("\u{26}")
#let fa-amp-guitar = fa-icon.with("\u{f8a1}")
#let fa-anchor = fa-icon.with("\u{f13d}")
#let fa-anchor-circle-check = fa-icon.with("\u{e4aa}")
#let fa-anchor-circle-exclamation = fa-icon.with("\u{e4ab}")
#let fa-anchor-circle-xmark = fa-icon.with("\u{e4ac}")
#let fa-anchor-lock = fa-icon.with("\u{e4ad}")
#let fa-android = fa-icon.with("\u{f17b}")
#let fa-angel = fa-icon.with("\u{f779}")
#let fa-angellist = fa-icon.with("\u{f209}")
#let fa-angle = fa-icon.with("\u{e08c}")
#let fa-angle-90 = fa-icon.with("\u{e08d}")
#let fa-angle-down = fa-icon.with("\u{f107}")
#let fa-angle-left = fa-icon.with("\u{f104}")
#let fa-angle-right = fa-icon.with("\u{f105}")
#let fa-angles-down = fa-icon.with("\u{f103}")
#let fa-angle-double-down = fa-icon.with("\u{f103}")
#let fa-angles-left = fa-icon.with("\u{f100}")
#let fa-angle-double-left = fa-icon.with("\u{f100}")
#let fa-angles-right = fa-icon.with("\u{f101}")
#let fa-angle-double-right = fa-icon.with("\u{f101}")
#let fa-angles-up = fa-icon.with("\u{f102}")
#let fa-angle-double-up = fa-icon.with("\u{f102}")
#let fa-angles-up-down = fa-icon.with("\u{e60d}")
#let fa-angle-up = fa-icon.with("\u{f106}")
#let fa-angrycreative = fa-icon.with("\u{f36e}")
#let fa-angular = fa-icon.with("\u{f420}")
#let fa-ankh = fa-icon.with("\u{f644}")
#let fa-ant = fa-icon.with("\u{e680}")
#let fa-apartment = fa-icon.with("\u{e468}")
#let fa-aperture = fa-icon.with("\u{e2df}")
#let fa-apostrophe = fa-icon.with("\u{27}")
#let fa-apper = fa-icon.with("\u{f371}")
#let fa-apple = fa-icon.with("\u{f179}")
#let fa-apple-core = fa-icon.with("\u{e08f}")
#let fa-apple-pay = fa-icon.with("\u{f415}")
#let fa-apple-whole = fa-icon.with("\u{f5d1}")
#let fa-apple-alt = fa-icon.with("\u{f5d1}")
#let fa-app-store = fa-icon.with("\u{f36f}")
#let fa-app-store-ios = fa-icon.with("\u{f370}")
#let fa-archway = fa-icon.with("\u{f557}")
#let fa-arrow-down = fa-icon.with("\u{f063}")
#let fa-arrow-down-1-9 = fa-icon.with("\u{f162}")
#let fa-sort-numeric-asc = fa-icon.with("\u{f162}")
#let fa-sort-numeric-down = fa-icon.with("\u{f162}")
#let fa-arrow-down-9-1 = fa-icon.with("\u{f886}")
#let fa-sort-numeric-desc = fa-icon.with("\u{f886}")
#let fa-sort-numeric-down-alt = fa-icon.with("\u{f886}")
#let fa-arrow-down-arrow-up = fa-icon.with("\u{f883}")
#let fa-sort-alt = fa-icon.with("\u{f883}")
#let fa-arrow-down-a-z = fa-icon.with("\u{f15d}")
#let fa-sort-alpha-asc = fa-icon.with("\u{f15d}")
#let fa-sort-alpha-down = fa-icon.with("\u{f15d}")
#let fa-arrow-down-big-small = fa-icon.with("\u{f88c}")
#let fa-sort-size-down = fa-icon.with("\u{f88c}")
#let fa-arrow-down-from-arc = fa-icon.with("\u{e614}")
#let fa-arrow-down-from-bracket = fa-icon.with("\u{e667}")
#let fa-arrow-down-from-dotted-line = fa-icon.with("\u{e090}")
#let fa-arrow-down-from-line = fa-icon.with("\u{f345}")
#let fa-arrow-from-top = fa-icon.with("\u{f345}")
#let fa-arrow-down-left = fa-icon.with("\u{e091}")
#let fa-arrow-down-left-and-arrow-up-right-to-center = fa-icon.with("\u{e092}")
#let fa-arrow-down-long = fa-icon.with("\u{f175}")
#let fa-long-arrow-down = fa-icon.with("\u{f175}")
#let fa-arrow-down-right = fa-icon.with("\u{e093}")
#let fa-arrow-down-short-wide = fa-icon.with("\u{f884}")
#let fa-sort-amount-desc = fa-icon.with("\u{f884}")
#let fa-sort-amount-down-alt = fa-icon.with("\u{f884}")
#let fa-arrow-down-small-big = fa-icon.with("\u{f88d}")
#let fa-sort-size-down-alt = fa-icon.with("\u{f88d}")
#let fa-arrow-down-square-triangle = fa-icon.with("\u{f889}")
#let fa-sort-shapes-down-alt = fa-icon.with("\u{f889}")
#let fa-arrow-down-to-arc = fa-icon.with("\u{e4ae}")
#let fa-arrow-down-to-bracket = fa-icon.with("\u{e094}")
#let fa-arrow-down-to-dotted-line = fa-icon.with("\u{e095}")
#let fa-arrow-down-to-line = fa-icon.with("\u{f33d}")
#let fa-arrow-to-bottom = fa-icon.with("\u{f33d}")
#let fa-arrow-down-to-square = fa-icon.with("\u{e096}")
#let fa-arrow-down-triangle-square = fa-icon.with("\u{f888}")
#let fa-sort-shapes-down = fa-icon.with("\u{f888}")
#let fa-arrow-down-up-across-line = fa-icon.with("\u{e4af}")
#let fa-arrow-down-up-lock = fa-icon.with("\u{e4b0}")
#let fa-arrow-down-wide-short = fa-icon.with("\u{f160}")
#let fa-sort-amount-asc = fa-icon.with("\u{f160}")
#let fa-sort-amount-down = fa-icon.with("\u{f160}")
#let fa-arrow-down-z-a = fa-icon.with("\u{f881}")
#let fa-sort-alpha-desc = fa-icon.with("\u{f881}")
#let fa-sort-alpha-down-alt = fa-icon.with("\u{f881}")
#let fa-arrow-left = fa-icon.with("\u{f060}")
#let fa-arrow-left-from-arc = fa-icon.with("\u{e615}")
#let fa-arrow-left-from-bracket = fa-icon.with("\u{e668}")
#let fa-arrow-left-from-line = fa-icon.with("\u{f344}")
#let fa-arrow-from-right = fa-icon.with("\u{f344}")
#let fa-arrow-left-long = fa-icon.with("\u{f177}")
#let fa-long-arrow-left = fa-icon.with("\u{f177}")
#let fa-arrow-left-long-to-line = fa-icon.with("\u{e3d4}")
#let fa-arrow-left-to-arc = fa-icon.with("\u{e616}")
#let fa-arrow-left-to-bracket = fa-icon.with("\u{e669}")
#let fa-arrow-left-to-line = fa-icon.with("\u{f33e}")
#let fa-arrow-to-left = fa-icon.with("\u{f33e}")
#let fa-arrow-pointer = fa-icon.with("\u{f245}")
#let fa-mouse-pointer = fa-icon.with("\u{f245}")
#let fa-arrow-progress = fa-icon.with("\u{e5df}")
#let fa-arrow-right = fa-icon.with("\u{f061}")
#let fa-arrow-right-arrow-left = fa-icon.with("\u{f0ec}")
#let fa-exchange = fa-icon.with("\u{f0ec}")
#let fa-arrow-right-from-arc = fa-icon.with("\u{e4b1}")
#let fa-arrow-right-from-bracket = fa-icon.with("\u{f08b}")
#let fa-sign-out = fa-icon.with("\u{f08b}")
#let fa-arrow-right-from-line = fa-icon.with("\u{f343}")
#let fa-arrow-from-left = fa-icon.with("\u{f343}")
#let fa-arrow-right-long = fa-icon.with("\u{f178}")
#let fa-long-arrow-right = fa-icon.with("\u{f178}")
#let fa-arrow-right-long-to-line = fa-icon.with("\u{e3d5}")
#let fa-arrow-right-to-arc = fa-icon.with("\u{e4b2}")
#let fa-arrow-right-to-bracket = fa-icon.with("\u{f090}")
#let fa-sign-in = fa-icon.with("\u{f090}")
#let fa-arrow-right-to-city = fa-icon.with("\u{e4b3}")
#let fa-arrow-right-to-line = fa-icon.with("\u{f340}")
#let fa-arrow-to-right = fa-icon.with("\u{f340}")
#let fa-arrow-rotate-left = fa-icon.with("\u{f0e2}")
#let fa-arrow-left-rotate = fa-icon.with("\u{f0e2}")
#let fa-arrow-rotate-back = fa-icon.with("\u{f0e2}")
#let fa-arrow-rotate-backward = fa-icon.with("\u{f0e2}")
#let fa-undo = fa-icon.with("\u{f0e2}")
#let fa-arrow-rotate-right = fa-icon.with("\u{f01e}")
#let fa-arrow-right-rotate = fa-icon.with("\u{f01e}")
#let fa-arrow-rotate-forward = fa-icon.with("\u{f01e}")
#let fa-redo = fa-icon.with("\u{f01e}")
#let fa-arrows-cross = fa-icon.with("\u{e0a2}")
#let fa-arrows-down-to-line = fa-icon.with("\u{e4b8}")
#let fa-arrows-down-to-people = fa-icon.with("\u{e4b9}")
#let fa-arrows-from-dotted-line = fa-icon.with("\u{e0a3}")
#let fa-arrows-from-line = fa-icon.with("\u{e0a4}")
#let fa-arrows-left-right = fa-icon.with("\u{f07e}")
#let fa-arrows-h = fa-icon.with("\u{f07e}")
#let fa-arrows-left-right-to-line = fa-icon.with("\u{e4ba}")
#let fa-arrows-maximize = fa-icon.with("\u{f31d}")
#let fa-expand-arrows = fa-icon.with("\u{f31d}")
#let fa-arrows-minimize = fa-icon.with("\u{e0a5}")
#let fa-compress-arrows = fa-icon.with("\u{e0a5}")
#let fa-arrows-repeat = fa-icon.with("\u{f364}")
#let fa-repeat-alt = fa-icon.with("\u{f364}")
#let fa-arrows-repeat-1 = fa-icon.with("\u{f366}")
#let fa-repeat-1-alt = fa-icon.with("\u{f366}")
#let fa-arrows-retweet = fa-icon.with("\u{f361}")
#let fa-retweet-alt = fa-icon.with("\u{f361}")
#let fa-arrows-rotate = fa-icon.with("\u{f021}")
#let fa-refresh = fa-icon.with("\u{f021}")
#let fa-sync = fa-icon.with("\u{f021}")
#let fa-arrows-rotate-reverse = fa-icon.with("\u{e630}")
#let fa-arrows-spin = fa-icon.with("\u{e4bb}")
#let fa-arrows-split-up-and-left = fa-icon.with("\u{e4bc}")
#let fa-arrows-to-circle = fa-icon.with("\u{e4bd}")
#let fa-arrows-to-dot = fa-icon.with("\u{e4be}")
#let fa-arrows-to-dotted-line = fa-icon.with("\u{e0a6}")
#let fa-arrows-to-eye = fa-icon.with("\u{e4bf}")
#let fa-arrows-to-line = fa-icon.with("\u{e0a7}")
#let fa-arrows-turn-right = fa-icon.with("\u{e4c0}")
#let fa-arrows-turn-to-dots = fa-icon.with("\u{e4c1}")
#let fa-arrows-up-down = fa-icon.with("\u{f07d}")
#let fa-arrows-v = fa-icon.with("\u{f07d}")
#let fa-arrows-up-down-left-right = fa-icon.with("\u{f047}")
#let fa-arrows = fa-icon.with("\u{f047}")
#let fa-arrows-up-to-line = fa-icon.with("\u{e4c2}")
#let fa-arrow-trend-down = fa-icon.with("\u{e097}")
#let fa-arrow-trend-up = fa-icon.with("\u{e098}")
#let fa-arrow-turn-down = fa-icon.with("\u{f149}")
#let fa-level-down = fa-icon.with("\u{f149}")
#let fa-arrow-turn-down-left = fa-icon.with("\u{e2e1}")
#let fa-arrow-turn-down-right = fa-icon.with("\u{e3d6}")
#let fa-arrow-turn-left = fa-icon.with("\u{e632}")
#let fa-arrow-turn-left-down = fa-icon.with("\u{e633}")
#let fa-arrow-turn-left-up = fa-icon.with("\u{e634}")
#let fa-arrow-turn-right = fa-icon.with("\u{e635}")
#let fa-arrow-turn-up = fa-icon.with("\u{f148}")
#let fa-level-up = fa-icon.with("\u{f148}")
#let fa-arrow-up = fa-icon.with("\u{f062}")
#let fa-arrow-up-1-9 = fa-icon.with("\u{f163}")
#let fa-sort-numeric-up = fa-icon.with("\u{f163}")
#let fa-arrow-up-9-1 = fa-icon.with("\u{f887}")
#let fa-sort-numeric-up-alt = fa-icon.with("\u{f887}")
#let fa-arrow-up-arrow-down = fa-icon.with("\u{e099}")
#let fa-sort-up-down = fa-icon.with("\u{e099}")
#let fa-arrow-up-a-z = fa-icon.with("\u{f15e}")
#let fa-sort-alpha-up = fa-icon.with("\u{f15e}")
#let fa-arrow-up-big-small = fa-icon.with("\u{f88e}")
#let fa-sort-size-up = fa-icon.with("\u{f88e}")
#let fa-arrow-up-from-arc = fa-icon.with("\u{e4b4}")
#let fa-arrow-up-from-bracket = fa-icon.with("\u{e09a}")
#let fa-arrow-up-from-dotted-line = fa-icon.with("\u{e09b}")
#let fa-arrow-up-from-ground-water = fa-icon.with("\u{e4b5}")
#let fa-arrow-up-from-line = fa-icon.with("\u{f342}")
#let fa-arrow-from-bottom = fa-icon.with("\u{f342}")
#let fa-arrow-up-from-square = fa-icon.with("\u{e09c}")
#let fa-arrow-up-from-water-pump = fa-icon.with("\u{e4b6}")
#let fa-arrow-up-left = fa-icon.with("\u{e09d}")
#let fa-arrow-up-left-from-circle = fa-icon.with("\u{e09e}")
#let fa-arrow-up-long = fa-icon.with("\u{f176}")
#let fa-long-arrow-up = fa-icon.with("\u{f176}")
#let fa-arrow-up-right = fa-icon.with("\u{e09f}")
#let fa-arrow-up-right-and-arrow-down-left-from-center = fa-icon.with("\u{e0a0}")
#let fa-arrow-up-right-dots = fa-icon.with("\u{e4b7}")
#let fa-arrow-up-right-from-square = fa-icon.with("\u{f08e}")
#let fa-external-link = fa-icon.with("\u{f08e}")
#let fa-arrow-up-short-wide = fa-icon.with("\u{f885}")
#let fa-sort-amount-up-alt = fa-icon.with("\u{f885}")
#let fa-arrow-up-small-big = fa-icon.with("\u{f88f}")
#let fa-sort-size-up-alt = fa-icon.with("\u{f88f}")
#let fa-arrow-up-square-triangle = fa-icon.with("\u{f88b}")
#let fa-sort-shapes-up-alt = fa-icon.with("\u{f88b}")
#let fa-arrow-up-to-arc = fa-icon.with("\u{e617}")
#let fa-arrow-up-to-bracket = fa-icon.with("\u{e66a}")
#let fa-arrow-up-to-dotted-line = fa-icon.with("\u{e0a1}")
#let fa-arrow-up-to-line = fa-icon.with("\u{f341}")
#let fa-arrow-to-top = fa-icon.with("\u{f341}")
#let fa-arrow-up-triangle-square = fa-icon.with("\u{f88a}")
#let fa-sort-shapes-up = fa-icon.with("\u{f88a}")
#let fa-arrow-up-wide-short = fa-icon.with("\u{f161}")
#let fa-sort-amount-up = fa-icon.with("\u{f161}")
#let fa-arrow-up-z-a = fa-icon.with("\u{f882}")
#let fa-sort-alpha-up-alt = fa-icon.with("\u{f882}")
#let fa-artstation = fa-icon.with("\u{f77a}")
#let fa-asterisk = fa-icon.with("\u{2a}")
#let fa-asymmetrik = fa-icon.with("\u{f372}")
#let fa-at = fa-icon.with("\u{40}")
#let fa-atlassian = fa-icon.with("\u{f77b}")
#let fa-atom = fa-icon.with("\u{f5d2}")
#let fa-atom-simple = fa-icon.with("\u{f5d3}")
#let fa-atom-alt = fa-icon.with("\u{f5d3}")
#let fa-audible = fa-icon.with("\u{f373}")
#let fa-audio-description = fa-icon.with("\u{f29e}")
#let fa-audio-description-slash = fa-icon.with("\u{e0a8}")
#let fa-austral-sign = fa-icon.with("\u{e0a9}")
#let fa-autoprefixer = fa-icon.with("\u{f41c}")
#let fa-avianex = fa-icon.with("\u{f374}")
#let fa-aviato = fa-icon.with("\u{f421}")
#let fa-avocado = fa-icon.with("\u{e0aa}")
#let fa-award = fa-icon.with("\u{f559}")
#let fa-award-simple = fa-icon.with("\u{e0ab}")
#let fa-aws = fa-icon.with("\u{f375}")
#let fa-axe = fa-icon.with("\u{f6b2}")
#let fa-axe-battle = fa-icon.with("\u{f6b3}")
#let fa-b = fa-icon.with("\u{42}")
#let fa-baby = fa-icon.with("\u{f77c}")
#let fa-baby-carriage = fa-icon.with("\u{f77d}")
#let fa-carriage-baby = fa-icon.with("\u{f77d}")
#let fa-backpack = fa-icon.with("\u{f5d4}")
#let fa-backward = fa-icon.with("\u{f04a}")
#let fa-backward-fast = fa-icon.with("\u{f049}")
#let fa-fast-backward = fa-icon.with("\u{f049}")
#let fa-backward-step = fa-icon.with("\u{f048}")
#let fa-step-backward = fa-icon.with("\u{f048}")
#let fa-bacon = fa-icon.with("\u{f7e5}")
#let fa-bacteria = fa-icon.with("\u{e059}")
#let fa-bacterium = fa-icon.with("\u{e05a}")
#let fa-badge = fa-icon.with("\u{f335}")
#let fa-badge-check = fa-icon.with("\u{f336}")
#let fa-badge-dollar = fa-icon.with("\u{f645}")
#let fa-badge-percent = fa-icon.with("\u{f646}")
#let fa-badger-honey = fa-icon.with("\u{f6b4}")
#let fa-badge-sheriff = fa-icon.with("\u{f8a2}")
#let fa-badminton = fa-icon.with("\u{e33a}")
#let fa-bagel = fa-icon.with("\u{e3d7}")
#let fa-bag-seedling = fa-icon.with("\u{e5f2}")
#let fa-bag-shopping = fa-icon.with("\u{f290}")
#let fa-shopping-bag = fa-icon.with("\u{f290}")
#let fa-bag-shopping-minus = fa-icon.with("\u{e650}")
#let fa-bag-shopping-plus = fa-icon.with("\u{e651}")
#let fa-bags-shopping = fa-icon.with("\u{f847}")
#let fa-baguette = fa-icon.with("\u{e3d8}")
#let fa-bahai = fa-icon.with("\u{f666}")
#let fa-haykal = fa-icon.with("\u{f666}")
#let fa-baht-sign = fa-icon.with("\u{e0ac}")
#let fa-balloon = fa-icon.with("\u{e2e3}")
#let fa-balloons = fa-icon.with("\u{e2e4}")
#let fa-ballot = fa-icon.with("\u{f732}")
#let fa-ballot-check = fa-icon.with("\u{f733}")
#let fa-ball-pile = fa-icon.with("\u{f77e}")
#let fa-ban = fa-icon.with("\u{f05e}")
#let fa-cancel = fa-icon.with("\u{f05e}")
#let fa-banana = fa-icon.with("\u{e2e5}")
#let fa-ban-bug = fa-icon.with("\u{f7f9}")
#let fa-debug = fa-icon.with("\u{f7f9}")
#let fa-bandage = fa-icon.with("\u{f462}")
#let fa-band-aid = fa-icon.with("\u{f462}")
#let fa-bandcamp = fa-icon.with("\u{f2d5}")
#let fa-bangladeshi-taka-sign = fa-icon.with("\u{e2e6}")
#let fa-banjo = fa-icon.with("\u{f8a3}")
#let fa-ban-parking = fa-icon.with("\u{f616}")
#let fa-parking-circle-slash = fa-icon.with("\u{f616}")
#let fa-ban-smoking = fa-icon.with("\u{f54d}")
#let fa-smoking-ban = fa-icon.with("\u{f54d}")
#let fa-barcode = fa-icon.with("\u{f02a}")
#let fa-barcode-read = fa-icon.with("\u{f464}")
#let fa-barcode-scan = fa-icon.with("\u{f465}")
#let fa-bars = fa-icon.with("\u{f0c9}")
#let fa-navicon = fa-icon.with("\u{f0c9}")
#let fa-bars-filter = fa-icon.with("\u{e0ad}")
#let fa-bars-progress = fa-icon.with("\u{f828}")
#let fa-tasks-alt = fa-icon.with("\u{f828}")
#let fa-bars-sort = fa-icon.with("\u{e0ae}")
#let fa-bars-staggered = fa-icon.with("\u{f550}")
#let fa-reorder = fa-icon.with("\u{f550}")
#let fa-stream = fa-icon.with("\u{f550}")
#let fa-baseball = fa-icon.with("\u{f433}")
#let fa-baseball-ball = fa-icon.with("\u{f433}")
#let fa-baseball-bat-ball = fa-icon.with("\u{f432}")
#let fa-basketball = fa-icon.with("\u{f434}")
#let fa-basketball-ball = fa-icon.with("\u{f434}")
#let fa-basketball-hoop = fa-icon.with("\u{f435}")
#let fa-basket-shopping = fa-icon.with("\u{f291}")
#let fa-shopping-basket = fa-icon.with("\u{f291}")
#let fa-basket-shopping-minus = fa-icon.with("\u{e652}")
#let fa-basket-shopping-plus = fa-icon.with("\u{e653}")
#let fa-basket-shopping-simple = fa-icon.with("\u{e0af}")
#let fa-shopping-basket-alt = fa-icon.with("\u{e0af}")
#let fa-bat = fa-icon.with("\u{f6b5}")
#let fa-bath = fa-icon.with("\u{f2cd}")
#let fa-bathtub = fa-icon.with("\u{f2cd}")
#let fa-battery-bolt = fa-icon.with("\u{f376}")
#let fa-battery-empty = fa-icon.with("\u{f244}")
#let fa-battery-0 = fa-icon.with("\u{f244}")
#let fa-battery-exclamation = fa-icon.with("\u{e0b0}")
#let fa-battery-full = fa-icon.with("\u{f240}")
#let fa-battery = fa-icon.with("\u{f240}")
#let fa-battery-5 = fa-icon.with("\u{f240}")
#let fa-battery-half = fa-icon.with("\u{f242}")
#let fa-battery-3 = fa-icon.with("\u{f242}")
#let fa-battery-low = fa-icon.with("\u{e0b1}")
#let fa-battery-1 = fa-icon.with("\u{e0b1}")
#let fa-battery-quarter = fa-icon.with("\u{f243}")
#let fa-battery-2 = fa-icon.with("\u{f243}")
#let fa-battery-slash = fa-icon.with("\u{f377}")
#let fa-battery-three-quarters = fa-icon.with("\u{f241}")
#let fa-battery-4 = fa-icon.with("\u{f241}")
#let fa-battle-net = fa-icon.with("\u{f835}")
#let fa-bed = fa-icon.with("\u{f236}")
#let fa-bed-bunk = fa-icon.with("\u{f8f8}")
#let fa-bed-empty = fa-icon.with("\u{f8f9}")
#let fa-bed-front = fa-icon.with("\u{f8f7}")
#let fa-bed-alt = fa-icon.with("\u{f8f7}")
#let fa-bed-pulse = fa-icon.with("\u{f487}")
#let fa-procedures = fa-icon.with("\u{f487}")
#let fa-bee = fa-icon.with("\u{e0b2}")
#let fa-beer-mug = fa-icon.with("\u{e0b3}")
#let fa-beer-foam = fa-icon.with("\u{e0b3}")
#let fa-beer-mug-empty = fa-icon.with("\u{f0fc}")
#let fa-beer = fa-icon.with("\u{f0fc}")
#let fa-behance = fa-icon.with("\u{f1b4}")
#let fa-bell = fa-icon.with("\u{f0f3}")
#let fa-bell-concierge = fa-icon.with("\u{f562}")
#let fa-concierge-bell = fa-icon.with("\u{f562}")
#let fa-bell-exclamation = fa-icon.with("\u{f848}")
#let fa-bell-on = fa-icon.with("\u{f8fa}")
#let fa-bell-plus = fa-icon.with("\u{f849}")
#let fa-bell-ring = fa-icon.with("\u{e62c}")
#let fa-bells = fa-icon.with("\u{f77f}")
#let fa-bell-school = fa-icon.with("\u{f5d5}")
#let fa-bell-school-slash = fa-icon.with("\u{f5d6}")
#let fa-bell-slash = fa-icon.with("\u{f1f6}")
#let fa-bench-tree = fa-icon.with("\u{e2e7}")
#let fa-bezier-curve = fa-icon.with("\u{f55b}")
#let fa-bicycle = fa-icon.with("\u{f206}")
#let fa-bilibili = fa-icon.with("\u{e3d9}")
#let fa-billboard = fa-icon.with("\u{e5cd}")
#let fa-bimobject = fa-icon.with("\u{f378}")
#let fa-binary = fa-icon.with("\u{e33b}")
#let fa-binary-circle-check = fa-icon.with("\u{e33c}")
#let fa-binary-lock = fa-icon.with("\u{e33d}")
#let fa-binary-slash = fa-icon.with("\u{e33e}")
#let fa-bin-bottles = fa-icon.with("\u{e5f5}")
#let fa-bin-bottles-recycle = fa-icon.with("\u{e5f6}")
#let fa-binoculars = fa-icon.with("\u{f1e5}")
#let fa-bin-recycle = fa-icon.with("\u{e5f7}")
#let fa-biohazard = fa-icon.with("\u{f780}")
#let fa-bird = fa-icon.with("\u{e469}")
#let fa-bitbucket = fa-icon.with("\u{f171}")
#let fa-bitcoin = fa-icon.with("\u{f379}")
#let fa-bitcoin-sign = fa-icon.with("\u{e0b4}")
#let fa-bity = fa-icon.with("\u{f37a}")
#let fa-blackberry = fa-icon.with("\u{f37b}")
#let fa-black-tie = fa-icon.with("\u{f27e}")
#let fa-blanket = fa-icon.with("\u{f498}")
#let fa-blanket-fire = fa-icon.with("\u{e3da}")
#let fa-blender = fa-icon.with("\u{f517}")
#let fa-blender-phone = fa-icon.with("\u{f6b6}")
#let fa-blinds = fa-icon.with("\u{f8fb}")
#let fa-blinds-open = fa-icon.with("\u{f8fc}")
#let fa-blinds-raised = fa-icon.with("\u{f8fd}")
#let fa-block = fa-icon.with("\u{e46a}")
#let fa-block-brick = fa-icon.with("\u{e3db}")
#let fa-wall-brick = fa-icon.with("\u{e3db}")
#let fa-block-brick-fire = fa-icon.with("\u{e3dc}")
#let fa-firewall = fa-icon.with("\u{e3dc}")
#let fa-block-question = fa-icon.with("\u{e3dd}")
#let fa-block-quote = fa-icon.with("\u{e0b5}")
#let fa-blog = fa-icon.with("\u{f781}")
#let fa-blogger = fa-icon.with("\u{f37c}")
#let fa-blogger-b = fa-icon.with("\u{f37d}")
#let fa-blueberries = fa-icon.with("\u{e2e8}")
#let fa-bluesky = fa-icon.with("\u{e671}")
#let fa-bluetooth = fa-icon.with("\u{f293}")
#let fa-bluetooth-b = fa-icon.with("\u{f294}")
#let fa-bold = fa-icon.with("\u{f032}")
#let fa-bolt = fa-icon.with("\u{f0e7}")
#let fa-zap = fa-icon.with("\u{f0e7}")
#let fa-bolt-auto = fa-icon.with("\u{e0b6}")
#let fa-bolt-lightning = fa-icon.with("\u{e0b7}")
#let fa-bolt-slash = fa-icon.with("\u{e0b8}")
#let fa-bomb = fa-icon.with("\u{f1e2}")
#let fa-bone = fa-icon.with("\u{f5d7}")
#let fa-bone-break = fa-icon.with("\u{f5d8}")
#let fa-bong = fa-icon.with("\u{f55c}")
#let fa-book = fa-icon.with("\u{f02d}")
#let fa-book-arrow-right = fa-icon.with("\u{e0b9}")
#let fa-book-arrow-up = fa-icon.with("\u{e0ba}")
#let fa-book-atlas = fa-icon.with("\u{f558}")
#let fa-atlas = fa-icon.with("\u{f558}")
#let fa-book-bible = fa-icon.with("\u{f647}")
#let fa-bible = fa-icon.with("\u{f647}")
#let fa-book-blank = fa-icon.with("\u{f5d9}")
#let fa-book-alt = fa-icon.with("\u{f5d9}")
#let fa-book-bookmark = fa-icon.with("\u{e0bb}")
#let fa-book-circle-arrow-right = fa-icon.with("\u{e0bc}")
#let fa-book-circle-arrow-up = fa-icon.with("\u{e0bd}")
#let fa-book-copy = fa-icon.with("\u{e0be}")
#let fa-book-font = fa-icon.with("\u{e0bf}")
#let fa-book-heart = fa-icon.with("\u{f499}")
#let fa-book-journal-whills = fa-icon.with("\u{f66a}")
#let fa-journal-whills = fa-icon.with("\u{f66a}")
#let fa-bookmark = fa-icon.with("\u{f02e}")
#let fa-bookmark-slash = fa-icon.with("\u{e0c2}")
#let fa-book-medical = fa-icon.with("\u{f7e6}")
#let fa-book-open = fa-icon.with("\u{f518}")
#let fa-book-open-cover = fa-icon.with("\u{e0c0}")
#let fa-book-open-alt = fa-icon.with("\u{e0c0}")
#let fa-book-open-reader = fa-icon.with("\u{f5da}")
#let fa-book-reader = fa-icon.with("\u{f5da}")
#let fa-book-quran = fa-icon.with("\u{f687}")
#let fa-quran = fa-icon.with("\u{f687}")
#let fa-books = fa-icon.with("\u{f5db}")
#let fa-book-section = fa-icon.with("\u{e0c1}")
#let fa-book-law = fa-icon.with("\u{e0c1}")
#let fa-book-skull = fa-icon.with("\u{f6b7}")
#let fa-book-dead = fa-icon.with("\u{f6b7}")
#let fa-books-medical = fa-icon.with("\u{f7e8}")
#let fa-book-sparkles = fa-icon.with("\u{f6b8}")
#let fa-book-spells = fa-icon.with("\u{f6b8}")
#let fa-book-tanakh = fa-icon.with("\u{f827}")
#let fa-tanakh = fa-icon.with("\u{f827}")
#let fa-book-user = fa-icon.with("\u{f7e7}")
#let fa-boombox = fa-icon.with("\u{f8a5}")
#let fa-boot = fa-icon.with("\u{f782}")
#let fa-booth-curtain = fa-icon.with("\u{f734}")
#let fa-boot-heeled = fa-icon.with("\u{e33f}")
#let fa-bootstrap = fa-icon.with("\u{f836}")
#let fa-border-all = fa-icon.with("\u{f84c}")
#let fa-border-bottom = fa-icon.with("\u{f84d}")
#let fa-border-bottom-right = fa-icon.with("\u{f854}")
#let fa-border-style-alt = fa-icon.with("\u{f854}")
#let fa-border-center-h = fa-icon.with("\u{f89c}")
#let fa-border-center-v = fa-icon.with("\u{f89d}")
#let fa-border-inner = fa-icon.with("\u{f84e}")
#let fa-border-left = fa-icon.with("\u{f84f}")
#let fa-border-none = fa-icon.with("\u{f850}")
#let fa-border-outer = fa-icon.with("\u{f851}")
#let fa-border-right = fa-icon.with("\u{f852}")
#let fa-border-top = fa-icon.with("\u{f855}")
#let fa-border-top-left = fa-icon.with("\u{f853}")
#let fa-border-style = fa-icon.with("\u{f853}")
#let fa-bore-hole = fa-icon.with("\u{e4c3}")
#let fa-bots = fa-icon.with("\u{e340}")
#let fa-bottle-baby = fa-icon.with("\u{e673}")
#let fa-bottle-droplet = fa-icon.with("\u{e4c4}")
#let fa-bottle-water = fa-icon.with("\u{e4c5}")
#let fa-bow-arrow = fa-icon.with("\u{f6b9}")
#let fa-bowl-chopsticks = fa-icon.with("\u{e2e9}")
#let fa-bowl-chopsticks-noodles = fa-icon.with("\u{e2ea}")
#let fa-bowl-food = fa-icon.with("\u{e4c6}")
#let fa-bowl-hot = fa-icon.with("\u{f823}")
#let fa-soup = fa-icon.with("\u{f823}")
#let fa-bowling-ball = fa-icon.with("\u{f436}")
#let fa-bowling-ball-pin = fa-icon.with("\u{e0c3}")
#let fa-bowling-pins = fa-icon.with("\u{f437}")
#let fa-bowl-rice = fa-icon.with("\u{e2eb}")
#let fa-bowl-scoop = fa-icon.with("\u{e3de}")
#let fa-bowl-shaved-ice = fa-icon.with("\u{e3de}")
#let fa-bowl-scoops = fa-icon.with("\u{e3df}")
#let fa-bowl-soft-serve = fa-icon.with("\u{e46b}")
#let fa-bowl-spoon = fa-icon.with("\u{e3e0}")
#let fa-box = fa-icon.with("\u{f466}")
#let fa-box-archive = fa-icon.with("\u{f187}")
#let fa-archive = fa-icon.with("\u{f187}")
#let fa-box-ballot = fa-icon.with("\u{f735}")
#let fa-box-check = fa-icon.with("\u{f467}")
#let fa-box-circle-check = fa-icon.with("\u{e0c4}")
#let fa-box-dollar = fa-icon.with("\u{f4a0}")
#let fa-box-usd = fa-icon.with("\u{f4a0}")
#let fa-boxes-packing = fa-icon.with("\u{e4c7}")
#let fa-boxes-stacked = fa-icon.with("\u{f468}")
#let fa-boxes = fa-icon.with("\u{f468}")
#let fa-boxes-alt = fa-icon.with("\u{f468}")
#let fa-box-heart = fa-icon.with("\u{f49d}")
#let fa-boxing-glove = fa-icon.with("\u{f438}")
#let fa-glove-boxing = fa-icon.with("\u{f438}")
#let fa-box-open = fa-icon.with("\u{f49e}")
#let fa-box-open-full = fa-icon.with("\u{f49c}")
#let fa-box-full = fa-icon.with("\u{f49c}")
#let fa-box-taped = fa-icon.with("\u{f49a}")
#let fa-box-alt = fa-icon.with("\u{f49a}")
#let fa-box-tissue = fa-icon.with("\u{e05b}")
#let fa-bracket-curly = fa-icon.with("\u{7b}")
#let fa-bracket-curly-left = fa-icon.with("\u{7b}")
#let fa-bracket-curly-right = fa-icon.with("\u{7d}")
#let fa-bracket-round = fa-icon.with("\u{28}")
#let fa-parenthesis = fa-icon.with("\u{28}")
#let fa-bracket-round-right = fa-icon.with("\u{29}")
#let fa-brackets-curly = fa-icon.with("\u{f7ea}")
#let fa-bracket-square = fa-icon.with("\u{5b}")
#let fa-bracket = fa-icon.with("\u{5b}")
#let fa-bracket-left = fa-icon.with("\u{5b}")
#let fa-bracket-square-right = fa-icon.with("\u{5d}")
#let fa-brackets-round = fa-icon.with("\u{e0c5}")
#let fa-parentheses = fa-icon.with("\u{e0c5}")
#let fa-brackets-square = fa-icon.with("\u{f7e9}")
#let fa-brackets = fa-icon.with("\u{f7e9}")
#let fa-braille = fa-icon.with("\u{f2a1}")
#let fa-brain = fa-icon.with("\u{f5dc}")
#let fa-brain-arrow-curved-right = fa-icon.with("\u{f677}")
#let fa-mind-share = fa-icon.with("\u{f677}")
#let fa-brain-circuit = fa-icon.with("\u{e0c6}")
#let fa-brake-warning = fa-icon.with("\u{e0c7}")
#let fa-brave = fa-icon.with("\u{e63c}")
#let fa-brave-reverse = fa-icon.with("\u{e63d}")
#let fa-brazilian-real-sign = fa-icon.with("\u{e46c}")
#let fa-bread-loaf = fa-icon.with("\u{f7eb}")
#let fa-bread-slice = fa-icon.with("\u{f7ec}")
#let fa-bread-slice-butter = fa-icon.with("\u{e3e1}")
#let fa-bridge = fa-icon.with("\u{e4c8}")
#let fa-bridge-circle-check = fa-icon.with("\u{e4c9}")
#let fa-bridge-circle-exclamation = fa-icon.with("\u{e4ca}")
#let fa-bridge-circle-xmark = fa-icon.with("\u{e4cb}")
#let fa-bridge-lock = fa-icon.with("\u{e4cc}")
#let fa-bridge-suspension = fa-icon.with("\u{e4cd}")
#let fa-bridge-water = fa-icon.with("\u{e4ce}")
#let fa-briefcase = fa-icon.with("\u{f0b1}")
#let fa-briefcase-arrow-right = fa-icon.with("\u{e2f2}")
#let fa-briefcase-blank = fa-icon.with("\u{e0c8}")
#let fa-briefcase-medical = fa-icon.with("\u{f469}")
#let fa-brightness = fa-icon.with("\u{e0c9}")
#let fa-brightness-low = fa-icon.with("\u{e0ca}")
#let fa-bring-forward = fa-icon.with("\u{f856}")
#let fa-bring-front = fa-icon.with("\u{f857}")
#let fa-broccoli = fa-icon.with("\u{e3e2}")
#let fa-broom = fa-icon.with("\u{f51a}")
#let fa-broom-ball = fa-icon.with("\u{f458}")
#let fa-quidditch = fa-icon.with("\u{f458}")
#let fa-quidditch-broom-ball = fa-icon.with("\u{f458}")
#let fa-broom-wide = fa-icon.with("\u{e5d1}")
#let fa-browser = fa-icon.with("\u{f37e}")
#let fa-browsers = fa-icon.with("\u{e0cb}")
#let fa-brush = fa-icon.with("\u{f55d}")
#let fa-btc = fa-icon.with("\u{f15a}")
#let fa-bucket = fa-icon.with("\u{e4cf}")
#let fa-buffer = fa-icon.with("\u{f837}")
#let fa-bug = fa-icon.with("\u{f188}")
#let fa-bugs = fa-icon.with("\u{e4d0}")
#let fa-bug-slash = fa-icon.with("\u{e490}")
#let fa-building = fa-icon.with("\u{f1ad}")
#let fa-building-circle-arrow-right = fa-icon.with("\u{e4d1}")
#let fa-building-circle-check = fa-icon.with("\u{e4d2}")
#let fa-building-circle-exclamation = fa-icon.with("\u{e4d3}")
#let fa-building-circle-xmark = fa-icon.with("\u{e4d4}")
#let fa-building-columns = fa-icon.with("\u{f19c}")
#let fa-bank = fa-icon.with("\u{f19c}")
#let fa-institution = fa-icon.with("\u{f19c}")
#let fa-museum = fa-icon.with("\u{f19c}")
#let fa-university = fa-icon.with("\u{f19c}")
#let fa-building-flag = fa-icon.with("\u{e4d5}")
#let fa-building-lock = fa-icon.with("\u{e4d6}")
#let fa-building-magnifying-glass = fa-icon.with("\u{e61c}")
#let fa-building-memo = fa-icon.with("\u{e61e}")
#let fa-building-ngo = fa-icon.with("\u{e4d7}")
#let fa-buildings = fa-icon.with("\u{e0cc}")
#let fa-building-shield = fa-icon.with("\u{e4d8}")
#let fa-building-un = fa-icon.with("\u{e4d9}")
#let fa-building-user = fa-icon.with("\u{e4da}")
#let fa-building-wheat = fa-icon.with("\u{e4db}")
#let fa-bulldozer = fa-icon.with("\u{e655}")
#let fa-bullhorn = fa-icon.with("\u{f0a1}")
#let fa-bullseye = fa-icon.with("\u{f140}")
#let fa-bullseye-arrow = fa-icon.with("\u{f648}")
#let fa-bullseye-pointer = fa-icon.with("\u{f649}")
#let fa-buoy = fa-icon.with("\u{e5b5}")
#let fa-buoy-mooring = fa-icon.with("\u{e5b6}")
#let fa-burger = fa-icon.with("\u{f805}")
#let fa-hamburger = fa-icon.with("\u{f805}")
#let fa-burger-cheese = fa-icon.with("\u{f7f1}")
#let fa-cheeseburger = fa-icon.with("\u{f7f1}")
#let fa-burger-fries = fa-icon.with("\u{e0cd}")
#let fa-burger-glass = fa-icon.with("\u{e0ce}")
#let fa-burger-lettuce = fa-icon.with("\u{e3e3}")
#let fa-burger-soda = fa-icon.with("\u{f858}")
#let fa-buromobelexperte = fa-icon.with("\u{f37f}")
#let fa-burrito = fa-icon.with("\u{f7ed}")
#let fa-burst = fa-icon.with("\u{e4dc}")
#let fa-bus = fa-icon.with("\u{f207}")
#let fa-business-time = fa-icon.with("\u{f64a}")
#let fa-briefcase-clock = fa-icon.with("\u{f64a}")
#let fa-bus-school = fa-icon.with("\u{f5dd}")
#let fa-bus-simple = fa-icon.with("\u{f55e}")
#let fa-bus-alt = fa-icon.with("\u{f55e}")
#let fa-butter = fa-icon.with("\u{e3e4}")
#let fa-buy-n-large = fa-icon.with("\u{f8a6}")
#let fa-buysellads = fa-icon.with("\u{f20d}")
#let fa-c = fa-icon.with("\u{43}")
#let fa-cabin = fa-icon.with("\u{e46d}")
#let fa-cabinet-filing = fa-icon.with("\u{f64b}")
#let fa-cable-car = fa-icon.with("\u{f7da}")
#let fa-tram = fa-icon.with("\u{f7da}")
#let fa-cactus = fa-icon.with("\u{f8a7}")
#let fa-caduceus = fa-icon.with("\u{e681}")
#let fa-cake-candles = fa-icon.with("\u{f1fd}")
#let fa-birthday-cake = fa-icon.with("\u{f1fd}")
#let fa-cake = fa-icon.with("\u{f1fd}")
#let fa-cake-slice = fa-icon.with("\u{e3e5}")
#let fa-shortcake = fa-icon.with("\u{e3e5}")
#let fa-calculator = fa-icon.with("\u{f1ec}")
#let fa-calculator-simple = fa-icon.with("\u{f64c}")
#let fa-calculator-alt = fa-icon.with("\u{f64c}")
#let fa-calendar = fa-icon.with("\u{f133}")
#let fa-calendar-arrow-down = fa-icon.with("\u{e0d0}")
#let fa-calendar-download = fa-icon.with("\u{e0d0}")
#let fa-calendar-arrow-up = fa-icon.with("\u{e0d1}")
#let fa-calendar-upload = fa-icon.with("\u{e0d1}")
#let fa-calendar-check = fa-icon.with("\u{f274}")
#let fa-calendar-circle-exclamation = fa-icon.with("\u{e46e}")
#let fa-calendar-circle-minus = fa-icon.with("\u{e46f}")
#let fa-calendar-circle-plus = fa-icon.with("\u{e470}")
#let fa-calendar-circle-user = fa-icon.with("\u{e471}")
#let fa-calendar-clock = fa-icon.with("\u{e0d2}")
#let fa-calendar-time = fa-icon.with("\u{e0d2}")
#let fa-calendar-day = fa-icon.with("\u{f783}")
#let fa-calendar-days = fa-icon.with("\u{f073}")
#let fa-calendar-alt = fa-icon.with("\u{f073}")
#let fa-calendar-exclamation = fa-icon.with("\u{f334}")
#let fa-calendar-heart = fa-icon.with("\u{e0d3}")
#let fa-calendar-image = fa-icon.with("\u{e0d4}")
#let fa-calendar-lines = fa-icon.with("\u{e0d5}")
#let fa-calendar-note = fa-icon.with("\u{e0d5}")
#let fa-calendar-lines-pen = fa-icon.with("\u{e472}")
#let fa-calendar-minus = fa-icon.with("\u{f272}")
#let fa-calendar-pen = fa-icon.with("\u{f333}")
#let fa-calendar-edit = fa-icon.with("\u{f333}")
#let fa-calendar-plus = fa-icon.with("\u{f271}")
#let fa-calendar-range = fa-icon.with("\u{e0d6}")
#let fa-calendars = fa-icon.with("\u{e0d7}")
#let fa-calendar-star = fa-icon.with("\u{f736}")
#let fa-calendar-users = fa-icon.with("\u{e5e2}")
#let fa-calendar-week = fa-icon.with("\u{f784}")
#let fa-calendar-xmark = fa-icon.with("\u{f273}")
#let fa-calendar-times = fa-icon.with("\u{f273}")
#let fa-camcorder = fa-icon.with("\u{f8a8}")
#let fa-video-handheld = fa-icon.with("\u{f8a8}")
#let fa-camera = fa-icon.with("\u{f030}")
#let fa-camera-alt = fa-icon.with("\u{f030}")
#let fa-camera-cctv = fa-icon.with("\u{f8ac}")
#let fa-cctv = fa-icon.with("\u{f8ac}")
#let fa-camera-movie = fa-icon.with("\u{f8a9}")
#let fa-camera-polaroid = fa-icon.with("\u{f8aa}")
#let fa-camera-retro = fa-icon.with("\u{f083}")
#let fa-camera-rotate = fa-icon.with("\u{e0d8}")
#let fa-camera-security = fa-icon.with("\u{f8fe}")
#let fa-camera-home = fa-icon.with("\u{f8fe}")
#let fa-camera-slash = fa-icon.with("\u{e0d9}")
#let fa-camera-viewfinder = fa-icon.with("\u{e0da}")
#let fa-screenshot = fa-icon.with("\u{e0da}")
#let fa-camera-web = fa-icon.with("\u{f832}")
#let fa-webcam = fa-icon.with("\u{f832}")
#let fa-camera-web-slash = fa-icon.with("\u{f833}")
#let fa-webcam-slash = fa-icon.with("\u{f833}")
#let fa-campfire = fa-icon.with("\u{f6ba}")
#let fa-campground = fa-icon.with("\u{f6bb}")
#let fa-canadian-maple-leaf = fa-icon.with("\u{f785}")
#let fa-candle-holder = fa-icon.with("\u{f6bc}")
#let fa-candy = fa-icon.with("\u{e3e7}")
#let fa-candy-bar = fa-icon.with("\u{e3e8}")
#let fa-chocolate-bar = fa-icon.with("\u{e3e8}")
#let fa-candy-cane = fa-icon.with("\u{f786}")
#let fa-candy-corn = fa-icon.with("\u{f6bd}")
#let fa-can-food = fa-icon.with("\u{e3e6}")
#let fa-cannabis = fa-icon.with("\u{f55f}")
#let fa-cannon = fa-icon.with("\u{e642}")
#let fa-capsules = fa-icon.with("\u{f46b}")
#let fa-car = fa-icon.with("\u{f1b9}")
#let fa-automobile = fa-icon.with("\u{f1b9}")
#let fa-caravan = fa-icon.with("\u{f8ff}")
#let fa-caravan-simple = fa-icon.with("\u{e000}")
#let fa-caravan-alt = fa-icon.with("\u{e000}")
#let fa-car-battery = fa-icon.with("\u{f5df}")
#let fa-battery-car = fa-icon.with("\u{f5df}")
#let fa-car-bolt = fa-icon.with("\u{e341}")
#let fa-car-building = fa-icon.with("\u{f859}")
#let fa-car-bump = fa-icon.with("\u{f5e0}")
#let fa-car-burst = fa-icon.with("\u{f5e1}")
#let fa-car-crash = fa-icon.with("\u{f5e1}")
#let fa-car-bus = fa-icon.with("\u{f85a}")
#let fa-car-circle-bolt = fa-icon.with("\u{e342}")
#let fa-card-club = fa-icon.with("\u{e3e9}")
#let fa-card-diamond = fa-icon.with("\u{e3ea}")
#let fa-card-heart = fa-icon.with("\u{e3eb}")
#let fa-cards = fa-icon.with("\u{e3ed}")
#let fa-cards-blank = fa-icon.with("\u{e4df}")
#let fa-card-spade = fa-icon.with("\u{e3ec}")
#let fa-caret-down = fa-icon.with("\u{f0d7}")
#let fa-caret-left = fa-icon.with("\u{f0d9}")
#let fa-caret-right = fa-icon.with("\u{f0da}")
#let fa-caret-up = fa-icon.with("\u{f0d8}")
#let fa-car-garage = fa-icon.with("\u{f5e2}")
#let fa-car-mirrors = fa-icon.with("\u{e343}")
#let fa-car-on = fa-icon.with("\u{e4dd}")
#let fa-car-rear = fa-icon.with("\u{f5de}")
#let fa-car-alt = fa-icon.with("\u{f5de}")
#let fa-carrot = fa-icon.with("\u{f787}")
#let fa-cars = fa-icon.with("\u{f85b}")
#let fa-car-side = fa-icon.with("\u{f5e4}")
#let fa-car-side-bolt = fa-icon.with("\u{e344}")
#let fa-cart-arrow-down = fa-icon.with("\u{f218}")
#let fa-cart-arrow-up = fa-icon.with("\u{e3ee}")
#let fa-cart-circle-arrow-down = fa-icon.with("\u{e3ef}")
#let fa-cart-circle-arrow-up = fa-icon.with("\u{e3f0}")
#let fa-cart-circle-check = fa-icon.with("\u{e3f1}")
#let fa-cart-circle-exclamation = fa-icon.with("\u{e3f2}")
#let fa-cart-circle-plus = fa-icon.with("\u{e3f3}")
#let fa-cart-circle-xmark = fa-icon.with("\u{e3f4}")
#let fa-cart-flatbed = fa-icon.with("\u{f474}")
#let fa-dolly-flatbed = fa-icon.with("\u{f474}")
#let fa-cart-flatbed-boxes = fa-icon.with("\u{f475}")
#let fa-dolly-flatbed-alt = fa-icon.with("\u{f475}")
#let fa-cart-flatbed-empty = fa-icon.with("\u{f476}")
#let fa-dolly-flatbed-empty = fa-icon.with("\u{f476}")
#let fa-cart-flatbed-suitcase = fa-icon.with("\u{f59d}")
#let fa-luggage-cart = fa-icon.with("\u{f59d}")
#let fa-car-tilt = fa-icon.with("\u{f5e5}")
#let fa-cart-minus = fa-icon.with("\u{e0db}")
#let fa-cart-plus = fa-icon.with("\u{f217}")
#let fa-cart-shopping = fa-icon.with("\u{f07a}")
#let fa-shopping-cart = fa-icon.with("\u{f07a}")
#let fa-cart-shopping-fast = fa-icon.with("\u{e0dc}")
#let fa-car-tunnel = fa-icon.with("\u{e4de}")
#let fa-cart-xmark = fa-icon.with("\u{e0dd}")
#let fa-car-wash = fa-icon.with("\u{f5e6}")
#let fa-car-wrench = fa-icon.with("\u{f5e3}")
#let fa-car-mechanic = fa-icon.with("\u{f5e3}")
#let fa-cash-register = fa-icon.with("\u{f788}")
#let fa-cassette-betamax = fa-icon.with("\u{f8a4}")
#let fa-betamax = fa-icon.with("\u{f8a4}")
#let fa-cassette-tape = fa-icon.with("\u{f8ab}")
#let fa-cassette-vhs = fa-icon.with("\u{f8ec}")
#let fa-vhs = fa-icon.with("\u{f8ec}")
#let fa-castle = fa-icon.with("\u{e0de}")
#let fa-cat = fa-icon.with("\u{f6be}")
#let fa-cat-space = fa-icon.with("\u{e001}")
#let fa-cauldron = fa-icon.with("\u{f6bf}")
#let fa-cc-amazon-pay = fa-icon.with("\u{f42d}")
#let fa-cc-amex = fa-icon.with("\u{f1f3}")
#let fa-cc-apple-pay = fa-icon.with("\u{f416}")
#let fa-cc-diners-club = fa-icon.with("\u{f24c}")
#let fa-cc-discover = fa-icon.with("\u{f1f2}")
#let fa-cc-jcb = fa-icon.with("\u{f24b}")
#let fa-cc-mastercard = fa-icon.with("\u{f1f1}")
#let fa-cc-paypal = fa-icon.with("\u{f1f4}")
#let fa-cc-stripe = fa-icon.with("\u{f1f5}")
#let fa-cc-visa = fa-icon.with("\u{f1f0}")
#let fa-cedi-sign = fa-icon.with("\u{e0df}")
#let fa-centercode = fa-icon.with("\u{f380}")
#let fa-centos = fa-icon.with("\u{f789}")
#let fa-cent-sign = fa-icon.with("\u{e3f5}")
#let fa-certificate = fa-icon.with("\u{f0a3}")
#let fa-chair = fa-icon.with("\u{f6c0}")
#let fa-chair-office = fa-icon.with("\u{f6c1}")
#let fa-chalkboard = fa-icon.with("\u{f51b}")
#let fa-blackboard = fa-icon.with("\u{f51b}")
#let fa-chalkboard-user = fa-icon.with("\u{f51c}")
#let fa-chalkboard-teacher = fa-icon.with("\u{f51c}")
#let fa-champagne-glass = fa-icon.with("\u{f79e}")
#let fa-glass-champagne = fa-icon.with("\u{f79e}")
#let fa-champagne-glasses = fa-icon.with("\u{f79f}")
#let fa-glass-cheers = fa-icon.with("\u{f79f}")
#let fa-charging-station = fa-icon.with("\u{f5e7}")
#let fa-chart-area = fa-icon.with("\u{f1fe}")
#let fa-area-chart = fa-icon.with("\u{f1fe}")
#let fa-chart-bar = fa-icon.with("\u{f080}")
#let fa-bar-chart = fa-icon.with("\u{f080}")
