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https://github.com/saYmd-moe/note-for-quantum--mechanics | https://raw.githubusercontent.com/saYmd-moe/note-for-quantum--mechanics/main/SPT.typ | typst | // 导入模板
#import "template.typ": *
// 文章信息设置
#show: conf.with(
title: "微扰理论（量子力学）",
shortitle: "Perturbation Theory in Quantum Mechanics",
author: "saYmd"
)
*写在前面：*
谐振子和不考虑相对论效应的氢原子具有简单的哈密顿算符，可以求出精确解析解。但是，对于更复杂的原子或分子（多电子原子），一般很难得到解析解。这时，我们可以通过一些 *近似方法* 得到本征值方程的近似解。
微扰理论就是其中的一种近似方法
#footnote([微扰理论是一种数学方法，并不只是运用在量子力学中，经典力学同样有非常类似的近似方法。])
，根据体系是否显含时间，可以分为定态微扰理论和含时微扰理论，根据体系是否存在简并，可以分为非简并微扰理论和简并微扰理论。使用微扰理论遵循的思想是：我们一般优先处理体系中起到主导作用的效应，将这部分解决后再去考虑在近似中忽略掉的次要效应。
= 定态微扰理论
== 方法概论
首先我们需要对微扰理论这一方法有一个大概的印象，考虑体系的哈密顿算符可写作下列形式：
$ H=H_0+H' $
#h(2em) $H^0$是 *未微扰哈密顿算符* ，它的本征方程应是容易解的，而$H'$是 *微扰项* ，考虑$H'$与时间无关时的 *定态微扰* 。为了方便标记，我们假设未微扰 哈密顿 算符的本征值构成一个 *离散谱*
#footnote([这里离散谱的假设是为了简化书写，微扰理论同样可以用于处理连续谱。])
。使用整数指标 n 来标记： $E_n^0$，对应本征态 $ket(n^0_i)$
#footnote([$ket(n^0_i)$，即$ket(psi_n^0)$，下标 i 用于区分简并。])
。这个未微扰的 哈密顿 算符的本征方程是可以解析求解的：
$ H^0 ket(n^0_i) = E_n^0 ket(n^0_i) $<non-pert>
微扰理论的作用就是近似求解施加微扰后的本征方程：
$ H ket(n_i) = (H^0+H') ket(n_i) = E_n ket(n_i) $<perted>
#h(2em) $H'$是 *微扰项* ，在实际物理问题中，微扰项可以来自外界扰动、体系相互作用或者体系内部结构的影响，比如放置在电磁场中的氢原子，$H'$就可以用来表示氢原子与电磁场相互作用引起的势能。@fig:inf_with_pert 展示了一个带有扰动的无限深方势阱。
#figure(
cetz.canvas({
import cetz.draw: *
// 坐标轴
let x = (-1,3)
let y = (-.5,2)
set-style(mark: (fill: none))
line((x.at(0),0),(x.at(1),0), mark: (end: ">"), stroke: (paint: luma(30%)))
content((x.at(1)-.1,-.2),[$x$])
line((0,y.at(0)),(0,y.at(1)), mark: (end: ">"), stroke: (paint: luma(30%)))
content((0,y.at(1)+.3),[$V(x)$])
// 无限深势阱
on-layer(
-1,{
rect((x.at(0)/4,0),(0,0.7 * y.at(1)), stroke: (none), fill: luma(50%))
rect((0.6 * x.at(1),0),(0.6 * x.at(1)-x.at(0)/4,0.7 * y.at(1)), stroke: (none), fill: luma(50%))
}
)
// 势能曲线
on-layer(
1,{
merge-path({
line((0,0.7 * y.at(1)),(0,0))
line((),(0.2 * x.at(1),0))
bezier-through((),(0.3 * x.at(1),0.2 * y.at(1)),(0.4 * x.at(1),0))
line((),(0.6 * x.at(1),0))
line((),(0.6 * x.at(1),0.7 * y.at(1)))
})
}
)
}),
caption: [带有扰动的无限深方势阱]
)<inf_with_pert>
下面引入一个连续实参量$lambda in [0,1]$：
$ H(lambda) = H^0 + lambda H' $
$lambda$用来表示我们引入微扰的强度，$lambda = 0$对应着无微扰的情况，$lambda = 1$对应着完全微扰的情况。对于某微扰体系，如果$lambda$从0连续变化到1时，$E_n^0$和$ket(n_i^0)$能够分别平滑过渡到$E_n$和$ket(n_i)$，微扰理论用在这个体系上就能够得到比较好的近似结果。
@eqt:non-pert[式] 说明$H^0$的本征函数集${ket(n^0_i)}$是完备的，进一步假设能量的谱不存在简并，将 @eqt:perted[式] 表示为$lambda$的函数形式：
$
(H^0 + lambda H') ket(n (lambda)) = E_n (lambda) ket(n (lambda))
$<eigen-eqt>
大部分量子力学教材在这一步都会直接将$ket(n(lambda))$和$E_n (lambda)$对$lambda$展开，这里根据 sakurai 的《现代量子力学》
#footnote([Sakurai, <NAME>, and <NAME>.
Modern Quantum Mechanics. 3rd ed, Cambridge University Press, 2021])
给出推导过程。
$lambda$从零递增意味着我们考虑的微扰强度越来越接近实际强度，定义第$n$个能级下微扰项提供的能量：
$
E'_n=E_n-E_n^0
$
将其带入 @eqt:eigen-eqt[式] 中，我们需要求解的方程就变为：
$
(E_n^0 - H^0) ket(n) = (lambda H' - E'_n) ket(n)
$<pert-lam-eqt>
其中$E_n^0$是已知项，通过该式解出微扰能量$E'_n$就能够得到能级的总能量$E_n$。看到这个式子不难想到需要取算符$(E_n^0 - H^0)$的逆算符，但由 @eqt:non-pert[式] 可知该算符作用于$ket(n^0)$上得到的结果是0，要保证算符可逆我们需要构造一个不包含$ket(n^0)$的子空间，引入 *投影算符* ：
$
phi_n equiv 1 - ketbra(n^0) = sum_(k eq.not n) ketbra(k^0)
$
在该子空间上，$(E_n^0 - H^0)$可逆，由于$ketbra(k^0)$同样是$H^0$的本征向量，所以：
$
1/(E_n^0 - H^0) phi_n = sum_(k eq.not n) 1/(E_n^0 - E_k^0) ketbra(k^0)
$<rev-op>
同时 @eqt:pert-lam-eqt[式] 右侧由于没有$ket(n^0)$方向上的分量，即$bra(n^0) (lambda H' - E'_n) ket(n) = 0$，因此我们有：
$
(lambda H' - E'_n) ket(n) = phi_n (lambda H' - E'_n) ket(n)
$
#h(2em) 现在对 @eqt:pert-lam-eqt[式] 左乘 @eqt:rev-op[式] ，得到：
$
ket(n) = 1/(E_n^0 - H^0) phi_n (lambda H' - E'_n) ket(n) + #text(red)[$display(c_n (lambda)ket(n^0))$]
$ |
|
https://github.com/clysto/polylux-ustc-theme | https://raw.githubusercontent.com/clysto/polylux-ustc-theme/main/ustc.typ | typst | #import "@preview/polylux:0.3.1": *
#let ustc-footer = state("ustc-footer", [])
#let ustc-theme(aspect-ratio: "16-9", footer: [], fontset: "noto", body) = {
set page(
paper: "presentation-" + aspect-ratio,
margin: 0pt,
)
ustc-footer.update(footer)
if fontset == "noto" {
set text(size: 25pt, font: ("Noto Sans CJK SC"), lang: "zh")
body
} else if fontset == "fz" {
set text(size: 25pt, font: ("Helvetica", "FZHei-B01"), lang: "zh")
show strong: set text(
font: ("Helvetica", "FZDaHei-B02"),
weight: "bold"
)
show heading: it => block[*#it.body*]
body
} else {
panic("Illegal fontset: " + fontset)
}
}
#let title-slide(title: [], subtitle: [], title-size: 30pt, ) = {
set heading(outlined: false)
let height = (100% - 180pt) * 0.7
polylux-slide([
#block(
width: 100%,
height: 100pt,
fill: rgb("#f3f3f3"),
inset: (x: 25pt),
below: 0pt,
align(horizon, image("imgs/ustc-logo.svg", width: 250pt))
)
#v(8pt)
#line(length: 100%, stroke: 4pt + rgb("#f3f3f3"))
#v(1fr)
#block(
width: 100%,
height: height,
fill: gradient.linear(rgb("#3366ad"), rgb("#004098")),
[
#place(top + left, image("imgs/banner.svg", height: 100%, width: 50%, fit: "stretch"))
#set align(center + horizon)
#set text(fill: white)
#pad(
x: 25pt,
[
#text(size: title-size, [*#title*])
#parbreak()
#subtitle
]
)
]
)
#v(1fr)
#line(length: 100%, stroke: 4pt + rgb("#f3f3f3"))
#v(8pt)
#block(
width: 100%,
height: 80pt,
fill: rgb("#f3f3f3"),
above: 0pt,
)
])
}
#let slide(title: [], alignment: start + top, title-size: 30pt, body) = {
show footnote.entry: it => {
set text(
size: 0.8em,
fill: rgb("#666666"),
)
pad(x: 10pt, it)
}
let footer = block(
width: 100%,
height: 25pt,
fill: rgb("#004098"),
stroke: (
top: (2pt + rgb("#eaebed"))
),
[
#set text(fill: white, size: 14pt)
#set align(center + horizon)
#pad(
x: 25pt,
top: 1pt,
{
ustc-footer.display()
h(1fr)
logic.logical-slide.display()
}
)
]
)
let header = block(
width: 100%,
height: 50pt,
fill: gradient.linear(rgb("#3366ad"), rgb("#004098")),
stroke: (
bottom: (2pt + rgb("#eaebed"))
),
[
#set align(horizon)
#place(top + left, image("imgs/banner.svg", height: 49pt, width: 50%, fit: "stretch"))
#pad(
x: 25pt,
stack(
dir: ltr,
spacing: 1fr,
align(horizon, text(fill: white, size: title-size, [*#title*])),
align(horizon, image("imgs/ustc-logo-white.svg", height: 40pt))
)
)
]
)
let content = align(alignment, pad(x: 25pt, y: 20pt, body))
set page(
margin: (bottom: 35pt, top: 50pt),
footer: footer,
header: header,
footer-descent: 10pt,
header-ascent: 0pt,
)
polylux-slide(content)
}
#let focus-slide(alignment: center + horizon, body) = {
let content = block(
width: 100%,
height: 100%,
fill: gradient.linear(rgb("#3366ad"), rgb("#004098")),
[
#place(top + left, image("imgs/banner.svg", height: 100%, fit: "stretch"))
#set align(alignment)
#set text(fill: white)
#pad(
x: 25pt,
y: 25pt,
body
)
]
)
logic.polylux-slide(content)
}
|
|
https://github.com/Hobr/njust_thesis_typst_template | https://raw.githubusercontent.com/Hobr/njust_thesis_typst_template/main/page/abstract.typ | typst | MIT License | // 字体
#import "../util/font.typ": fonts, fontSize
// 摘要
#let showAbstract(abstract, keywords: none, lang: "zh") = align(
left,
par(
// 无缩进
first-line-indent: 0em,
text(
font: (fonts.en, fonts.zh_宋体),
size: fontSize.五号,
(if lang == "zh" [ *摘 要*: ] else [*Abstract—*]) + [#abstract] + (
if keywords != none {
[\ ] + (if lang == "zh" [*关键词*: ] else [*Index Terms—*]) + [#keywords]
}
),
)
),
)
|
https://github.com/Otto-AA/definitely-not-tuw-thesis | https://raw.githubusercontent.com/Otto-AA/definitely-not-tuw-thesis/main/src/styles/all.typ | typst | MIT No Attribution | #import "front-matter.typ": front-matter-styles
#import "main-matter.typ": main-matter-styles
#import "back-matter.typ": back-matter-styles
#import "appendix.typ": appendix-styles
#import "toc.typ": toc-styles
#import "flex-captions.typ": flex-caption-styles, flex-caption
#import "general.typ": general-styles
#import "page-header.typ": page-header-styles |
https://github.com/ymgyt/techbook | https://raw.githubusercontent.com/ymgyt/techbook/master/programmings/rust/tool/cargo/cargo_lambda.md | markdown | # cargo-lambda
* [Getting started](https://www.cargo-lambda.info/guide/getting-started.html)
## Install
use nix package `cargo-lambda`
## Usage
```sh
# Create project dir
cargo lambda new foo
# Run local lambda emulator
cargo lambda watch
# Invoke lambda
cargo lambda invoke --data-ascii '{"key": "value"}'
# Build
cargo lambda build --release
```
* `cargo lambda invoke`
* 事前にwatchが別terminalで実行されている前提
* `--data-ascii`に渡すのはpayloadのjson. contextは渡さなくてよい
* `cargo lambda build`
* `target/lambda/<crate_name>`にbuildされる
* このpathをcdk等のlambdaのassetとして渡せる
## CDK
cdkでcargo lambdaで作成したlambdaをdeploy
```typescript
import { Code, Function, Runtime } from "aws-cdk-lib/aws-lambda";
import { Construct } from "constructs";
import * as iam from "aws-cdk-lib/aws-iam";
import * as path from "path";
export function lambda(scope: Construct, dynamodbTableArn: string): Function {
const role = new iam.Role(scope, "MyLambdaRole", {
assumedBy: new iam.ServicePrincipal("lambda.amazonaws.com"),
description: "Lambda role",
roleName: "MyLambda",
inlinePolicies: {
dynamodb: new iam.PolicyDocument({
statements: [
new iam.PolicyStatement({
actions: ["dynamodb:*"],
resources: [dynamodbTableArn],
effect: iam.Effect.ALLOW,
sid: "allowDynamodbOperation",
}),
],
}),
},
});
const f = new Function(scope, "MyLambda", {
functionName: "MyLambda",
code: Code.fromAsset(
path.join(
__dirname,
"../path/to/cargo_lambda_project/target/lambda/crate_name"
)
),
runtime: Runtime.PROVIDED_AL2,
handler: "not_used_in_custom_runtime",
role,
});
return f;
}
```
* `code`: cargo lambdaでbuildしたtargetへのpath
* `runtime`: `provided.al2`を使えばよいらしい
* `handler`: custom runtimeでは利用されないので、なんでもよい
|
|
https://github.com/jbro/supernote-templates | https://raw.githubusercontent.com/jbro/supernote-templates/main/work-notes.typ | typst | The Unlicense | #import "include/a5x-template.typ": template
#show: doc => template(doc)
#import "include/elements.typ": titled-box, note-lines
#grid(columns: (1fr, 220pt),
[
#set text(size: 20pt)
#h(5pt)
Notes
],
titled-box(title: "", text(size: 24pt, v(1em))),
)
#titled-box(title: "", note-lines(21)) |
https://github.com/typst/packages | https://raw.githubusercontent.com/typst/packages/main/packages/preview/unichar/0.1.0/ucd/block-1D100.typ | typst | Apache License 2.0 | #let data = (
("MUSICAL SYMBOL SINGLE BARLINE", "So", 0),
("MUSICAL SYMBOL DOUBLE BARLINE", "So", 0),
("MUSICAL SYMBOL FINAL BARLINE", "So", 0),
("MUSICAL SYMBOL REVERSE FINAL BARLINE", "So", 0),
("MUSICAL SYMBOL DASHED BARLINE", "So", 0),
("MUSICAL SYMBOL SHORT BARLINE", "So", 0),
("MUSICAL SYMBOL LEFT REPEAT SIGN", "So", 0),
("MUSICAL SYMBOL RIGHT REPEAT SIGN", "So", 0),
("MUSICAL SYMBOL REPEAT DOTS", "So", 0),
("MUSICAL SYMBOL DAL SEGNO", "So", 0),
("MUSICAL SYMBOL DA CAPO", "So", 0),
("MUSICAL SYMBOL SEGNO", "So", 0),
("MUSICAL SYMBOL CODA", "So", 0),
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("MUSICAL SYMBOL BRACKET", "So", 0),
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("MUSICAL SYMBOL SIX-STRING FRETBOARD", "So", 0),
("MUSICAL SYMBOL FOUR-STRING FRETBOARD", "So", 0),
("MUSICAL SYMBOL G CLEF", "So", 0),
("MUSICAL SYMBOL G CLEF OTTAVA ALTA", "So", 0),
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("MUSICAL SYMBOL F CLEF OTTAVA ALTA", "So", 0),
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("MUSICAL SYMBOL DRUM CLEF-1", "So", 0),
("MUSICAL SYMBOL DRUM CLEF-2", "So", 0),
(),
(),
("MUSICAL SYMBOL MULTIPLE MEASURE REST", "So", 0),
("MUSICAL SYMBOL DOUBLE SHARP", "So", 0),
("MUSICAL SYMBOL DOUBLE FLAT", "So", 0),
("MUSICAL SYMBOL FLAT UP", "So", 0),
("MUSICAL SYMBOL FLAT DOWN", "So", 0),
("MUSICAL SYMBOL NATURAL UP", "So", 0),
("MUSICAL SYMBOL NATURAL DOWN", "So", 0),
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("MUSICAL SYMBOL SHARP DOWN", "So", 0),
("MUSICAL SYMBOL QUARTER TONE SHARP", "So", 0),
("MUSICAL SYMBOL QUARTER TONE FLAT", "So", 0),
("MUSICAL SYMBOL COMMON TIME", "So", 0),
("MUSICAL SYMBOL CUT TIME", "So", 0),
("MUSICAL SYMBOL OTTAVA ALTA", "So", 0),
("MUSICAL SYMBOL OTTAVA BASSA", "So", 0),
("MUSICAL SYMBOL QUINDICESIMA ALTA", "So", 0),
("MUSICAL SYMBOL QUINDICESIMA BASSA", "So", 0),
("MUSICAL SYMBOL MULTI REST", "So", 0),
("MUSICAL SYMBOL WHOLE REST", "So", 0),
("MUSICAL SYMBOL HALF REST", "So", 0),
("MUSICAL SYMBOL QUARTER REST", "So", 0),
("MUSICAL SYMBOL EIGHTH REST", "So", 0),
("MUSICAL SYMBOL SIXTEENTH REST", "So", 0),
("MUSICAL SYMBOL THIRTY-SECOND REST", "So", 0),
("MUSICAL SYMBOL SIXTY-FOURTH REST", "So", 0),
("MUSICAL SYMBOL ONE HUNDRED TWENTY-EIGHTH REST", "So", 0),
("MUSICAL SYMBOL X NOTEHEAD", "So", 0),
("MUSICAL SYMBOL PLUS NOTEHEAD", "So", 0),
("MUSICAL SYMBOL CIRCLE X NOTEHEAD", "So", 0),
("MUSICAL SYMBOL SQUARE NOTEHEAD WHITE", "So", 0),
("MUSICAL SYMBOL SQUARE NOTEHEAD BLACK", "So", 0),
("MUSICAL SYMBOL TRIANGLE NOTEHEAD UP WHITE", "So", 0),
("MUSICAL SYMBOL TRIANGLE NOTEHEAD UP BLACK", "So", 0),
("MUSICAL SYMBOL TRIANGLE NOTEHEAD LEFT WHITE", "So", 0),
("MUSICAL SYMBOL TRIANGLE NOTEHEAD LEFT BLACK", "So", 0),
("MUSICAL SYMBOL TRIANGLE NOTEHEAD RIGHT WHITE", "So", 0),
("MUSICAL SYMBOL TRIANGLE NOTEHEAD RIGHT BLACK", "So", 0),
("MUSICAL SYMBOL TRIANGLE NOTEHEAD DOWN WHITE", "So", 0),
("MUSICAL SYMBOL TRIANGLE NOTEHEAD DOWN BLACK", "So", 0),
("MUSICAL SYMBOL TRIANGLE NOTEHEAD UP RIGHT WHITE", "So", 0),
("MUSICAL SYMBOL TRIANGLE NOTEHEAD UP RIGHT BLACK", "So", 0),
("MUSICAL SYMBOL MOON NOTEHEAD WHITE", "So", 0),
("MUSICAL SYMBOL MOON NOTEHEAD BLACK", "So", 0),
("MUSICAL SYMBOL TRIANGLE-ROUND NOTEHEAD DOWN WHITE", "So", 0),
("MUSICAL SYMBOL TRIANGLE-ROUND NOTEHEAD DOWN BLACK", "So", 0),
("MUSICAL SYMBOL PARENTHESIS NOTEHEAD", "So", 0),
("MUSICAL SYMBOL VOID NOTEHEAD", "So", 0),
("MUSICAL SYMBOL NOTEHEAD BLACK", "So", 0),
("MUSICAL SYMBOL NULL NOTEHEAD", "So", 0),
("MUSICAL SYMBOL CLUSTER NOTEHEAD WHITE", "So", 0),
("MUSICAL SYMBOL CLUSTER NOTEHEAD BLACK", "So", 0),
("MUSICAL SYMBOL BREVE", "So", 0),
("MUSICAL SYMBOL WHOLE NOTE", "So", 0),
("MUSICAL SYMBOL HALF NOTE", "So", 0),
("MUSICAL SYMBOL QUARTER NOTE", "So", 0),
("MUSICAL SYMBOL EIGHTH NOTE", "So", 0),
("MUSICAL SYMBOL SIXTEENTH NOTE", "So", 0),
("MUSICAL SYMBOL THIRTY-SECOND NOTE", "So", 0),
("MUSICAL SYMBOL SIXTY-FOURTH NOTE", "So", 0),
("MUSICAL SYMBOL ONE HUNDRED TWENTY-EIGHTH NOTE", "So", 0),
("MUSICAL SYMBOL COMBINING STEM", "Mc", 216),
("MUSICAL SYMBOL COMBINING SPRECHGESANG STEM", "Mc", 216),
("MUSICAL SYMBOL COMBINING TREMOLO-1", "Mn", 1),
("MUSICAL SYMBOL COMBINING TREMOLO-2", "Mn", 1),
("MUSICAL SYMBOL COMBINING TREMOLO-3", "Mn", 1),
("MUSICAL SYMBOL FINGERED TREMOLO-1", "So", 0),
("MUSICAL SYMBOL FINGERED TREMOLO-2", "So", 0),
("MUSICAL SYMBOL FINGERED TREMOLO-3", "So", 0),
("MUSICAL SYMBOL COMBINING AUGMENTATION DOT", "Mc", 226),
("MUSICAL SYMBOL COMBINING FLAG-1", "Mc", 216),
("MUSICAL SYMBOL COMBINING FLAG-2", "Mc", 216),
("MUSICAL SYMBOL COMBINING FLAG-3", "Mc", 216),
("MUSICAL SYMBOL COMBINING FLAG-4", "Mc", 216),
("MUSICAL SYMBOL COMBINING FLAG-5", "Mc", 216),
("MUSICAL SYMBOL BEGIN BEAM", "Cf", 0),
("MUSICAL SYMBOL END BEAM", "Cf", 0),
("MUSICAL SYMBOL BEGIN TIE", "Cf", 0),
("MUSICAL SYMBOL END TIE", "Cf", 0),
("MUSICAL SYMBOL BEGIN SLUR", "Cf", 0),
("MUSICAL SYMBOL END SLUR", "Cf", 0),
("MUSICAL SYMBOL BEGIN PHRASE", "Cf", 0),
("MUSICAL SYMBOL END PHRASE", "Cf", 0),
("MUSICAL SYMBOL COMBINING ACCENT", "Mn", 220),
("MUSICAL SYMBOL COMBINING STACCATO", "Mn", 220),
("MUSICAL SYMBOL COMBINING TENUTO", "Mn", 220),
("MUSICAL SYMBOL COMBINING STACCATISSIMO", "Mn", 220),
("MUSICAL SYMBOL COMBINING MARCATO", "Mn", 220),
("MUSICAL SYMBOL COMBINING MARCATO-STACCATO", "Mn", 220),
("MUSICAL SYMBOL COMBINING ACCENT-STACCATO", "Mn", 220),
("MUSICAL SYMBOL COMBINING LOURE", "Mn", 220),
("MUSICAL SYMBOL ARPEGGIATO UP", "So", 0),
("MUSICAL SYMBOL ARPEGGIATO DOWN", "So", 0),
("MUSICAL SYMBOL COMBINING DOIT", "Mn", 230),
("MUSICAL SYMBOL COMBINING RIP", "Mn", 230),
("MUSICAL SYMBOL COMBINING FLIP", "Mn", 230),
("MUSICAL SYMBOL COMBINING SMEAR", "Mn", 230),
("MUSICAL SYMBOL COMBINING BEND", "Mn", 230),
("MUSICAL SYMBOL COMBINING DOUBLE TONGUE", "Mn", 220),
("MUSICAL SYMBOL COMBINING TRIPLE TONGUE", "Mn", 220),
("MUSICAL SYMBOL RINFORZANDO", "So", 0),
("MUSICAL SYMBOL SUBITO", "So", 0),
("MUSICAL SYMBOL Z", "So", 0),
("MUSICAL SYMBOL PIANO", "So", 0),
("MUSICAL SYMBOL MEZZO", "So", 0),
("MUSICAL SYMBOL FORTE", "So", 0),
("MUSICAL SYMBOL CRESCENDO", "So", 0),
("MUSICAL SYMBOL DECRESCENDO", "So", 0),
("MUSICAL SYMBOL GRACE NOTE SLASH", "So", 0),
("MUSICAL SYMBOL GRACE NOTE NO SLASH", "So", 0),
("MUSICAL SYMBOL TR", "So", 0),
("MUSICAL SYMBOL TURN", "So", 0),
("MUSICAL SYMBOL INVERTED TURN", "So", 0),
("MUSICAL SYMBOL TURN SLASH", "So", 0),
("MUSICAL SYMBOL TURN UP", "So", 0),
("MUSICAL SYMBOL ORNAMENT STROKE-1", "So", 0),
("MUSICAL SYMBOL ORNAMENT STROKE-2", "So", 0),
("MUSICAL SYMBOL ORNAMENT STROKE-3", "So", 0),
("MUSICAL SYMBOL ORNAMENT STROKE-4", "So", 0),
("MUSICAL SYMBOL ORNAMENT STROKE-5", "So", 0),
("MUSICAL SYMBOL ORNAMENT STROKE-6", "So", 0),
("MUSICAL SYMBOL ORNAMENT STROKE-7", "So", 0),
("MUSICAL SYMBOL ORNAMENT STROKE-8", "So", 0),
("MUSICAL SYMBOL ORNAMENT STROKE-9", "So", 0),
("MUSICAL SYMBOL ORNAMENT STROKE-10", "So", 0),
("MUSICAL SYMBOL ORNAMENT STROKE-11", "So", 0),
("MUSICAL SYMBOL HAUPTSTIMME", "So", 0),
("MUSICAL SYMBOL NEBENSTIMME", "So", 0),
("MUSICAL SYMBOL END OF STIMME", "So", 0),
("MUSICAL SYMBOL DEGREE SLASH", "So", 0),
("MUSICAL SYMBOL COMBINING DOWN BOW", "Mn", 230),
("MUSICAL SYMBOL COMBINING UP BOW", "Mn", 230),
("MUSICAL SYMBOL COMBINING HARMONIC", "Mn", 230),
("MUSICAL SYMBOL COMBINING SNAP PIZZICATO", "Mn", 230),
("MUSICAL SYMBOL PEDAL MARK", "So", 0),
("MUSICAL SYMBOL PEDAL UP MARK", "So", 0),
("MUSICAL SYMBOL HALF PEDAL MARK", "So", 0),
("MUSICAL SYMBOL GLISSANDO UP", "So", 0),
("MUSICAL SYMBOL GLISSANDO DOWN", "So", 0),
("MUSICAL SYMBOL WITH FINGERNAILS", "So", 0),
("MUSICAL SYMBOL DAMP", "So", 0),
("MUSICAL SYMBOL DAMP ALL", "So", 0),
("MUSICAL SYMBOL MAXIMA", "So", 0),
("MUSICAL SYMBOL LONGA", "So", 0),
("MUSICAL SYMBOL BREVIS", "So", 0),
("MUSICAL SYMBOL SEMIBREVIS WHITE", "So", 0),
("MUSICAL SYMBOL SEMIBREVIS BLACK", "So", 0),
("MUSICAL SYMBOL MINIMA", "So", 0),
("MUSICAL SYMBOL MINIMA BLACK", "So", 0),
("MUSICAL SYMBOL SEMIMINIMA WHITE", "So", 0),
("MUSICAL SYMBOL SEMIMINIMA BLACK", "So", 0),
("MUSICAL SYMBOL FUSA WHITE", "So", 0),
("MUSICAL SYMBOL FUSA BLACK", "So", 0),
("MUSICAL SYMBOL LONGA PERFECTA REST", "So", 0),
("MUSICAL SYMBOL LONGA IMPERFECTA REST", "So", 0),
("MUSICAL SYMBOL BREVIS REST", "So", 0),
("MUSICAL SYMBOL SEMIBREVIS REST", "So", 0),
("MUSICAL SYMBOL MINIMA REST", "So", 0),
("MUSICAL SYMBOL SEMIMINIMA REST", "So", 0),
("MUSICAL SYMBOL TEMPUS PERFECTUM CUM PROLATIONE PERFECTA", "So", 0),
("MUSICAL SYMBOL TEMPUS PERFECTUM CUM PROLATIONE IMPERFECTA", "So", 0),
("MUSICAL SYMBOL TEMPUS PERFECTUM CUM PROLATIONE PERFECTA DIMINUTION-1", "So", 0),
("MUSICAL SYMBOL TEMPUS IMPERFECTUM CUM PROLATIONE PERFECTA", "So", 0),
("MUSICAL SYMBOL TEMPUS IMPERFECTUM CUM PROLATIONE IMPERFECTA", "So", 0),
("MUSICAL SYMBOL TEMPUS IMPERFECTUM CUM PROLATIONE IMPERFECTA DIMINUTION-1", "So", 0),
("MUSICAL SYMBOL TEMPUS IMPERFECTUM CUM PROLATIONE IMPERFECTA DIMINUTION-2", "So", 0),
("MUSICAL SYMBOL TEMPUS IMPERFECTUM CUM PROLATIONE IMPERFECTA DIMINUTION-3", "So", 0),
("MUSICAL SYMBOL CROIX", "So", 0),
("MUSICAL SYMBOL GREGORIAN C CLEF", "So", 0),
("MUSICAL SYMBOL GREGORIAN F CLEF", "So", 0),
("MUSICAL SYMBOL SQUARE B", "So", 0),
("MUSICAL SYMBOL VIRGA", "So", 0),
("MUSICAL SYMBOL PODATUS", "So", 0),
("MUSICAL SYMBOL CLIVIS", "So", 0),
("MUSICAL SYMBOL SCANDICUS", "So", 0),
("MUSICAL SYMBOL CLIMACUS", "So", 0),
("MUSICAL SYMBOL TORCULUS", "So", 0),
("MUSICAL SYMBOL PORRECTUS", "So", 0),
("MUSICAL SYMBOL PORRECTUS FLEXUS", "So", 0),
("MUSICAL SYMBOL SCANDICUS FLEXUS", "So", 0),
("MUSICAL SYMBOL TORCULUS RESUPINUS", "So", 0),
("MUSICAL SYMBOL PES SUBPUNCTIS", "So", 0),
("MUSICAL SYMBOL KIEVAN C CLEF", "So", 0),
("MUSICAL SYMBOL KIEVAN END OF PIECE", "So", 0),
("MUSICAL SYMBOL KIEVAN FINAL NOTE", "So", 0),
("MUSICAL SYMBOL KIEVAN RECITATIVE MARK", "So", 0),
("MUSICAL SYMBOL KIEVAN WHOLE NOTE", "So", 0),
("MUSICAL SYMBOL KIEVAN HALF NOTE", "So", 0),
("MUSICAL SYMBOL KIEVAN QUARTER NOTE STEM DOWN", "So", 0),
("MUSICAL SYMBOL KIEVAN QUARTER NOTE STEM UP", "So", 0),
("MUSICAL SYMBOL KIEVAN EIGHTH NOTE STEM DOWN", "So", 0),
("MUSICAL SYMBOL KIEVAN EIGHTH NOTE STEM UP", "So", 0),
("MUSICAL SYMBOL KIEVAN FLAT SIGN", "So", 0),
("MUSICAL SYMBOL SORI", "So", 0),
("MUSICAL SYMBOL KORON", "So", 0),
)
|
https://github.com/remigerme/typst-polytechnique | https://raw.githubusercontent.com/remigerme/typst-polytechnique/main/assets/README.md | markdown | MIT License | # Assets
## Licensing
Use the assets accordingly with [École polytechnique corporate identity](https://www.polytechnique.edu/en/press-room).