#let fa-chart-bullet = fa-icon.with("\u{e0e1}")
#let fa-chart-candlestick = fa-icon.with("\u{e0e2}")
#let fa-chart-column = fa-icon.with("\u{e0e3}")
#let fa-chart-gantt = fa-icon.with("\u{e0e4}")
#let fa-chart-kanban = fa-icon.with("\u{e64f}")
#let fa-chart-line = fa-icon.with("\u{f201}")
#let fa-line-chart = fa-icon.with("\u{f201}")
#let fa-chart-line-down = fa-icon.with("\u{f64d}")
#let fa-chart-line-up = fa-icon.with("\u{e0e5}")
#let fa-chart-line-up-down = fa-icon.with("\u{e5d7}")
#let fa-chart-mixed = fa-icon.with("\u{f643}")
#let fa-analytics = fa-icon.with("\u{f643}")
#let fa-chart-mixed-up-circle-currency = fa-icon.with("\u{e5d8}")
#let fa-chart-mixed-up-circle-dollar = fa-icon.with("\u{e5d9}")
#let fa-chart-network = fa-icon.with("\u{f78a}")
#let fa-chart-pie = fa-icon.with("\u{f200}")
#let fa-pie-chart = fa-icon.with("\u{f200}")
#let fa-chart-pie-simple = fa-icon.with("\u{f64e}")
#let fa-chart-pie-alt = fa-icon.with("\u{f64e}")
#let fa-chart-pie-simple-circle-currency = fa-icon.with("\u{e604}")
#let fa-chart-pie-simple-circle-dollar = fa-icon.with("\u{e605}")
#let fa-chart-pyramid = fa-icon.with("\u{e0e6}")
#let fa-chart-radar = fa-icon.with("\u{e0e7}")
#let fa-chart-scatter = fa-icon.with("\u{f7ee}")
#let fa-chart-scatter-3d = fa-icon.with("\u{e0e8}")
#let fa-chart-scatter-bubble = fa-icon.with("\u{e0e9}")
#let fa-chart-simple = fa-icon.with("\u{e473}")
#let fa-chart-simple-horizontal = fa-icon.with("\u{e474}")
#let fa-chart-tree-map = fa-icon.with("\u{e0ea}")
#let fa-chart-user = fa-icon.with("\u{f6a3}")
#let fa-user-chart = fa-icon.with("\u{f6a3}")
#let fa-chart-waterfall = fa-icon.with("\u{e0eb}")
#let fa-check = fa-icon.with("\u{f00c}")
#let fa-check-double = fa-icon.with("\u{f560}")
#let fa-check-to-slot = fa-icon.with("\u{f772}")
#let fa-vote-yea = fa-icon.with("\u{f772}")
#let fa-cheese = fa-icon.with("\u{f7ef}")
#let fa-cheese-swiss = fa-icon.with("\u{f7f0}")
#let fa-cherries = fa-icon.with("\u{e0ec}")
#let fa-chess = fa-icon.with("\u{f439}")
#let fa-chess-bishop = fa-icon.with("\u{f43a}")
#let fa-chess-bishop-piece = fa-icon.with("\u{f43b}")
#let fa-chess-bishop-alt = fa-icon.with("\u{f43b}")
#let fa-chess-board = fa-icon.with("\u{f43c}")
#let fa-chess-clock = fa-icon.with("\u{f43d}")
#let fa-chess-clock-flip = fa-icon.with("\u{f43e}")
#let fa-chess-clock-alt = fa-icon.with("\u{f43e}")
#let fa-chess-king = fa-icon.with("\u{f43f}")
#let fa-chess-king-piece = fa-icon.with("\u{f440}")
#let fa-chess-king-alt = fa-icon.with("\u{f440}")
#let fa-chess-knight = fa-icon.with("\u{f441}")
#let fa-chess-knight-piece = fa-icon.with("\u{f442}")
#let fa-chess-knight-alt = fa-icon.with("\u{f442}")
#let fa-chess-pawn = fa-icon.with("\u{f443}")
#let fa-chess-pawn-piece = fa-icon.with("\u{f444}")
#let fa-chess-pawn-alt = fa-icon.with("\u{f444}")
#let fa-chess-queen = fa-icon.with("\u{f445}")
#let fa-chess-queen-piece = fa-icon.with("\u{f446}")
#let fa-chess-queen-alt = fa-icon.with("\u{f446}")
#let fa-chess-rook = fa-icon.with("\u{f447}")
#let fa-chess-rook-piece = fa-icon.with("\u{f448}")
#let fa-chess-rook-alt = fa-icon.with("\u{f448}")
#let fa-chestnut = fa-icon.with("\u{e3f6}")
#let fa-chevron-down = fa-icon.with("\u{f078}")
#let fa-chevron-left = fa-icon.with("\u{f053}")
#let fa-chevron-right = fa-icon.with("\u{f054}")
#let fa-chevrons-down = fa-icon.with("\u{f322}")
#let fa-chevron-double-down = fa-icon.with("\u{f322}")
#let fa-chevrons-left = fa-icon.with("\u{f323}")
#let fa-chevron-double-left = fa-icon.with("\u{f323}")
#let fa-chevrons-right = fa-icon.with("\u{f324}")
#let fa-chevron-double-right = fa-icon.with("\u{f324}")
#let fa-chevrons-up = fa-icon.with("\u{f325}")
#let fa-chevron-double-up = fa-icon.with("\u{f325}")
#let fa-chevron-up = fa-icon.with("\u{f077}")
#let fa-chf-sign = fa-icon.with("\u{e602}")
#let fa-child = fa-icon.with("\u{f1ae}")
#let fa-child-combatant = fa-icon.with("\u{e4e0}")
#let fa-child-rifle = fa-icon.with("\u{e4e0}")
#let fa-child-dress = fa-icon.with("\u{e59c}")
#let fa-child-reaching = fa-icon.with("\u{e59d}")
#let fa-children = fa-icon.with("\u{e4e1}")
#let fa-chimney = fa-icon.with("\u{f78b}")
#let fa-chopsticks = fa-icon.with("\u{e3f7}")
#let fa-chrome = fa-icon.with("\u{f268}")
#let fa-chromecast = fa-icon.with("\u{f838}")
#let fa-church = fa-icon.with("\u{f51d}")
#let fa-circle = fa-icon.with("\u{f111}")
#let fa-circle-0 = fa-icon.with("\u{e0ed}")
#let fa-circle-1 = fa-icon.with("\u{e0ee}")
#let fa-circle-2 = fa-icon.with("\u{e0ef}")
#let fa-circle-3 = fa-icon.with("\u{e0f0}")
#let fa-circle-4 = fa-icon.with("\u{e0f1}")
#let fa-circle-5 = fa-icon.with("\u{e0f2}")
#let fa-circle-6 = fa-icon.with("\u{e0f3}")
#let fa-circle-7 = fa-icon.with("\u{e0f4}")
#let fa-circle-8 = fa-icon.with("\u{e0f5}")
#let fa-circle-9 = fa-icon.with("\u{e0f6}")
#let fa-circle-a = fa-icon.with("\u{e0f7}")
#let fa-circle-ampersand = fa-icon.with("\u{e0f8}")
#let fa-circle-arrow-down = fa-icon.with("\u{f0ab}")
#let fa-arrow-circle-down = fa-icon.with("\u{f0ab}")
#let fa-circle-arrow-down-left = fa-icon.with("\u{e0f9}")
#let fa-circle-arrow-down-right = fa-icon.with("\u{e0fa}")
#let fa-circle-arrow-left = fa-icon.with("\u{f0a8}")
#let fa-arrow-circle-left = fa-icon.with("\u{f0a8}")
#let fa-circle-arrow-right = fa-icon.with("\u{f0a9}")
#let fa-arrow-circle-right = fa-icon.with("\u{f0a9}")
#let fa-circle-arrow-up = fa-icon.with("\u{f0aa}")
#let fa-arrow-circle-up = fa-icon.with("\u{f0aa}")
#let fa-circle-arrow-up-left = fa-icon.with("\u{e0fb}")
#let fa-circle-arrow-up-right = fa-icon.with("\u{e0fc}")
#let fa-circle-b = fa-icon.with("\u{e0fd}")
#let fa-circle-bolt = fa-icon.with("\u{e0fe}")
#let fa-circle-bookmark = fa-icon.with("\u{e100}")
#let fa-bookmark-circle = fa-icon.with("\u{e100}")
#let fa-circle-book-open = fa-icon.with("\u{e0ff}")
#let fa-book-circle = fa-icon.with("\u{e0ff}")
#let fa-circle-c = fa-icon.with("\u{e101}")
#let fa-circle-calendar = fa-icon.with("\u{e102}")
#let fa-calendar-circle = fa-icon.with("\u{e102}")
#let fa-circle-camera = fa-icon.with("\u{e103}")
#let fa-camera-circle = fa-icon.with("\u{e103}")
#let fa-circle-caret-down = fa-icon.with("\u{f32d}")
#let fa-caret-circle-down = fa-icon.with("\u{f32d}")
#let fa-circle-caret-left = fa-icon.with("\u{f32e}")
#let fa-caret-circle-left = fa-icon.with("\u{f32e}")
#let fa-circle-caret-right = fa-icon.with("\u{f330}")
#let fa-caret-circle-right = fa-icon.with("\u{f330}")
#let fa-circle-caret-up = fa-icon.with("\u{f331}")
#let fa-caret-circle-up = fa-icon.with("\u{f331}")
#let fa-circle-check = fa-icon.with("\u{f058}")
#let fa-check-circle = fa-icon.with("\u{f058}")
#let fa-circle-chevron-down = fa-icon.with("\u{f13a}")
#let fa-chevron-circle-down = fa-icon.with("\u{f13a}")
#let fa-circle-chevron-left = fa-icon.with("\u{f137}")
#let fa-chevron-circle-left = fa-icon.with("\u{f137}")
#let fa-circle-chevron-right = fa-icon.with("\u{f138}")
#let fa-chevron-circle-right = fa-icon.with("\u{f138}")
#let fa-circle-chevron-up = fa-icon.with("\u{f139}")
#let fa-chevron-circle-up = fa-icon.with("\u{f139}")
#let fa-circle-d = fa-icon.with("\u{e104}")
#let fa-circle-dashed = fa-icon.with("\u{e105}")
#let fa-circle-divide = fa-icon.with("\u{e106}")
#let fa-circle-dollar = fa-icon.with("\u{f2e8}")
#let fa-dollar-circle = fa-icon.with("\u{f2e8}")
#let fa-usd-circle = fa-icon.with("\u{f2e8}")
#let fa-circle-dollar-to-slot = fa-icon.with("\u{f4b9}")
#let fa-donate = fa-icon.with("\u{f4b9}")
#let fa-circle-dot = fa-icon.with("\u{f192}")
#let fa-dot-circle = fa-icon.with("\u{f192}")
#let fa-circle-down = fa-icon.with("\u{f358}")
#let fa-arrow-alt-circle-down = fa-icon.with("\u{f358}")
#let fa-circle-down-left = fa-icon.with("\u{e107}")
#let fa-circle-down-right = fa-icon.with("\u{e108}")
#let fa-circle-e = fa-icon.with("\u{e109}")
#let fa-circle-ellipsis = fa-icon.with("\u{e10a}")
#let fa-circle-ellipsis-vertical = fa-icon.with("\u{e10b}")
#let fa-circle-envelope = fa-icon.with("\u{e10c}")
#let fa-envelope-circle = fa-icon.with("\u{e10c}")
#let fa-circle-euro = fa-icon.with("\u{e5ce}")
#let fa-circle-exclamation = fa-icon.with("\u{f06a}")
#let fa-exclamation-circle = fa-icon.with("\u{f06a}")
#let fa-circle-exclamation-check = fa-icon.with("\u{e10d}")
#let fa-circle-f = fa-icon.with("\u{e10e}")
#let fa-circle-g = fa-icon.with("\u{e10f}")
#let fa-circle-gf = fa-icon.with("\u{e67f}")
#let fa-circle-h = fa-icon.with("\u{f47e}")
#let fa-hospital-symbol = fa-icon.with("\u{f47e}")
#let fa-circle-half = fa-icon.with("\u{e110}")
#let fa-circle-half-stroke = fa-icon.with("\u{f042}")
#let fa-adjust = fa-icon.with("\u{f042}")
#let fa-circle-heart = fa-icon.with("\u{f4c7}")
#let fa-heart-circle = fa-icon.with("\u{f4c7}")
#let fa-circle-i = fa-icon.with("\u{e111}")
#let fa-circle-info = fa-icon.with("\u{f05a}")
#let fa-info-circle = fa-icon.with("\u{f05a}")
#let fa-circle-j = fa-icon.with("\u{e112}")
#let fa-circle-k = fa-icon.with("\u{e113}")
#let fa-circle-l = fa-icon.with("\u{e114}")
#let fa-circle-left = fa-icon.with("\u{f359}")
#let fa-arrow-alt-circle-left = fa-icon.with("\u{f359}")
#let fa-circle-location-arrow = fa-icon.with("\u{f602}")
#let fa-location-circle = fa-icon.with("\u{f602}")
#let fa-circle-m = fa-icon.with("\u{e115}")
#let fa-circle-microphone = fa-icon.with("\u{e116}")
#let fa-microphone-circle = fa-icon.with("\u{e116}")
#let fa-circle-microphone-lines = fa-icon.with("\u{e117}")
#let fa-microphone-circle-alt = fa-icon.with("\u{e117}")
#let fa-circle-minus = fa-icon.with("\u{f056}")
#let fa-minus-circle = fa-icon.with("\u{f056}")
#let fa-circle-n = fa-icon.with("\u{e118}")
#let fa-circle-nodes = fa-icon.with("\u{e4e2}")
#let fa-circle-notch = fa-icon.with("\u{f1ce}")
#let fa-circle-o = fa-icon.with("\u{e119}")
#let fa-circle-p = fa-icon.with("\u{e11a}")
#let fa-circle-parking = fa-icon.with("\u{f615}")
#let fa-parking-circle = fa-icon.with("\u{f615}")
#let fa-circle-pause = fa-icon.with("\u{f28b}")
#let fa-pause-circle = fa-icon.with("\u{f28b}")
#let fa-circle-phone = fa-icon.with("\u{e11b}")
#let fa-phone-circle = fa-icon.with("\u{e11b}")
#let fa-circle-phone-flip = fa-icon.with("\u{e11c}")
#let fa-phone-circle-alt = fa-icon.with("\u{e11c}")
#let fa-circle-phone-hangup = fa-icon.with("\u{e11d}")
#let fa-phone-circle-down = fa-icon.with("\u{e11d}")
#let fa-circle-play = fa-icon.with("\u{f144}")
#let fa-play-circle = fa-icon.with("\u{f144}")
#let fa-circle-plus = fa-icon.with("\u{f055}")
#let fa-plus-circle = fa-icon.with("\u{f055}")
#let fa-circle-q = fa-icon.with("\u{e11e}")
#let fa-circle-quarter = fa-icon.with("\u{e11f}")
#let fa-circle-quarters = fa-icon.with("\u{e3f8}")
#let fa-circle-quarter-stroke = fa-icon.with("\u{e5d3}")
#let fa-circle-question = fa-icon.with("\u{f059}")
#let fa-question-circle = fa-icon.with("\u{f059}")
#let fa-circle-r = fa-icon.with("\u{e120}")
#let fa-circle-radiation = fa-icon.with("\u{f7ba}")
#let fa-radiation-alt = fa-icon.with("\u{f7ba}")
#let fa-circle-right = fa-icon.with("\u{f35a}")
#let fa-arrow-alt-circle-right = fa-icon.with("\u{f35a}")
#let fa-circle-s = fa-icon.with("\u{e121}")
#let fa-circle-small = fa-icon.with("\u{e122}")
#let fa-circle-sort = fa-icon.with("\u{e030}")
#let fa-sort-circle = fa-icon.with("\u{e030}")
#let fa-circle-sort-down = fa-icon.with("\u{e031}")
#let fa-sort-circle-down = fa-icon.with("\u{e031}")
#let fa-circle-sort-up = fa-icon.with("\u{e032}")
#let fa-sort-circle-up = fa-icon.with("\u{e032}")
#let fa-circles-overlap = fa-icon.with("\u{e600}")
#let fa-circle-star = fa-icon.with("\u{e123}")
#let fa-star-circle = fa-icon.with("\u{e123}")
#let fa-circle-sterling = fa-icon.with("\u{e5cf}")
#let fa-circle-stop = fa-icon.with("\u{f28d}")
#let fa-stop-circle = fa-icon.with("\u{f28d}")
#let fa-circle-t = fa-icon.with("\u{e124}")
#let fa-circle-three-quarters = fa-icon.with("\u{e125}")
#let fa-circle-three-quarters-stroke = fa-icon.with("\u{e5d4}")
#let fa-circle-trash = fa-icon.with("\u{e126}")
#let fa-trash-circle = fa-icon.with("\u{e126}")
#let fa-circle-u = fa-icon.with("\u{e127}")
#let fa-circle-up = fa-icon.with("\u{f35b}")
#let fa-arrow-alt-circle-up = fa-icon.with("\u{f35b}")
#let fa-circle-up-left = fa-icon.with("\u{e128}")
#let fa-circle-up-right = fa-icon.with("\u{e129}")
#let fa-circle-user = fa-icon.with("\u{f2bd}")
#let fa-user-circle = fa-icon.with("\u{f2bd}")
#let fa-circle-v = fa-icon.with("\u{e12a}")
#let fa-circle-video = fa-icon.with("\u{e12b}")
#let fa-video-circle = fa-icon.with("\u{e12b}")
#let fa-circle-w = fa-icon.with("\u{e12c}")
#let fa-circle-waveform-lines = fa-icon.with("\u{e12d}")
#let fa-waveform-circle = fa-icon.with("\u{e12d}")
#let fa-circle-wifi = fa-icon.with("\u{e67d}")
#let fa-circle-wifi-circle-wifi = fa-icon.with("\u{e67e}")
#let fa-circle-wifi-group = fa-icon.with("\u{e67e}")
#let fa-circle-x = fa-icon.with("\u{e12e}")
#let fa-circle-xmark = fa-icon.with("\u{f057}")
#let fa-times-circle = fa-icon.with("\u{f057}")
#let fa-xmark-circle = fa-icon.with("\u{f057}")
#let fa-circle-y = fa-icon.with("\u{e12f}")
#let fa-circle-yen = fa-icon.with("\u{e5d0}")
#let fa-circle-z = fa-icon.with("\u{e130}")
#let fa-citrus = fa-icon.with("\u{e2f4}")
#let fa-citrus-slice = fa-icon.with("\u{e2f5}")
#let fa-city = fa-icon.with("\u{f64f}")
#let fa-clapperboard = fa-icon.with("\u{e131}")
#let fa-clapperboard-play = fa-icon.with("\u{e132}")
#let fa-clarinet = fa-icon.with("\u{f8ad}")
#let fa-claw-marks = fa-icon.with("\u{f6c2}")
#let fa-clipboard = fa-icon.with("\u{f328}")
#let fa-clipboard-check = fa-icon.with("\u{f46c}")
#let fa-clipboard-list = fa-icon.with("\u{f46d}")
#let fa-clipboard-list-check = fa-icon.with("\u{f737}")
#let fa-clipboard-medical = fa-icon.with("\u{e133}")
#let fa-clipboard-prescription = fa-icon.with("\u{f5e8}")
#let fa-clipboard-question = fa-icon.with("\u{e4e3}")
#let fa-clipboard-user = fa-icon.with("\u{f7f3}")
#let fa-clock = fa-icon.with("\u{f017}")
#let fa-clock-four = fa-icon.with("\u{f017}")
#let fa-clock-desk = fa-icon.with("\u{e134}")
#let fa-clock-eight = fa-icon.with("\u{e345}")
#let fa-clock-eight-thirty = fa-icon.with("\u{e346}")
#let fa-clock-eleven = fa-icon.with("\u{e347}")
#let fa-clock-eleven-thirty = fa-icon.with("\u{e348}")
#let fa-clock-five = fa-icon.with("\u{e349}")
#let fa-clock-five-thirty = fa-icon.with("\u{e34a}")
#let fa-clock-four-thirty = fa-icon.with("\u{e34b}")
#let fa-clock-nine = fa-icon.with("\u{e34c}")
#let fa-clock-nine-thirty = fa-icon.with("\u{e34d}")
#let fa-clock-one = fa-icon.with("\u{e34e}")
#let fa-clock-one-thirty = fa-icon.with("\u{e34f}")
#let fa-clock-rotate-left = fa-icon.with("\u{f1da}")
#let fa-history = fa-icon.with("\u{f1da}")
#let fa-clock-seven = fa-icon.with("\u{e350}")
#let fa-clock-seven-thirty = fa-icon.with("\u{e351}")
#let fa-clock-six = fa-icon.with("\u{e352}")
#let fa-clock-six-thirty = fa-icon.with("\u{e353}")
#let fa-clock-ten = fa-icon.with("\u{e354}")
#let fa-clock-ten-thirty = fa-icon.with("\u{e355}")
#let fa-clock-three = fa-icon.with("\u{e356}")
#let fa-clock-three-thirty = fa-icon.with("\u{e357}")
#let fa-clock-twelve = fa-icon.with("\u{e358}")
#let fa-clock-twelve-thirty = fa-icon.with("\u{e359}")
#let fa-clock-two = fa-icon.with("\u{e35a}")
#let fa-clock-two-thirty = fa-icon.with("\u{e35b}")
#let fa-clone = fa-icon.with("\u{f24d}")
#let fa-closed-captioning = fa-icon.with("\u{f20a}")
#let fa-closed-captioning-slash = fa-icon.with("\u{e135}")
#let fa-clothes-hanger = fa-icon.with("\u{e136}")
#let fa-cloud = fa-icon.with("\u{f0c2}")
#let fa-cloud-arrow-down = fa-icon.with("\u{f0ed}")
#let fa-cloud-download = fa-icon.with("\u{f0ed}")
#let fa-cloud-download-alt = fa-icon.with("\u{f0ed}")
#let fa-cloud-arrow-up = fa-icon.with("\u{f0ee}")
#let fa-cloud-upload = fa-icon.with("\u{f0ee}")
#let fa-cloud-upload-alt = fa-icon.with("\u{f0ee}")
#let fa-cloud-binary = fa-icon.with("\u{e601}")
#let fa-cloud-bolt = fa-icon.with("\u{f76c}")
#let fa-thunderstorm = fa-icon.with("\u{f76c}")
#let fa-cloud-bolt-moon = fa-icon.with("\u{f76d}")
#let fa-thunderstorm-moon = fa-icon.with("\u{f76d}")
#let fa-cloud-bolt-sun = fa-icon.with("\u{f76e}")
#let fa-thunderstorm-sun = fa-icon.with("\u{f76e}")
#let fa-cloud-check = fa-icon.with("\u{e35c}")
#let fa-cloud-drizzle = fa-icon.with("\u{f738}")
#let fa-cloud-exclamation = fa-icon.with("\u{e491}")
#let fa-cloudflare = fa-icon.with("\u{e07d}")
#let fa-cloud-fog = fa-icon.with("\u{f74e}")
#let fa-fog = fa-icon.with("\u{f74e}")
#let fa-cloud-hail = fa-icon.with("\u{f739}")
#let fa-cloud-hail-mixed = fa-icon.with("\u{f73a}")
#let fa-cloud-meatball = fa-icon.with("\u{f73b}")
#let fa-cloud-minus = fa-icon.with("\u{e35d}")
#let fa-cloud-moon = fa-icon.with("\u{f6c3}")
#let fa-cloud-moon-rain = fa-icon.with("\u{f73c}")
#let fa-cloud-music = fa-icon.with("\u{f8ae}")
#let fa-cloud-plus = fa-icon.with("\u{e35e}")
#let fa-cloud-question = fa-icon.with("\u{e492}")
#let fa-cloud-rain = fa-icon.with("\u{f73d}")
#let fa-cloud-rainbow = fa-icon.with("\u{f73e}")
#let fa-clouds = fa-icon.with("\u{f744}")
#let fa-cloudscale = fa-icon.with("\u{f383}")
#let fa-cloud-showers = fa-icon.with("\u{f73f}")
#let fa-cloud-showers-heavy = fa-icon.with("\u{f740}")
#let fa-cloud-showers-water = fa-icon.with("\u{e4e4}")
#let fa-cloud-slash = fa-icon.with("\u{e137}")
#let fa-cloud-sleet = fa-icon.with("\u{f741}")
#let fa-cloudsmith = fa-icon.with("\u{f384}")
#let fa-clouds-moon = fa-icon.with("\u{f745}")
#let fa-cloud-snow = fa-icon.with("\u{f742}")
#let fa-clouds-sun = fa-icon.with("\u{f746}")
#let fa-cloud-sun = fa-icon.with("\u{f6c4}")
#let fa-cloud-sun-rain = fa-icon.with("\u{f743}")
#let fa-cloudversify = fa-icon.with("\u{f385}")
#let fa-cloud-word = fa-icon.with("\u{e138}")
#let fa-cloud-xmark = fa-icon.with("\u{e35f}")
#let fa-clover = fa-icon.with("\u{e139}")
#let fa-club = fa-icon.with("\u{f327}")
#let fa-cmplid = fa-icon.with("\u{e360}")
#let fa-coconut = fa-icon.with("\u{e2f6}")
#let fa-code = fa-icon.with("\u{f121}")
#let fa-code-branch = fa-icon.with("\u{f126}")
#let fa-code-commit = fa-icon.with("\u{f386}")
#let fa-code-compare = fa-icon.with("\u{e13a}")
#let fa-code-fork = fa-icon.with("\u{e13b}")
#let fa-code-merge = fa-icon.with("\u{f387}")
#let fa-codepen = fa-icon.with("\u{f1cb}")
#let fa-code-pull-request = fa-icon.with("\u{e13c}")
#let fa-code-pull-request-closed = fa-icon.with("\u{e3f9}")
#let fa-code-pull-request-draft = fa-icon.with("\u{e3fa}")
#let fa-code-simple = fa-icon.with("\u{e13d}")
#let fa-codiepie = fa-icon.with("\u{f284}")
#let fa-coffee-bean = fa-icon.with("\u{e13e}")
#let fa-coffee-beans = fa-icon.with("\u{e13f}")
#let fa-coffee-pot = fa-icon.with("\u{e002}")
#let fa-coffin = fa-icon.with("\u{f6c6}")
#let fa-coffin-cross = fa-icon.with("\u{e051}")
#let fa-coin = fa-icon.with("\u{f85c}")
#let fa-coin-blank = fa-icon.with("\u{e3fb}")
#let fa-coin-front = fa-icon.with("\u{e3fc}")
#let fa-coins = fa-icon.with("\u{f51e}")
#let fa-coin-vertical = fa-icon.with("\u{e3fd}")
#let fa-colon = fa-icon.with("\u{3a}")
#let fa-colon-sign = fa-icon.with("\u{e140}")
#let fa-columns-3 = fa-icon.with("\u{e361}")
#let fa-comet = fa-icon.with("\u{e003}")
#let fa-comma = fa-icon.with("\u{2c}")
#let fa-command = fa-icon.with("\u{e142}")
#let fa-comment = fa-icon.with("\u{f075}")
#let fa-comment-arrow-down = fa-icon.with("\u{e143}")
#let fa-comment-arrow-up = fa-icon.with("\u{e144}")
#let fa-comment-arrow-up-right = fa-icon.with("\u{e145}")
#let fa-comment-captions = fa-icon.with("\u{e146}")
#let fa-comment-check = fa-icon.with("\u{f4ac}")
#let fa-comment-code = fa-icon.with("\u{e147}")
#let fa-comment-dollar = fa-icon.with("\u{f651}")
#let fa-comment-dots = fa-icon.with("\u{f4ad}")
#let fa-commenting = fa-icon.with("\u{f4ad}")
#let fa-comment-exclamation = fa-icon.with("\u{f4af}")
#let fa-comment-heart = fa-icon.with("\u{e5c8}")
#let fa-comment-image = fa-icon.with("\u{e148}")
#let fa-comment-lines = fa-icon.with("\u{f4b0}")
#let fa-comment-medical = fa-icon.with("\u{f7f5}")
#let fa-comment-middle = fa-icon.with("\u{e149}")
#let fa-comment-middle-top = fa-icon.with("\u{e14a}")
#let fa-comment-minus = fa-icon.with("\u{f4b1}")
#let fa-comment-music = fa-icon.with("\u{f8b0}")
#let fa-comment-pen = fa-icon.with("\u{f4ae}")
#let fa-comment-edit = fa-icon.with("\u{f4ae}")
#let fa-comment-plus = fa-icon.with("\u{f4b2}")
#let fa-comment-question = fa-icon.with("\u{e14b}")
#let fa-comment-quote = fa-icon.with("\u{e14c}")
#let fa-comments = fa-icon.with("\u{f086}")
#let fa-comments-dollar = fa-icon.with("\u{f653}")
#let fa-comment-slash = fa-icon.with("\u{f4b3}")
#let fa-comment-smile = fa-icon.with("\u{f4b4}")
#let fa-comment-sms = fa-icon.with("\u{f7cd}")
#let fa-sms = fa-icon.with("\u{f7cd}")
#let fa-comments-question = fa-icon.with("\u{e14e}")
#let fa-comments-question-check = fa-icon.with("\u{e14f}")
#let fa-comment-text = fa-icon.with("\u{e14d}")
#let fa-comment-xmark = fa-icon.with("\u{f4b5}")
#let fa-comment-times = fa-icon.with("\u{f4b5}")
#let fa-compact-disc = fa-icon.with("\u{f51f}")
#let fa-compass = fa-icon.with("\u{f14e}")
#let fa-compass-drafting = fa-icon.with("\u{f568}")
#let fa-drafting-compass = fa-icon.with("\u{f568}")
#let fa-compass-slash = fa-icon.with("\u{f5e9}")
#let fa-compress = fa-icon.with("\u{f066}")
#let fa-compress-wide = fa-icon.with("\u{f326}")
#let fa-computer = fa-icon.with("\u{e4e5}")
#let fa-computer-classic = fa-icon.with("\u{f8b1}")
#let fa-computer-mouse = fa-icon.with("\u{f8cc}")
#let fa-mouse = fa-icon.with("\u{f8cc}")
#let fa-computer-mouse-scrollwheel = fa-icon.with("\u{f8cd}")
#let fa-mouse-alt = fa-icon.with("\u{f8cd}")
#let fa-computer-speaker = fa-icon.with("\u{f8b2}")
#let fa-confluence = fa-icon.with("\u{f78d}")
#let fa-connectdevelop = fa-icon.with("\u{f20e}")
#let fa-container-storage = fa-icon.with("\u{f4b7}")
#let fa-contao = fa-icon.with("\u{f26d}")
#let fa-conveyor-belt = fa-icon.with("\u{f46e}")
#let fa-conveyor-belt-arm = fa-icon.with("\u{e5f8}")
#let fa-conveyor-belt-boxes = fa-icon.with("\u{f46f}")
#let fa-conveyor-belt-alt = fa-icon.with("\u{f46f}")
#let fa-conveyor-belt-empty = fa-icon.with("\u{e150}")
#let fa-cookie = fa-icon.with("\u{f563}")
#let fa-cookie-bite = fa-icon.with("\u{f564}")
#let fa-copy = fa-icon.with("\u{f0c5}")
#let fa-copyright = fa-icon.with("\u{f1f9}")
#let fa-corn = fa-icon.with("\u{f6c7}")
#let fa-corner = fa-icon.with("\u{e3fe}")
#let fa-cotton-bureau = fa-icon.with("\u{f89e}")
#let fa-couch = fa-icon.with("\u{f4b8}")
#let fa-court-sport = fa-icon.with("\u{e643}")
#let fa-cow = fa-icon.with("\u{f6c8}")
#let fa-cowbell = fa-icon.with("\u{f8b3}")
#let fa-cowbell-circle-plus = fa-icon.with("\u{f8b4}")
#let fa-cowbell-more = fa-icon.with("\u{f8b4}")
#let fa-cpanel = fa-icon.with("\u{f388}")
#let fa-crab = fa-icon.with("\u{e3ff}")
#let fa-crate-apple = fa-icon.with("\u{f6b1}")
#let fa-apple-crate = fa-icon.with("\u{f6b1}")
#let fa-crate-empty = fa-icon.with("\u{e151}")
#let fa-creative-commons = fa-icon.with("\u{f25e}")
#let fa-creative-commons-by = fa-icon.with("\u{f4e7}")
#let fa-creative-commons-nc = fa-icon.with("\u{f4e8}")
#let fa-creative-commons-nc-eu = fa-icon.with("\u{f4e9}")
#let fa-creative-commons-nc-jp = fa-icon.with("\u{f4ea}")
#let fa-creative-commons-nd = fa-icon.with("\u{f4eb}")
#let fa-creative-commons-pd = fa-icon.with("\u{f4ec}")
#let fa-creative-commons-pd-alt = fa-icon.with("\u{f4ed}")
#let fa-creative-commons-remix = fa-icon.with("\u{f4ee}")
#let fa-creative-commons-sa = fa-icon.with("\u{f4ef}")
#let fa-creative-commons-sampling = fa-icon.with("\u{f4f0}")
#let fa-creative-commons-sampling-plus = fa-icon.with("\u{f4f1}")
#let fa-creative-commons-share = fa-icon.with("\u{f4f2}")
#let fa-creative-commons-zero = fa-icon.with("\u{f4f3}")
#let fa-credit-card = fa-icon.with("\u{f09d}")
#let fa-credit-card-alt = fa-icon.with("\u{f09d}")
#let fa-credit-card-blank = fa-icon.with("\u{f389}")
#let fa-credit-card-front = fa-icon.with("\u{f38a}")
#let fa-cricket-bat-ball = fa-icon.with("\u{f449}")
#let fa-cricket = fa-icon.with("\u{f449}")
#let fa-critical-role = fa-icon.with("\u{f6c9}")
#let fa-croissant = fa-icon.with("\u{f7f6}")
#let fa-crop = fa-icon.with("\u{f125}")
#let fa-crop-simple = fa-icon.with("\u{f565}")
#let fa-crop-alt = fa-icon.with("\u{f565}")
#let fa-cross = fa-icon.with("\u{f654}")
#let fa-crosshairs = fa-icon.with("\u{f05b}")
#let fa-crosshairs-simple = fa-icon.with("\u{e59f}")
#let fa-crow = fa-icon.with("\u{f520}")
#let fa-crown = fa-icon.with("\u{f521}")
#let fa-crutch = fa-icon.with("\u{f7f7}")
#let fa-crutches = fa-icon.with("\u{f7f8}")
#let fa-cruzeiro-sign = fa-icon.with("\u{e152}")
#let fa-crystal-ball = fa-icon.with("\u{e362}")
#let fa-css3 = fa-icon.with("\u{f13c}")
#let fa-css3-alt = fa-icon.with("\u{f38b}")
#let fa-cube = fa-icon.with("\u{f1b2}")
#let fa-cubes = fa-icon.with("\u{f1b3}")
#let fa-cubes-stacked = fa-icon.with("\u{e4e6}")
#let fa-cucumber = fa-icon.with("\u{e401}")
#let fa-cupcake = fa-icon.with("\u{e402}")
#let fa-cup-straw = fa-icon.with("\u{e363}")
#let fa-cup-straw-swoosh = fa-icon.with("\u{e364}")
#let fa-cup-togo = fa-icon.with("\u{f6c5}")
#let fa-coffee-togo = fa-icon.with("\u{f6c5}")
#let fa-curling-stone = fa-icon.with("\u{f44a}")
#let fa-curling = fa-icon.with("\u{f44a}")
#let fa-custard = fa-icon.with("\u{e403}")
#let fa-cuttlefish = fa-icon.with("\u{f38c}")
#let fa-d = fa-icon.with("\u{44}")
#let fa-dagger = fa-icon.with("\u{f6cb}")
#let fa-dailymotion = fa-icon.with("\u{e052}")
#let fa-d-and-d = fa-icon.with("\u{f38d}")
#let fa-d-and-d-beyond = fa-icon.with("\u{f6ca}")
#let fa-dart-lang = fa-icon.with("\u{e693}")
#let fa-dash = fa-icon.with("\u{e404}")
#let fa-minus-large = fa-icon.with("\u{e404}")
#let fa-dashcube = fa-icon.with("\u{f210}")
#let fa-database = fa-icon.with("\u{f1c0}")
#let fa-debian = fa-icon.with("\u{e60b}")
#let fa-deer = fa-icon.with("\u{f78e}")
#let fa-deer-rudolph = fa-icon.with("\u{f78f}")
#let fa-deezer = fa-icon.with("\u{e077}")
#let fa-delete-left = fa-icon.with("\u{f55a}")
#let fa-backspace = fa-icon.with("\u{f55a}")
#let fa-delete-right = fa-icon.with("\u{e154}")
#let fa-delicious = fa-icon.with("\u{f1a5}")
#let fa-democrat = fa-icon.with("\u{f747}")
#let fa-deploydog = fa-icon.with("\u{f38e}")
#let fa-deskpro = fa-icon.with("\u{f38f}")
#let fa-desktop = fa-icon.with("\u{f390}")
#let fa-desktop-alt = fa-icon.with("\u{f390}")
#let fa-desktop-arrow-down = fa-icon.with("\u{e155}")
#let fa-dev = fa-icon.with("\u{f6cc}")
#let fa-deviantart = fa-icon.with("\u{f1bd}")
#let fa-dharmachakra = fa-icon.with("\u{f655}")
#let fa-dhl = fa-icon.with("\u{f790}")
#let fa-diagram-cells = fa-icon.with("\u{e475}")
#let fa-diagram-lean-canvas = fa-icon.with("\u{e156}")
#let fa-diagram-nested = fa-icon.with("\u{e157}")
#let fa-diagram-next = fa-icon.with("\u{e476}")
#let fa-diagram-predecessor = fa-icon.with("\u{e477}")
#let fa-diagram-previous = fa-icon.with("\u{e478}")
#let fa-diagram-project = fa-icon.with("\u{f542}")
#let fa-project-diagram = fa-icon.with("\u{f542}")
#let fa-diagram-sankey = fa-icon.with("\u{e158}")
#let fa-diagram-subtask = fa-icon.with("\u{e479}")
#let fa-diagram-successor = fa-icon.with("\u{e47a}")
#let fa-diagram-venn = fa-icon.with("\u{e15a}")
#let fa-dial = fa-icon.with("\u{e15b}")
#let fa-dial-med-high = fa-icon.with("\u{e15b}")
#let fa-dial-high = fa-icon.with("\u{e15c}")
#let fa-dial-low = fa-icon.with("\u{e15d}")
#let fa-dial-max = fa-icon.with("\u{e15e}")
#let fa-dial-med = fa-icon.with("\u{e15f}")
#let fa-dial-med-low = fa-icon.with("\u{e160}")
#let fa-dial-min = fa-icon.with("\u{e161}")
#let fa-dial-off = fa-icon.with("\u{e162}")
#let fa-diamond = fa-icon.with("\u{f219}")
#let fa-diamond-exclamation = fa-icon.with("\u{e405}")
#let fa-diamond-half = fa-icon.with("\u{e5b7}")
#let fa-diamond-half-stroke = fa-icon.with("\u{e5b8}")
#let fa-diamonds-4 = fa-icon.with("\u{e68b}")
#let fa-diamond-turn-right = fa-icon.with("\u{f5eb}")
#let fa-directions = fa-icon.with("\u{f5eb}")
#let fa-diaspora = fa-icon.with("\u{f791}")
#let fa-dice = fa-icon.with("\u{f522}")
#let fa-dice-d10 = fa-icon.with("\u{f6cd}")
#let fa-dice-d12 = fa-icon.with("\u{f6ce}")
#let fa-dice-d20 = fa-icon.with("\u{f6cf}")
#let fa-dice-d4 = fa-icon.with("\u{f6d0}")
#let fa-dice-d6 = fa-icon.with("\u{f6d1}")
#let fa-dice-d8 = fa-icon.with("\u{f6d2}")
#let fa-dice-five = fa-icon.with("\u{f523}")
#let fa-dice-four = fa-icon.with("\u{f524}")
#let fa-dice-one = fa-icon.with("\u{f525}")
#let fa-dice-six = fa-icon.with("\u{f526}")
#let fa-dice-three = fa-icon.with("\u{f527}")
#let fa-dice-two = fa-icon.with("\u{f528}")
#let fa-digg = fa-icon.with("\u{f1a6}")
#let fa-digital-ocean = fa-icon.with("\u{f391}")
#let fa-dinosaur = fa-icon.with("\u{e5fe}")
#let fa-diploma = fa-icon.with("\u{f5ea}")
#let fa-scroll-ribbon = fa-icon.with("\u{f5ea}")
#let fa-disc-drive = fa-icon.with("\u{f8b5}")
#let fa-discord = fa-icon.with("\u{f392}")
#let fa-discourse = fa-icon.with("\u{f393}")
#let fa-disease = fa-icon.with("\u{f7fa}")
#let fa-display = fa-icon.with("\u{e163}")
#let fa-display-arrow-down = fa-icon.with("\u{e164}")
#let fa-display-chart-up = fa-icon.with("\u{e5e3}")
#let fa-display-chart-up-circle-currency = fa-icon.with("\u{e5e5}")
#let fa-display-chart-up-circle-dollar = fa-icon.with("\u{e5e6}")
#let fa-display-code = fa-icon.with("\u{e165}")
#let fa-desktop-code = fa-icon.with("\u{e165}")
#let fa-display-medical = fa-icon.with("\u{e166}")
#let fa-desktop-medical = fa-icon.with("\u{e166}")
#let fa-display-slash = fa-icon.with("\u{e2fa}")
#let fa-desktop-slash = fa-icon.with("\u{e2fa}")
#let fa-distribute-spacing-horizontal = fa-icon.with("\u{e365}")
#let fa-distribute-spacing-vertical = fa-icon.with("\u{e366}")
#let fa-ditto = fa-icon.with("\u{22}")
#let fa-divide = fa-icon.with("\u{f529}")
#let fa-dna = fa-icon.with("\u{f471}")
#let fa-dochub = fa-icon.with("\u{f394}")
#let fa-docker = fa-icon.with("\u{f395}")
#let fa-dog = fa-icon.with("\u{f6d3}")
#let fa-dog-leashed = fa-icon.with("\u{f6d4}")
#let fa-dollar-sign = fa-icon.with("\u{24}")
#let fa-dollar = fa-icon.with("\u{24}")
#let fa-usd = fa-icon.with("\u{24}")
#let fa-dolly = fa-icon.with("\u{f472}")
#let fa-dolly-box = fa-icon.with("\u{f472}")
#let fa-dolly-empty = fa-icon.with("\u{f473}")
#let fa-dolphin = fa-icon.with("\u{e168}")
#let fa-dong-sign = fa-icon.with("\u{e169}")
#let fa-do-not-enter = fa-icon.with("\u{f5ec}")
#let fa-donut = fa-icon.with("\u{e406}")
#let fa-doughnut = fa-icon.with("\u{e406}")
#let fa-door-closed = fa-icon.with("\u{f52a}")
#let fa-door-open = fa-icon.with("\u{f52b}")
#let fa-dove = fa-icon.with("\u{f4ba}")
#let fa-down = fa-icon.with("\u{f354}")
#let fa-arrow-alt-down = fa-icon.with("\u{f354}")
#let fa-down-from-bracket = fa-icon.with("\u{e66b}")
#let fa-down-from-dotted-line = fa-icon.with("\u{e407}")
#let fa-down-from-line = fa-icon.with("\u{f349}")
#let fa-arrow-alt-from-top = fa-icon.with("\u{f349}")
#let fa-down-left = fa-icon.with("\u{e16a}")
#let fa-down-left-and-up-right-to-center = fa-icon.with("\u{f422}")
#let fa-compress-alt = fa-icon.with("\u{f422}")
#let fa-download = fa-icon.with("\u{f019}")
#let fa-down-long = fa-icon.with("\u{f309}")
#let fa-long-arrow-alt-down = fa-icon.with("\u{f309}")
#let fa-down-right = fa-icon.with("\u{e16b}")
#let fa-down-to-bracket = fa-icon.with("\u{e4e7}")
#let fa-down-to-dotted-line = fa-icon.with("\u{e408}")
#let fa-down-to-line = fa-icon.with("\u{f34a}")
#let fa-arrow-alt-to-bottom = fa-icon.with("\u{f34a}")
#let fa-draft2digital = fa-icon.with("\u{f396}")
#let fa-dragon = fa-icon.with("\u{f6d5}")
#let fa-draw-circle = fa-icon.with("\u{f5ed}")
#let fa-draw-polygon = fa-icon.with("\u{f5ee}")
#let fa-draw-square = fa-icon.with("\u{f5ef}")
#let fa-dreidel = fa-icon.with("\u{f792}")
#let fa-dribbble = fa-icon.with("\u{f17d}")
#let fa-drone = fa-icon.with("\u{f85f}")
#let fa-drone-front = fa-icon.with("\u{f860}")
#let fa-drone-alt = fa-icon.with("\u{f860}")
#let fa-dropbox = fa-icon.with("\u{f16b}")
#let fa-droplet = fa-icon.with("\u{f043}")
#let fa-tint = fa-icon.with("\u{f043}")
#let fa-droplet-degree = fa-icon.with("\u{f748}")
#let fa-dewpoint = fa-icon.with("\u{f748}")
#let fa-droplet-percent = fa-icon.with("\u{f750}")
#let fa-humidity = fa-icon.with("\u{f750}")
#let fa-droplet-slash = fa-icon.with("\u{f5c7}")
#let fa-tint-slash = fa-icon.with("\u{f5c7}")
#let fa-drum = fa-icon.with("\u{f569}")
#let fa-drum-steelpan = fa-icon.with("\u{f56a}")
#let fa-drumstick = fa-icon.with("\u{f6d6}")
#let fa-drumstick-bite = fa-icon.with("\u{f6d7}")
#let fa-drupal = fa-icon.with("\u{f1a9}")
#let fa-dryer = fa-icon.with("\u{f861}")
#let fa-dryer-heat = fa-icon.with("\u{f862}")
#let fa-dryer-alt = fa-icon.with("\u{f862}")
#let fa-duck = fa-icon.with("\u{f6d8}")
#let fa-dumbbell = fa-icon.with("\u{f44b}")
#let fa-dumpster = fa-icon.with("\u{f793}")
#let fa-dumpster-fire = fa-icon.with("\u{f794}")
#let fa-dungeon = fa-icon.with("\u{f6d9}")
#let fa-dyalog = fa-icon.with("\u{f399}")
#let fa-e = fa-icon.with("\u{45}")
#let fa-ear = fa-icon.with("\u{f5f0}")
#let fa-ear-deaf = fa-icon.with("\u{f2a4}")
#let fa-deaf = fa-icon.with("\u{f2a4}")
#let fa-deafness = fa-icon.with("\u{f2a4}")
#let fa-hard-of-hearing = fa-icon.with("\u{f2a4}")
#let fa-ear-listen = fa-icon.with("\u{f2a2}")
#let fa-assistive-listening-systems = fa-icon.with("\u{f2a2}")
#let fa-earlybirds = fa-icon.with("\u{f39a}")
#let fa-ear-muffs = fa-icon.with("\u{f795}")
#let fa-earth-africa = fa-icon.with("\u{f57c}")
#let fa-globe-africa = fa-icon.with("\u{f57c}")
#let fa-earth-americas = fa-icon.with("\u{f57d}")
#let fa-earth = fa-icon.with("\u{f57d}")
#let fa-earth-america = fa-icon.with("\u{f57d}")
#let fa-globe-americas = fa-icon.with("\u{f57d}")
#let fa-earth-asia = fa-icon.with("\u{f57e}")
#let fa-globe-asia = fa-icon.with("\u{f57e}")
#let fa-earth-europe = fa-icon.with("\u{f7a2}")
#let fa-globe-europe = fa-icon.with("\u{f7a2}")
#let fa-earth-oceania = fa-icon.with("\u{e47b}")
#let fa-globe-oceania = fa-icon.with("\u{e47b}")
#let fa-ebay = fa-icon.with("\u{f4f4}")
#let fa-eclipse = fa-icon.with("\u{f749}")
#let fa-edge = fa-icon.with("\u{f282}")
#let fa-edge-legacy = fa-icon.with("\u{e078}")
#let fa-egg = fa-icon.with("\u{f7fb}")
#let fa-egg-fried = fa-icon.with("\u{f7fc}")
#let fa-eggplant = fa-icon.with("\u{e16c}")
#let fa-eject = fa-icon.with("\u{f052}")
#let fa-elementor = fa-icon.with("\u{f430}")
#let fa-elephant = fa-icon.with("\u{f6da}")
#let fa-elevator = fa-icon.with("\u{e16d}")
#let fa-ellipsis = fa-icon.with("\u{f141}")
#let fa-ellipsis-h = fa-icon.with("\u{f141}")
#let fa-ellipsis-stroke = fa-icon.with("\u{f39b}")
#let fa-ellipsis-h-alt = fa-icon.with("\u{f39b}")
#let fa-ellipsis-stroke-vertical = fa-icon.with("\u{f39c}")
#let fa-ellipsis-v-alt = fa-icon.with("\u{f39c}")
#let fa-ellipsis-vertical = fa-icon.with("\u{f142}")
#let fa-ellipsis-v = fa-icon.with("\u{f142}")
#let fa-ello = fa-icon.with("\u{f5f1}")
#let fa-ember = fa-icon.with("\u{f423}")
#let fa-empire = fa-icon.with("\u{f1d1}")
#let fa-empty-set = fa-icon.with("\u{f656}")
#let fa-engine = fa-icon.with("\u{e16e}")
#let fa-engine-warning = fa-icon.with("\u{f5f2}")
#let fa-engine-exclamation = fa-icon.with("\u{f5f2}")
#let fa-envelope = fa-icon.with("\u{f0e0}")
#let fa-envelope-circle-check = fa-icon.with("\u{e4e8}")
#let fa-envelope-dot = fa-icon.with("\u{e16f}")
#let fa-envelope-badge = fa-icon.with("\u{e16f}")
#let fa-envelope-open = fa-icon.with("\u{f2b6}")
#let fa-envelope-open-dollar = fa-icon.with("\u{f657}")
#let fa-envelope-open-text = fa-icon.with("\u{f658}")
#let fa-envelopes = fa-icon.with("\u{e170}")
#let fa-envelopes-bulk = fa-icon.with("\u{f674}")
#let fa-mail-bulk = fa-icon.with("\u{f674}")
#let fa-envira = fa-icon.with("\u{f299}")
#let fa-equals = fa-icon.with("\u{3d}")
#let fa-eraser = fa-icon.with("\u{f12d}")
#let fa-erlang = fa-icon.with("\u{f39d}")
#let fa-escalator = fa-icon.with("\u{e171}")
#let fa-ethereum = fa-icon.with("\u{f42e}")
#let fa-ethernet = fa-icon.with("\u{f796}")
#let fa-etsy = fa-icon.with("\u{f2d7}")
#let fa-euro-sign = fa-icon.with("\u{f153}")
#let fa-eur = fa-icon.with("\u{f153}")
#let fa-euro = fa-icon.with("\u{f153}")
#let fa-evernote = fa-icon.with("\u{f839}")
#let fa-excavator = fa-icon.with("\u{e656}")
#let fa-exclamation = fa-icon.with("\u{21}")
#let fa-expand = fa-icon.with("\u{f065}")
#let fa-expand-wide = fa-icon.with("\u{f320}")
#let fa-expeditedssl = fa-icon.with("\u{f23e}")
#let fa-explosion = fa-icon.with("\u{e4e9}")
#let fa-eye = fa-icon.with("\u{f06e}")
#let fa-eye-dropper = fa-icon.with("\u{f1fb}")
#let fa-eye-dropper-empty = fa-icon.with("\u{f1fb}")
#let fa-eyedropper = fa-icon.with("\u{f1fb}")
#let fa-eye-dropper-full = fa-icon.with("\u{e172}")
#let fa-eye-dropper-half = fa-icon.with("\u{e173}")
#let fa-eye-evil = fa-icon.with("\u{f6db}")
#let fa-eye-low-vision = fa-icon.with("\u{f2a8}")
#let fa-low-vision = fa-icon.with("\u{f2a8}")
#let fa-eyes = fa-icon.with("\u{e367}")
#let fa-eye-slash = fa-icon.with("\u{f070}")
#let fa-f = fa-icon.with("\u{46}")
#let fa-face-angry = fa-icon.with("\u{f556}")
#let fa-angry = fa-icon.with("\u{f556}")
#let fa-face-angry-horns = fa-icon.with("\u{e368}")
#let fa-face-anguished = fa-icon.with("\u{e369}")
#let fa-face-anxious-sweat = fa-icon.with("\u{e36a}")
#let fa-face-astonished = fa-icon.with("\u{e36b}")
#let fa-face-awesome = fa-icon.with("\u{e409}")
#let fa-gave-dandy = fa-icon.with("\u{e409}")
#let fa-face-beam-hand-over-mouth = fa-icon.with("\u{e47c}")
#let fa-facebook = fa-icon.with("\u{f09a}")
#let fa-facebook-f = fa-icon.with("\u{f39e}")
#let fa-facebook-messenger = fa-icon.with("\u{f39f}")
#let fa-face-clouds = fa-icon.with("\u{e47d}")
#let fa-face-confounded = fa-icon.with("\u{e36c}")
#let fa-face-confused = fa-icon.with("\u{e36d}")
#let fa-face-cowboy-hat = fa-icon.with("\u{e36e}")
#let fa-face-diagonal-mouth = fa-icon.with("\u{e47e}")
#let fa-face-disappointed = fa-icon.with("\u{e36f}")
#let fa-face-disguise = fa-icon.with("\u{e370}")
#let fa-face-dizzy = fa-icon.with("\u{f567}")
#let fa-dizzy = fa-icon.with("\u{f567}")
#let fa-face-dotted = fa-icon.with("\u{e47f}")
#let fa-face-downcast-sweat = fa-icon.with("\u{e371}")
#let fa-face-drooling = fa-icon.with("\u{e372}")
#let fa-face-exhaling = fa-icon.with("\u{e480}")
#let fa-face-explode = fa-icon.with("\u{e2fe}")
#let fa-exploding-head = fa-icon.with("\u{e2fe}")
#let fa-face-expressionless = fa-icon.with("\u{e373}")
#let fa-face-eyes-xmarks = fa-icon.with("\u{e374}")
#let fa-face-fearful = fa-icon.with("\u{e375}")
#let fa-face-flushed = fa-icon.with("\u{f579}")
#let fa-flushed = fa-icon.with("\u{f579}")
#let fa-face-frown = fa-icon.with("\u{f119}")
#let fa-frown = fa-icon.with("\u{f119}")
#let fa-face-frown-open = fa-icon.with("\u{f57a}")
#let fa-frown-open = fa-icon.with("\u{f57a}")
#let fa-face-frown-slight = fa-icon.with("\u{e376}")
#let fa-face-glasses = fa-icon.with("\u{e377}")
#let fa-face-grimace = fa-icon.with("\u{f57f}")
#let fa-grimace = fa-icon.with("\u{f57f}")
#let fa-face-grin = fa-icon.with("\u{f580}")
#let fa-grin = fa-icon.with("\u{f580}")
#let fa-face-grin-beam = fa-icon.with("\u{f582}")
#let fa-grin-beam = fa-icon.with("\u{f582}")
#let fa-face-grin-beam-sweat = fa-icon.with("\u{f583}")
#let fa-grin-beam-sweat = fa-icon.with("\u{f583}")
#let fa-face-grin-hearts = fa-icon.with("\u{f584}")
#let fa-grin-hearts = fa-icon.with("\u{f584}")
#let fa-face-grin-squint = fa-icon.with("\u{f585}")
#let fa-grin-squint = fa-icon.with("\u{f585}")
#let fa-face-grin-squint-tears = fa-icon.with("\u{f586}")
#let fa-grin-squint-tears = fa-icon.with("\u{f586}")
#let fa-face-grin-stars = fa-icon.with("\u{f587}")
#let fa-grin-stars = fa-icon.with("\u{f587}")
#let fa-face-grin-tears = fa-icon.with("\u{f588}")
#let fa-grin-tears = fa-icon.with("\u{f588}")
#let fa-face-grin-tongue = fa-icon.with("\u{f589}")
#let fa-grin-tongue = fa-icon.with("\u{f589}")
#let fa-face-grin-tongue-squint = fa-icon.with("\u{f58a}")
#let fa-grin-tongue-squint = fa-icon.with("\u{f58a}")
#let fa-face-grin-tongue-wink = fa-icon.with("\u{f58b}")
#let fa-grin-tongue-wink = fa-icon.with("\u{f58b}")
#let fa-face-grin-wide = fa-icon.with("\u{f581}")
#let fa-grin-alt = fa-icon.with("\u{f581}")
#let fa-face-grin-wink = fa-icon.with("\u{f58c}")
#let fa-grin-wink = fa-icon.with("\u{f58c}")
#let fa-face-hand-over-mouth = fa-icon.with("\u{e378}")
#let fa-face-hand-peeking = fa-icon.with("\u{e481}")
#let fa-face-hand-yawn = fa-icon.with("\u{e379}")
#let fa-face-head-bandage = fa-icon.with("\u{e37a}")
#let fa-face-holding-back-tears = fa-icon.with("\u{e482}")
#let fa-face-hushed = fa-icon.with("\u{e37b}")
#let fa-face-icicles = fa-icon.with("\u{e37c}")
#let fa-face-kiss = fa-icon.with("\u{f596}")
#let fa-kiss = fa-icon.with("\u{f596}")
#let fa-face-kiss-beam = fa-icon.with("\u{f597}")
#let fa-kiss-beam = fa-icon.with("\u{f597}")
#let fa-face-kiss-closed-eyes = fa-icon.with("\u{e37d}")
#let fa-face-kiss-wink-heart = fa-icon.with("\u{f598}")
#let fa-kiss-wink-heart = fa-icon.with("\u{f598}")
#let fa-face-laugh = fa-icon.with("\u{f599}")
#let fa-laugh = fa-icon.with("\u{f599}")
#let fa-face-laugh-beam = fa-icon.with("\u{f59a}")
#let fa-laugh-beam = fa-icon.with("\u{f59a}")
#let fa-face-laugh-squint = fa-icon.with("\u{f59b}")
#let fa-laugh-squint = fa-icon.with("\u{f59b}")
#let fa-face-laugh-wink = fa-icon.with("\u{f59c}")
#let fa-laugh-wink = fa-icon.with("\u{f59c}")
#let fa-face-lying = fa-icon.with("\u{e37e}")
#let fa-face-mask = fa-icon.with("\u{e37f}")
#let fa-face-meh = fa-icon.with("\u{f11a}")
#let fa-meh = fa-icon.with("\u{f11a}")
#let fa-face-meh-blank = fa-icon.with("\u{f5a4}")
#let fa-meh-blank = fa-icon.with("\u{f5a4}")
#let fa-face-melting = fa-icon.with("\u{e483}")
#let fa-face-monocle = fa-icon.with("\u{e380}")
#let fa-face-nauseated = fa-icon.with("\u{e381}")
#let fa-face-nose-steam = fa-icon.with("\u{e382}")
#let fa-face-party = fa-icon.with("\u{e383}")
#let fa-face-pensive = fa-icon.with("\u{e384}")
#let fa-face-persevering = fa-icon.with("\u{e385}")
#let fa-face-pleading = fa-icon.with("\u{e386}")
#let fa-face-pouting = fa-icon.with("\u{e387}")
#let fa-face-raised-eyebrow = fa-icon.with("\u{e388}")
#let fa-face-relieved = fa-icon.with("\u{e389}")
#let fa-face-rolling-eyes = fa-icon.with("\u{f5a5}")
#let fa-meh-rolling-eyes = fa-icon.with("\u{f5a5}")
#let fa-face-sad-cry = fa-icon.with("\u{f5b3}")
#let fa-sad-cry = fa-icon.with("\u{f5b3}")
#let fa-face-sad-sweat = fa-icon.with("\u{e38a}")
#let fa-face-sad-tear = fa-icon.with("\u{f5b4}")
#let fa-sad-tear = fa-icon.with("\u{f5b4}")
#let fa-face-saluting = fa-icon.with("\u{e484}")
#let fa-face-scream = fa-icon.with("\u{e38b}")
#let fa-face-shush = fa-icon.with("\u{e38c}")
#let fa-face-sleeping = fa-icon.with("\u{e38d}")
#let fa-face-sleepy = fa-icon.with("\u{e38e}")
#let fa-face-smile = fa-icon.with("\u{f118}")
#let fa-smile = fa-icon.with("\u{f118}")
#let fa-face-smile-beam = fa-icon.with("\u{f5b8}")
#let fa-smile-beam = fa-icon.with("\u{f5b8}")
#let fa-face-smile-halo = fa-icon.with("\u{e38f}")
#let fa-face-smile-hearts = fa-icon.with("\u{e390}")
#let fa-face-smile-horns = fa-icon.with("\u{e391}")
#let fa-face-smile-plus = fa-icon.with("\u{f5b9}")
#let fa-smile-plus = fa-icon.with("\u{f5b9}")
#let fa-face-smile-relaxed = fa-icon.with("\u{e392}")
#let fa-face-smile-tear = fa-icon.with("\u{e393}")
#let fa-face-smile-tongue = fa-icon.with("\u{e394}")
#let fa-face-smile-upside-down = fa-icon.with("\u{e395}")
#let fa-face-smile-wink = fa-icon.with("\u{f4da}")
#let fa-smile-wink = fa-icon.with("\u{f4da}")
#let fa-face-smiling-hands = fa-icon.with("\u{e396}")
#let fa-face-smirking = fa-icon.with("\u{e397}")
#let fa-face-spiral-eyes = fa-icon.with("\u{e485}")
#let fa-face-sunglasses = fa-icon.with("\u{e398}")
#let fa-face-surprise = fa-icon.with("\u{f5c2}")
#let fa-surprise = fa-icon.with("\u{f5c2}")
#let fa-face-swear = fa-icon.with("\u{e399}")
#let fa-face-thermometer = fa-icon.with("\u{e39a}")
#let fa-face-thinking = fa-icon.with("\u{e39b}")
#let fa-face-tired = fa-icon.with("\u{f5c8}")
#let fa-tired = fa-icon.with("\u{f5c8}")
#let fa-face-tissue = fa-icon.with("\u{e39c}")
#let fa-face-tongue-money = fa-icon.with("\u{e39d}")
#let fa-face-tongue-sweat = fa-icon.with("\u{e39e}")
#let fa-face-unamused = fa-icon.with("\u{e39f}")
#let fa-face-viewfinder = fa-icon.with("\u{e2ff}")
#let fa-face-vomit = fa-icon.with("\u{e3a0}")
#let fa-face-weary = fa-icon.with("\u{e3a1}")
#let fa-face-woozy = fa-icon.with("\u{e3a2}")
#let fa-face-worried = fa-icon.with("\u{e3a3}")
#let fa-face-zany = fa-icon.with("\u{e3a4}")
#let fa-face-zipper = fa-icon.with("\u{e3a5}")
#let fa-falafel = fa-icon.with("\u{e40a}")
#let fa-family = fa-icon.with("\u{e300}")
#let fa-family-dress = fa-icon.with("\u{e301}")
#let fa-family-pants = fa-icon.with("\u{e302}")
#let fa-fan = fa-icon.with("\u{f863}")
#let fa-fan-table = fa-icon.with("\u{e004}")
#let fa-fantasy-flight-games = fa-icon.with("\u{f6dc}")
#let fa-farm = fa-icon.with("\u{f864}")
#let fa-barn-silo = fa-icon.with("\u{f864}")
#let fa-faucet = fa-icon.with("\u{e005}")
#let fa-faucet-drip = fa-icon.with("\u{e006}")
#let fa-fax = fa-icon.with("\u{f1ac}")
#let fa-feather = fa-icon.with("\u{f52d}")
#let fa-feather-pointed = fa-icon.with("\u{f56b}")
#let fa-feather-alt = fa-icon.with("\u{f56b}")
#let fa-fedex = fa-icon.with("\u{f797}")
#let fa-fedora = fa-icon.with("\u{f798}")
#let fa-fence = fa-icon.with("\u{e303}")
#let fa-ferris-wheel = fa-icon.with("\u{e174}")
#let fa-ferry = fa-icon.with("\u{e4ea}")
#let fa-field-hockey-stick-ball = fa-icon.with("\u{f44c}")
#let fa-field-hockey = fa-icon.with("\u{f44c}")
#let fa-figma = fa-icon.with("\u{f799}")
#let fa-file = fa-icon.with("\u{f15b}")
#let fa-file-arrow-down = fa-icon.with("\u{f56d}")
#let fa-file-download = fa-icon.with("\u{f56d}")
#let fa-file-arrow-up = fa-icon.with("\u{f574}")
#let fa-file-upload = fa-icon.with("\u{f574}")
#let fa-file-audio = fa-icon.with("\u{f1c7}")
#let fa-file-binary = fa-icon.with("\u{e175}")
#let fa-file-cad = fa-icon.with("\u{e672}")
#let fa-file-certificate = fa-icon.with("\u{f5f3}")
#let fa-file-award = fa-icon.with("\u{f5f3}")
#let fa-file-chart-column = fa-icon.with("\u{f659}")
#let fa-file-chart-line = fa-icon.with("\u{f659}")
#let fa-file-chart-pie = fa-icon.with("\u{f65a}")
#let fa-file-check = fa-icon.with("\u{f316}")
#let fa-file-circle-check = fa-icon.with("\u{e5a0}")
#let fa-file-circle-exclamation = fa-icon.with("\u{e4eb}")
#let fa-file-circle-info = fa-icon.with("\u{e493}")
#let fa-file-circle-minus = fa-icon.with("\u{e4ed}")
#let fa-file-circle-plus = fa-icon.with("\u{e494}")
#let fa-file-circle-question = fa-icon.with("\u{e4ef}")
#let fa-file-circle-xmark = fa-icon.with("\u{e5a1}")
#let fa-file-code = fa-icon.with("\u{f1c9}")
#let fa-file-contract = fa-icon.with("\u{f56c}")
#let fa-file-csv = fa-icon.with("\u{f6dd}")
#let fa-file-dashed-line = fa-icon.with("\u{f877}")
#let fa-page-break = fa-icon.with("\u{f877}")
#let fa-file-doc = fa-icon.with("\u{e5ed}")
#let fa-file-eps = fa-icon.with("\u{e644}")
#let fa-file-excel = fa-icon.with("\u{f1c3}")
#let fa-file-exclamation = fa-icon.with("\u{f31a}")
#let fa-file-export = fa-icon.with("\u{f56e}")
#let fa-arrow-right-from-file = fa-icon.with("\u{f56e}")
#let fa-file-gif = fa-icon.with("\u{e645}")
#let fa-file-heart = fa-icon.with("\u{e176}")
#let fa-file-image = fa-icon.with("\u{f1c5}")
#let fa-file-import = fa-icon.with("\u{f56f}")
#let fa-arrow-right-to-file = fa-icon.with("\u{f56f}")
#let fa-file-invoice = fa-icon.with("\u{f570}")
#let fa-file-invoice-dollar = fa-icon.with("\u{f571}")
#let fa-file-jpg = fa-icon.with("\u{e646}")
#let fa-file-lines = fa-icon.with("\u{f15c}")
#let fa-file-alt = fa-icon.with("\u{f15c}")
#let fa-file-text = fa-icon.with("\u{f15c}")
#let fa-file-lock = fa-icon.with("\u{e3a6}")
#let fa-file-magnifying-glass = fa-icon.with("\u{f865}")
#let fa-file-search = fa-icon.with("\u{f865}")
#let fa-file-medical = fa-icon.with("\u{f477}")
#let fa-file-minus = fa-icon.with("\u{f318}")
#let fa-file-mov = fa-icon.with("\u{e647}")
#let fa-file-mp3 = fa-icon.with("\u{e648}")
#let fa-file-mp4 = fa-icon.with("\u{e649}")
#let fa-file-music = fa-icon.with("\u{f8b6}")
#let fa-file-pdf = fa-icon.with("\u{f1c1}")
#let fa-file-pen = fa-icon.with("\u{f31c}")
#let fa-file-edit = fa-icon.with("\u{f31c}")
#let fa-file-plus = fa-icon.with("\u{f319}")
#let fa-file-plus-minus = fa-icon.with("\u{e177}")
#let fa-file-png = fa-icon.with("\u{e666}")
#let fa-file-powerpoint = fa-icon.with("\u{f1c4}")
#let fa-file-ppt = fa-icon.with("\u{e64a}")
#let fa-file-prescription = fa-icon.with("\u{f572}")
#let fa-files = fa-icon.with("\u{e178}")
#let fa-file-shield = fa-icon.with("\u{e4f0}")
#let fa-file-signature = fa-icon.with("\u{f573}")
#let fa-file-slash = fa-icon.with("\u{e3a7}")
#let fa-files-medical = fa-icon.with("\u{f7fd}")
#let fa-file-spreadsheet = fa-icon.with("\u{f65b}")
#let fa-file-svg = fa-icon.with("\u{e64b}")
#let fa-file-user = fa-icon.with("\u{f65c}")
#let fa-file-vector = fa-icon.with("\u{e64c}")
#let fa-file-video = fa-icon.with("\u{f1c8}")
#let fa-file-waveform = fa-icon.with("\u{f478}")
#let fa-file-medical-alt = fa-icon.with("\u{f478}")
#let fa-file-word = fa-icon.with("\u{f1c2}")
#let fa-file-xls = fa-icon.with("\u{e64d}")
#let fa-file-xmark = fa-icon.with("\u{f317}")
#let fa-file-times = fa-icon.with("\u{f317}")
#let fa-file-xml = fa-icon.with("\u{e654}")
#let fa-file-zip = fa-icon.with("\u{e5ee}")
#let fa-file-zipper = fa-icon.with("\u{f1c6}")
#let fa-file-archive = fa-icon.with("\u{f1c6}")
#let fa-fill = fa-icon.with("\u{f575}")
#let fa-fill-drip = fa-icon.with("\u{f576}")
#let fa-film = fa-icon.with("\u{f008}")
#let fa-film-canister = fa-icon.with("\u{f8b7}")
#let fa-film-cannister = fa-icon.with("\u{f8b7}")
#let fa-films = fa-icon.with("\u{e17a}")
#let fa-film-simple = fa-icon.with("\u{f3a0}")
#let fa-film-alt = fa-icon.with("\u{f3a0}")
#let fa-film-slash = fa-icon.with("\u{e179}")
#let fa-filter = fa-icon.with("\u{f0b0}")
#let fa-filter-circle-dollar = fa-icon.with("\u{f662}")
#let fa-funnel-dollar = fa-icon.with("\u{f662}")
#let fa-filter-circle-xmark = fa-icon.with("\u{e17b}")
#let fa-filter-list = fa-icon.with("\u{e17c}")
#let fa-filters = fa-icon.with("\u{e17e}")
#let fa-filter-slash = fa-icon.with("\u{e17d}")
#let fa-fingerprint = fa-icon.with("\u{f577}")
#let fa-fire = fa-icon.with("\u{f06d}")
#let fa-fire-burner = fa-icon.with("\u{e4f1}")
#let fa-fire-extinguisher = fa-icon.with("\u{f134}")
#let fa-fire-flame = fa-icon.with("\u{f6df}")
#let fa-flame = fa-icon.with("\u{f6df}")
#let fa-fire-flame-curved = fa-icon.with("\u{f7e4}")
#let fa-fire-alt = fa-icon.with("\u{f7e4}")
#let fa-fire-flame-simple = fa-icon.with("\u{f46a}")
#let fa-burn = fa-icon.with("\u{f46a}")
#let fa-firefox = fa-icon.with("\u{f269}")
#let fa-firefox-browser = fa-icon.with("\u{e007}")
#let fa-fire-hydrant = fa-icon.with("\u{e17f}")
#let fa-fireplace = fa-icon.with("\u{f79a}")
#let fa-fire-smoke = fa-icon.with("\u{f74b}")
#let fa-firstdraft = fa-icon.with("\u{f3a1}")
#let fa-first-order = fa-icon.with("\u{f2b0}")
#let fa-first-order-alt = fa-icon.with("\u{f50a}")
#let fa-fish = fa-icon.with("\u{f578}")
#let fa-fish-bones = fa-icon.with("\u{e304}")
#let fa-fish-cooked = fa-icon.with("\u{f7fe}")
#let fa-fish-fins = fa-icon.with("\u{e4f2}")
#let fa-fishing-rod = fa-icon.with("\u{e3a8}")
#let fa-flag = fa-icon.with("\u{f024}")
#let fa-flag-checkered = fa-icon.with("\u{f11e}")
#let fa-flag-pennant = fa-icon.with("\u{f456}")
#let fa-pennant = fa-icon.with("\u{f456}")
#let fa-flag-swallowtail = fa-icon.with("\u{f74c}")
#let fa-flag-alt = fa-icon.with("\u{f74c}")
#let fa-flag-usa = fa-icon.with("\u{f74d}")
#let fa-flashlight = fa-icon.with("\u{f8b8}")
#let fa-flask = fa-icon.with("\u{f0c3}")
#let fa-flask-gear = fa-icon.with("\u{e5f1}")
#let fa-flask-round-poison = fa-icon.with("\u{f6e0}")
#let fa-flask-poison = fa-icon.with("\u{f6e0}")
#let fa-flask-round-potion = fa-icon.with("\u{f6e1}")
#let fa-flask-potion = fa-icon.with("\u{f6e1}")
#let fa-flask-vial = fa-icon.with("\u{e4f3}")
#let fa-flatbread = fa-icon.with("\u{e40b}")
#let fa-flatbread-stuffed = fa-icon.with("\u{e40c}")
#let fa-flickr = fa-icon.with("\u{f16e}")
#let fa-flipboard = fa-icon.with("\u{f44d}")
#let fa-floppy-disk = fa-icon.with("\u{f0c7}")
#let fa-save = fa-icon.with("\u{f0c7}")
#let fa-floppy-disk-circle-arrow-right = fa-icon.with("\u{e180}")
#let fa-save-circle-arrow-right = fa-icon.with("\u{e180}")
#let fa-floppy-disk-circle-xmark = fa-icon.with("\u{e181}")
#let fa-floppy-disk-times = fa-icon.with("\u{e181}")
#let fa-save-circle-xmark = fa-icon.with("\u{e181}")
#let fa-save-times = fa-icon.with("\u{e181}")
#let fa-floppy-disk-pen = fa-icon.with("\u{e182}")
#let fa-floppy-disks = fa-icon.with("\u{e183}")
#let fa-florin-sign = fa-icon.with("\u{e184}")
#let fa-flower = fa-icon.with("\u{f7ff}")
#let fa-flower-daffodil = fa-icon.with("\u{f800}")
#let fa-flower-tulip = fa-icon.with("\u{f801}")
#let fa-flute = fa-icon.with("\u{f8b9}")
#let fa-flutter = fa-icon.with("\u{e694}")
#let fa-flux-capacitor = fa-icon.with("\u{f8ba}")
#let fa-fly = fa-icon.with("\u{f417}")
#let fa-flying-disc = fa-icon.with("\u{e3a9}")
#let fa-folder = fa-icon.with("\u{f07b}")
#let fa-folder-blank = fa-icon.with("\u{f07b}")
#let fa-folder-arrow-down = fa-icon.with("\u{e053}")
#let fa-folder-download = fa-icon.with("\u{e053}")
#let fa-folder-arrow-up = fa-icon.with("\u{e054}")
#let fa-folder-upload = fa-icon.with("\u{e054}")
#let fa-folder-bookmark = fa-icon.with("\u{e186}")
#let fa-folder-check = fa-icon.with("\u{e64e}")
#let fa-folder-closed = fa-icon.with("\u{e185}")
#let fa-folder-gear = fa-icon.with("\u{e187}")
#let fa-folder-cog = fa-icon.with("\u{e187}")
#let fa-folder-grid = fa-icon.with("\u{e188}")
#let fa-folder-heart = fa-icon.with("\u{e189}")
#let fa-folder-image = fa-icon.with("\u{e18a}")
#let fa-folder-magnifying-glass = fa-icon.with("\u{e18b}")
#let fa-folder-search = fa-icon.with("\u{e18b}")
#let fa-folder-medical = fa-icon.with("\u{e18c}")
#let fa-folder-minus = fa-icon.with("\u{f65d}")
#let fa-folder-music = fa-icon.with("\u{e18d}")
#let fa-folder-open = fa-icon.with("\u{f07c}")
#let fa-folder-plus = fa-icon.with("\u{f65e}")
#let fa-folders = fa-icon.with("\u{f660}")
#let fa-folder-tree = fa-icon.with("\u{f802}")
#let fa-folder-user = fa-icon.with("\u{e18e}")
#let fa-folder-xmark = fa-icon.with("\u{f65f}")
#let fa-folder-times = fa-icon.with("\u{f65f}")
#let fa-fondue-pot = fa-icon.with("\u{e40d}")
#let fa-font = fa-icon.with("\u{f031}")
#let fa-font-awesome = fa-icon.with("\u{f2b4}")
#let fa-font-awesome-flag = fa-icon.with("\u{f2b4}")
#let fa-font-awesome-logo-full = fa-icon.with("\u{f2b4}")
#let fa-font-case = fa-icon.with("\u{f866}")
#let fa-fonticons = fa-icon.with("\u{f280}")
#let fa-fonticons-fi = fa-icon.with("\u{f3a2}")
#let fa-football = fa-icon.with("\u{f44e}")
#let fa-football-ball = fa-icon.with("\u{f44e}")
#let fa-football-helmet = fa-icon.with("\u{f44f}")
#let fa-fork = fa-icon.with("\u{f2e3}")
#let fa-utensil-fork = fa-icon.with("\u{f2e3}")
#let fa-fork-knife = fa-icon.with("\u{f2e6}")
#let fa-utensils-alt = fa-icon.with("\u{f2e6}")
#let fa-forklift = fa-icon.with("\u{f47a}")
#let fa-fort = fa-icon.with("\u{e486}")
#let fa-fort-awesome = fa-icon.with("\u{f286}")
#let fa-fort-awesome-alt = fa-icon.with("\u{f3a3}")
#let fa-forumbee = fa-icon.with("\u{f211}")
#let fa-forward = fa-icon.with("\u{f04e}")
#let fa-forward-fast = fa-icon.with("\u{f050}")
#let fa-fast-forward = fa-icon.with("\u{f050}")
#let fa-forward-step = fa-icon.with("\u{f051}")
#let fa-step-forward = fa-icon.with("\u{f051}")
#let fa-foursquare = fa-icon.with("\u{f180}")
#let fa-frame = fa-icon.with("\u{e495}")
#let fa-franc-sign = fa-icon.with("\u{e18f}")
#let fa-freebsd = fa-icon.with("\u{f3a4}")
#let fa-free-code-camp = fa-icon.with("\u{f2c5}")
#let fa-french-fries = fa-icon.with("\u{f803}")
#let fa-frog = fa-icon.with("\u{f52e}")
#let fa-fulcrum = fa-icon.with("\u{f50b}")
#let fa-function = fa-icon.with("\u{f661}")
#let fa-futbol = fa-icon.with("\u{f1e3}")
#let fa-futbol-ball = fa-icon.with("\u{f1e3}")
#let fa-soccer-ball = fa-icon.with("\u{f1e3}")
#let fa-g = fa-icon.with("\u{47}")
#let fa-galactic-republic = fa-icon.with("\u{f50c}")
#let fa-galactic-senate = fa-icon.with("\u{f50d}")
#let fa-galaxy = fa-icon.with("\u{e008}")
#let fa-gallery-thumbnails = fa-icon.with("\u{e3aa}")
#let fa-game-board = fa-icon.with("\u{f867}")
#let fa-game-board-simple = fa-icon.with("\u{f868}")
#let fa-game-board-alt = fa-icon.with("\u{f868}")
#let fa-game-console-handheld = fa-icon.with("\u{f8bb}")
#let fa-game-console-handheld-crank = fa-icon.with("\u{e5b9}")
#let fa-gamepad = fa-icon.with("\u{f11b}")
#let fa-gamepad-modern = fa-icon.with("\u{e5a2}")
#let fa-gamepad-alt = fa-icon.with("\u{e5a2}")
#let fa-garage = fa-icon.with("\u{e009}")
#let fa-garage-car = fa-icon.with("\u{e00a}")
#let fa-garage-open = fa-icon.with("\u{e00b}")
#let fa-garlic = fa-icon.with("\u{e40e}")
#let fa-gas-pump = fa-icon.with("\u{f52f}")
#let fa-gas-pump-slash = fa-icon.with("\u{f5f4}")
#let fa-gauge = fa-icon.with("\u{f624}")
#let fa-dashboard = fa-icon.with("\u{f624}")
#let fa-gauge-med = fa-icon.with("\u{f624}")
#let fa-tachometer-alt-average = fa-icon.with("\u{f624}")
#let fa-gauge-circle-bolt = fa-icon.with("\u{e496}")
#let fa-gauge-circle-minus = fa-icon.with("\u{e497}")
#let fa-gauge-circle-plus = fa-icon.with("\u{e498}")
#let fa-gauge-high = fa-icon.with("\u{f625}")
#let fa-tachometer-alt = fa-icon.with("\u{f625}")
#let fa-tachometer-alt-fast = fa-icon.with("\u{f625}")
#let fa-gauge-low = fa-icon.with("\u{f627}")
#let fa-tachometer-alt-slow = fa-icon.with("\u{f627}")
#let fa-gauge-max = fa-icon.with("\u{f626}")
#let fa-tachometer-alt-fastest = fa-icon.with("\u{f626}")
#let fa-gauge-min = fa-icon.with("\u{f628}")
#let fa-tachometer-alt-slowest = fa-icon.with("\u{f628}")
#let fa-gauge-simple = fa-icon.with("\u{f629}")
#let fa-gauge-simple-med = fa-icon.with("\u{f629}")
#let fa-tachometer-average = fa-icon.with("\u{f629}")
#let fa-gauge-simple-high = fa-icon.with("\u{f62a}")
#let fa-tachometer = fa-icon.with("\u{f62a}")
#let fa-tachometer-fast = fa-icon.with("\u{f62a}")
#let fa-gauge-simple-low = fa-icon.with("\u{f62c}")
#let fa-tachometer-slow = fa-icon.with("\u{f62c}")
#let fa-gauge-simple-max = fa-icon.with("\u{f62b}")
#let fa-tachometer-fastest = fa-icon.with("\u{f62b}")
#let fa-gauge-simple-min = fa-icon.with("\u{f62d}")
#let fa-tachometer-slowest = fa-icon.with("\u{f62d}")
#let fa-gavel = fa-icon.with("\u{f0e3}")
#let fa-legal = fa-icon.with("\u{f0e3}")
#let fa-gear = fa-icon.with("\u{f013}")
#let fa-cog = fa-icon.with("\u{f013}")
#let fa-gear-code = fa-icon.with("\u{e5e8}")
#let fa-gear-complex = fa-icon.with("\u{e5e9}")
#let fa-gear-complex-code = fa-icon.with("\u{e5eb}")
#let fa-gears = fa-icon.with("\u{f085}")
#let fa-cogs = fa-icon.with("\u{f085}")
#let fa-gem = fa-icon.with("\u{f3a5}")
#let fa-genderless = fa-icon.with("\u{f22d}")
#let fa-get-pocket = fa-icon.with("\u{f265}")
#let fa-gg = fa-icon.with("\u{f260}")
#let fa-gg-circle = fa-icon.with("\u{f261}")
#let fa-ghost = fa-icon.with("\u{f6e2}")
#let fa-gif = fa-icon.with("\u{e190}")
#let fa-gift = fa-icon.with("\u{f06b}")
#let fa-gift-card = fa-icon.with("\u{f663}")
#let fa-gifts = fa-icon.with("\u{f79c}")
#let fa-gingerbread-man = fa-icon.with("\u{f79d}")
#let fa-git = fa-icon.with("\u{f1d3}")
#let fa-git-alt = fa-icon.with("\u{f841}")
#let fa-github = fa-icon.with("\u{f09b}")
#let fa-github-alt = fa-icon.with("\u{f113}")
#let fa-gitkraken = fa-icon.with("\u{f3a6}")
#let fa-gitlab = fa-icon.with("\u{f296}")
#let fa-gitter = fa-icon.with("\u{f426}")
#let fa-glass = fa-icon.with("\u{f804}")
#let fa-glass-citrus = fa-icon.with("\u{f869}")
#let fa-glass-empty = fa-icon.with("\u{e191}")
#let fa-glasses = fa-icon.with("\u{f530}")
#let fa-glasses-round = fa-icon.with("\u{f5f5}")
#let fa-glasses-alt = fa-icon.with("\u{f5f5}")
#let fa-glass-half = fa-icon.with("\u{e192}")
#let fa-glass-half-empty = fa-icon.with("\u{e192}")
#let fa-glass-half-full = fa-icon.with("\u{e192}")
#let fa-glass-water = fa-icon.with("\u{e4f4}")
#let fa-glass-water-droplet = fa-icon.with("\u{e4f5}")
#let fa-glide = fa-icon.with("\u{f2a5}")
#let fa-glide-g = fa-icon.with("\u{f2a6}")
#let fa-globe = fa-icon.with("\u{f0ac}")
#let fa-globe-pointer = fa-icon.with("\u{e60e}")
#let fa-globe-snow = fa-icon.with("\u{f7a3}")
#let fa-globe-stand = fa-icon.with("\u{f5f6}")
#let fa-globe-wifi = fa-icon.with("\u{e685}")
#let fa-goal-net = fa-icon.with("\u{e3ab}")
#let fa-gofore = fa-icon.with("\u{f3a7}")
#let fa-golang = fa-icon.with("\u{e40f}")
#let fa-golf-ball-tee = fa-icon.with("\u{f450}")
#let fa-golf-ball = fa-icon.with("\u{f450}")
#let fa-golf-club = fa-icon.with("\u{f451}")
#let fa-golf-flag-hole = fa-icon.with("\u{e3ac}")
#let fa-goodreads = fa-icon.with("\u{f3a8}")
#let fa-goodreads-g = fa-icon.with("\u{f3a9}")
#let fa-google = fa-icon.with("\u{f1a0}")
#let fa-google-drive = fa-icon.with("\u{f3aa}")
#let fa-google-pay = fa-icon.with("\u{e079}")
#let fa-google-play = fa-icon.with("\u{f3ab}")
#let fa-google-plus = fa-icon.with("\u{f2b3}")
#let fa-google-plus-g = fa-icon.with("\u{f0d5}")
#let fa-google-scholar = fa-icon.with("\u{e63b}")
#let fa-google-wallet = fa-icon.with("\u{f1ee}")
#let fa-gopuram = fa-icon.with("\u{f664}")
#let fa-graduation-cap = fa-icon.with("\u{f19d}")
#let fa-mortar-board = fa-icon.with("\u{f19d}")
#let fa-gramophone = fa-icon.with("\u{f8bd}")
#let fa-grapes = fa-icon.with("\u{e306}")
#let fa-grate = fa-icon.with("\u{e193}")
#let fa-grate-droplet = fa-icon.with("\u{e194}")
#let fa-gratipay = fa-icon.with("\u{f184}")
#let fa-grav = fa-icon.with("\u{f2d6}")
#let fa-greater-than = fa-icon.with("\u{3e}")
#let fa-greater-than-equal = fa-icon.with("\u{f532}")
#let fa-grid = fa-icon.with("\u{e195}")
#let fa-grid-3 = fa-icon.with("\u{e195}")
#let fa-grid-2 = fa-icon.with("\u{e196}")
#let fa-grid-2-plus = fa-icon.with("\u{e197}")
#let fa-grid-4 = fa-icon.with("\u{e198}")
#let fa-grid-5 = fa-icon.with("\u{e199}")
#let fa-grid-dividers = fa-icon.with("\u{e3ad}")
#let fa-grid-horizontal = fa-icon.with("\u{e307}")
#let fa-grid-round = fa-icon.with("\u{e5da}")
#let fa-grid-round-2 = fa-icon.with("\u{e5db}")
#let fa-grid-round-2-plus = fa-icon.with("\u{e5dc}")
#let fa-grid-round-4 = fa-icon.with("\u{e5dd}")
#let fa-grid-round-5 = fa-icon.with("\u{e5de}")
#let fa-grill = fa-icon.with("\u{e5a3}")
#let fa-grill-fire = fa-icon.with("\u{e5a4}")
#let fa-grill-hot = fa-icon.with("\u{e5a5}")
#let fa-grip = fa-icon.with("\u{f58d}")
#let fa-grip-horizontal = fa-icon.with("\u{f58d}")
#let fa-grip-dots = fa-icon.with("\u{e410}")
#let fa-grip-dots-vertical = fa-icon.with("\u{e411}")
#let fa-gripfire = fa-icon.with("\u{f3ac}")
#let fa-grip-lines = fa-icon.with("\u{f7a4}")
#let fa-grip-lines-vertical = fa-icon.with("\u{f7a5}")
#let fa-grip-vertical = fa-icon.with("\u{f58e}")
#let fa-group-arrows-rotate = fa-icon.with("\u{e4f6}")
#let fa-grunt = fa-icon.with("\u{f3ad}")
#let fa-guarani-sign = fa-icon.with("\u{e19a}")
#let fa-guilded = fa-icon.with("\u{e07e}")
#let fa-guitar = fa-icon.with("\u{f7a6}")
#let fa-guitar-electric = fa-icon.with("\u{f8be}")
#let fa-guitars = fa-icon.with("\u{f8bf}")
#let fa-gulp = fa-icon.with("\u{f3ae}")
#let fa-gun = fa-icon.with("\u{e19b}")
#let fa-gun-slash = fa-icon.with("\u{e19c}")
#let fa-gun-squirt = fa-icon.with("\u{e19d}")
#let fa-h = fa-icon.with("\u{48}")
#let fa-h1 = fa-icon.with("\u{f313}")
#let fa-h2 = fa-icon.with("\u{f314}")
#let fa-h3 = fa-icon.with("\u{f315}")
#let fa-h4 = fa-icon.with("\u{f86a}")
#let fa-h5 = fa-icon.with("\u{e412}")
#let fa-h6 = fa-icon.with("\u{e413}")
#let fa-hacker-news = fa-icon.with("\u{f1d4}")
#let fa-hackerrank = fa-icon.with("\u{f5f7}")
#let fa-hammer = fa-icon.with("\u{f6e3}")
#let fa-hammer-brush = fa-icon.with("\u{e620}")
#let fa-hammer-crash = fa-icon.with("\u{e414}")
#let fa-hammer-war = fa-icon.with("\u{f6e4}")
#let fa-hamsa = fa-icon.with("\u{f665}")
#let fa-hand = fa-icon.with("\u{f256}")
#let fa-hand-paper = fa-icon.with("\u{f256}")
#let fa-hand-back-fist = fa-icon.with("\u{f255}")
#let fa-hand-rock = fa-icon.with("\u{f255}")
#let fa-hand-back-point-down = fa-icon.with("\u{e19e}")
#let fa-hand-back-point-left = fa-icon.with("\u{e19f}")
#let fa-hand-back-point-ribbon = fa-icon.with("\u{e1a0}")
#let fa-hand-back-point-right = fa-icon.with("\u{e1a1}")
#let fa-hand-back-point-up = fa-icon.with("\u{e1a2}")
#let fa-handcuffs = fa-icon.with("\u{e4f8}")
#let fa-hand-dots = fa-icon.with("\u{f461}")
#let fa-allergies = fa-icon.with("\u{f461}")
#let fa-hand-fingers-crossed = fa-icon.with("\u{e1a3}")
#let fa-hand-fist = fa-icon.with("\u{f6de}")
#let fa-fist-raised = fa-icon.with("\u{f6de}")
#let fa-hand-heart = fa-icon.with("\u{f4bc}")
#let fa-hand-holding = fa-icon.with("\u{f4bd}")
#let fa-hand-holding-box = fa-icon.with("\u{f47b}")
#let fa-hand-holding-circle-dollar = fa-icon.with("\u{e621}")
#let fa-hand-holding-dollar = fa-icon.with("\u{f4c0}")
#let fa-hand-holding-usd = fa-icon.with("\u{f4c0}")
#let fa-hand-holding-droplet = fa-icon.with("\u{f4c1}")
#let fa-hand-holding-water = fa-icon.with("\u{f4c1}")
#let fa-hand-holding-hand = fa-icon.with("\u{e4f7}")
#let fa-hand-holding-heart = fa-icon.with("\u{f4be}")
#let fa-hand-holding-magic = fa-icon.with("\u{f6e5}")
#let fa-hand-holding-medical = fa-icon.with("\u{e05c}")
#let fa-hand-holding-seedling = fa-icon.with("\u{f4bf}")
#let fa-hand-holding-skull = fa-icon.with("\u{e1a4}")
#let fa-hand-horns = fa-icon.with("\u{e1a9}")
#let fa-hand-lizard = fa-icon.with("\u{f258}")
#let fa-hand-love = fa-icon.with("\u{e1a5}")
#let fa-hand-middle-finger = fa-icon.with("\u{f806}")
#let fa-hand-peace = fa-icon.with("\u{f25b}")
#let fa-hand-point-down = fa-icon.with("\u{f0a7}")
#let fa-hand-pointer = fa-icon.with("\u{f25a}")
#let fa-hand-point-left = fa-icon.with("\u{f0a5}")
#let fa-hand-point-ribbon = fa-icon.with("\u{e1a6}")
#let fa-hand-point-right = fa-icon.with("\u{f0a4}")
#let fa-hand-point-up = fa-icon.with("\u{f0a6}")
#let fa-hands = fa-icon.with("\u{f2a7}")
#let fa-sign-language = fa-icon.with("\u{f2a7}")
#let fa-signing = fa-icon.with("\u{f2a7}")
#let fa-hands-asl-interpreting = fa-icon.with("\u{f2a3}")
#let fa-american-sign-language-interpreting = fa-icon.with("\u{f2a3}")
#let fa-asl-interpreting = fa-icon.with("\u{f2a3}")
#let fa-hands-american-sign-language-interpreting = fa-icon.with("\u{f2a3}")
#let fa-hands-bound = fa-icon.with("\u{e4f9}")
#let fa-hands-bubbles = fa-icon.with("\u{e05e}")
#let fa-hands-wash = fa-icon.with("\u{e05e}")
#let fa-hand-scissors = fa-icon.with("\u{f257}")
#let fa-hands-clapping = fa-icon.with("\u{e1a8}")
#let fa-handshake = fa-icon.with("\u{f2b5}")
#let fa-handshake-angle = fa-icon.with("\u{f4c4}")
#let fa-hands-helping = fa-icon.with("\u{f4c4}")
#let fa-handshake-simple = fa-icon.with("\u{f4c6}")
#let fa-handshake-alt = fa-icon.with("\u{f4c6}")
#let fa-handshake-simple-slash = fa-icon.with("\u{e05f}")
#let fa-handshake-alt-slash = fa-icon.with("\u{e05f}")
#let fa-handshake-slash = fa-icon.with("\u{e060}")
#let fa-hands-holding = fa-icon.with("\u{f4c2}")
#let fa-hands-holding-child = fa-icon.with("\u{e4fa}")
#let fa-hands-holding-circle = fa-icon.with("\u{e4fb}")
#let fa-hands-holding-diamond = fa-icon.with("\u{f47c}")
#let fa-hand-receiving = fa-icon.with("\u{f47c}")
#let fa-hands-holding-dollar = fa-icon.with("\u{f4c5}")
#let fa-hands-usd = fa-icon.with("\u{f4c5}")
#let fa-hands-holding-heart = fa-icon.with("\u{f4c3}")
#let fa-hands-heart = fa-icon.with("\u{f4c3}")
#let fa-hand-sparkles = fa-icon.with("\u{e05d}")
#let fa-hand-spock = fa-icon.with("\u{f259}")
#let fa-hands-praying = fa-icon.with("\u{f684}")
#let fa-praying-hands = fa-icon.with("\u{f684}")
#let fa-hand-wave = fa-icon.with("\u{e1a7}")
#let fa-hanukiah = fa-icon.with("\u{f6e6}")
#let fa-hard-drive = fa-icon.with("\u{f0a0}")
#let fa-hdd = fa-icon.with("\u{f0a0}")
#let fa-hashnode = fa-icon.with("\u{e499}")
#let fa-hashtag = fa-icon.with("\u{23}")
#let fa-hashtag-lock = fa-icon.with("\u{e415}")
#let fa-hat-beach = fa-icon.with("\u{e606}")
#let fa-hat-chef = fa-icon.with("\u{f86b}")
#let fa-hat-cowboy = fa-icon.with("\u{f8c0}")
#let fa-hat-cowboy-side = fa-icon.with("\u{f8c1}")
#let fa-hat-santa = fa-icon.with("\u{f7a7}")
#let fa-hat-winter = fa-icon.with("\u{f7a8}")
#let fa-hat-witch = fa-icon.with("\u{f6e7}")
#let fa-hat-wizard = fa-icon.with("\u{f6e8}")
#let fa-heading = fa-icon.with("\u{f1dc}")
#let fa-header = fa-icon.with("\u{f1dc}")
#let fa-headphones = fa-icon.with("\u{f025}")
#let fa-headphones-simple = fa-icon.with("\u{f58f}")
#let fa-headphones-alt = fa-icon.with("\u{f58f}")
#let fa-headset = fa-icon.with("\u{f590}")
#let fa-head-side = fa-icon.with("\u{f6e9}")
#let fa-head-side-brain = fa-icon.with("\u{f808}")
#let fa-head-side-cough = fa-icon.with("\u{e061}")
#let fa-head-side-cough-slash = fa-icon.with("\u{e062}")
#let fa-head-side-gear = fa-icon.with("\u{e611}")
#let fa-head-side-goggles = fa-icon.with("\u{f6ea}")
#let fa-head-vr = fa-icon.with("\u{f6ea}")
#let fa-head-side-headphones = fa-icon.with("\u{f8c2}")
#let fa-head-side-heart = fa-icon.with("\u{e1aa}")
#let fa-head-side-mask = fa-icon.with("\u{e063}")
#let fa-head-side-medical = fa-icon.with("\u{f809}")
#let fa-head-side-virus = fa-icon.with("\u{e064}")
#let fa-heart = fa-icon.with("\u{f004}")
#let fa-heart-circle-bolt = fa-icon.with("\u{e4fc}")
#let fa-heart-circle-check = fa-icon.with("\u{e4fd}")
#let fa-heart-circle-exclamation = fa-icon.with("\u{e4fe}")
#let fa-heart-circle-minus = fa-icon.with("\u{e4ff}")
#let fa-heart-circle-plus = fa-icon.with("\u{e500}")
#let fa-heart-circle-xmark = fa-icon.with("\u{e501}")
#let fa-heart-crack = fa-icon.with("\u{f7a9}")
#let fa-heart-broken = fa-icon.with("\u{f7a9}")
#let fa-heart-half = fa-icon.with("\u{e1ab}")
#let fa-heart-half-stroke = fa-icon.with("\u{e1ac}")
#let fa-heart-half-alt = fa-icon.with("\u{e1ac}")
#let fa-heart-pulse = fa-icon.with("\u{f21e}")
#let fa-heartbeat = fa-icon.with("\u{f21e}")
#let fa-heat = fa-icon.with("\u{e00c}")
#let fa-helicopter = fa-icon.with("\u{f533}")
#let fa-helicopter-symbol = fa-icon.with("\u{e502}")
#let fa-helmet-battle = fa-icon.with("\u{f6eb}")
#let fa-helmet-safety = fa-icon.with("\u{f807}")
#let fa-hard-hat = fa-icon.with("\u{f807}")
#let fa-hat-hard = fa-icon.with("\u{f807}")
#let fa-helmet-un = fa-icon.with("\u{e503}")
#let fa-hexagon = fa-icon.with("\u{f312}")
#let fa-hexagon-check = fa-icon.with("\u{e416}")
#let fa-hexagon-divide = fa-icon.with("\u{e1ad}")
#let fa-hexagon-exclamation = fa-icon.with("\u{e417}")
#let fa-hexagon-image = fa-icon.with("\u{e504}")
#let fa-hexagon-minus = fa-icon.with("\u{f307}")
#let fa-minus-hexagon = fa-icon.with("\u{f307}")
#let fa-hexagon-plus = fa-icon.with("\u{f300}")
#let fa-plus-hexagon = fa-icon.with("\u{f300}")
#let fa-hexagon-vertical-nft = fa-icon.with("\u{e505}")
#let fa-hexagon-vertical-nft-slanted = fa-icon.with("\u{e506}")
#let fa-hexagon-xmark = fa-icon.with("\u{f2ee}")
#let fa-times-hexagon = fa-icon.with("\u{f2ee}")
#let fa-xmark-hexagon = fa-icon.with("\u{f2ee}")
#let fa-high-definition = fa-icon.with("\u{e1ae}")
#let fa-rectangle-hd = fa-icon.with("\u{e1ae}")
#let fa-highlighter = fa-icon.with("\u{f591}")
#let fa-highlighter-line = fa-icon.with("\u{e1af}")
#let fa-hill-avalanche = fa-icon.with("\u{e507}")
#let fa-hill-rockslide = fa-icon.with("\u{e508}")
#let fa-hippo = fa-icon.with("\u{f6ed}")
#let fa-hips = fa-icon.with("\u{f452}")
#let fa-hire-a-helper = fa-icon.with("\u{f3b0}")
#let fa-hive = fa-icon.with("\u{e07f}")
#let fa-hockey-mask = fa-icon.with("\u{f6ee}")
#let fa-hockey-puck = fa-icon.with("\u{f453}")
#let fa-hockey-stick-puck = fa-icon.with("\u{e3ae}")
#let fa-hockey-sticks = fa-icon.with("\u{f454}")
#let fa-holly-berry = fa-icon.with("\u{f7aa}")
#let fa-honey-pot = fa-icon.with("\u{e418}")
#let fa-hood-cloak = fa-icon.with("\u{f6ef}")
#let fa-hooli = fa-icon.with("\u{f427}")
#let fa-horizontal-rule = fa-icon.with("\u{f86c}")
#let fa-hornbill = fa-icon.with("\u{f592}")
#let fa-horse = fa-icon.with("\u{f6f0}")
#let fa-horse-head = fa-icon.with("\u{f7ab}")
#let fa-horse-saddle = fa-icon.with("\u{f8c3}")
#let fa-hose = fa-icon.with("\u{e419}")
#let fa-hose-reel = fa-icon.with("\u{e41a}")
#let fa-hospital = fa-icon.with("\u{f0f8}")
#let fa-hospital-alt = fa-icon.with("\u{f0f8}")
#let fa-hospital-wide = fa-icon.with("\u{f0f8}")
#let fa-hospitals = fa-icon.with("\u{f80e}")
#let fa-hospital-user = fa-icon.with("\u{f80d}")
#let fa-hotdog = fa-icon.with("\u{f80f}")
#let fa-hotel = fa-icon.with("\u{f594}")
#let fa-hotjar = fa-icon.with("\u{f3b1}")
#let fa-hot-tub-person = fa-icon.with("\u{f593}")
#let fa-hot-tub = fa-icon.with("\u{f593}")
#let fa-hourglass = fa-icon.with("\u{f254}")
#let fa-hourglass-empty = fa-icon.with("\u{f254}")
#let fa-hourglass-clock = fa-icon.with("\u{e41b}")
#let fa-hourglass-end = fa-icon.with("\u{f253}")
#let fa-hourglass-3 = fa-icon.with("\u{f253}")
#let fa-hourglass-half = fa-icon.with("\u{f252}")
#let fa-hourglass-2 = fa-icon.with("\u{f252}")
#let fa-hourglass-start = fa-icon.with("\u{f251}")
#let fa-hourglass-1 = fa-icon.with("\u{f251}")
#let fa-house = fa-icon.with("\u{f015}")
#let fa-home = fa-icon.with("\u{f015}")
#let fa-home-alt = fa-icon.with("\u{f015}")
#let fa-home-lg-alt = fa-icon.with("\u{f015}")
#let fa-house-blank = fa-icon.with("\u{e487}")
#let fa-home-blank = fa-icon.with("\u{e487}")
#let fa-house-building = fa-icon.with("\u{e1b1}")
#let fa-house-chimney = fa-icon.with("\u{e3af}")
#let fa-home-lg = fa-icon.with("\u{e3af}")
#let fa-house-chimney-blank = fa-icon.with("\u{e3b0}")
#let fa-house-chimney-crack = fa-icon.with("\u{f6f1}")
#let fa-house-damage = fa-icon.with("\u{f6f1}")
#let fa-house-chimney-heart = fa-icon.with("\u{e1b2}")
#let fa-house-chimney-medical = fa-icon.with("\u{f7f2}")
#let fa-clinic-medical = fa-icon.with("\u{f7f2}")
#let fa-house-chimney-user = fa-icon.with("\u{e065}")
#let fa-house-chimney-window = fa-icon.with("\u{e00d}")
#let fa-house-circle-check = fa-icon.with("\u{e509}")
#let fa-house-circle-exclamation = fa-icon.with("\u{e50a}")
#let fa-house-circle-xmark = fa-icon.with("\u{e50b}")
#let fa-house-crack = fa-icon.with("\u{e3b1}")
#let fa-house-day = fa-icon.with("\u{e00e}")
#let fa-house-fire = fa-icon.with("\u{e50c}")
#let fa-house-flag = fa-icon.with("\u{e50d}")
#let fa-house-flood-water = fa-icon.with("\u{e50e}")
#let fa-house-flood-water-circle-arrow-right = fa-icon.with("\u{e50f}")
#let fa-house-heart = fa-icon.with("\u{f4c9}")
#let fa-home-heart = fa-icon.with("\u{f4c9}")
#let fa-house-laptop = fa-icon.with("\u{e066}")
#let fa-laptop-house = fa-icon.with("\u{e066}")
#let fa-house-lock = fa-icon.with("\u{e510}")
#let fa-house-medical = fa-icon.with("\u{e3b2}")
#let fa-house-medical-circle-check = fa-icon.with("\u{e511}")
#let fa-house-medical-circle-exclamation = fa-icon.with("\u{e512}")
#let fa-house-medical-circle-xmark = fa-icon.with("\u{e513}")
#let fa-house-medical-flag = fa-icon.with("\u{e514}")
#let fa-house-night = fa-icon.with("\u{e010}")
#let fa-house-person-leave = fa-icon.with("\u{e00f}")
#let fa-house-leave = fa-icon.with("\u{e00f}")
#let fa-house-person-depart = fa-icon.with("\u{e00f}")
#let fa-house-person-return = fa-icon.with("\u{e011}")
#let fa-house-person-arrive = fa-icon.with("\u{e011}")
#let fa-house-return = fa-icon.with("\u{e011}")
#let fa-house-signal = fa-icon.with("\u{e012}")
#let fa-house-tree = fa-icon.with("\u{e1b3}")
#let fa-house-tsunami = fa-icon.with("\u{e515}")
#let fa-house-turret = fa-icon.with("\u{e1b4}")
#let fa-house-user = fa-icon.with("\u{e1b0}")
#let fa-home-user = fa-icon.with("\u{e1b0}")
#let fa-house-water = fa-icon.with("\u{f74f}")
#let fa-house-flood = fa-icon.with("\u{f74f}")
#let fa-house-window = fa-icon.with("\u{e3b3}")
#let fa-houzz = fa-icon.with("\u{f27c}")
#let fa-hryvnia-sign = fa-icon.with("\u{f6f2}")
#let fa-hryvnia = fa-icon.with("\u{f6f2}")
#let fa-html5 = fa-icon.with("\u{f13b}")
#let fa-hubspot = fa-icon.with("\u{f3b2}")
#let fa-hundred-points = fa-icon.with("\u{e41c}")
#let fa-100 = fa-icon.with("\u{e41c}")
#let fa-hurricane = fa-icon.with("\u{f751}")
#let fa-hydra = fa-icon.with("\u{e686}")
#let fa-hyphen = fa-icon.with("\u{2d}")
#let fa-i = fa-icon.with("\u{49}")
#let fa-ice-cream = fa-icon.with("\u{f810}")
#let fa-ice-skate = fa-icon.with("\u{f7ac}")
#let fa-icicles = fa-icon.with("\u{f7ad}")
#let fa-icons = fa-icon.with("\u{f86d}")
#let fa-heart-music-camera-bolt = fa-icon.with("\u{f86d}")
#let fa-i-cursor = fa-icon.with("\u{f246}")
#let fa-id-badge = fa-icon.with("\u{f2c1}")
#let fa-id-card = fa-icon.with("\u{f2c2}")
#let fa-drivers-license = fa-icon.with("\u{f2c2}")
#let fa-id-card-clip = fa-icon.with("\u{f47f}")
#let fa-id-card-alt = fa-icon.with("\u{f47f}")
#let fa-ideal = fa-icon.with("\u{e013}")
#let fa-igloo = fa-icon.with("\u{f7ae}")
#let fa-image = fa-icon.with("\u{f03e}")
#let fa-image-landscape = fa-icon.with("\u{e1b5}")
#let fa-landscape = fa-icon.with("\u{e1b5}")
#let fa-image-polaroid = fa-icon.with("\u{f8c4}")
#let fa-image-polaroid-user = fa-icon.with("\u{e1b6}")