## Generation
Typst currently only supports `svg` integration. I generated `svg` assets using inkscape to convert `eps` files to `svg`, and remplaced colors to use colors from École polytechnique corporate identity.
```bash
for f in *.eps; do inkscape --export-type=svg $f; done
sed -i 's/2e6886/00677f/' filet-court.svg
sed -i 's/a62125/ce0037/' filet-long.svg
sed -i 's/dae0e5/ccd8df/' armes.svg
sed -i 's/0d355c/01426a/' logo-x.svg
sed -i 's/1e3f6a/01426a/' logo-x-ip-paris.svg
```
Note : macOS users need to add an empty string `''` after `-i` flag : `sed -i '' 's/.../.../' file.svg'` or install `gnu-sed` and use it instead of macOS provided `sed`.
|
https://github.com/Myriad-Dreamin/typst.ts | https://raw.githubusercontent.com/Myriad-Dreamin/typst.ts/main/docs/cookery/guide/compiler/service.typ | typst | Apache License 2.0 | #import "/docs/cookery/book.typ": book-page
#import "/docs/cookery/term.typ" as term
#show: book-page.with(title: "Compiler in Rust")
#let compile-middleware = ```rs trait CompileMiddleware```
#let compiler-trait = ```rs trait Compiler```
#include "../claim.typ"
The compiler services help you build a precompiler CLI or an incremental compilation server Program for #term.vector-format.
== Creating and Using a `TypstSystemUniverse` Instance
Note: The ```rs struct TypstSystemUniverse``` can create multiple snapshots at the same time, ```rs struct TypstSystemWorld```, implementing ```rs trait typst::World```.
Example: #link("https://github.com/Myriad-Dreamin/typst.ts/blob/9a4f0537f7d8443b3920a27cabc51bb5ea64ee0a/cli/src/compile.rs#L30")[fn create_driver in compile.rs]
```rs
let verse = TypstSystemUniverse::new(CompileOpts {
root_dir: workspace_dir.clone(),
font_paths: args.font.paths.clone(),
with_embedded_fonts: EMBEDDED_FONT.to_owned(),
..CompileOpts::default()
})
.unwrap_or_exit();
// usage
let mut tracer = Tracer::default();
typst::compile(&verse.snapshot(), tracer);
```
== Creating and Using a `PureCompiler` Instance
#[
#set par(justify: false)
Note: The ```rs struct PureCompiler``` implements #compiler-trait. #linebreak()
]
Example:
```rs
std::marker::PhantomData.compile(
&verse.snapshot(), &mut Default::default());
```
== Creating and Using a `CompileExporter` Instance
#[
#set par(justify: false)
Note: The ```rs struct CompileExporter``` implements #compile-middleware. #linebreak()
Note: The ```rs struct CompileExporter``` derives #compiler-trait. #linebreak()
]
Retrieve an exporter instance that is executed on each sucessful compilation (more useful for incremental compilation).
```ts
let driver = CompileExporter::default()
.with_exporter(exporter)
```
See #link("https://github.com/Myriad-Dreamin/typst.ts/blob/main/cli/src/export.rs")[exporter.rs] for usage of the exporter feature.
Glance at current available exporters:
```rs
type WithAst = reflexo_typst::AstExporter;
type WithPdf = reflexo_typst::PdfDocExporter;
type WithSvg = reflexo_typst::PureSvgExporter;
type WithSvgHtml = reflexo_typst::SvgHtmlExporter<DefaultExportFeature>;
type WithSIR = reflexo_typst::SvgModuleExporter;
type WithText = reflexo_typst::TextExporter;
```
== Creating and Using a `DynamicLayoutCompiler` Instance
#[
#set par(justify: false)
Note: The ```rs struct DynamicLayoutCompiler``` implements #compile-middleware. #linebreak()
Note: The ```rs struct DynamicLayoutCompiler``` derives #compiler-trait. #linebreak()
]
Enable dynamic layout based on a #compiler-trait.
```rs
let driver = DynamicLayoutCompiler::new(driver, output_dir);
```
== Creating and Using a `CompileActor` Instance
Specifical for incremental compilation (Specifically, it watches files and compiles on demand) based on some universe instance.
Example: #link("https://github.com/Myriad-Dreamin/tinymist/blob/main/crates/tinymist/src/tool/preview.rs")[use of struct CompileActor in tool/preview.rs in tinymist]
```rs
let (intr_tx, intr_rx) = mpsc::unbounded_channel();
let actor = CompileActor::new(verse,
intr_tx, intr_rx).with_watch(Some(handle.clone()));
```
Example: #link("https://github.com/Myriad-Dreamin/tinymist/blob/main/crates/tinymist/src/actor/typ_client.rs")[use of `intr_tx` in actor/typ_client.rs in tinymist]
Access the service of the `CompileActor` instance.
```rs
/// Updates the overlay layer of VFS (Virtual File System)
let _ = self.intr_tx.send(Interrupt::Memory(event));
/// Reads the snapshot of the current compilation
let (tx, rx) = oneshot::channel();
self.intr_tx.send(Interrupt::SnapshotRead(tx))?;
let snapshot = rx.await
```
// todo: reporter option
// === Example: use a lambda (closure) exporter
// Example: #link("https://github.com/Myriad-Dreamin/tinymist/blob/main/crates/tinymist/src/tool/preview.rs")[fn create_driver in compile.rs]
// ```rs
// let driver = CompileExporter::new(compiler_driver).with_exporter(
// move |_world: &dyn World, doc: Arc<Document>| {
// let _ = doc_sender.send(Some(doc)); // it is ok to ignore the error here
// let _ = renderer_sender.send(RenderActorRequest::RenderIncremental);
// Ok(())
// },
// );
// ```
=== Adding Exporters to a `CompileActor` Instance
Example #link("https://github.com/Myriad-Dreamin/typst.ts/blob/main/cli/src/compile.rs")[fn compile_export in compile.rs in typst-ts-cli]
```rs
let mut exporters: Vec<DynExporter<CompileSnapshot<_>>> = vec![];
if args.dynamic_layout {
let driver = DynamicLayoutCompiler::new(
std::marker::PhantomData, output_dir);
exporters.push(Box::new(CompileStarter::new(driver)));
}
let actor = CompileActor::new_with(
verse, intr_tx, intr_rx,
CompileServerOpts {
exporter: GroupExporter::new(exporters),
..Default::default()
},
)
.with_enable_watch(args.watch);
```
|
https://github.com/yhtq/Notes | https://raw.githubusercontent.com/yhtq/Notes/main/抽象代数/作业/hw4.typ | typst | #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4",
author: "YHTQ ",
date: none,
logo: none,
withOutlined: false
)
#set heading(outlined: false)
（10月9日作业上次已交，这是12日作业）
= P25
23.
#answer[
设 $H$ 是 $G$ 中指数为二的子群，从而：
$
G = H union x H = H union H x\
$
对 $forall g = x h in x H = G- H$，有：
$
g H Inv(g) = x h H Inv((x h)) = x h H Inv(h) Inv(x) = x H Inv(h) Inv(x) = x H Inv(x)
$
而由前式知，$x H = H x => x H Inv(x) = H => g H Inv(g) = H$\
这表明 $G- H subset N_G (H)$，进而 $G = N_G (H)$，$H$ 是正规子群。
]
25.
#answer[
$D_20 = generatedBy(r\, s | r^20 = e\, r s = s r^19)$。设 $H$ 是非平凡正规子群，断言：
+ $normalSub(generatedBy(r), D_20)$，这由 $s r s = Inv(r)$ 给出
+ $H = generatedBy(r^k) <= generatedBy(r) => normalSub(H, G)$，类似的这是因为 $s r^k s = Inv((r^k))$
+ 若 $s in H$，则有：
- $r s Inv(r) = s Inv((r^2)) = r^(18) in H$
- $generatedBy(r^18) = generatedBy(r^2) subset H$
- $H supset generatedBy(r^2\, s)$
- $H = generatedBy(r^2\, s)$
这是因为注意到：
$
D_20 = generatedBy(r^2\, s) union r generatedBy(r^2\, s)
$
其中 $r^k, r^k$ 都含于等号右侧是显然的，而：
$
s r^k = Inv((r^k))s in generatedBy(r^2\, s) union r generatedBy(r^2\, s)
$
这给出 $H$ 的指数为 $2$，从而它是正规子群，并且不存在满足上述要求的更大的非平凡正规子群。
+ 若 $r^k s in H$：
事实上，由于 $[r -> r, s -> r^k s]$ 是群同构，因此此种情况和上一种情况本质是相同的，从而 $H = generatedBy(r^2\, r^k s)$
综上，$D_20$ 的非平凡正规子群分别为：
$
H "with" H <= generatedBy(r)\
generatedBy(r^2\, r^k s), forall k in ZZ
$
]
26.
#answer[
#set enum(numbering: "(1)")
+ \
- $a, b in C_G (S) =>forall x in S: x a = a x, x b = b x \ => forall x in S: (a Inv(b))x=a x Inv(b) = x a Inv(b) => a Inv(b) in C_G (S)$
- $a, b in N_G (s) => a S Inv(a) = b S Inv(s) = S => a Inv(b) S b Inv(a) = a S Inv(a) = S => a Inv(b) in N_G (S)$
+ 设 $n in N_G (S), c in C_G (S)$，则：
$
forall a in S\
Inv(n) a n in S => (Inv(n) a n) c = c (Inv(n) a n) => a (n c Inv(n)) = (n c Inv(n)) a
$
从而 $n c Inv(n) in C_G (S)$。\
这说明 $n C_G (S) Inv(n) subset C_G (S)$，类似有 $Inv(n) C_G (S) n subset C_G (S) => C_G (S) subset n C_G (S) Inv(n)$，从而 $n C_G (S) Inv(n) = C_G (S)$
]
27.
#answer[
#set enum(numbering: "(1)")
+
$
H K Inv(H) &= union_(h_1, h_2 in H) h_1 K h_2
\ &= union_(h_1, h_2 in H) h_1 K Inv(h_1) h_1 h_2
\ &= union_(h_1, h_2 in H) K h_1 h_2
\ &= K H
$
这表明：
$
H K = K H H = K H\
(H K)^2 = H K K H = H K H = K H = H K\
$
进而 $H K <= G$
+
$
forall g in G: g H K Inv(g) = g H Inv(g) g K Inv(g) = H K
$
这就给出了 $normalSub(H K, G)$
]
29.
#answer[
注意到：
$
(a N)^(ord(a)) = N => ord(a N) | ord(a) | |N|
$
但 $ord(a N) | |quotient(G, N)|$\
这就说明了 $ord(a N) = 1 => a in N$
]
32.
#answer[
设：
$
G = union_i x_i H = union_i H x_i
$
断言 $sect_i x_i H Inv(x_i)$ 是正规子群。事实上，设 $G$ 中任意元素为 $h x$，则：
$
h x (sect_i x_i H Inv(x_i)) Inv(x) Inv(h)
\ = sect_i h x x_i H Inv(x_i) Inv(x) Inv(h)
$
断言若 $x_i, x_j$ 在不同陪集中，则 $g x_i, g x_j$ 也在不同陪集中。因此记 $x'_i = h x x_i$，则它们也是新的一组代表元，因此：
$
sect_i h x x_i H Inv(x_i) Inv(x) Inv(h) = sect_i x'_i H Inv(x'_i) = sect_i x_i H Inv(x_i)
$
这就给出了 $normalSub(sect_i x_i H Inv(x_i), G)$。另一方面，由 31 题结论，它的指数有限。\
]
39.
#answer[
+ $A(B sect C) subset A B sect A C = A B sect C$ 是显然的
+ 任取 $a b = c in A B sect C$，从而 $b = Inv(a) c in C$，因此 $a b in A(B sect C)$
]
40.
#answer[
$
A = A (A sect C) = A(B sect C) = B sect A C = B sect B C = B
$
]
42.
#answer[
设 $normalSub({1, x}, G)$，断言对于任意 $g in G$，有：
$
g x Inv(g) = x
$
否则由 $g x Inv(g) in {1, x}$ 知 $g x Inv(g) = 1 => x = 1$，矛盾\
上式已经给出了 $x in C_G (G)$
]
45.
#answer[
二面体群显然可以由两个二阶元素 $s, r s$ 生成，因此只证充分性：\
设两个二阶元素分别为 $x, y$，再记 $r = x y, ord(r) = n$。
+ $r y = x$
+ $generatedBy(r\, y) = generatedBy(x\, y)$
+ $y r y = y (x y) y = y x = Inv((x y)) = Inv(r)$
上述事实表明了 $generatedBy(x\, y) tilde.eq D_(2n)$
]
= P57
15.
#answer[
设 $x in Z(S_n)$，则对任意 $i, j in Z_n, i!=j$，有：
$
x (i, j)(i) = x(j)\
= (i, j)x(i) = (i, j)(x(i))
$
由于 $x(i) != x(j)$，故 $x(i) = i$ 或 $j$。而由 $n > 2$，取异于 $i, j$ 的 $k$，则有 $x(i) = i$ 或 $k$。\
这表明 $x(i) = i$，进而由 $i$ 的任意性知 $x = 1$
]
16.
#answer[
设 $H$ 是 $G$ 的非平凡正规子群，通过取共轭容易知道若 $H$ 含有某个型的元素，则将含有该型的所由元素。\
断言 $H$ 含有一个 $3$ 阶元素。\
取 $x = (i_1 i_2 .. i_t)gamma in H$，其中 $(i_1 i_2 .. i_t)$ 是最长的轮换，则：
+ 若 $t >= 4$
-
$
(i_1 i_2 i_3) (i_1 i_2 .. i_t)gamma (i_1 i_3 i_2) = (i_2 i_3 i_1 ... i_t) gamma in H
$
-
$
(i_2 i_3 i_1 i_4 ... i_t) gamma Inv(((i_1 i_2 .. i_t)gamma)) = (i_2 i_3 i_1 i_4 ... i_t) Inv((i_1 i_2 .. i_t)) = (i_1 i_2 i_4) in H
$
+ 若 $t = 3$
-
$
(i_2 i_3)(i_1 i_2 i_3) gamma (i_2 i_3) = (i_1 i_3 i_2) gamma in H
$
-
$
(i_1 i_2 i_3) gamma Inv(((i_1 i_3 i_2) gamma)) = (i_1 i_2 i_3) Inv((i_1 i_3 i_2)) = (i_1 i_3 i_2)
$
- 若 $t = 2$
- 若只有一个二轮换，则易知 $H = S_n$
- 若至少有两个二轮换，设 $x = (i_1 i_2)(i_3 i_4)sigma$，（再取 $i_5$ 不同于之前的元素）则：
$
(i_2 i_3) x (i_3 i_2) = (i_1 i_3)(i_2 i_4)sigma in H\
(1_2 i_5) x (i_5 i_2) = (i_1 i_5)(i_3 i_4)sigma in H\
(i_1 i_3)(i_2 i_4)sigma Inv(((i_1 i_5)(i_3 i_4)sigma)) = (i_1 i_3)(i_2 i_4)(i_3 i_4)(i_1 i_5) = (i_1 i_5 i_3 i_2 i_4) in H
$
这就回到了之前的情况。
由此以及 $A_n$ 可由三轮换生成知，知 $A_n <= H$，但 $A_n$ 的指数已经为 $2$，从而 $H$ 要么是 $A_n$ 要么是 $S_n$。\
]
= 补充题
1.
#answer[
#set enum(numbering: "(1)")
+ 由子集的交还是子集，这是显然的。
+ 由陪集分解：
$
S_n = A_n union x A_n\
G = (G sect A_n) union (x G sect A_n)
$
显然后者也是陪集分解，分别表示 $G$ 中偶置换与奇置换，由陪集性质知它们数量相等。
]
2.
#answer[
#set enum(numbering: "(1)")
+ 注意到满足：
$
Inv(x) (123...n) x = (123...n)
$
的 $x$ 由 $x(1)$ 唯一决定。事实上，任取 $y in ZZ_n$，则：
$
x(i) = y + (i - 1)
$
是唯一一个在 $C_G ((123...n))$ 之中且满足 $x(1) = y$ 的置换。\
从而 $|C_G ((123...n))| = n$
+ 容易得到 $C_G (sigma) = 1^(l_1) 2^(l_2) ... n^(l_n) l_1 ! l_2 ! .. l_n !$，进而考虑共轭作用，与其共轭的元素即其所在轨道的阶数，恰为 $(|G|) / (C_G (sigma)) = n! / (1^(l_1) 2^(l_2) ... n^(l_n) l_1 ! l_2 ! .. l_n !)$
]
3.
#answer[
断言：$Stab_G (m) = Stab_H (m) sect H$\
对于任意 $m_1, m_2 in M$，存在 $g in G$ 使得：
$
Stab_G (m_1) = g Stab_H (m_2) Inv(g)
$
从而：
$
Stab_H (m_1) = Stab_G (m_1) sect H \ = g Stab_H (m_2) Inv(g) sect H = g Stab_H (m_2) Inv(g) sect g H Inv(g) \ = g (Stab_H (m_2) sect H) Inv(g) = g Stab_H (m_2) Inv(g)
$
这就表明在 $H$ 作用下 $M$ 所有元素对应的稳定化子的阶相等，从而所有轨道的长度相等。
]
4.
#answer[
注意到若 $x$ 是不动点，则 $|"orb"(x)| = 1$。反之若不然，则 $|"orb"(x)| = |G : Stab_G(x)|$ 将是 $p$ 的倍数。\
在轨道分解：
$
|G| = sum_("orbit" O) |O|
$
的右侧中，除 $1$ 外的项都是 $p$ 的倍数，而项 $1$ 恰有 $M_0$ 个。\
从而模 $p$ 立得原结论。
] |
|
https://github.com/EpicEricEE/typst-marge | https://raw.githubusercontent.com/EpicEricEE/typst-marge/main/tests/overlap/simple/test.typ | typst | MIT License | #import "/src/lib.typ": sidenote
#set par(justify: true)
#set page(width: 8cm, height: auto, margin: (outside: 4cm, rest: 5mm))
#let sidenote = sidenote.with(numbering: "1")
#lorem(5)
#sidenote[This is the first sidenote.]
#lorem(1)
#sidenote[This one is moved down to prevent overlap.]