#let fa-image-portrait = fa-icon.with("\u{f3e0}")
#let fa-portrait = fa-icon.with("\u{f3e0}")
#let fa-images = fa-icon.with("\u{f302}")
#let fa-image-slash = fa-icon.with("\u{e1b7}")
#let fa-images-user = fa-icon.with("\u{e1b9}")
#let fa-image-user = fa-icon.with("\u{e1b8}")
#let fa-imdb = fa-icon.with("\u{f2d8}")
#let fa-inbox = fa-icon.with("\u{f01c}")
#let fa-inboxes = fa-icon.with("\u{e1bb}")
#let fa-inbox-full = fa-icon.with("\u{e1ba}")
#let fa-inbox-in = fa-icon.with("\u{f310}")
#let fa-inbox-arrow-down = fa-icon.with("\u{f310}")
#let fa-inbox-out = fa-icon.with("\u{f311}")
#let fa-inbox-arrow-up = fa-icon.with("\u{f311}")
#let fa-indent = fa-icon.with("\u{f03c}")
#let fa-indian-rupee-sign = fa-icon.with("\u{e1bc}")
#let fa-indian-rupee = fa-icon.with("\u{e1bc}")
#let fa-inr = fa-icon.with("\u{e1bc}")
#let fa-industry = fa-icon.with("\u{f275}")
#let fa-industry-windows = fa-icon.with("\u{f3b3}")
#let fa-industry-alt = fa-icon.with("\u{f3b3}")
#let fa-infinity = fa-icon.with("\u{f534}")
#let fa-info = fa-icon.with("\u{f129}")
#let fa-inhaler = fa-icon.with("\u{f5f9}")
#let fa-input-numeric = fa-icon.with("\u{e1bd}")
#let fa-input-pipe = fa-icon.with("\u{e1be}")
#let fa-input-text = fa-icon.with("\u{e1bf}")
#let fa-instagram = fa-icon.with("\u{f16d}")
#let fa-instalod = fa-icon.with("\u{e081}")
#let fa-integral = fa-icon.with("\u{f667}")
#let fa-intercom = fa-icon.with("\u{f7af}")
#let fa-internet-explorer = fa-icon.with("\u{f26b}")
#let fa-interrobang = fa-icon.with("\u{e5ba}")
#let fa-intersection = fa-icon.with("\u{f668}")
#let fa-invision = fa-icon.with("\u{f7b0}")
#let fa-ioxhost = fa-icon.with("\u{f208}")
#let fa-island-tropical = fa-icon.with("\u{f811}")
#let fa-island-tree-palm = fa-icon.with("\u{f811}")
#let fa-italic = fa-icon.with("\u{f033}")
#let fa-itch-io = fa-icon.with("\u{f83a}")
#let fa-itunes = fa-icon.with("\u{f3b4}")
#let fa-itunes-note = fa-icon.with("\u{f3b5}")
#let fa-j = fa-icon.with("\u{4a}")
#let fa-jack-o-lantern = fa-icon.with("\u{f30e}")
#let fa-jar = fa-icon.with("\u{e516}")
#let fa-jar-wheat = fa-icon.with("\u{e517}")
#let fa-java = fa-icon.with("\u{f4e4}")
#let fa-jedi = fa-icon.with("\u{f669}")
#let fa-jedi-order = fa-icon.with("\u{f50e}")
#let fa-jenkins = fa-icon.with("\u{f3b6}")
#let fa-jet-fighter = fa-icon.with("\u{f0fb}")
#let fa-fighter-jet = fa-icon.with("\u{f0fb}")
#let fa-jet-fighter-up = fa-icon.with("\u{e518}")
#let fa-jira = fa-icon.with("\u{f7b1}")
#let fa-joget = fa-icon.with("\u{f3b7}")
#let fa-joint = fa-icon.with("\u{f595}")
#let fa-joomla = fa-icon.with("\u{f1aa}")
#let fa-joystick = fa-icon.with("\u{f8c5}")
#let fa-js = fa-icon.with("\u{f3b8}")
#let fa-jsfiddle = fa-icon.with("\u{f1cc}")
#let fa-jug = fa-icon.with("\u{f8c6}")
#let fa-jug-bottle = fa-icon.with("\u{e5fb}")
#let fa-jug-detergent = fa-icon.with("\u{e519}")
#let fa-jxl = fa-icon.with("\u{e67b}")
#let fa-k = fa-icon.with("\u{4b}")
#let fa-kaaba = fa-icon.with("\u{f66b}")
#let fa-kaggle = fa-icon.with("\u{f5fa}")
#let fa-kazoo = fa-icon.with("\u{f8c7}")
#let fa-kerning = fa-icon.with("\u{f86f}")
#let fa-key = fa-icon.with("\u{f084}")
#let fa-keybase = fa-icon.with("\u{f4f5}")
#let fa-keyboard = fa-icon.with("\u{f11c}")
#let fa-keyboard-brightness = fa-icon.with("\u{e1c0}")
#let fa-keyboard-brightness-low = fa-icon.with("\u{e1c1}")
#let fa-keyboard-down = fa-icon.with("\u{e1c2}")
#let fa-keyboard-left = fa-icon.with("\u{e1c3}")
#let fa-keycdn = fa-icon.with("\u{f3ba}")
#let fa-keynote = fa-icon.with("\u{f66c}")
#let fa-key-skeleton = fa-icon.with("\u{f6f3}")
#let fa-key-skeleton-left-right = fa-icon.with("\u{e3b4}")
#let fa-khanda = fa-icon.with("\u{f66d}")
#let fa-kickstarter = fa-icon.with("\u{f3bb}")
#let fa-square-kickstarter = fa-icon.with("\u{f3bb}")
#let fa-kickstarter-k = fa-icon.with("\u{f3bc}")
#let fa-kidneys = fa-icon.with("\u{f5fb}")
#let fa-kip-sign = fa-icon.with("\u{e1c4}")
#let fa-kitchen-set = fa-icon.with("\u{e51a}")
#let fa-kite = fa-icon.with("\u{f6f4}")
#let fa-kit-medical = fa-icon.with("\u{f479}")
#let fa-first-aid = fa-icon.with("\u{f479}")
#let fa-kiwi-bird = fa-icon.with("\u{f535}")
#let fa-kiwi-fruit = fa-icon.with("\u{e30c}")
#let fa-knife = fa-icon.with("\u{f2e4}")
#let fa-utensil-knife = fa-icon.with("\u{f2e4}")
#let fa-knife-kitchen = fa-icon.with("\u{f6f5}")
#let fa-korvue = fa-icon.with("\u{f42f}")
#let fa-l = fa-icon.with("\u{4c}")
#let fa-lacrosse-stick = fa-icon.with("\u{e3b5}")
#let fa-lacrosse-stick-ball = fa-icon.with("\u{e3b6}")
#let fa-lambda = fa-icon.with("\u{f66e}")
#let fa-lamp = fa-icon.with("\u{f4ca}")
#let fa-lamp-desk = fa-icon.with("\u{e014}")
#let fa-lamp-floor = fa-icon.with("\u{e015}")
#let fa-lamp-street = fa-icon.with("\u{e1c5}")
#let fa-landmark = fa-icon.with("\u{f66f}")
#let fa-landmark-dome = fa-icon.with("\u{f752}")
#let fa-landmark-alt = fa-icon.with("\u{f752}")
#let fa-landmark-flag = fa-icon.with("\u{e51c}")
#let fa-landmark-magnifying-glass = fa-icon.with("\u{e622}")
#let fa-land-mine-on = fa-icon.with("\u{e51b}")
#let fa-language = fa-icon.with("\u{f1ab}")
#let fa-laptop = fa-icon.with("\u{f109}")
#let fa-laptop-arrow-down = fa-icon.with("\u{e1c6}")
#let fa-laptop-binary = fa-icon.with("\u{e5e7}")
#let fa-laptop-code = fa-icon.with("\u{f5fc}")
#let fa-laptop-file = fa-icon.with("\u{e51d}")
#let fa-laptop-medical = fa-icon.with("\u{f812}")
#let fa-laptop-mobile = fa-icon.with("\u{f87a}")
#let fa-phone-laptop = fa-icon.with("\u{f87a}")
#let fa-laptop-slash = fa-icon.with("\u{e1c7}")
#let fa-laravel = fa-icon.with("\u{f3bd}")
#let fa-lari-sign = fa-icon.with("\u{e1c8}")
#let fa-lasso = fa-icon.with("\u{f8c8}")
#let fa-lasso-sparkles = fa-icon.with("\u{e1c9}")
#let fa-lastfm = fa-icon.with("\u{f202}")
#let fa-layer-group = fa-icon.with("\u{f5fd}")
#let fa-layer-minus = fa-icon.with("\u{f5fe}")
#let fa-layer-group-minus = fa-icon.with("\u{f5fe}")
#let fa-layer-plus = fa-icon.with("\u{f5ff}")
#let fa-layer-group-plus = fa-icon.with("\u{f5ff}")
#let fa-leaf = fa-icon.with("\u{f06c}")
#let fa-leaf-heart = fa-icon.with("\u{f4cb}")
#let fa-leaf-maple = fa-icon.with("\u{f6f6}")
#let fa-leaf-oak = fa-icon.with("\u{f6f7}")
#let fa-leafy-green = fa-icon.with("\u{e41d}")
#let fa-leanpub = fa-icon.with("\u{f212}")
#let fa-left = fa-icon.with("\u{f355}")
#let fa-arrow-alt-left = fa-icon.with("\u{f355}")
#let fa-left-from-bracket = fa-icon.with("\u{e66c}")
#let fa-left-from-line = fa-icon.with("\u{f348}")
#let fa-arrow-alt-from-right = fa-icon.with("\u{f348}")
#let fa-left-long = fa-icon.with("\u{f30a}")
#let fa-long-arrow-alt-left = fa-icon.with("\u{f30a}")
#let fa-left-long-to-line = fa-icon.with("\u{e41e}")
#let fa-left-right = fa-icon.with("\u{f337}")
#let fa-arrows-alt-h = fa-icon.with("\u{f337}")
#let fa-left-to-bracket = fa-icon.with("\u{e66d}")
#let fa-left-to-line = fa-icon.with("\u{f34b}")
#let fa-arrow-alt-to-left = fa-icon.with("\u{f34b}")
#let fa-lemon = fa-icon.with("\u{f094}")
#let fa-less = fa-icon.with("\u{f41d}")
#let fa-less-than = fa-icon.with("\u{3c}")
#let fa-less-than-equal = fa-icon.with("\u{f537}")
#let fa-letterboxd = fa-icon.with("\u{e62d}")
#let fa-life-ring = fa-icon.with("\u{f1cd}")
#let fa-lightbulb = fa-icon.with("\u{f0eb}")
#let fa-lightbulb-cfl = fa-icon.with("\u{e5a6}")
#let fa-lightbulb-cfl-on = fa-icon.with("\u{e5a7}")
#let fa-lightbulb-dollar = fa-icon.with("\u{f670}")
#let fa-lightbulb-exclamation = fa-icon.with("\u{f671}")
#let fa-lightbulb-exclamation-on = fa-icon.with("\u{e1ca}")
#let fa-lightbulb-gear = fa-icon.with("\u{e5fd}")
#let fa-lightbulb-message = fa-icon.with("\u{e687}")
#let fa-lightbulb-on = fa-icon.with("\u{f672}")
#let fa-lightbulb-slash = fa-icon.with("\u{f673}")
#let fa-light-ceiling = fa-icon.with("\u{e016}")
#let fa-light-emergency = fa-icon.with("\u{e41f}")
#let fa-light-emergency-on = fa-icon.with("\u{e420}")
#let fa-lighthouse = fa-icon.with("\u{e612}")
#let fa-lights-holiday = fa-icon.with("\u{f7b2}")
#let fa-light-switch = fa-icon.with("\u{e017}")
#let fa-light-switch-off = fa-icon.with("\u{e018}")
#let fa-light-switch-on = fa-icon.with("\u{e019}")
#let fa-line = fa-icon.with("\u{f3c0}")
#let fa-line-columns = fa-icon.with("\u{f870}")
#let fa-line-height = fa-icon.with("\u{f871}")
#let fa-lines-leaning = fa-icon.with("\u{e51e}")
#let fa-link = fa-icon.with("\u{f0c1}")
#let fa-chain = fa-icon.with("\u{f0c1}")
#let fa-linkedin = fa-icon.with("\u{f08c}")
#let fa-linkedin-in = fa-icon.with("\u{f0e1}")
#let fa-link-horizontal = fa-icon.with("\u{e1cb}")
#let fa-chain-horizontal = fa-icon.with("\u{e1cb}")
#let fa-link-horizontal-slash = fa-icon.with("\u{e1cc}")
#let fa-chain-horizontal-slash = fa-icon.with("\u{e1cc}")
#let fa-link-simple = fa-icon.with("\u{e1cd}")
#let fa-link-simple-slash = fa-icon.with("\u{e1ce}")
#let fa-link-slash = fa-icon.with("\u{f127}")
#let fa-chain-broken = fa-icon.with("\u{f127}")
#let fa-chain-slash = fa-icon.with("\u{f127}")
#let fa-unlink = fa-icon.with("\u{f127}")
#let fa-linode = fa-icon.with("\u{f2b8}")
#let fa-linux = fa-icon.with("\u{f17c}")
#let fa-lips = fa-icon.with("\u{f600}")
#let fa-lira-sign = fa-icon.with("\u{f195}")
#let fa-list = fa-icon.with("\u{f03a}")
#let fa-list-squares = fa-icon.with("\u{f03a}")
#let fa-list-check = fa-icon.with("\u{f0ae}")
#let fa-tasks = fa-icon.with("\u{f0ae}")
#let fa-list-dropdown = fa-icon.with("\u{e1cf}")
#let fa-list-music = fa-icon.with("\u{f8c9}")
#let fa-list-ol = fa-icon.with("\u{f0cb}")
#let fa-list-1-2 = fa-icon.with("\u{f0cb}")
#let fa-list-numeric = fa-icon.with("\u{f0cb}")
#let fa-list-radio = fa-icon.with("\u{e1d0}")
#let fa-list-timeline = fa-icon.with("\u{e1d1}")
#let fa-list-tree = fa-icon.with("\u{e1d2}")
#let fa-list-ul = fa-icon.with("\u{f0ca}")
#let fa-list-dots = fa-icon.with("\u{f0ca}")
#let fa-litecoin-sign = fa-icon.with("\u{e1d3}")
#let fa-loader = fa-icon.with("\u{e1d4}")
#let fa-lobster = fa-icon.with("\u{e421}")
#let fa-location-arrow = fa-icon.with("\u{f124}")
#let fa-location-arrow-up = fa-icon.with("\u{e63a}")
#let fa-location-check = fa-icon.with("\u{f606}")
#let fa-map-marker-check = fa-icon.with("\u{f606}")
#let fa-location-crosshairs = fa-icon.with("\u{f601}")
#let fa-location = fa-icon.with("\u{f601}")
#let fa-location-crosshairs-slash = fa-icon.with("\u{f603}")
#let fa-location-slash = fa-icon.with("\u{f603}")
#let fa-location-dot = fa-icon.with("\u{f3c5}")
#let fa-map-marker-alt = fa-icon.with("\u{f3c5}")
#let fa-location-dot-slash = fa-icon.with("\u{f605}")
#let fa-map-marker-alt-slash = fa-icon.with("\u{f605}")
#let fa-location-exclamation = fa-icon.with("\u{f608}")
#let fa-map-marker-exclamation = fa-icon.with("\u{f608}")
#let fa-location-minus = fa-icon.with("\u{f609}")
#let fa-map-marker-minus = fa-icon.with("\u{f609}")
#let fa-location-pen = fa-icon.with("\u{f607}")
#let fa-map-marker-edit = fa-icon.with("\u{f607}")
#let fa-location-pin = fa-icon.with("\u{f041}")
#let fa-map-marker = fa-icon.with("\u{f041}")
#let fa-location-pin-lock = fa-icon.with("\u{e51f}")
#let fa-location-pin-slash = fa-icon.with("\u{f60c}")
#let fa-map-marker-slash = fa-icon.with("\u{f60c}")
#let fa-location-plus = fa-icon.with("\u{f60a}")
#let fa-map-marker-plus = fa-icon.with("\u{f60a}")
#let fa-location-question = fa-icon.with("\u{f60b}")
#let fa-map-marker-question = fa-icon.with("\u{f60b}")
#let fa-location-smile = fa-icon.with("\u{f60d}")
#let fa-map-marker-smile = fa-icon.with("\u{f60d}")
#let fa-location-xmark = fa-icon.with("\u{f60e}")
#let fa-map-marker-times = fa-icon.with("\u{f60e}")
#let fa-map-marker-xmark = fa-icon.with("\u{f60e}")
#let fa-lock = fa-icon.with("\u{f023}")
#let fa-lock-a = fa-icon.with("\u{e422}")
#let fa-lock-hashtag = fa-icon.with("\u{e423}")
#let fa-lock-keyhole = fa-icon.with("\u{f30d}")
#let fa-lock-alt = fa-icon.with("\u{f30d}")
#let fa-lock-keyhole-open = fa-icon.with("\u{f3c2}")
#let fa-lock-open-alt = fa-icon.with("\u{f3c2}")
#let fa-lock-open = fa-icon.with("\u{f3c1}")
#let fa-locust = fa-icon.with("\u{e520}")
#let fa-lollipop = fa-icon.with("\u{e424}")
#let fa-lollypop = fa-icon.with("\u{e424}")
#let fa-loveseat = fa-icon.with("\u{f4cc}")
#let fa-couch-small = fa-icon.with("\u{f4cc}")
#let fa-luchador-mask = fa-icon.with("\u{f455}")
#let fa-luchador = fa-icon.with("\u{f455}")
#let fa-mask-luchador = fa-icon.with("\u{f455}")
#let fa-lungs = fa-icon.with("\u{f604}")
#let fa-lungs-virus = fa-icon.with("\u{e067}")
#let fa-lyft = fa-icon.with("\u{f3c3}")
#let fa-m = fa-icon.with("\u{4d}")
#let fa-mace = fa-icon.with("\u{f6f8}")
#let fa-magento = fa-icon.with("\u{f3c4}")
#let fa-magnet = fa-icon.with("\u{f076}")
#let fa-magnifying-glass = fa-icon.with("\u{f002}")
#let fa-search = fa-icon.with("\u{f002}")
#let fa-magnifying-glass-arrow-right = fa-icon.with("\u{e521}")
#let fa-magnifying-glass-arrows-rotate = fa-icon.with("\u{e65e}")
#let fa-magnifying-glass-chart = fa-icon.with("\u{e522}")
#let fa-magnifying-glass-dollar = fa-icon.with("\u{f688}")
#let fa-search-dollar = fa-icon.with("\u{f688}")
#let fa-magnifying-glass-location = fa-icon.with("\u{f689}")
#let fa-search-location = fa-icon.with("\u{f689}")
#let fa-magnifying-glass-minus = fa-icon.with("\u{f010}")
#let fa-search-minus = fa-icon.with("\u{f010}")
#let fa-magnifying-glass-music = fa-icon.with("\u{e65f}")
#let fa-magnifying-glass-play = fa-icon.with("\u{e660}")
#let fa-magnifying-glass-plus = fa-icon.with("\u{f00e}")
#let fa-search-plus = fa-icon.with("\u{f00e}")
#let fa-magnifying-glass-waveform = fa-icon.with("\u{e661}")
#let fa-mailbox = fa-icon.with("\u{f813}")
#let fa-mailbox-flag-up = fa-icon.with("\u{e5bb}")
#let fa-mailchimp = fa-icon.with("\u{f59e}")
#let fa-manat-sign = fa-icon.with("\u{e1d5}")
#let fa-mandalorian = fa-icon.with("\u{f50f}")
#let fa-mandolin = fa-icon.with("\u{f6f9}")
#let fa-mango = fa-icon.with("\u{e30f}")
#let fa-manhole = fa-icon.with("\u{e1d6}")
#let fa-map = fa-icon.with("\u{f279}")
#let fa-map-location = fa-icon.with("\u{f59f}")
#let fa-map-marked = fa-icon.with("\u{f59f}")
#let fa-map-location-dot = fa-icon.with("\u{f5a0}")
#let fa-map-marked-alt = fa-icon.with("\u{f5a0}")
#let fa-map-pin = fa-icon.with("\u{f276}")
#let fa-markdown = fa-icon.with("\u{f60f}")
#let fa-marker = fa-icon.with("\u{f5a1}")
#let fa-mars = fa-icon.with("\u{f222}")
#let fa-mars-and-venus = fa-icon.with("\u{f224}")
#let fa-mars-and-venus-burst = fa-icon.with("\u{e523}")
#let fa-mars-double = fa-icon.with("\u{f227}")
#let fa-mars-stroke = fa-icon.with("\u{f229}")
#let fa-mars-stroke-right = fa-icon.with("\u{f22b}")
#let fa-mars-stroke-h = fa-icon.with("\u{f22b}")
#let fa-mars-stroke-up = fa-icon.with("\u{f22a}")
#let fa-mars-stroke-v = fa-icon.with("\u{f22a}")
#let fa-martini-glass = fa-icon.with("\u{f57b}")
#let fa-glass-martini-alt = fa-icon.with("\u{f57b}")
#let fa-martini-glass-citrus = fa-icon.with("\u{f561}")
#let fa-cocktail = fa-icon.with("\u{f561}")
#let fa-martini-glass-empty = fa-icon.with("\u{f000}")
#let fa-glass-martini = fa-icon.with("\u{f000}")
#let fa-mask = fa-icon.with("\u{f6fa}")
#let fa-mask-face = fa-icon.with("\u{e1d7}")
#let fa-mask-snorkel = fa-icon.with("\u{e3b7}")
#let fa-masks-theater = fa-icon.with("\u{f630}")
#let fa-theater-masks = fa-icon.with("\u{f630}")
#let fa-mask-ventilator = fa-icon.with("\u{e524}")
#let fa-mastodon = fa-icon.with("\u{f4f6}")
#let fa-mattress-pillow = fa-icon.with("\u{e525}")
#let fa-maxcdn = fa-icon.with("\u{f136}")
#let fa-maximize = fa-icon.with("\u{f31e}")
#let fa-expand-arrows-alt = fa-icon.with("\u{f31e}")
#let fa-mdb = fa-icon.with("\u{f8ca}")
#let fa-meat = fa-icon.with("\u{f814}")
#let fa-medal = fa-icon.with("\u{f5a2}")
#let fa-medapps = fa-icon.with("\u{f3c6}")
#let fa-medium = fa-icon.with("\u{f23a}")
#let fa-medium-m = fa-icon.with("\u{f23a}")
#let fa-medrt = fa-icon.with("\u{f3c8}")
#let fa-meetup = fa-icon.with("\u{f2e0}")
#let fa-megaphone = fa-icon.with("\u{f675}")
#let fa-megaport = fa-icon.with("\u{f5a3}")
#let fa-melon = fa-icon.with("\u{e310}")
#let fa-melon-slice = fa-icon.with("\u{e311}")
#let fa-memo = fa-icon.with("\u{e1d8}")
#let fa-memo-circle-check = fa-icon.with("\u{e1d9}")
#let fa-memo-circle-info = fa-icon.with("\u{e49a}")
#let fa-memo-pad = fa-icon.with("\u{e1da}")
#let fa-memory = fa-icon.with("\u{f538}")
#let fa-mendeley = fa-icon.with("\u{f7b3}")
#let fa-menorah = fa-icon.with("\u{f676}")
#let fa-mercury = fa-icon.with("\u{f223}")
#let fa-merge = fa-icon.with("\u{e526}")
#let fa-message = fa-icon.with("\u{f27a}")
#let fa-comment-alt = fa-icon.with("\u{f27a}")
#let fa-message-arrow-down = fa-icon.with("\u{e1db}")
#let fa-comment-alt-arrow-down = fa-icon.with("\u{e1db}")
#let fa-message-arrow-up = fa-icon.with("\u{e1dc}")
#let fa-comment-alt-arrow-up = fa-icon.with("\u{e1dc}")
#let fa-message-arrow-up-right = fa-icon.with("\u{e1dd}")
#let fa-message-bot = fa-icon.with("\u{e3b8}")
#let fa-message-captions = fa-icon.with("\u{e1de}")
#let fa-comment-alt-captions = fa-icon.with("\u{e1de}")
#let fa-message-check = fa-icon.with("\u{f4a2}")
#let fa-comment-alt-check = fa-icon.with("\u{f4a2}")
#let fa-message-code = fa-icon.with("\u{e1df}")
#let fa-message-dollar = fa-icon.with("\u{f650}")
#let fa-comment-alt-dollar = fa-icon.with("\u{f650}")
#let fa-message-dots = fa-icon.with("\u{f4a3}")
#let fa-comment-alt-dots = fa-icon.with("\u{f4a3}")
#let fa-messaging = fa-icon.with("\u{f4a3}")
#let fa-message-exclamation = fa-icon.with("\u{f4a5}")
#let fa-comment-alt-exclamation = fa-icon.with("\u{f4a5}")
#let fa-message-heart = fa-icon.with("\u{e5c9}")
#let fa-message-image = fa-icon.with("\u{e1e0}")
#let fa-comment-alt-image = fa-icon.with("\u{e1e0}")
#let fa-message-lines = fa-icon.with("\u{f4a6}")
#let fa-comment-alt-lines = fa-icon.with("\u{f4a6}")
#let fa-message-medical = fa-icon.with("\u{f7f4}")
#let fa-comment-alt-medical = fa-icon.with("\u{f7f4}")
#let fa-message-middle = fa-icon.with("\u{e1e1}")
#let fa-comment-middle-alt = fa-icon.with("\u{e1e1}")
#let fa-message-middle-top = fa-icon.with("\u{e1e2}")
#let fa-comment-middle-top-alt = fa-icon.with("\u{e1e2}")
#let fa-message-minus = fa-icon.with("\u{f4a7}")
#let fa-comment-alt-minus = fa-icon.with("\u{f4a7}")
#let fa-message-music = fa-icon.with("\u{f8af}")
#let fa-comment-alt-music = fa-icon.with("\u{f8af}")
#let fa-message-pen = fa-icon.with("\u{f4a4}")
#let fa-comment-alt-edit = fa-icon.with("\u{f4a4}")
#let fa-message-edit = fa-icon.with("\u{f4a4}")
#let fa-message-plus = fa-icon.with("\u{f4a8}")
#let fa-comment-alt-plus = fa-icon.with("\u{f4a8}")
#let fa-message-question = fa-icon.with("\u{e1e3}")
#let fa-message-quote = fa-icon.with("\u{e1e4}")
#let fa-comment-alt-quote = fa-icon.with("\u{e1e4}")
#let fa-messages = fa-icon.with("\u{f4b6}")
#let fa-comments-alt = fa-icon.with("\u{f4b6}")
#let fa-messages-dollar = fa-icon.with("\u{f652}")
#let fa-comments-alt-dollar = fa-icon.with("\u{f652}")
#let fa-message-slash = fa-icon.with("\u{f4a9}")
#let fa-comment-alt-slash = fa-icon.with("\u{f4a9}")
#let fa-message-smile = fa-icon.with("\u{f4aa}")
#let fa-comment-alt-smile = fa-icon.with("\u{f4aa}")
#let fa-message-sms = fa-icon.with("\u{e1e5}")
#let fa-messages-question = fa-icon.with("\u{e1e7}")
#let fa-message-text = fa-icon.with("\u{e1e6}")
#let fa-comment-alt-text = fa-icon.with("\u{e1e6}")
#let fa-message-xmark = fa-icon.with("\u{f4ab}")
#let fa-comment-alt-times = fa-icon.with("\u{f4ab}")
#let fa-message-times = fa-icon.with("\u{f4ab}")
#let fa-meta = fa-icon.with("\u{e49b}")
#let fa-meteor = fa-icon.with("\u{f753}")
#let fa-meter = fa-icon.with("\u{e1e8}")
#let fa-meter-bolt = fa-icon.with("\u{e1e9}")
#let fa-meter-droplet = fa-icon.with("\u{e1ea}")
#let fa-meter-fire = fa-icon.with("\u{e1eb}")
#let fa-microblog = fa-icon.with("\u{e01a}")
#let fa-microchip = fa-icon.with("\u{f2db}")
#let fa-microchip-ai = fa-icon.with("\u{e1ec}")
#let fa-microphone = fa-icon.with("\u{f130}")
#let fa-microphone-lines = fa-icon.with("\u{f3c9}")
#let fa-microphone-alt = fa-icon.with("\u{f3c9}")
#let fa-microphone-lines-slash = fa-icon.with("\u{f539}")
#let fa-microphone-alt-slash = fa-icon.with("\u{f539}")
#let fa-microphone-slash = fa-icon.with("\u{f131}")
#let fa-microphone-stand = fa-icon.with("\u{f8cb}")
#let fa-microscope = fa-icon.with("\u{f610}")
#let fa-microsoft = fa-icon.with("\u{f3ca}")
#let fa-microwave = fa-icon.with("\u{e01b}")
#let fa-mill-sign = fa-icon.with("\u{e1ed}")
#let fa-minimize = fa-icon.with("\u{f78c}")
#let fa-compress-arrows-alt = fa-icon.with("\u{f78c}")
#let fa-mintbit = fa-icon.with("\u{e62f}")
#let fa-minus = fa-icon.with("\u{f068}")
#let fa-subtract = fa-icon.with("\u{f068}")
#let fa-mistletoe = fa-icon.with("\u{f7b4}")
#let fa-mitten = fa-icon.with("\u{f7b5}")
#let fa-mix = fa-icon.with("\u{f3cb}")
#let fa-mixcloud = fa-icon.with("\u{f289}")
#let fa-mixer = fa-icon.with("\u{e056}")
#let fa-mizuni = fa-icon.with("\u{f3cc}")
#let fa-mobile = fa-icon.with("\u{f3ce}")
#let fa-mobile-android = fa-icon.with("\u{f3ce}")
#let fa-mobile-phone = fa-icon.with("\u{f3ce}")
#let fa-mobile-button = fa-icon.with("\u{f10b}")
#let fa-mobile-notch = fa-icon.with("\u{e1ee}")
#let fa-mobile-iphone = fa-icon.with("\u{e1ee}")
#let fa-mobile-retro = fa-icon.with("\u{e527}")
#let fa-mobile-screen = fa-icon.with("\u{f3cf}")
#let fa-mobile-android-alt = fa-icon.with("\u{f3cf}")
#let fa-mobile-screen-button = fa-icon.with("\u{f3cd}")
#let fa-mobile-alt = fa-icon.with("\u{f3cd}")
#let fa-mobile-signal = fa-icon.with("\u{e1ef}")
#let fa-mobile-signal-out = fa-icon.with("\u{e1f0}")
#let fa-modx = fa-icon.with("\u{f285}")
#let fa-monero = fa-icon.with("\u{f3d0}")
#let fa-money-bill = fa-icon.with("\u{f0d6}")
#let fa-money-bill-1 = fa-icon.with("\u{f3d1}")
#let fa-money-bill-alt = fa-icon.with("\u{f3d1}")
#let fa-money-bill-1-wave = fa-icon.with("\u{f53b}")
#let fa-money-bill-wave-alt = fa-icon.with("\u{f53b}")
#let fa-money-bills = fa-icon.with("\u{e1f3}")
#let fa-money-bill-simple = fa-icon.with("\u{e1f1}")
#let fa-money-bill-simple-wave = fa-icon.with("\u{e1f2}")
#let fa-money-bills-simple = fa-icon.with("\u{e1f4}")
#let fa-money-bills-alt = fa-icon.with("\u{e1f4}")
#let fa-money-bill-transfer = fa-icon.with("\u{e528}")
#let fa-money-bill-trend-up = fa-icon.with("\u{e529}")
#let fa-money-bill-wave = fa-icon.with("\u{f53a}")
#let fa-money-bill-wheat = fa-icon.with("\u{e52a}")
#let fa-money-check = fa-icon.with("\u{f53c}")
#let fa-money-check-dollar = fa-icon.with("\u{f53d}")
#let fa-money-check-alt = fa-icon.with("\u{f53d}")
#let fa-money-check-dollar-pen = fa-icon.with("\u{f873}")
#let fa-money-check-edit-alt = fa-icon.with("\u{f873}")
#let fa-money-check-pen = fa-icon.with("\u{f872}")
#let fa-money-check-edit = fa-icon.with("\u{f872}")
#let fa-money-from-bracket = fa-icon.with("\u{e312}")
#let fa-money-simple-from-bracket = fa-icon.with("\u{e313}")
#let fa-monitor-waveform = fa-icon.with("\u{f611}")
#let fa-monitor-heart-rate = fa-icon.with("\u{f611}")
#let fa-monkey = fa-icon.with("\u{f6fb}")
#let fa-monument = fa-icon.with("\u{f5a6}")
#let fa-moon = fa-icon.with("\u{f186}")
#let fa-moon-cloud = fa-icon.with("\u{f754}")
#let fa-moon-over-sun = fa-icon.with("\u{f74a}")
#let fa-eclipse-alt = fa-icon.with("\u{f74a}")
#let fa-moon-stars = fa-icon.with("\u{f755}")
#let fa-moped = fa-icon.with("\u{e3b9}")
#let fa-mortar-pestle = fa-icon.with("\u{f5a7}")
#let fa-mosque = fa-icon.with("\u{f678}")
#let fa-mosquito = fa-icon.with("\u{e52b}")
#let fa-mosquito-net = fa-icon.with("\u{e52c}")
#let fa-motorcycle = fa-icon.with("\u{f21c}")
#let fa-mound = fa-icon.with("\u{e52d}")
#let fa-mountain = fa-icon.with("\u{f6fc}")
#let fa-mountain-city = fa-icon.with("\u{e52e}")
#let fa-mountains = fa-icon.with("\u{f6fd}")
#let fa-mountain-sun = fa-icon.with("\u{e52f}")
#let fa-mouse-field = fa-icon.with("\u{e5a8}")
#let fa-mp3-player = fa-icon.with("\u{f8ce}")
#let fa-mug = fa-icon.with("\u{f874}")
#let fa-mug-hot = fa-icon.with("\u{f7b6}")
#let fa-mug-marshmallows = fa-icon.with("\u{f7b7}")
#let fa-mug-saucer = fa-icon.with("\u{f0f4}")
#let fa-coffee = fa-icon.with("\u{f0f4}")
#let fa-mug-tea = fa-icon.with("\u{f875}")
#let fa-mug-tea-saucer = fa-icon.with("\u{e1f5}")
#let fa-mushroom = fa-icon.with("\u{e425}")
#let fa-music = fa-icon.with("\u{f001}")
#let fa-music-magnifying-glass = fa-icon.with("\u{e662}")
#let fa-music-note = fa-icon.with("\u{f8cf}")
#let fa-music-alt = fa-icon.with("\u{f8cf}")
#let fa-music-note-slash = fa-icon.with("\u{f8d0}")
#let fa-music-alt-slash = fa-icon.with("\u{f8d0}")
#let fa-music-slash = fa-icon.with("\u{f8d1}")
#let fa-mustache = fa-icon.with("\u{e5bc}")
#let fa-n = fa-icon.with("\u{4e}")
#let fa-naira-sign = fa-icon.with("\u{e1f6}")
#let fa-napster = fa-icon.with("\u{f3d2}")
#let fa-narwhal = fa-icon.with("\u{f6fe}")
#let fa-neos = fa-icon.with("\u{f612}")
#let fa-nesting-dolls = fa-icon.with("\u{e3ba}")
#let fa-network-wired = fa-icon.with("\u{f6ff}")
#let fa-neuter = fa-icon.with("\u{f22c}")
#let fa-newspaper = fa-icon.with("\u{f1ea}")
#let fa-nfc = fa-icon.with("\u{e1f7}")
#let fa-nfc-directional = fa-icon.with("\u{e530}")
#let fa-nfc-lock = fa-icon.with("\u{e1f8}")
#let fa-nfc-magnifying-glass = fa-icon.with("\u{e1f9}")
#let fa-nfc-pen = fa-icon.with("\u{e1fa}")
#let fa-nfc-signal = fa-icon.with("\u{e1fb}")
#let fa-nfc-slash = fa-icon.with("\u{e1fc}")
#let fa-nfc-symbol = fa-icon.with("\u{e531}")
#let fa-nfc-trash = fa-icon.with("\u{e1fd}")
#let fa-nimblr = fa-icon.with("\u{f5a8}")
#let fa-node = fa-icon.with("\u{f419}")
#let fa-node-js = fa-icon.with("\u{f3d3}")
#let fa-nose = fa-icon.with("\u{e5bd}")
#let fa-notdef = fa-icon.with("\u{e1fe}")
#let fa-note = fa-icon.with("\u{e1ff}")
#let fa-notebook = fa-icon.with("\u{e201}")
#let fa-note-medical = fa-icon.with("\u{e200}")
#let fa-not-equal = fa-icon.with("\u{f53e}")
#let fa-notes = fa-icon.with("\u{e202}")
#let fa-notes-medical = fa-icon.with("\u{f481}")
#let fa-note-sticky = fa-icon.with("\u{f249}")
#let fa-sticky-note = fa-icon.with("\u{f249}")
#let fa-npm = fa-icon.with("\u{f3d4}")
#let fa-ns8 = fa-icon.with("\u{f3d5}")
#let fa-nutritionix = fa-icon.with("\u{f3d6}")
#let fa-o = fa-icon.with("\u{4f}")
#let fa-object-exclude = fa-icon.with("\u{e49c}")
#let fa-object-group = fa-icon.with("\u{f247}")
#let fa-object-intersect = fa-icon.with("\u{e49d}")
#let fa-objects-align-bottom = fa-icon.with("\u{e3bb}")
#let fa-objects-align-center-horizontal = fa-icon.with("\u{e3bc}")
#let fa-objects-align-center-vertical = fa-icon.with("\u{e3bd}")
#let fa-objects-align-left = fa-icon.with("\u{e3be}")
#let fa-objects-align-right = fa-icon.with("\u{e3bf}")
#let fa-objects-align-top = fa-icon.with("\u{e3c0}")
#let fa-objects-column = fa-icon.with("\u{e3c1}")
#let fa-object-subtract = fa-icon.with("\u{e49e}")
#let fa-object-ungroup = fa-icon.with("\u{f248}")
#let fa-object-union = fa-icon.with("\u{e49f}")
#let fa-octagon = fa-icon.with("\u{f306}")
#let fa-octagon-check = fa-icon.with("\u{e426}")
#let fa-octagon-divide = fa-icon.with("\u{e203}")
#let fa-octagon-exclamation = fa-icon.with("\u{e204}")
#let fa-octagon-minus = fa-icon.with("\u{f308}")
#let fa-minus-octagon = fa-icon.with("\u{f308}")
#let fa-octagon-plus = fa-icon.with("\u{f301}")
#let fa-plus-octagon = fa-icon.with("\u{f301}")
#let fa-octagon-xmark = fa-icon.with("\u{f2f0}")
#let fa-times-octagon = fa-icon.with("\u{f2f0}")
#let fa-xmark-octagon = fa-icon.with("\u{f2f0}")
#let fa-octopus = fa-icon.with("\u{e688}")
#let fa-octopus-deploy = fa-icon.with("\u{e082}")
#let fa-odnoklassniki = fa-icon.with("\u{f263}")
#let fa-odysee = fa-icon.with("\u{e5c6}")
#let fa-oil-can = fa-icon.with("\u{f613}")
#let fa-oil-can-drip = fa-icon.with("\u{e205}")
#let fa-oil-temperature = fa-icon.with("\u{f614}")
#let fa-oil-temp = fa-icon.with("\u{f614}")
#let fa-oil-well = fa-icon.with("\u{e532}")
#let fa-old-republic = fa-icon.with("\u{f510}")
#let fa-olive = fa-icon.with("\u{e316}")
#let fa-olive-branch = fa-icon.with("\u{e317}")
#let fa-om = fa-icon.with("\u{f679}")
#let fa-omega = fa-icon.with("\u{f67a}")
#let fa-onion = fa-icon.with("\u{e427}")
#let fa-opencart = fa-icon.with("\u{f23d}")
#let fa-openid = fa-icon.with("\u{f19b}")
#let fa-opensuse = fa-icon.with("\u{e62b}")
#let fa-opera = fa-icon.with("\u{f26a}")
#let fa-optin-monster = fa-icon.with("\u{f23c}")
#let fa-option = fa-icon.with("\u{e318}")
#let fa-orcid = fa-icon.with("\u{f8d2}")
#let fa-ornament = fa-icon.with("\u{f7b8}")
#let fa-osi = fa-icon.with("\u{f41a}")
#let fa-otter = fa-icon.with("\u{f700}")
#let fa-outdent = fa-icon.with("\u{f03b}")
#let fa-dedent = fa-icon.with("\u{f03b}")
#let fa-outlet = fa-icon.with("\u{e01c}")
#let fa-oven = fa-icon.with("\u{e01d}")
#let fa-overline = fa-icon.with("\u{f876}")
#let fa-p = fa-icon.with("\u{50}")
#let fa-padlet = fa-icon.with("\u{e4a0}")
#let fa-page = fa-icon.with("\u{e428}")
#let fa-page4 = fa-icon.with("\u{f3d7}")
#let fa-page-caret-down = fa-icon.with("\u{e429}")
#let fa-file-caret-down = fa-icon.with("\u{e429}")
#let fa-page-caret-up = fa-icon.with("\u{e42a}")
#let fa-file-caret-up = fa-icon.with("\u{e42a}")
#let fa-pagelines = fa-icon.with("\u{f18c}")
#let fa-pager = fa-icon.with("\u{f815}")
#let fa-paintbrush = fa-icon.with("\u{f1fc}")
#let fa-paint-brush = fa-icon.with("\u{f1fc}")
#let fa-paintbrush-fine = fa-icon.with("\u{f5a9}")
#let fa-paint-brush-alt = fa-icon.with("\u{f5a9}")
#let fa-paint-brush-fine = fa-icon.with("\u{f5a9}")
#let fa-paintbrush-alt = fa-icon.with("\u{f5a9}")
#let fa-paintbrush-pencil = fa-icon.with("\u{e206}")
#let fa-paint-roller = fa-icon.with("\u{f5aa}")
#let fa-palette = fa-icon.with("\u{f53f}")
#let fa-palfed = fa-icon.with("\u{f3d8}")
#let fa-pallet = fa-icon.with("\u{f482}")
#let fa-pallet-box = fa-icon.with("\u{e208}")
#let fa-pallet-boxes = fa-icon.with("\u{f483}")
#let fa-palette-boxes = fa-icon.with("\u{f483}")
#let fa-pallet-alt = fa-icon.with("\u{f483}")
#let fa-pancakes = fa-icon.with("\u{e42d}")
#let fa-panel-ews = fa-icon.with("\u{e42e}")
#let fa-panel-fire = fa-icon.with("\u{e42f}")
#let fa-pan-food = fa-icon.with("\u{e42b}")
#let fa-pan-frying = fa-icon.with("\u{e42c}")
#let fa-panorama = fa-icon.with("\u{e209}")
#let fa-paperclip = fa-icon.with("\u{f0c6}")
#let fa-paperclip-vertical = fa-icon.with("\u{e3c2}")
#let fa-paper-plane = fa-icon.with("\u{f1d8}")
#let fa-paper-plane-top = fa-icon.with("\u{e20a}")
#let fa-paper-plane-alt = fa-icon.with("\u{e20a}")
#let fa-send = fa-icon.with("\u{e20a}")
#let fa-parachute-box = fa-icon.with("\u{f4cd}")
#let fa-paragraph = fa-icon.with("\u{f1dd}")
#let fa-paragraph-left = fa-icon.with("\u{f878}")
#let fa-paragraph-rtl = fa-icon.with("\u{f878}")
#let fa-party-bell = fa-icon.with("\u{e31a}")
#let fa-party-horn = fa-icon.with("\u{e31b}")
#let fa-passport = fa-icon.with("\u{f5ab}")
#let fa-paste = fa-icon.with("\u{f0ea}")
#let fa-file-clipboard = fa-icon.with("\u{f0ea}")
#let fa-patreon = fa-icon.with("\u{f3d9}")
#let fa-pause = fa-icon.with("\u{f04c}")
#let fa-paw = fa-icon.with("\u{f1b0}")
#let fa-paw-claws = fa-icon.with("\u{f702}")
#let fa-paw-simple = fa-icon.with("\u{f701}")
#let fa-paw-alt = fa-icon.with("\u{f701}")
#let fa-paypal = fa-icon.with("\u{f1ed}")
#let fa-peace = fa-icon.with("\u{f67c}")
#let fa-peach = fa-icon.with("\u{e20b}")
#let fa-peanut = fa-icon.with("\u{e430}")
#let fa-peanuts = fa-icon.with("\u{e431}")
#let fa-peapod = fa-icon.with("\u{e31c}")
#let fa-pear = fa-icon.with("\u{e20c}")
#let fa-pedestal = fa-icon.with("\u{e20d}")
#let fa-pegasus = fa-icon.with("\u{f703}")
#let fa-pen = fa-icon.with("\u{f304}")
#let fa-pencil = fa-icon.with("\u{f303}")
#let fa-pencil-alt = fa-icon.with("\u{f303}")
#let fa-pencil-mechanical = fa-icon.with("\u{e5ca}")
#let fa-pencil-slash = fa-icon.with("\u{e215}")
#let fa-pen-circle = fa-icon.with("\u{e20e}")
#let fa-pen-clip = fa-icon.with("\u{f305}")
#let fa-pen-alt = fa-icon.with("\u{f305}")
#let fa-pen-clip-slash = fa-icon.with("\u{e20f}")
#let fa-pen-alt-slash = fa-icon.with("\u{e20f}")
#let fa-pen-fancy = fa-icon.with("\u{f5ac}")
#let fa-pen-fancy-slash = fa-icon.with("\u{e210}")
#let fa-pen-field = fa-icon.with("\u{e211}")
#let fa-pen-line = fa-icon.with("\u{e212}")
#let fa-pen-nib = fa-icon.with("\u{f5ad}")
#let fa-pen-nib-slash = fa-icon.with("\u{e4a1}")
#let fa-pen-paintbrush = fa-icon.with("\u{f618}")
#let fa-pencil-paintbrush = fa-icon.with("\u{f618}")
#let fa-pen-ruler = fa-icon.with("\u{f5ae}")
#let fa-pencil-ruler = fa-icon.with("\u{f5ae}")
#let fa-pen-slash = fa-icon.with("\u{e213}")
#let fa-pen-swirl = fa-icon.with("\u{e214}")
#let fa-pen-to-square = fa-icon.with("\u{f044}")
#let fa-edit = fa-icon.with("\u{f044}")
#let fa-people = fa-icon.with("\u{e216}")
#let fa-people-arrows = fa-icon.with("\u{e068}")
#let fa-people-arrows-left-right = fa-icon.with("\u{e068}")
#let fa-people-carry-box = fa-icon.with("\u{f4ce}")
#let fa-people-carry = fa-icon.with("\u{f4ce}")
#let fa-people-dress = fa-icon.with("\u{e217}")
#let fa-people-dress-simple = fa-icon.with("\u{e218}")
#let fa-people-group = fa-icon.with("\u{e533}")
#let fa-people-line = fa-icon.with("\u{e534}")
#let fa-people-pants = fa-icon.with("\u{e219}")
#let fa-people-pants-simple = fa-icon.with("\u{e21a}")
#let fa-people-pulling = fa-icon.with("\u{e535}")
#let fa-people-robbery = fa-icon.with("\u{e536}")
#let fa-people-roof = fa-icon.with("\u{e537}")
#let fa-people-simple = fa-icon.with("\u{e21b}")
#let fa-pepper = fa-icon.with("\u{e432}")
#let fa-pepper-hot = fa-icon.with("\u{f816}")
#let fa-perbyte = fa-icon.with("\u{e083}")
#let fa-percent = fa-icon.with("\u{25}")
#let fa-percentage = fa-icon.with("\u{25}")
#let fa-period = fa-icon.with("\u{2e}")
#let fa-periscope = fa-icon.with("\u{f3da}")
#let fa-person = fa-icon.with("\u{f183}")
#let fa-male = fa-icon.with("\u{f183}")
#let fa-person-arrow-down-to-line = fa-icon.with("\u{e538}")
#let fa-person-arrow-up-from-line = fa-icon.with("\u{e539}")
#let fa-person-biking = fa-icon.with("\u{f84a}")
#let fa-biking = fa-icon.with("\u{f84a}")
#let fa-person-biking-mountain = fa-icon.with("\u{f84b}")
#let fa-biking-mountain = fa-icon.with("\u{f84b}")
#let fa-person-booth = fa-icon.with("\u{f756}")
#let fa-person-breastfeeding = fa-icon.with("\u{e53a}")
#let fa-person-burst = fa-icon.with("\u{e53b}")
#let fa-person-cane = fa-icon.with("\u{e53c}")
#let fa-person-carry-box = fa-icon.with("\u{f4cf}")
#let fa-person-carry = fa-icon.with("\u{f4cf}")
#let fa-person-chalkboard = fa-icon.with("\u{e53d}")
#let fa-person-circle-check = fa-icon.with("\u{e53e}")
#let fa-person-circle-exclamation = fa-icon.with("\u{e53f}")
#let fa-person-circle-minus = fa-icon.with("\u{e540}")
#let fa-person-circle-plus = fa-icon.with("\u{e541}")
#let fa-person-circle-question = fa-icon.with("\u{e542}")
#let fa-person-circle-xmark = fa-icon.with("\u{e543}")
#let fa-person-digging = fa-icon.with("\u{f85e}")
#let fa-digging = fa-icon.with("\u{f85e}")
#let fa-person-dolly = fa-icon.with("\u{f4d0}")
#let fa-person-dolly-empty = fa-icon.with("\u{f4d1}")
#let fa-person-dots-from-line = fa-icon.with("\u{f470}")
#let fa-diagnoses = fa-icon.with("\u{f470}")
#let fa-person-dress = fa-icon.with("\u{f182}")
#let fa-female = fa-icon.with("\u{f182}")
#let fa-person-dress-burst = fa-icon.with("\u{e544}")
#let fa-person-dress-fairy = fa-icon.with("\u{e607}")
#let fa-person-dress-simple = fa-icon.with("\u{e21c}")
#let fa-person-drowning = fa-icon.with("\u{e545}")
#let fa-person-fairy = fa-icon.with("\u{e608}")
#let fa-person-falling = fa-icon.with("\u{e546}")
#let fa-person-falling-burst = fa-icon.with("\u{e547}")
#let fa-person-from-portal = fa-icon.with("\u{e023}")
#let fa-portal-exit = fa-icon.with("\u{e023}")
#let fa-person-half-dress = fa-icon.with("\u{e548}")
#let fa-person-harassing = fa-icon.with("\u{e549}")
#let fa-person-hiking = fa-icon.with("\u{f6ec}")
#let fa-hiking = fa-icon.with("\u{f6ec}")
#let fa-person-military-pointing = fa-icon.with("\u{e54a}")
#let fa-person-military-rifle = fa-icon.with("\u{e54b}")
#let fa-person-military-to-person = fa-icon.with("\u{e54c}")
#let fa-person-pinball = fa-icon.with("\u{e21d}")
#let fa-person-praying = fa-icon.with("\u{f683}")
#let fa-pray = fa-icon.with("\u{f683}")
#let fa-person-pregnant = fa-icon.with("\u{e31e}")
#let fa-person-rays = fa-icon.with("\u{e54d}")
#let fa-person-rifle = fa-icon.with("\u{e54e}")
#let fa-person-running = fa-icon.with("\u{f70c}")
#let fa-running = fa-icon.with("\u{f70c}")
#let fa-person-running-fast = fa-icon.with("\u{e5ff}")
#let fa-person-seat = fa-icon.with("\u{e21e}")
#let fa-person-seat-reclined = fa-icon.with("\u{e21f}")
#let fa-person-shelter = fa-icon.with("\u{e54f}")
#let fa-person-sign = fa-icon.with("\u{f757}")
#let fa-person-simple = fa-icon.with("\u{e220}")
#let fa-person-skating = fa-icon.with("\u{f7c5}")
#let fa-skating = fa-icon.with("\u{f7c5}")
#let fa-person-skiing = fa-icon.with("\u{f7c9}")
#let fa-skiing = fa-icon.with("\u{f7c9}")
#let fa-person-skiing-nordic = fa-icon.with("\u{f7ca}")
#let fa-skiing-nordic = fa-icon.with("\u{f7ca}")
#let fa-person-ski-jumping = fa-icon.with("\u{f7c7}")
#let fa-ski-jump = fa-icon.with("\u{f7c7}")
#let fa-person-ski-lift = fa-icon.with("\u{f7c8}")
#let fa-ski-lift = fa-icon.with("\u{f7c8}")
#let fa-person-sledding = fa-icon.with("\u{f7cb}")
#let fa-sledding = fa-icon.with("\u{f7cb}")
#let fa-person-snowboarding = fa-icon.with("\u{f7ce}")
#let fa-snowboarding = fa-icon.with("\u{f7ce}")
#let fa-person-snowmobiling = fa-icon.with("\u{f7d1}")
#let fa-snowmobile = fa-icon.with("\u{f7d1}")
#let fa-person-swimming = fa-icon.with("\u{f5c4}")
#let fa-swimmer = fa-icon.with("\u{f5c4}")
#let fa-person-through-window = fa-icon.with("\u{e5a9}")
#let fa-person-to-door = fa-icon.with("\u{e433}")
#let fa-person-to-portal = fa-icon.with("\u{e022}")
#let fa-portal-enter = fa-icon.with("\u{e022}")
#let fa-person-walking = fa-icon.with("\u{f554}")
#let fa-walking = fa-icon.with("\u{f554}")
#let fa-person-walking-arrow-loop-left = fa-icon.with("\u{e551}")
#let fa-person-walking-arrow-right = fa-icon.with("\u{e552}")
#let fa-person-walking-dashed-line-arrow-right = fa-icon.with("\u{e553}")
#let fa-person-walking-luggage = fa-icon.with("\u{e554}")
#let fa-person-walking-with-cane = fa-icon.with("\u{f29d}")
#let fa-blind = fa-icon.with("\u{f29d}")
#let fa-peseta-sign = fa-icon.with("\u{e221}")
#let fa-peso-sign = fa-icon.with("\u{e222}")
#let fa-phabricator = fa-icon.with("\u{f3db}")
#let fa-phoenix-framework = fa-icon.with("\u{f3dc}")
#let fa-phoenix-squadron = fa-icon.with("\u{f511}")
#let fa-phone = fa-icon.with("\u{f095}")
#let fa-phone-arrow-down-left = fa-icon.with("\u{e223}")
#let fa-phone-arrow-down = fa-icon.with("\u{e223}")