#lorem(18)
|
https://github.com/TGM-HIT/typst-diploma-thesis | https://raw.githubusercontent.com/TGM-HIT/typst-diploma-thesis/main/template/chapters/kurzfassung.typ | typst | MIT License | #import "../lib.typ": *
#abstract(lang: "de")[
#lorem(150)
]
#abstract(lang: "en")[
#lorem(150)
]
|
https://github.com/An-314/Note-of-Quantum_Mechanics | https://raw.githubusercontent.com/An-314/Note-of-Quantum_Mechanics/main/chap2.typ | typst | #import "@preview/physica:0.9.2": *
#import "@local/mytemplate:1.0.0": *
= 波函数和薛定谔方程
== 波函数及其统计解释
=== 波函数和波粒二象性
==== 波函数
#figure(
table(
columns: (auto, auto, auto),
inset: 10pt,
align: horizon,
[],[*保留经典概念的哪些特征*],[*不具有经典概念的哪些特征*],
[粒子性],[有确定的质量、电荷、自旋等],[没有确定的轨道],
[波动性],[有干涉、衍射等现象],[振幅不直接可测]
),
caption: [
波粒二象性
],
)
对于微观粒子或量子力学体系，可以用与时间和空间相关的复函数来描写：
$
psi = psi(arrow(r), t)
$
被称为波函数。
Schrodinger方程所描述的波函数，并不是象经典波那样的代表实在的物理量的波动，而是刻画粒子在空间的几率分布的几率波
$
|psi(arrow(r), t)|^2
$
波函数在某点的强度（绝对值的平方）与在该点找到粒子的*几率密度*成正比。波函数本身称为*几率振幅*。
例如电子的双缝干涉：
$
P_(12) &= |psi_1 + psi_2|^2 = |psi_1|^2 + |psi_2|^2 + (psi_1^*psi_2 + psi_2^*psi_1)\
&= P_1 + P_2 + 2sqrt(P_1P_2)cos(phi)
$
电子呈现的波动性反应了微观客体运动的一种统计特性，因此波函数也被称为概率波幅。
==== 波函数的归一
可以看到$psi(arrow(r))$和$c psi(arrow(r))$描述的相对几率分布是完全相同的。
对于空间中两点$arrow(r_1)$和$arrow(r_2)$，粒子出现在这两点的几率之比为：
$
(|psi(arrow(r_1))|^2)/(|psi(arrow(r_2))|^2) = (|c psi(arrow(r_1))|^2)/(|c psi(arrow(r_2))|^2)
$
对于$psi(arrow(r))$是某个波函数，按照几率解释，在点$(arrow(r),t)$附近的体积元 $d tau$ 中发现粒子的几率是：
$
dd(W(arrow(r),t)) = |psi(arrow(r),t)|^2 dd(tau)
$
粒子的空间几率密度是：
$
w(arrow(r),t) = dd(W(arrow(r),t)) / dd(tau) = |psi(arrow(r),t)|^2
$
因此在全空间发现粒子的几率是：
$
W(t) = integral w(arrow(r),t) dd(tau) = integral |psi(arrow(r),t)|^2 dd(tau)
$
根据波函数的统计诠释，很自然地要求粒子不产生，不湮灭，取归一化:
$
W(t) = 1
$
即：
$
integral |psi(arrow(r),t)|^2 dd(tau) = 1
$
这就是波函数的归一条件。
_注：_
- _即使要求波函数是归一的，它仍然有一个整体的相位因子$e^(i theta)$（$theta$为实常数）不能确定。_
- _如果积分_
$
integral |psi(arrow(r),t)|^2 dd(tau)
$
_是无穷大，相当于粒子的运动范围没有限制，粒子可以达到无穷远处。【正交归一化为delta函数】这样的波函数就是不能（有限地）归一的例如平面波（自由粒子的de Broglie波），此时_
$
|psi(arrow(r),t)|^2
$
_代表“相对几率密度”。_
==== 波的相干性
两个独立无关的粒子的波函数，由于各自存在相位不定性，所以两个粒子之间没有干涉（相干性coherence）。
例如，两束自然光之间是没有相干性的。为了具有相干性，可以采用同一个光源的波前分割，或者振幅分割的方法。或者利用量子力学原理，使得不同光源之间具有强相干性，例如激光。
两个不相干粒子的整体波函数不是写成相加的数学形式，而是相乘，即所谓的*直积态*。
$
Psi(x_1, x_2) = psi(x_1)Phi(x_2)
$
则
$
(P(x_1 = 1, x_2))/(P(x_1 = 2, x_2)) = (|psi(1)|^2)/(|psi(2)|^2) (|Phi(x_2)|^2)/(|Phi(x_2)|^2) = (|psi(1)|^2)/(|psi(2)|^2)
$
即两个粒子的几率分布是独立的。
N个粒子的系统，对于一个由N个粒子构成的系统，系统的波函数是N个粒子的坐标和时间的复函数：
$
Psi(arrow(r_1), arrow(r_2), ..., arrow(r_N), t)
$
==== 态叠加原理
如果$Psi_(1(2))$是体系的可能状态，那么
$
Psi = c_1 Psi_1 + c_2 Psi_2
$
也是体系的可能状态，其中$c_1$和$c_2$是复数。
$
|Psi|^2 = |c_1 Psi_1 + c_2 Psi_2|^2 = |c_1|^2 |Psi_1|^2 + |c_2|^2 |Psi_2|^2 + (c_1^*c_2 Psi_1 Psi_2 + c_2^*c_1 Psi_2 Psi_1)
$
其中$c_1^*c_2 Psi_1 Psi_2 + c_2^*c_1 Psi_2 Psi_1$是干涉项。
一般地说，叠加原理可以写成：
$
Psi = sum_n c_n Psi_n
$
对于一个指定的量子体系，如果我们找到了它的“完备的基本状态”，例如：
$
{Psi_n(n = 1, 2, 3, ...)}
$
那么任何一个体系的波函数都可以用这些基本状态的线性组合来表示，处于状态$n$的几率是$|c_n|^2$。
由于量子态满足叠加原理，一个量子系统的全部状态构成了线性空间，称为这个量子系统的Hilbert空间。
这里补充一些重要的公式：
- Fourier变换：
$
f(x) = 1/sqrt(2pi) integral_(-oo)^oo F(k) e^(i k x) dd(k)
$
- 逆变换：
$
F(k) = 1/sqrt(2pi) integral_(-oo)^oo f(x) e^(-i k x) dd(x)
$
- $delta$函数的Fourier变换：
$
delta(x) = 1/(2pi) integral_(-oo)^oo e^(i k x) dd(k)
$
_例：*动量几率分布*_
_一个自由粒子以动量 $arrow(p)$ 和能量_
$
E = p^2/(2mu)
$
_运动的状态是平面波：_
$
psi_arrow(p)(arrow(r), t) = e^(i/hbar (arrow(p)dot arrow(r) - E t))
$
_根据叠加原理，任何的波函数(不一定是自由粒子)都可以写成：_
$
psi(arrow(r), t) = sum_arrow(p) c_arrow(p) psi_arrow(p)(arrow(r), t)
$
_即是各种不同动量的平面波的叠加。这个例子在数学上就是函数的Fourier变换 – 任何函数（在分段光滑、绝对可积等条件下）都可以展开为正、余弦函数的线形叠加。_
_定义：_
$
psi_arrow(p) (arrow(r)) = sqrt(1/(2 pi hbar)^3) e^(i/hbar (arrow(p)dot arrow(r)))
$
_那么任何波函数（不一定是自由粒子的）都可以写成 :_
$
psi(arrow(r), t) = integral c(arrow(p), t) sqrt(1/(2 pi hbar)^3) psi_arrow(p) (arrow(r)) dd(""^3arrow(p))
$
_其中的展开系数由下式得出（Fourier变换）：_
$
c(arrow(p), t) = integral psi(arrow(r), t) sqrt(1/(2 pi hbar)^3) psi_arrow(p)^* (arrow(r)) dd(""^3arrow(r))
$
_$c(arrow(p), t)$的物理意义是“动量测量几率振幅”。_
_Fourier变换相当于作频谱分析，代表在$psi(arrow(r), t)$中出现动量为$arrow(p)$能量为$E$的平面单色波的概率为$|c(arrow(p), t)|^2$。_
_$|c(arrow(p), t)|^2$代表粒子在$t$时刻具有动量$arrow(p)$的概率密度，或者说$psi(arrow(p), t)$中包含平面波$e^(i/hbar arrow(p) dot arrow(r))$的成分有多少。_
_可以证明归一化：_
$
integral |c(arrow(p), t)|^2 dd(""^3arrow(p)) = integral |psi(arrow(r), t)|^2 dd(""^3arrow(r))
$
_对于一维情况，Fourier变换为：_
$
psi(x , t) = 1/sqrt(2 pi hbar) integral c(p, t) e^(i/hbar p x) dd(p)\
c(p, t) = 1/sqrt(2 pi hbar) integral psi(x, t) e^(-i/hbar p x) dd(x)
$
事实上$ψ(r,t)$是波函数在*坐标表象*的表示形式，$c(p,t)$是波函数在*动量表象*的表示形式。它们在描述粒子状态方面是等价的，只是具体描述方式不同。
== 薛定谔方程
薛定谔方程应满足:
1. 线性齐次 —— 波函数线性叠加原理。
2. 方程系数不应包含如动量,能量等系统参量 —— 方程的解应描述所有可能的粒子状态。
量子力学的基本定律是波函数所满足的偏微分方程。这个基本定律在本质上是一个假说。
=== 从De Broglie波到薛定谔方程
de Broglie波 $psi(arrow(r), t) = e^(i/hbar (arrow(p)dot arrow(r) - E t))$ 有等式：
$
diff/(diff t) psi = -i/hbar E psi
$
$
nabla psi = i arrow(p)/hbar psi
$
$
nabla^2 psi = -p^2/hbar^2 psi
$
这可以看作是在经典能量-动量关系：
$
E = p^2/(2m)
$
中进行代换：
$
cases(
E -> i hbar diff/(diff t),
p -> -i hbar nabla
)
$
并且把它们作用于波函数得到的。
推广到粒子在外势场 $U(arrow(r))$ 中运动，其能量的表达式为：
$
E = p^2/(2m) + U(arrow(r))
$
得到单粒子运动的*薛定谔(Schrodinger)方程*：
$
i hbar diff/(diff t) psi = -hbar^2/(2m) nabla^2 psi + U(arrow(r)) psi
$
_例：相对论粒子所满足的Klein-Gorden方程_
静止质量为$m_0$的粒子自由运动时，能量-动量关系为：
$
E^2 = p^2c^2 + m_0^2c^4
$
因此，相对论波动方程为：
$
(c^2 hat(p)^2 + m_0^2c^4) psi = hat(E)^2 psi
$
可以描述相对论性玻色子的运动。但该方程可能解出负能量的解，有不可逾越的困难。
=== 几率守恒定律
在*非相对论*情况下，实物粒子没有产生和湮灭的现象，所以随时间演化的过程中，*粒子数目守恒*，即*几率守恒*。
粒子的空间几率密度是
$
w(arrow(r),t) = |psi(arrow(r),t)|^2 = psi^*psi
$
可以计算时间的变化率：
$
diff/(diff t) w = diff/(diff t) (psi^*psi) = (diff/(diff t) psi^*) psi + psi^* (diff/(diff t) psi)
$
利用Schrodinger方程：
$
diff/(diff t) psi &= (i hbar)/(2m) nabla^2 psi - i/hbar U psi\
diff/(diff t) psi^* &= (-i hbar)/(2m) nabla^2 psi^* + i/hbar U psi^*
$
认为势能是实函数，从而：
$
diff/(diff t) w = (i hbar)/(2m) (nabla^2 psi^* psi - psi^* nabla^2 psi)
$
设*几率流密度*为：
$
arrow(J) = (i hbar)/(2m) (psi^* nabla psi - psi nabla psi^*)
$
则：
$
diff/(diff t) w + nabla dot arrow(J) = 0
$
即*几率守恒定律*。
$arrow(J)$是“几率流密度”，而上式表现了几率守恒。将体积$V$扩展到全空间，在非相对论情况下，实物粒子没有产生和湮灭的现象，所以在随时间演化的过程中，粒子数目将保持不变。对于一个粒子而言，在全空间找到它的概率应不随时间改变，即：
$
dd("")/dd(t) integral_oo | psi(arrow(r),t) |^2 dd(tau) = - integral.cont_oo arrow(J) dot arrow(n) dd(S) = 0
$
*几率守恒也就是粒子数守恒。*
一个粒子既不可能凭空产生，也不可能凭空消失。当粒子在空间某处的概率减少时，必然在空间某个地方的概率增加了。
=== 波函数应满足的条件
从波函数的几率解释以及波函数满足二阶微分方程这一要求，一般地说，波函数应该满足以下三个条件：
+ *单值性*（波函数是处处单值的）
+ *有限性*（波函数是处处有限的）
+ *连续性*（波函数及其一阶导数是处处连续的）：由于有波函数对时间和空间的微商，波函数应在时空坐标$(arrow(r),t)$上连续，并且对空间的一阶微商$(nabla Y)$也连续，否则方程中空间二阶导数项发散
但是连续性允许有例外：在势能有无穷大跳跃的地方，波函数的一阶导数可以是不连续的
== 定态薛定谔方程
若势能$U$不显含时间，则薛定谔方程为：
$
i hbar diff/(diff t) psi = (-hbar^2/(2m) nabla^2 + U(arrow(r))) psi(arrow(r),t)
$
记Hamilton算符为：
$
hat(H) = -hbar^2/(2m) nabla^2 + U(arrow(r))
$
时间算符$i hbar diff/(diff t)$与Hamilton算符$hat(H)$都是*能量算符*。
分离变量法：
$
Psi(arrow(r),t) = psi(arrow(r)) f(t)
$
代入薛定谔方程得：
$
i hbar psi(arrow(r)) (dd(f(t)))/(dd(t)) &= f(t) hat(H) psi(arrow(r))\
(i hbar)/(f(t)) (dd(f(t)))/(dd(t)) &= (hat(H) psi(arrow(r)))/(psi(arrow(r))) = E
$
得到*本征方程*：
$
hat(H) psi(arrow(r)) = E psi(arrow(r))
$
和$f(t)$满足的方程：
$
(dd(f(t)))/(dd(t)) &= -i E f(t)/hbar\
f(t) &= C e^(-i/hbar E t)
$
为时间震动因子，$C$为常数。
因此，定态薛定谔方程的解为：
$
psi(arrow(r)) = sum C_n psi_n (arrow(r)) e^(-i/hbar E_n t)
$
#newpara()
*本征方程*就是*定态薛定谔方程*：
$
E psi(arrow(r)) = (-hbar^2/(2m) nabla^2 + U(arrow(r))) psi_n (arrow(r))
$
多粒子系统的Hamilton算符为：
$
hat(H) = sum_(i = 1)^N (-hbar^2/(2m_i) nabla_i^2 + U_i(arrow(r_i))) + V(arrow(r)_1, arrow(r)_2, ..., arrow(r)_N)
$
其中$V(arrow(r)_1, arrow(r)_2, ..., arrow(r)_N)$是粒子间相互作用势能。 |
|
https://github.com/Vortezz/fiches-mp2i-physique | https://raw.githubusercontent.com/Vortezz/fiches-mp2i-physique/main/tp/euler.typ | typst | #import "@preview/cetz:0.0.1"
#set page(header: box(width: 100%, grid(
columns: (100%),
rows: (20pt, 8pt),
align(right, text("FICHE TP - MÉTHODE D'EULER")),
line(length: 100%),
)), footer: box(width: 100%, grid(
columns: (50%, 50%),
rows: (8pt, 20pt),
line(length: 100%),
line(length: 100%),
align(left, text("<NAME> - MP2I")),
align(right, text("<NAME> - 2023/2024")),
)))
#set heading(numbering: "I.1.a")
#let titleBox(title) = align(center, block(below: 20pt, box(height: auto, fill: rgb("#eeeeee"), width: auto, inset: 40pt, text(title, size: 20pt, weight: "bold"))))
#let proof(content) = text("Preuve", weight: "semibold", fill: rgb("#666666")) + h(1em) + text(content, size: 10pt, fill: rgb("#888888"))
#titleBox("Méthode d'Euler")
= Présentation
La méthode d'Euler est une méthode de résolution numérique d'équations différentielles. Elle est basée sur le principe de la tangente à la courbe représentative de la solution de l'équation différentielle.
= Principe algorithmique
On considère une équation différentielle de la forme $y' = f(x, y)$, avec $f$ une fonction continue. On cherche à déterminer une fonction $y$ telle que $y' = f(x, y)$.
On divise l'intervalle $[t_"min", t_"max"]$ en $n$ sous-intervalles de longueur $Delta t$ (appelé pas de résolution). Et on a donc $t_k$ = $t_"min" + k * Delta t$.
On cherche à déterminer $y_k$ tel que $y_k$ = $y(t_k)$. Puisque l'on connaît $y_0$ (on connaît $y(t_"min")$), on peut déterminer tous les $y_k$ en utilisant la relation de récurrence suivante :
$ y_(k+1) = y_k + f(t_k, y_k) * Delta t $
= Exemple d'application
On considère la fonction `euler` suivante :
```python
def euler(F, y_0, tmin, tmax, dt):
list_t = np.arange(tmin, tmax + dt, dt)
N = len(list_t)
y = np.zeros(N)
y[0] = y_0
for k in range(N - 1):
y[k + 1] = y[k] + F(y[k], tmin + k * dt) * dt
return list_t, y
```
On considère l'équation différentielle $y' = y$ avec $y(0) = 1$.
On a donc $f(x, y) = y$ et $y_0 = 1$.
On peut donc définir la fonction `F` suivante :
```python
def F(y, x):
return y
```
On peut alors tracer la solution de l'équation différentielle sur l'intervalle $[0, 10]$ avec un pas de résolution de $0.1$ (valeurs prises pour l'exemple) :
```python
import matplotlib.pyplot as plt
t, y = euler(F, 1, 0, 10, 0.1)
plt.clf()
plt.figure()
plt.plot(t, y, ".") # On ne relie pas les points en physique
plt.xlabel("X (unité)")
plt.ylabel("Y (unité)")
plt.legend()
plt.show()
```
Il sera donc possible de visualiser l'allure de la solution de l'équation différentielle.
= Bonnes pratiques
Il faut toujours vérifier que le pas de résolution est suffisamment petit pour que la solution obtenue soit proche de la solution réelle.
Si le pas de résolution est trop grand, la solution obtenue sera très éloignée de la solution réelle.
Mais si le pas de résolution est trop petit, le temps de calcul sera très long.
Il faut donc trouver un compromis entre la précision de la solution et le temps de calcul. |
|
https://github.com/typst-jp/typst-jp.github.io | https://raw.githubusercontent.com/typst-jp/typst-jp.github.io/main/tests/README.md | markdown | Apache License 2.0 | # Tests
## Directory structure
Top level directory structure:
- `src`: Testing code.
- `suite`: Input files. Mostly organized in parallel to the code. Each file can
contain multiple tests, each of which is a section of Typst code
following `--- {name} ---`.
- `ref`: Reference images which the output is compared with to determine whether
a test passed or failed.
- `store`: Store for PNG, PDF, and SVG output files produced by the tests.
## Running the tests
Running all tests (including unit tests):
```bash
cargo test --workspace
```
Running just the integration tests (the tests in this directory):
```bash
cargo test --workspace --test tests
```
You may want to [make yourself an alias](#making-an-alias) `testit` so that you can
write shorter commands. In the examples below, we will use this alias.
Running all tests with the given name pattern. You can use
[regular expression](https://docs.rs/regex/latest/regex/)s.
```bash
testit math # The name has "math" anywhere
testit math page # The name has "math" or "page" anywhere
testit "^math" "^page" # The name begins with "math" or "page"
testit "^(math|page)" # Same as above.
```
Running all tests discovered under given paths:
```bash
testit -p tests/suite/math/attach.typ
testit -p tests/suite/model -p tests/suite/text
```
Running tests that begin with `issue` under a given path:
```bash
testit "^issue" -p tests/suite/model
```
Running a test with the exact test name `math-attach-mixed`.
```bash
testit --exact math-attach-mixed
```
You may find more options in the help message:
```bash
testit --help
```
To make the integration tests go faster they don't generate PDFs by default.
Pass the `--pdf` flag to generate those. Mind that PDFs are not tested
automatically at the moment, so you should always check the output manually when
making changes.
```bash
testit --pdf
```
## Writing tests
The syntax for an individual test is `--- {name} ---` followed by some Typst
code that should be tested. The name must be globally unique in the test suite,
so that tests can be easily migrated across files.
There are, broadly speaking, three kinds of tests:
- Tests that just ensure that the code runs successfully: Those typically make
use of `test` or `assert.eq` (both are very similar, `test` is just shorter)
to ensure certain properties hold when executing the Typst code.
- Tests that ensure the code emits particular diagnostic messages: Those have
inline annotations like `// Error: 2-7 thing was wrong`. An annotation can
start with either "Error", "Warning", or "Hint". The range designates the
code span the diagnostic message refers to in the first non-comment line
below. If the code span is in a line further below, you can write ranges
like `3:2-3:7` to indicate the 2-7 column in the 3rd non-comment line.
- Tests that ensure certain visual output is produced: Those render the result
of the test with the `typst-render` crate and compare against a reference
image stored in the repository. The test runner automatically detects whether
a test has visual output and requires a reference image in this case.
To prevent bloat, it is important that the test images are kept as small as
possible. To that effect, the test runner enforces a maximum size of 20 KiB.
If you're updating a test and hit `reference image size exceeds`, see the
section on "Updating reference images" below. If truly necessary, the size
limit can be lifted by adding `// LARGE` as the first line of a test, but this
should be the case very rarely.
If you have the choice between writing a test using assertions or using
reference images, prefer assertions. This makes the test easier to understand
in isolation and prevents bloat due to images.
## Updating reference images
If you created a new test or fixed a bug in an existing test, you need to update
the reference image used for comparison. For this, you can use the `--update`
flag:
```bash
testit --exact my-test-name --update
```
This will generally generate compressed reference images (to remain within the
above size limit).
If you use the VS Code test helper extension (see the `tools` folder), you can
alternatively use the save button to update the reference image.
## Making an alias
If you want to have a quicker way to run the tests, consider adding a shortcut
to your shell profile so that you can simply write something like:
```bash
testit --exact my-test-name
```
### Bash
Open your Bash configuration by executing `nano ~/.bashrc`.
```bash
alias testit="cargo test --workspace --test tests --"
```
### PowerShell
Open your PowerShell profile by executing `notepad $profile`.
```ps
function testit {
cargo test --workspace --test tests -- $args
}
```
|
https://github.com/JvandeLocht/assignment-template-typst-hfh | https://raw.githubusercontent.com/JvandeLocht/assignment-template-typst-hfh/main/registration_certificate.typ | typst | MIT License | #import "/layout/registration_certificate.typ": *
#import "/metadata.typ": *
#set text(lang: "de")
#show: registrationCertificate.with(
author: author,
title: titleGerman,
birthdate: birthdate,
degree: degree,
program: program,
supervisor: supervisor,
startDate: startDate,
submissionDate: submissionDate,
currentDate: datetime.today(),
)
// You can write additional text for the registration certificate here. |
https://github.com/drupol/master-thesis | https://raw.githubusercontent.com/drupol/master-thesis/main/resources/typst/essawy-table.typ | typst | Other | #import "../../src/thesis/imports/preamble.typ": *
#import table: cell, header
#{
table(
columns: 7,
align: (right,) + (center,) * 2,
stroke: none,
table.header(
cell(rowspan: 2)[],
table.vline(stroke: .5pt),
cell(colspan: 3)[*Original*],
table.vline(stroke: .5pt),
cell(colspan: 3)[*Other*],
[*researcher*],
[*machine*],
[*data*],
[*researcher*],
[*machine*],
[*data*],
table.hline(stroke: .5pt),
),
[*Repeatability*],
[\u{2713}],
[\u{2713}],
[\u{2713}],
[],
[],
[],
table.hline(stroke: .5pt + black.lighten(75%)),
[*Runnability*],
[\u{2713}],
[],
[\u{2713}],
[],
[\u{2713}],
[],
table.hline(stroke: .5pt + black.lighten(75%)),
[*Reproducibility*],
[],
[],
[\u{2713}],
[\u{2713}],
[\u{2713}],
[],
table.hline(stroke: .5pt + black.lighten(75%)),
[*Replicability*],
[],
[],
[],
[\u{2713}],
[\u{2713}],
[\u{2713}],
)
}
|
https://github.com/Myriad-Dreamin/typst.ts | https://raw.githubusercontent.com/Myriad-Dreamin/typst.ts/main/fuzzers/corpora/layout/grid-1_01.typ | typst | Apache License 2.0 |
#import "/contrib/templates/std-tests/preset.typ": *
#show: test-page
#set rect(inset: 0pt)
#grid(
columns: (auto, auto, 40%),
column-gutter: 1fr,
row-gutter: 1fr,
rect(fill: eastern)[dddaa aaa aaa],
rect(fill: conifer)[ccc],
rect(fill: rgb("dddddd"))[aaa],
)
|
https://github.com/Laikaiyong/Resume | https://raw.githubusercontent.com/Laikaiyong/Resume/main/vandyck-typst.typ | typst | #let primary_colour = rgb("#C52530") // red
#let link_colour = rgb("#12348e") // blue
#let styled-link(dest, content) = emph(text(
fill: link_colour,
link(dest, content)
))
#let unstyled-link(dest, content) = emph(text(
link(dest, content)
))
#let view-more-block(text, link) = unstyled-link(
link
)[
#block(
fill: rgb("#D47D83"),
inset: 8pt,
radius: 4pt
)[#text]
]
#let button-badge(item) = {
box(
fill: rgb("#D47D83"),
inset: (x: 3pt, y: 0.5pt),
outset: (y: 3pt),
radius: 2pt
)[#text(
fill: white,
item
)]
}
#let project-heading(title) = {
text(
fill: primary_colour,
title
)
}
#let badge-text(badge, item) = {
grid(
columns: (60pt, 1fr),
rows: auto,
gutter: 3pt,
button-badge(
badge
),
item
)
}
#let icon(name, shift: 1.5pt) = {
box(
baseline: shift,
height: 10pt,
image("icons/" + name + ".svg")
)
h(3pt)
}
#let findMe(services) = {
set text(8pt)
let icon = icon.with(shift: 2.5pt)
services.map(service => {
icon(service.name)
if "display" in service.keys() {
styled-link(service.link)[#{service.display}]
} else {
link(service.link)
}
}).join(h(10pt))
[
]
}
#let term(period, location) = {
text(9pt)[#icon("calendar") #period #h(1fr) #icon("location") #location]
}
#let max_rating = 5
#let skill(name, rating) = {
let done = false
let i = 1
name
h(1fr)
while (not done){
let colour = rgb("#c0c0c0") // grey
if (i <= rating){
colour = primary_colour
}
box(circle(
radius: 4pt,
fill: colour
))
if (max_rating == i){
done = true
} else {
// no spacing on last
h(2pt)
}
i += 1
}
[\ ]
}
#let resume(
name: "",
content,
) = {
set document(
title: name + "'s CV",
author: name,
)
set text(9.8pt, font: "IBM Plex Sans")
set page(
margin: (x: 20pt, y: 20pt),
)
show heading.where(
level: 2
): it => text(
fill: primary_colour,
[
#{it.body}
#v(-7pt)
#line(length: 100%, stroke: 1pt + primary_colour)
]
)
show heading.where(
level: 3
): it => text(it.body)
show heading.where(
level: 4
): it => text(
fill: primary_colour,
it.body
)
columns(
2,
gutter: 15pt,
content,
)
} |
|
https://github.com/TJ-CSCCG/tongji-undergrad-thesis-typst | https://raw.githubusercontent.com/TJ-CSCCG/tongji-undergrad-thesis-typst/main/CONTRIBUTING.md | markdown | MIT License | # CONTRIBUTING
## Contents
- source files: as a template repository, "source files" are ".typ", ".bib" and some related files with other extension names.
- doc files: including all ".typ" files and even "main.typ", which show how to use "source files".
- config files: These files make our development and use of templates more standardlized (e.g. .gitignore).
## How to contribute
### How to ask for help?
Providing conditions where people ask for help and solve problems is also part of community. We hope to provide technique support in [Discussions](https://github.com/TJ-CSCCG/tongji-undergrad-thesis-typst/discussions).
It has to be **NOTICED** that: **DO NOT CONTACT WITH ANY CONTRIBUTOR THROUGH IM**!
### How to report a bug?
If a bug is confirmed, you can raise it in the [Issues](https://github.com/TJ-CSCCG/tongji-undergrad-thesis-typst/issues).
### How to pull request?
We recommend to follow this workflow step by step:
1. Fork this repository as upstream repository.
2. Clone the repository forked from remote to local.
3. Create a new local branch as a work branch.
4. Commit some changes on the work branch.
5. Push the new local branch to remote with commits.
6. Pull request, from the new remote branch to any branch of upstream repository.
### Before your pull request
Remember to check whether you have added, renamed or removed file in `init-files/`. If so, please update the `.github/patches/package_release.diff` and commit it along with your pull request.
如果你新增、移动或删除了`init-files/`目录下的文件，请检查是否需要更新`.github/patches/package_release.diff`，并将其随PR一同提出。
> [!TIP]
> You can use `git diff HEAD~1 HEAD > package_release.diff` to generate a patch that can be accepted.
> [!IMPORTANT]
> We use `git apply` to apply the patch and generate a package-release branch. Please check if your patch can be applied successfully. If not, we may not be able to merge your branch.
>
> 请务必确保patch可以被`git apply`命令应用。如果patch未更新或无法被正确应用，我们可能将无法合并您的分支。
|
https://github.com/LDemetrios/Typst4k | https://raw.githubusercontent.com/LDemetrios/Typst4k/master/src/test/resources/suite/scripting/field.typ | typst | // Test field access.
--- field-function ---
// Test fields on function scopes.
#enum.item
#assert.eq
#assert.ne
--- field-normal-function-invalid ---
// Error: 9-16 function `assert` does not contain field `invalid`
#assert.invalid
--- field-elem-function-invalid ---
// Error: 7-14 function `enum` does not contain field `invalid`
#enum.invalid
--- field-elem-function-invalid-call ---
// Error: 7-14 function `enum` does not contain field `invalid`
#enum.invalid()
--- field-closure-invalid ---
// Closures cannot have fields.
#let f(x) = x
// Error: 4-11 cannot access fields on user-defined functions
#f.invalid
--- field-bool-invalid ---
// Error: 8-10 cannot access fields on type boolean
#false.ok
--- field-bool-keyword-invalid ---
// Error: 9-13 cannot access fields on type boolean
#{false.true}
--- field-invalid-none ---
#{
let object = none
// Error: 3-9 none does not have accessible fields
object.property = "value"
}
--- field-invalid-int ---
#{
let object = 10
// Error: 3-9 integer does not have accessible fields
object.property = "value"
}
--- field-mutable-invalid-symbol ---
#{
let object = sym.eq.not
// Error: 3-9 cannot mutate fields on symbol
object.property = "value"
}
--- field-mutable-invalid-module ---
#{
let object = calc
// Error: 3-9 cannot mutate fields on module
object.property = "value"
}
--- field-mutable-invalid-function ---
#{
let object = calc.sin
// Error: 3-9 cannot mutate fields on function
object.property = "value"
}
--- field-mutable-invalid-stroke ---
#{
let s = 1pt + red
// Error: 3-4 fields on stroke are not yet mutable
// Hint: 3-4 try creating a new stroke with the updated field value instead
s.thickness = 5pt
}
|
|
https://github.com/eliapasquali/typst-thesis-template | https://raw.githubusercontent.com/eliapasquali/typst-thesis-template/main/chapters/product-testing.typ | typst | Other | #pagebreak(to:"odd")
= Verifica e validazione
<cap:verifica-validazione>
#v(1em)
#text(style: "italic", [
Breve introduzione al capitolo
])
#v(1em)
|
https://github.com/QQKdeGit/bupt-typst | https://raw.githubusercontent.com/QQKdeGit/bupt-typst/master/template.typ | typst | MIT License | #let chineseNumMap(num) = {
let chineseNum = (
"一", "二", "三", "四", "五", "六", "七", "八", "九", "十",
"十一", "十二", "十三", "十四", "十五", "十六", "十七", "十八", "十九", "二十",
"二十一", "二十二", "二十三", "二十四", "二十五", "二十六", "二十七", "二十八", "二十九", "三十",
"三十一", "三十二", "三十三", "三十四", "三十五", "三十六", "三十七", "三十八", "三十九", "四十",
)
chineseNum.at(num - 1)
}
#let romanNumMap(num) = {
let romanNum = (
"I", "II", "III", "IV", "V", "VI", "VII", "VIII", "IX", "X",
"XI", "XII", "XIII", "XIV", "XV", "XVI", "XVII", "XVIII", "XIX", "XX",
"XXI", "XXII", "XXIII", "XXIV", "XXV", "XXVI", "XXVII", "XXVIII", "XXIX", "XXX",
"XXXI", "XXXII", "XXXIII", "XXXIV", "XXXV", "XXXVI", "XXXVII", "XXXVIII", "XXXIX", "XL",
)
romanNum.at(num - 1)
}
#let FONTSIZE = (
SanHao: 16pt,
XiaoSan: 15pt,
SiHao: 14pt,
XiaoSi: 12pt,
WuHao: 10.5pt,
XiaoWu: 9pt,
)
#let FONTSET = (
Hei: ("Inter", "Noto Sans CJK SC"),
Song: "Noto Serif CJK SC",
Kai: "FZKai-Z03",
English: "STIX Two Text",
)
#let tableCounter = counter("Table")
#let figureCounter = counter("Figure")
#let equationCounter = counter("Equation")
#let BUPTBachelorThesis(
titleZH: "",
abstractZH: "",
keywordsZH: (),
titleEN: "",
abstractEN: "",
keywordsEN: (),
body
) = {
// 页面配置
set page(paper: "a4", margin: 2.5cm)
set text(font: (FONTSET.at("English"), FONTSET.at("Song")), weight: "regular", size: FONTSIZE.XiaoSi)
// 数学公式
show math.equation: it => if it.block {
locate(loc => {
set par(leading: 1.5em)
let chapterLevel = counter(heading).at(loc).at(0)
grid(
columns: (100pt, 1fr, 100pt),
[],
align(center, it),
align(horizon + right)[
#text(
font: (FONTSET.at("English"), FONTSET.at("Song")),
[式（#chapterLevel\-#equationCounter.display()）]
)
]
)
equationCounter.step()
})
} else {
it
}
// 代码
show raw.where(block: true): it => {
set block(stroke: 0.5pt, width: 100%, inset: 1em)
it
}
// 中文摘要
align(center)[
#set text(font: FONTSET.at("Hei"), weight: "bold")
#text(size: FONTSIZE.SanHao, titleZH) \ \
#text(size: FONTSIZE.XiaoSan, tracking: 1em, "摘要") \ \
]
set par(first-line-indent: 2em, leading: 1.2em) // 段内行间距为1.2倍
show par: set block(spacing: 1.2em) // 段间距同样为1.2倍
abstractZH
[\ \ ]
text(font: FONTSET.at("Hei"), weight: "bold", size: FONTSIZE.XiaoSi, h(2em) + "关键词")
text(size: FONTSIZE.XiaoSi,
for value in keywordsZH {
h(1em) + value
}
)
pagebreak()
// 英文摘要
align(center)[
#text(weight: "bold", size: FONTSIZE.SanHao, titleEN) \ \
#text(weight: "bold", size: FONTSIZE.XiaoSan, "ABSTRACT") \ \
]
abstractEN
[\ \ ]
text(weight: "bold", size: FONTSIZE.XiaoSi, h(2em) + "KEY WORDS")
text(size: FONTSIZE.XiaoSi,
for value in keywordsEN {
h(1em) + value
}
)
pagebreak()
// 目录
set page(
footer: locate(loc => {
[
#align(center)[
#text(font: FONTSET.at("English"), size: FONTSIZE.XiaoWu)[
#romanNumMap(counter(page).at(loc).at(0))
]
]
]
})
)
counter(page).update(1)
show outline: it => locate(loc => {
set par(first-line-indent: 0em)
align(center)[
#text(font: FONTSET.at("Hei"), weight: "bold", tracking: 2em, size: FONTSIZE.SanHao, [目录\ \ ])
]
let chapterCounter = 1
let sectionCounter = 1
let subsectionCounter = 1
let headingList = query(selector(heading).after(loc), loc)
for i in headingList {
if i.outlined == false {
break
}
if i.level == 1 {
set text(font: (FONTSET.at("Hei")), size: FONTSIZE.XiaoSi, weight: "bold")
if i.body != [参考文献] and i.body != [致#h(2em)谢] and i.body != [附#h(2em)录] {
[第#chineseNumMap(chapterCounter)章#h(1em)]
}
if i.body == [致#h(2em)谢] {
[致#h(2em)谢 #box(width: 1fr, repeat[.]) #counter(page).at(i.location()).at(0)\ ]
} else if i.body == [附#h(2em)录] {
[附#h(2em)录 #box(width: 1fr, repeat[.]) #counter(page).at(i.location()).at(0)\ ]
} else {
[#i.body #box(width: 1fr, repeat[.]) #counter(page).at(i.location()).at(0)\ ]
}
chapterCounter = chapterCounter + 1
sectionCounter = 1
} else if i.level == 2 {
[#h(1em)#calc.abs(chapterCounter - 1)\.#sectionCounter#h(1em)#i.body #box(width: 1fr, repeat[.]) #counter(page).at(i.location()).at(0)\ ]
sectionCounter += 1
subsectionCounter = 1
} else if i.level == 3 {
[#h(2em)#calc.abs(chapterCounter - 1)\.#calc.abs(sectionCounter - 1)\.#subsectionCounter#h(1em)#i.body #box(width: 1fr, repeat[.]) #counter(page).at(i.location()).at(0)\ ]
subsectionCounter += 1
}
}
})
outline(title: none, depth: 3, indent: true)
// 章节标题配置
set heading(numbering: "1.1")
show heading: it => {
locate(loc => {
let levels = counter(heading).at(loc)
// 重置段首空格
set par(first-line-indent: 0em)
set text(font: FONTSET.at("Hei"), weight: "bold")
if it.level == 1 {
// 重置计数器
tableCounter.update(1)
figureCounter.update(1)
equationCounter.update(1)
align(center)[
#grid(
rows: (1em),
row-gutter: 0.2em,
columns: (1fr),
[],
text(size: FONTSIZE.SanHao, [第#chineseNumMap(levels.at(0))章#h(1em)#it.body]),
[]
)
]
} else if it.level == 2 {
grid(
rows: (0.5em, 1em, 0.5em),
columns: (1fr),
[],
[#numbering("1.1", ..levels)
#text(size: FONTSIZE.SiHao, h(1em) + it.body)],
[]
)
} else {
grid(
rows: (0.5em, 1em, 0.5em),
columns: (1fr),
[],
[#h(2em) #numbering("1.1", ..levels)
#text(size: FONTSIZE.XiaoSi, h(1em) + it.body)],
[]
)
}
})
text()[#v(-0.6em, weak: true)];text()[#h(0em)]
}
// 引用
show cite: it => {
text(font: FONTSET.at("English"), it)
}
// 页眉页脚
set page(
header: [
#align(center)[
#pad(bottom: -8pt)[
#pad(bottom: -8pt,
text(font: FONTSET.at("Song"), size: FONTSIZE.XiaoWu, "北京邮电大学本科毕业设计（论文）")
)
#line(length: 100%, stroke: 0.5pt)
]
]
],
footer: [
#align(center)[
#text(font: FONTSET.at("English"), size: FONTSIZE.XiaoWu)[
#counter(page).display()
]
]
]
)
counter(page).update(1)
// 正文
body
}
#let primary_heading(
title
) = {
grid(
columns: (1fr),
row-gutter: 0.2em,
rows: (1em, 1em, 1em),
[], [#title], []
)
}
// 附录部分
#let Appendix(
bibliographyFile: none,
body
) = {
show heading: it => locate(loc => {
set par(first-line-indent: 0em)
let levels = counter(heading).at(loc)
if it.level == 1 {
align(center)[
#text(font: FONTSET.at("Hei"), size: FONTSIZE.SanHao, it.body)
]
} else if it.level == 2 {
text(size: FONTSIZE.SiHao, it.body)
}
})
// 参考文献
if bibliographyFile != none {
pagebreak()
primary_heading([= 参考文献])
set text(
font: (FONTSET.at("English"),
FONTSET.at("Song")),
size: FONTSIZE.WuHao,
lang: "zh"
)
set par(first-line-indent: 0em)
bibliography(
bibliographyFile,
title: none,
style: "gb-7714-2015-numeric"
)
show bibliography: it => {
}
}
body
}
// 图
#let Figure(
file,
caption,
width,
) = {
show figure: it => locate(loc => {
let chapterLevel = counter(heading).at(loc).at(0)
align(center)[
#it.body
#text(
font: (FONTSET.at("English"), FONTSET.at("Kai")),
size: FONTSIZE.WuHao,
[图 #chapterLevel\-#figureCounter.display() #caption]
)
]
figureCounter.step()
})
figure(
image(file, width: width)
)
}
// 表
#let Table(caption, columnsSet, alignSet, body) = {
show table: it => locate(loc => {
let chapterLevel = counter(heading).at(loc).at(0)
align(center)[
#text(
font: (FONTSET.at("English"), FONTSET.at("Kai")),
size: FONTSIZE.WuHao,
[表 #chapterLevel\-#tableCounter.display() #caption]
)
#it
]
tableCounter.step()
})
table(
columns: columnsSet,
align: alignSet,
inset: 8pt,
stroke: 0.5pt,
..body
)
} |
https://github.com/Myriad-Dreamin/typst.ts | https://raw.githubusercontent.com/Myriad-Dreamin/typst.ts/main/fuzzers/corpora/bugs/flow-3_00.typ | typst | Apache License 2.0 |
#import "/contrib/templates/std-tests/preset.typ": *
#show: test-page
#set page(height: 60pt)
#rect(inset: 0pt, columns(2)[
Text
#v(12pt)
Hi
#v(10pt, weak: true)
At column break.
])
|
https://github.com/Isaac-Fate/booxtyp | https://raw.githubusercontent.com/Isaac-Fate/booxtyp/master/example/example.typ | typst | Apache License 2.0 | #import "../src/lib.typ": *
#show: book
#cover([BooxType Template], image("coffee.jpg"), authors: ("<NAME>",))
#preface(
)[
This is A Typst template for books.
You can create a preface using `preface` template:
```typ
#preface()[
Your preface goes here...
]
```
The preface chapter will not be numbered or outlined in the table of contnets.
You may change the title of the preface:
```typ
#preface(title: [My Preface])[
Your preface goes here...
]
```
I generated a long paragraph of lorem ipsum text below so that you can see the
page number at the top of the page. Note that the page number is Roman numeral
before the first chapter.
#lorem(1500)
]
#outline()
= Introduction
== Mathematical Context
The following sentance shows how to reference a theorem and make an index entry:
```typ
@thm:1 is known as #index[Fermat's Last Theorem].
```
@thm:1 is known as #index[Fermat's Last Theorem].
State a theorem and give it a label so that you can reference it:
```typ
#theorem(title: "Fermat's Last Theorem")[
No three positive integers $a$, $b$, and $c$ can satisfy the equation
$ a^n + b^n = c^n $
for any integer value of $n$ greater than $2$.
]<thm:1>
```
The `title` argument is optional. The round brackets will not be shown if the
title is not given.
#theorem(title: "Fermat's Last Theorem")[
No three positive integers $a$, $b$, and $c$ can satisfy the equation
$ a^n + b^n = c^n $
for any integer value of $n$ greater than $2$.
]<thm:1>
Prove a theorem:
```typ
#proof[
I have discovered a truly marvelous proof of this, which this margin is too
narrow to contain.
]
```
#proof[
I have discovered a truly marvelous proof of this, which this margin is too
narrow to contain.
]
The templates `theorem`, `proposition`, `lemma`, `corollary`, `definition`,
`example`, `note`, `exercise` and `solution` can be used in the same way.
#theorem(
title: "Rank-Nullity Theorem",
)[
Let $T: V -> W$ be a linear map between two finite-dimensional vector spaces.
Then
$ dim V = dim ker T + dim im T $
]
#definition[
The number $e$ is defined as
$ e := sum_(n = 0)^oo 1 / n! $
]
#note[
Though some texts define $e$ as $lim_(n -> oo) (1 + 1 / n)^n$, the above
definition is more convenient for our purpose.
]
#definition(title: [Definiton of the Exponential Function])[
The exponential function, denoted by $exp(x)$, is defined as
$ exp(x) := sum_(n = 0)^oo x^n / n! $<eq:1>
]<def:1>
Putting $x = 1$ in @eq:1, we obtain $exp(1) = e$.
#exercise[
Show that $exp(x + y) = exp(x) exp(y), space forall x, y in RR$.
]
#solution[
I am too lazy to write the solution 🤪. But I know I need to apply the Cauchy
product.
]
#lorem(500)
== Figures
Reference a figure:
```typ
@fig:1 depicts the topologist's sine curve.
```
@fig:1 depicts the topologist's sine curve.
Insert a figure:
```typ
#figure(
image("topologist-sine-curve.svg", width: 60%),
caption: "Topologist's sine Curve.",
)<fig:1>
```
#figure(
image("topologist-sine-curve.svg", width: 60%),
caption: "Topologist's sine Curve.",
)<fig:1>
= Point-Set Topology
The knowledge from topology is too important to be neglected. The following
content is mainly based on the book _Topology_ by <NAME>
@munkresTopology2000.
== 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.
]
// References
#bibliography("references.bib", title: "References")
// Index page
#index-page()
|
https://github.com/typst/packages | https://raw.githubusercontent.com/typst/packages/main/packages/preview/cetz/0.3.0/src/mark-shapes.typ | typst | Apache License 2.0 | #import "drawable.typ"
#import "path-util.typ"
#import "vector.typ"
// Calculate triangular tip offset, depending on the strokes
// join type.
//
// The angle is calculated for an isosceles triangle of base style.widh
// and height style.length
#let _calculate-tip-offset(style) = {
if style.stroke.join == "round" {
return style.stroke.thickness / 2
}
if style.length == 0 {
return 0
}
let angle = calc.atan(style.width / (2 * style.length) / if style.harpoon { 2 } else { 1 } ) * 2
// If the miter length divided by the stroke width exceeds
// the stroke miter limit then the miter join is converted to a bevel.
// See: https://svgwg.org/svg2-draft/painting.html#LineJoin
if style.stroke.join == "miter" {
let angle = calc.abs(angle)
if angle > 0deg {
let miter-limit = 1 / calc.sin(angle / 2)
if miter-limit <= style.stroke.miter-limit {
return miter-limit * (style.stroke.thickness / 2)
}
}
}
// style.stroke.join must be "bevel"
return calc.sin(angle/2) * (style.stroke.thickness / 2)
}
#let create-tip-and-base-anchor(style, tip, base, center: none) = {
if base == tip { base = vector.add(tip, (1e-8, 0, 0)) }
let dir = vector.norm(vector.sub(tip, base))
import "/src/draw.typ": *
anchor("tip", vector.add(tip, vector.scale(dir, style.stroke.thickness / 2)))
anchor("base", vector.sub(base, vector.scale(dir, style.stroke.thickness / 2)))
}
#let create-triangle-tip-and-base-anchor(style, tip, base, center: none) = {
if base == tip { base = vector.add(tip, (1e-8, 0, 0)) }
let dir = vector.norm(vector.sub(tip, base))
import "/src/draw.typ": *
if style.reverse {
anchor("tip", tip)
} else {
anchor("tip", vector.add(tip, vector.scale(dir, _calculate-tip-offset(style))))
}
anchor("base", vector.sub(base, vector.scale(dir, style.stroke.thickness / 2)))
}
#let create-diamond-tip-and-base-anchor(style, tip, base, center: none, ratio: 50%) = {
if base == tip { base = vector.add(tip, (1e-8, 0, 0)) }
let dir = vector.norm(vector.sub(tip, base))
import "/src/draw.typ": *
let tip-style = style
tip-style.length = style.length * (ratio / 100%)
if style.reverse {
anchor("tip", tip)
} else {
anchor("tip", vector.add(tip, vector.scale(dir, _calculate-tip-offset(tip-style))))
}
if style.reverse {
anchor("base", vector.sub(base, vector.scale(dir, _calculate-tip-offset(tip-style))))
} else {
anchor("base", base)
}
}
// Dictionary of built-in mark styles
//
// (style) => (<elements..>)
#let marks = (
triangle: (style) => {
import "/src/draw.typ": *
if style.harpoon {
line((0,0), (style.length, 0), (style.length, +style.width / 2), close: true)
} else {
line((0,0), (style.length, -style.width / 2), (style.length, +style.width / 2), close: true)
}
create-triangle-tip-and-base-anchor(style, (0, 0), (style.length, 0))
},
// A mark in the shape of an arrow tip.
stealth: (style) => {
import "/src/draw.typ": *
let (l, w, i) = (style.length, style.width, style.inset)
if style.harpoon {
line((0,0), (l, w / 2), (l - i, 0), close: true)
} else {
line((0,0), (l, w / 2), (l - i, 0), (l, -w / 2), close: true)
}
create-triangle-tip-and-base-anchor(style, (0, 0), (l - i, 0))
},
bar: (style) => {
import "/src/draw.typ": *
let w = style.width
if style.harpoon {
line((0, w / 2), (0, 0))
} else {
line((0, w / 2), (0, -w / 2))
}
create-tip-and-base-anchor(style, (0, 0), (0, 0))
},
ellipse: (style) => {
import "/src/draw.typ": *
let r = (style.length / 2, style.width / 2)
if style.harpoon {
arc((0, 0), delta: -180deg, start: 0deg, radius: r, anchor: "origin", mode: "PIE")
} else {
circle((0, 0), radius: r)
}
create-tip-and-base-anchor(style, (r.at(0), 0), (-r.at(0), 0))
},
circle: (style) => {
import "/src/draw.typ": *
let r = calc.min(style.length, style.width) / 2
if style.harpoon {
arc((0, 0), delta: -180deg, start: 0deg, radius: r, anchor: "origin", mode: "PIE")
} else {
circle((0, 0), radius: r)
}
create-tip-and-base-anchor(style, (r, 0), (-r, 0))
},
bracket: (style) => {
import "/src/draw.typ": *
let (l, w, i) = (style.length, style.width, style.inset)
if style.harpoon {
line((-l - i, w / 2), (0, w / 2), (0, 0), fill: none)
} else {
line((-l - i, w / 2), (0, w / 2), (0, -w / 2), (-l - i, -w / 2), fill: none)
}
create-tip-and-base-anchor(style, (0, 0), (-1e-8, 0), center: ((-l - i) / 2, 0))
},
diamond: (style) => {
import "/src/draw.typ": *
let (l, w) = (style.length, style.width)
if style.harpoon {
line((0,0), (l / 2, w / 2), (l, 0), close: true)
} else {
line((0,0), (l / 2, w / 2), (l, 0), (l / 2, -w / 2), close: true)
}
create-diamond-tip-and-base-anchor(style, (0, 0), (l, 0))
},
rect: (style) => {
import "/src/draw.typ": *
let (l, w) = (style.length, style.width)
if style.harpoon {
rect((0, -w / 2), (-l, +w / 2))
} else {
rect((0, -w / 2), (-l, +w / 2))
}
create-tip-and-base-anchor(style, (0, 0), (-l, 0))
},
hook: (style) => {
import "/src/draw.typ": *
let r = calc.min(style.length, style.width / 2) / 2
let (l, i) = (style.length, style.inset)
merge-path({
line((i, -2 * r), (0, -2 * r))
arc((0, 0), delta: -180deg, start: -90deg, radius: r, anchor: "end")
if not style.harpoon {
arc((0, 0), delta: -180deg, start: -90deg, radius: r, anchor: "start")
line((i, +2 * r), (0, +2 * r))
}
}, fill: none)
line((0, 0), (l - r, 0))
create-tip-and-base-anchor(style, (-r, 0), (l - r, 0), center: ((-r + i) / 2, 0))
},
// An unfilled mark in the shape of an angle bracket (>).
straight: (style) => {
import "/src/draw.typ": *
let (l, w) = (style.length, style.width)
if style.harpoon {
line((l, w / 2), (0, 0), fill: none)
} else {
line((l, w / 2), (0, 0), (l, -w / 2), fill: none)
}
create-triangle-tip-and-base-anchor(style, (0, 0), (0, 0))
},
barbed: (style) => {
import "/src/draw.typ": *
let style = style
style.stroke.join = "round"
let (l, w) = (style.length, style.width)
let ctrl-a = (l, 0)
let ctrl-b = (0, 0)
merge-path({
bezier((l, w / 2), (0, 0), ctrl-a, ctrl-b)
if not style.harpoon {
bezier((0, 0), (l, -w / 2), ctrl-b, ctrl-a)
}
}, ..style)
create-tip-and-base-anchor(style, (0, 0), (1e-6, 0))
},
plus: (style) => {
import "/src/draw.typ": *
let style = style
style.stroke.join = "round"
let (l, w) = (style.length, style.width)
line((-l / 2, 0), (+l / 2, 0))
line((0, -w / 2), (0, +w / 2))
create-tip-and-base-anchor(style, (0, 0), (l / 2, 0))
},
x: (style) => {
import "/src/draw.typ": *
let style = style
style.stroke.join = "round"
let (l, w) = (style.length, style.width)
line((-l / 2, w / 2), (+l / 2, -w / 2))
line((-l / 2, -w / 2), (+l / 2, +w / 2))
create-tip-and-base-anchor(style, (0, 0), (0, 0))
},
star: (style) => {
import "/src/draw.typ": *
let (l, w) = (style.length, style.width)
let n = 5
for i in range(0, n) {
let a = 360deg / n * i
line((0, 0), (calc.cos(a) * l / 2, calc.sin(a) * w / 2))
}
create-tip-and-base-anchor(style, (0, 0), (l / 2, 0))
},
)
#let names = marks.keys()
// Mark mnemonics
// Each mnemonic maps to a dictionary of:
// - reverse (bool)
// - flip (bool)
// - harpoon (bool)
// TODO: Resolve mark styles at a later point, to support all style keys here
#let mnemonics = (
">": ("triangle", (:)),
"<": ("triangle", (reverse: true)),
"<>": ("diamond", (:)),
"[]": ("rect", (:)),
"]": ("bracket", (:)),
"[": ("bracket", (reverse: true)),
"|": ("bar", (:)),
"o": ("circle", (:)),
"+": ("plus", (:)),
"x": ("x", (:)),
"*": ("star", (:)),
)
// Get a mark shape + reverse tuple for a mark name
#let get-mark(ctx, symbol) = {
symbol = ctx.marks.mnemonics.at(symbol, default: symbol)
if symbol in ctx.marks.marks {
return (ctx.marks.marks.at(symbol), (:))
}
let (symbol, defaults) = mnemonics.at(symbol, default: (symbol, (:)))
assert(symbol in marks, message: "Unknown mark '" + symbol + "'")
return (marks.at(symbol), defaults)
}
|
https://github.com/typst-community/mantodea | https://raw.githubusercontent.com/typst-community/mantodea/main/src/component.typ | typst | MIT License | #import "component/title-page.typ": make-title-page
#import "component/table-of-contents.typ": make-table-of-contents
|
https://github.com/rabotaem-incorporated/calculus-notes-2course | https://raw.githubusercontent.com/rabotaem-incorporated/calculus-notes-2course/master/sections/04-parametric-and-curves/05-line-integrals.typ | typst | #import "../../utils/core.typ": *
== Криволинейные интегралы
#remind(label: "def-path")[
Путь --- отображение $gamma: [a, b] -> RR^n$ непрерывное.
Пути эквивалентны ($gamma tilde tilde(gamma)$, где $gamma: [a, b] --> RR^n$ и $tilde(gamma): [c, d] --> RR^n$) когда существует непрерывная строго возрастающая биекция $tau: [a, b] -> [c, d]$ такая, что $gamma = tilde(gamma) compose tau$.
Кривая --- класс эквивалентности путей.
Параметрицация кривой --- конкретный представитель класса.
]
#def(label: "def-curve-integral-1")[
_Криволинейный интеграл первого рода функции $f$ по гладкой кривой $s$#rf("def-path")_ (или _интеграл по длине дуги_):
$
integral_gamma f dif s := integral_a^b f(gamma(t)) norm(gamma'(t)) dif t,
$
где $gamma$ --- какая-то параметризация#rf("def-path") $s$.
Напомню, что норма производной равна $sqrt((gamma'_1 (t))^2 + ... + (gamma'_n (t))^2)$.
]
#props(label: "curve-integral-1-props")[
1. #sublabel("param-indep")
Не зависит от параметризации.
2. #sublabel("dir-indep")
Не зависит от направления.
3. #sublabel("length")
$integral_gamma dif s = l(gamma)$ --- формула длины гладкой кривой.
4. #sublabel("linear")
Линейность $integral_gamma (alpha f + beta g) dif s = alpha integral_gamma f dif s + beta integral_gamma f dif s$
5. #sublabel("curve-additive")
Аддитивность по кривой: $gamma: [a, b] --> RR^n$ и $gamma_1 := gamma bar_[a, c]$, $gamma_2 := gamma bar_[c, b]$. Тогда $integral_gamma f dif s = integral_(gamma_1) f dif s + integral_(gamma_2) f dif s$.
6. #sublabel("inequality")
Неравенство сохраняется: если $f <= g$ на $gamma[a, b]$ (носитель кривой), то $integral_gamma f dif s <= integral_gamma g dif s$.
7. #sublabel("abs-bound")
$abs(integral_gamma) <= integral_gamma abs(f) dif s$.
]
#proof[
1. Пусть $gamma = tilde(gamma) compose tau$.
$
integral_tilde(gamma) t dif s =^rf("def-curve-integral-1")
integral_c^d f(tilde(gamma)(t)) norm(tilde(gamma)'(t)) dif t =^(t = tau(u))
integral_a^b f(tilde(gamma)(tau(u))) norm(tilde(gamma)'(tau(u))) dot underbrace(tau'(u), >0) dif u
newline(=)
integral_a^b f underbrace(
(tilde(gamma)(tau(u))),
tilde(gamma) compose tau = gamma
)
underbrace(norm(tau'(u) dot tilde(gamma)'(tau(u))), norm(gamma')) dif u =
integral_a^b f(gamma(u)) norm(gamma') dif u =^rf("def-curve-integral-1")
integral_gamma f dif s.
$
2. То же самое.
3. Ну да, это и правда формула длины гладкой кривой#rf("curve-length").
4.
$
integral_gamma (alpha f + beta g) dif s =^rf("def-curve-integral-1")
integral_a^b (alpha f(gamma(t)) + beta g(gamma(t))) norm(gamma'(t)) dif t =^(rf("sfn-props", "linear") rf("def-curve-integral-1"))
alpha integral_gamma f dif s + beta integral_gamma f dif s.
$
5. Аналогично, надо расписать по определению#rf("def-curve-integral-1").
6. Опять аналогично. Так как нормы неотрицательные, неравентсва сохраняются.
7. $-abs(f) <= f <= abs(f)$ и 6#rf("curve-integral-1-props", "inequality").
]
#exercise[
Интегральная сумма: если есть отрезок $[a, b]$ нарезанный каким-то дроблением в точках $a = t_0, t_1, t_2, ..., t_m = b$ и имеется оснащение $xi_1 in [t_0, t_1], xi_2 in [t_1, t_2], ..., xi_m in [t_(m - 1), t_m]$, то
$
integral_gamma f dif s = lim sum_(k = 1)^m f(gamma(xi_k)) dot l(gamma bar_[t_(k - 1), t_k]),
$
где $gamma$ --- гладкая кривая (конечной длины), а предел при мелкости дробления стремящейся к нулю.
]
#def(label: "def-differential-form")[
_Дифференциальной формой первого порядка_ называется формальная конструкция
$
omega := f_1 dif x_1 + f_2 dif x_2 + ... + f_n dif x_n,
$
где $f_1, ..., f_n$ --- функции от $n$ переменных.
Далее мы будем интересоваться только дифференциальными формами первого порядка, поэтому порядок упоминать мы не будем.
]
#def(label: "def-curve-integral-2")[
_Криволинейным интегралом второго рода_ (или _интегралом от дифференциальной формы_) называется
$
integral_gamma omega := integral_a^b sum_(k = 1)^n f_k (gamma(t)) gamma'_k (t) dif t.
$
]
#let vf = $arrow(f)$
#let vsigma = $arrow(sigma)$
#props(label: "curve-integral-2-props")[
1. #sublabel("indep-param") Не зависит от параметризации.
2. #sublabel("sign-dir") Меняет знак при изменении направления.
3. #sublabel("tangent") Если $arrow(f) = (f_1, f_2, ..., f_n)$ и $arrow(sigma)(t)$ --- единичный касательный вектор к кривой в точке $gamma(t)$, то $integral_gamma omega = integral_gamma dotp(arrow(f), arrow(sigma)) dif s$.
4. #sublabel("curve-additive") Аддитивность по кривой: если $gamma_1 = gamma |_[a, c]$, $gamma_2 = gamma |_[c, b]$, то $integral_gamma omega = integral_(gamma_1) omega + integral_(gamma_2) omega$.
5. #sublabel("linear") Линейность по форме: если $alpha_1, alpha_2 in RR$, $omega_1, omega_2$ --- дифф. формы, то $integral_gamma (alpha_1 omega_1 + alpha_2 omega_2) = alpha_1 integral_gamma omega_1 + alpha_2 integral_gamma omega_2$.
6. #sublabel("norm-bound") $abs(integral_gamma omega) <= integral_gamma norm(vf) dif s <= l(gamma) dot max_(gamma[a, b]) norm(vf)$.
]
#proof[
1. Пусть $gamma = tilde(gamma) compose tau$.
$
integral_tilde(gamma) omega =^rf("def-curve-integral-2")
integral_c^d sum_(k = 1)^n f_k (tilde(gamma)(t)) tilde(gamma)'_k (t) dif t newline(=^(t = tau(u)))
integral_a^b sum_(k = 1)^n f_k (tilde(gamma)(tau(u))) tilde(gamma)'_k (tau(u)) tau'(u) dif u =^rf("def-curve-integral-2")
integral_a^b sum_(k = 1)^n f_k (gamma(u)) gamma'_k (u) dif u.
$
2. Аналогично.
3. $gamma'(t)$ --- касательный вектор в точке $gamma(t)$, $arrow(sigma)(t) = (gamma'(t)) / norm(gamma'(t))$.
$
integral_gamma dotp(vf, vsigma) dif s =
integral_a^b sum_(k = 1)^n f_k (gamma(t)) dot (gamma'_k (t))/norm(gamma'(t)) dot norm(gamma'(t)) dif t =^rf("def-curve-integral-2")
integral_gamma omega.
$
4. Тривиально получается по определению#rf("def-curve-integral-2").
5. Очевидно получается по определению#rf("def-curve-integral-2").
6.
Первое неравенство:
$
abs(integral_gamma omega) =^rf("curve-integral-2-props", "tangent")
abs(integral_gamma dotp(vf, vsigma) dif s) <=
integral_gamma abs(dotp(vf, vsigma)) dif s <=
integral_gamma norm(vf) dot underbrace(norm(vsigma), 1) dif s =
integral_gamma norm(vf) dif s.
$
Второе неравентсво:
$
integral_gamma norm(vf) dif s <= integral_gamma max_(gamma[a, b]) norm(vf) dif s =
max_(gamma[a, b]) norm(vf) dot integral_gamma dif s =^rf("curve-integral-1-props", "length")
max_(gamma[a, b]) norm(vf) dot l(gamma).
$
]
#exercise[
Доказать, что
$ integral_gamma omega = lim sum_(j = 1)^m sum_(k = 1)^n f_k (gamma(xi_j)) (gamma_k (t_j) - gamma_k (t_(j - 1))), $
где $a = t_0 < t_1 < ... < t_m = b$ --- разбиение $[a, b]$, $xi_j in [t_(j - 1), t_j]$ --- оснащение, в пределе у последовательности разбиений мелкость дробления стремиться к нулю.
]
#notice[
Пусть $F: Omega --> RR$, $Omega subset RR^n$.
Рассмотрим $dif_x F$ --- дифференциал (линейное отображение из $RR^n$ в $RR$).
Тогда $F(x + h) = F(x) + dif_x F(h) + o(h)$, при $h --> 0$. Возьмем $g_i (x) = x_i$.
Тогда
$
underbrace(g_i (x + h), x_i + h_i) =
underbrace(g_i (x), x_i) + underbrace(dif_x g_i (h), h_i) + o(h).
$
Такое отображение $dif_x g_i (h)$ обозначают $dif x_i$.
Более того, все $dif x_i$ линейно независимы,
поэтому $dif x_i$ --- базис в пространстве линейных отображений из $RR^n$ в $RR$.
Разложим вектор $dif_x F$ в этом базисе:
$
dif_x F (h) =
(diff F)/(diff x_1) dif x_1 (h) + (diff F)/(diff x_2) dif x_2 (h) + ... + (diff F)/(diff x_n) dif x_n (h).
$
Что такое дифференциальная форма#rf("def-differential-form") в $Omega$? Вообще говоря, просто формальная конструкция, но раз в каждой точке $Omega$ есть свое линейное отображение $RR^n --> RR$, то
$ omega = f_1 dif x_1 + f_2 dif x_2 + ... + f_n dif x_n, $
где $f_j$ --- коэффициенты при разложении по базису.
Примерно так можно понимать дифференциальные формы.
]
#def(label: "def-region")[
$Omega$ --- _область_, если $Omega$ открыто и линейно связно (то есть между любыми двумя точками можно провести путь в $Omega$, которых их соединяет).
]
#def(label: "def-form-antiderivative")[
В $Omega subset RR^n$ задана форма#rf("def-differential-form") $omega$.
$F: Omega --> RR$ --- _первообразная формы_ $omega$,
если $dif F = omega$,
то есть $f_k = (diff F) / (diff x_k)$.
]
#th(label: "curve-integral-2-from-antiderivative")[
Пусть $F$ --- первообразная#rf("def-form-antiderivative") формы#rf("def-differential-form") $omega$ заданной в $Omega$#rf("def-region"), а $gamma$ --- кривая в $Omega$, соединяющая точки $a$ и $b$. Тогда криволинейный интеграл от дифференциальной формы считается как
$ integral_gamma omega = F(b) - F(a). $
]
#proof[
Пусть $gamma: [alpha, beta] --> Omega$.