#let fa-phone-incoming = fa-icon.with("\u{e223}")
#let fa-phone-arrow-right = fa-icon.with("\u{e5be}")
#let fa-phone-arrow-up-right = fa-icon.with("\u{e224}")
#let fa-phone-arrow-up = fa-icon.with("\u{e224}")
#let fa-phone-outgoing = fa-icon.with("\u{e224}")
#let fa-phone-flip = fa-icon.with("\u{f879}")
#let fa-phone-alt = fa-icon.with("\u{f879}")
#let fa-phone-hangup = fa-icon.with("\u{e225}")
#let fa-phone-intercom = fa-icon.with("\u{e434}")
#let fa-phone-missed = fa-icon.with("\u{e226}")
#let fa-phone-office = fa-icon.with("\u{f67d}")
#let fa-phone-plus = fa-icon.with("\u{f4d2}")
#let fa-phone-rotary = fa-icon.with("\u{f8d3}")
#let fa-phone-slash = fa-icon.with("\u{f3dd}")
#let fa-phone-volume = fa-icon.with("\u{f2a0}")
#let fa-volume-control-phone = fa-icon.with("\u{f2a0}")
#let fa-phone-xmark = fa-icon.with("\u{e227}")
#let fa-photo-film = fa-icon.with("\u{f87c}")
#let fa-photo-video = fa-icon.with("\u{f87c}")
#let fa-photo-film-music = fa-icon.with("\u{e228}")
#let fa-php = fa-icon.with("\u{f457}")
#let fa-pi = fa-icon.with("\u{f67e}")
#let fa-piano = fa-icon.with("\u{f8d4}")
#let fa-piano-keyboard = fa-icon.with("\u{f8d5}")
#let fa-pickaxe = fa-icon.with("\u{e5bf}")
#let fa-pickleball = fa-icon.with("\u{e435}")
#let fa-pie = fa-icon.with("\u{f705}")
#let fa-pied-piper = fa-icon.with("\u{f2ae}")
#let fa-pied-piper-alt = fa-icon.with("\u{f1a8}")
#let fa-pied-piper-hat = fa-icon.with("\u{f4e5}")
#let fa-pied-piper-pp = fa-icon.with("\u{f1a7}")
#let fa-pig = fa-icon.with("\u{f706}")
#let fa-piggy-bank = fa-icon.with("\u{f4d3}")
#let fa-pills = fa-icon.with("\u{f484}")
#let fa-pinata = fa-icon.with("\u{e3c3}")
#let fa-pinball = fa-icon.with("\u{e229}")
#let fa-pineapple = fa-icon.with("\u{e31f}")
#let fa-pinterest = fa-icon.with("\u{f0d2}")
#let fa-pinterest-p = fa-icon.with("\u{f231}")
#let fa-pipe = fa-icon.with("\u{7c}")
#let fa-pipe-circle-check = fa-icon.with("\u{e436}")
#let fa-pipe-collar = fa-icon.with("\u{e437}")
#let fa-pipe-section = fa-icon.with("\u{e438}")
#let fa-pipe-smoking = fa-icon.with("\u{e3c4}")
#let fa-pipe-valve = fa-icon.with("\u{e439}")
#let fa-pix = fa-icon.with("\u{e43a}")
#let fa-pixiv = fa-icon.with("\u{e640}")
#let fa-pizza = fa-icon.with("\u{f817}")
#let fa-pizza-slice = fa-icon.with("\u{f818}")
#let fa-place-of-worship = fa-icon.with("\u{f67f}")
#let fa-plane = fa-icon.with("\u{f072}")
#let fa-plane-arrival = fa-icon.with("\u{f5af}")
#let fa-plane-circle-check = fa-icon.with("\u{e555}")
#let fa-plane-circle-exclamation = fa-icon.with("\u{e556}")
#let fa-plane-circle-xmark = fa-icon.with("\u{e557}")
#let fa-plane-departure = fa-icon.with("\u{f5b0}")
#let fa-plane-engines = fa-icon.with("\u{f3de}")
#let fa-plane-alt = fa-icon.with("\u{f3de}")
#let fa-plane-lock = fa-icon.with("\u{e558}")
#let fa-plane-prop = fa-icon.with("\u{e22b}")
#let fa-plane-slash = fa-icon.with("\u{e069}")
#let fa-plane-tail = fa-icon.with("\u{e22c}")
#let fa-planet-moon = fa-icon.with("\u{e01f}")
#let fa-planet-ringed = fa-icon.with("\u{e020}")
#let fa-plane-up = fa-icon.with("\u{e22d}")
#let fa-plane-up-slash = fa-icon.with("\u{e22e}")
#let fa-plant-wilt = fa-icon.with("\u{e5aa}")
#let fa-plate-utensils = fa-icon.with("\u{e43b}")
#let fa-plate-wheat = fa-icon.with("\u{e55a}")
#let fa-play = fa-icon.with("\u{f04b}")
#let fa-play-pause = fa-icon.with("\u{e22f}")
#let fa-playstation = fa-icon.with("\u{f3df}")
#let fa-plug = fa-icon.with("\u{f1e6}")
#let fa-plug-circle-bolt = fa-icon.with("\u{e55b}")
#let fa-plug-circle-check = fa-icon.with("\u{e55c}")
#let fa-plug-circle-exclamation = fa-icon.with("\u{e55d}")
#let fa-plug-circle-minus = fa-icon.with("\u{e55e}")
#let fa-plug-circle-plus = fa-icon.with("\u{e55f}")
#let fa-plug-circle-xmark = fa-icon.with("\u{e560}")
#let fa-plus = fa-icon.with("\u{2b}")
#let fa-add = fa-icon.with("\u{2b}")
#let fa-plus-large = fa-icon.with("\u{e59e}")
#let fa-plus-minus = fa-icon.with("\u{e43c}")
#let fa-podcast = fa-icon.with("\u{f2ce}")
#let fa-podium = fa-icon.with("\u{f680}")
#let fa-podium-star = fa-icon.with("\u{f758}")
#let fa-police-box = fa-icon.with("\u{e021}")
#let fa-poll-people = fa-icon.with("\u{f759}")
#let fa-pompebled = fa-icon.with("\u{e43d}")
#let fa-poo = fa-icon.with("\u{f2fe}")
#let fa-pool-8-ball = fa-icon.with("\u{e3c5}")
#let fa-poop = fa-icon.with("\u{f619}")
#let fa-poo-storm = fa-icon.with("\u{f75a}")
#let fa-poo-bolt = fa-icon.with("\u{f75a}")
#let fa-popcorn = fa-icon.with("\u{f819}")
#let fa-popsicle = fa-icon.with("\u{e43e}")
#let fa-potato = fa-icon.with("\u{e440}")
#let fa-pot-food = fa-icon.with("\u{e43f}")
#let fa-power-off = fa-icon.with("\u{f011}")
#let fa-prescription = fa-icon.with("\u{f5b1}")
#let fa-prescription-bottle = fa-icon.with("\u{f485}")
#let fa-prescription-bottle-medical = fa-icon.with("\u{f486}")
#let fa-prescription-bottle-alt = fa-icon.with("\u{f486}")
#let fa-prescription-bottle-pill = fa-icon.with("\u{e5c0}")
#let fa-presentation-screen = fa-icon.with("\u{f685}")
#let fa-presentation = fa-icon.with("\u{f685}")
#let fa-pretzel = fa-icon.with("\u{e441}")
#let fa-print = fa-icon.with("\u{f02f}")
#let fa-print-magnifying-glass = fa-icon.with("\u{f81a}")
#let fa-print-search = fa-icon.with("\u{f81a}")
#let fa-print-slash = fa-icon.with("\u{f686}")
#let fa-product-hunt = fa-icon.with("\u{f288}")
#let fa-projector = fa-icon.with("\u{f8d6}")
#let fa-pump = fa-icon.with("\u{e442}")
#let fa-pumpkin = fa-icon.with("\u{f707}")
#let fa-pump-medical = fa-icon.with("\u{e06a}")
#let fa-pump-soap = fa-icon.with("\u{e06b}")
#let fa-pushed = fa-icon.with("\u{f3e1}")
#let fa-puzzle = fa-icon.with("\u{e443}")
#let fa-puzzle-piece = fa-icon.with("\u{f12e}")
#let fa-puzzle-piece-simple = fa-icon.with("\u{e231}")
#let fa-puzzle-piece-alt = fa-icon.with("\u{e231}")
#let fa-python = fa-icon.with("\u{f3e2}")
#let fa-q = fa-icon.with("\u{51}")
#let fa-qq = fa-icon.with("\u{f1d6}")
#let fa-qrcode = fa-icon.with("\u{f029}")
#let fa-question = fa-icon.with("\u{3f}")
#let fa-quinscape = fa-icon.with("\u{f459}")
#let fa-quora = fa-icon.with("\u{f2c4}")
#let fa-quote-left = fa-icon.with("\u{f10d}")
#let fa-quote-left-alt = fa-icon.with("\u{f10d}")
#let fa-quote-right = fa-icon.with("\u{f10e}")
#let fa-quote-right-alt = fa-icon.with("\u{f10e}")
#let fa-quotes = fa-icon.with("\u{e234}")
#let fa-r = fa-icon.with("\u{52}")
#let fa-rabbit = fa-icon.with("\u{f708}")
#let fa-rabbit-running = fa-icon.with("\u{f709}")
#let fa-rabbit-fast = fa-icon.with("\u{f709}")
#let fa-raccoon = fa-icon.with("\u{e613}")
#let fa-racquet = fa-icon.with("\u{f45a}")
#let fa-radar = fa-icon.with("\u{e024}")
#let fa-radiation = fa-icon.with("\u{f7b9}")
#let fa-radio = fa-icon.with("\u{f8d7}")
#let fa-radio-tuner = fa-icon.with("\u{f8d8}")
#let fa-radio-alt = fa-icon.with("\u{f8d8}")
#let fa-rainbow = fa-icon.with("\u{f75b}")
#let fa-raindrops = fa-icon.with("\u{f75c}")
#let fa-ram = fa-icon.with("\u{f70a}")
#let fa-ramp-loading = fa-icon.with("\u{f4d4}")
#let fa-ranking-star = fa-icon.with("\u{e561}")
#let fa-raspberry-pi = fa-icon.with("\u{f7bb}")
#let fa-ravelry = fa-icon.with("\u{f2d9}")
#let fa-raygun = fa-icon.with("\u{e025}")
#let fa-react = fa-icon.with("\u{f41b}")
#let fa-reacteurope = fa-icon.with("\u{f75d}")
#let fa-readme = fa-icon.with("\u{f4d5}")
#let fa-rebel = fa-icon.with("\u{f1d0}")
#let fa-receipt = fa-icon.with("\u{f543}")
#let fa-record-vinyl = fa-icon.with("\u{f8d9}")
#let fa-rectangle = fa-icon.with("\u{f2fa}")
#let fa-rectangle-landscape = fa-icon.with("\u{f2fa}")
#let fa-rectangle-ad = fa-icon.with("\u{f641}")
#let fa-ad = fa-icon.with("\u{f641}")
#let fa-rectangle-barcode = fa-icon.with("\u{f463}")
#let fa-barcode-alt = fa-icon.with("\u{f463}")
#let fa-rectangle-code = fa-icon.with("\u{e322}")
#let fa-rectangle-history = fa-icon.with("\u{e4a2}")
#let fa-rectangle-history-circle-plus = fa-icon.with("\u{e4a3}")
#let fa-rectangle-history-circle-user = fa-icon.with("\u{e4a4}")
#let fa-rectangle-list = fa-icon.with("\u{f022}")
#let fa-list-alt = fa-icon.with("\u{f022}")
#let fa-rectangle-pro = fa-icon.with("\u{e235}")
#let fa-pro = fa-icon.with("\u{e235}")
#let fa-rectangles-mixed = fa-icon.with("\u{e323}")
#let fa-rectangle-terminal = fa-icon.with("\u{e236}")
#let fa-rectangle-vertical = fa-icon.with("\u{f2fb}")
#let fa-rectangle-portrait = fa-icon.with("\u{f2fb}")
#let fa-rectangle-vertical-history = fa-icon.with("\u{e237}")
#let fa-rectangle-wide = fa-icon.with("\u{f2fc}")
#let fa-rectangle-xmark = fa-icon.with("\u{f410}")
#let fa-rectangle-times = fa-icon.with("\u{f410}")
#let fa-times-rectangle = fa-icon.with("\u{f410}")
#let fa-window-close = fa-icon.with("\u{f410}")
#let fa-recycle = fa-icon.with("\u{f1b8}")
#let fa-reddit = fa-icon.with("\u{f1a1}")
#let fa-reddit-alien = fa-icon.with("\u{f281}")
#let fa-redhat = fa-icon.with("\u{f7bc}")
#let fa-red-river = fa-icon.with("\u{f3e3}")
#let fa-reel = fa-icon.with("\u{e238}")
#let fa-reflect-both = fa-icon.with("\u{e66f}")
#let fa-reflect-horizontal = fa-icon.with("\u{e664}")
#let fa-reflect-vertical = fa-icon.with("\u{e665}")
#let fa-refrigerator = fa-icon.with("\u{e026}")
#let fa-registered = fa-icon.with("\u{f25d}")
#let fa-renren = fa-icon.with("\u{f18b}")
#let fa-repeat = fa-icon.with("\u{f363}")
#let fa-repeat-1 = fa-icon.with("\u{f365}")
#let fa-reply = fa-icon.with("\u{f3e5}")
#let fa-mail-reply = fa-icon.with("\u{f3e5}")
#let fa-reply-all = fa-icon.with("\u{f122}")
#let fa-mail-reply-all = fa-icon.with("\u{f122}")
#let fa-reply-clock = fa-icon.with("\u{e239}")
#let fa-reply-time = fa-icon.with("\u{e239}")
#let fa-replyd = fa-icon.with("\u{f3e6}")
#let fa-republican = fa-icon.with("\u{f75e}")
#let fa-researchgate = fa-icon.with("\u{f4f8}")
#let fa-resolving = fa-icon.with("\u{f3e7}")
#let fa-restroom = fa-icon.with("\u{f7bd}")
#let fa-restroom-simple = fa-icon.with("\u{e23a}")
#let fa-retweet = fa-icon.with("\u{f079}")
#let fa-rev = fa-icon.with("\u{f5b2}")
#let fa-rhombus = fa-icon.with("\u{e23b}")
#let fa-ribbon = fa-icon.with("\u{f4d6}")
#let fa-right = fa-icon.with("\u{f356}")
#let fa-arrow-alt-right = fa-icon.with("\u{f356}")
#let fa-right-from-bracket = fa-icon.with("\u{f2f5}")
#let fa-sign-out-alt = fa-icon.with("\u{f2f5}")
#let fa-right-from-line = fa-icon.with("\u{f347}")
#let fa-arrow-alt-from-left = fa-icon.with("\u{f347}")
#let fa-right-left = fa-icon.with("\u{f362}")
#let fa-exchange-alt = fa-icon.with("\u{f362}")
#let fa-right-left-large = fa-icon.with("\u{e5e1}")
#let fa-right-long = fa-icon.with("\u{f30b}")
#let fa-long-arrow-alt-right = fa-icon.with("\u{f30b}")
#let fa-right-long-to-line = fa-icon.with("\u{e444}")
#let fa-right-to-bracket = fa-icon.with("\u{f2f6}")
#let fa-sign-in-alt = fa-icon.with("\u{f2f6}")
#let fa-right-to-line = fa-icon.with("\u{f34c}")
#let fa-arrow-alt-to-right = fa-icon.with("\u{f34c}")
#let fa-ring = fa-icon.with("\u{f70b}")
#let fa-ring-diamond = fa-icon.with("\u{e5ab}")
#let fa-rings-wedding = fa-icon.with("\u{f81b}")
#let fa-road = fa-icon.with("\u{f018}")
#let fa-road-barrier = fa-icon.with("\u{e562}")
#let fa-road-bridge = fa-icon.with("\u{e563}")
#let fa-road-circle-check = fa-icon.with("\u{e564}")
#let fa-road-circle-exclamation = fa-icon.with("\u{e565}")
#let fa-road-circle-xmark = fa-icon.with("\u{e566}")
#let fa-road-lock = fa-icon.with("\u{e567}")
#let fa-road-spikes = fa-icon.with("\u{e568}")
#let fa-robot = fa-icon.with("\u{f544}")
#let fa-robot-astromech = fa-icon.with("\u{e2d2}")
#let fa-rocket = fa-icon.with("\u{f135}")
#let fa-rocketchat = fa-icon.with("\u{f3e8}")
#let fa-rocket-launch = fa-icon.with("\u{e027}")
#let fa-rockrms = fa-icon.with("\u{f3e9}")
#let fa-roller-coaster = fa-icon.with("\u{e324}")
#let fa-rotate = fa-icon.with("\u{f2f1}")
#let fa-sync-alt = fa-icon.with("\u{f2f1}")
#let fa-rotate-exclamation = fa-icon.with("\u{e23c}")
#let fa-rotate-left = fa-icon.with("\u{f2ea}")
#let fa-rotate-back = fa-icon.with("\u{f2ea}")
#let fa-rotate-backward = fa-icon.with("\u{f2ea}")
#let fa-undo-alt = fa-icon.with("\u{f2ea}")
#let fa-rotate-reverse = fa-icon.with("\u{e631}")
#let fa-rotate-right = fa-icon.with("\u{f2f9}")
#let fa-redo-alt = fa-icon.with("\u{f2f9}")
#let fa-rotate-forward = fa-icon.with("\u{f2f9}")
#let fa-route = fa-icon.with("\u{f4d7}")
#let fa-route-highway = fa-icon.with("\u{f61a}")
#let fa-route-interstate = fa-icon.with("\u{f61b}")
#let fa-router = fa-icon.with("\u{f8da}")
#let fa-r-project = fa-icon.with("\u{f4f7}")
#let fa-rss = fa-icon.with("\u{f09e}")
#let fa-feed = fa-icon.with("\u{f09e}")
#let fa-ruble-sign = fa-icon.with("\u{f158}")
#let fa-rouble = fa-icon.with("\u{f158}")
#let fa-rub = fa-icon.with("\u{f158}")
#let fa-ruble = fa-icon.with("\u{f158}")
#let fa-rug = fa-icon.with("\u{e569}")
#let fa-rugby-ball = fa-icon.with("\u{e3c6}")
#let fa-ruler = fa-icon.with("\u{f545}")
#let fa-ruler-combined = fa-icon.with("\u{f546}")
#let fa-ruler-horizontal = fa-icon.with("\u{f547}")
#let fa-ruler-triangle = fa-icon.with("\u{f61c}")
#let fa-ruler-vertical = fa-icon.with("\u{f548}")
#let fa-rupee-sign = fa-icon.with("\u{f156}")
#let fa-rupee = fa-icon.with("\u{f156}")
#let fa-rupiah-sign = fa-icon.with("\u{e23d}")
#let fa-rust = fa-icon.with("\u{e07a}")
#let fa-rv = fa-icon.with("\u{f7be}")
#let fa-s = fa-icon.with("\u{53}")
#let fa-sack = fa-icon.with("\u{f81c}")
#let fa-sack-dollar = fa-icon.with("\u{f81d}")
#let fa-sack-xmark = fa-icon.with("\u{e56a}")
#let fa-safari = fa-icon.with("\u{f267}")
#let fa-sailboat = fa-icon.with("\u{e445}")
#let fa-salad = fa-icon.with("\u{f81e}")
#let fa-bowl-salad = fa-icon.with("\u{f81e}")
#let fa-salesforce = fa-icon.with("\u{f83b}")
#let fa-salt-shaker = fa-icon.with("\u{e446}")
#let fa-sandwich = fa-icon.with("\u{f81f}")
#let fa-sass = fa-icon.with("\u{f41e}")
#let fa-satellite = fa-icon.with("\u{f7bf}")
#let fa-satellite-dish = fa-icon.with("\u{f7c0}")
#let fa-sausage = fa-icon.with("\u{f820}")
#let fa-saxophone = fa-icon.with("\u{f8dc}")
#let fa-saxophone-fire = fa-icon.with("\u{f8db}")
#let fa-sax-hot = fa-icon.with("\u{f8db}")
#let fa-scale-balanced = fa-icon.with("\u{f24e}")
#let fa-balance-scale = fa-icon.with("\u{f24e}")
#let fa-scale-unbalanced = fa-icon.with("\u{f515}")
#let fa-balance-scale-left = fa-icon.with("\u{f515}")
#let fa-scale-unbalanced-flip = fa-icon.with("\u{f516}")
#let fa-balance-scale-right = fa-icon.with("\u{f516}")
#let fa-scalpel = fa-icon.with("\u{f61d}")
#let fa-scalpel-line-dashed = fa-icon.with("\u{f61e}")
#let fa-scalpel-path = fa-icon.with("\u{f61e}")
#let fa-scanner-gun = fa-icon.with("\u{f488}")
#let fa-scanner = fa-icon.with("\u{f488}")
#let fa-scanner-image = fa-icon.with("\u{f8f3}")
#let fa-scanner-keyboard = fa-icon.with("\u{f489}")
#let fa-scanner-touchscreen = fa-icon.with("\u{f48a}")
#let fa-scarecrow = fa-icon.with("\u{f70d}")
#let fa-scarf = fa-icon.with("\u{f7c1}")
#let fa-schlix = fa-icon.with("\u{f3ea}")
#let fa-school = fa-icon.with("\u{f549}")
#let fa-school-circle-check = fa-icon.with("\u{e56b}")
#let fa-school-circle-exclamation = fa-icon.with("\u{e56c}")
#let fa-school-circle-xmark = fa-icon.with("\u{e56d}")
#let fa-school-flag = fa-icon.with("\u{e56e}")
#let fa-school-lock = fa-icon.with("\u{e56f}")
#let fa-scissors = fa-icon.with("\u{f0c4}")
#let fa-cut = fa-icon.with("\u{f0c4}")
#let fa-screencast = fa-icon.with("\u{e23e}")
#let fa-screenpal = fa-icon.with("\u{e570}")
#let fa-screen-users = fa-icon.with("\u{f63d}")
#let fa-users-class = fa-icon.with("\u{f63d}")
#let fa-screwdriver = fa-icon.with("\u{f54a}")
#let fa-screwdriver-wrench = fa-icon.with("\u{f7d9}")
#let fa-tools = fa-icon.with("\u{f7d9}")
#let fa-scribble = fa-icon.with("\u{e23f}")
#let fa-scribd = fa-icon.with("\u{f28a}")
#let fa-scroll = fa-icon.with("\u{f70e}")
#let fa-scroll-old = fa-icon.with("\u{f70f}")
#let fa-scroll-torah = fa-icon.with("\u{f6a0}")
#let fa-torah = fa-icon.with("\u{f6a0}")
#let fa-scrubber = fa-icon.with("\u{f2f8}")
#let fa-scythe = fa-icon.with("\u{f710}")
#let fa-sd-card = fa-icon.with("\u{f7c2}")
#let fa-sd-cards = fa-icon.with("\u{e240}")
#let fa-seal = fa-icon.with("\u{e241}")
#let fa-seal-exclamation = fa-icon.with("\u{e242}")
#let fa-seal-question = fa-icon.with("\u{e243}")
#let fa-searchengin = fa-icon.with("\u{f3eb}")
#let fa-seat-airline = fa-icon.with("\u{e244}")
#let fa-section = fa-icon.with("\u{e447}")
#let fa-seedling = fa-icon.with("\u{f4d8}")
#let fa-sprout = fa-icon.with("\u{f4d8}")
#let fa-sellcast = fa-icon.with("\u{f2da}")
#let fa-sellsy = fa-icon.with("\u{f213}")
#let fa-semicolon = fa-icon.with("\u{3b}")
#let fa-send-back = fa-icon.with("\u{f87e}")
#let fa-send-backward = fa-icon.with("\u{f87f}")
#let fa-sensor = fa-icon.with("\u{e028}")
#let fa-sensor-cloud = fa-icon.with("\u{e02c}")
#let fa-sensor-smoke = fa-icon.with("\u{e02c}")
#let fa-sensor-fire = fa-icon.with("\u{e02a}")
#let fa-sensor-on = fa-icon.with("\u{e02b}")
#let fa-sensor-triangle-exclamation = fa-icon.with("\u{e029}")
#let fa-sensor-alert = fa-icon.with("\u{e029}")
#let fa-server = fa-icon.with("\u{f233}")
#let fa-servicestack = fa-icon.with("\u{f3ec}")
#let fa-shapes = fa-icon.with("\u{f61f}")
#let fa-triangle-circle-square = fa-icon.with("\u{f61f}")
#let fa-share = fa-icon.with("\u{f064}")
#let fa-mail-forward = fa-icon.with("\u{f064}")
#let fa-share-all = fa-icon.with("\u{f367}")
#let fa-share-from-square = fa-icon.with("\u{f14d}")
#let fa-share-square = fa-icon.with("\u{f14d}")
#let fa-share-nodes = fa-icon.with("\u{f1e0}")
#let fa-share-alt = fa-icon.with("\u{f1e0}")
#let fa-sheep = fa-icon.with("\u{f711}")
#let fa-sheet-plastic = fa-icon.with("\u{e571}")
#let fa-shekel-sign = fa-icon.with("\u{f20b}")
#let fa-ils = fa-icon.with("\u{f20b}")
#let fa-shekel = fa-icon.with("\u{f20b}")
#let fa-sheqel = fa-icon.with("\u{f20b}")
#let fa-sheqel-sign = fa-icon.with("\u{f20b}")
#let fa-shelves = fa-icon.with("\u{f480}")
#let fa-inventory = fa-icon.with("\u{f480}")
#let fa-shelves-empty = fa-icon.with("\u{e246}")
#let fa-shield = fa-icon.with("\u{f132}")
#let fa-shield-blank = fa-icon.with("\u{f132}")
#let fa-shield-cat = fa-icon.with("\u{e572}")
#let fa-shield-check = fa-icon.with("\u{f2f7}")
#let fa-shield-cross = fa-icon.with("\u{f712}")
#let fa-shield-dog = fa-icon.with("\u{e573}")
#let fa-shield-exclamation = fa-icon.with("\u{e247}")
#let fa-shield-halved = fa-icon.with("\u{f3ed}")
#let fa-shield-alt = fa-icon.with("\u{f3ed}")
#let fa-shield-heart = fa-icon.with("\u{e574}")
#let fa-shield-keyhole = fa-icon.with("\u{e248}")
#let fa-shield-minus = fa-icon.with("\u{e249}")
#let fa-shield-plus = fa-icon.with("\u{e24a}")
#let fa-shield-quartered = fa-icon.with("\u{e575}")
#let fa-shield-slash = fa-icon.with("\u{e24b}")
#let fa-shield-virus = fa-icon.with("\u{e06c}")
#let fa-shield-xmark = fa-icon.with("\u{e24c}")
#let fa-shield-times = fa-icon.with("\u{e24c}")
#let fa-ship = fa-icon.with("\u{f21a}")
#let fa-shirt = fa-icon.with("\u{f553}")
#let fa-t-shirt = fa-icon.with("\u{f553}")
#let fa-tshirt = fa-icon.with("\u{f553}")
#let fa-shirt-long-sleeve = fa-icon.with("\u{e3c7}")
#let fa-shirt-running = fa-icon.with("\u{e3c8}")
#let fa-shirtsinbulk = fa-icon.with("\u{f214}")
#let fa-shirt-tank-top = fa-icon.with("\u{e3c9}")
#let fa-shish-kebab = fa-icon.with("\u{f821}")
#let fa-shoelace = fa-icon.with("\u{e60c}")
#let fa-shoe-prints = fa-icon.with("\u{f54b}")
#let fa-shop = fa-icon.with("\u{f54f}")
#let fa-store-alt = fa-icon.with("\u{f54f}")
#let fa-shopify = fa-icon.with("\u{e057}")
#let fa-shop-lock = fa-icon.with("\u{e4a5}")
#let fa-shop-slash = fa-icon.with("\u{e070}")
#let fa-store-alt-slash = fa-icon.with("\u{e070}")
#let fa-shopware = fa-icon.with("\u{f5b5}")
#let fa-shovel = fa-icon.with("\u{f713}")
#let fa-shovel-snow = fa-icon.with("\u{f7c3}")
#let fa-shower = fa-icon.with("\u{f2cc}")
#let fa-shower-down = fa-icon.with("\u{e24d}")
#let fa-shower-alt = fa-icon.with("\u{e24d}")
#let fa-shredder = fa-icon.with("\u{f68a}")
#let fa-shrimp = fa-icon.with("\u{e448}")
#let fa-shuffle = fa-icon.with("\u{f074}")
#let fa-random = fa-icon.with("\u{f074}")
#let fa-shutters = fa-icon.with("\u{e449}")
#let fa-shuttlecock = fa-icon.with("\u{f45b}")
#let fa-shuttle-space = fa-icon.with("\u{f197}")
#let fa-space-shuttle = fa-icon.with("\u{f197}")
#let fa-sickle = fa-icon.with("\u{f822}")
#let fa-sidebar = fa-icon.with("\u{e24e}")
#let fa-sidebar-flip = fa-icon.with("\u{e24f}")
#let fa-sigma = fa-icon.with("\u{f68b}")
#let fa-signal = fa-icon.with("\u{f012}")
#let fa-signal-5 = fa-icon.with("\u{f012}")
#let fa-signal-perfect = fa-icon.with("\u{f012}")
#let fa-signal-bars = fa-icon.with("\u{f690}")
#let fa-signal-alt = fa-icon.with("\u{f690}")
#let fa-signal-alt-4 = fa-icon.with("\u{f690}")
#let fa-signal-bars-strong = fa-icon.with("\u{f690}")
#let fa-signal-bars-fair = fa-icon.with("\u{f692}")
#let fa-signal-alt-2 = fa-icon.with("\u{f692}")
#let fa-signal-bars-good = fa-icon.with("\u{f693}")
#let fa-signal-alt-3 = fa-icon.with("\u{f693}")
#let fa-signal-bars-slash = fa-icon.with("\u{f694}")
#let fa-signal-alt-slash = fa-icon.with("\u{f694}")
#let fa-signal-bars-weak = fa-icon.with("\u{f691}")
#let fa-signal-alt-1 = fa-icon.with("\u{f691}")
#let fa-signal-fair = fa-icon.with("\u{f68d}")
#let fa-signal-2 = fa-icon.with("\u{f68d}")
#let fa-signal-good = fa-icon.with("\u{f68e}")
#let fa-signal-3 = fa-icon.with("\u{f68e}")
#let fa-signal-messenger = fa-icon.with("\u{e663}")
#let fa-signal-slash = fa-icon.with("\u{f695}")
#let fa-signal-stream = fa-icon.with("\u{f8dd}")
#let fa-signal-stream-slash = fa-icon.with("\u{e250}")
#let fa-signal-strong = fa-icon.with("\u{f68f}")
#let fa-signal-4 = fa-icon.with("\u{f68f}")
#let fa-signal-weak = fa-icon.with("\u{f68c}")
#let fa-signal-1 = fa-icon.with("\u{f68c}")
#let fa-signature = fa-icon.with("\u{f5b7}")
#let fa-signature-lock = fa-icon.with("\u{e3ca}")
#let fa-signature-slash = fa-icon.with("\u{e3cb}")
#let fa-sign-hanging = fa-icon.with("\u{f4d9}")
#let fa-sign = fa-icon.with("\u{f4d9}")
#let fa-sign-post = fa-icon.with("\u{e624}")
#let fa-sign-posts = fa-icon.with("\u{e625}")
#let fa-sign-posts-wrench = fa-icon.with("\u{e626}")
#let fa-signs-post = fa-icon.with("\u{f277}")
#let fa-map-signs = fa-icon.with("\u{f277}")
#let fa-sim-card = fa-icon.with("\u{f7c4}")
#let fa-sim-cards = fa-icon.with("\u{e251}")
#let fa-simplybuilt = fa-icon.with("\u{f215}")
#let fa-sink = fa-icon.with("\u{e06d}")
#let fa-siren = fa-icon.with("\u{e02d}")
#let fa-siren-on = fa-icon.with("\u{e02e}")
#let fa-sistrix = fa-icon.with("\u{f3ee}")
#let fa-sitemap = fa-icon.with("\u{f0e8}")
#let fa-sith = fa-icon.with("\u{f512}")
#let fa-sitrox = fa-icon.with("\u{e44a}")
#let fa-skeleton = fa-icon.with("\u{f620}")
#let fa-skeleton-ribs = fa-icon.with("\u{e5cb}")
#let fa-sketch = fa-icon.with("\u{f7c6}")
#let fa-ski-boot = fa-icon.with("\u{e3cc}")
#let fa-ski-boot-ski = fa-icon.with("\u{e3cd}")
#let fa-skull = fa-icon.with("\u{f54c}")
#let fa-skull-cow = fa-icon.with("\u{f8de}")
#let fa-skull-crossbones = fa-icon.with("\u{f714}")
#let fa-skyatlas = fa-icon.with("\u{f216}")
#let fa-skype = fa-icon.with("\u{f17e}")
#let fa-slack = fa-icon.with("\u{f198}")
#let fa-slack-hash = fa-icon.with("\u{f198}")
#let fa-slash = fa-icon.with("\u{f715}")
#let fa-slash-back = fa-icon.with("\u{5c}")
#let fa-slash-forward = fa-icon.with("\u{2f}")
#let fa-sleigh = fa-icon.with("\u{f7cc}")
#let fa-slider = fa-icon.with("\u{e252}")
#let fa-sliders = fa-icon.with("\u{f1de}")
#let fa-sliders-h = fa-icon.with("\u{f1de}")
#let fa-sliders-simple = fa-icon.with("\u{e253}")
#let fa-sliders-up = fa-icon.with("\u{f3f1}")
#let fa-sliders-v = fa-icon.with("\u{f3f1}")
#let fa-slideshare = fa-icon.with("\u{f1e7}")
#let fa-slot-machine = fa-icon.with("\u{e3ce}")
#let fa-smog = fa-icon.with("\u{f75f}")
#let fa-smoke = fa-icon.with("\u{f760}")
#let fa-smoking = fa-icon.with("\u{f48d}")
#let fa-snake = fa-icon.with("\u{f716}")
#let fa-snapchat = fa-icon.with("\u{f2ab}")
#let fa-snapchat-ghost = fa-icon.with("\u{f2ab}")
#let fa-snooze = fa-icon.with("\u{f880}")
#let fa-zzz = fa-icon.with("\u{f880}")
#let fa-snow-blowing = fa-icon.with("\u{f761}")
#let fa-snowflake = fa-icon.with("\u{f2dc}")
#let fa-snowflake-droplets = fa-icon.with("\u{e5c1}")
#let fa-snowflakes = fa-icon.with("\u{f7cf}")
#let fa-snowman = fa-icon.with("\u{f7d0}")
#let fa-snowman-head = fa-icon.with("\u{f79b}")
#let fa-frosty-head = fa-icon.with("\u{f79b}")
#let fa-snowplow = fa-icon.with("\u{f7d2}")
#let fa-soap = fa-icon.with("\u{e06e}")
#let fa-socks = fa-icon.with("\u{f696}")
#let fa-soft-serve = fa-icon.with("\u{e400}")
#let fa-creemee = fa-icon.with("\u{e400}")
#let fa-solar-panel = fa-icon.with("\u{f5ba}")
#let fa-solar-system = fa-icon.with("\u{e02f}")
#let fa-sort = fa-icon.with("\u{f0dc}")
#let fa-unsorted = fa-icon.with("\u{f0dc}")
#let fa-sort-down = fa-icon.with("\u{f0dd}")
#let fa-sort-desc = fa-icon.with("\u{f0dd}")
#let fa-sort-up = fa-icon.with("\u{f0de}")
#let fa-sort-asc = fa-icon.with("\u{f0de}")
#let fa-soundcloud = fa-icon.with("\u{f1be}")
#let fa-sourcetree = fa-icon.with("\u{f7d3}")
#let fa-spa = fa-icon.with("\u{f5bb}")
#let fa-space-awesome = fa-icon.with("\u{e5ac}")
#let fa-space-station-moon = fa-icon.with("\u{e033}")
#let fa-space-station-moon-construction = fa-icon.with("\u{e034}")
#let fa-space-station-moon-alt = fa-icon.with("\u{e034}")
#let fa-spade = fa-icon.with("\u{f2f4}")
#let fa-spaghetti-monster-flying = fa-icon.with("\u{f67b}")
#let fa-pastafarianism = fa-icon.with("\u{f67b}")
#let fa-sparkle = fa-icon.with("\u{e5d6}")
#let fa-sparkles = fa-icon.with("\u{f890}")
#let fa-speakap = fa-icon.with("\u{f3f3}")
#let fa-speaker = fa-icon.with("\u{f8df}")
#let fa-speaker-deck = fa-icon.with("\u{f83c}")
#let fa-speakers = fa-icon.with("\u{f8e0}")
#let fa-spell-check = fa-icon.with("\u{f891}")
#let fa-spider = fa-icon.with("\u{f717}")
#let fa-spider-black-widow = fa-icon.with("\u{f718}")
#let fa-spider-web = fa-icon.with("\u{f719}")
#let fa-spinner = fa-icon.with("\u{f110}")
#let fa-spinner-scale = fa-icon.with("\u{e62a}")
#let fa-spinner-third = fa-icon.with("\u{f3f4}")
#let fa-split = fa-icon.with("\u{e254}")
#let fa-splotch = fa-icon.with("\u{f5bc}")
#let fa-spoon = fa-icon.with("\u{f2e5}")
#let fa-utensil-spoon = fa-icon.with("\u{f2e5}")
#let fa-sportsball = fa-icon.with("\u{e44b}")
#let fa-spotify = fa-icon.with("\u{f1bc}")
#let fa-spray-can = fa-icon.with("\u{f5bd}")
#let fa-spray-can-sparkles = fa-icon.with("\u{f5d0}")
#let fa-air-freshener = fa-icon.with("\u{f5d0}")
#let fa-sprinkler = fa-icon.with("\u{e035}")
#let fa-sprinkler-ceiling = fa-icon.with("\u{e44c}")
#let fa-square = fa-icon.with("\u{f0c8}")
#let fa-square-0 = fa-icon.with("\u{e255}")
#let fa-square-1 = fa-icon.with("\u{e256}")
#let fa-square-2 = fa-icon.with("\u{e257}")
#let fa-square-3 = fa-icon.with("\u{e258}")
#let fa-square-4 = fa-icon.with("\u{e259}")
#let fa-square-5 = fa-icon.with("\u{e25a}")
#let fa-square-6 = fa-icon.with("\u{e25b}")
#let fa-square-7 = fa-icon.with("\u{e25c}")
#let fa-square-8 = fa-icon.with("\u{e25d}")
#let fa-square-9 = fa-icon.with("\u{e25e}")
#let fa-square-a = fa-icon.with("\u{e25f}")
#let fa-square-a-lock = fa-icon.with("\u{e44d}")
#let fa-square-ampersand = fa-icon.with("\u{e260}")
#let fa-square-arrow-down = fa-icon.with("\u{f339}")
#let fa-arrow-square-down = fa-icon.with("\u{f339}")
#let fa-square-arrow-down-left = fa-icon.with("\u{e261}")
#let fa-square-arrow-down-right = fa-icon.with("\u{e262}")
#let fa-square-arrow-left = fa-icon.with("\u{f33a}")
#let fa-arrow-square-left = fa-icon.with("\u{f33a}")
#let fa-square-arrow-right = fa-icon.with("\u{f33b}")
#let fa-arrow-square-right = fa-icon.with("\u{f33b}")
#let fa-square-arrow-up = fa-icon.with("\u{f33c}")
#let fa-arrow-square-up = fa-icon.with("\u{f33c}")
#let fa-square-arrow-up-left = fa-icon.with("\u{e263}")
#let fa-square-arrow-up-right = fa-icon.with("\u{f14c}")
#let fa-external-link-square = fa-icon.with("\u{f14c}")
#let fa-square-b = fa-icon.with("\u{e264}")
#let fa-square-behance = fa-icon.with("\u{f1b5}")
#let fa-behance-square = fa-icon.with("\u{f1b5}")
#let fa-square-bolt = fa-icon.with("\u{e265}")
#let fa-square-c = fa-icon.with("\u{e266}")
#let fa-square-caret-down = fa-icon.with("\u{f150}")
#let fa-caret-square-down = fa-icon.with("\u{f150}")
#let fa-square-caret-left = fa-icon.with("\u{f191}")
#let fa-caret-square-left = fa-icon.with("\u{f191}")
#let fa-square-caret-right = fa-icon.with("\u{f152}")
#let fa-caret-square-right = fa-icon.with("\u{f152}")
#let fa-square-caret-up = fa-icon.with("\u{f151}")
#let fa-caret-square-up = fa-icon.with("\u{f151}")
#let fa-square-check = fa-icon.with("\u{f14a}")
#let fa-check-square = fa-icon.with("\u{f14a}")
#let fa-square-chevron-down = fa-icon.with("\u{f329}")
#let fa-chevron-square-down = fa-icon.with("\u{f329}")
#let fa-square-chevron-left = fa-icon.with("\u{f32a}")
#let fa-chevron-square-left = fa-icon.with("\u{f32a}")
#let fa-square-chevron-right = fa-icon.with("\u{f32b}")
#let fa-chevron-square-right = fa-icon.with("\u{f32b}")
#let fa-square-chevron-up = fa-icon.with("\u{f32c}")
#let fa-chevron-square-up = fa-icon.with("\u{f32c}")
#let fa-square-code = fa-icon.with("\u{e267}")
#let fa-square-d = fa-icon.with("\u{e268}")
#let fa-square-dashed = fa-icon.with("\u{e269}")
#let fa-square-dashed-circle-plus = fa-icon.with("\u{e5c2}")
#let fa-square-divide = fa-icon.with("\u{e26a}")
#let fa-square-dollar = fa-icon.with("\u{f2e9}")
#let fa-dollar-square = fa-icon.with("\u{f2e9}")
#let fa-usd-square = fa-icon.with("\u{f2e9}")
#let fa-square-down = fa-icon.with("\u{f350}")
#let fa-arrow-alt-square-down = fa-icon.with("\u{f350}")
#let fa-square-down-left = fa-icon.with("\u{e26b}")
#let fa-square-down-right = fa-icon.with("\u{e26c}")
#let fa-square-dribbble = fa-icon.with("\u{f397}")
#let fa-dribbble-square = fa-icon.with("\u{f397}")
#let fa-square-e = fa-icon.with("\u{e26d}")
#let fa-square-ellipsis = fa-icon.with("\u{e26e}")
#let fa-square-ellipsis-vertical = fa-icon.with("\u{e26f}")
#let fa-square-envelope = fa-icon.with("\u{f199}")
#let fa-envelope-square = fa-icon.with("\u{f199}")
#let fa-square-exclamation = fa-icon.with("\u{f321}")
#let fa-exclamation-square = fa-icon.with("\u{f321}")
#let fa-square-f = fa-icon.with("\u{e270}")
#let fa-square-facebook = fa-icon.with("\u{f082}")
#let fa-facebook-square = fa-icon.with("\u{f082}")
#let fa-square-font-awesome = fa-icon.with("\u{e5ad}")
#let fa-square-font-awesome-stroke = fa-icon.with("\u{f35c}")
#let fa-font-awesome-alt = fa-icon.with("\u{f35c}")
#let fa-square-fragile = fa-icon.with("\u{f49b}")
#let fa-box-fragile = fa-icon.with("\u{f49b}")
#let fa-square-wine-glass-crack = fa-icon.with("\u{f49b}")
#let fa-square-full = fa-icon.with("\u{f45c}")
#let fa-square-g = fa-icon.with("\u{e271}")
#let fa-square-git = fa-icon.with("\u{f1d2}")
#let fa-git-square = fa-icon.with("\u{f1d2}")
#let fa-square-github = fa-icon.with("\u{f092}")
#let fa-github-square = fa-icon.with("\u{f092}")
#let fa-square-gitlab = fa-icon.with("\u{e5ae}")
#let fa-gitlab-square = fa-icon.with("\u{e5ae}")
#let fa-square-google-plus = fa-icon.with("\u{f0d4}")
#let fa-google-plus-square = fa-icon.with("\u{f0d4}")
#let fa-square-h = fa-icon.with("\u{f0fd}")
#let fa-h-square = fa-icon.with("\u{f0fd}")
#let fa-square-hacker-news = fa-icon.with("\u{f3af}")
#let fa-hacker-news-square = fa-icon.with("\u{f3af}")
#let fa-square-heart = fa-icon.with("\u{f4c8}")
#let fa-heart-square = fa-icon.with("\u{f4c8}")
#let fa-square-i = fa-icon.with("\u{e272}")
#let fa-square-info = fa-icon.with("\u{f30f}")
#let fa-info-square = fa-icon.with("\u{f30f}")
#let fa-square-instagram = fa-icon.with("\u{e055}")
#let fa-instagram-square = fa-icon.with("\u{e055}")
#let fa-square-j = fa-icon.with("\u{e273}")
#let fa-square-js = fa-icon.with("\u{f3b9}")
#let fa-js-square = fa-icon.with("\u{f3b9}")
#let fa-square-k = fa-icon.with("\u{e274}")
#let fa-square-kanban = fa-icon.with("\u{e488}")
#let fa-square-l = fa-icon.with("\u{e275}")
#let fa-square-lastfm = fa-icon.with("\u{f203}")
#let fa-lastfm-square = fa-icon.with("\u{f203}")
#let fa-square-left = fa-icon.with("\u{f351}")
#let fa-arrow-alt-square-left = fa-icon.with("\u{f351}")
#let fa-square-letterboxd = fa-icon.with("\u{e62e}")
#let fa-square-list = fa-icon.with("\u{e489}")
#let fa-square-m = fa-icon.with("\u{e276}")
#let fa-square-minus = fa-icon.with("\u{f146}")
#let fa-minus-square = fa-icon.with("\u{f146}")
#let fa-square-n = fa-icon.with("\u{e277}")
#let fa-square-nfi = fa-icon.with("\u{e576}")
#let fa-square-o = fa-icon.with("\u{e278}")
#let fa-square-odnoklassniki = fa-icon.with("\u{f264}")
#let fa-odnoklassniki-square = fa-icon.with("\u{f264}")
#let fa-square-p = fa-icon.with("\u{e279}")
#let fa-square-parking = fa-icon.with("\u{f540}")
#let fa-parking = fa-icon.with("\u{f540}")
#let fa-square-parking-slash = fa-icon.with("\u{f617}")
#let fa-parking-slash = fa-icon.with("\u{f617}")
#let fa-square-pen = fa-icon.with("\u{f14b}")
#let fa-pen-square = fa-icon.with("\u{f14b}")
#let fa-pencil-square = fa-icon.with("\u{f14b}")
#let fa-square-person-confined = fa-icon.with("\u{e577}")
#let fa-square-phone = fa-icon.with("\u{f098}")
#let fa-phone-square = fa-icon.with("\u{f098}")
#let fa-square-phone-flip = fa-icon.with("\u{f87b}")
#let fa-phone-square-alt = fa-icon.with("\u{f87b}")
#let fa-square-phone-hangup = fa-icon.with("\u{e27a}")
#let fa-phone-square-down = fa-icon.with("\u{e27a}")
#let fa-square-pied-piper = fa-icon.with("\u{e01e}")
#let fa-pied-piper-square = fa-icon.with("\u{e01e}")
#let fa-square-pinterest = fa-icon.with("\u{f0d3}")
#let fa-pinterest-square = fa-icon.with("\u{f0d3}")
#let fa-square-plus = fa-icon.with("\u{f0fe}")
#let fa-plus-square = fa-icon.with("\u{f0fe}")
#let fa-square-poll-horizontal = fa-icon.with("\u{f682}")
#let fa-poll-h = fa-icon.with("\u{f682}")
#let fa-square-poll-vertical = fa-icon.with("\u{f681}")
#let fa-poll = fa-icon.with("\u{f681}")
#let fa-square-q = fa-icon.with("\u{e27b}")
#let fa-square-quarters = fa-icon.with("\u{e44e}")
#let fa-square-question = fa-icon.with("\u{f2fd}")
#let fa-question-square = fa-icon.with("\u{f2fd}")
#let fa-square-quote = fa-icon.with("\u{e329}")
#let fa-square-r = fa-icon.with("\u{e27c}")
#let fa-square-reddit = fa-icon.with("\u{f1a2}")
#let fa-reddit-square = fa-icon.with("\u{f1a2}")
#let fa-square-right = fa-icon.with("\u{f352}")
#let fa-arrow-alt-square-right = fa-icon.with("\u{f352}")
#let fa-square-ring = fa-icon.with("\u{e44f}")
#let fa-square-root = fa-icon.with("\u{f697}")
#let fa-square-root-variable = fa-icon.with("\u{f698}")
#let fa-square-root-alt = fa-icon.with("\u{f698}")
#let fa-square-rss = fa-icon.with("\u{f143}")
#let fa-rss-square = fa-icon.with("\u{f143}")
#let fa-square-s = fa-icon.with("\u{e27d}")
#let fa-square-share-nodes = fa-icon.with("\u{f1e1}")
#let fa-share-alt-square = fa-icon.with("\u{f1e1}")
#let fa-square-sliders = fa-icon.with("\u{f3f0}")
#let fa-sliders-h-square = fa-icon.with("\u{f3f0}")
#let fa-square-sliders-vertical = fa-icon.with("\u{f3f2}")
#let fa-sliders-v-square = fa-icon.with("\u{f3f2}")
#let fa-square-small = fa-icon.with("\u{e27e}")
#let fa-square-snapchat = fa-icon.with("\u{f2ad}")
#let fa-snapchat-square = fa-icon.with("\u{f2ad}")
#let fa-squarespace = fa-icon.with("\u{f5be}")
#let fa-square-star = fa-icon.with("\u{e27f}")
#let fa-square-steam = fa-icon.with("\u{f1b7}")
#let fa-steam-square = fa-icon.with("\u{f1b7}")
#let fa-square-t = fa-icon.with("\u{e280}")
#let fa-square-terminal = fa-icon.with("\u{e32a}")
#let fa-square-this-way-up = fa-icon.with("\u{f49f}")
#let fa-box-up = fa-icon.with("\u{f49f}")
#let fa-square-threads = fa-icon.with("\u{e619}")
#let fa-square-tumblr = fa-icon.with("\u{f174}")
#let fa-tumblr-square = fa-icon.with("\u{f174}")
#let fa-square-twitter = fa-icon.with("\u{f081}")
#let fa-twitter-square = fa-icon.with("\u{f081}")
#let fa-square-u = fa-icon.with("\u{e281}")
#let fa-square-up = fa-icon.with("\u{f353}")
#let fa-arrow-alt-square-up = fa-icon.with("\u{f353}")
#let fa-square-up-left = fa-icon.with("\u{e282}")
#let fa-square-up-right = fa-icon.with("\u{f360}")
#let fa-external-link-square-alt = fa-icon.with("\u{f360}")
#let fa-square-upwork = fa-icon.with("\u{e67c}")
#let fa-square-user = fa-icon.with("\u{e283}")
#let fa-square-v = fa-icon.with("\u{e284}")
#let fa-square-viadeo = fa-icon.with("\u{f2aa}")
#let fa-viadeo-square = fa-icon.with("\u{f2aa}")
#let fa-square-vimeo = fa-icon.with("\u{f194}")
#let fa-vimeo-square = fa-icon.with("\u{f194}")
#let fa-square-virus = fa-icon.with("\u{e578}")
#let fa-square-w = fa-icon.with("\u{e285}")
#let fa-square-web-awesome = fa-icon.with("\u{e683}")
#let fa-square-web-awesome-stroke = fa-icon.with("\u{e684}")
#let fa-square-whatsapp = fa-icon.with("\u{f40c}")
#let fa-whatsapp-square = fa-icon.with("\u{f40c}")
#let fa-square-x = fa-icon.with("\u{e286}")
#let fa-square-xing = fa-icon.with("\u{f169}")
#let fa-xing-square = fa-icon.with("\u{f169}")
#let fa-square-xmark = fa-icon.with("\u{f2d3}")
#let fa-times-square = fa-icon.with("\u{f2d3}")
#let fa-xmark-square = fa-icon.with("\u{f2d3}")
#let fa-square-x-twitter = fa-icon.with("\u{e61a}")
#let fa-square-y = fa-icon.with("\u{e287}")
#let fa-square-youtube = fa-icon.with("\u{f431}")
#let fa-youtube-square = fa-icon.with("\u{f431}")
#let fa-square-z = fa-icon.with("\u{e288}")
#let fa-squid = fa-icon.with("\u{e450}")
#let fa-squirrel = fa-icon.with("\u{f71a}")
#let fa-stack-exchange = fa-icon.with("\u{f18d}")
#let fa-stack-overflow = fa-icon.with("\u{f16c}")
#let fa-stackpath = fa-icon.with("\u{f842}")
#let fa-staff = fa-icon.with("\u{f71b}")
#let fa-staff-snake = fa-icon.with("\u{e579}")
#let fa-rod-asclepius = fa-icon.with("\u{e579}")
#let fa-rod-snake = fa-icon.with("\u{e579}")
#let fa-staff-aesculapius = fa-icon.with("\u{e579}")
#let fa-stairs = fa-icon.with("\u{e289}")
#let fa-stamp = fa-icon.with("\u{f5bf}")
#let fa-standard-definition = fa-icon.with("\u{e28a}")
#let fa-rectangle-sd = fa-icon.with("\u{e28a}")
#let fa-stapler = fa-icon.with("\u{e5af}")
#let fa-star = fa-icon.with("\u{f005}")
#let fa-star-and-crescent = fa-icon.with("\u{f699}")
#let fa-star-christmas = fa-icon.with("\u{f7d4}")
#let fa-star-exclamation = fa-icon.with("\u{f2f3}")
#let fa-starfighter = fa-icon.with("\u{e037}")
#let fa-starfighter-twin-ion-engine = fa-icon.with("\u{e038}")
#let fa-starfighter-alt = fa-icon.with("\u{e038}")
#let fa-starfighter-twin-ion-engine-advanced = fa-icon.with("\u{e28e}")
#let fa-starfighter-alt-advanced = fa-icon.with("\u{e28e}")
#let fa-star-half = fa-icon.with("\u{f089}")