$
integral_gamma omega =^rf("def-curve-integral-2")
integral_alpha^beta sum_(k = 1)^n f_k (gamma(t)) gamma'_k (t) dif t =^rf("def-form-antiderivative")
integral_alpha^beta sum_(k = 1)^n (diff F)/(diff x_k) (gamma(t)) (gamma'_k (t)) dif t newline(=)
integral_alpha^beta (F compose gamma)' (t) dif t =
F(gamma(beta)) - F(gamma(alpha)) =
F(b) - f(a).
$
]
#follow(plural: true, label: "form-antiderivative-props")[
1. Если у формы $omega$ есть первообразная#rf("def-form-antiderivative"), то $integral_gamma omega$ зависит только от концов кривой, и не зависит от самой кривой.
2. Если $omega$ --- область#rf("def-region"), то все первообразные#rf("def-form-antiderivative") отличаются друг от друга на константу.
]
#proof[
1. Очевидно из теоремы#rf("curve-integral-2-from-antiderivative").
2. Пусть $F$ и $tilde(F)$ --- первообразные#rf("def-form-antiderivative") в $Omega$#rf("def-region"). Зафиксируем $a$, будем менять $b$. Для каждой пары точек рассмотрим путь из $a$ в $b$. Тогда
$ integral_gamma omega = F(b) - F(a) = tilde(F)(b) - tilde(F)(a) ==> tilde(F)(b) = F(b) + underbrace((tilde(F)(a) - F(a)), const). $
]
#lemma(label: "broken-line-from-curve")[
$Omega$ --- область#rf("def-region"). Тогда между любыми двумя точками из $Omega$, можно провести несамопересекающуюся ломаную, такую, что все ее звенья параллельны осям координат.
]
#proof[
Рассмотрим#rf("def-region") кривую, которая соединяет $a$ и $b$. Для каждой точки на кривой, заведем шарик $B_(r(t)) (gamma(t)) in Omega$. Тогда носитель кривой $gamma[a, b]$ покрывается этими шариками. Так как носитель --- компакт, покроем его конечным количеством шариков.
#figure(cetz.canvas(length: 0.6cm, {
import cetz.draw: *
catmull((0, 0), (3, 2), (6, 6), (8, 1), (4, -2), close: true, tension: 0.5)
place-anchors(
name: "p",
bezier-through((2, 0), (3, 0), (6, 5), stroke: red + 2pt),
..for i in range(21) { ((name: str(i), pos: i/20),) },
)
circle("p.0", radius: 0.15, stroke: none, fill: blue)
circle("p.0", radius: 1, stroke: (paint: blue, dash: "dashed"))
circle("p.3", radius: 0.15, stroke: none, fill: blue)
circle("p.3", radius: 0.7, stroke: (paint: blue, dash: "dashed"))
circle("p.9", radius: 0.15, stroke: none, fill: blue)
circle("p.9", radius: 1.1, stroke: (paint: blue, dash: "dashed"))
circle("p.14", radius: 0.15, stroke: none, fill: blue)
circle("p.14", radius: 1, stroke: (paint: blue, dash: "dashed"))
circle("p.16", radius: 0.15, stroke: none, fill: blue)
circle("p.16", radius: 0.7, stroke: (paint: blue, dash: "dashed"))
circle("p.18", radius: 0.15, stroke: none, fill: blue)
circle("p.18", radius: 1.1, stroke: (paint: blue, dash: "dashed"))
circle("p.20", radius: 0.15, stroke: none, fill: blue)
circle("p.20", radius: 0.7, stroke: (paint: blue, dash: "dashed"))
}))
Занумеруем шарики, и пойдем последовательно от первого шарика до последнего. Мы можем так сделать: в рамках каждого шарика будем идти до точки на пересечении границы и следующего шарика. Ломаная может получиться самопересекающиейся, но из нее можно убрать все петли. Короче, доделывается, зуб даю.
#figure(cetz.canvas(length: 1cm, {
import cetz.draw: *
catmull((0, 0), (3, 2), (6, 6), (8, 1), (4, -2), close: true, tension: 0.5)
place-anchors(
name: "p",
bezier-through((2, 0), (3, 0), (6, 5), stroke: red + 2pt),
..for i in range(21) { ((name: str(i), pos: i/20),) },
)
line(
..for i in range(20, step: 2) {
("p." + str(i), (horizontal: (), vertical: "p." + str(i + 2)))
}, "p.20",
stroke: green + 3pt)
circle("p.0", radius: 0.15, stroke: none, fill: blue)
circle("p.0", radius: 1, stroke: (paint: blue, dash: "dashed"))
circle("p.3", radius: 0.15, stroke: none, fill: blue)
circle("p.3", radius: 0.7, stroke: (paint: blue, dash: "dashed"))
circle("p.9", radius: 0.15, stroke: none, fill: blue)
circle("p.9", radius: 1.1, stroke: (paint: blue, dash: "dashed"))
circle("p.14", radius: 0.15, stroke: none, fill: blue)
circle("p.14", radius: 1, stroke: (paint: blue, dash: "dashed"))
circle("p.16", radius: 0.15, stroke: none, fill: blue)
circle("p.16", radius: 0.7, stroke: (paint: blue, dash: "dashed"))
circle("p.18", radius: 0.15, stroke: none, fill: blue)
circle("p.18", radius: 1.1, stroke: (paint: blue, dash: "dashed"))
circle("p.20", radius: 0.15, stroke: none, fill: blue)
circle("p.20", radius: 0.7, stroke: (paint: blue, dash: "dashed"))
}))
]
#th(label: "closed-curve-integral-2")[
Пусть $Omega$ --- область#rf("def-region"), $omega$ --- форма#rf("def-differential-form") в $Omega$. Коэффициенты формы $f_1, f_2, ..., f_n: Omega --> RR$ непрерывны.
Тогда следующие условия равносильны:
1. $omega$ имеет первообразную#rf("def-form-antiderivative").
2. $integral_gamma omega = 0$, для любой замкнутой кривой $gamma$.
3. $integral_gamma omega = 0$, для любой замкнутой несамопересекающейся ломаной, все звенья которой параллельны осям координат.
]
#proof[
- "$1 ==> 2$": очевидно по предыдущей теореме#rf("curve-integral-2-from-antiderivative").
- "$2 ==> 3$": вообще очев: если для любой кривой, то для ломаной тем более.
- "$3 ==> 1$": зафиксируем $a in Omega$ и $forall x in Omega$ проведем из $a$ в $x$ ломаную $gamma$ со звеньями параллельными осям.
Она есть по лемме#rf("broken-line-from-curve").
Рассмотрим $F(x) := integral_gamma omega$.
Этот интеграл не зависит от выбора $gamma$,
так как если к одной кривой добавить в конец вторую перевернутую, получится ломаная из $a$ в $a$.
Она, может быть, самопересекается. Давайте немного подвигаем отрезки так, чтобы точек пересечения было не более чем счетно (какие-то отрезки могут совпасть). Тогда по $3)$, значение интеграла не изменится, и если порезать ее точками пересечения,
получаться интегралы по замкнутым несамопересекающемся ломаным, которые, по $3)$, равны 0.
Ну значит интегралы тоже равны.
#figure(
cetz.canvas(length: 0.6cm, {
import cetz.draw: *
catmull((0, 0), (3, 2), (6, 6), (8, 1), (4, -2), close: true, tension: 0.5)
place-anchors(
name: "p",
bezier-through((2, 0), (3, 0), (6, 5), stroke: red + 2pt),
..for i in range(21) { ((name: str(i), pos: i/20),) },
)
line(
..for i in range(20, step: 5) {
("p." + str(i), (horizontal: (), vertical: "p." + str(i + 5)))
}, "p.20",
mark: (end: ">"),
stroke: green + 2pt
)
line(
..for i in range(20, step: 4) {
("p." + str(i), (vertical: (), horizontal: "p." + str(i + 4)))
}, "p.20",
mark: (start: ">"),
stroke: blue + 2pt
)
}))
Проверим, что $F$ подходит: не умаляя общности, проверим первую координату.
$
(diff F)/(diff x_1) (x) =
lim_(t -> 0) (F(x_1 + t, x_2, ..., x_n) - F(x_1, ..., x_n)) / t =^rf("curve-integral-2-from-antiderivative")
lim_(t -> 0) 1/t integral_[x, (x_1 + t, ..., x_n)] omega.
$
Рассмотрим интеграл:
$
integral_[x, (x_1 + t, ..., x_n)] omega = integral_0^t sum_(k = 1)^n f_k (gamma(tau)) underbrace(gamma'_k (tau), [k = 1]) dif tau = integral_0^t f_1(x_1 + tau, x_2, ..., x_n) dif tau.
$
Здесь $gamma$ --- параметризация $(x_1 + tau, x_2, ..., x_n)$.
Значит,
$
(diff F)/(diff x_1) (x) =
lim_(t -> 0) 1/t integral_0^t f_1(x_1 + tau, x_2, ..., x_n) dif tau =^rf("barrow")
f_1 (x).
$
]
#let pfill = pattern(
size: (3pt, 3pt),
place(line(
start: (0%, 0%),
end: (100%, 100%),
stroke: (paint: blue, thickness: 0.5pt, cap: "square", join: "miter")
))
)
#def(label: "def-primitive-region")[
$Omega subset RR^2$ --- элементарная область#rf("def-region"), если $Omega$ можно представить в виде $ Omega &= {(x, y) : a < x < b and phi(x) < y < psi(x)} \ &= {(x, y): c < y < d and alpha(y) < x < beta(y)}. $
#grid(columns: (1fr, 1fr, 1fr), figure(
supplement: none,
caption: [Удовлетворяет первому условию],
cetz.canvas(length: 0.9cm, {
import cetz.draw: *
line((-0.5, 0), (5.5, 0), mark: (end: ">"))
content((rel: (0.2, 0)), $x$)
line((0, -0.5), (0, 5.5), mark: (end: ">"))
content((rel: (0, 0.3)), $y$)
line((1, 5.5), (1, -0.5), stroke: (paint: gray, dash: "dashed"))
content((rel: (0.2, 0.3)), $a$)
line((4, 5.5), (4, -0.5), stroke: (paint: gray, dash: "dashed"))
content((rel: (0.2, 0.3)), $b$)
merge-path({
line((1, 0.5), (1, 4))
bezier-through((1, 4), (2, 3), (3, 5))
bezier-through((3, 5), (3.5, 4.5), (4, 3))
line((4, 3), (4, 1))
bezier-through((4, 1), (3, 2), (1, 0.5))
}, stroke: blue + 2pt, fill: pfill, close: true)
})
), figure(
supplement: none,
caption: [Удовлетворяет второму условию],
cetz.canvas(length: 0.9cm, {
let std-line = line
import cetz.draw: *
line((-0.5, 0), (5.5, 0), mark: (end: ">"))
content((rel: (0.2, 0)), $x$)
line((0, -0.5), (0, 5.5), mark: (end: ">"))
content((rel: (0, 0.3)), $y$)
line((5.5, 1), (-0.5, 1), stroke: (paint: gray, dash: "dashed"))
content((rel: (0.3, 0.2)), $c$)
line((5.5, 4), (-0.5, 4), stroke: (paint: gray, dash: "dashed"))
content((rel: (0.3, 0.2)), $d$)
merge-path({
line((1, 1), (5, 1))
bezier-through((5, 1), (3, 3), (4, 4))
line((4, 4), (0.5, 4))
bezier-through((0.5, 4), (0.5, 2), (1, 1))
}, stroke: blue + 2pt, fill: pfill, close: true)
})
),figure(
supplement: none,
caption: [Удовлетворяет обоим условиям],
cetz.canvas(length: 0.9cm, {
let std-line = line
import cetz.draw: *
line((-0.5, 0), (5.5, 0), mark: (end: ">"))
content((rel: (0.2, 0)), $x$)
line((0, -0.5), (0, 5.5), mark: (end: ">"))
content((rel: (0, 0.3)), $y$)
line((1, 5.5), (1, -0.5), stroke: (paint: gray, dash: "dashed"))
content((rel: (0.2, 0.3)), $a$)
line((4, 5.5), (4, -0.5), stroke: (paint: gray, dash: "dashed"))
content((rel: (0.2, 0.3)), $b$)
line((5.5, 1), (-0.5, 1), stroke: (paint: gray, dash: "dashed"))
content((rel: (0.3, 0.2)), $c$)
line((5.5, 4), (-0.5, 4), stroke: (paint: gray, dash: "dashed"))
content((rel: (0.3, 0.2)), $d$)
merge-path({
line((1, 1), (4, 1))
bezier-through((4, 1), (3, 1.5), (2.5, 2.5))
bezier-through((2.5, 2.5), (2, 3), (1.5, 4))
line((1.5, 4), (1, 4))
line((1, 4), (1, 1))
}, stroke: blue + 2pt, fill: pfill, close: true)
})
))
]
#th(name: "<NAME>", label: "green")[
$Omega subset RR^2$ --- ограниченная на плоскости область#rf("def-region"), граница которой представляет собой конечное объединение непересекающихся простых кусочно-гладких замкнутых кривых. $P, Q: Cl Omega --> RR$ --- непрерывные, такие, что $(diff P)/(diff y)$ и $(diff Q)/(diff x)$ непрерывны на $Cl Omega$. Тогда
$ integral_Omega ((diff Q)/(diff x) - (diff P)/(diff y)) dif lambda_2 = integral_(diff Omega) (P dif x + Q dif y), $
где $diff Omega$ --- границы, причем направления кривых выбраны так, что область интегрирования всегда лежит слева от границы:
#figure(
cetz.canvas(length: 0.6cm, {
let std-line = line
import cetz.draw: *
let no-fill = th_color.lighten(90%)
let pfill = pattern(
size: (3pt, 3pt),
place(std-line(
start: (0%, 0%),
end: (100%, 100%),
stroke: (paint: blue, thickness: 0.5pt, cap: "square", join: "miter")
))
)
content((4.4, 0), text(blue, size: 2em, $Omega$))
set-style(mark: (fill: blue), stroke: blue)
place-marks(
catmull(
(0, -2), (8, -1), (6, 4), (2, 3),
close: true, fill: pfill,
),
..for i in range(7) {
((mark: ">", size: 0.2, pos: i / 7), )
}
)
set-style(mark: (fill: green), stroke: green)
place-marks(
catmull(
(1, -1), (3, 0), (3.5, -1), (2, -2),
close: true, fill: no-fill
),
..for i in range(5) {
((mark: ">", size: 0.2, pos: i / 5), )
}
)
place-marks(
catmull(
(4, 2), (3, 1), (2, 2), (3, 3),
close: true, fill: no-fill
),
..for i in range(7) {
((mark: ">", size: 0.2, pos: i / 7), )
}
)
place-marks(
catmull(
(5, 2.5), (6, 0), (6.6, 1.5), (5.5, 3),
close: true, fill: no-fill
),
..for i in range(7) {
((mark: ">", size: 0.2, pos: i / 7), )
}
)
})
)
]
#proof[
Надо доказать две формулы:
$ integral_Omega (diff Q) / (diff x) dif lambda_2 = integral_(dif Omega) Q dif y quad "и" quad integral_Omega (diff P) / (diff y) dif lambda_2 = - integral_(diff Omega) P dif x. $
Мы докажем вторую, первая аналогична.
*Шаг 1: $Omega$ --- элементарная область#rf("def-primitive-region")*.
$ integral_Omega (diff P)/(diff y) dif lambda_2 =^rf("fubini") integral_a^b integral_(phi(x))^(psi(x)) (diff P)/(diff y) (x, y) dif y dif x = integral_a^b (P(x, psi(x)) - P(x, phi(x))) dif x. $
С другой стороны, $integral_(diff Omega) P dif x$ равен сумме интегралов по четырем границам элементарной области (сверху, снизу, справа, слева):
$ integral_(diff Omega) P dif x = integral_"I" + integral_"II" + integral_"III" + integral_"IV". $
#figure[
#cetz.canvas({
import cetz.draw: *
line((1, 3.5), (1, 0), stroke: (paint: gray, dash: "dashed"))
content((rel: (0.2, 0.3)), $a$)
line((4, 3.5), (4, 0), stroke: (paint: gray, dash: "dashed"))
content((rel: (0.2, 0.3)), $b$)
merge-path({
line((1, 0.5), (1, 3))
bezier-through((1, 3), (2, 3.2), (4, 3))
line((4, 3), (4, 1))
bezier-through((4, 1), (3, 0.6), (1, 0.5))
}, stroke: blue + 2pt, fill: pfill, close: true)
content((2.5, 0.35))[I]
content((4.3, 2))[II]
content((2.5, 3.4))[III]
content((0.7, 1.75))[IV]
content((4.3, 1), $phi$)
content((4.3, 3), $psi$)
})
]
Правый интеграл равен $integral_"II" = integral_phi(b)^psi(b) P(gamma(t)) gamma'_1 (t) dif t = 0$, так как производная равна 0. Аналогично интеграл слева $integral_"IV" = 0$. Снизу интеграл равен $integral_"I" = integral_a^b P(t, phi(t)) dif t$, а сверху $integral_"III" = integral_b^a P(t, psi(t)) dif t$, а в сумме они дают $integral_a^b P(t, phi(t)) dif t - integral_a^b P(t, psi(t)) dif t$. Получили что хотели, даже знаки получились разными.
*Шаг 2*. Если область $Omega$ по кривой $gamma$ разрезали на $Omega_1$ и $Omega_2$, и формула была верна в $Omega_1$ и $Omega_2$, то она была верна и в $Omega$.
$ -integral_(diff Omega_i) P dif x = integral_(Omega_i) (diff P)/(diff y) dif lambda_2 ==> -integral_(diff Omega) P dif x = -integral_(diff Omega_1 union diff Omega_2) P dif x = integral_(Omega_1 union Omega_2) (diff P)/(diff y) dif lambda_2 = integral_Omega (diff P)/(diff y) dif lambda_2. $
#figure[
#cetz.canvas({
import cetz.draw: *
place-marks(
place-anchors(name: "Omega", catmull((0, 0), (2, -0.5), (3, 0.5), (4, 0), (5, 1.5), (4, 3), (2, 2.5), close: true), (name: "a", pos: 0.25), (name: "b", pos: 0.7, fill: black)),
fill: black,
..for i in range(7) {
((mark: ">", size: 0.2, pos: i / 7), )
}
)
place-marks(
place-anchors(bezier("Omega.a", "Omega.b", (1.0, 1.5)), name: "gamma", pos: 0.5),
stroke: green, fill: green,
..for i in range(3) {
(
(mark: "<", size: 0.2, pos: i / 3 + 2/9),
)
}
)
place-marks(
bezier("Omega.a", "Omega.b", (1.0, 1.5), stroke: none),
stroke: blue, fill: blue,
..for i in range(3) {
(
(mark: ">", size: 0.2, pos: i / 3 + 1/9),
)
}
)
content((rel: (-0.2, 0), to: "gamma"), $gamma$)
content((1.5, .5), text(blue, 2em, $Omega_1$))
content((3.5, 1.7), text(green, 2em, $Omega_2$))
})
]
*Шаг 3*. Формула верна для конечного объединения элементраных областей. Это индукция.
*Шаг 4*. Любая область из формулировки так получается. Проверять не будем. В любом случае на практике интегралы так представляются точно.
]
#follow(label: "region-measure-through-green")[
$ lambda_2 Omega = -integral_(diff Omega) y dif x = integral_(diff Omega) x dif y = 1/2 integral_(diff Omega) x dif y - y dif x. $
]
|
|
https://github.com/ern1/typiskt | https://raw.githubusercontent.com/ern1/typiskt/main/templates/icons.typ | typst | //#let path = (
// ico: "templates/assets/icons",
// dev: "templates/assets/dev-icons",
//)
#let social = (
email: "email.svg",
linkedin: "linkedin.svg",
github: "github.svg",
pdf: "pdf.svg",
phone: "phone.svg",
slack: "slack.svg",
steam: "steam.svg",
wechat: "wechat.svg",
)
#let dev-icons = (
amazon_s3: "amazon_s3.svg",
android: "android.svg",
cpp: "cplusplus.svg",
css: "css3.svg",
docker: "docker.svg",
git: "git.svg",
gradle: "gradle.svg",
html5: "html5.svg",
java: "java.svg",
js: "javascript.svg",
kotlin: "kotlin.svg",
linux: "linux.svg",
npm: "npm.svg",
python: "python.svg",
react: "react.svg",
rust: "rust.svg",
svg: "svg.svg",
ts: "typescript.svg",
ubuntu: "ubuntu.svg",
windows: "windows",
)
#let getPath(name) = {
if name in social {
"assets/icons/" + social.at(name)
}
else if name in dev-icons {
"assets/dev-icons/" + dev-icons.at(name)
} else [
#sym.quest
]
}
/* FOR SIMPLE ICONS */
// https://simpleicons.org/
/*#let siBasePath = (
default: "assets/simple-icons/",
color: "assets/simple-icons/colored/",
)
#let simplePath(brandName, colored: false) = {
let basePath = siBasePath.default
if colored {
basePath = siBasePath.color
}
basePath + brandName + "-color.svg"
}*/
#let siBasePath = "assets/simple-icons/"
#let simplePath(brandName) = {
siBasePath + brandName + ".svg"
}
/*
// https://typst.app/docs/reference/visualize/image/
#let original = read("diagram.svg")
#let changed = original.replace(
"#2B80FF", // blue
green.to-hex(),
)
#image.decode(original)
#image.decode(changed)
*/ |
|
https://github.com/ChristophVanDeest/FH-Kiel-Typst-Template | https://raw.githubusercontent.com/ChristophVanDeest/FH-Kiel-Typst-Template/main/lib/pages/cover.typ | typst | MIT License | #import "../translations.typ": translations
#let cover_page(
is-thesis: true,
is-master-thesis: false,
is-bachelor-thesis: true,
is-report: false,
title: "",
author: "",
faculty: "",
department: "",
study-course: "",
supervisors: (),
submission-date: none,
) = {
// Set the document's basic properties.
set page(
margin: (left: 0mm, right: 0mm, top: 0mm, bottom: 0mm),
numbering: none,
number-align: center,
)
// HAW Logo
place(
top + right,
dx: -13mm,
dy: 10mm,
image("../assets/logo.svg", width: 164pt)
)
// Title etc.
pad(
left: 57mm,
top: 66mm,
right: 18mm,
stack(
// Type
if is-thesis {
let thesis-title = translations.bachelor-thesis
if is-master-thesis {
thesis-title = translations.master-thesis
}
upper(text(thesis-title, size: 9pt, weight: "bold"))
v(2mm)
},
// Author
text(author, size: 9pt),
v(13mm),
// Title
par(
leading: 9pt,
text(title, size: 31pt, weight: 500, font: "New Computer Modern"),
),
v(5mm),
line(start: (0pt, 0pt), length: 30pt, stroke: 1mm),
v(12mm),
// Faculty
text(translations.faculty-of + " " + faculty, size: 10pt, weight: "bold"),
v(2mm),
// Department
text(translations.department-of + " " + department, size: 10pt),
)
)
// University name text
place(
right + bottom,
dx: -11mm,
dy: -35mm,
box(
align(
left,
stack(
line(start: (0pt, 0pt), length: 25pt, stroke: 0.9mm),
v(3mm),
text("<NAME>", size: 9pt, weight: "bold", font: "Open Sans"),
v(2mm),
text("Sokratespl. 1", size: 9pt, font: "Open Sans"),
v(2mm),
text("24149 Kiel", size: 9pt, font: "Open Sans"),
)
)
)
)
if is-thesis {
// Second cover page
pagebreak()
// Set the document's basic properties.
set page(
margin: (left: 31.5mm, right: 32mm, top: 55mm, bottom: 67mm),
numbering: none,
number-align: center,
)
// Title etc.
stack(
// Author
align(
center,
text(author, size: 14pt, font: "Open Sans"),
),
v(23mm),
// Title
align(
center,
par(
leading: 13pt,
text(title, size: 18pt, font: "Open Sans"),
),
),
v(22mm),
)
v(1fr)
stack(
// Content
stack(
spacing: 3mm,
if is-bachelor-thesis {
text(translations.bachelor-thesis-submitted-for-examination-in-bachelors-degree)
},
if is-master-thesis {
text(translations.master-thesis-submitted-for-examination-in-masters-degree)
},
text(translations.in-the-study-course + " " + text(study-course, style: "italic")),
text(translations.at-the-department + " " + department),
text(translations.at-the-faculty-of + " " + faculty),
text(translations.at-university-fh-kiel),
),
v(4mm),
line(start: (0pt, 0pt), length: 25pt, stroke: 1mm),
v(4mm),
// Supervision
if supervisors.len() > 0 {
if type(supervisors) != array {
text(translations.supervising-examiner + ": " + text(upper(supervisors), weight: "bold"), size: 10pt)
} else {
text(translations.supervising-examiner + ": " + text(upper(supervisors.first()), weight: "bold"), size: 10pt)
if supervisors.len() > 1 {
linebreak()
text(translations.second-examiner + ": " + text(upper(supervisors.at(1)), weight: "bold"), size: 10pt)
}
}
},
// Submission date
if submission-date != none {
stack(
v(4mm),
line(start: (0pt, 0pt), length: 25pt, stroke: 1mm),
v(4mm),
text(
translations.submitted + ": " + submission-date.display("[day]. [month repr:long] [year]"),
size: 10pt,
),
)
},
)
}
}
|
https://github.com/Clamentos/FabRISC | https://raw.githubusercontent.com/Clamentos/FabRISC/main/src/spec/Main.typ | typst | Creative Commons Attribution Share Alike 4.0 International | ///
#import "Macros.typ": *
///
// General configuration.
#set page(paper: "a4", margin: (x: 2cm, y: 2cm))
#set text(font: "New Computer Modern", size: 12pt, hyphenate: true)
#set par(justify: true)
#set figure.caption(position: top)
#set table.cell(breakable: false)
#set table(stroke: 0.75pt, inset: 8pt, fill: (_, y) => if(calc.rem(y, 2) == 0) { rgb("#eaeaea") })
#show figure: set block(breakable: true)
#show figure.caption: emph
///
// Front page.
#align(center, image("../resources/LOGO-1.png", height: 25%))
#align(center, text(32pt)[Instruction Set Architecture])
#align(center, text(12pt)[Specification version 1.0])
#align(center, text(12pt)[Document version 1.2.0])
#linebreak()
#align(center, text(16pt)[<NAME>])
#align(center, text(14pt)[25/08/2024])
#linebreak()
#align(left + bottom, text(12pt)[
FabRISC is licensed under a
Creative Commons Attribution-ShareAlike 4.0 International License.
You should have received a copy of the license along with this
work. If not, see #monospace(link("https://creativecommons.org/licenses/by-sa/4.0/")).
])
#align(right + bottom, image("../resources/LICENSE.png", height: 3%))
#pagebreak()
///
// Contents.
#outline(indent: true)
#outline(title: [Tables], target: figure.where(kind: table), indent: true)
#pagebreak()
///
#set page(numbering: "1")
#set heading(numbering: "1.")
#set enum(indent: 0.5cm)
///
// Actual content.
#include "Section1.typ"
#include "Section2.typ"
#include "Section3.typ"
#include "Section4.typ"
#include "Section5.typ"
#include "Section6.typ"
#include "Section7.typ"
#include "Section8.typ"
///
|
https://github.com/pluttan/bdkurs | https://raw.githubusercontent.com/pluttan/bdkurs/main/repkurs.typ | typst | #import "@docs/bmstu:1.0.0":*
#import "@preview/tablex:0.0.8": tablex, rowspanx, colspanx, cellx
#let work(content) = {
set page(
paper: "a4",
margin: (left: 30mm, right: 15mm, top: 20mm, bottom: 20mm),
numbering: "1"
)
set text(font: "Times New Roman", size: 14pt, lang: "ru")
set list(marker: [--])
// Покажем основное содержимое работы.
{
let indent = 1.25cm
set list(indent: indent)
set heading(numbering:
(..nums) => {
if (nums.pos().len() == 2) {nums.pos().at(1)}
if (nums.pos().len() == 3) [#{nums.pos().at(1)}.#{nums.pos().at(2)}];
})
show heading.where(level:1): it => {
// if breakfirst == true {pagebreak()}
set text(16pt, hyphenate: false)
it
}
show heading.where(level:2): it => {
set text(16pt, hyphenate: false)
it
}
show heading.where(level:3): it => {
set text(14pt, hyphenate: false)
it
}
set par(justify: true, first-line-indent: indent)
show list: it => {
for p in (..it.children){[#par([--#h(5pt) #p.body])]}
}
set enum(indent: 1.25cm)
show enum: it => {
let listit = counter("1")
listit.update(0)
for p in (..it.children){[#par([#listit.step() #listit.display(). #p.body])]}
}
show raw: it => {
box(
inset: (x:6pt, y:0pt),
outset: (y:3pt),
stroke: luma(0),
align(left)[#it]
)
}
content
}
}
#let theme = "themes/Catppuccin Latte.tmTheme"
#let parserasm(lst) = {
let carr = ()
let i = 0
let fnc = ""
let nocol = 1
lst = lst.split("")
let func = 0
while (i < lst.len()) {
let dict = (
text: "",
tab : 0,
func: func,
nocol: nocol,
len: 0,
)
let predi = i
let tab = true
while (i < lst.len() and lst.at(i)!="\n"){
if (tab and lst.at(i)==" "){
dict.tab+=1
}
if (tab and lst.at(i) != " "){
if (dict.tab == 0){
func = nocol
}
tab = false
}
dict.text += lst.at(i)
i += 1
}
dict.len = i - predi
dict.func = func
carr.push(dict)
nocol += 1
i += 1
}
return carr
}
#let parsercpp(lst) = {
let carr = ()
let i = 0
let fnc = ""
let nocol = 1
lst = lst.split("")
let func = 0
while (i < lst.len()) {
let dict = (
text: "",
tab : 0,
func: func,
nocol: nocol,
len: 0,
)
let predi = i
let tab = true
while (i < lst.len() and lst.at(i)!="\n"){
if (tab and lst.at(i)==" "){
dict.tab+=1
}
if (tab and lst.at(i) != " "){
if (dict.tab == 0){
func = nocol
}
tab = false
}
dict.text += lst.at(i)
i += 1
}
dict.len = i - predi
dict.func = func
carr.push(dict)
nocol += 1
i += 1
}
return carr
}
#let writeft(lst, f, t) = {
let fi = 0
let i = 0
let fo = 0
let out = ""
let nlst = ()
lst = lst.split("\n")
while (i < lst.len()) {
i += 1
if (i >= f and i <= t) {
nlst.push(lst.at(i))
}
}
return nlst.join("\n")
}
#let funcno(carr, no) = {
let out = ""
for i in carr {
if (i.func == no){
out += i.text + "\n"
}
}
return out
}
#let funcstr(carr, func) = {
let out = ""
for i in carr {
if (i.text == func){
return funcno(carr, i.func)
}
}
return ""
}
#let lst = counter("listing")
#let code(data, lang, lable, num: false, size: 14pt) = {
set par(justify: true, first-line-indent: 0pt)
lst.step()
align(left)[
Листинг #lst.display() #sym.bar.h #lable
]
v(-8pt)
set text(size)
if (num){
show raw.line: it => {
if (it.number < 10){h(0.6em)}
text(fill: gray)[#it.number]
// text(fill: gray)[|]
it.body
}
raw(data, lang:lang, theme:theme)
} else {
raw(data, lang:lang, theme:theme)
}
set text(14pt)
set par(justify: true, first-line-indent: 1.25pt)
}
#show par: it => {
it
}
#set raw(theme:theme)
#pagebreak()
#counter(page).update(2)
#pagebreak()
#show: work
#set page(numbering:"1")
#align(center)[*РЕФЕРАТ*]
Рассчетно-пояснительная записка состоит из 43 страницы, включающих 20 рисунков, 37 листингов, 10 таблиц и 4 приложения.
Перечень ключевых слов: База данных, PostgreSQL, Python, Ruby, PGAdmin4, Актеры театра, Занятость, Репетиции, Сцены, Роли, Инфологическая модель, Датологическая модель, Бизнеспроцессы, СУБД, Реализация базы данных
Целью создания данной базы данных является организация и хранение структурированной информации о занятости актеров.
Для реализации этой базы данных используются следующие инструменты и технологии:
- Система управления базами данных (СУБД) PostgreSQL: мощная объектно-реляционная СУБД, обеспечивающая высокую производительность, надежность и расширяемость для управления данными.
- Языки программирования Python и Ruby: используются для написания скриптов и выполнения операций с базой данных, таких как вставка и обновление данных.
- Среда разработки PGAdmin4: универсальная многофункциональная программа для работы с базами данных, предоставляющая удобный графический интерфейс для разработки, администрирования и управления базами данных.
#pagebreak()
#set par(justify: true, first-line-indent: 0cm)
#align(center)[*СОДЕРЖАНИЕ*]
#v(-15pt)#h(-35pt)#outline(title: [], indent: n => {if (n >1){h(1em)}})
#set par(justify: true, first-line-indent: 1.25cm)
#show heading.where(level:1): it => {
pagebreak()
align(center)[#text(16pt, hyphenate: false)[#upper[#it]]]
}
= Введение
Цель данной курсовой работы — разработка комплексной базы данных для организации, хранения и управления структурированной информацией о занятости актеров театра. Эта база данных будет предназначена для эффективного учета и отслеживания всех аспектов участия актеров в театральных постановках, включая данные о репетициях, спектаклях, ролях и контрактах.
Основная задача этой базы данных — централизовать и упростить хранение данных, что позволит улучшить доступ к информации, упростить её обработку и анализ, а также повысить прозрачность и эффективность работы театрального коллектива.
Основная проблема, которую необходимо решить с помощью этой базы данных, — эффективное управление большими объемами разнородной информации, связанной с занятостью актеров. В настоящее время данные часто хранятся в разных форматах и местах, что затрудняет их поиск и использование. Кроме того, отсутствие централизованного хранилища данных может привести к потере информации, дублированию записей и увеличению времени на обработку запросов.
Актуальность данной работы обусловлена ростом числа выпускников актерских вузов, которые будут нуждаться в работе в театре. Эффективное управление данными позволит сократить время на поиск и обработку информации, повысить точность и надежность данных о занятости актеров, а также улучшить взаимодействие между различными подразделениями театра.
Для достижения поставленных целей необходимо решить следующие задачи:
- Разработать структуру базы данных для удобного и эффективного хранения информации о репетициях, спектаклях, ролях и контрактах.
- Реализовать функциональность для учета актеров, включая сохранение их данных и фотографий.
- Организовать хранение информации о спектаклях, включая название, бюджет, год постановки и возрастные ограничения.
- Обеспечить учет занятости актеров, включая их участие в репетициях и спектаклях, а также распределение ролей.
- Управлять информацией о контрактах, включая даты приема и увольнения, а также ставки.
#pagebreak()
== Анализ предметной области
Для анализа предметной области занятости актеров театра были выявлены несколько ключевых сущностей, которые необходимы для полного и точного отражения всех аспектов функционирования театра. Эти сущности включают информацию о актерах, спектаклях, контрактах, занятости в спектаклях, репетициях, пьесах, сценах и ролях. Каждая сущность играет важную роль в обеспечении целостности и полноты данных, необходимых для эффективного управления занятостью актеров театра.
Ниже приведен анализ каждой из выявленных сущностей:
- *Актеры* - включает информацию о театральных актерах, например ФИО, дата рождения, фото, стаж работы и звания/награды.
- *Спектакли* - содержит информацию о театральных спектаклях, включая название, бюджет, год постановки, возрастное ограничение и код пьесы.
- *Контракт* - охватывает данные о контрактах актеров, включая дату приема, дату увольнения и ставку.
- *Занятость в спектаклях* - включает информацию о занятости актеров в спектаклях.
- *Репетиции* - содержит данные о репетициях спектаклей, такие как дата и время, продолжительность, является ли репетиция читкой и код спектакля.
- *Сцены в репетициях* - охватывает информацию о сценах, репетируемых в конкретных репетициях.
- *Пьесы* - включает данные о пьесах, таких как название, год выпуска и автор.
- *Сцены* - содержит информацию о сценах в пьесах, включая название, продолжительность и код пьесы.
- *Роли* - охватывает данные о ролях, исполняемых актерами в пьесах, включая название роли, является ли роль главной, код пьесы и код актера.
- *Занятость ролей в сценах* - включает информацию о занятости ролей в конкретных сценах.
Этот анализ помогает структурировать данные для эффективного управления занятостью актеров в театре и обеспечивает точное и полное представление всех аспектов театральной деятельности.
=== Инфологическая модель базы данных
Исходя из сущностей и их свойств, построим инфологическую модель базы данных.
#img(image("1.png", width:87%), [Инфологическая модель базы данных])
=== Датологическая модель базы данных
На основе анализа предметной области театра и выявленных ключевых сущностей и их взаимосвязей, можно построить ERD-диаграмму (датологическую модель базы данных).
#img(image("2.png", width:87%), [Датологическая модель базы данных])
На основе этой диаграммы создадим 10 таблиц.
=== Таблицы базы данных
#h(-35pt)
Таблица 1 -- Актеры
#v(-10pt)
#tablex(
columns: 3,
inset: 10pt,
align: center + horizon,
[Название колонки] ,[ Описание] ,[ Тип ],
[КодАктера] ,[ Код актера (первичный ключ)],[ ```sql SERIAL``` ],
[ФИО] ,[ ФИО] ,[ ```sql VARCHAR(50)``` ],
[ДатаРождения] ,[ Дата рождения] ,[ ```sql DATE``` ],
[Фото] ,[ Фото] ,[ ```sql VARCHAR(100)``` ],
[СтажРаботы] ,[ Стаж работы] ,[ ```sql VARCHAR(100)``` ],
[ЗваниеНаграды] ,[ Звания и награды] ,[ ```sql VARCHAR(50)[]```],
)
#pagebreak()
Таблица 2 -- Спектакли
#v(-10pt)
#tablex(
columns: 3,
inset: 10pt,
align: center + horizon,
[Название колонки] ,[ Описание] ,[ Тип ],
[КодСпектакля] ,[ Код спектакля (первичный ключ)],[ ```sql SERIAL``` ],
[Название] ,[ Название] ,[ ```sql VARCHAR(50)``` ],
[Бюджет] ,[ Бюджет] ,[ ```sql INTEGER``` ],
[ГодПостановки] ,[ Год постановки] ,[ ```sql INTEGER``` ],
[ОграничениеПоВозрасту] ,[ Ограничение по возрасту] ,[ ```sql VARCHAR(3)``` ],
[КодПьесы] ,[ Код пьесы] ,[ ```sql SERIAL``` ]
)
#v(20pt)
Таблица 3 -- Контракт
#v(-10pt)
#tablex(
columns: 3,
inset: 10pt,
align: center + horizon,
[Название колонки] ,[ Описание] ,[ Тип ],
[КодКонтракта] ,[ Код контракта (первичный ключ)],[ ```sql SERIAL``` ],
[ДатаПриема] ,[ Дата приема] ,[ ```sql DATE``` ],
[ДатаУвольнения] ,[ Дата увольнения] ,[ ```sql DATE``` ],
[Ставка] ,[ Ставка] ,[ ```sql INTEGER``` ],
[КодАктера] ,[ Код актера (внешний ключ) ],[ ```sql SERIAL``` ]
)
#v(20pt)
Таблица 4 -- Занятость в спектаклях
#v(-10pt)
#tablex(
columns: 3,
inset: 10pt,
align: center + horizon,
[Название колонки] ,[ Описание] ,[ Тип ],
[КодЗанятости] ,[ Код занятости (первичный ключ)],[ ```sql SERIAL``` ],
[КодСпектакля] ,[ Код спектакля (внешний ключ) ],[ ```sql SERIAL``` ],
[КодАктера] ,[ Код актера (внешний ключ) ],[ ```sql SERIAL``` ]
)
#pagebreak()
Таблица 5 -- Репетиции
#v(-10pt)
#tablex(
columns: 3,
inset: 10pt,
align: center + horizon,
[Название колонки] ,[ Описание] ,[ Тип ],
[КодРепетиции] ,[ Код репетиции (первичный ключ)],[ ```sql SERIAL``` ],
[ДатаВремя] ,[ Дата и время] ,[ ```sql TIMESTAMP``` ],
[Продолжительность] ,[ Продолжительность] ,[ ```sql INTERVAL``` ],
[Читка] ,[ Читка] ,[ ```sql BOOLEAN``` ],
[КодСпектакля] ,[ Код спектакля (внешний ключ) ],[ ```sql SERIAL``` ]
)
#v(20pt)
Таблица 6 -- Сцены в репетициях
#v(-10pt)
#tablex(
columns: 3,
inset: 10pt,
align: center + horizon,
[Название колонки] ,[ Описание] ,[ Тип ],
[КодСценыВРепетиции],[ Код сцены в репетиции (первичный ключ)],[ ```sql SERIAL``` ],
[КодРепетиции] ,[ Код репетиции (внешний ключ) ],[ ```sql SERIAL``` ],
[КодСцены] ,[ Код сцены (внешний ключ) ],[ ```sql SERIAL``` ]
)
#v(20pt)
Таблица 7 -- Пьесы
#v(-10pt)
#tablex(
columns: 3,
inset: 10pt,
align: center + horizon,
[Название колонки] ,[ Описание] ,[ Тип ],
[КодПьесы] ,[ Код пьесы (первичный ключ)],[ ```sql SERIAL``` ],
[Название] ,[ Название] ,[ ```sql VARCHAR(50)``` ],
[ГодВыпуска] ,[ Год выпуска] ,[ ```sql INTEGER``` ],
[Автор] ,[ Автор] ,[ ```sql VARCHAR(50)``` ]
)
#pagebreak()
Таблица 8 -- Сцены
#v(-10pt)
#tablex(
columns: 3,
inset: 10pt,
align: center + horizon,
[Название колонки] ,[ Описание] ,[ Тип ],
[КодСцены] ,[ Код сцены (первичный ключ) ],[ ```sql SERIAL``` ],
[Название] ,[ Название] ,[ ```sql VARCHAR(50)``` ],
[Продолжительность] ,[ Продолжительность] ,[ ```sql INTERVAL``` ],
[КодПьесы] ,[ Код пьесы (внешний ключ) ],[ ```sql SERIAL``` ]
)
#v(20pt)
Таблица 9 -- Роли
#v(-10pt)
#tablex(
columns: 3,
inset: 10pt,
align: center + horizon,
[Название колонки] ,[ Описание] ,[ Тип ],
[КодРоли] ,[ Код роли (первичный ключ) ],[ ```sql SERIAL``` ],
[НазваниеРоли] ,[ Название роли] ,[ ```sql VARCHAR(50)``` ],
[Главная] ,[ Главная роль] ,[ ```sql BOOLEAN``` ],
[КодПьесы] ,[ Код пьесы (внешний ключ) ],[ ```sql SERIAL``` ],
[КодАктера] ,[ Код актера (внешний ключ) ],[ ```sql SERIAL``` ]
)
#v(20pt)
Таблица 10 -- Занятость роли в сценах
#v(-10pt)
#tablex(
columns: 3,
inset: 10pt,
align: center + horizon,
[Название колонки] ,[ Описание] ,[ Тип ],
[КодЗанятостиРоли] ,[ Код занятости роли в сценах (первичный ключ)],[ ```sql SERIAL``` ],
[КодРоли] ,[ Код роли (внешний ключ) ],[ ```sql SERIAL``` ],
[КодСцены] ,[ Код сцены (внешний ключ) ],[ ```sql SERIAL``` ]
)
#pagebreak()
=== Разработка бизнес-процессов предметной области
1. Регистрация нового актера
#h(-35pt)
[Запрос на регистрацию на роль получен] $arrow$ (Проверка полноты данных) $arrow$ [Данные полные] $arrow$ (Регистрация актера) $arrow$ [Актер зарегистрирован] $arrow$ (Заключение контракта с актером) $arrow$ [Контракт заключен]
2. Перенос репетиций и спектакля
#h(-35pt)
[Запрос на перенос получен]$arrow$(Изменение времени проведения спектакля)$arrow$[Спектакль перенесен]$arrow$(Проверка занятости актеров, с учетом занятости перенос репетиций)$arrow$ [Репетиции перенесены]
3. Постановка спектакля
#h(-35pt)
(Поиск пьесы)$arrow$
[Пьеса найдена]$arrow$
(Распределение ролей)$arrow$
[Роли распределены]$arrow$
(Читка)$arrow$
[Читка проведена]$arrow$
(Распределение сцен и репетиций)$arrow$
[Сцены и репетиции распределены]$arrow$
(Репетиции)$arrow$
[Репетиции завершены]$arrow$
(Назначение премьеры)$arrow$
[Спектакль поставлен]
== Реализация базы данных
=== Создание базы данных и таблиц
После анализа предметной области и создания датологической и инфологической моделей базы данных, приступим к ее реализации. Для анчала создадим саму базу данных в PostgreSQL (листинг 1).
#let ct = parserasm(read("createTables.sql"))
#code(funcstr(ct, "CREATE DATABASE Занятость_актеров_театра"), "sql", [Создаем новую базу данных])
Разработаем, на основании выделенных сущностей, таблицы в PostgreSQL (листинги 2-11).
#pagebreak()
#code(funcstr(ct, "CREATE TABLE Актеры (")+");", "sql", [Таблица Актеры])
#code(funcstr(ct, "CREATE TABLE Спектакли (")+");", "sql", [Таблица Спектакли])
#code(funcstr(ct, "CREATE TABLE Контракт (")+");", "sql", [Таблица Контракт])
#code(funcstr(ct, "CREATE TABLE ЗанятостьВСпектаклях (")+");", "sql", [Таблица ЗанятостьВСпектаклях])
#code(funcstr(ct, "CREATE TABLE Репетиции (")+");", "sql", [Таблица Репетиции])
#pagebreak()
#code(funcstr(ct, "CREATE TABLE СценыВРепетициях (")+");", "sql", [Таблица СценыВРепетициях])
#code(funcstr(ct, "CREATE TABLE Пьесы (")+");", "sql", [Таблица Пьесы])
#code(funcstr(ct, "CREATE TABLE Сцены (")+");", "sql", [Таблица Сцены])
#code(funcstr(ct, "CREATE TABLE Роли (")+");", "sql", [Таблица Роли])
#code(funcstr(ct, "CREATE TABLE ЗанятостьРолиВСценах (")+");", "sql", [Таблица ЗанятостьРолиВСценах])
=== Связывание таблиц
После создания таблиц необходимо вторичные ключи связать с первичными, для этого немного изменим таблицы (Листинги 12-24):
#v(10pt)
#pagebreak()
#code("ALTER TABLE Контракт
ADD CONSTRAINT fk_Контракт_Актеры FOREIGN KEY (КодАктера)
REFERENCES Актеры (КодАктера);", "sql", [Добавление внешнего ключа, связывающего\ актеров и контракты])
#v(10pt)
#code("ALTER TABLE ЗанятостьВСпектаклях
ADD CONSTRAINT fk_ЗанятостьВСпектаклях_Актеры FOREIGN KEY (КодАктера)
REFERENCES Актеры (КодАктера);", "sql", [Добавление внешнего ключа, связывающего\ актеров и их занятость в спектаклях])
#v(20pt)
#code("ALTER TABLE ЗанятостьВСпектаклях
ADD CONSTRAINT fk_ЗанятостьВСпектаклях_Спектакли FOREIGN KEY (КодСпектакля)
REFERENCES Спектакли (КодСпектакля);", "sql", [Добавление внешнего ключа, связывающего\ спектакли и занятость актеров в них])
#v(10pt)
#code("ALTER TABLE Репетиции
ADD CONSTRAINT fk_Репетиции_Спектакли FOREIGN KEY (КодСпектакля)
REFERENCES Спектакли (КодСпектакля);", "sql", [Добавление внешнего ключа, связывающего\ спектакли и репетиции])
#v(10pt)
#code("ALTER TABLE СценыВРепетициях
ADD CONSTRAINT fk_СценыВРепетициях_Репетиции FOREIGN KEY (КодРепетиции)
REFERENCES Репетиции (КодРепетиции);", "sql", [Добавление внешнего ключа, связывающего\ сцены в репетициях и репетиции])
#v(10pt)
#code("ALTER TABLE СценыВРепетициях
ADD CONSTRAINT fk_СценыВРепетициях_Сцены FOREIGN KEY (КодСцены)
REFERENCES Сцены (КодСцены);", "sql", [Добавление внешнего ключа, связывающего\ сцены в репетициях и сцены])
#v(10pt)
#pagebreak()
#code("ALTER TABLE Сцены
ADD CONSTRAINT fk_Сцены_Пьесы FOREIGN KEY (КодПьесы)
REFERENCES Пьесы (КодПьесы);", "sql", [Добавление внешнего ключа, связывающего\ пьесы и сцены])
#v(10pt)
#code("ALTER TABLE Роли
ADD CONSTRAINT fk_Роли_Пьесы FOREIGN KEY (КодПьесы)
REFERENCES Пьесы (КодПьесы);", "sql", [Добавление внешнего ключа, связывающего\ пьесы и роли])
#v(10pt)
#code("ALTER TABLE Роли
ADD CONSTRAINT fk_Роли_Актеры FOREIGN KEY (КодАктера)
REFERENCES Актеры (КодАктера);", "sql", [Добавление внешнего ключа, связывающего\ актеров и роли])
#v(10pt)
#code("ALTER TABLE ЗанятостьРолиВСценах
ADD CONSTRAINT fk_ЗанятостьРолиВСценах_Роли FOREIGN KEY (КодРоли)
REFERENCES Роли (КодРоли);", "sql", [Добавление внешнего ключа, связывающего\ занятость роли в сценах и роли])
#v(10pt)
#code("ALTER TABLE ЗанятостьРолиВСценах
ADD CONSTRAINT fk_ЗанятостьРолиВСценах_Сцены FOREIGN KEY (КодСцены)
REFERENCES Сцены (КодСцены);", "sql", [Добавление внешнего ключа, связывающего\ занятость роли в сценах и сцены])
#v(10pt)
#code("ALTER TABLE Спектакли
ADD CONSTRAINT fk_Спектакли_Пьесы FOREIGN KEY (КодПьесы)
REFERENCES Пьесы (КодПьесы);", "sql", [Добавление внешнего ключа, связывающего\ пьесы и спектакли])
=== Заполнение базы данных
Для начала необходимо продумать заполнение базы данных. Основной таблицей базы данных будет таблица занятости актеров в спектаклях -- в ней будет больше всего записей. По условию, данных записей должно быть не меньше миллиона. Количество актеров возьмем меньшее -- 1000 человек. Таким образом контрактов тоже должно быть не меньше 1000 (предположим, что у всех актеров один контракт -- контрактов тоже будет ровно 1000). Количество спектаклей возьмем побольше -- 2000 записей. Для одного спектакля в среднем требуется 30-40 репетиций, поэтому количество репетиций возьмем равным 80000. Количество сцен возьмем в 2 раза меньше -- 40000, а количество пьес пусть будет равно количеству спектаклей -- 2000. Количество ролей в спектакле совпадет с количеством занятости актеров, так как на одну роль предусмотрен один актер, то есть ролей тоже будет 1000000.
Для данного набора данных логическая составляющая все еще не очень верная, так как актер не может играть в 1000 спектаклях. Но если увеличивать количество актеров хотя бы до 100000 база данных будет весить около 60 Гб. Поэтому возьмем количество актеров меньшее, чем того требует логика, для тестирования хранения и управления данными этого хватит.
Перед тем, как перейти к заполнению таблиц необходимо разобраться с фото. Основных способов хранения фото в БД всего 2:
1. Хранение фото на внешнем носителе/в интернете, а в базе только ссылки/пути, таким образом сама база будет весить меньше, но это будет требовать дополнительной обработки, постоянный доступ к ресурсам, то есть уменьшается централизованность данных
2. Хранение фото в виде бинарной строки непосредственно в базе данных. Этот способ позволяет хранить фото непосредственно внутри базы.
Так как фото будут храниться в небольшом разрешении и для повышения централизованности данных я выбрал 2 способ хранения.
Сгенерировать осмысленные текстовые данные с помощью кода достаточно просто, но генерация картинок требует большой вычислительной мощности и хорошего обучения, поэтому для генерации фотографий актеров воспользуемя интернет-сервисом по генерации фото несуществующих людей #link("https://thispersondoesnotexist.com/"). Сервис не имеет защиты от ботов, поэтому напишем код, который 1000 раз обновит страницу и сохранит все 1000 сгенерированных людей в одну папку (Приложение А).
Добавление больших данных в базу требует небольшой подготовки. Необходимо отключить всю индексацию для столбца. Для этого выполним: ```sql ALTER TABLE "Актеры" DROP CONSTRAINT "Актеры_Фото_key";``` Теперь индексация для столбца Фото производиться не будет.
Общее время, которое ушло на генерацию 1000 фото заняло около 15 минут, при учете того, что в коде есть тайм-аут, чтобы не слишком сильно нагружать сайт.
Вот пример сгенерированного фото.
#img(image("imgs/6.jpeg", width:37%), [Пример сгенерированного изображения])
После генерации всех картинок остается только написать код для генерации остальных данных и вставки всех данных в БД.
Тут необходимо выбрать какой именно язык программирования использовать для наилучшей генерации данных. Я остановился на python, так как в библиотеке faker уже встроен русский язык. При такой генерации была обнаружена одна проблема: нельзя генерировать названия пьес и спектаклей. Для начала, как названия пьес и спектаклей, я взял просто обычные слова. Таким образом удалось за несколько минут сгенерировать и загрузить в базу данных основной набор данных. Так как данные грузились не равномерно во все таблицы, коды, которые представлены в листингах 12-23, я выполнил только после окончания генерации. (Приложение Б)
Но названия пьес и спектаклей все еще не были осмысленными. Поэтому я решиб обратиться к библеотеки faker, написанной для ruby. В этоой библиотеке нет русского языка, но есть генерация названий книг, поэтому я сгенерировал все названия пьес и спектаклей и внес их в таблицу. (Приложение В)
Так как названия были на английском их оставалось только перевести на русский. Поэтому был написан код, который делает именно это. (Приложение Г)
Итак, вот заполненные таблицы:
#img(image("10.png", width:50%), [Результат заполнения таблицы Актеры])
#img(image("11.png", width:45%), [Результат заполнения таблицы ЗанятостьВСпектклях])
#img(image("12.png", width:50%), [Результат заполнения таблицы ЗанятостьРолиВСценах])
#img(image("13.png", width:50%), [Результат заполнения таблицы Контракт])
#img(image("14.png", width:50%), [Результат заполнения таблицы Пьесы])
#img(image("15.png", width:50%), [Результат заполнения таблицы Репетиции])
#img(image("16.png", width:50%), [Результат заполнения таблицы Роли])
#img(image("17.png", width:50%), [Результат заполнения таблицы Спектакли])
#img(image("18.png", width:50%), [Результат заполнения таблицы Сцены])
#img(image("19.png", width:50%), [Результат заполнения таблицы СценыВРепетициях])
#pagebreak()
== Запросы и триггеры
=== Запрос 1
Запрос выбирает актеров, которые заняты более чем в одном спектакле, имеют более трех наград и хотя бы одну премию. Возвращаются их ФИО, список премий, количество спектаклей и звание награды. (Листинг 25, результат на рис. 14)
#code(funcstr(ct, "SELECT a.ФИО, премии.Премии, subquery.NumberOfPlays, a.ЗваниеНаграды"), "sql", [Запрос 1], size:14pt)
#img(image("3.png", width:100%), [Результат выполнения 1 запроса])
Используемые функции и концепции:
- `JOIN`: Объединение таблиц для получения данных.
- `GROUP BY` и `HAVING`: Группировка данных и фильтрация групп.
- `ARRAY_AGG` и `UNNEST`: Работа с массивами в PostgreSQL.
- `EXISTS`: Проверка наличия записей.
#pagebreak()
=== Запрос 2
Запрос выводит информацию об актерах, играющих главную роль в спектакле с бюджетом выше среднего и имеющих больше 5 сцен в этом спектакле, включая название спектакля, бюджет, ФИО актера, количество главных ролей и количество сцен в этих ролях. (Листинг 26, результат на рис. 15)
#code(funcstr(ct, "SELECT DISTINCT s.Название AS НазваниеСпектакля,"), "sql", [Запрос 2], size:14pt)
#img(image("4.png", width:100%), [Результат выполнения 2 запроса])
Используемые функции и концепции:
- `JOIN`: Объединение таблиц для получения данных.
- `GROUP BY`: Группировка данных.
- `HAVING`: Фильтрация групп.
- `COUNT`: Подсчет записей.
- `AVG`: Вычисление среднего значения.
- `ORDER BY`: Сортировка результатов.
#pagebreak()
=== Запрос 3
Запрос выводит информацию о действующих контрактах актеров, включая ФИО актера, дату подписания текущего контракта и список спектаклей, в которых актеры заняты. (Листинг 27, результат на рис. 16)
#code(funcstr(ct, "WITH CurrentContracts AS (") + funcstr(ct, "SELECT a.ФИО, cc.ДатаПриема AS ДатаПодписанияДействующегоКонтракта, ap.Спектакли"), "sql", [Запрос 3], size:12pt)
#img(image("5.png", width:80%), [Результат выполнения 3 запроса])
Используемые функции и концепции:
- `WITH`: Создание временных таблиц для упрощения запроса.
- `ARRAY_AGG`: Агрегация значений в массив.
- `JOIN`: Объединение таблиц для получения данных.
- `ORDER BY`: Сортировка результатов.
#pagebreak()
=== Запрос 4
Запрос выводит информацию о пьесах, включая название пьесы, название спектакля, количество наград и количество репетиций. В выборку входят только пьесы с наградами. (Листинг 28, результат на рис. 17)
#code(funcstr(ct, "SELECT p.Название AS НазваниеПьесы,"), "sql", [Запрос 4], size:10pt)
#img(image("6.png", width:55%), [Результат выполнения 4 запроса])
Используемые функции и концепции:
- `JOIN`: Объединение таблиц для получения данных.
- `LEFT JOIN`: Левое объединение для включения всех записей из левой таблицы.
- `UNNEST`: Работа с массивами в PostgreSQL.
- `GROUP BY`: Группировка данных.
- `HAVING`: Фильтрация групп.
- `COUNT`: Подсчет записей.
- `ORDER BY`: Сортировка результатов.
=== Запрос 5
Запрос выводит информацию о спектаклях, включая название спектакля, бюджет, количество актеров и количество сцен. Сортируется по количеству актеров. (Листинг 29, результат на рис. 18)
Так же добавим график зависимости количества сцен в спектакле и количества актеров от бюджета.(рис. 19)
#code(funcstr(ct, "SELECT s.Название AS НазваниеСпектакля, s.Бюджет, COUNT(DISTINCT z.КодАктера) AS КоличествоАктеров, "), "sql", [Запрос 5], size:14pt)
#img(image("7.png", width:70%), [Результат выполнения 5 запроса])
#img(image("9.png", width:90%), [Зависимость количества сцен в спектакле и количества актеров от бюджета])
Используемые функции и концепции:
- `JOIN`: Объединение таблиц для получения данных.