#let fa-star-half-stroke = fa-icon.with("\u{f5c0}")
#let fa-star-half-alt = fa-icon.with("\u{f5c0}")
#let fa-star-of-david = fa-icon.with("\u{f69a}")
#let fa-star-of-life = fa-icon.with("\u{f621}")
#let fa-stars = fa-icon.with("\u{f762}")
#let fa-star-sharp = fa-icon.with("\u{e28b}")
#let fa-star-sharp-half = fa-icon.with("\u{e28c}")
#let fa-star-sharp-half-stroke = fa-icon.with("\u{e28d}")
#let fa-star-sharp-half-alt = fa-icon.with("\u{e28d}")
#let fa-starship = fa-icon.with("\u{e039}")
#let fa-starship-freighter = fa-icon.with("\u{e03a}")
#let fa-star-shooting = fa-icon.with("\u{e036}")
#let fa-staylinked = fa-icon.with("\u{f3f5}")
#let fa-steak = fa-icon.with("\u{f824}")
#let fa-steam = fa-icon.with("\u{f1b6}")
#let fa-steam-symbol = fa-icon.with("\u{f3f6}")
#let fa-steering-wheel = fa-icon.with("\u{f622}")
#let fa-sterling-sign = fa-icon.with("\u{f154}")
#let fa-gbp = fa-icon.with("\u{f154}")
#let fa-pound-sign = fa-icon.with("\u{f154}")
#let fa-stethoscope = fa-icon.with("\u{f0f1}")
#let fa-sticker-mule = fa-icon.with("\u{f3f7}")
#let fa-stocking = fa-icon.with("\u{f7d5}")
#let fa-stomach = fa-icon.with("\u{f623}")
#let fa-stop = fa-icon.with("\u{f04d}")
#let fa-stopwatch = fa-icon.with("\u{f2f2}")
#let fa-stopwatch-20 = fa-icon.with("\u{e06f}")
#let fa-store = fa-icon.with("\u{f54e}")
#let fa-store-lock = fa-icon.with("\u{e4a6}")
#let fa-store-slash = fa-icon.with("\u{e071}")
#let fa-strava = fa-icon.with("\u{f428}")
#let fa-strawberry = fa-icon.with("\u{e32b}")
#let fa-street-view = fa-icon.with("\u{f21d}")
#let fa-stretcher = fa-icon.with("\u{f825}")
#let fa-strikethrough = fa-icon.with("\u{f0cc}")
#let fa-stripe = fa-icon.with("\u{f429}")
#let fa-stripe-s = fa-icon.with("\u{f42a}")
#let fa-stroopwafel = fa-icon.with("\u{f551}")
#let fa-stubber = fa-icon.with("\u{e5c7}")
#let fa-studiovinari = fa-icon.with("\u{f3f8}")
#let fa-stumbleupon = fa-icon.with("\u{f1a4}")
#let fa-stumbleupon-circle = fa-icon.with("\u{f1a3}")
#let fa-subscript = fa-icon.with("\u{f12c}")
#let fa-subtitles = fa-icon.with("\u{e60f}")
#let fa-subtitles-slash = fa-icon.with("\u{e610}")
#let fa-suitcase = fa-icon.with("\u{f0f2}")
#let fa-suitcase-medical = fa-icon.with("\u{f0fa}")
#let fa-medkit = fa-icon.with("\u{f0fa}")
#let fa-suitcase-rolling = fa-icon.with("\u{f5c1}")
#let fa-sun = fa-icon.with("\u{f185}")
#let fa-sun-bright = fa-icon.with("\u{e28f}")
#let fa-sun-alt = fa-icon.with("\u{e28f}")
#let fa-sun-cloud = fa-icon.with("\u{f763}")
#let fa-sun-dust = fa-icon.with("\u{f764}")
#let fa-sunglasses = fa-icon.with("\u{f892}")
#let fa-sun-haze = fa-icon.with("\u{f765}")
#let fa-sun-plant-wilt = fa-icon.with("\u{e57a}")
#let fa-sunrise = fa-icon.with("\u{f766}")
#let fa-sunset = fa-icon.with("\u{f767}")
#let fa-superpowers = fa-icon.with("\u{f2dd}")
#let fa-superscript = fa-icon.with("\u{f12b}")
#let fa-supple = fa-icon.with("\u{f3f9}")
#let fa-suse = fa-icon.with("\u{f7d6}")
#let fa-sushi = fa-icon.with("\u{e48a}")
#let fa-nigiri = fa-icon.with("\u{e48a}")
#let fa-sushi-roll = fa-icon.with("\u{e48b}")
#let fa-maki-roll = fa-icon.with("\u{e48b}")
#let fa-makizushi = fa-icon.with("\u{e48b}")
#let fa-swap = fa-icon.with("\u{e609}")
#let fa-swap-arrows = fa-icon.with("\u{e60a}")
#let fa-swatchbook = fa-icon.with("\u{f5c3}")
#let fa-swift = fa-icon.with("\u{f8e1}")
#let fa-sword = fa-icon.with("\u{f71c}")
#let fa-sword-laser = fa-icon.with("\u{e03b}")
#let fa-sword-laser-alt = fa-icon.with("\u{e03c}")
#let fa-swords = fa-icon.with("\u{f71d}")
#let fa-swords-laser = fa-icon.with("\u{e03d}")
#let fa-symbols = fa-icon.with("\u{f86e}")
#let fa-icons-alt = fa-icon.with("\u{f86e}")
#let fa-symfony = fa-icon.with("\u{f83d}")
#let fa-synagogue = fa-icon.with("\u{f69b}")
#let fa-syringe = fa-icon.with("\u{f48e}")
#let fa-t = fa-icon.with("\u{54}")
#let fa-table = fa-icon.with("\u{f0ce}")
#let fa-table-cells = fa-icon.with("\u{f00a}")
#let fa-th = fa-icon.with("\u{f00a}")
#let fa-table-cells-column-lock = fa-icon.with("\u{e678}")
#let fa-table-cells-column-unlock = fa-icon.with("\u{e690}")
#let fa-table-cells-large = fa-icon.with("\u{f009}")
#let fa-th-large = fa-icon.with("\u{f009}")
#let fa-table-cells-lock = fa-icon.with("\u{e679}")
#let fa-table-cells-row-lock = fa-icon.with("\u{e67a}")
#let fa-table-cells-row-unlock = fa-icon.with("\u{e691}")
#let fa-table-cells-unlock = fa-icon.with("\u{e692}")
#let fa-table-columns = fa-icon.with("\u{f0db}")
#let fa-columns = fa-icon.with("\u{f0db}")
#let fa-table-layout = fa-icon.with("\u{e290}")
#let fa-table-list = fa-icon.with("\u{f00b}")
#let fa-th-list = fa-icon.with("\u{f00b}")
#let fa-table-picnic = fa-icon.with("\u{e32d}")
#let fa-table-pivot = fa-icon.with("\u{e291}")
#let fa-table-rows = fa-icon.with("\u{e292}")
#let fa-rows = fa-icon.with("\u{e292}")
#let fa-tablet = fa-icon.with("\u{f3fb}")
#let fa-tablet-android = fa-icon.with("\u{f3fb}")
#let fa-tablet-button = fa-icon.with("\u{f10a}")
#let fa-table-tennis-paddle-ball = fa-icon.with("\u{f45d}")
#let fa-ping-pong-paddle-ball = fa-icon.with("\u{f45d}")
#let fa-table-tennis = fa-icon.with("\u{f45d}")
#let fa-table-tree = fa-icon.with("\u{e293}")
#let fa-tablet-rugged = fa-icon.with("\u{f48f}")
#let fa-tablets = fa-icon.with("\u{f490}")
#let fa-tablet-screen = fa-icon.with("\u{f3fc}")
#let fa-tablet-android-alt = fa-icon.with("\u{f3fc}")
#let fa-tablet-screen-button = fa-icon.with("\u{f3fa}")
#let fa-tablet-alt = fa-icon.with("\u{f3fa}")
#let fa-tachograph-digital = fa-icon.with("\u{f566}")
#let fa-digital-tachograph = fa-icon.with("\u{f566}")
#let fa-taco = fa-icon.with("\u{f826}")
#let fa-tag = fa-icon.with("\u{f02b}")
#let fa-tags = fa-icon.with("\u{f02c}")
#let fa-tally = fa-icon.with("\u{f69c}")
#let fa-tally-5 = fa-icon.with("\u{f69c}")
#let fa-tally-1 = fa-icon.with("\u{e294}")
#let fa-tally-2 = fa-icon.with("\u{e295}")
#let fa-tally-3 = fa-icon.with("\u{e296}")
#let fa-tally-4 = fa-icon.with("\u{e297}")
#let fa-tamale = fa-icon.with("\u{e451}")
#let fa-tank-water = fa-icon.with("\u{e452}")
#let fa-tape = fa-icon.with("\u{f4db}")
#let fa-tarp = fa-icon.with("\u{e57b}")
#let fa-tarp-droplet = fa-icon.with("\u{e57c}")
#let fa-taxi = fa-icon.with("\u{f1ba}")
#let fa-cab = fa-icon.with("\u{f1ba}")
#let fa-taxi-bus = fa-icon.with("\u{e298}")
#let fa-teamspeak = fa-icon.with("\u{f4f9}")
#let fa-teddy-bear = fa-icon.with("\u{e3cf}")
#let fa-teeth = fa-icon.with("\u{f62e}")
#let fa-teeth-open = fa-icon.with("\u{f62f}")
#let fa-telegram = fa-icon.with("\u{f2c6}")
#let fa-telegram-plane = fa-icon.with("\u{f2c6}")
#let fa-telescope = fa-icon.with("\u{e03e}")
#let fa-temperature-arrow-down = fa-icon.with("\u{e03f}")
#let fa-temperature-down = fa-icon.with("\u{e03f}")
#let fa-temperature-arrow-up = fa-icon.with("\u{e040}")
#let fa-temperature-up = fa-icon.with("\u{e040}")
#let fa-temperature-empty = fa-icon.with("\u{f2cb}")
#let fa-temperature-0 = fa-icon.with("\u{f2cb}")
#let fa-thermometer-0 = fa-icon.with("\u{f2cb}")
#let fa-thermometer-empty = fa-icon.with("\u{f2cb}")
#let fa-temperature-full = fa-icon.with("\u{f2c7}")
#let fa-temperature-4 = fa-icon.with("\u{f2c7}")
#let fa-thermometer-4 = fa-icon.with("\u{f2c7}")
#let fa-thermometer-full = fa-icon.with("\u{f2c7}")
#let fa-temperature-half = fa-icon.with("\u{f2c9}")
#let fa-temperature-2 = fa-icon.with("\u{f2c9}")
#let fa-thermometer-2 = fa-icon.with("\u{f2c9}")
#let fa-thermometer-half = fa-icon.with("\u{f2c9}")
#let fa-temperature-high = fa-icon.with("\u{f769}")
#let fa-temperature-list = fa-icon.with("\u{e299}")
#let fa-temperature-low = fa-icon.with("\u{f76b}")
#let fa-temperature-quarter = fa-icon.with("\u{f2ca}")
#let fa-temperature-1 = fa-icon.with("\u{f2ca}")
#let fa-thermometer-1 = fa-icon.with("\u{f2ca}")
#let fa-thermometer-quarter = fa-icon.with("\u{f2ca}")
#let fa-temperature-snow = fa-icon.with("\u{f768}")
#let fa-temperature-frigid = fa-icon.with("\u{f768}")
#let fa-temperature-sun = fa-icon.with("\u{f76a}")
#let fa-temperature-hot = fa-icon.with("\u{f76a}")
#let fa-temperature-three-quarters = fa-icon.with("\u{f2c8}")
#let fa-temperature-3 = fa-icon.with("\u{f2c8}")
#let fa-thermometer-3 = fa-icon.with("\u{f2c8}")
#let fa-thermometer-three-quarters = fa-icon.with("\u{f2c8}")
#let fa-tencent-weibo = fa-icon.with("\u{f1d5}")
#let fa-tenge-sign = fa-icon.with("\u{f7d7}")
#let fa-tenge = fa-icon.with("\u{f7d7}")
#let fa-tennis-ball = fa-icon.with("\u{f45e}")
#let fa-tent = fa-icon.with("\u{e57d}")
#let fa-tent-arrow-down-to-line = fa-icon.with("\u{e57e}")
#let fa-tent-arrow-left-right = fa-icon.with("\u{e57f}")
#let fa-tent-arrows-down = fa-icon.with("\u{e581}")
#let fa-tent-arrow-turn-left = fa-icon.with("\u{e580}")
#let fa-tent-double-peak = fa-icon.with("\u{e627}")
#let fa-tents = fa-icon.with("\u{e582}")
#let fa-terminal = fa-icon.with("\u{f120}")
#let fa-text = fa-icon.with("\u{f893}")
#let fa-text-height = fa-icon.with("\u{f034}")
#let fa-text-size = fa-icon.with("\u{f894}")
#let fa-text-slash = fa-icon.with("\u{f87d}")
#let fa-remove-format = fa-icon.with("\u{f87d}")
#let fa-text-width = fa-icon.with("\u{f035}")
#let fa-themeco = fa-icon.with("\u{f5c6}")
#let fa-themeisle = fa-icon.with("\u{f2b2}")
#let fa-the-red-yeti = fa-icon.with("\u{f69d}")
#let fa-thermometer = fa-icon.with("\u{f491}")
#let fa-theta = fa-icon.with("\u{f69e}")
#let fa-think-peaks = fa-icon.with("\u{f731}")
#let fa-thought-bubble = fa-icon.with("\u{e32e}")
#let fa-threads = fa-icon.with("\u{e618}")
#let fa-thumbs-down = fa-icon.with("\u{f165}")
#let fa-thumbs-up = fa-icon.with("\u{f164}")
#let fa-thumbtack = fa-icon.with("\u{f08d}")
#let fa-thumb-tack = fa-icon.with("\u{f08d}")
#let fa-thumbtack-slash = fa-icon.with("\u{e68f}")
#let fa-thumb-tack-slash = fa-icon.with("\u{e68f}")
#let fa-tick = fa-icon.with("\u{e32f}")
#let fa-ticket = fa-icon.with("\u{f145}")
#let fa-ticket-airline = fa-icon.with("\u{e29a}")
#let fa-ticket-perforated-plane = fa-icon.with("\u{e29a}")
#let fa-ticket-plane = fa-icon.with("\u{e29a}")
#let fa-ticket-perforated = fa-icon.with("\u{e63e}")
#let fa-tickets = fa-icon.with("\u{e658}")
#let fa-tickets-airline = fa-icon.with("\u{e29b}")
#let fa-tickets-perforated-plane = fa-icon.with("\u{e29b}")
#let fa-tickets-plane = fa-icon.with("\u{e29b}")
#let fa-ticket-simple = fa-icon.with("\u{f3ff}")
#let fa-ticket-alt = fa-icon.with("\u{f3ff}")
#let fa-tickets-perforated = fa-icon.with("\u{e63f}")
#let fa-tickets-simple = fa-icon.with("\u{e659}")
#let fa-tiktok = fa-icon.with("\u{e07b}")
#let fa-tilde = fa-icon.with("\u{7e}")
#let fa-timeline = fa-icon.with("\u{e29c}")
#let fa-timeline-arrow = fa-icon.with("\u{e29d}")
#let fa-timer = fa-icon.with("\u{e29e}")
#let fa-tire = fa-icon.with("\u{f631}")
#let fa-tire-flat = fa-icon.with("\u{f632}")
#let fa-tire-pressure-warning = fa-icon.with("\u{f633}")
#let fa-tire-rugged = fa-icon.with("\u{f634}")
#let fa-toggle-large-off = fa-icon.with("\u{e5b0}")
#let fa-toggle-large-on = fa-icon.with("\u{e5b1}")
#let fa-toggle-off = fa-icon.with("\u{f204}")
#let fa-toggle-on = fa-icon.with("\u{f205}")
#let fa-toilet = fa-icon.with("\u{f7d8}")
#let fa-toilet-paper = fa-icon.with("\u{f71e}")
#let fa-toilet-paper-blank = fa-icon.with("\u{f71f}")
#let fa-toilet-paper-alt = fa-icon.with("\u{f71f}")
#let fa-toilet-paper-blank-under = fa-icon.with("\u{e29f}")
#let fa-toilet-paper-reverse-alt = fa-icon.with("\u{e29f}")
#let fa-toilet-paper-check = fa-icon.with("\u{e5b2}")
#let fa-toilet-paper-slash = fa-icon.with("\u{e072}")
#let fa-toilet-paper-under = fa-icon.with("\u{e2a0}")
#let fa-toilet-paper-reverse = fa-icon.with("\u{e2a0}")
#let fa-toilet-paper-under-slash = fa-icon.with("\u{e2a1}")
#let fa-toilet-paper-reverse-slash = fa-icon.with("\u{e2a1}")
#let fa-toilet-paper-xmark = fa-icon.with("\u{e5b3}")
#let fa-toilet-portable = fa-icon.with("\u{e583}")
#let fa-toilets-portable = fa-icon.with("\u{e584}")
#let fa-tomato = fa-icon.with("\u{e330}")
#let fa-tombstone = fa-icon.with("\u{f720}")
#let fa-tombstone-blank = fa-icon.with("\u{f721}")
#let fa-tombstone-alt = fa-icon.with("\u{f721}")
#let fa-toolbox = fa-icon.with("\u{f552}")
#let fa-tooth = fa-icon.with("\u{f5c9}")
#let fa-toothbrush = fa-icon.with("\u{f635}")
#let fa-torii-gate = fa-icon.with("\u{f6a1}")
#let fa-tornado = fa-icon.with("\u{f76f}")
#let fa-tower-broadcast = fa-icon.with("\u{f519}")
#let fa-broadcast-tower = fa-icon.with("\u{f519}")
#let fa-tower-cell = fa-icon.with("\u{e585}")
#let fa-tower-control = fa-icon.with("\u{e2a2}")
#let fa-tower-observation = fa-icon.with("\u{e586}")
#let fa-tractor = fa-icon.with("\u{f722}")
#let fa-trade-federation = fa-icon.with("\u{f513}")
#let fa-trademark = fa-icon.with("\u{f25c}")
#let fa-traffic-cone = fa-icon.with("\u{f636}")
#let fa-traffic-light = fa-icon.with("\u{f637}")
#let fa-traffic-light-go = fa-icon.with("\u{f638}")
#let fa-traffic-light-slow = fa-icon.with("\u{f639}")
#let fa-traffic-light-stop = fa-icon.with("\u{f63a}")
#let fa-trailer = fa-icon.with("\u{e041}")
#let fa-train = fa-icon.with("\u{f238}")
#let fa-train-subway = fa-icon.with("\u{f239}")
#let fa-subway = fa-icon.with("\u{f239}")
#let fa-train-subway-tunnel = fa-icon.with("\u{e2a3}")
#let fa-subway-tunnel = fa-icon.with("\u{e2a3}")
#let fa-train-track = fa-icon.with("\u{e453}")
#let fa-train-tram = fa-icon.with("\u{e5b4}")
#let fa-train-tunnel = fa-icon.with("\u{e454}")
#let fa-transformer-bolt = fa-icon.with("\u{e2a4}")
#let fa-transgender = fa-icon.with("\u{f225}")
#let fa-transgender-alt = fa-icon.with("\u{f225}")
#let fa-transporter = fa-icon.with("\u{e042}")
#let fa-transporter-1 = fa-icon.with("\u{e043}")
#let fa-transporter-2 = fa-icon.with("\u{e044}")
#let fa-transporter-3 = fa-icon.with("\u{e045}")
#let fa-transporter-4 = fa-icon.with("\u{e2a5}")
#let fa-transporter-5 = fa-icon.with("\u{e2a6}")
#let fa-transporter-6 = fa-icon.with("\u{e2a7}")
#let fa-transporter-7 = fa-icon.with("\u{e2a8}")
#let fa-transporter-empty = fa-icon.with("\u{e046}")
#let fa-trash = fa-icon.with("\u{f1f8}")
#let fa-trash-arrow-up = fa-icon.with("\u{f829}")
#let fa-trash-restore = fa-icon.with("\u{f829}")
#let fa-trash-can = fa-icon.with("\u{f2ed}")
#let fa-trash-alt = fa-icon.with("\u{f2ed}")
#let fa-trash-can-arrow-up = fa-icon.with("\u{f82a}")
#let fa-trash-restore-alt = fa-icon.with("\u{f82a}")
#let fa-trash-can-check = fa-icon.with("\u{e2a9}")
#let fa-trash-can-clock = fa-icon.with("\u{e2aa}")
#let fa-trash-can-list = fa-icon.with("\u{e2ab}")
#let fa-trash-can-plus = fa-icon.with("\u{e2ac}")
#let fa-trash-can-slash = fa-icon.with("\u{e2ad}")
#let fa-trash-alt-slash = fa-icon.with("\u{e2ad}")
#let fa-trash-can-undo = fa-icon.with("\u{f896}")
#let fa-trash-can-arrow-turn-left = fa-icon.with("\u{f896}")
#let fa-trash-undo-alt = fa-icon.with("\u{f896}")
#let fa-trash-can-xmark = fa-icon.with("\u{e2ae}")
#let fa-trash-check = fa-icon.with("\u{e2af}")
#let fa-trash-clock = fa-icon.with("\u{e2b0}")
#let fa-trash-list = fa-icon.with("\u{e2b1}")
#let fa-trash-plus = fa-icon.with("\u{e2b2}")
#let fa-trash-slash = fa-icon.with("\u{e2b3}")
#let fa-trash-undo = fa-icon.with("\u{f895}")
#let fa-trash-arrow-turn-left = fa-icon.with("\u{f895}")
#let fa-trash-xmark = fa-icon.with("\u{e2b4}")
#let fa-treasure-chest = fa-icon.with("\u{f723}")
#let fa-tree = fa-icon.with("\u{f1bb}")
#let fa-tree-christmas = fa-icon.with("\u{f7db}")
#let fa-tree-city = fa-icon.with("\u{e587}")
#let fa-tree-deciduous = fa-icon.with("\u{f400}")
#let fa-tree-alt = fa-icon.with("\u{f400}")
#let fa-tree-decorated = fa-icon.with("\u{f7dc}")
#let fa-tree-large = fa-icon.with("\u{f7dd}")
#let fa-tree-palm = fa-icon.with("\u{f82b}")
#let fa-trees = fa-icon.with("\u{f724}")
#let fa-trello = fa-icon.with("\u{f181}")
#let fa-t-rex = fa-icon.with("\u{e629}")
#let fa-triangle = fa-icon.with("\u{f2ec}")
#let fa-triangle-exclamation = fa-icon.with("\u{f071}")
#let fa-exclamation-triangle = fa-icon.with("\u{f071}")
#let fa-warning = fa-icon.with("\u{f071}")
#let fa-triangle-instrument = fa-icon.with("\u{f8e2}")
#let fa-triangle-music = fa-icon.with("\u{f8e2}")
#let fa-triangle-person-digging = fa-icon.with("\u{f85d}")
#let fa-construction = fa-icon.with("\u{f85d}")
#let fa-tricycle = fa-icon.with("\u{e5c3}")
#let fa-tricycle-adult = fa-icon.with("\u{e5c4}")
#let fa-trillium = fa-icon.with("\u{e588}")
#let fa-trophy = fa-icon.with("\u{f091}")
#let fa-trophy-star = fa-icon.with("\u{f2eb}")
#let fa-trophy-alt = fa-icon.with("\u{f2eb}")
#let fa-trowel = fa-icon.with("\u{e589}")
#let fa-trowel-bricks = fa-icon.with("\u{e58a}")
#let fa-truck = fa-icon.with("\u{f0d1}")
#let fa-truck-arrow-right = fa-icon.with("\u{e58b}")
#let fa-truck-bolt = fa-icon.with("\u{e3d0}")
#let fa-truck-clock = fa-icon.with("\u{f48c}")
#let fa-shipping-timed = fa-icon.with("\u{f48c}")
#let fa-truck-container = fa-icon.with("\u{f4dc}")
#let fa-truck-container-empty = fa-icon.with("\u{e2b5}")
#let fa-truck-droplet = fa-icon.with("\u{e58c}")
#let fa-truck-fast = fa-icon.with("\u{f48b}")
#let fa-shipping-fast = fa-icon.with("\u{f48b}")
#let fa-truck-field = fa-icon.with("\u{e58d}")
#let fa-truck-field-un = fa-icon.with("\u{e58e}")
#let fa-truck-fire = fa-icon.with("\u{e65a}")
#let fa-truck-flatbed = fa-icon.with("\u{e2b6}")
#let fa-truck-front = fa-icon.with("\u{e2b7}")
#let fa-truck-ladder = fa-icon.with("\u{e657}")
#let fa-truck-medical = fa-icon.with("\u{f0f9}")
#let fa-ambulance = fa-icon.with("\u{f0f9}")
#let fa-truck-monster = fa-icon.with("\u{f63b}")
#let fa-truck-moving = fa-icon.with("\u{f4df}")
#let fa-truck-pickup = fa-icon.with("\u{f63c}")
#let fa-truck-plane = fa-icon.with("\u{e58f}")
#let fa-truck-plow = fa-icon.with("\u{f7de}")
#let fa-truck-ramp = fa-icon.with("\u{f4e0}")
#let fa-truck-ramp-box = fa-icon.with("\u{f4de}")
#let fa-truck-loading = fa-icon.with("\u{f4de}")
#let fa-truck-ramp-couch = fa-icon.with("\u{f4dd}")
#let fa-truck-couch = fa-icon.with("\u{f4dd}")
#let fa-truck-tow = fa-icon.with("\u{e2b8}")
#let fa-truck-utensils = fa-icon.with("\u{e628}")
#let fa-trumpet = fa-icon.with("\u{f8e3}")
#let fa-tty = fa-icon.with("\u{f1e4}")
#let fa-teletype = fa-icon.with("\u{f1e4}")
#let fa-tty-answer = fa-icon.with("\u{e2b9}")
#let fa-teletype-answer = fa-icon.with("\u{e2b9}")
#let fa-tugrik-sign = fa-icon.with("\u{e2ba}")
#let fa-tumblr = fa-icon.with("\u{f173}")
#let fa-turkey = fa-icon.with("\u{f725}")
#let fa-turkish-lira-sign = fa-icon.with("\u{e2bb}")
#let fa-try = fa-icon.with("\u{e2bb}")
#let fa-turkish-lira = fa-icon.with("\u{e2bb}")
#let fa-turn-down = fa-icon.with("\u{f3be}")
#let fa-level-down-alt = fa-icon.with("\u{f3be}")
#let fa-turn-down-left = fa-icon.with("\u{e331}")
#let fa-turn-down-right = fa-icon.with("\u{e455}")
#let fa-turn-left = fa-icon.with("\u{e636}")
#let fa-turn-left-down = fa-icon.with("\u{e637}")
#let fa-turn-left-up = fa-icon.with("\u{e638}")
#let fa-turn-right = fa-icon.with("\u{e639}")
#let fa-turntable = fa-icon.with("\u{f8e4}")
#let fa-turn-up = fa-icon.with("\u{f3bf}")
#let fa-level-up-alt = fa-icon.with("\u{f3bf}")
#let fa-turtle = fa-icon.with("\u{f726}")
#let fa-tv = fa-icon.with("\u{f26c}")
#let fa-television = fa-icon.with("\u{f26c}")
#let fa-tv-alt = fa-icon.with("\u{f26c}")
#let fa-tv-music = fa-icon.with("\u{f8e6}")
#let fa-tv-retro = fa-icon.with("\u{f401}")
#let fa-twitch = fa-icon.with("\u{f1e8}")
#let fa-twitter = fa-icon.with("\u{f099}")
#let fa-typewriter = fa-icon.with("\u{f8e7}")
#let fa-typo3 = fa-icon.with("\u{f42b}")
#let fa-u = fa-icon.with("\u{55}")
#let fa-uber = fa-icon.with("\u{f402}")
#let fa-ubuntu = fa-icon.with("\u{f7df}")
#let fa-ufo = fa-icon.with("\u{e047}")
#let fa-ufo-beam = fa-icon.with("\u{e048}")
#let fa-uikit = fa-icon.with("\u{f403}")
#let fa-umbraco = fa-icon.with("\u{f8e8}")
#let fa-umbrella = fa-icon.with("\u{f0e9}")
#let fa-umbrella-beach = fa-icon.with("\u{f5ca}")
#let fa-umbrella-simple = fa-icon.with("\u{e2bc}")
#let fa-umbrella-alt = fa-icon.with("\u{e2bc}")
#let fa-uncharted = fa-icon.with("\u{e084}")
#let fa-underline = fa-icon.with("\u{f0cd}")
#let fa-unicorn = fa-icon.with("\u{f727}")
#let fa-uniform-martial-arts = fa-icon.with("\u{e3d1}")
#let fa-union = fa-icon.with("\u{f6a2}")
#let fa-uniregistry = fa-icon.with("\u{f404}")
#let fa-unity = fa-icon.with("\u{e049}")
#let fa-universal-access = fa-icon.with("\u{f29a}")
#let fa-unlock = fa-icon.with("\u{f09c}")
#let fa-unlock-keyhole = fa-icon.with("\u{f13e}")
#let fa-unlock-alt = fa-icon.with("\u{f13e}")
#let fa-unsplash = fa-icon.with("\u{e07c}")
#let fa-untappd = fa-icon.with("\u{f405}")
#let fa-up = fa-icon.with("\u{f357}")
#let fa-arrow-alt-up = fa-icon.with("\u{f357}")
#let fa-up-down = fa-icon.with("\u{f338}")
#let fa-arrows-alt-v = fa-icon.with("\u{f338}")
#let fa-up-down-left-right = fa-icon.with("\u{f0b2}")
#let fa-arrows-alt = fa-icon.with("\u{f0b2}")
#let fa-up-from-bracket = fa-icon.with("\u{e590}")
#let fa-up-from-dotted-line = fa-icon.with("\u{e456}")
#let fa-up-from-line = fa-icon.with("\u{f346}")
#let fa-arrow-alt-from-bottom = fa-icon.with("\u{f346}")
#let fa-up-left = fa-icon.with("\u{e2bd}")
#let fa-upload = fa-icon.with("\u{f093}")
#let fa-up-long = fa-icon.with("\u{f30c}")
#let fa-long-arrow-alt-up = fa-icon.with("\u{f30c}")
#let fa-up-right = fa-icon.with("\u{e2be}")
#let fa-up-right-and-down-left-from-center = fa-icon.with("\u{f424}")
#let fa-expand-alt = fa-icon.with("\u{f424}")
#let fa-up-right-from-square = fa-icon.with("\u{f35d}")
#let fa-external-link-alt = fa-icon.with("\u{f35d}")
#let fa-ups = fa-icon.with("\u{f7e0}")
#let fa-up-to-bracket = fa-icon.with("\u{e66e}")
#let fa-up-to-dotted-line = fa-icon.with("\u{e457}")
#let fa-up-to-line = fa-icon.with("\u{f34d}")
#let fa-arrow-alt-to-top = fa-icon.with("\u{f34d}")
#let fa-upwork = fa-icon.with("\u{e641}")
#let fa-usb = fa-icon.with("\u{f287}")
#let fa-usb-drive = fa-icon.with("\u{f8e9}")
#let fa-user = fa-icon.with("\u{f007}")
#let fa-user-alien = fa-icon.with("\u{e04a}")
#let fa-user-astronaut = fa-icon.with("\u{f4fb}")
#let fa-user-beard-bolt = fa-icon.with("\u{e689}")
#let fa-user-bounty-hunter = fa-icon.with("\u{e2bf}")
#let fa-user-check = fa-icon.with("\u{f4fc}")
#let fa-user-chef = fa-icon.with("\u{e3d2}")
#let fa-user-clock = fa-icon.with("\u{f4fd}")
#let fa-user-cowboy = fa-icon.with("\u{f8ea}")
#let fa-user-crown = fa-icon.with("\u{f6a4}")
#let fa-user-doctor = fa-icon.with("\u{f0f0}")
#let fa-user-md = fa-icon.with("\u{f0f0}")
#let fa-user-doctor-hair = fa-icon.with("\u{e458}")
#let fa-user-doctor-hair-long = fa-icon.with("\u{e459}")
#let fa-user-doctor-message = fa-icon.with("\u{f82e}")
#let fa-user-md-chat = fa-icon.with("\u{f82e}")
#let fa-user-gear = fa-icon.with("\u{f4fe}")
#let fa-user-cog = fa-icon.with("\u{f4fe}")
#let fa-user-graduate = fa-icon.with("\u{f501}")
#let fa-user-group = fa-icon.with("\u{f500}")
#let fa-user-friends = fa-icon.with("\u{f500}")
#let fa-user-group-crown = fa-icon.with("\u{f6a5}")
#let fa-users-crown = fa-icon.with("\u{f6a5}")
#let fa-user-group-simple = fa-icon.with("\u{e603}")
#let fa-user-hair = fa-icon.with("\u{e45a}")
#let fa-user-hair-buns = fa-icon.with("\u{e3d3}")
#let fa-user-hair-long = fa-icon.with("\u{e45b}")
#let fa-user-hair-mullet = fa-icon.with("\u{e45c}")
#let fa-business-front = fa-icon.with("\u{e45c}")
#let fa-party-back = fa-icon.with("\u{e45c}")
#let fa-trian-balbot = fa-icon.with("\u{e45c}")
#let fa-user-headset = fa-icon.with("\u{f82d}")
#let fa-user-helmet-safety = fa-icon.with("\u{f82c}")
#let fa-user-construction = fa-icon.with("\u{f82c}")
#let fa-user-hard-hat = fa-icon.with("\u{f82c}")
#let fa-user-hoodie = fa-icon.with("\u{e68a}")
#let fa-user-injured = fa-icon.with("\u{f728}")
#let fa-user-large = fa-icon.with("\u{f406}")
#let fa-user-alt = fa-icon.with("\u{f406}")
#let fa-user-large-slash = fa-icon.with("\u{f4fa}")
#let fa-user-alt-slash = fa-icon.with("\u{f4fa}")
#let fa-user-lock = fa-icon.with("\u{f502}")
#let fa-user-magnifying-glass = fa-icon.with("\u{e5c5}")
#let fa-user-minus = fa-icon.with("\u{f503}")
#let fa-user-music = fa-icon.with("\u{f8eb}")
#let fa-user-ninja = fa-icon.with("\u{f504}")
#let fa-user-nurse = fa-icon.with("\u{f82f}")
#let fa-user-nurse-hair = fa-icon.with("\u{e45d}")
#let fa-user-nurse-hair-long = fa-icon.with("\u{e45e}")
#let fa-user-pen = fa-icon.with("\u{f4ff}")
#let fa-user-edit = fa-icon.with("\u{f4ff}")
#let fa-user-pilot = fa-icon.with("\u{e2c0}")
#let fa-user-pilot-tie = fa-icon.with("\u{e2c1}")
#let fa-user-plus = fa-icon.with("\u{f234}")
#let fa-user-police = fa-icon.with("\u{e333}")
#let fa-user-police-tie = fa-icon.with("\u{e334}")
#let fa-user-robot = fa-icon.with("\u{e04b}")
#let fa-user-robot-xmarks = fa-icon.with("\u{e4a7}")
#let fa-users = fa-icon.with("\u{f0c0}")
#let fa-users-between-lines = fa-icon.with("\u{e591}")
#let fa-user-secret = fa-icon.with("\u{f21b}")
#let fa-users-gear = fa-icon.with("\u{f509}")
#let fa-users-cog = fa-icon.with("\u{f509}")
#let fa-user-shakespeare = fa-icon.with("\u{e2c2}")
#let fa-user-shield = fa-icon.with("\u{f505}")
#let fa-user-slash = fa-icon.with("\u{f506}")
#let fa-users-line = fa-icon.with("\u{e592}")
#let fa-users-medical = fa-icon.with("\u{f830}")
#let fa-users-rays = fa-icon.with("\u{e593}")
#let fa-users-rectangle = fa-icon.with("\u{e594}")
#let fa-users-slash = fa-icon.with("\u{e073}")
#let fa-users-viewfinder = fa-icon.with("\u{e595}")
#let fa-user-tag = fa-icon.with("\u{f507}")
#let fa-user-tie = fa-icon.with("\u{f508}")
#let fa-user-tie-hair = fa-icon.with("\u{e45f}")
#let fa-user-tie-hair-long = fa-icon.with("\u{e460}")
#let fa-user-unlock = fa-icon.with("\u{e058}")
#let fa-user-visor = fa-icon.with("\u{e04c}")
#let fa-user-vneck = fa-icon.with("\u{e461}")
#let fa-user-vneck-hair = fa-icon.with("\u{e462}")
#let fa-user-vneck-hair-long = fa-icon.with("\u{e463}")
#let fa-user-xmark = fa-icon.with("\u{f235}")
#let fa-user-times = fa-icon.with("\u{f235}")
#let fa-usps = fa-icon.with("\u{f7e1}")
#let fa-ussunnah = fa-icon.with("\u{f407}")
#let fa-utensils = fa-icon.with("\u{f2e7}")
#let fa-cutlery = fa-icon.with("\u{f2e7}")
#let fa-utensils-slash = fa-icon.with("\u{e464}")
#let fa-utility-pole = fa-icon.with("\u{e2c3}")
#let fa-utility-pole-double = fa-icon.with("\u{e2c4}")
#let fa-v = fa-icon.with("\u{56}")
#let fa-vaadin = fa-icon.with("\u{f408}")
#let fa-vacuum = fa-icon.with("\u{e04d}")
#let fa-vacuum-robot = fa-icon.with("\u{e04e}")
#let fa-value-absolute = fa-icon.with("\u{f6a6}")
#let fa-van-shuttle = fa-icon.with("\u{f5b6}")
#let fa-shuttle-van = fa-icon.with("\u{f5b6}")
#let fa-vault = fa-icon.with("\u{e2c5}")
#let fa-vector-circle = fa-icon.with("\u{e2c6}")
#let fa-vector-polygon = fa-icon.with("\u{e2c7}")
#let fa-vector-square = fa-icon.with("\u{f5cb}")
#let fa-vent-damper = fa-icon.with("\u{e465}")
#let fa-venus = fa-icon.with("\u{f221}")
#let fa-venus-double = fa-icon.with("\u{f226}")
#let fa-venus-mars = fa-icon.with("\u{f228}")
#let fa-vest = fa-icon.with("\u{e085}")
#let fa-vest-patches = fa-icon.with("\u{e086}")
#let fa-viacoin = fa-icon.with("\u{f237}")
#let fa-viadeo = fa-icon.with("\u{f2a9}")
#let fa-vial = fa-icon.with("\u{f492}")
#let fa-vial-circle-check = fa-icon.with("\u{e596}")
#let fa-vials = fa-icon.with("\u{f493}")
#let fa-vial-virus = fa-icon.with("\u{e597}")
#let fa-viber = fa-icon.with("\u{f409}")
#let fa-video = fa-icon.with("\u{f03d}")
#let fa-video-camera = fa-icon.with("\u{f03d}")
#let fa-video-arrow-down-left = fa-icon.with("\u{e2c8}")
#let fa-video-arrow-up-right = fa-icon.with("\u{e2c9}")
#let fa-video-plus = fa-icon.with("\u{f4e1}")
#let fa-video-slash = fa-icon.with("\u{f4e2}")
#let fa-vihara = fa-icon.with("\u{f6a7}")
#let fa-vimeo = fa-icon.with("\u{f40a}")
#let fa-vimeo-v = fa-icon.with("\u{f27d}")
#let fa-vine = fa-icon.with("\u{f1ca}")
#let fa-violin = fa-icon.with("\u{f8ed}")
#let fa-virus = fa-icon.with("\u{e074}")
#let fa-virus-covid = fa-icon.with("\u{e4a8}")
#let fa-virus-covid-slash = fa-icon.with("\u{e4a9}")
#let fa-viruses = fa-icon.with("\u{e076}")
#let fa-virus-slash = fa-icon.with("\u{e075}")
#let fa-vk = fa-icon.with("\u{f189}")
#let fa-vnv = fa-icon.with("\u{f40b}")
#let fa-voicemail = fa-icon.with("\u{f897}")
#let fa-volcano = fa-icon.with("\u{f770}")
#let fa-volleyball = fa-icon.with("\u{f45f}")
#let fa-volleyball-ball = fa-icon.with("\u{f45f}")
#let fa-volume = fa-icon.with("\u{f6a8}")
#let fa-volume-medium = fa-icon.with("\u{f6a8}")
#let fa-volume-high = fa-icon.with("\u{f028}")
#let fa-volume-up = fa-icon.with("\u{f028}")
#let fa-volume-low = fa-icon.with("\u{f027}")
#let fa-volume-down = fa-icon.with("\u{f027}")
#let fa-volume-off = fa-icon.with("\u{f026}")
#let fa-volume-slash = fa-icon.with("\u{f2e2}")
#let fa-volume-xmark = fa-icon.with("\u{f6a9}")
#let fa-volume-mute = fa-icon.with("\u{f6a9}")
#let fa-volume-times = fa-icon.with("\u{f6a9}")
#let fa-vr-cardboard = fa-icon.with("\u{f729}")
#let fa-vuejs = fa-icon.with("\u{f41f}")
#let fa-w = fa-icon.with("\u{57}")
#let fa-waffle = fa-icon.with("\u{e466}")
#let fa-wagon-covered = fa-icon.with("\u{f8ee}")
#let fa-walker = fa-icon.with("\u{f831}")
#let fa-walkie-talkie = fa-icon.with("\u{f8ef}")
#let fa-wallet = fa-icon.with("\u{f555}")
#let fa-wand = fa-icon.with("\u{f72a}")
#let fa-wand-magic = fa-icon.with("\u{f0d0}")
#let fa-magic = fa-icon.with("\u{f0d0}")
#let fa-wand-magic-sparkles = fa-icon.with("\u{e2ca}")
#let fa-magic-wand-sparkles = fa-icon.with("\u{e2ca}")
#let fa-wand-sparkles = fa-icon.with("\u{f72b}")
#let fa-warehouse = fa-icon.with("\u{f494}")
#let fa-warehouse-full = fa-icon.with("\u{f495}")
#let fa-warehouse-alt = fa-icon.with("\u{f495}")
#let fa-washing-machine = fa-icon.with("\u{f898}")
#let fa-washer = fa-icon.with("\u{f898}")
#let fa-watch = fa-icon.with("\u{f2e1}")
#let fa-watch-apple = fa-icon.with("\u{e2cb}")
#let fa-watch-calculator = fa-icon.with("\u{f8f0}")
#let fa-watch-fitness = fa-icon.with("\u{f63e}")
#let fa-watchman-monitoring = fa-icon.with("\u{e087}")
#let fa-watch-smart = fa-icon.with("\u{e2cc}")
#let fa-water = fa-icon.with("\u{f773}")
#let fa-water-arrow-down = fa-icon.with("\u{f774}")
#let fa-water-lower = fa-icon.with("\u{f774}")
#let fa-water-arrow-up = fa-icon.with("\u{f775}")
#let fa-water-rise = fa-icon.with("\u{f775}")
#let fa-water-ladder = fa-icon.with("\u{f5c5}")
#let fa-ladder-water = fa-icon.with("\u{f5c5}")
#let fa-swimming-pool = fa-icon.with("\u{f5c5}")
#let fa-watermelon-slice = fa-icon.with("\u{e337}")
#let fa-wave = fa-icon.with("\u{e65b}")
#let fa-waveform = fa-icon.with("\u{f8f1}")
#let fa-waveform-lines = fa-icon.with("\u{f8f2}")
#let fa-waveform-path = fa-icon.with("\u{f8f2}")
#let fa-wave-pulse = fa-icon.with("\u{f5f8}")
#let fa-heart-rate = fa-icon.with("\u{f5f8}")
#let fa-wave-sine = fa-icon.with("\u{f899}")
#let fa-wave-square = fa-icon.with("\u{f83e}")
#let fa-waves-sine = fa-icon.with("\u{e65d}")
#let fa-wave-triangle = fa-icon.with("\u{f89a}")
#let fa-waze = fa-icon.with("\u{f83f}")
#let fa-web-awesome = fa-icon.with("\u{e682}")
#let fa-webflow = fa-icon.with("\u{e65c}")
#let fa-webhook = fa-icon.with("\u{e5d5}")
#let fa-weebly = fa-icon.with("\u{f5cc}")
#let fa-weibo = fa-icon.with("\u{f18a}")
#let fa-weight-hanging = fa-icon.with("\u{f5cd}")
#let fa-weight-scale = fa-icon.with("\u{f496}")
#let fa-weight = fa-icon.with("\u{f496}")
#let fa-weixin = fa-icon.with("\u{f1d7}")
#let fa-whale = fa-icon.with("\u{f72c}")
#let fa-whatsapp = fa-icon.with("\u{f232}")
#let fa-wheat = fa-icon.with("\u{f72d}")
#let fa-wheat-awn = fa-icon.with("\u{e2cd}")
#let fa-wheat-alt = fa-icon.with("\u{e2cd}")
#let fa-wheat-awn-circle-exclamation = fa-icon.with("\u{e598}")
#let fa-wheat-awn-slash = fa-icon.with("\u{e338}")
#let fa-wheat-slash = fa-icon.with("\u{e339}")
#let fa-wheelchair = fa-icon.with("\u{f193}")
#let fa-wheelchair-move = fa-icon.with("\u{e2ce}")
#let fa-wheelchair-alt = fa-icon.with("\u{e2ce}")
#let fa-whiskey-glass = fa-icon.with("\u{f7a0}")
#let fa-glass-whiskey = fa-icon.with("\u{f7a0}")
#let fa-whiskey-glass-ice = fa-icon.with("\u{f7a1}")
#let fa-glass-whiskey-rocks = fa-icon.with("\u{f7a1}")
#let fa-whistle = fa-icon.with("\u{f460}")
#let fa-whmcs = fa-icon.with("\u{f40d}")
#let fa-wifi = fa-icon.with("\u{f1eb}")
#let fa-wifi-3 = fa-icon.with("\u{f1eb}")
#let fa-wifi-strong = fa-icon.with("\u{f1eb}")
#let fa-wifi-exclamation = fa-icon.with("\u{e2cf}")
#let fa-wifi-fair = fa-icon.with("\u{f6ab}")
#let fa-wifi-2 = fa-icon.with("\u{f6ab}")
#let fa-wifi-slash = fa-icon.with("\u{f6ac}")
#let fa-wifi-weak = fa-icon.with("\u{f6aa}")
#let fa-wifi-1 = fa-icon.with("\u{f6aa}")
#let fa-wikipedia-w = fa-icon.with("\u{f266}")
#let fa-wind = fa-icon.with("\u{f72e}")
#let fa-window = fa-icon.with("\u{f40e}")
#let fa-window-flip = fa-icon.with("\u{f40f}")
#let fa-window-alt = fa-icon.with("\u{f40f}")
#let fa-window-frame = fa-icon.with("\u{e04f}")
#let fa-window-frame-open = fa-icon.with("\u{e050}")
#let fa-window-maximize = fa-icon.with("\u{f2d0}")
#let fa-window-minimize = fa-icon.with("\u{f2d1}")
#let fa-window-restore = fa-icon.with("\u{f2d2}")
#let fa-windows = fa-icon.with("\u{f17a}")
#let fa-windsock = fa-icon.with("\u{f777}")
#let fa-wind-turbine = fa-icon.with("\u{f89b}")
#let fa-wind-warning = fa-icon.with("\u{f776}")
#let fa-wind-circle-exclamation = fa-icon.with("\u{f776}")
#let fa-wine-bottle = fa-icon.with("\u{f72f}")
#let fa-wine-glass = fa-icon.with("\u{f4e3}")
#let fa-wine-glass-crack = fa-icon.with("\u{f4bb}")
#let fa-fragile = fa-icon.with("\u{f4bb}")
#let fa-wine-glass-empty = fa-icon.with("\u{f5ce}")
#let fa-wine-glass-alt = fa-icon.with("\u{f5ce}")
#let fa-wirsindhandwerk = fa-icon.with("\u{e2d0}")
#let fa-wsh = fa-icon.with("\u{e2d0}")
#let fa-wix = fa-icon.with("\u{f5cf}")
#let fa-wizards-of-the-coast = fa-icon.with("\u{f730}")
#let fa-wodu = fa-icon.with("\u{e088}")
#let fa-wolf-pack-battalion = fa-icon.with("\u{f514}")
#let fa-won-sign = fa-icon.with("\u{f159}")
#let fa-krw = fa-icon.with("\u{f159}")
#let fa-won = fa-icon.with("\u{f159}")
#let fa-wordpress = fa-icon.with("\u{f19a}")
#let fa-wordpress-simple = fa-icon.with("\u{f411}")
#let fa-worm = fa-icon.with("\u{e599}")
#let fa-wpbeginner = fa-icon.with("\u{f297}")
#let fa-wpexplorer = fa-icon.with("\u{f2de}")
#let fa-wpforms = fa-icon.with("\u{f298}")
#let fa-wpressr = fa-icon.with("\u{f3e4}")
#let fa-rendact = fa-icon.with("\u{f3e4}")
#let fa-wreath = fa-icon.with("\u{f7e2}")
#let fa-wreath-laurel = fa-icon.with("\u{e5d2}")
#let fa-wrench = fa-icon.with("\u{f0ad}")
#let fa-wrench-simple = fa-icon.with("\u{e2d1}")
#let fa-x = fa-icon.with("\u{58}")
#let fa-xbox = fa-icon.with("\u{f412}")
#let fa-xing = fa-icon.with("\u{f168}")
#let fa-xmark = fa-icon.with("\u{f00d}")
#let fa-close = fa-icon.with("\u{f00d}")
#let fa-multiply = fa-icon.with("\u{f00d}")
#let fa-remove = fa-icon.with("\u{f00d}")
#let fa-times = fa-icon.with("\u{f00d}")
#let fa-xmark-large = fa-icon.with("\u{e59b}")
#let fa-xmarks-lines = fa-icon.with("\u{e59a}")
#let fa-xmark-to-slot = fa-icon.with("\u{f771}")
#let fa-times-to-slot = fa-icon.with("\u{f771}")
#let fa-vote-nay = fa-icon.with("\u{f771}")
#let fa-x-ray = fa-icon.with("\u{f497}")
#let fa-x-twitter = fa-icon.with("\u{e61b}")
#let fa-y = fa-icon.with("\u{59}")
#let fa-yahoo = fa-icon.with("\u{f19e}")
#let fa-yammer = fa-icon.with("\u{f840}")
#let fa-yandex = fa-icon.with("\u{f413}")
#let fa-yandex-international = fa-icon.with("\u{f414}")
#let fa-yarn = fa-icon.with("\u{f7e3}")
#let fa-y-combinator = fa-icon.with("\u{f23b}")
#let fa-yelp = fa-icon.with("\u{f1e9}")
#let fa-yen-sign = fa-icon.with("\u{f157}")
#let fa-cny = fa-icon.with("\u{f157}")
#let fa-jpy = fa-icon.with("\u{f157}")
#let fa-rmb = fa-icon.with("\u{f157}")
#let fa-yen = fa-icon.with("\u{f157}")
#let fa-yin-yang = fa-icon.with("\u{f6ad}")
#let fa-yoast = fa-icon.with("\u{f2b1}")
#let fa-youtube = fa-icon.with("\u{f167}")
#let fa-z = fa-icon.with("\u{5a}")
#let fa-zhihu = fa-icon.with("\u{f63f}")
|
https://github.com/duskmoon314/THU_AMA | https://raw.githubusercontent.com/duskmoon314/THU_AMA/main/book.typ | typst | Creative Commons Attribution 4.0 International |
#import "@preview/book:0.2.5": *
#show: book
#book-meta(
title: "应用近世代数：笔记",
description: "暮月上清华大学「应用近世代数」课程时记下的笔记",
authors: ("暮月",),
language: "zh",
repository: "https://github.com/duskmoon314/THU_AMA",
summary: [
- #chapter("docs/ch1/0-序论与背景知识.typ", section: "1")[序论与背景知识]
- #chapter("docs/ch1/1-背景.typ", section: "1.1")[背景]
- #chapter("docs/ch1/2-发展史.typ", section: "1.2")[发展史]
- #chapter("docs/ch1/3-例题与应用.typ", section: "1.3")[例题与应用]
- #chapter("docs/ch2/0-群论.typ", section: "2")[群论]
- #chapter("docs/ch2/1-概念与例子.typ", section: "2.1")[概念与例子]
- #chapter("docs/ch2/2-内部结构.typ", section: "2.2")[内部结构]
- #chapter("docs/ch2/3-外部联系.typ", section: "2.3")[外部联系]
- #chapter("docs/ch2/4-群在集合上的作用.typ", section: "2.4")[群在集合上的作用]
- #chapter("docs/ch2/5-群的应用.typ", section: "2.5")[群的应用]
- #chapter("docs/ch3/0-环论.typ", section: "3")[环论]
- #chapter("docs/ch3/1-基本概念与例子.typ", section: "3.1")[基本概念与例子]
- #chapter("docs/ch3/2-环的内部结构.typ", section: "3.2")[环的内部结构]
- #chapter("docs/ch3/3-特殊环.typ", section: "3.3")[特殊环]
- #chapter("docs/ch3/4-环的应用.typ", section: "3.4")[环的应用]
- #chapter("docs/ch4/0-域论.typ", section: "4")[域论]
- #chapter("docs/ch4/1-域和域扩张.typ", section: "4.1")[域和域扩张]
],
)
// re-export page template
#import "/templates/page.typ": project
#let book-page = project
// Other preamble
#import "@preview/ctheorems:1.1.2": *
#let thmrules = thmrules.with(qed-symbol: $square$)
#let theorem = thmbox("theorem", "定理", fill: rgb("#b3e2cd"))
#let definition = thmbox("definition", "定义", fill: rgb("#fdcdac"))
#let example = thmbox("example", "例", fill: rgb("#cbd5e8"))
#let corollary = thmbox("corollary", "推论", fill: rgb("#f4cae4"))
#let property = thmbox("property", "性质", fill: rgb("#e6f5c9"))
#let proposition = thmbox("proposition", "命题", fill: rgb("#fff2ae"))
#let remark = thmplain("remark", "注").with(number: none)
#let proof = thmplain("proof", "证明").with(number: none)
#let solution = thmplain("solution", "解").with(number: none)
#let cyclicgroup(body) = {
$angle.l #body angle.r$
} |
https://github.com/piggsoft/mdbook-typst-piggsoft | https://raw.githubusercontent.com/piggsoft/mdbook-typst-piggsoft/master/src/assets/template.typ | typst | #set text(lang: "zh", region: "cn")
#set document(title: document_title, author: document_authors, keywords: document_keywords, date: auto)
#set page(
numbering: "1 / 1",
number-align: right,
)
// [
// #set align(right)
// #set text(13pt)
// #counter(page).display(
// "1 / 1",
// both: true,
// )
// ]
#set pagebreak(weak: true)
#set par(justify: true)
#set heading(numbering: "1.1.")