- `GROUP BY`: Группировка данных.
- `COUNT`: Подсчет записей.
- `ORDER BY`: Сортировка результатов.
#pagebreak()
=== Запрос 6
Запрос выводит информацию о занятости актеров в спектаклях и репетициях, включая ФИО актера, название спектакля, роль, дата и время репетиции, сцена и продолжительность сцены. (Листинг 30, результат на рис. 20)
#code(funcstr(ct, "SELECT a.ФИО AS Актер,"), "sql", [Запрос 6], size:12pt)
#img(image("8.png", width:80%), [Результат выполнения 6 запроса])
Используемые функции и концепции:
- `JOIN и LEFT JOIN`: Объединение таблиц для получения данных.
- `ORDER BY`: Сортировка результатов.
#pagebreak()
=== Триггер
Триггер обновляет стаж работы актера при вставке, обновлении или удалении записей в таблице "Контракт".(Листинг 31)
#code(funcstr(ct, "CREATE OR REPLACE FUNCTION обновить_стаж_работы() RETURNS TRIGGER AS $$") + funcstr(ct, "CREATE TRIGGER обновить_стаж_работы_триггер"), "sql", [Триггер])
Используемые функции и концепции:
- `TRIGGER`: Автоматическое выполнение функций при определенных действиях.
- `PL/pgSQL`: Процедурный язык PostgreSQL для написания триггерных функций.
- `AGE`: Вычисление разницы между датами.
- `COALESCE`: Возвращение первого ненулевого значения.
- `MIN и MAX`: Нахождение минимального и максимального значений.
= Заключение
В процессе выполнения данной работы были проведены анализы и проектирование базы данных "Занятость актеров театра".
- Был проведен детальный анализ предметной области, а ходе которого были выявлены следующие сущности: Контракт, Актеры, Занятость в спектаклях, Роли, Спектакли, Пьесы, Репетиции, Занятость роли в сценах, Сцены, Сцены в репетициях.
- Определены основные связи между сущностями, построена инфологическая и датологическая модель базы данных, разработаны бизнес-процессы.
- Был написан код для создания базы данных и таблиц.
- Была разработана модель вставки псеводорандомных, осмысленных данных и написан код для их генерации.
- Было написано 6 сложных запросов и триггер для базы данных.
= Список использованной литературы
+ Моргунов, Е. <NAME>. Основы языка SQL: учеб. пособие / Е. <NAME>; под ред. Е. <NAME>, <NAME>. — СПб.: БХВ-Петербург, 2018. — 336 с.: ил.
+ Новиков <NAME>. Основы технологий баз данных: учебное пособие / <NAME>, <NAME>, <NAME>; под ред. Е. В. Рогова. — 2-е изд. — М.: ДМК Пресс, 2020. — 582 с.
// Бунатян, Г. Г. Прогулки по рекам и каналам Санкт-Петербурга :
// путеводитель / Г. Г. Бунатян, <NAME>. – Санкт-Петербург : Паритет,
// 2007. – 254 с. – ISBN 978-5-93437-164-8.
#set heading(numbering: (..numbers) => {
})
#pagebreak()
#align(center)[#text(16pt)[*ПРИЛОЖЕНИЯ*]]
== Приложение А Генерация фотографий
#code(read("genphoto.py"), "py", [Генерируем 1000 фото людей])
#pagebreak()
== Приложение Б Генерация основного объема данных
#code(
"
import psycopg2
from faker import Faker
import random
fake = Faker('ru_RU')
awards_list = [
'Лучшая мужская роль', 'Лучшая женская роль', 'Лучшая роль второго плана',
'Выдающееся исполнение', 'Премия за вклад в искусство', 'Лучшая новая звезда',
'Премия критиков', 'Премия зрительских симпатий', 'Лучшая комедийная роль',
'Лучшая драматическая роль', 'Лучший актерский ансамбль', 'Лучший актер озвучивания',
'Лучший международный актер', 'Лучшая роль в главной роли', 'Лучшая роль второго плана',
'Лучшее исполнение в короткометражке', 'Лучшее исполнение в полнометражном фильме',
'Лучшее исполнение в спектакле', 'Лучшее исполнение в мюзикле',
'Лучшее исполнение в телесериале', 'Лучшее исполнение в веб-сериале',
'Лучшее исполнение в рекламе', 'Лучшее исполнение в музыкальном видео',
'Лучшее исполнение в анимационном фильме', 'Лучшее исполнение в видеоигре',
'Лучший детский актер', 'Лучший подростковый актер', 'Лучший актер старшего возраста',
'Лучший мужской актер', 'Лучшая женская актерская роль', 'Лучший трансгендерный актер',
'Актер года', 'Лучший прорыв', 'Лучшее гостевое исполнение', 'Лучшее камео',
'Лучший злодей', 'Лучший герой', 'Лучший дуэт', 'Лучший актерский дебют',
'Лучшее исполнение в исторической роли', 'Лучшее исполнение в научно-фантастической роли',
'Лучшее исполнение в фэнтезийной роли', 'Лучшее исполнение в роли ужасов',
'Лучшее исполнение в боевой роли', 'Лучшее исполнение в комедийной роли',
'Лучшее исполнение в драматической роли', 'Лучшее исполнение в романтической роли',
'Лучшее исполнение в триллере', 'Лучшее исполнение в военной роли',
'Лучшее исполнение в вестерне', 'Лучшее исполнение в документальном фильме'
]
def insert_actors(cursor):
for i in range(1000):
name = fake.name()
birth_date = fake.date_of_birth(minimum_age=18, maximum_age=65)
f = open(f'/Volumes/pr/BDkurs/imgs/{i+1}.jpeg', 'rb')
photo = f.read()
f.close()
experience = f'{random.randint(1, 50)} years'
awards = random.sample(awards_list, random.randint(0, 10))
cursor.execute(
'INSERT INTO \'Актеры\' (\'ФИО\', \'ДатаРождения\', \'Фото\', \'СтажРаботы\', \'ЗваниеНаграды\') '
'VALUES (%s, %s, %s, %s, %s)',
(name, birth_date, photo, experience, awards)
)
"
, "py", [Генерируем актеров], size:10pt)
#pagebreak()
#code(
"
def insert_plays(cursor):
for i in range(2000):
title = fake.sentence(nb_words=random.randint(2,3), variable_nb_words=True)
budget = random.randint(1000, 10000)
year = random.randint(1900, 2023)
age_limit = f'{random.randint(0, 18)}+'
cursor.execute(
'INSERT INTO \'Спектакли\' (\'Название\', \'Бюджет\', \'ГодПостановки\', \'ОграничениеПоВозрасту\', \'КодПьесы\') '
'VALUES (%s, %s, %s, %s, %s)',
(title, budget, year, age_limit, i + 1)
)
def insert_contracts(cursor):
for i in range(1000):
start_date = fake.date_between(start_date='-20y', end_date='today')
end_date = fake.date_between(start_date='today', end_date='+7y')
salary = random.randint(30000, 100000)
cursor.execute(
'INSERT INTO \'Контракт\' (\'ДатаПриема\', \'ДатаУвольнения\', \'Ставка\', \'КодАктера\') '
'VALUES (%s, %s, %s, %s)',
(start_date, end_date, salary, i + 1)
)
def insert_employment(cursor):
for _ in range(1000000):
actor_id = random.randint(1, 1000)
play_id = random.randint(1, 2000)
cursor.execute(
'INSERT INTO \'ЗанятостьВСпектаклях\' (\'КодСпектакля\', \'КодАктера\') '
'VALUES (%s, %s)',
(play_id, actor_id)
)
def insert_rehearsals(cursor):
for _ in range(80000):
date_time = fake.date_time_between(start_date='-20y', end_date='now')
duration = f'{random.randint(1,4)}:{random.randint(0, 59)}:00'
read_through = fake.boolean()
play_id = random.randint(1, 2000)
cursor.execute(
'INSERT INTO \'Репетиции\' (\'ДатаВремя\', \'Продолжительность\', \'Читка\', \'КодСпектакля\') '
'VALUES (%s, %s, %s, %s)',
(date_time, duration, read_through, play_id)
)
def insert_scenes(cursor):
for i in range(40000):
title = f'{fake.sentence(nb_words=random.randint(2,3), variable_nb_words=True)}'
duration = f'00:{random.randint(1, 30)}:00'
play_id = random.randint(1, 2000)
cursor.execute(
'INSERT INTO \'Сцены\' (\'Название\', \'Продолжительность\', \'КодПьесы\') '
'VALUES (%s, %s, %s)',
(title, duration, play_id)
)
"
, "py", [Генерируем пьесы, контракты, занятость, репетиции и сцены], size:10pt)
#pagebreak()
#code(
"
def insert_roles(cursor):
for i in range(1000000):
title = fake.first_name() + ' ' + fake.last_name()
main_role = fake.boolean()
play_id = random.randint(1, 2000)
actor_id = random.randint(1, 1000)
cursor.execute(
'INSERT INTO \'Роли\' (\'НазваниеРоли\', \'Главная\', \'КодПьесы\', \'КодАктера\') '
'VALUES (%s, %s, %s, %s)',
(title, main_role, play_id, actor_id)
)
def insert_role_engagement(cursor):
for _ in range(1000000):
role_id = random.randint(1, 1000000)
scene_id = random.randint(1, 40000)
cursor.execute(
'INSERT INTO \'ЗанятостьРолиВСценах\' (\'КодРоли\', \'КодСцены\') '
'VALUES (%s, %s)',
(role_id, scene_id)
)
def insert_scenes_in_rehearsals(cursor):
for _ in range(80000):
rehearsal_id = random.randint(1, 80000)
scene_id = random.randint(1, 40000)
cursor.execute(
'INSERT INTO \'СценыВРепетициях\' (\'КодРепетиции\', \'КодСцены\') '
'VALUES (%s, %s)',
(rehearsal_id, scene_id)
)
def insert_plays_details(cursor):
for i in range(2000):
title = f'{fake.sentence(nb_words=random.randint(2,3), variable_nb_words=True)}'
year = random.randint(1900, 2023)
author = fake.name()
cursor.execute(
'INSERT INTO \'Пьесы\' (\'Название\', \'ГодВыпуска\', \'Автор\') '
'VALUES (%s, %s, %s)',
(title, year, author)
)
"
, "py", [Генерируем роли, роли в сценах, сцены в репетициях, пьесы], size:12pt)
#pagebreak()
#code(
"
def main():
try:
conn = psycopg2.connect(
dbname='Занятость актеров театра',
user='pluttan',
password=input('Password: '),
host='localhost',
port='5432'
)
print('Connected to the database')
cursor = conn.cursor()
print('generation actors')
insert_actors(cursor)
conn.commit()
print('generation plays')
insert_plays(cursor)
conn.commit()
print('generation contracts')
insert_contracts(cursor)
conn.commit()
print('generation employment')
insert_employment(cursor)
conn.commit()
print('generation rehearsals')
insert_rehearsals(cursor)
conn.commit()
print('generation scenes')
insert_scenes(cursor)
conn.commit()
print('generation roles')
insert_roles(cursor)
conn.commit()
print('generation role engagement')
insert_role_engagement(cursor)
conn.commit()
print('generation scenes in rehearsals')
insert_scenes_in_rehearsals(cursor)
conn.commit()
print('generation plays details')
insert_plays_details(cursor)
conn.commit()
print('Data inserted successfully')
except Exception as e:
print(f'Error: {e}')
finally:
if conn:
conn.close()
if __name__ == '__main__':
main()
"
, "py", [Вызываем все функции и записываем в базу], size:12pt)
#pagebreak()
== Приложение B Генерация названий пьес и спектаклей
#code(read("genbook.rb"), "rb", [Перегенерируем названия пьес и спектаклей, заменяя их на осмысленные], size:11pt)
#pagebreak()
== Приложение Г Перевод названий пьес и спектаклей
#code(read("genbook.py"), "py", [Переводим все названия на русский язык], size:11pt)
// = Использованная литература
|
|
https://github.com/SoraShu/HITsz-Lab-report-Template | https://raw.githubusercontent.com/SoraShu/HITsz-Lab-report-Template/main/README.md | markdown | # HITsz Lab-report Template
用于 HITsz 实验报告的 Typst 模版，轻量、低配置。
## 目的
此模版目标在于解决以下问题：
- 实验报告只能使用可以编辑 docx/doc 格式文件的富文本编辑器。这类编辑器大多存在兼容性问题，不一定在各个系统上运作良好，给使用某些操作系统的用户带来了困扰。
- 实验报告模版由 [MS Word](https://www.microsoft.com/en-ww/microsoft-365/word) 制作，在其它编辑器上可能出现排版错位。~~且 MS Word 需要付费购买，购买此软件可能给经济困难的同学带来经济压力。~~
- 实验老师对于是否使用模版态度比较模糊，但如果使用无格式的 plaintext 或者通过 markdown 等标记语言不加排版地生成 PDF 实验报告，实验老师可能不接受，而且给实验批改带来障碍。
因此本模版致力于提供一个开源跨平台的编写实验报告的方案，且此方案生成接近实验报告模版的产物。
## Why Typst
下面列出使用 Typst 之前我尝试过的工具，以及我为什么最终放弃使用。
- Markdown: 热门的标记语言。他的主要问题在于他只是一个等价于 HTML 的标记语言（甚至比 HTML 更弱，使用时时常需要嵌入 HTML），并不能很方便地支持复杂排版，且对于某些格式需要如何实现我毫无头绪，如页脚和页眉。
- Latex: 著名的排版系统。我在编写 Latex 模版上缺乏经验，整理出来的模版效果不佳。且 Latex 整套工具链较重。
Typst 可以说是介于以上两者之间。用它来编写文档上手很快，但它同时是一个较为完整的排版系统。同时 Typst 是一个轻量级的工具，本身配置也较为简单，0 配置下的效果就相当不错。
## 如何使用
安装 Typst 的 cli 工具，具体安装参考 [typst#installation](https://github.com/typst/typst#installation)。
clone 本项目，将本项目安装为本地包
```bash
./install.sh
```
该脚本默认会将包安装到 `${XDG_DATA_DIR}/typst/packages/${TYPST_LOCAL_NAMESPACE}/hitsz-lab-report-template/${VERSION}`。可以通过 export 对应环境变量的形式自定义该路径。
随后可以使用 Typst 自带的模版初始化功能在对应目录下初始化您的项目:
```bash
# 若您使用了自定义的环境变量, 请自行修改下面的命令
typst init @local/hitsz-lab-report-template:1.0.0 ${PROJECT_NAME}
```
## 说明
没有看过其它专业的实验报告模版，不确定是否可用于非计算机科学与技术学院的实验报告。
目前模版排版和实验报告的模版并不是 1:1 复刻，鉴于实验报告模版格式也不尽相同，本模版也无力 cover 实验报告的所有格式变体。
对于实验报告能否用本模版编写，以及本模版的产物能否作为实验报告提交，最终解释权在于接收实验报告的老师或助教，本项目不做任何保证。
## TODO
- [ ] 支持自定义各级标题的序号格式。
- [ ] 支持代码块显示行号。（等待 Typst 支持此特性）
- [ ] 线上编辑。（需要将字体同时上传）
## 参考
本模版几乎是从 [github:werifu/HUST-typst-template](https://github.com/werifu/HUST-typst-template) 修改而成，在此特别感谢。
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https://github.com/Myriad-Dreamin/apollo-typst | https://raw.githubusercontent.com/Myriad-Dreamin/apollo-typst/main/typ/posts/simple-se/main.typ | typst | #import "/typ/template/pages.typ": *
#show: blog-page.with(title: "Simple SE")
这篇博客是一篇随笔。每个小段之间的直接联系不大，但具有渐进性和隐含关联。
== 笨蛋如何进行架构设计
每个人都应该有追求其梦想的权利，但是梦想不是每个人都能实现的。f例如，每个程序员可能或多或少地拥有几个他们设计的软件，他们将以不成熟的经验接触艰难的软件架构。但当回顾最终软件以怎样意外的方式运行的时候，他可能便会认识到当初在软件架构上犯下了某些严重的错误。但也正和追逐梦想一样，只有最顶尖的程序员才能设计出一个很好的软件架构实际上不是一个严格成立的东西。我觉得，至少有一些值得分享的东西。
== 阅读和学习软件设计的方法
有一个我个人觉得很好的习惯，那就是会时常快速浏览一些可能有趣的仓库代码，并尝试总结这个仓库在控制流过程中以怎么样的方式展开他们的代码。你需要时常找一些项目，并尝试在数分钟或数十分钟内渐进地了解该软件的总体架构。这是一个需要锻炼的技能，并且是我认为一个好的程序员最需要掌握的基础技能之一。
有时候，一个人不尝试便总是高估他在这方面的能力。一个有趣的随堂测试是：当你在阅读一个超级项目的时候，是否曾经查找过它的程序入口在哪个文件里。这里，我用了程序入口这个更泛指的名词，因为“一段代码”可能没有main函数。“一段代码”可能还是某个大组件的小组件。这时候并没有一个明显的main，而只有一个constructor或者init函数供其他代码调用。
例如，在很多年前研究QEMU的某个虚拟设备的时候。首先我看到它的main函数首先解析了相当多的配置，并创建了一系列注入了配置的QObject。然后主线程会进入main loop。接着主线程还会区分IO线程和非IO线程（CPU线程）。当虚拟中断来临的时候，如果这个虚拟机以KVM Backend的方式启动的时候，一个回调会从KVM退出开始处理中断，并有可能发送事件给IO线程。最终虚拟设备会接受事件，模拟硬件并作出响应。
这里，你不需要多仔细，只需要快速浏览，把控制流简单梳理一遍，就能对你阅读虚拟设备的代码大有裨益。从虚拟设备视角来看，当虚拟设备所掌握的内存被分配出来后，它无论如何会挂在Machine设备树上的某处。这个设备树是在解析配置的时候形成的，有可能调用虚拟设备相关的初始化代码。接着在main loop里，在IO线程上下文中，以例如MMIO的方式，调用虚拟设备的处理函数代码。
如果你梳理了这些东西，你很容易就能判断一个代码中复杂的条件嵌套的代码之间的关联，在脑中模拟和思考代码背后的逻辑。同时，你也能更好地理解代码的软件结构，理解庞大宏伟的软件如何将组件井井有条地组织和使用起来。
== 最小状态设计和局部推理
我学习的第一个程序语言是`C++`。我从前辈学到的第一个诫言是：不要使用`using namespace std;`。紧接着我学到的第二个诫言是：如非必要，少使用全局变量。我在后来的学习过程中找到了一个合理诠释这些警世名言较好的总结：它不利于局部推理。
局部推理是一个比较老但有趣的哲学概念，并在程序分析领域（据我所知）中有所借鉴。它是指在某些假设下你可以根据一部分逻辑推断程序整体的性质。我无意详细介绍和展开局部推理这一概念，但是我会以不严谨但夸张的描述表述这一概念。
对于不要使用`using namespace std;`，从两例可以看出一些端倪。首先，如果你在全局引入了`std`中所有的对象，当你快速浏览到一些函数调用的时候，便很难快速思考调用的作用和影响。例如，一个`bind`函数，在引入`std`前，它可能是linux的bind系统调用，与网络相关；引入之后就变成了`std::bind`，一个抽象的c++内置函数。在引入`std`之后，阅读代码的时候便需要额外思考这个函数究竟是其中的哪一个；如果你忽略了这个语句，甚至会进行误判。如果你的代码让人相信没有使用`using namespace std;`，反之，你的代码就和`std`本身隐式无关了。其次，个人认为，引入`std`中所有的对象并非严格不可取。例如，你可以在某个函数的函数体中使用`using namespace std;`，节省反复使用`std::`引用标准库函数。这同样可以用局部推理解释。当我们在看这个函数实现的时候，首先被提醒引入了`std`的所有对象，我们便局部性让脑中的编译器记得加载`std`所有相关函数。
那么，少使用全局变量呢？这个问题的答案也是类似的。因为全局变量可能会在任何地方被修改。很夸张地举一个例子，你的代码对局部某个计数器加一的时候，都有可能导致全局变量内容的变化。比如，这个全局变量可能是一个桩，在虚拟机中运行的时候，虚拟机会知道你改了局部计数器，同步帮助修改全局变量的内容。
少使用全局变量在人类推理程序逻辑时是小问题，但在机器证明程序正确性的时候其严重性便被放大很多。不夸张地举一个例子，相比C++，Rust为了方便机器推断变量的借用，它对访问全局变量进行了限制。Safe Rust无法访问全局变量，所以Rust可以知道全局变量不会对Safe代码造成任何*借用*上的影响。Unsafe Rust可以访问全局变量，这个时候读代码的时候就很累了，Rust编译器则甚至摆烂不再进行严格的借用检查。
这同时还涉及到一个软件架构上的设计。为什么说我们推崇最小状态设计。因为，这样不仅人类和机器更有可能正确推理你的代码逻辑，条理性的背后还诱导我们编写更不易出错的代码。
== 最简抽象和单体对象架构
我理解你在软件架构上可能遇到了设计难点，所以为什么不选择摆烂呢。借用一句名言：没有设计，亦是设计（No Design is a Design，By me）。所谓：始终摆烂，亦是自律（划去）。
这句话是有道理的，抽象得越多就越难理解，没用的代码也随之增加。很多时候，将main函数分成很多个函数不如所有事情只在main函数中做完。在代码后期，这个规则可能被打破，但是一定不是在早期。因为我经常会考虑你对程序背后代表的逻辑认识还不够充分，这个时候，并没有必要抽象出接口，甚至是结构体来细化逻辑。
考虑对一个用户密码进行校验的C语言程序。按照直觉，应该先读取用户名，再读取用户密码。如果密码有误，就`return 1`。
```c
int main() {
std::string username;
std::string password;
// Read Username
// Read Password
// Check Password
return 0;
}
```
接下来，猜猜要怎么做。正常人可能会说，要继续完成注释所指示的代码。但是，夸张一点说，这个程序已经编写完了。因为不做任何校验的话，这个程序没有安全漏洞，并且“做了校验这一件事”。在main函数的最后，我们返回了`0`，表示程序认为用户密码没有问题。
我认为，你软件的第一步已经做到了，至少在这一步，从构建程序到程序运行，所有流程都走通了。甚至，你的代码里还包含了对该程序的宏伟设想，并让人觉得这真的是一个用户密码进行校验的C语言程序。
再接下来，我们思考，`username`应该会从stdin输入，`password`则是从一些特定权限的文件夹中读取。
```c
int main() {
std::string username;
std::string password;
// Read Username
{
std::cin >> username;
}
// Read Password
{
std::ifstream password_file("<PASSWORD>");
password_file >> password;
}
// Check Password
{
std::string password_input;
std::cin >> password_input;
if (password_input != password) {
return 1;
}
}
return 0;
}
```
再接下来，可能会有很多抽象，但是我觉得这一步也足够了。首先，它是一份面向过程代码，简明意赅，无法出错。虽然，它可能存在很多问题，甚至一点也不安全，但是这比直接返回`0`要更安全不是么？
我觉得到这里，两个重要的软件架构思想就已经足够易懂了。
所谓最简抽象，就是你的代码始终更专注具体的事情。这样代码会始终保持在众多提供该功能的可能性中，始终维持一个容易理解和修改的复杂度。举一个现实中的例子，著名的项目rsync在它的第一个Commit https://github.com/RsyncProject/rsync/blob/c627d61324e9dcd5df833ee6236dd10415f5bac4/main.c，就体现了这种思想。main函数思路清晰，展开了逻辑，并且甚至有部分逻辑沿用至今。
最简抽象的代码不是不作出抽象。例如，就以上代码，很容易作出正确的抽象。首先我们会有一个`Password Provider`抽象，它声明了某种获取密码的方式。然后，`password`和`// Check Password`可以抽象为`Password Provider`的一个方法，以防止密码明文出现在栈上。最后`username`可能不必抽象，在相当长的一段时间内维持从`cin`读入的代码。
所谓单体对象架构，就是有一个最主要的对象，它从`main`演化而来。众多抽象机制和对象栖居在这个对象上，生生灭灭。例如，Linux系统就保持了这样的架构，并获得了成功。
最简抽象的代码不一定遵守单体架构，但很容易整体或局部形成单体架构。我认为这样的代码是非常容易阅读和改进的。
== 模块化和敏捷开发思想
接着，我想将话题切入另一个极端，谈谈如何模块化。但是，我将要说的并不违背之前的逻辑。
我们不谈模块化具体如何实施。我想说的一件事是模块甚至接口是如何自然形成的。我们还是举一个极端例子。在巨型的项目中，我们该如何让一个功能具体而敏捷地落地。假设，我们已经说服了功能的必要性。根据最简抽象，我认为，最简单的方法就是首先引入一个flag，这个flag决定你写的简陋代码是否运行。然后在flag条件分支下，实现你第一份简陋代码。随着开发，直到项目的维护人员和你都觉得代码足够好了，再把flag移除或者默认打开。如果flag不移除，一个模块就自然诞生了。
这在某种程度上符合了敏捷开发思想，但是我认为却比敏捷开发要更直指核心。我们总是倾向于将代码逻辑以无争议的方式一步步引入项目并加以复杂化。如果你的代码完整实现预估有1万行，那么是否能拆分成20个PR。每个PR都只有500行，并恰当地将一部分代码复杂化，引入一些容易讨论的抽象。我想这将有可能比一次性PR所有内容要来得更快。因为，你可以中途还会额外写几万行自以为是的代码（至少未经讨论），可能都在最终的代码中移除。甚至，假设一个功能需要由1000行代码实现，如果我有一个方式允许将其拆分，并且先后都可以验证各自的正确性，由于*flag*技巧的存在性，我们不如将残缺功能的PR先提出来。首先，一部分代码在更早的时机开始被讨论。其次，还会减少完整功能PR在经历项目开发过程中遭到意外损坏而不得不修复的额外工作量。
我还想指出的是，移除抽象并非可耻或者令人尴尬的。为了敏捷开发，很多的时候我们会大致描摹可能的发展方向，并且适当引入复数的，相互合作的抽象。这个时候，如果有机会，在观察到一些可以合并的抽象的时候，根据最简抽象。别忘了我们还假设自己是笨蛋，那么便不总会作出正确的决定，那么这样的PR就应当会发生。这样，你的项目将更容易引入其他更合适的抽象或者实现。
不仅如此，一个成功的抽象，最终经常会被反复使用，甚至被滥用。这也符合最简抽象原则。在Linux系统中，一切皆文件是大家所熟知的。但是众多的文件实现中，有多少是真正无争议的文件也是大家心知肚明的。这其中的缘由就是，文件抽象是最详尽定义的，最广泛支持的。一旦你的对象实现了文件抽象，相当多的假设就引入了读你代码的人们的脑中。设想他们在《阅读和学习你的软件设计》，那么一旦读到你的对象支持文件抽象，那么这个对象可以如何在系统中被初始化和使用就变得不言而喻了。
== 后记
写得有点累了，为了防止博客难产（），我决定先将我的500行代码，以草稿的内容放出。后续还会对这篇博客分批多次进行更新。
// == 文档和类型标记
// == 大而粗放的集成测试
// == 小而精确的单元测试
// == 观察与测试程序的方法
// == 为你的软件组织一次报告会
// 接下来我会分为几点讲述软件工程方法：
// - 开发。作为一个软件项目，至少应该写点代码吧......
// - 测试。作为一个笨蛋写出的代码，不测试肯定会以很滑稽的方式运行把......