#show outline.entry.where(level: 1):it => {
v(11pt, weak: true)
strong(it)
}
#show heading: it => [
#block(above: 2em, below: 2em, it)
]
#set table(
fill: (col, row) =>
if calc.odd(row) {
luma(240)
} else {
white
}
)
#set quote(block: true)
#show link: underline
#show link: set text(blue)
//---------------------content start-----------------
#align(center, text(17pt)[
*#document_title*
])
#let jb = linebreak(justify: true)
#align(right, text(15pt)[
#let index = 4
#while index > 0 {
index = index - 1
jb
}
#for author in document_authors {
author
jb
}
])
#pagebreak()
#outline(depth: section_depth, /*indent: 2em*/)
#pagebreak()
|
|
https://github.com/Brndan/formalettre | https://raw.githubusercontent.com/Brndan/formalettre/main/README.md | markdown | BSD 3-Clause "New" or "Revised" License | # Formalettre : writing french letters with typst
Un template destiné à écrire des lettres selon une typographie francophone, et inspiré du package LaTeX [lettre](https://ctan.org/pkg/lettre).
Pour utiliser le template, il est possible de recopier le fichier exemple.
## Documentation des variables
### Expéditeur
- `expediteur.nom` : nom de famille de l'expéditeur·ice, **requis**.
- `expediteur.prenom` : prénom de l'expéditeur·ice, **requis**.
- `expediteur.voie` : numéro de voie et nom de la voie, **requis**.
- `expediteur.complement_adresse` : la seconde ligne parfois requise dans une adresse, *facultatif*.
- `expediteur.code_postal` : code postal, **requis**.
- `expediteur.commune` : commune de l'expéditeur·ice, **requis**.
- `expediteur.telephone` : numéro de téléphone. Le format est libre et l'affichage en police mono. *Facultatif*.
- `expediteur.email` : l'email fourni sera affiché en police mono et cliquable. *Facultatif*
- `expediteur.signature` : peut être `true` ou `false`, par défaut `false`. Prévient le paquet qu’une image de signature sera ajoutée, de manière à organiser la superposition de la signature et du nom apposé en fin de courrier.
## Destinataire
- `destinataire.titre` : titre du ou de la destinataire, **requis**.
- `destinataire.voie` : numéro de voie et nom de la voie, **requis**.
- `destinataire.complement_adresse` : la seconde ligne parfois requise dans une adresse, *facultatif*.
- `destinataire.code_postal` : code postal, **requis**.
- `destinataire.commune` : commune de l'expéditeur·ice, **requis**.
- `destinataire.sc` : si le courrier est envoyé “sous couvert” d'une hiérarchie intermédiaire, spécifier cette autorité. *Facultatif*.
## Lettre
- `objet` : l'objet du courrier, **requis**.
- `date` : date à indiquer sous forme libre, **requis**.
- `lieu` : lieu de rédaction, **requis**.
- `pj` : permet d'indiquer la présence de pièces jointes. Il est possible d'en faire une liste, par exemple :
```
pj: [
+ Dossier n°1
+ Dossier n° 2
+ Attestation
]
```
Le texte de la lettre proprement dite se situe après la configuration de la lettre.
À la fin de la lettre, il est possible de décommenter les deux dernières lignes pour ajouter une image en guise de signature. Veillez dans ce cas à positionner la varibale `expediteur.signature` à `true`.
|
https://github.com/LDemetrios/Typst4k | https://raw.githubusercontent.com/LDemetrios/Typst4k/master/src/test/resources/suite/layout/inline/baseline.typ | typst | // Test baseline handling.
--- baseline-text ---
Hi #text(1.5em)[You], #text(0.75em)[how are you?]
Our cockatoo was one of the
#text(baseline: -0.2em)[#box(circle(radius: 2pt)) first]
#text(baseline: 0.2em)[birds #box(circle(radius: 2pt))]
that ever learned to mimic a human voice.
--- baseline-box ---
Hey #box(baseline: 40%, image("/assets/images/tiger.jpg", width: 1.5cm)) there!
--- issue-2214-baseline-math ---
// The math content should also be affected by the TextElem baseline.
hello #text(baseline: -5pt)[123 #sym.WW\orld]\
hello #text(baseline: -5pt)[$123 WW#text[or]$ld]\
|
|
https://github.com/Enter-tainer/typstyle | https://raw.githubusercontent.com/Enter-tainer/typstyle/master/tests/assets/unit/escape.typ | typst | Apache License 2.0 | I got an ice cream for
\$1.50! \u{1f600}
|
https://github.com/jomaway/typst-teacher-templates | https://raw.githubusercontent.com/jomaway/typst-teacher-templates/main/ttt-utils/lib/components.typ | typst | MIT License | /// Helper and utility functions
/// Create a block of lines like in a lined notebook.
///
/// - rows (int): number of rows to
/// -> content
#let lines(rows) = {
for _ in range(rows) {
block(above: 0.9cm, line(length:100%, stroke: 0.3pt + black.lighten(20%)) )
}
}
/// Create a checked grid like in a checkered notebook.
///
/// - rows (int): number of rows to
/// - cols (auto, int): define the number of cols, if auto cols are 0.5cm wide.
/// -> content
#let caro(rows, cols:auto) = {
layout(size => {
let cols = if( cols == auto ){ int(size.width.cm() / 0.5) } else { cols }
table(
columns: (0.5cm,) * cols,
rows: (0.5cm,) * rows,
stroke: 0.3pt + luma(140),
table.cell(y: rows - 1)[],
)
})
}
/// Create a small line with a label like a signature field in a form.
///
/// - label (string): label which is rendered underneath the line.
/// - width (length): width of the field.
/// - value (content, any): content which is shown inside the field.
/// -> content
#let field(label, width: 3.5cm, value: none) = {
box(
stroke: (bottom: 0.5pt),
width: width,
height: 0.8cm,
inset: (bottom: 3pt)
)[
#align(bottom + center,value)
#place(bottom + end,dy: 12pt)[#text(10pt, label)]
]
}
/// Create a checkbox
///
/// - fill (color): background color of the box
/// - tick (bool): if true a checkmark symbol is shown inside the box.
/// -> content
#let checkbox(fill: none, tick: false) = box(
width: 0.8em,
height: 0.8em,
stroke: 0.7pt,
radius: 1pt,
fill: fill,
if (tick) { align(horizon + center, sym.checkmark) }
)
/// Create a rounded box around some content.
///
/// - body (content): the content to show.
/// - ..args (arguments): passed to typst `box` function
#let frame(body, ..args) = box(radius: 3pt, stroke: 0.5pt, inset: 1em, ..args, body)
/// Create a autosized small colored and rounded box around the content.
///
/// - value (content): the content to show
/// - fill (color): background of the box
/// -> content
#let tag(value, fill: orange.lighten(45%)) = {
if value != none {
context {
let size = measure(value)
box(
width: size.width + 6pt,
inset: (x: 3pt, y: 0pt),
outset: (y: 3pt),
radius: 2pt,
fill: fill
)[#value]
}
}
}
/// Create a small tag label with the given amount of points.
///
/// - points (int): given get_points
/// -> content
#let point-tag(points) = {
assert.eq(type(points),int)
tag(fill: gray.lighten(35%))[#points #text(0.8em,smallcaps[#if points==1 [PT$\u{0020}$] else [PTs]])]
} |
https://github.com/KrisjanisP/lu-icpc-notebook | https://raw.githubusercontent.com/KrisjanisP/lu-icpc-notebook/main/7-dynamic.typ | typst |
= Dynamic programming
== Convex hull trick
```cpp
// Convex Hull Trick
// ATTENTION: This is the maximum convex hull. If you need the minimum
// CHT use {-b, -m} and modify the query function.
// In case of floating point parameters swap long long with long double
typedef long long type;
struct line { type b, m; };
line v[N]; // lines from input
int n; // number of lines
// Sort slopes in ascending order (in main):
sort(v, v+n, [](line s, line t){
return (s.m == t.m) ? (s.b < t.b) : (s.m < t.m); });
// nh: number of lines on convex hull
// pos: position for linear time search
// hull: lines in the convex hull
int nh, pos;
line hull[N];
bool check(line s, line t, line u) {
// verify if it can overflow. If it can just divide using long double
return (s.b - t.b)*(u.m - s.m) < (s.b - u.b)*(t.m - s.m);
}
// Add new line to convex hull, if possible
// Must receive lines in the correct order, otherwise it won't work
void update(line s) {
// 1. if first lines have the same b, get the one with bigger m
// 2. if line is parallel to the one at the top, ignore
// 3. pop lines that are worse
// 3.1 if you can do a linear time search, use
// 4. add new line
if (nh == 1 and hull[nh-1].b == s.b) nh--;
if (nh > 0 and hull[nh-1].m >= s.m) return;
while (nh >= 2 and !check(hull[nh-2], hull[nh-1], s)) nh--;
pos = min(pos, nh);
hull[nh++] = s;
}
type eval(int id, type x) { return hull[id].b + hull[id].m * x; }
// Linear search query - O(n) for all queries
// Only possible if the queries always move to the right
type query(type x) {
while (pos+1 < nh and eval(pos, x) < eval(pos+1, x)) pos++;
return eval(pos, x);
// return -eval(pos, x); ATTENTION: Uncomment for minimum CHT
}
```
#block( breakable: false,[
== Online Convex Hull Trick
```cpp
// Source: KTH notebook
struct Line {
mutable ll k, m, p;
bool operator<(const Line& o) const { return k < o.k; }
bool operator<(ll x) const { return p < x; }
};
struct LineContainer : multiset<Line, less<>> {
// (for doubles, use inf = 1/.0, div(a,b) = a/b)
static const ll inf = LLONG_MAX;
ll div(ll a, ll b) { // floored division
return a / b - ((a ^ b) < 0 && a % b); }
bool isect(iterator x, iterator y) {
if (y == end()) return x->p = inf, 0;
if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
else x->p = div(y->m - x->m, x->k - y->k);
return x->p >= y->p;
}
void add(ll k, ll m) {
auto z = insert({k, m, 0}), y = z++, x = y;
while (isect(y, z)) z = erase(z);
if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
while ((y = x) != begin() && (--x)->p >= y->p)
isect(x, erase(y));
}
ll query(ll x) {
assert(!empty());
auto l = *lower_bound(x);
return l.k * x + l.m;
}
};
```
])
#block( breakable: false,[
== Longest Increasing Subsequence
```cpp
memset(dp, 63, sizeof dp);
for (int i = 0; i < n; ++i) {
// increasing: lower_bound
// non-decreasing: upper_bound
int j = lower_bound(dp, dp + lis, v[i]) - dp;
dp[j] = min(dp[j], v[i]); lis = max(lis, j + 1);
}
```
])
#block( breakable: false,[
== SOS DP (Sum over Subsets)
Sum over subsets (SOS) DP trick efficiently computes the sum of all the subsets of an array with time complexity $O("bits" dot 2^"bits")$.
```cpp
const int bits = 20;
vector<int> a(1<<bits); // initial value of each subset
vector<int> f(1<<bits); // sum over all subsets
// (at f[011] = a[011]+a[001]+a[010]+a[000])
for (int i = 0; i<(1<<bits); i++){f[i] = a[i];}
for (int i = 0; i < bits; i++) {
for(int mask = 0; mask < (1<<bits); mask++){
if(mask & (1<<i)){f[mask] += f[mask^(1<<i)];}
}
}
```
]) |
|
https://github.com/xhalo32/constructive-logic-course | https://raw.githubusercontent.com/xhalo32/constructive-logic-course/master/slides/03-aritmetiikka.typ | typst | #import "@preview/touying:0.4.2": *
#import "slidetheme.typ"
#import "@preview/note-me:0.2.1": *
#import "@preview/prooftrees:0.1.0": *
#let palette = (
rgb("#7287fd"), // lavender
rgb("#209fb5"), // sapphire
rgb("#40a02b"), // green
rgb("#df8e1d"), // yellow
rgb("#fe640b"), // peach
rgb("#e64553"), // maroon
)
#let math-palette = palette.map(c => c.darken(20%))
#show raw: slidetheme.colorize-code(palette)
#show math.equation: it => slidetheme.colorize-math(math-palette, it)
#set raw(syntaxes: "Lean4.sublime-syntax", theme: "Catppuccin Latte.tmTheme")
#set text(font: "Fira Sans", weight: "light", size: 20pt)
// #show raw: it => box(
// fill: rgb("#eff1f5"),
// inset: 8pt,
// radius: 12pt,
// text(fill: rgb("#4c4f69"), it)
// )
#let s = slidetheme.register(aspect-ratio: "16-9")
#let s = (s.methods.info)(
self: s,
title: [Konstruktiivinen logiikka ja formaali todistaminen],
subtitle: [3 -- Aritmetiikka],
author: [<NAME> & <NAME>],
date: datetime.today(),
institution: [Otaniemen lukio],
)
#let (init, slides, touying-outline, alert, speaker-note) = utils.methods(s)
#show: init
#show strong: alert
#let (slide, empty-slide, title-slide, new-section-slide, focus-slide) = utils.slides(s)
#show: slides
== TODO
#todo[
- Peano-aksioomat ympäripyöreästi
- Yhtäsuuruus ja yhtäsuuruustodistukset
- rfl, määritelmällinen yhtäsuuruus
- rw, tapa purkaa yhtäsuuruus (Genzenin inversioperiaate)
- Yhteenlasku funktionaalisessa ohjelmoinnissa
- Kertolasku funktionaalisessa ohjelmoinnissa
- Potenssilaskut funktionaalisessa ohjelmoinnissa
- Liitännäisyys ja vaihdannaisuus luonnollisten lukujen laskutoimituksille
- Johdatus induktioon
- Spoileri (pelkkää rekursiota)
- Käydään läpi todistus siitä, että $x : "Nat" tack.r 0 + x = x$
- Määritelmällinen yhtäsuuruus ja miksi eroaa $x + 0 = x$:stä
]
== Peano-aksioomat
Nolla on luonnollinen luku.
Jos n on luonnollinen luku, `succ n` on luonnollinen luku.
Kaikki luonnolliset luvut ovat joko `zero` tai `succ n`, jossa n on luonnollinen luku.
==
Lause "Nolla on luonnollinen luku.", voidaan ilmaista Leanissä seuraavalla tavalla:
```lean4 zero : Nat```
"Jos n on luonnollinen luku, `succ n` on luonnollinen luku.", voidaan ilmaista:
```lean4 succ (n : Nat) : Nat```
== Induktiivinen määritelmä
"Kaikki luonnolliset luvut ovat joko `zero` tai `succ n`, jossa n on luonnollinen luku."
Ilmaistaan Leanissä käyttäen *induktiivista* määritelmää:
```lean4
inductive Nat where
| zero : Nat
| succ (n : Nat) : Nat
```
Näin ollen saadaan luonnollisten lukujen induktioperiaate, johon palataan myöhemmin. (Kuuluisa yhdeksäs aksiooma)
== Mitä tarkoittaa luonnollisten lukujen yhteenlasku?
Tapa muodostaa kahdesta luvusta kolmas, joka on suuruudeltaan ne molemmat yhdessä.
```lean4
a : Nat
b : Nat
a + b : Nat
```
== Yhteenlaskun neutraalialkio
Luonnollisilla luvuilla on yhteenlaskun suhteen neutraalialkio nolla, jonka lisääminen mihin tahansa lukuun x tuottaa saman luvun x.
```lean4
x : Nat
x + 0 ≡ x
0 + x = x
```
#note[
≡ selitetään pian
]
== Yhteenlaskun määritelmä
```lean4
n : Nat
m : Nat
n + succ m ≡ succ (n + m)
```
#todo[
- palkki-visualisaatio
- rekursiivinen ajattelu
- Miksi yhteenlaskua saadaan käyttää yhteenlaskun määritelmässä?
- Miten vältytään viime tunnilla opitusta kehäpäätelmästä
]
== Luonnollisten lukujen yhteenlaskun vaihdannaisuus
```lean4
n : Nat
m : Nat
n + m = m + n
```
== Luonnollisten lukujen yhteenlaskun liitännäisyys
```lean4
n : Nat
m : Nat
k : Nat
n + (m + k) = (n + m) + k
```
== Peanon yhdeksäs aksiooma
== Luonnollisten lukujen päättelysäännöt
#tree(
axi[],
uni[```lean4 zero : Nat```]
)
#tree(
axi[```lean4 n : Nat```],
uni[```lean4 succ n : Nat```]
)
#tree(
axi[```lean4 motive : Nat → Type*```],
axi[```lean4 hZero : motive zero```],
axi[```lean4 hSucc : motive n → motive (succ n)```],
tri[```lean4 ∀ (n : Nat), motive n```]
)
#todo[
- Selitetään kaikki auki
- ```lean4 Type* ```
- ```lean4 motive ```
]
== Induktiotodistus
#tree(
axi[],
uni[$A$],
axi[],
uni[$B$],
bin[$A and B$],
uni[$B -> (A and B)$],
uni[$A -> (B -> (A and B))$]
) |
|
https://github.com/teshu0/CLIT-report-typst | https://raw.githubusercontent.com/teshu0/CLIT-report-typst/main/class/12/assignment.typ | typst | Creative Commons Zero v1.0 Universal | #import "../../template/utils.typ": title, author, date
#import "../../template/reset.typ": reset
#show: reset
#title("コンピュータリテラシレポート＃12")
#author("2400123, 電通太郎")
#date() // 中を空にすると自動的に今日の日付になる
= 課題の再掲
( ここに課題の要約を記入 )
= レポートの本文
( ここにレポートの本文を記入（適宜章立てを設定すると良い） )
// （ここに作成したWebページの図を入れる）
// （読み手が確認できるようURLも載せる。\url{...} とするとPDFからハイパーリンクされる。「x2410XXX」以降を正しく修正する。）
\url{http://www.edu.cc.uec.ac.jp/~x2410XXX/mypage.html}
= 考察
( ここに考察を記入 )
= アンケート
== Q1：HTMLによるページの記述はどれくらい知っていましたか。今回やってみてどうでしたか。
( ここにQ1の回答を記入 )
== Q2：CSSによる表現の指定はどれくらい知っていましたか。今回やってみてどうでしたか。
( ここにQ2の回答を記入 )
== Q3：リフレクション (今回の課題で分かったこと)・感想・要望をどうぞ。
( ここにQ3の回答を記入 )
|
https://github.com/yhtq/Notes | https://raw.githubusercontent.com/yhtq/Notes/main/常微分方程/作业/2100012990 郭子荀 常微分方程 3.typ | typst | #import "../../template.typ": proof, note, corollary, lemma, theorem, definition, example, remark, proposition,der, partialDer, Spec
#import "../../template.typ": *
// Take a look at the file `template.typ` in the file panel
// to customize this template and discover how it works.
#show: note.with(
title: "作业1",
author: "YHTQ",
date: none,
logo: none,
withOutlined : false,
withTitle :false,
)
应交时间为 4月3日
#set heading(numbering: none)
= 3.18
== p85
=== 1
#let phi = math.phi.alt
设 $Phi(x) = integral_a^t chi(s) phi(s) dif s$，则有：
$
Phi' = chi phi <= chi psi + chi Phi
$
令 $h(x) = e^(integral_(a)^(x) chi(s) dif s), Phi = u h$，则：
$
u' h + u h' &<= chi psi + chi u h\
u' h &<= chi psi quad (u h' = chi u h)\
u' &<= (chi psi)/h \
u(x) - u(a) &<= integral_(a)^(x) (chi(t) psi(t))/h(t) dif t \
$
其中 $Phi(a) = 0 => u(a) = 0$，因此：
$
u(x) &<= integral_(a)^(x) (chi(t) psi(t))/h(t) dif t \
Phi(x) = u(x) h(x) &<= h(x) integral_(a)^(x) (chi(t) psi(t))/h(t) dif t \
&= e^(integral_(a)^(x) chi(t) dif t) integral_(a)^(x) chi(t) psi(t)e^(-integral_(a)^(t) chi(t) dif t) dif t\
&= integral_(a)^(x) chi(t) psi(t)e^(integral_(a)^(x) chi(t) dif t -integral_(a)^(t) chi(t) dif t) dif t\
&= integral_(a)^(x) chi(t) psi(t)e^(integral_(t)^(x) chi(t) dif t ) dif t\
$
因此：
$
phi(t) - psi(t) <= Phi(t) <= integral_(a)^(t) chi(s) psi(s)e^(integral_(s)^(t) chi(s) dif s ) dif s
$
证毕
=== 2
由题设：
$
abs(phi_1 (t) - phi_2 (t)) &= abs(phi_1 (tau) - phi_2 (tau) + integral_(tau)^(t) f(s, phi_1 (s)) -f(s, phi_2 (s)) dif s + E_1 (t) - E_2 (t))\
&<= abs(phi_1 (tau) - phi_2 (tau)) + abs(integral_(tau)^(t) f(s, phi_1 (s)) -f(s, phi_2 (s)) dif s) + abs(E_1 (t) - E_2 (t))\
&<= delta + integral_(tau)^(t) abs(f(s, phi_1 (s)) -f(s, phi_2 (s))) dif s + E(t)\
&<= delta + integral_(tau)^(t) k(s) abs(phi_1 (t) - phi_2 (t)) dif s + E(t)\
$
取 $phi(t) = abs(phi_1 (t) - phi_2 (t)), psi(t) = delta + E(t), chi(t) = k(t)$，由习题 1 结论可得（注意到条件显然蕴含了 $k(t) >= 0$，而习题 1 的证明过程并不需要 $k(t) != 0$）：
$
abs(phi_1 (t) - phi_2 (t)) &<= E(t) + integral_(tau)^(t) k(s)(E(s) + delta) e^(integral_(s)^(t) k(u) dif u) dif s\
&= E(t) + integral_(tau)^(t) k(s)delta e^(integral_(s)^(t) k(u) dif u) dif s + integral_(tau)^(t) k(s)E(s) e^(integral_(s)^(t) k(u) dif u) dif s\
&= E(t) - delta integral_(tau)^(t) dif e^(integral_(s)^(t) k(u) dif u) + integral_(tau)^(t) k(s)E(s) e^(integral_(s)^(t) k(u) dif u) dif s\
&= E(t) + delta e^(integral_(tau)^(t) k(u) dif u) + integral_(tau)^(t) k(s)E(s) e^(integral_(s)^(t) k(u) dif u) dif s\
$
证毕
== p103
=== 1
容易验证 Tonelli 序列等度连续（恒有 $y'_n (x) <= max_DD abs(f)$），一致有界（$abs(y_n (x) - y_0) <= integral_(x_0)^(x_0+h) max_DD abs(f) dif s$），从而它有收敛子列，无妨设 $y_n (x)$ 一致收敛于 $y(x)$\
注意到 $f$ 是紧集上连续函数，进而一致连续，从而序列 $f(x, y_n (x))$ 一致收敛于 $f(x, y(x))$，因此我们有：
$
y(x) - y_0 - integral_(x_0)^(x) f(s, y(s)) dif s = lim_(n->infinity) (y_n (x) - y_0 - integral_(x_0)^(x) f(s, y_n (s)) dif s)
$
只需验证对于每个 $x$ 上式右侧极限为零，进而 $y(x)$ 就是原方程的解。\
$x = x_0$ 时显然成立，否则由于可将 $n$ 取充分大，不妨设 $x > x_0 + 1/n = x_1$，计算：
$
abs(y_n (x) - y_0 - integral_(x_0)^(x) f(s, y_n (s)) dif s) &= abs(integral_(x_0)^(x - d_n) f(s, y_n (s)) dif s - integral_(x_0)^(x) f(s, y_n (s)) dif s)\
&= abs(integral_(x - d_n)^(x) f(s, y_n (s)) dif s)\
&<= integral_(x - d_n)^(x) abs(f(s, y_n (s))) dif s\
&<= h/n max_(DD) f\
$
显然 $n -> +infinity$ 时上式 $-> 0$ ，因此结论自然成立
假设 $f$ Lipschitz 连续，已经证明了原方程的解唯一。上面的证明事实上表示所有一致收敛的子列的极限都是原方程的解，换言之 Tonelli 所有一致收敛子列有公共的极限，进而当然一致收敛。
=== 2
考虑欧拉折线 $phi_n (x)$ 的值：
+ 第一个区间 $[0, 1/n]$ 上由于 $y(0) = 0, f(0, 0) = 0$，因此 $phi_n (x) = 0$
+ 第二个区间上，有：
$
phi_n (1/n) = 0\
f(1/n, 0) = 1/n cos (n pi)
$
因此：
$
forall t in [0, 1/n]:\ phi(1/n + t) = cases(
t/n quad n = 0 mod 2,
-t/n quad n = 1 mod 2
)
$
+ 由对称性，我们可以只证明 $n$ 为偶数情形，证明过程中同时给出 $phi_n (x) !=0 , x >= 1/n$ ，因此奇数情形是完全对称的
- 这里 $phi_n (1/n) = 0, alpha(1/n) > 0$，结论已经错误不知是否写错了
- 注意到 $phi_n (2/n) = 1/n^2$，而：
$
alpha(2/n) -1/n^2 &= integral_0^(2/n) e^(-1/s^2) dif s - 1/n^2
// &= integral_(n/2)^(infinity) t^2 e^(-t^2) dif t\
// &= - 1/2 integral_(n/2)^(infinity) t dif e^(-t^2)\
// &= n/4 e^(-n^2/4) + 1/2 integral_(n/2)^(infinity) e^(-t^2) dif t \
// &<= n/4 e^(-n^2/4) + 1/n integral_(n/2)^(infinity) t e^(-t^2) dif t \
// &<= n/4 e^(-n^2/4) - 1/(2n )integral_(n/2)^(infinity) dif e^(-t^2) \
// &<= n/4 e^(-n^2/4) + 1/(2 n) e^(-n^2/4) \
$
设 $f(t) = integral_0^(2/t) e^(-1/s^2) dif s - 1/t^2$:
//至少当 $n$ 足够大时上式 $< 1/n^2$
$
f'(t) = -(2 e^(-t^2/4) )/t^2+ 2/t^3 = 2/t^3(1 - t e^(-t^2/4)) > 0, forall t > 1
$
同时，不难验证 $f(t) -> 0, t -> +infinity$，进而恒有 $f(t) < 0$
- 若 $y_k > alpha(x_k)$，则下一段中 $phi_n (x)$ 的斜率将为 $x_k = k/n$，但：
$
alpha'(x) = e^(-1/x^2) <= e^(-1/(x_k + 1/n)^2)
$
设 $g(t) = t -e^(-1/(t+ 1/n)^2)$，则：
-
$
g(1/n) = 1/n - e^(-1/(1/n+ 1/n)^2) = 1/n - e^(-n^2/4) = e^(-n^2/4)/n (e^(n^2/4) - n) > 0
$
- $
g' = 1 - 2/(t + 1/n)^3 e^(-1/(t+ 1/n)^2) = e^(-1/(t+ 1/n)^2)/(t + 1/n)^3 (e^(1/(t+ 1/n)^2)(t + 1/n)^3 - 2) > 0
$
从而 $g(t) > 0, forall t in [1/n, 1]$，表明 $phi_n (x)$ 的斜率将大于 $alpha(x)$，进而在其上方
- 对 $k$ 归纳可得结论成立
= 3.20
== p96
=== 1
$
y_0 (x) &= y_0\
y_1 (x) &= y_0 + integral_(x_0)^(x) f(s, y_0 (s)) dif s = y_0 + integral_(x_0)^(x) s - y_0^2 dif s\
&= y_0 + 1/2 (x^2 - x_0^2) - (x - x_0) y_0^2\
y_2 (x) &= y_0 + integral_(x_0)^(x) f(s, y_1 (s)) dif s = y_0 + integral_(x_0)^(x) s - y_1^2 dif s\
&= y_0 + integral_(x_0)^(x) s - (y_0 + 1/2 (s^2 - x_0^2) - (s - x_0) y_0^2)^2 dif s\
&= y_0 -1/60 (x - x_0) (3 x^4 + 3 x_0 x^3 - 15 x^3 y_0^2 - 7 x^2 x_0^2 + 5 x_0 x^2 y_0^2 + 20 x^2 y_0^4 + 20 y_0 x^2 - 7 x x_0^3 + 35 x x_0^2 y_0^2 -\ &40 x x_0 y_0^4 + 20 x x_0 y_0 - 60 x y_0^3 - 30 x + 8 x_0^4 - 25 x_0^3 y_0^2 + 20 x_0^2 y_0^4 - 40 y_0 x_0^2 + 60 x_0 y_0^3 - 30 x_0 + 60 y_0^2)\
$
=== 2
$
y_0 (x) &= 0\
y_1 (x) &= integral_(0)^(x) s + y_0 (x) + 1 dif s\
&= integral_(0)^(x) s + 1 dif s\
&= 1/2 x^2 + x\
y_2 (x) &= integral_(0)^(x) s + 1/2 s^2 + s +1 dif s\
&= 1/6 x^3 + x^2 + x
$
设：
$
r_n (x) = y_n (x) - sum_(i=1)^(n+1) 1/(i!) x^(i)
$
则：
$
r_(n+1) (x) = integral_(0)^(s) sum_(i=1)^(n+1) 1/(i!) s^(i) + r_n (s) + s + 1 dif s -sum_(i=1)^(n+2) 1/(i!) x^(i)\
= integral_(0)^(x) r_n (s) + s dif s \
r_(n+1) (x) + x+1 - e^(x) = integral_(0)^(x) r_n (s) + s +1 - e^(s) dif s
$
再令 $t_n (x) = r_(n+1) (x) + x+1 - e^(x)$，将有：
$
t_n (x) = integral_(0)^(x) t_(n-1) (s) dif s
$
$t_n (x)$ 的一致收敛性由定理是显然的，因此上式给出 $t_n (x) -> A e^x $，因此：
$
r_n (x) -> A' e^x - x - 1 \
y_n (x) -> A'' e^x - x - 2
$
代入 $y(0) = 0$ 知 $y_n (x) -> 2 e^x - x - 2$，这就是原方程的解
=== 3
限制 $abs(x - x_0) <= h$ ，按照同样的方式可以递归定义：
$
y_0 (x) = y_0\
y_n (x) = y_0 + integral_(x_0)^(x) f(s, y_(n-1) (s)) dif s
$
计算：
$
abs(y_n (x) - y_(n-1) (x)) = abs(integral_(x_0)^(x) f(s, y_(n-1) (s)) - f(s, y_(n-2) (s))dif s)\
<= integral_(x_0)^(x) abs(f(s, y_(n-1) (s)) - f(s, y_(n-2) (s))) dif s\
<= integral_(x_0)^(x) k(s) abs(y_(n-1) (s) - y_(n-2) (s)) dif s\
<= integral_(x_0)^(x) k(s) dif s integral_(x_0)^(x) abs(y_(n-1) (s) - y_(n-2) (s)) dif s
$
最后一步利用了柯西不等式\
之后用完全一样的技术可以证明 $y_n (x)$ 一致收敛于原方程的解
== 4
需要证明：
$
T(h) = y_0 + integral_(x_0)^(x) f(s, h(s)) dif s
$
在 $L^infinity$ 空间中是压缩映射，为此计算：
$
norm(T(h) - T(g)) = norm(integral_(x_0)^(x) f(s, h(s)) - f(s, g(s)) dif s)\
<= integral_(x_0)^(x) norm(f(t, h(t)) - f(t, g(t))) dif s\
<= L norm(h(t) - g(t)) abs(x - x_0)\
$
为了使其为压缩映射，需要进一步缩小 $x$ 区间使得 $abs(x - x_0) L < 1$，此时当然成立压缩映射
== 5
构造和原定理类似，注意到：
$
y_n (x) - y_(n-1) (x) = integral_(x)^(0) f(s, y_(n-1) (s)) - f(s, y_(n-2) (s)) dif s
$
由题设，将有 $y_n (x) - y_(n-1) (x)$ 与 $y_(n-1) (x) - y_(n-2) (x)$ 同号，而条件说明了:
$
y_1 (x) = integral_(0)^(x) f(s, 0) dif s >= 0 = y_0 (x)
$
因此对于每个 $x$，序列 $y_n (x)$ 是单调递增的，同时有上界，进而有极限。设 $y(x)$ 为其极限，由 Dini 定理，只需要验证 $y(x)$ 连续即可给出一致收敛性\
事实上，显有：
$
abs(y(x_1) - y(x_2)) = lim_(n->infinity) abs(y_n (x_1) - y_n (x_2)) <= lim_(n->infinity) integral_(x_1)^(x_2) abs(f(s, y_(n-1) (s))) dif s\
<= abs(x_2 - x_1) M
$
当然有极限函数连续，因此序列一致收敛
== p110
=== 2
首先容易验证它满足局部 Lipschitz 条件，因此至少在每点附近都有解，而解总可以延拓到有界闭区域的边界。\
取定 $x_0, y_0$ 及过该点的解 $y(x)$，假设它不能延拓到无穷区间，则一定有垂直渐近线 $x = x_1$\
在渐近线左侧，有：
$
y' = x^3 - y^3 <= x_1^3 - y^3
$
取 $I = [x_1 - delta, x_1]$，显然 $y(x)$ 在区间内的极值点满足：
$
y' = 0 => y = x => y in I
$<maximum>
注意到由延拓定理，一定有 $y(x)$ 在 $x_1$ 附近无界，无妨设其无上界，则：
$
h(t) = max_(x in [x_1 -delta, t]) y(x)
$
关于 $t$ 单调递增趋于无穷，不妨设当 $t > t_1$ 时 $h(t) > x_1, h(t) > y(x_1 - delta)$，此时@maximum 给出最大值只能在区间边界处取得，进一步只能在右端点取得，因此：
$
h(t) = y(t) > x_1, forall t > t_1
$
然而观察原式可得：
$
y' = x^3 - y^3 <= x_1^3 - y^3 <= 0, forall x > t_1
$
换言之，$y(x)$ 将在 $(t_1, x_1)$ 单调递减，与其无上界矛盾！\
证毕
=== 4
记 $y(x) = phi.alt(x, xi)$，则它是原方程的解且 $y(0) = xi$\
由于 $f$ 是开区域 $0 < x < a, - infinity < y < =infinity$ 上的连续函数，微分方程的解可以延拓到该开区域内任何有界闭区域的边界。
- 若 $lim_(x -> overline(x)-0) y(x)$ 存在且有限，自然定义 $y(overline(x)) = lim_(x -> overline(x)-0) y(x)$仍然连续。为了证明新的 $y$ 还是原方程的解，只需验证他在 $overline(x)$ 处的左导数即可。\
然而注意到：
$
y'(x) = f(x, y(x))， forall x in [0, overline(a))\
=> lim_(x -> overline(x)-0) y'(x) = f(overline(x), lim_(x -> overline(x)-0) y(x)) = f(overline(x), y(overline(x)))
$
上式左侧是导数的左极限，它恰为 $overline(x)$ 处的左导数，因此延拓的 $y$ 确实还是原方程的解
- 另一方面，解可以延拓到 $overline(x)$ 当然蕴含着 $lim_(x -> overline(x)-0) y(x)$ 存在且有限，因此下设 $y(x)$ 在 $(0, overline(x))$ 上无界。无妨设其无上界，只需证明：
$
lim_(x -> overline(x)-0) y(x) = +infinity
$
（另一种情况是类似的）\
如若不然，设 $l = liminf_(x -> overline(x)-0) y(x) < +infinity$，再取 $l_1 > l_2 > l$，递归定义：
- 在 $(0, overline(x))$ 上任取 $u_0$ 使得 $y(u_0) = l_1$（由下极限定义和介值定理保证）
- 取 $v_1 = inf {x in [u_1, overline(x)) | y(x) = l_2}$\
这里下极限定义和介值定理保证右边集合非空，而该集合作为连续函数在闭集上的逆像仍是（相对于 $[u_1, overline(x))$ 的）闭集，进而有 $y(v_1) = l_2$ 并且显有 $v_1 > u_1$
- 再取 $u_2 = inf {x in [v_1, overline(x)) | y(x) = l_1}$
- ...
- 以此类推，取得
$
u_i, v_i space s.t. space y(u_i) = l_1, y(v_i) = l_2
$
- 更进一步，有 $u_i, v_i -> overline(x)$，这是因为由定义知任取 $u_i, v_i$ 单调上升有上界，并且两数列互相控制，因此有相同的极限 $xi$，同时 $lim_(x -> xi) y(x)$ 不存在，因此只能有 $xi = overline(x)$
$
f(theta_i, y(theta_i)) = y'(theta_i) = (y(v_i) - y(u_i))/(v_i - u_i) = (l_2 - l_1)/(v_i - u_i),theta_i in [v_i, u_i]
$
同时由定义过程可以看出：
$
forall x in [v_i, u_i], y(x) in [l_1, l_2] => y(theta_i) in [l_1, l_2]
$
- 等式左侧 $f(theta_i, y(theta_i)) in f([0, a] times [l_1, l_2])$，由连续性右侧是有界集合，因此左侧有公共上界\
- 等式右侧由 $u_i - v_i -> 0$ 显然无界
矛盾！
- 综上，原结论成立
=== 5
如若不然，假设 $y(x)$ 只在 $[0, a)$ 上都是原方程的解，由上题结论不妨设：
$
lim_(x -> a-0) y(x) = +infinity
$
不妨取 $b$ 使得 $forall x in [b, a), y(x) > 0$，我们有：
$
abs(y') = abs(f(x, y)) <= psi(abs(y))\
abs(y')/(psi(abs(y))) <= 1\
integral_(b)^(s) abs(y')/(psi(y)) dif x <= s- b\
integral_(b)^(s) y'/(psi(y)) dif x <= integral_(0)^(s) abs(y')/(psi(abs(y))) dif x <= s - b\
integral_(y(0))^(y(s)) 1/(psi(t)) dif t <= s - b\
$
然而当 $s -> a-0$ 时，上式左侧有界而右侧无界，矛盾！
= 3.25
== p120
=== 1
#lemmaLinear[][
设 $g_1, g_2$ 在区间 $I$ 上均满足 $g'_i (x) = f(x, g_i (x))$，则 $max(g_1, g_2), min(g_1, g_2)$ 也满足
]
#proof[
只证 $max$，$min$ 类似\
设 $h = max(g_1, g_2)$，验证上面的等式只需逐点验证即可：
- 任取 $x in I$，讨论：
- 若 $g_1(x) > g_2(x)$，则有 $g_1, g_2$ 连续性知存在 $x$ 的开邻域 $B$ 使得：
$
h|_B = g_1
$
此时由于 $g_1$ 在该点是微分方程的解，$h$ 当然也是
- 若 $g_1(x) < g_2(x)$，同理
- 若 $g_1(x) = g_2(x)$，注意到：
$
g'_1(x) = f(x, g_1(x)) = f(x, g_2(x)) = g'_2(x) := d
$
因此：
$
abs((h(x + Delta x) - h(x))/(Delta x) - d) &<= abs((h(x + Delta x) - g_1 (x + Delta x))/(Delta x)) + abs((g_1 (x + Delta x) - g_1 (x))/(Delta x) - g'_1 (x))\
&<= abs((g_2(x + Delta x) - g_1 (x + Delta x))/(Delta x)) + abs((g_1 (x + Delta x) - g_1 (x))/(Delta x) - g'_1 (x))\
&<= abs(((g_2(x + Delta x) - g_1 (x + Delta x)) - (g_2 (x) - g_1 (x)))/(Delta x)) + abs((g_1 (x + Delta x) - g_1 (x))/(Delta x) - g'_1 (x))\
&<= abs(g'_2 (xi) - g'_1 (xi)) + abs((g_1 (x + Delta x) - g_1 (x))/(Delta x) - g'_1 (x))\
&"（对" g_2(x) - g_1(x) 在 x, x + Delta x "上利用微分中值定理）"
$
其中 $xi$ 在 $x, x + Delta x$ 之间。注意到由微分方程，$g_1, g_2$ 当然连续可导，进而当 $Delta x -> 0$ 时上式 $-> 0$，这就保证了：
$
h'(x) = d = f(x, h(x))
$
也即 $h$ 在该点满足微分方程
得证
]
考虑微分方程：
$
cases(
y' = f(x, y) ,
y(x_1) = y_1
)
$
它在 $x_1$ 的某个邻域内有解 $h$，又可不妨设 $h$ 在 $I$ 内某个极大的区间 $I_1$（也即所有可延拓闭区间的并）上是原方程的解，并设：
$
h_1 = max(min(h, Z), W), x in I_1
$
将满足 $h'_1 (x) = f(x, h_1 (x))$，同时也不难验证 $h_1(x_1) = y_1$，因此是过该点的微分方程的解\
另一方面，显然有：
$
max(min(h, Z), W) >= W\
max(min(h, Z), W) <= max(Z, W) = Z
$
因此 $h_1$ 是区间上有界的微分方程的解
从而：
- 若 $x_0 in I_1$，由上面的条件和引理知 $h_1$ 就是要找的解
- 否则，设 $I_1$ 闭包中距 $x_0$ 最近的点为 $x_2$，注意到 $h_1$ 在 $I_1$ 上有界，因此由延拓定理要么意味着存在 $x'$ 使得 $abs(h_1(x') - y_0) = b$，要么 $h_1$ 一定可以至少延拓到 $x_2 := x'$，然而已经假设 $h$ 不能再延拓，因此该点附近一定取 $Z$ 或 $W$ ，无论如何一定有：
$
exists x', h_1(x') = Z(x') 或 W(x')
$
无论何者，都意味着 $h_1$ 可以与 $Z$ 或 $W$ 的其中之一拼接起来，这就是所要找的解。
=== 2
存在唯一性是容易的。对于存在区间，只证明第一个方程\
显然它的解单调递减，若解的存在区间不是 $(a, b)$ ，则必然在某点 $x_0 in (a, b)$ 处的左/右极限为 $+\/minus infinity$，不妨设为左极限为负无穷\
这意味着存在 $delta, (x_0 - delta, delta)$ 上时有：
$
exists M_1, M_2, der(y, x) = -A(x) abs(y) - B(x) = A(x) y - B(x) > M_1 y + M_2
$
但稍加计算可得 $der(y, x) = M_1 y + M_2$ 的解不可能在有界区间内趋于无穷，进而该方程的解由比较定理被控制在有界区间，矛盾！
|
|
https://github.com/goshakowska/Typstdiff | https://raw.githubusercontent.com/goshakowska/Typstdiff/main/tests/test_complex/text_formats/text_formats_deleted_result.typ | typst | = Heading1
Paragraph with quotes#strike[ ];#strike[“This];#strike[
];#strike[is];#strike[ ];#strike[in];#strike[ ];#strike[quotes.”]
#strike[#strong[Date:];];#strike[ ];#strike[26.12.2022];#strike[ \
];Date used in paragraph #strong[Date:] 26.12.2022#strike[ \
];#strike[#strong[Topic:];];#strike[ ];#strike[Infrastructure];#strike[
];#strike[Test] \
#strong[Severity:] High \
= Heading3
#emph[emphasis]
Some normal text
Italic
#strike[#strong[MY TEXT];];#strike[ \
];ALREADY HIGH
#link("https://typst.app/")
= Heading4
abc
Link in paragraph:#strike[ ];#strike[#link("https://typst.app/");]
= #strike[Heading5]
|
|
https://github.com/polarkac/MTG-Stories | https://raw.githubusercontent.com/polarkac/MTG-Stories/master/typst_packages/mtgset/0.1.0/mtgset.typ | typst | #let conf(set_name, doc) = {
set document(title: set_name)
[
#set text(size: 24pt)
#set align(center + horizon)
#heading(level: 1)[#set_name]
]
doc
}
|
|
https://github.com/YDX-2147483647/herglotz | https://raw.githubusercontent.com/YDX-2147483647/herglotz/main/template.typ | typst | #import "@preview/ctheorems:1.1.2": thmrules, thmbox
#let _thmbox_fmt = (
// 开头的负空白用于抵消 head、name 之间的空格。
namefmt: (name) => text(weight: "bold", [#h(-1em/4)（#name] + box(width: 1em)[）#h(-1em/4).]),
separator: h(0.5em),
breakable: true,
)
#let remark = thmbox(
"remark",
"注",
titlefmt: text.with(fill: purple.darken(10%), weight: "bold"),
stroke: (left: purple),
.._thmbox_fmt,
).with(numbering: none)
#let example = thmbox(
"example",
"例",
titlefmt: text.with(fill: green.darken(10%), weight: "bold"),
stroke: (left: green),
.._thmbox_fmt,
).with(numbering: none)
#let small = text.with(size: 0.8em, fill: gray.darken(70%))
// A stylized table header
// TODO: Use a show rule on `table.header`.
// It is not possible at least in typst v0.11. “That will be fixed in a future release.”
// https://typst.app/docs/guides/table-guide/#basic-tables
// https://github.com/typst/typst/issues/3640
#let table-header(..headers) = {
table.header(..headers.pos().map(strong))
}
#let project(title: "", authors: (), date: none, body) = {
// Set the document's basic properties.
set document(author: authors, title: title)
set page(numbering: "1", number-align: center)
// Save heading and body font families in variables.
let body-fonts = ("Linux Libertine", "Source Han Serif")
let sans-fonts = ("Inria Sans", "Source Han Sans")
let script-fonts = ("Inria Sans", "STKai")
// Set body font family.
set text(font: body-fonts, lang: "zh", region: "CN")
// 中西共用标点默认全宽，破折号应不离不弃
// TODO: 这样无法区分正文和`figure.caption`，引号高度可能不匹配汉字。
// https://github.com/typst/typst/issues/3331
show regex("[“‘’”]|——|……"): it => {
set text(font: body-fonts.at(1)) if text.lang == "zh"
it
}
show heading: set text(font: sans-fonts)
show raw: set text(font: ("Fira Code", ..sans-fonts))
show figure.caption: set text(font: script-fonts)
set heading(numbering: "1.1", supplement: [§])
// Make the empty set round
// https://github.com/typst/typst/pull/1526#issuecomment-1596326198
show sym.emptyset: sym.diameter
// Title row.
align(center)[
#block(text(font: sans-fonts, weight: 700, 1.75em, title))
#v(1em, weak: true)
#date
]
// Author information.
pad(top: 0.5em, bottom: 0.5em, x: 2em, grid(
columns: (1fr,) * calc.min(3, authors.len()),
gutter: 1em,
..authors.map(author => align(center, strong(author))),
))
// Main body.
set par(justify: true)
set table(
align: (x, y) => (if y == 0 { center } else { start }) + horizon,
stroke: (x, y) => (
if y == 0 { (bottom: 1pt + black) },
if x > 0 { (left: 1pt + black) },
).sum(),
)
show: thmrules
show strong: set text(fill: blue.darken(10%))
show link: set text(fill: blue)
show link: underline
body
}
/// 列出化名
/// path: pseudonym 模块所在路径
/// subset: 要列出的化名范围，默认全列
/// sort: 是否排序，默认排
#let pseudonyms(path, subset: none, sort: true) = {
// Load and drop field names
let hashes = csv(path + "/hashes.csv")
assert.eq(hashes.at(0), ("化名", "hash"))
if subset != none {
hashes = (hashes.at(0), ..hashes.slice(1).filter(row => row.at(0) in subset))
}
if sort {
hashes = (hashes.at(0), ..hashes.slice(1).sorted(key: row => repr(row.at(0))))
}
[#hashes.slice(1).map(row => row.at(0)).join("、")当然是化名，他们的真名按 UTF-8 编码的 SHA256
如下。]
figure(table(
columns: 2,
table-header(..hashes.at(0)),
..hashes.slice(1).map(row => (row.at(0), raw(row.at(1)))).flatten(),
), caption: [化名与真名的 hash])
figure(
raw(read(path + "/hash.py"), lang: "python", block: true),
caption: [计算 hash 的 Python 脚本],
)
}
|
|
https://github.com/L-N1988/typst-snippets | https://raw.githubusercontent.com/L-N1988/typst-snippets/main/README.md | markdown | # Introduction
Snippets for typst using ultisnip. Most contents come from [Gilles Castel](https://castel.dev/)'s talented [latex-snippets](https://github.com/gillescastel/latex-snippets).
# Prerequisite
Install [ultisnips](https://github.com/SirVer/ultisnips) first.
# Usage
Put `typst.snippets` to `~/.vim/Ultisnips/` folder.
|
|
https://github.com/Myriad-Dreamin/tinymist | https://raw.githubusercontent.com/Myriad-Dreamin/tinymist/main/crates/tinymist-query/src/fixtures/type_check/infer.typ | typst | Apache License 2.0 | #image("test.jpg");
#read("test.jpg");
#json("test.json");
#yaml("test.yaml");
#xml("test.xml");
#toml("test.toml"); |
https://github.com/wcshds/manual-of-chinese-phonology | https://raw.githubusercontent.com/wcshds/manual-of-chinese-phonology/main/tools/prelude.typ | typst | #import "xsampa.typ": xsampa
#let xs(it) = box[
#set text(font: ("Doulos SIL"));
#h(0.1em)
#block(spacing: 0em, above: 0em, below: 0em)[#xsampa(it)]
#h(0.1em)
]
#let sup-xs(it) = {
if it.match(regex("^(a|e|i|o|u|g|n|d|l|M|N)$")) != none {
box(move(dx: 0em, dy: 0.1em, super(xs(it))))
} else {
it
}
}; |
|
https://github.com/catppuccin/typst | https://raw.githubusercontent.com/catppuccin/typst/main/src/tidy/show-module.typ | typst | MIT License | #import "../catppuccin.typ": themes, get-palette
#import "styles.typ" as styles
#import "@preview/tidy:0.3.0"
#let show-module(docs, theme: themes.mocha, ..args) = {
let palette = get-palette(theme)
let tidy-colors = styles.get-tidy-colors(theme: theme)
tidy.show-module(
docs,
colors: tidy-colors,
style: styles,
..args,
)
}
|
https://github.com/CarlColglazier/northwestern-thesis-quarto | https://raw.githubusercontent.com/CarlColglazier/northwestern-thesis-quarto/master/_extensions/northwestern-thesis/typst/biblio.typ | typst | MIT License | $if(citations)$
$if(csl)$
#set bibliography(style: "$csl$")
$elseif(bibliographystyle)$
#set bibliography(style: "$bibliographystyle$")
$endif$
$if(bibliography)$
////#set text(top-edge: 0.7em, bottom-edge: -0.3em)
#set text(top-edge: "cap-height", bottom-edge: "baseline")
#set par(
first-line-indent: 0em,
//hanging-indent: 2.5in,
justify: false,
leading: 0.65em,
)
#bibliography(
$for(bibliography)$"$bibliography$"$sep$,$endfor$,
title: none,
)
$endif$
$endif$ |
https://github.com/sitandr/typst-examples-book | https://raw.githubusercontent.com/sitandr/typst-examples-book/main/src/snippets/chapters/outlines.md | markdown | MIT License | # Outlines
# Outlines
> Lots of outlines examples are already available in [official reference](https://typst.app/docs/reference/meta/outline/)
## Table of contents
```typ
#outline()
= Introduction
#lorem(5)
= Prior work
#lorem(10)
```
## Outline of figures
```typ
#outline(
title: [List of Figures],
target: figure.where(kind: table),
)
#figure(
table(
columns: 4,
[t], [1], [2], [3],
[y], [0.3], [0.7], [0.5],
),
caption: [Experiment results],
)
```
You can use arbitrary selector there, so you can do any crazy things.
<!--TODO: crazy example with labels and selector combinations-->
## Ignore low-level headings
```typ
#set heading(numbering: "1.")
#outline(depth: 2)
= Yes
Top-level section.
== Still
Subsection.
=== Nope
Not included.
```
## Set indentation
```typ
#set heading(numbering: "1.a.")
#outline(
title: [Contents (Automatic)],
indent: auto,
)
#outline(
title: [Contents (Length)],
indent: 2em,
)
#outline(
title: [Contents (Function)],
indent: n => [→ ] * n,
)
= About ACME Corp.
== History
=== Origins
#lorem(10)
== Products
#lorem(10)
```
## Replace default dots
```typ
#outline(fill: line(length: 100%), indent: 2em)
= First level
== Second level
```
## Make different outline levels look different
```typ
#set heading(numbering: "1.")
#show outline.entry.where(
level: 1
): it => {
v(12pt, weak: true)
strong(it)
}
#outline(indent: auto)
= Introduction
= Background
== History
== State of the Art
= Analysis
== Setup
```
## Long and short captions for the outline
```typ
// author: laurmaedje
// Put this somewhere in your template or at the start of your document.
#let in-outline = state("in-outline", false)
#show outline: it => {
in-outline.update(true)
it
in-outline.update(false)
}
#let flex-caption(long, short) = context if in-outline.get() { short } else { long }
// And this is in the document.
#outline(title: [Figures], target: figure)
#figure(
rect(),
caption: flex-caption(
[This is my long caption text in the document.],
[This is short],
)
)
```
## Ignore citations and footnotes
That's a workaround a problem that if you make a footnote a heading, its number will be displayed in outline:
```typ
= Heading #footnote[A footnote]
Text
#outline() // bad :(
#pagebreak()
#{
set footnote.entry(
separator: none
)
show footnote.entry: hide
show ref: none
show footnote: none
outline()
}
```
|
https://github.com/eduardz1/Bachelor-Thesis | https://raw.githubusercontent.com/eduardz1/Bachelor-Thesis/main/chapters/tools-and-technologies.typ | typst | #import "../utils/common.typ": *
= Tools and Technologies <tools-and-technologies>
In this chapter, we will explore the tools and technologies used in the project. In particular, in @influxdb-section we will introduce InfluxDB and after that, we will touch on the three main programming languages that we had to work with. After that, we'll briefly touch on the concepts of the Semantic Web @semanticweb from @rdf-section onwards, which is an extension of the World Wide Web through standards that aim to make internet data machine-readable. These concepts serve as the underlying foundation for our project.
#_content(
[
== InfluxDB <influxdb-section>
InfluxDB @influxdb is a powerful open-source time-series database that in our context is used to store the data collected by the _data collectors_ (see @influx-python). It is designed to handle high volume and high frequency time-stamped data and provides a SQL-like language with specific time-centric functions useful for querying a data structure primarily composed of measurements, streams of data, and points @influxdb-wiki. Being a NoSQL database, it is schemaless and it allows for a flexible data model.
InfluxDB is also directly integrated with the SMOL language, in the `access` expression (see @smol-twinning-program for an example of how we use it in practice), an InfluxDB query with a single answer variable can be directly executed on an external database without the need for external tooling.
The way our data is organized is in structures called _buckets_ that are used to store the _measurements_. Each _measurement_ is composed of: #v(600pt) /* FIXME: remove once issue #466 is implemented */
- _measurement name_
- _tag set_
- Used as keys to index the data
- _field set_
- Used to store the actual data
- _timestamp_
For example, the following query will return the last moisture measurement, given a measurement range of 30 days, from the bucket named _greenhouse_:
```SQL
from(bucket: "greenhouse")
|> range(start: -30d)
|> filter(fn: (r) => r["_measurement"] == "ast:pot")
|> filter(fn: (r) => r["_field"] == "moisture")
|> filter(fn: (r) => r["plant_id"] == %1)
|> keep(columns: ["_value"])
|> last()
```
Chronograf @chronograf is a web application included in the InfluxDB 2.0 package, it is the tool that we chose to visualize the data stored in the database and to create dashboards. It can be also used to create alerts and automation rules.
#figure(
block(
radius: 4pt,
stroke: 0pt + red, // FIXME: https://github.com/typst/typst/issues/2533
clip: true,
image("../img/chronograf.jpg"),
),
caption: [
An example of the visualization tools offered by the Chronograf Dashboard @chronograf-img
]
)
== Raspberry Pi
Every part of the system is either managed by or communicates with a Raspberry Pi, in particular, we used a series of Raspberry Pi 4, small single-board computers that are extremely versatile due to their open design, low cost and modularity. The integrated J8 header provides a standard pin pinout for interfacing with sensors and such @raspberry-pi-wiki.
== Python
When working with the Raspberry Pi 4 the obvious choice for a programming language is Python as it is the most widely used language for the Raspberry Pi due to the amount of libraries available for it and the wide community support. We will talk more in detail in @software-components about the specifics of the code.
The goal was to make it extremely modular allowing for easy integration of new sensors and actuators, the field of digital twins is modular by nature.
== SMOL
SMOL is an Object Oriented programming language in its early development stages, it allows us to:
- Interact with the Influx Database and read data from it, directly without the need for third-party libraries.
- Read and query the asset model (that we discuss in @asset-model), mapping the data to objects in the heap.
- Map the program state to a knowledge graph through semantic lifting (a concept that will be further discussed in @semantical-lifting), the program state can be then queried to extract information about the state of the system.
- Represent and run the simulation and interact with FMU simulation files, something that we didn't cover in this project but is the next logical step that should be taken. In @fmi-section we will briefly cover the theory behind FMUs.
SMOL programs are compiled to Java bytecode and can be run natively on the JVM.
== Java
We use Java to interface with the SMOL program by making use of the Kotlin (a language designed to fully interoperate with Java) classes that are the building blocks of the REPL (Read-Evel-Print-Loop) interactive interpreter for SMOL @semanticobjects. The REPL is used to query the lifted state of the SMOL program.
The Java program is also responsible for sending commands to the Raspberry Pi through SSH in the local network we set up by using the `JSch` library.
== RDF <rdf-section>
RDF is a standard model for data interchange on the Web. The acronym stands for Resource Description Framework, RDF has features that facilitate data merging even when the underlying schemas differ and it specifically supports the evolution of schemas over time without requiring all the data consumers to be changed @rdf.
Each RDF statement represents knowledge graphs as a set of triples in the form _\<subject\> \<predicate\> \<object\>_ @ksosu.
More specifically the triplets are composed of three basic elements @rdfandowl:
- *Resources* - the thing described
- *Properties* - the relationship between things
- *Classes* - the bucket used to group the things
An example related to our knowledge graph is the formalization of the value `50` as ideal moisture for the individual encoded as `basilicum1`:
```turtle
<basilicum1> <hasIdealMoisture> <50>
```
The three-part structure consists of resources identified by a URI (Universal Resource Identifier). RDF extends the linking structure of the Web by using URIs to name the relationship between things, this method allows the mixing of structured and semi-structured data.
These characteristics make RDF a flexible and efficient way to represent knowledge. When thinking about large-scale applications, data can be read quickly due to its structure not being linear like a traditional database and not being hierarchical like XML.
=== Namespaces
Namespaces are used to define a set of short strings to represent long URIs (Uniform Resource Identifiers) that are used in RDF data.
For example instead of:
```turtle
<http://www.w3.org/2002/07/owl#ObjectProperty>
```
we can more concisely write `<owl:ObjectProperty>` and define the namespace `owl` as:
```turtle
@prefix owl: <http://www.w3.org/2002/07/owl#> .
```
by defining it at the top of the Turtle document, the aforementioned is a language used to #v(600pt) /* FIXME: remove once issue #466 is implemented */write down RDF graphs in a compact textual form @turtle.
== OWL
The W3C Web Ontology Language (OWL) is a Semantic Web language designed to represent rich and complex knowledge about things, groups of things, and relations between things @owl.
OWL is based on RDF and extends it with more vocabulary for the description of properties and classes.
We use OWL in the asset model of the greenhouse to create a formal description of its physical structure and formalize the relationships between the different components.
=== Ontologies
In the context of RDF and OWL, an ontology is a formal description providing users with a shared understanding of a given domain @webdam. They define the concepts and entities that exist in a domain and the relationships between them.
== SPARQL
After having understood the basics of RDF and OWL, we can now talk about SPARQL, which is the query language for RDF @sparql. For example, the following query will return the ideal moisture for each plant:
```sparql
PREFIX ast: <http://www.semanticweb.org/gianl/ontologies/2023/1/sirius-greenhouse#>
SELECT ?plantId ?idealMoisture
WHERE {
?plant rdf:type ast:Plant ;
ast:hasPlantId ?plantId ;
ast:hasIdealMoisture ?idealMoisture .
}
```
In the query, we prefix variables with a question mark `?`.
#v(600pt) /* FIXME: remove once issue #466 is implemented */
== Protégé
Protégé is a free and open-source ontology editor and framework for building intelligent systems @protege.
It is developed by a team from Stanford University and it provides a suite of tools to construct domain models and knowledge-based applications with ontologies.
Protégé fully supports the OWL 2 Web Ontology Language and RDF specifications and that made it the tool of choice for the project, #v(600pt) /* FIXME: remove once issue #466 is implemented */the following is an image of the interface in which we can see details about the Basilicum class and related instances.
#figure(
block(
radius: 4pt,
stroke: 0pt + red, // FIXME: https://github.com/typst/typst/issues/2533
clip: true,
image("../img/protege.png")
)
)
]
)
|
|
https://github.com/lyzynec/orr-go-brr | https://raw.githubusercontent.com/lyzynec/orr-go-brr/main/07/main.typ | typst | #import "../lib.typ": *
#knowledge[
#question(name: [Discuss what kind of changes to the necessary conditions of
optimality in the form of Euler--Lagrange equations must be made if the
final time is relaxed. Consider, in addition, that the final state must be
on some (hyper)surface.])[
In addition to regular Euler--Lagrange conditions
$
(diff L(x, y(x), y'(x))) / (diff y(x))
- upright(d)/(upright(d) x) (diff L(x, y(x), y'(x))) / (diff y'(x)) = 0
$
there is new condition added
$
(diff L (x, y(x), y'(x)))/(diff y') |_(x = b) delta y(b)
+ L(x, y(x), y'(x))|_(x=b) Delta b = 0
$
]
#question(name: [Explain the essence of Pontryagin's principle of maximum.
Give the first-order necessary conditions of optimality (for optimal
control) using Pontryagin's principle (instead of the equation of
stationarity).])[
It states, that for the optimal control trajectory, the Hamiltonian
will be maximized, with state and costate being derived from it.
$
H(t, bold(x)^*, bold(u)^*, bold(lambda)^*) >=
H(t, bold(x)^*, bold(u), bold(lambda)^*), bold(u) in cal(U)
$
The Hamiltonian is defined as
$
H(t, bold(x), bold(u), bold(lambda))
= bold(lambda)^T bold(f)(bold(x), bold(u), t) - L(bold(x), bold(u), t)
$
this is so called "eastern notation" and it means we want to maximize
the Hamiltonian.
As a result
$
(diff H)/(diff bold(u)) = 0
$
These are the first--order necessary conditions
$
dot(bold(x)) &= gradient_bold(lambda) H\
dot(bold(lambda)) &= - gradient_bold(x) H
$
]
#question(name: [Give (a sketch of) the derivation of time--optimal control
for a double integrator with bounds on the control signal -- bang-bang
control. Discuss the key properties of the resulting controller. Discuss
also the practical issues related to implementation. What kind of heuristics
could be used to compensate those issues?])[
The point is, that by setting $L = 1$, we get a cost function
$
J = integral_(t_i)^(t_f) 1 upright(d) t = (t_f - t_i)
$
Now for the system
$
dot(bold(x)) = bold(A) bold(x) + bold(B) bold(u)\
t_i = 0, bold(x)(t_i) = bold(r)_0
$
with
$
bold(x)(t_f) = bold(0)
$
With boundary set on control to
$
abs(bold(u)_i (t)) <= 1
$
The hamiltonian is formed as
$
H = bold(lambda)^T (bold(A) bold(x) + bold(B) bold(u)) -1
$
meaning the necessary conditions are
$
dot(bold(x)) &= gradient_bold(lambda) H
= bold(A) bold(x) + bold(B) bold(u)\
dot(bold(lambda)) &= - gradient_bold(x) H
= - bold(A)^T bold(lambda)
$
Now applying the Pontryagin principle of maximality
$
H(t, bold(x)^*, bold(u)^*, bold(lambda)^*) >=
H(t, bold(x)^*, bold(u), bold(lambda)^*), bold(u) in cal(U)
$
after cancellations
$
(bold(lambda)^*)^T bold(B) bold(u)^* >=
(bold(lambda)^*)^T bold(B) bold(u), u_i in [-1, 1]
$
the only valid way to get this result is
$
bold(u)^* = op("sgn")((bold(lambda)^*)^T bold(B))
$
Now for the double integrator
$
bold(A) = mat(0, 1; 0, 0), bold(B) = mat(0; 1);
$
it means the switching function is simply
$
u(t) = op("sgn")(lambda_2 (t))
$
in order to get values of the $lambda_2 (t)$ costate, we need to solve
$
dot(bold(lambda)) = - gradient_bold(x) H = - bold(A)^T bold(lambda)
= - mat(0, 1; 0, 0) mat(lambda_1; lambda_2)
$
This can be solved analyticaly as
$
lambda_1 (t) &= c_1\
lambda_2 (t) &= c_1 t + c_2
$
Now the boundary constraint for the dinal time is simple. As condition
$
H(t_f) = 0 => lambda_2 (t_f) u (t_f) = 1
$
That means that at final time, as the $u(t_f) = plus.minus 1$ the
costate is $lambda_2 (t_f) = 1/(u(t_f)) => lambda_2 (t_f) = u(t_f)$.
That this, rather odd, observation states, is that as $lambda_2 (t)$ is
a linear function, regardless of where it starts, it will switch the
output signal
$
u(t) = op("sgn")(lambda_2 (t))
$
at most once.
The final issue is usability while facing the real world:
- hysteresis -- works fine, does not gurantee anything
- PTOC (_proximate time--optimal control_)
]
]
#skills[
#question(name: [Design a time--optimal controller for a continuous--time
systems.])[]
]
|
|
https://github.com/VisualFP/docs | https://raw.githubusercontent.com/VisualFP/docs/main/SA/design_concept/content/introduction/introduction.typ | typst | #import "../../../style.typ": *
#part("Introduction")
This part discusses the motivation behind VisualFP, what it aims to achieve,
and the research that was done on existing alternatives.
@motivation Motivation and @goals Goals are based on this project's task description, which can be found in full in @appendix_task_description.
#include_section("design_concept/content/introduction/motivation.typ")
#include_section("design_concept/content/introduction/goals.typ")
#include_section("design_concept/content/introduction/tool_research.typ")
|
|
https://github.com/yhtq/Notes | https://raw.githubusercontent.com/yhtq/Notes/main/代数学二/作业/hw9.typ | typst | #import "../../template.typ": proof, note, corollary, lemma, theorem, definition, example, remark, proposition,der, partialDer, Spec, AModule, lemmaLinear, tensorProduct, directSum, directLimit
#import "../../template.typ": *
#import "@preview/commute:0.2.0": node, arr, commutative-diagram
#show: note.with(
title: "作业9",
author: "YHTQ",
date: none,
logo: none,
withOutlined : false,
withTitle :false,
)
（应交时间为4月30日）
#set heading(numbering: none)
= p69
== 16
设 $A = k[x_1, x_2, ..., x_n]$，可以找到 $x_1, x_2, ..., x_n$ 的一个极大代数无关组，不妨设为 $x_1, x_2, ..., x_r$（若其中全部都是 $k$ 上的代数元则 $r = 0$，否则选出一个超越元成为 $x_1$，再寻找是否存在 $k[x_1]$ 上的代数元，以此类推） 若 $r = n$ 或 $r = 0$ 结论已经成立，下设 $0 < r < n$\
此时，当然有 $x_1, x_2, ..., x_r, x_n$ 代数相关，因此设 $n$ 次多项式 $f != 0$ 满足：
$
0 = f(x_1, x_2, ..., x_r, x_n) := sum_(d_n = 0)^n (sum_(l_1 + l_2 + ... +l_(r) + d_n <= n) a_(l_1, l_2, ..., l_(r), d_n) x_1^(l_1) x_2^(l_2) ... x_(r)^(l_(r))) x_n^(d_n)
$
- 首先，设：
$
f'(x) = sum_(d_n = 0)^n (sum_(l_1 + l_2 + ... +l_(r) + d_n <= n) a_(l_1, l_2, ..., l_(r), d_n) x_1^(l_1) x_2^(l_2) ... x_(r)^(l_(r))) x^(d_n)
$
当然就有 $f'(x_n) = 0$。同时，$f'$ 不可能是零多项式，否则每个系数都是 $x_1, x_2, ..., x_r$ 的零化多项式，由代数无关性这些多项式也是零多项式，表明 $f = 0$ ，与假设矛盾\
然而它未必首一。观察发现 $f'$ 的 $n$ 次项仅有常系数，若恰非零则除去可逆元后成为首一多项式，但可能为零导致 $f'$ 不是首一多项式。为此，希望取得 $lambda_i$ 以及 $x'_i = x_i - lambda_i x_n, i = 1, 2, ..., r$，代入上式将有：
$
0 = sum_(d_n = 0)^n (sum_(l_1 + l_2 + ... +l_(r) + d_n <= n) a_(l_1, l_2, ..., l_(r), d_n) (x'_1 + lambda_1 x_n)^(l_1) (x'_2 + lambda_2 x_n)^(l_2) ... (x'_r + lambda_2 x_r)^(l_(r))) x_n^(d_n)
$
不难发现它关于 $x_n$ 的 $n$ 次项系数为：
$
sum_(l_1 + l_2 + ... +l_(r) + d_n = n) a_(l_1, l_2, ..., l_(r), d_n) lambda_1^(l_1) lambda_2^(l_2) ... lambda_r^(l_r)
$
若设 $f$ 的 $n$ 次项恰为 $F(x_1, x_2, ..., x_r, x_n) != 0$，上式就是 $F(lambda_1, lambda_2, ..., lambda_r, 1)$ 为了证明可以取到一组 $lambda_i$ 使得前式非零（进而可逆，可以将多项式化为首一），注意到 $F$ 形如：
$
sum_(d_n = 0)^n (sum_(l_1 + l_2 + ... +l_(r) + d_n = n) a_(l_1, l_2, ..., l_(r), d_n) x_1^(l_1) x_2^(l_2) ... x_(r)^(l_(r))) x_n^(d_n)
$
假设对于所有 $lambda_i$ 都有前式为零，由无限域的性质将有代入 $x_n = 1$ 的结果：
$
sum_(d_n = 0)^n (sum_(l_1 + l_2 + ... +l_(r) + d_n = n) a_(l_1, l_2, ..., l_(r), d_n) x_1^(l_1) x_2^(l_2) ... x_(r)^(l_(r)))
$
是零多项式，观察形式将有每个系数 $a_(l_1, l_2, ..., l_(r), d_n)$ 都是零，进而 $F$ 是零，这是荒谬的。因此我们希望的 $lambda_i$ 是存在的。
- 上面结果已经表明，存在系数落在 $k[x'_1, x'_2, ..., x'_r] subset A' := k[x'_1, x'_2, ..., x'_r, x_(r+1), ..., x_(n-1)]$ 之中的 $x_n$ 的首一零化多项式，也即 $x_n$ 在 $A'$ 上整。$A'$ 的生成元个数严格减少，因此可以归纳并假设存在 $y'_1, ..., y'_s$ 代数无关并且 $A'$ 在 $k[y'_1, ..., y'_s]$ 上整，进而由传递性 $x_n$ 在其上整，同时由 $x_i = x'_i + lambda_i x_n$ 及 $x'_i in A', i = 1, 2, ..., r$ 知 $x_i$ 也在其上整，$x_(r+1) ... x_n$ 当然也整，因此 $A$ 的所有生成元都在其上整，证毕
- 对于第二个结论，注意到 $A = k[t_1, ..., t_n] quo I(X)$ 是有限生成 $k-$代数，由该题结论存在 $y_1 + I(X), ..., y_r + I(X) in A$ 满足上述的条件。\
由第一章的习题，这 $r$ 个多项式产生多项式映射 $Phi: k^n -> k^r$，往证 $Phi|_X$ 确实是满射。为此，任取 $y' in k^r$，令：
$
funcDef(f_(y'), k[y_1 + I(x), y_2 + I(x), ..., y_r + I(x)], k, f(y_1, y_2, ..., y_r), f(y'_1, y'_2, ..., y'_r))
$
不难验证这是一个 $k-$代数同态，由之前的习题它可以被提升到 $f'_(y') : A -> k$\
注意到 $f_(y')$ 是满射，$f'_(y')$ 自然也是，由同构定理不难得到 $ker f'_(y')$ 是极大理想。我们暂且利用希尔伯特零点定理，设其形如：
$
ker f'_(y') = m_x = {f in A | f(x) = 0}
$
再取：
$
f'_x : f: A -> f(x) : k
$
不难发现 $f'_x$ 与 $f'_(y')$ 都诱导 $A quo m_x tilde.eq k$ 的域自同构，结合它们都是 $k-$ 代数同态可得它们相等，立得：
$
y'_i = f'_(y') (y_i) = y_i (x), forall i = 1, 2, ..., r
$
这就给出了 $x in X$ 成为 $y'$ 的原像，证毕
== 17
题干似乎应该是若设 $X = Z(alpha)$ 且 $alpha != (1)$ 则 $X$ 非空\
若这个事实成立，则极大理想 $alpha$ 对应的 $Z(alpha)$ 非空，结合极大性知只能是单点集，如此立得 $alpha = m_x$ 也即结论成立。\
然而看起来上面的事实并不容易从上题结论推出（何况上题第二个结论已经利用了希尔伯特零点定理的结果）
== 18
#lemmaLinear[][
设 $A$ 是唯一分解整环，则 $A$ 是整闭的
]
#proof[
设 $x = a/b$ 位于 $A$ 的分式环中，不妨设 $a, b$ 互素。若它在 $A$ 上整，则：
$
x^n + a_(n-1) x^(n-1) + ... + a_0 = 0\
(a/b)^n + a_(n-1) (a/b)^(n-1) + ... + a_0 = 0\
a^n + a_(n-1) a^(n-1) b + ... + a_0 b^n = 0
$
然而观察上式立得 $b | a$ ，除非 $x in A$ 否则这是荒谬的
]
设 $B = k[x_1, x_2,..., x_n], A = k[x_1], k_A = k(x_1)$\
利用归纳法，$B$ 将是 $k_A$ 的有限代数扩张，假设 $x_1$ 在 $k$ 上代数则由传递性结论显然，否则 $A$ 当然是唯一分解整环，继而 $A$ 是整闭的。
由有限代数扩张，$x_2, ..., x_n$ 在 $k_A$ 上有首一的零化多项式。注意到这些系数都位于 $k(x_1)$ 之中，不妨设其公分母为 $f$，进而 $B$ 在 $A_f supset k_A$ 上整，然而 $A$ 整闭表明 $A_S$ 也整闭，这表明：
$
A_f = k_A
$
然而注意到 $A$ 是整环，$A$ 可以嵌入 $A_f$ 继而 $A_f = A[1/f]$ 是有限生成 $A-$代数，但由 $x_1$ 的超越性 $k(x_1)$ 当然不是 $k[x_1]$ 的有限生成代数，矛盾！
== 19
任取 $m$ 是极大理想，考虑 $k' := k[t_1, t_2, ..., t_n] quo m$
- 它是有限生成 $k-$代数
- 它是域
因此它是 $k$ 的有限代数扩张，然而 $k$ 是代数闭域，表明：
$
k' tilde.eq k
$
设同构 $sigma: k' -> k$，上述过程表明一定有 $sigma(x + m) = x, forall x in k$，继而：
$
sigma(t_i - sigma(t_i) + m) = sigma(t_i) - sigma(t_i) = 0 => t_i - sigma(t_i) in m
$
表明 $(t_1 - sigma(t_1), ..., t_n - sigma(t_n)) subset m$ ，而左侧已经是极大理想，因此取等，证毕
== 20
设 $A$ 的分式域为 $k$，则 $k tensorProduct B$ 是有限生成代数。由正规化引理存在 $x_i in k tensorProduct B$ 使得：
- $x_i$ 代数独立
- $k tensorProduct B$ 在 $k[x_1, x_2, ..., x_n]$ 上整
设 $B = plus.circle_(i) A b_i$，则：
$
k tensorProduct B = k tensorProduct (plus.circle_(i) A b_i) = plus.circle_(i) (Inv(S) A) tensorProduct A b_i = plus.circle_(i) (A) tensorProduct (S A b_i) = plus.circle_(i) A (1 tensorProduct b_i)
$
由假设 $1 tensorProduct b_i$ 都是 $k[x_1, x_2, ..., x_n]$ 上整元，因此存在各自的首一多项式 $f_i in (k[x_1, x_2, ..., x_n])[t]$ 将其零化。不妨设所有这些多项式的系数有公分母 $s$，继而：
$
f_i in (A_s [x_1, x_2, ..., x_n])[t]
$
继而 $B$ 在 $A_s [x_1, x_2, ..., x_n]$ 上整\
同时，设 $x_i = a_i tensorProduct b'_i$，再取 $s' = s a_1 ... a_n$，断言：
- $b'_i$ 在 $A$ 上代数独立，否则 $f(b'_1, ..., b'_n) = 0 => (a_1 a_2 ... a_n)^m f(1 tensorProduct b'_1, ..., 1 tensorProduct b'_n) = 0$ \
只要 $m$ 充分大，上式将给出一个 $x_1, ..., x_n$ 的零化多项式，结合整环无零因子可得 $f = 0$
- $B_s'$ 在 $(A[b'_1, ..., b'_n])_s'$ 上整，这是因为显然有 $B_s'$ 在：
$
(A_s [x_1, x_2, ..., x_n])_s' = A_s' [(x_1)_s', ..., (x_n)_s']
$ 上整，而 $(b'_i)_s'$ 与 $(x_i)_s' = (a_i (1 tensorProduct b'_i))_s' $ 只差可逆元，因此结论成立
这就表明结论成立
= p99
== 1
注意到若 $A$ 是整闭的一维诺特整环，则 $Inv(S) A$ 当然也是，进而它要么是域要么是戴德金整环。
考虑理想类群，为了保证 $H -> H'$ 是满射，注意到 $H'$ 中元素均形如 $i P_(Inv(S) A)$ 其中 $i$ 是 $Inv(S) A$ 的分式理想，它是 $K$ 上的有限生成模 $(a_1/b_1, a_2/b_2, ..., a_n/b_n)$ ，不妨通分设生成元为 $(a_1/s, a_2/s, ..., a_n/s)$，而：
$
(a_1/s, a_2/s, ..., a_n/s) P_(Inv(S) A) = (a_1/s, a_2/s, ..., a_n/s) (s) P_(Inv(S) A) = (a_1, a_2, ..., a_n) P_(Inv(S) A)
$
上式左侧是一个拓展理想，因此 $H -> H'$ 是满射
== 2
任取极大理想做局部化，可以不妨设 $A$ 是局部环，进而由 $A$ 是戴德金整环它将成为离散赋值环。可设：
$
c(f) = (t^r)\
c(g) = (t^s)
$
因此可设：
$
f = t^r (a'_n x^n + ... + a'_0)\
g = t^s (b'_m x^m + ... + b'_0)
$
其中 $(a'_n, ..., a'_0) = (b'_m, ..., b'_0) = (1)$（否则可以再次提出 $t$）\
如此：
$
f g = t^(r+s) (a'_n x^n + ... + a'_0)(b'_m x^m + ... + b'_0)
$
设 $(a'_n x^n + ... + a'_0)(b'_m x^m + ... + b'_0)$ 系数的生成理想为 $(t^l)$，断言 $l = 0$，否则考虑 $A quo (t)$ （这是域）中将有 $(a'_n x^n + ... + a'_0)(b'_m x^m + ... + b'_0) = 0 => (a'_n x^n + ... + a'_0) = 0 or (b'_m x^m + ... + b'_0) = 0$，这意味着 $(a'_n, ..., a'_0) subset (t)$ 或者 $(b'_m, ..., b'_0) subset (t)$ ，都与假设矛盾！
== 3
一方面离散赋值环当然是诺特的赋值环，另一方面，赋值环中有限生成理想都是主理想，而诺特环中理想都是主理想，因此 $A$ 是（局部）主理想整环，它当然是离散赋值环，证毕！
== 4
设 $m = (x)$，任取非零元素 $t$，可设：
$
x^r in (t), x^(r-1) in.not (t)
$
（否则将有 $I subset sect_m (x^m) = 0$）\
不难验证 $r$ 对每个 $t$ 是唯一定义的（对于可逆元 $t$ 定 $r = 0$）\
进一步，我们证明 $t$ 与 $x^(v(t))$ 只差一个可逆元。事实上由定义，可设：
$
t = k x^(v(t))\
k = s x^(v(k))\
t = s x^(v(t) + v(k))
$
而由 $v(t)$ 的最小性，一定有 $v(k) = 0 => k in.not m$ 表明 $k$ 是可逆元\
进而可以验证 $v$ 是离散赋值：
- $v(t) >= 0$ 显然
- $s = u x^(v(s)), t = v x^(v(t)) => s t = u v x^(v(s)+v(t))$ 而 $u, v, u v$ 是可逆元，表明 $v(s t) = v(s) + v(t)$\
- 设 $v(s) <= v(t)$ 则可设 $s = u x^(v(s)), t = v x^(v(t)) = v x^(v(t) - v(s)) x^(v(s))$，进而：
$
x^(v(s)) | s + t => v(s + t) >= v(s)
$
这就验证了离散赋值的定义
== 5
由之前的习题，无挠/平坦都是局部性质，因此不妨设 $A$ 是局部环，进而是离散赋值环，设其极大理想为 $(x)$。\
之前已经证明局部环上的有限生成理想平坦当且仅当自由，因此只需证明无挠当且仅当自由即可。自由模当然无挠，而若 $M$ 无挠，不妨设 $x_1, ..., x_n$ 是数量最少的生成元，只需证明这是一组基。假设存在非零的线性组合使得：
$
sum_i a_i x_i = 0
$
- 若存在某个 $a_i$ 为可逆元，则相应 $x_i$ 被其他元素表示，与生成元数量最少矛盾！
- 反之，取最大的 $r$ 使得：
$
a_i = a'_i x^r, forall i
$
将有：
$
x^r (sum_i a'_i x_i) = 0
$
由无挠性，将有 $sum_i a'_i x_i = 0$，而 $a'_i$ 中一定有可逆元（否则 $r$ 可以取更大），继而回到上一种情形
== 6
不妨设 $M!=0$\
- 断言 $"Supp"(M)$ 有限集，这是因为若设 $x_i$ 是一组生成元，则：
$
"Supp"(M) = union_i "Supp"(x_i)
$
只需证明 $"Supp"(x_i) = V(Ann(x_i))$ 有限。事实上,$Ann(x_i) != 0(arrow.double.l x_i in T(M))$ 可被唯一素理想分解：
$
Ann(x_i) = p_1^(n_1) p_2^(n_2) ... p_k^(n_k)
$
继而 $V(Ann(x_i)) = {p_1, p_2, ..., p_k}$
- 设 $p in "Supp"(M)$ 先处理 $M_p$，对其利用主理想整环上的有限生成模分类，将有：
$
M_p = plus.circle_(i) A_p quo (alpha_i)
$
然而 $A_p$ 是离散赋值环，上式也可写作：
$
M_p = plus.circle_(i) A_p quo (p A_p)^(n_i^p)
$
令 $M' = plus.circle_(p in "Supp"(M)) plus.circle_(i) A quo p^(n_i^p)$，不难验证 $"Supp"(M') = "Supp"(M)$，且它们在每个素理想处的局部化都相等，继而 $M = M'$ 证毕
== 7
考虑 $alpha$ 的素分解：
$
alpha = p_1^(n_1) p_2^(n_2) ... p_k^(n_k)
$
由中国剩余定理（注意到这些素理想都极大，因此互素，而互素理想的幂次也互素）：
$
A quo alpha = A quo p_1^(n_1) times A quo p_2^(n_2) times ... times A quo p_k^(n_k)
$
- 首先由于 $p_i$ 是非零素理想，显然包含 $p_i^(n_i)$ 的素理想仅有 $p_i$，因此 $A quo p_1^(n_1)$ 是只有一个素理想的局部环，进而：
$
A quo p_i^(n_i) = (A quo p_i^(n_i))_(p_i quo p_i^(n_i)) = A_(p_i) quo (p_i A_(p_i)) ^(n_i)
$
但上式右侧当然是主理想环，因此左侧也是
- 其次，既然环直积的理想都形如理想的直积，主理想环的直积当然也是主理想环，证毕
对于第二个结论，任取 $x in alpha$，将有 $alpha quo (x)$ 是主理想，当然 $alpha$ 由至多两个元素生成
== 8
不妨设 $A$ 是局部环，进而可设：
$
a = (x^u)\
b = (x^v)\
c = (x^w)
$
计算：
$
a sect (b + c) = (x^u) sect (x^v + x^w) = (x^u) sect (x^(min(v, w))) = (x^(max(u, min(v, w))))\
(a sect b) + (a sect c) = (x^(max (u, v))) + (x^(max(u, w))) = (x^(min(max(u, v), max(u, w))))
$
不难验证两式相等
$
a + (b sect c) = (x^(min(u, max(v, w))))\
(a + b) sect (a + c) = (x^(max(min(u, w), min(u, v))))
$
类似的两式相等
== 9
首先，证明 $A -> plus.circle_(i) A quo alpha_i -> directSum_(i < j) A quo (alpha_i +alpha_j)$ 正合。由于可做局部化，不妨设 $A$ 是局部环，进而是离散赋值环。\
此时注意到理想之间存在全序，因此不妨设 $alpha_1 subset alpha_2 ... subset alpha_n$，因此：
$
directSum_(i < j) A quo (alpha_i +alpha_j) = directSum_(i < j) A quo alpha_j
$
任取 $(x_i + alpha_i) in ker(plus.circle_(i) A quo alpha_i -> directSum_(i < j) A quo (alpha_i +alpha_j))$，将有：
$
forall i < j, x_i - x_j in alpha_j
$
因此：
- $x_2 - x_1 in alpha_2 => x_1 + alpha_2 = x_2 + alpha_2$
- $x_3 - x_1 in alpha_3 => x_1 + alpha_3 = x_3 + alpha_3 = x_2 + alpha_3$
- ...
因此可以不妨设 $x_1 = x_2 = ... = x_n$ ，证毕
由此正合列，方程组有解 $x$ 当且仅当 $x in ker(plus.circle_(i) A quo alpha_i -> directSum_(i < j) A quo (alpha_i +alpha_j)) = im(A -> plus.circle_(i) A quo alpha_i)$
|
|
https://github.com/Ngan-Ngoc-Dang-Nguyen/thesis | https://raw.githubusercontent.com/Ngan-Ngoc-Dang-Nguyen/thesis/main/hoi-nghi-Nha-Trang/eqref.typ | typst | #let ieeeEqfmt = (nums) => [(#numbering("1.1", ..nums))]
#let eqref(
label,
fmt: ieeeEqfmt,
//fmt: nums => [(#numbering("1.1", ..nums))],
style: x => x,
makelink: true,
) = {
locate(loc => {
let elements = query(label, loc)
let locationreps = elements.map(x => repr(x.location().position())).join(", ")
assert(elements.len() > 0, message: "label <" + str(label) + "> does not exist in the document: referenced at " + repr(loc.position()))
assert(elements.len() == 1, message: "label <" + str(label) + "> occurs multiple times in the document: found at " + locationreps)
let target = elements.first().location()
let number = counter(math.equation).at(target)
if makelink {
return [
#show link: style
#link(target, fmt(number))
]
}
return fmt(number)
})
} |
|
https://github.com/404Wolf/stainless-technical-breifing-natug | https://raw.githubusercontent.com/404Wolf/stainless-technical-breifing-natug/main/document.typ | typst | #let title = "Nucleic Acid Nanotube Grapher"
#let author = "<NAME>"
#set document(author: author, title: title)
#set cite(form: "author")
#show cite : it => [
(#emph(it))
]
#set page("us-letter", margin: 1in, header: [
#set text(12pt)
#author
#h(1fr)
NATuG Technical Brief
], footer: [
#counter(page).display() #h(1fr)
])
#align(center + horizon)[
#move(dy: -0.50in)[
#block(text(weight: 700, 1.75em, [
#title \ Technical Brief \
#text(size: 12pt)[for Stainless Interview]
#v(.5in)
]), below: 0.15in)
#v(.25in)
#block(text(1.25em, author))
]
]
#pagebreak()
#set page(numbering: "1", number-align: center, columns: 2)
= Introduction
== Background
=== Structural DNA Nanotechnology
#figure(
image("./resources/nanotube.png", width: 50%), caption: [Example of a DNA Nanotube @shermanNanotubeDesign],
) <fig:example-nanotube-rendering>
#v(0.05in)
Creating nanoscale structures is a tricky task, as it is hard to achieve
precision and rigidity at such small scale. One unique way is with _Structural DNA Nanotechnology_,
a field of biochemestry that uses DNA as a nanoscale building block. Instead of
using DNA for its biological purpose, one can program base sequences so the DNA "automatically"
combines to form predetermined custom structures.
Here, we focus on tubular nanostructures. A _DNA nanotube_ is made by placing
double helices adjacently, "weaving" them together to create a larger tube (see
@fig:example-nanotube-rendering). They can be used to study cellular membrane
proteins with NMR, for drug delivery, optics, and more.
The theory for the design processes that NATuG (Nucleic Acid Nanotube Grapher)
facilitates are laid out in <NAME> and <NAME>'s paper, _Design of Minimally Strained Nucleic Acid Nanotubes_ @shermanNanotubeDesign.
They introduce an Excel tool to help design DNA nanotubes with specialized plots
(see @fig:natug-1). Eventually, this was reimplemented at Brookhaven National
laboratory as a desktop application (@fig:natug-2). It was better at graphing,
but failed handling "weaving" _multiple_ strands together, and was designed in a
nonmodular way, restrictive to further development.
This briefing introduces _NATuG 3.0_, a significantly more feature-rich
iteration of the program. I, <NAME>, was responsible for all software,
and worked closely with Dr. <NAME> to implement his DNA nanotube design
methodologies.
NATuG is a Python application available via `pypi` or `nix`
```bash
pip install natug && natug
nix run "github:natug3/natug"
```
#figure(
scope: "parent", placement: auto, grid(
gutter: 0.25in, columns: (1.67fr, 1fr), [
#figure(
image("./resources/natug2.png", width: 90%), caption: [NATuG 2.0 Desktop Application],
) <fig:natug-2>
], [#figure(
image("./resources/natug1.png", width: 90%), caption: [NATuG 1.0 Excel Spreadsheet],
) <fig:natug-1>],
),
)
== Designing DNA Nanotubes
Designing DNA nanotubes is a complex process, but it is helpful to have an idea
to understand what NATuG does.
To design a DNA nanotube, first you choose a type of nucleic acid, like "B-Form
DNA", defining parameters like the diameter.
#v(.05in)
#[
#set figure.caption(position: top)
#figure(
[
#set figure.caption(position: bottom)
#v(0.025in)
#grid(
columns: 2, gutter: .1in, figure(
image("./resources/top-view-example-2.png", width: 80%), caption: [Domain \#2 has a small angle (see angle between \#1 \#2 and \#3)], numbering: none,
), figure(
image("./resources/top-view-example-1.png", width: 80%), caption: [Domain \#2 has a big angle (see angle between \#1 \#2 and \#3)], numbering: none,
),
)
], caption: [Choosing the shape of the nanotube by setting angles between helical domains],
) <fig:top-view-example>
]
#v(.05in)
#figure(
scope: "parent", placement: auto, grid(
gutter: 0.25in, columns: 2, [#figure(
image("./resources/cross-strand-exchange.png", height: 1.6in), caption: [Creating a cross-strand exchange],
) <fig:cross-strand-exchange>], [#figure(
image("./resources/holliday.png", height: 1.6in), caption: [A 4 way Holliday junction],
) <fig:holliday-junction>],
),
)
Then, you find a tube shape by strategically setting angles between _helical domains_ (the
area that the DNA double helices take up) (see @fig:top-view-example).
Now you create cross-strand exchanges to hold the structure together (see
@fig:cross-strand-exchange), redirecting strands, some what like Holliday
junctions (see @fig:holliday-junction).
#figure(
scope: "parent", placement: auto, image("./resources/staple-strands.png", height: 2in), caption: [DNA staple strands @unsw2017capsid],
) <fig:staple-strands>
Then, you cut strands to create "staple" strands. Usually, one long virus strand
will run through the structure, and be "stitched" together (see
@fig:staple-strands) (synthesizing custom DNA is expensive and restricted to
short lengths).
Finally, you choose base sequences and send for synthesis.
#pagebreak()
= The NATuG Program
#figure(
scope: "parent", placement: bottom, block[#grid(
columns: (1.5fr, 1fr), gutter: 0.6in, [#figure(
image("./resources/program-overview.png", height: 2.625in), caption: [NATuG Program Layout],
) <fig:program-layout>], [#figure(
image("./resources/creating-cross-strand-exchanges.png", height: 2in), caption: [You can create cross-strand exchanges in "juncter" mode with just a click, "weaving"
together helical domains],
) <fig:creating-cross-strand-exchanges>],
)
#v(0.15in)],
)
NATuG is a custom-made desktop application to streamline this process. The UI is
broken up into panes for focus on one step at a time (see @fig:program-layout);
a flow similar to doing it "manually."
The _Side View Plot_ (center region) displays an "unrolled" view. It is modal;
modes determines what clicks do, like having clicking between DNA bases create
strand-exchanges, or break apart DNA strands. The _Top View Plot_ (left side) is
a "bird's eye" view of the tube.
The plots update live and are interactive. For example, you can click in the _Top View Plot_ to
modify angles in certain ways.
The _Config Panel_ (right side) has tabs for configuring parameters. For
example, entering DNA parameters, placing the double helices, or setting base
sequences.
You can then click on nucleoside midpoints to create cross-strand exchanges (see
@fig:creating-cross-strand-exchanges). You can chop-up strands and create
linkages. You assign sequences in the _Sequencing Tab_, or by clicking on
strands.
Finally, you can export the sequences to a spreadsheet for synthesis.
= Technical Overview
NATuG is a `Python` application that uses `PyQt6`, and `pyqtplot` for graphics.
It takes advantage of a `numpy` and `pandas` for vectorizing optimizations and
for features like file exports.
=== General Design
NATuG follows `oop` principals for managing state and exposing functionality.
References off a "runner" object provide a source of truth for state, and "manager"
instances are passed along to UI elements to access and update parts of it. In
the future, it will be possible to have multiple `Runners`, to edit multiple
nanotubes simultaneously.
Biological structures are represented using special data structures designed to
be as simple/modularized as possible. For instance, it is common in nanotube
design to take advantage of symmetries for choosing angles between helical
domains. NATuG stores `Domain`s in groups called `Subunit`s, which go into `Subunits` collection.
This lets us do nice things like modifying or intelligently exporting angles of
all symmetrical groups at once.
#figure(
scope: "parent", placement: bottom, block[
#grid(
columns: (1fr, 1fr), [#figure(
image("./resources/sequence-editor-manual-input.png", height: 2in), caption: [Custom base pair sequence editor/entry modal],
) <fig:bp-editor>], [#figure(
image("./resources/domain-config-table-counts.png", height: 2in), caption: [Domain triple spinbox container for choosing the number of nucleosides per
strand],
)],
)
],
)
`PyQt` is somewhat restrictive; it ships with predefined widgets and it is
annoying, but sometimes necessary, to compose complex new ones, like the
sequence editor that auto-fills the complementary bases to prevent mistakes (see
@fig:bp-editor). Designing custom widgets like this is tricky, both technically,
and because there are usage implications to consider.
=== Plotting
The first iteration of NATuG was a spreadsheet, and used non-interactive
spreadsheet plots. NATuG 2.0 used `Matplotlib`, which was considered for NATuG
3.0. Ultimately, we chose `pyqtgraph`, a very powerful plotting library designed
for great support with PyQt, because of its real time capabilities and deep
interactivity.
NATuG is able to compute the positions of all of the `Point`s (e.g. DNA
nucleosides) by first computing their angles as they wind about their helices,
and then converting those angles to $x$ coordinates, while the $z$ coordinates
grow steadily.
Computing the _Top View Plot_ is more straight forward. Starting at the first
domain, we place each domain relative to the previous at some angle
displacement. It is useful to be able to determine which domain in this plot
corresponds to which in the _Side View Plot_; clicking domains navigates to
them, but in the future we may add color coding.
=== Conjuncting
The most interesting algorithm within NATuG is the strand "conjoining" feature.
Given two arbitrary midpoints between nucleosides, we want to be able to cut and
then reroute the strands. Sometimes this will result in loops, which we need to
deal with.
#figure(
scope: "parent", placement: top, block[
#figure(
image("./mermaid/out/conjoin-graph.png", width: 100%), caption: [All the unique ways NATuG has to handle resolving clicks on junctions #v(0.07in)],
) <fig:junction-conjoin-tree>
#figure(
[
#let height = 1.4in
#grid(
columns: 5, gutter: 15pt, [
#figure(
image("./resources/junction-case-1A.png", height: height), caption: [Case 1A],
) <fig:junction-case-1a>
], [
#figure(
image("./resources/junction-case-1B.png", height: height), caption: [Case 1B],
) <fig:junction-case-1b>
], [
#figure(
image("./resources/junction-case-2A.png", height: height), caption: [Case 2A],
) <fig:junction-case-2a>
], [
#figure(
image("./resources/junction-case-2B.png", height: height), caption: [Case 2B],
) <fig:junction-case-2b>
], [#figure(
image("./resources/junction-case-2C.png", height: height), caption: [Case 2C],
)<fig:junction-case-2c> ],
)
], caption: [Examples for all the possible junction cases],
)
],
)
Generally, how to create a junction is intuitive. NATuG handles breaking down
the cases based on whether the two points are along the same strand, and whether
the strand(s) are open; for all the cases, see @fig:junction-conjoin-tree.
=== Data Exchange
You can export/import state to `.natug` files, which are `zip` archives
containing metadata about every all artifacts, linking objects together with `uuid`s.
We trade redundancy for fast reloads and data accessibility. It also lets us
implement undo/redo with frequent `.natug` saves.
Pickling for state saving was considered, but `python` pickles ended up being
too inaccessible and fragile.
Work is in progress to support exporting to spreadsheets using `openpyxl`.
Spreadsheets are popular among professionals in the field, are easy to analyze,
and are highly portable.
For the `.natug` save, we give artifacts unique identifiers to link them
together with. For a spreadsheet, it would be ideal to reference by spreadsheet
cell instead.
You can also export/import certain parts of the program alone. For example, DNA
parameters in the _Nucleic Acid Tab_ are stored in `json` files and profiles
automatically get loaded in/exported.
== Next Steps
As this iteration is completed, a paper is being drafted on program
algorithms/functionalities. We have been increasingly considering end users:
NATuG is very good at designing tubular structures, but since it is relatively
intuitive and straight forward, it also is suitable for non-tubular structures
as well, and potentially educational purposes.
#bibliography("works.bib")
#pagebreak()
#set page(columns: 1)
#set page(header: [], footer: [])
On the next page I have included an academic poster created at the time of
working on NATuG 3.0, not part of the "technical briefing," in case a more
visual overview of the program is helpful.
|
|
https://github.com/YabusameHoulen/Statistics | https://raw.githubusercontent.com/YabusameHoulen/Statistics/main/Bayes_Inference/GWBayes.typ | typst | #import "../Template/pset.typ": pset
#import "@preview/cuti:0.2.1": show-cn-fakebold
#show: show-cn-fakebold
#set text(12pt, font: ("Times New Roman", "寒蟬錦書宋"))
#set math.equation(numbering: "(1)", supplement: [ 公式: ])
#show: pset.with(
class: "Statistics",
student: "Yabusame",
title: "Bayesian Inference",
date: datetime.today(),
)
= 概念介绍
#figure(
image("/Bayes_Inference/graph/GW示意.png", width: 60%),
caption: [ GW 示意图 ],
)
== 参数估计&&假设检验
事件和概率定义(不同的概率诠释)，数学书上有要(Ω,F,P)---样本空间 Ω 、事件空间 F 和概率测度 P\。Kolmogorov axiom: 考虑集合 $SS$ 和它的子集
A,B...概率公理如下：
#enum(
indent: 4em,
[$forall A subset SS, P(A) >= 0 $ 非负性],
[$P(SS) = 1$ 归一化],
[$A sect B = emptyset, P(A union B)=P(A)+P(B)$ 可加性],
)
#h(2em)贝叶斯定理
$ P(A|B) = (P(B|A)P(A))/P(B) $
#h(2em)全概率公式
$ P(A|B) &= (P(B|A)P(A))/P(B) \
&= (P(B|A)P(A))/display(sum_i P(B|A_i)P(A_i)) $
#h(2em) GW detection:
$ d(t)=cases(n(t) "if signal not present", n(t)+h(t;theta) "if signal " h" present") $
$ P(h|d) &= (P(d|h)pi(h))/P(d) = (P(d|h)pi(h))/(P(d|h)pi(h)+p(d|0)pi(0)) \
&= Lambda[Lambda+pi(0)/pi(h)]^(-1) "where " Lambda = (P(d|h))/(P(d|0))=P(d-h|0)/P(d|0) ("Finn 1992") \
& "最后分子变换的解释： 把引力波的信号去除剩下的是噪声" \
& "假设噪声是稳态高斯白噪声，可以对噪声的概率分布写出表达式" \
& "用噪声的分布模拟引力波信号 ？"$
不可排除的假信息： glich (e.g. 风、地震等等，人为消除、关联已知数据消除)\
Stationary, Gaussian white noise:
$ P(n|0) = NN e^(-1/2(n|n)) = NN e^(-1/2(n^TT dot C^(-1) dot n)) $
log-likelihood ratio:
$ ln(Lambda) = -1/2(d-h|d-h)+1/2(d|d) = (d|h)-1/2(h|h) $
对其求导得到SNR的平方$arrow Lambda$会有一个阈值(90%，$1.645 sigma$)对应着:SNR=8\
log-likelihood ratio 很大$arrow$探测到引力波
The Law of Large Number && The Central Limit Theorem
Bayesian Inference
- Parameter estimation : #text(red)[Posterior]
- Find the Posterior probability density $P(theta|d,HH)$
- Model Selection : #text(red)[Evidence]
- compare different hypotheses through an odds ratio ($HH_1 "is perfer when" > 1 $)
$ O^(HH_1)_(HH_2) = P(HH_1|d)/P(HH_2|d) = (P(d|HH_1)P(HH_1))/(P(d|HH_2)P(HH_2)) prop Z_1/Z_2 ("Evidence ratio") $
== Bayesian Computation method
Bayes-factor(Zimmerman et al. 2019)
#figure(
image("/Bayes_Inference/graph/采样器.png", width: 70%),
caption: [
采样器列表
],
)
=== MCMC
+ Direct Sampling
+ Rejection Sampling (要能包起来，heavy tail分布用这种方法不行)
Detail Balance Condition : $pi(i)P(i,j)=pi(j)P(j,i)$
Limitation of MCMC:
+ 收敛到极值点
+ 采样结果不收敛
+ 结束条件
Burn-in && Thin-in && Auto-correlation Statistics && Gelman-Rubin Statistics\
多峰结构：可能被困在局域极值上\
可以用PTMCMC(parallel-tempering)并行退火算法（多个温度）\
(MCMC不能计算Evdience, 但2019年时Maturana-Russel 提出将MCMC与Stepping-stone联合使用 $arrow$Evdience)
=== Nest-Sampling
(Ashton et al 2022)
- Well-defined stopping criteria
- Calculate the Evdience
- Solve multimodal problem
K-L divergence 之类的数据处理方法用进来啊啊啊啊啊啊啊
#figure(
image("/Bayes_Inference/graph/坐标转换.png", width: 80%),
caption: [先验和坐标参数有关($r^2 ,cos theta,phi$)一般对体积元平权],
)
|
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.