// - 运营。作为一个笨蛋写出的项目，不运营一下难道会主动有人来看你吗？
// 同时，我会按照时间顺序讲述，项目的各个阶段有哪些注意的点。
// - 起始阶段，这时我应该开始写项目或开始写项目的子项目。
// - 发展阶段，我要开始盘项目了，过程有可能惨不忍睹。
// - 优化阶段，项目写完了该是要改进一下。
// 同时，读者应该注意，接下来所有的策略都是可以灵活择取实施的。第一原则：无论做什么事情，都不如不做更简单，除非你觉得有什么用；第二原则：无论做什么，都应该以你开心为主。
// == 项目应该始终维持在稳定状态
// == 优先采用让项目更快恢复到稳定状态的方法
// == 优先采用更易定位问题的架构
// == 优先健康指标
// ==
// // == 在代码量为零的时候，我该如何起手
// // 个人有两种起手式，并且我推荐在不同的知识储备前提下使用不同的起手式。
// // 如果我对我的项目所使用的语言或框架很不熟悉，那么我应该先去找找有没有*任意*一个项目模板，甚至是成熟项目。对于流行语言或者流行框架，找一个模板是很容易的事情。如果能找到这样一个模板，我就避免了项目跑不起来的窘境。如果框架不是那么流行，那总该有至少有一个拿这个框架写的项目吧，找其中最多人用且较简单的项目起手则是较好的选择。
// // 这里还有一个重点。我应该先想办法不修改任何代码，把demo跑起来。如果demo跑不起来，说明我环境有问题。否则，应该检查环境。在环境有问题的情况下开始项目，有可能将来会为解决一些微妙的环境问题而花费一整天，甚至数天时间。
// // 如果我对语言或框架挺熟悉的，*而且我打算完成一个长期项目*，那么我应该从空项目或我完全掌握的模板开始，从编写我项目Build System脚本开始，一步步将一个最小可运行demo构建起来。
// // 这便是我们常说的跑demo阶段。
// // == 见微知著解决问题的能力
// // 从零开始，这也是非常重要的一点。我们可能不是高手，但仍然需要有对我将来项目中所能见的任何问题都有*见微知著*的能力。不然，糊里糊涂地开始将会为我们项目的发展埋下重大隐患。比如，将来可能发生耗费几天时间解决一个小问题的情况。
// // *见微知著*事实上是一个相对概念。说得哲学一点，究竟多微末的原因，才能反应一个显著的结论；究竟原因探究到何种程度，才能得到严格基础性的结论。这个程度，取决于我们的笨蛋值。拿米粒作比喻，一粒米不是一堆米，一千粒米应该是一堆米，但是具体到多少粒米算作一堆米，这个取决于客观米堆的形状和主观人的感受。真正的高手，恐怕能够不探究任何原因，就推断出可能问题所在。但很不幸，我们可能真的是笨蛋。
// // 那么，既然*见微知著*有这样的特性：我能把握项目的每个*层级*的细节就变得尤为重要。这些将会帮助我们更好地定位问题。同时还要知道，这个世界是残酷的，将来的问题有可能发生在任何*层级*上。如果定位错了*层级*，可能会灾难性地浪费漫长的时间解决简单的问题。项目是有*层级*的，所谓，环境上有构建系统，构建系统构建项目，项目包含组件，组件实现功能，功能由多个函数协作完成，函数内每个语句都负责一个*原子逻辑*。
// // 那么，*见微知著*的能力似乎也是可以后天改进的。想象当我遇到一个问题的时候，我应该*二分*地在大的层级上定位一个问题，然后在小的层级里捉到那导致的问题的寥寥几行代码。这就要求我们对是否在该层级下发生问题做出准确判断。
// == 为什么说从空项目开始是重要的
// 回到软件工程主题。这并非严格指一定要真的从空项目开始，这是指上手一个复杂的工程项目，你一定要对每一个步骤都非常熟悉。当然并非要一开始就掌握所有步骤的每个细节，但是若想成为高手，你最终仍需掌握每个细节。
// 这个掌握的过程，很有可能是分多层的广度优先搜索的过程。
// // - 天地未分，神写下了世界上第一个编译器，那个元编译器。
// // - 我用的编译器是由元编译器编译出来的。
// // - 我用的操作系统是由编译器编译出来的。
// // - 我的环境是由操作系统和Profile脚本构造出来的。
// // - 我的程序是由环境下的Build System构建出来的。
// // - 我的软件从一个程序入口开始，逐渐启动多个程序，为用户构建服务。
// // - 我的每个程序可能还有会话或状态，用户每次点击都要累计一个可能有问题的状态。
// // 用户在你写的酒吧软件，点了一盘炒饭，然后酒吧爆炸了。现在要探究问题了，问题又未必不是元编译器里的某个bug导致的。你可能会说：这怎么可能是高手代码导致的问题，肯定是我的代码有问题。不错，事实上，这句反驳已经反映了获得*见微知著*能力的方法。常规下只不过将第一个检查的点放在思考程序问题本身之上。
// // 设想你自己已经成功在你自己机器上成功用炒饭炸掉了酒吧，现在是解决问题时间。
// // - 如果曾经某个版本的酒吧软件不会有炒饭问题，那么我们可以定位到一个版本期间所作的事情导致了炒饭问题。
// // - 回退到版本：
// // - 构建的软件复现了问题。很好，不是构建步骤及以前的问题。
// // - 构建的软件没能复现问题。那么应该就是构建/发布脚本的问题，构建出了一个有问题的软件。
// // - 检查构建/发布脚本的修改情况。
// // - 检查构建机器。
// // - 一路检查到发电厂......
// == 起手式可能关乎到我们头发的数量
|
|
https://github.com/typst/packages | https://raw.githubusercontent.com/typst/packages/main/packages/preview/fletcher/0.3.0/src/marks.typ | typst | Apache License 2.0 | #import "@preview/cetz:0.1.2"
#import "utils.typ": *
#import calc: sqrt, abs, sin, cos, max, pow
#let EDGE_ARGUMENT_SHORTHANDS = (
"dashed": (dash: "dashed"),
"dotted": (dash: "dotted"),
"double": (extrude: (-2, +2), mark-scale: 110%, mark-variant: 2),
"triple": (extrude: (-4, 0, +4), mark-scale: 150%, mark-variant: 3),
"crossing": (crossing: true),
)
#let parse-arrow-shorthand(str) = {
let caps = (
"": (none, none),
">": ("tail", "head"),
">>": ("twotail", "twohead"),
"<": ("head", "tail"),
"<<": ("twohead", "twotail"),
"|>": ("solidtail", "solidhead"),
"<|": ("solidhead", "solidtail"),
"|": ("bar", "bar"),
"||": ("twobar", "twobar"),
"o": ("circle", "circle"),
"O": ("bigcircle", "bigcircle"),
)
let lines = (
"-": (:),
"=": EDGE_ARGUMENT_SHORTHANDS.double,
"==": EDGE_ARGUMENT_SHORTHANDS.triple,
"--": EDGE_ARGUMENT_SHORTHANDS.dashed,
"..": EDGE_ARGUMENT_SHORTHANDS.dotted,
)
let cap-selector = "(|<|>|<<|>>|hook[s']?|harpoon'?|\|\|?|o|O|<\||\|>)"
let line-selector = "(-|=|--|==|::|\.\.)"
let match = str.match(regex("^" + cap-selector + line-selector + cap-selector + "$"))
if match == none {
panic("Failed to parse '" + str + "' as a edge style shorthand.")
}
let (from, line, to) = match.captures
from = if from in caps { caps.at(from).at(0) } else { from }
to = if to in caps { caps.at(to).at(1) } else { to }
if line == "=" {
// make arrows slightly larger, suited for double stroked line
if from == "head" { from = "doublehead" }
if to == "head" { to = "doublehead" }
} else if line == "==" {
if from == "head" { from = "triplehead" }
if to == "head" { to = "triplehead" }
}
(
marks: (from, to),
..lines.at(line),
)
}
/// Take a string or dictionary specifying a mark and return a dictionary,
/// adding defaults for any necessary missing parameters.
#let interpret-mark(mark) = {
if mark == none { return none }
if type(mark) == str {
mark = (kind: mark)
}
mark.flip = mark.at("flip", default: +1)
if mark.kind.at(-1) == "'" {
mark.flip = -mark.flip
mark.kind = mark.kind.slice(0, -1)
}
let round-style = (
size: 7, // radius of curvature, multiples of stroke thickness
sharpness: 24deg, // angle at vertex between central line and arrow's edge
delta: 54deg, // angle spanned by arc of curved arrow edge
)
if mark.kind in ("head", "harpoon", "tail") {
round-style + mark
} else if mark.kind == "twohead" {
round-style + mark + (kind: "head", extrude: (-3, 0))
} else if mark.kind == "twotail" {
round-style + mark + (kind: "tail", extrude: (-3, 0))
} else if mark.kind == "twobar" {
(size: 4.5) + mark + (kind: "bar", extrude: (-3, 0))
} else if mark.kind == "doublehead" {
// tuned to match sym.arrow.double
(
kind: "head",
size: 9.6,
sharpness: 19deg,
delta: 43.7deg,
)
} else if mark.kind == "triplehead" {
// tuned to match sym.arrow.triple
(
kind: "head",
size: 9,
sharpness: 25deg,
delta: 43deg,
)
} else if mark.kind == "bar" {
(size: 4.5) + mark
} else if mark.kind in ("hook", "hooks") {
(size: 2.88, rim: 0.85) + mark
} else if mark.kind == "circle" {
(size: 2) + mark
} else if mark.kind == "bigcircle" {
(size: 4) + mark + (kind: "circle")
} else if mark.kind in ("solidhead", "solidtail") {
(size: 10, sharpness: 19deg) + mark
} else {
panic("Cannot interpret mark: " + mark.kind)
}
}
/// Calculate cap offset of round-style arrow cap,
/// $r (sin θ - sqrt(1 - (cos θ - (|y|)/r)^2))$.
///
/// - r (length): Radius of curvature of arrow cap.
/// - θ (angle): Angle made at the the arrow's vertex, from the central stroke
/// line to the arrow's edge.
/// - y (length): Lateral offset from the central stroke line.
#let round-arrow-cap-offset(r, θ, y) = {
r*(sin(θ) - sqrt(1 - pow(cos(θ) - abs(y)/r, 2)))
}
#let cap-offset(mark, y) = {
mark = interpret-mark(mark)
if mark == none { return 0 }
let offset() = round-arrow-cap-offset(mark.size, mark.sharpness, y)
if mark.kind == "head" { offset() }
else if mark.kind in ("hook", "hook'", "hooks") { -2.65 }
else if mark.kind == "tail" { -3 - offset() }
else if mark.kind == "twohead" { offset() - 3 }
else if mark.kind == "twotail" { -3 - offset() - 3 }
else if mark.kind == "circle" {
let r = mark.size
-sqrt(max(0, r*r - y*y)) - r
} else if mark.kind == "solidhead" {
-mark.size*cos(mark.sharpness)
} else if mark.kind == "solidtail" {
-1
} else { 0 }
}
#let draw-arrow-cap(p, θ, stroke, mark) = {
mark = interpret-mark(mark)
let shift(p, x) = vector.add(p, vector-polar(stroke.thickness*x, θ))
// extrude draws multiple copies of the mark
// at shifted positions
if "extrude" in mark {
for x in mark.extrude {
let mark = mark
let _ = mark.remove("extrude")
draw-arrow-cap(shift(p, x), θ, stroke, mark)
}
return
}
let stroke = (thickness: stroke.thickness, paint: stroke.paint, cap: "round")
if mark.kind == "harpoon" {
cetz.draw.arc(
p,
radius: mark.size*stroke.thickness,
start: θ + mark.flip*(90deg + mark.sharpness),
delta: mark.flip*mark.delta,
stroke: stroke,
)
} else if mark.kind == "head" {
draw-arrow-cap(p, θ, stroke, mark + (kind: "harpoon"))
draw-arrow-cap(p, θ, stroke, mark + (kind: "harpoon'"))
} else if mark.kind == "tail" {
p = shift(p, cap-offset(mark, 0))
draw-arrow-cap(p, θ + 180deg, stroke, mark + (kind: "head"))
} else if mark.kind == "hook" {
p = shift(p, cap-offset(mark, 0))
cetz.draw.arc(
p,
radius: mark.size*stroke.thickness,
start: θ + mark.flip*90deg,
delta: -mark.flip*180deg,
stroke: stroke,
)
let q = vector.add(p, vector-polar(2*mark.size*stroke.thickness, θ - mark.flip*90deg))
let rim = vector-polar(-mark.rim*stroke.thickness, θ)
cetz.draw.line(
q,
(rel: rim, to: q),
stroke: stroke
)
} else if mark.kind == "hooks" {
draw-arrow-cap(p, θ, stroke, mark + (kind: "hook"))
draw-arrow-cap(p, θ, stroke, mark + (kind: "hook'"))
} else if mark.kind == "bar" {
let v = vector-polar(mark.size*stroke.thickness, θ + 90deg)
cetz.draw.line(
(to: p, rel: v),
(to: p, rel: vector.scale(v, -1)),
stroke: stroke,
)
} else if mark.kind == "circle" {
p = shift(p, -mark.size)
cetz.draw.circle(
p,
radius: mark.size*stroke.thickness,
stroke: stroke,
)
} else if mark.kind == "solidhead" {
cetz.draw.line(
p,
(to: p, rel: vector-polar(-mark.size*stroke.thickness, θ + mark.sharpness)),
(to: p, rel: vector-polar(-mark.size*stroke.thickness, θ - mark.sharpness)),
fill: stroke.paint,
stroke: none,
)
} else if mark.kind == "solidtail" {
mark += (kind: "solidhead")
p = shift(p, cap-offset(mark, 0))
draw-arrow-cap(p, θ + 180deg, stroke, mark)
} else {
panic("unknown mark kind:", mark)
}
}
|
https://github.com/j10ccc/zjut-social-practice-report-typst | https://raw.githubusercontent.com/j10ccc/zjut-social-practice-report-typst/main/constants/fonts.typ | typst | #let font_family = (
songti: "Songti SC"
) |
|
https://github.com/typst/packages | https://raw.githubusercontent.com/typst/packages/main/packages/preview/anatomy/0.1.1/README.md | markdown | Apache License 2.0 | # Anatomy
*Anatomy of a Font*. Visualise metrics.
Import the `anatomy` package:
``` typ
#import "@preview/anatomy:0.1.1": metrics
```
## Display Metrics
`metrics(72pt, "EB Garamond", display: "Typewriter")` will be rendered as
follows:
Additionally, a closure using `metrics` dictionary as parameter can be
used to layout additional elements below:
``` typ
#metrics(54pt, "一點明體",
display: "電傳打字機",
use: metrics => table(
columns: 2,
..metrics.pairs().flatten().map(x => [ #x ])
)
)
```
It will generate:
## Remark on Hybrid Typesetting
To typeset CJK text, adopting font's ascender/descender as
`top-edge`/`bottom-edge` makes more sense in some cases. As for most CJK
fonts, the difference between ascender and descender heights will be
exact 1em.
Tested with `metrics(54pt, "Hiragino Mincho ProN", "テレタイプ端末")`:
Since Typst will use metrics of the font which has the largest advance
height amongst the list provided in `set text(font: ( ... ))` to set up
top and bottom edges of a line, leading might not work as expected in
hybrid typesetting. This issue can be solved by passing the document to
`metrics(use: metrics => { ... })` like this:
``` typ
#show: doc => metrics(font.size, font.main,
// Retrieve the metrics of the CJK font
use: metrics => {
set text(
font.size,
font: ( font.latin, font.main ),
features: ( "pkna", ),
// Use CJK font’s ascender/descender as top/bottom edges
top-edge: metrics.ascender,
bottom-edge: metrics.descender,
// ...
)
doc
}
)
```
|
https://github.com/seven-mile/blog-ng-content | https://raw.githubusercontent.com/seven-mile/blog-ng-content/master/blog/gatsby-typst-support.typ | typst | #import "/content/_typst_ts_tmpl/template.typ": *
#show: project.with(title: "Write modern weblog with typst.ts", date: datetime(
year: 2024,
month: 3,
day: 17,
hour: 16,
minute: 30,
second: 0,
), description: "A small gift for you")
过去的 Hexo 博客差不多有 3 年没有监修，受到 #link("https://github.com/memset0/gatsby-blog")[`memset0/gatsby-blog`] 的启发，我用 Gatsby.js 重新构建了这套生成器。
为了一切的一切，我加上了 Typst 的支持。这套年轻的排版引擎可以胜任我的所有编辑需求，透过 #link("https://github.com/Myriad-Dreamin/typst.ts")[`typst.ts`] 我可以仅书写少量代码就将 Typst 的复杂渲染结果交互式地呈现到 Web 页面上。
如果对这套工具链的任何环节感兴趣，你可以参考这些 repo，它们都是公开的：
+ #link("https://github.com/seven-mile/blog-ng")[`seven-mile/blog-ng`]
+ #link("https://github.com/seven-mile/blog-ng-content")[`seven-mile/blog-ng-content`]
+ #link("https://github.com/seven-mile/gatsby-transformer-typst")[`seven-mile/gatsby-transformer-typst`]
下面是 Showcase
$qed$
// Font size
#let scriptsize = 10pt
#let normalsize = 16pt
#let large = 20pt
#set text(size: normalsize, lang: "en")
// Some horizontal spacing
#let kern(length) = h(length, weak: true)
#let enspace = kern(0.5em)
#let qquad = h(2em)
// For table/grid, something like "lhs \enspace rhs"
#let cell(lhs, rhs) = box(lhs + enspace + rhs)
// Grid for code blocks
#set grid(columns: (2em, auto))
// Table for math-code listing
#set table(stroke: none, align: horizon + left, inset: 0pt, row-gutter: 0.45em)
// LaTeX and TeX logos
#let TeX = style(styles => {
let e = measure(text(normalsize, "E"), styles)
let T = "T"
let E = text(normalsize, baseline: e.height / 2, "E")
let X = "X"
box(T + kern(-0.1667em) + E + kern(-0.125em) + X)
})
#let LaTeX = style(styles => {
let l = measure(text(10pt, "L"), styles)
let a = measure(text(7pt, "A"), styles)
let L = "L"
let A = text(7pt, baseline: a.height - l.height, "A")
box(L + kern(-0.36em) + A + kern(-0.15em) + TeX)
})
// Update date
#let date = "2023-07-22"
// Unavailable (last check date)
#show "??": box(text(red, [#date #emoji.crossmark]))
// Tricky
#show "!!": box(text(blue, emoji.drops))
// No idea
#show "?!": box(text(orange, [No idea #emoji.face.unhappy]))
// Tricky figure numbering
#set figure(numbering: n => {
([??], [!!], [?!]).at(n - 1)
})
// No prefix
#set ref(supplement: "")
// Justified paragraphs
#set par(justify: true)
#show: rest => columns(1, rest)
// headcolor
#let headcolor = rgb("004225")
// Run-in sections, like LaTeX \paragraph
#show heading.where(
level: 1
): it => text(
size: normalsize,
weight: "bold",
fill: headcolor,
it.body + h(0.67em)
)
// Black raw code
#show raw.where(block: false): it => { it.text }
// Title
#align(center, link("https://github.com/johanvx/typst-undergradmath")[
#text(large, headcolor)[*Typst Math for Undergrads*]
])
// Put this here to avoid affecting the title
#show link: underline
This is a Typst port of _#LaTeX Math for Undergrads_ by <NAME>.
The original version is available at #link("https://gitlab.com/jim.hefferon/undergradmath").
= Meaning of annotations
#figure(
table(
columns: (1fr, 2fr),
[??], [This is unavailable. Last check date is #date.],
)
) <unavailable>
#figure(
table(
columns: (1fr, 2fr),
[!!], [Get this in a tricky way. Need a simpler method.],
)
) <tricky>
// #figure(
// table(
// columns: (1fr, 2fr),
// [?!], [Don't know how to get this.],
// )
// ) <noidea>
= Rule One
Any mathematics at all, even a single character, gets a mathematical setting.
Thus, for "the value of $x$ is $7$" enter `the value of $x$ is $7$`.
= Template
Your document should contain at least this.
#grid(
"",
```
-- document body here --
```
)
= Common constructs
#align(center, table(
columns: 4,
align: (right, left, right, left),
column-gutter: (1em, 1.5em, 1em),
[$x^2$], [`x^2`],
[$sqrt(2)$, $root(n, 3)$], [`sqrt(2)`, `root(n, 3)`],
[$x_(i, j)$], [`x_(i, j)`],
[$2 / 3$, $2 \/ 3$], [`2 / 3`, `2 \/ 3` or `2 slash 3`], // Maybe use `slash`?
))
= Calligraphic letters
Use as in `$cal(A)$`.
$ cal(A B C D E F G H I J K L M N O P Q R S T U V W X Y Z) $
Getting script letters is @unavailable.
= Greek
#align(center, table(
columns: 4,
align: (right, left, right, left),
column-gutter: (1em, 1.5em, 1em),
[$alpha$], [`alpha`], [$xi$, $Xi$], [`xi`, `Xi`],
[$beta$], [`beta`], [$omicron$], [`omicron`],
[$gamma$, $Gamma$], [`gamma`, `Gamma`], [$pi$, $Pi$], [`pi`, `Pi`],
[$delta$, $Delta$], [`delta`, `Delta`], [$pi.alt$], [`pi.alt`],
[$epsilon.alt$], [`epsilon.alt`], [$rho$], [`rho`],
[$epsilon$], [`epsilon`], [$rho.alt$], [`rho.alt`],
[$zeta$], [`zeta`], [$sigma$, $Sigma$], [`sigma`, `Sigma`],
[$eta$], [`eta`], [$sigma.alt$], [`sigma.alt`],
[$theta$, $Theta$], [`theta`, `Theta`], [$tau$], [`tau`],
[$theta.alt$], [`theta.alt`], [$upsilon$, $Upsilon$], [`upsilon`, `Upsilon`],
[$iota$], [`iota`], [$phi.alt$, $Phi$], [`phi.alt`, `Phi`],
[$kappa$], [`kappa`], [$phi$], [`phi`],
[$lambda$, $Lambda$], [`lambda`, `Lambda`], [$chi$], [`chi`],
[$mu$], [`mu`], [$psi$, $Psi$], [`psi`, `Psi`],
[$nu$], [`nu`], [$omega$, $Omega$], [`omega`, `Omega`],
))
= Sets and logic
#align(center, table(
columns: 6,
align: (right, left, right, left, right, left),
column-gutter: (1em, 1.5em, 1em, 1.5em, 1em),
[$union$], [`union`], [$RR$], [`RR`, `bb(R)`], [$forall$], [`forall`],
[$sect$], [`sect`], [$bb(Z)$], [`ZZ`, `bb(Z)`], [$exists$], [`exists`],
[$subset$], [`subset`], [$bb(Q)$], [`QQ`, `bb(Q)`], [$not$], [`not`],
[$subset.eq$], [`subset.eq`], [$bb(N)$], [`NN`, `bb(N)`], [$or$], [`or`],
[$supset$], [`supset`], [$bb(C)$], [`CC`, `bb(C)`], [$and$], [`and`],
[$supset.eq$], [`supset.eq`], [$diameter$], [`diameter`], [$tack.r$], [`tack.r`],
[$in$], [`in`], [$nothing$], [`nothing`], [$models$], [`models`],
[$in.not$], [`in.not`], [$alef$], [`alef`], [$without$], [`without`],
))
Negate an operator, as in $subset.not$, with `subset.not`.
Get the set complement $A^(sans(c))$ with `A^(sans(c))` (or $A^(complement)$ with `A^(complement)`, or $overline(A)$ with `overline(A)`).
// https://www.ctan.org/tex-archive/fonts/newcomputermodern
//
// README
//
// Version 3.93
//
// Provides access to Russian and Greek guillemotleft and guillemotright
// using the character variant tables cv3 and cv4 respectively.
//
// The Math fonts provide the character \varnothing, an alternative to \emptyset,
// through Character Variant cv01. The fontsetup package provides the option
// 'varnothing' to easily switch to the alternative character.
// https://mirrors.sustech.edu.cn/CTAN/fonts/newcomputermodern/doc/newcm-doc.pdf
// The NewComputerModern FontFamily §13.3
// The Math fonts provide the character \varnothing (⌀, U+2300), as an alternative to \emptyset (a slashed zero), through Character Variant cv01.
// The fontsetup package provides the option ‘varnothing’ to easily switch to the alternative character.
/ Remark: Using `diameter` for `\varnothing` may cause some confusion. However, #LaTeX also uses $diameter$ (`\u{2300}`) instead of $\u{2205}$ (`\u{2205}`), see #link("https://mirrors.sustech.edu.cn/CTAN/fonts/newcomputermodern/doc/newcm-doc.pdf")[newcm $section$13.3].
Another solution is to use `text(font: "Fira Sans", nothing)`, but the resultant glyph $text(font: "Fira Sans", nothing)$ is subtly different from the widely used one.
Ultimately, the choice is always *your decision*.
= Decorations
#align(center, table(
columns: 6,
align: (right, left, right, left, right, left),
column-gutter: (1em, 1.5em, 1em, 1.5em, 1em),
[$f'$], [`f'`, `f prime`], [$dot(a)$], [`dot(a)`], [$tilde(a)$], [`tilde(a)`],
[$f prime.double$], [`f prime.double`], [$diaer(a)$], [`diaer(a)`], [$macron(a)$], [`macron(a)`],
[$Sigma^*$], [`Sigma^*`], [$hat(a)$], [`hat(a)`], [$arrow(a)$], [`arrow(a)`],
))
If the decorated letter is $i$ or $j$ then some decorations need `dotless.i` and `dotless.j`, as in $arrow(dotless.i)$ with `arrow(dotless.i)`.
Some authors use boldface for vectors: `bold(x)`.
Entering `overline(x + y)` produces $overline(x + y)$, and `hat(x + y)` gives $hat(x + y)$.
Comment on an expression as here (there is also `overbrace(..)`).
#align(center, table(
columns: 2,
column-gutter: 1em,
[$ underbrace(x + y, |A|) $],
[
```
underbrace(x + y, |A|)
```
],
))
= Dots
Use low dots in a list ${0, 1, 2, ...}$, entered as `{0, 1, 2, ...}`.
Use centered dots in a sum or product $1 + dots.h.c + 100$, entered as `1 + dots.h.c + 100`.
You can also get vertical dots `dots.v`, diagonal dots `dots.down` and anti-diagonal dots `dots.up`.
= Roman names
Just type them!
#align(center, table(
columns: 6,
align: (right, left, right, left, right, left),
column-gutter: (1em, 1.5em, 1em, 1.5em, 1em),
[$sin$], [`sin`], [$sinh$], [`sinh`], [$arcsin$], [`arcsin`],
[$cos$], [`cos`], [$cosh$], [`cosh`], [$arccos$], [`arccos`],
[$tan$], [`tan`], [$tanh$], [`tanh`], [$arctan$], [`arctan`],
[$sec$], [`sec`], [$coth$], [`coth`], [$min$], [`min`],
[$csc$], [`csc`], [$det$], [`det`], [$max$], [`max`],
[$cot$], [`cot`], [$dim$], [`dim`], [$inf$], [`inf`],
[$exp$], [`exp`], [$ker$], [`ker`], [$sup$], [`sup`],
[$log$], [`log`], [$deg$], [`deg`], [$liminf$], [`liminf`],
[$ln$], [`ln`], [$arg$], [`arg`], [$limsup$], [`limsup`],
[$lg$], [`lg`], [$gcd$], [`gcd`], [$lim$], [`lim`],
))
= Other symbols
#align(center, table(
columns: 6,
align: (right, left, right, left, right, left),
column-gutter: (0.5em, 1em, 0.5em, 1em, 0.5em),
[$<$], [`<`, `lt`], [$angle$], [`angle`], [$dot$], [`dot`],
[$<=$], [`<=`, `lt.eq`], [$angle.arc$], [`angle.arc`], [$plus.minus$], [`plus.minus`],
[$>$], [`>`, `gt`], [$ell$], [`ell`], [$minus.plus$], [`minus.plus`],
[$>=$], [`>=`, `gt.eq`], [$parallel$], [`parallel`], [$times$], [`times`],
[$!=$], [`!=`, `eq.not`], [$45 degree$], [`45 degree`], [$div$], [`div`],
[$<<$], [`<<`, `lt.double`], [$tilde.equiv$], [`tilde.equiv`], [$*$], [`*`, `ast`],
[$>>$], [`>>`, `gt.double`], [$tilde.equiv.not$], [`tilde.equiv.not`], [$divides$], [`divides`],
[$approx$], [`approx`], [$tilde$], [`tilde`], [$divides.not$], [`divides.not`],
[$\u{224D}$], [`\u{224D}` @tricky], [$tilde.eq$], [`tilde.eq`], [$n!$], [`n!`],
[$equiv$], [`equiv`], [$tilde.not$], [`tilde.not`], [$diff$], [`diff`],
[$prec$], [`prec`], [$plus.circle$], [`plus.circle`], [$nabla$], [`nabla`],
[$prec.eq$], [`prec.eq`], [$minus.circle$], [`minus.cirle`], [$planck.reduce$], [`planck.reduce`],
[$succ$], [`succ`], [$dot.circle$], [`dot.circle`], [$compose$], [`compose`],
[$succ.eq$], [`succ.eq`], [$times.circle$], [`times.circle`], [$star$], [`star`],
[$prop$], [`prop`], [$\u{2298}$], [`\u{2298}` @tricky], [$sqrt("")$], [`sqrt("")`],
[$\u{2250}$], [`\u{2250}` @tricky], [$harpoon.tr$], [`harpoon.tr`], [$checkmark$], [`checkmark`],
))
Use `a divides b` for the divides relation, $a divides b$, and `a divides.not b` for the negation, $a divides.not b$.
Use `|` to get set builder notation ${a in S | a "is odd"}$ with `{a in S | a "is odd"}`.
= Arrows
#align(center, table(
columns: 4,
align: (right, left, right, left),
column-gutter: (1em, 1.5em, 1em),
[$->$], [`->`, `arrow.r`], [$|->$], [`|->`, `arrow.r.bar`],
[$arrow.r.not$], [`arrow.r.not`], [$arrow.r.long.bar$], [`arrow.r.long.bar`],
[$-->$], [`-->`, `arrow.r.long`], [$<-$], [`<-`, `arrow.l`],
[$=>$], [`=>`, `arrow.r.double`], [$<->$], [`<->`, `arrow.l.r`],
[$arrow.r.double.not$], [`arrow.r.double.not`], [$arrow.b$], [`arrow.b`],
[$==>$], [`==>`, `arrow.r.double.long`], [$arrow.t$], [`arrow.t`],
[$arrow.squiggly$], [`arrow.squiggly`], [$arrow.t.b$], [`arrow.t.b`],
))
The right arrows in the first column have matching left arrows, such as `arrow.l.not`, and there are some other matches for down arrows, etc.
= Variable-sized operators
The summation $sum_(j = 0)^3 j^2$ `sum_(j = 0)^3 j^2` and the integral $integral_(x = 0)^3 x^2 dif x$ `integral_(x = 0)^3 x^2 dif x` expand when displayed.
$ sum_(j = 0)^3 j^2 qquad integral_(x = 0)^3 x^2 dif x $
These do the same.
#align(center, table(
columns: 4,
align: (right, left, right, left),
column-gutter: (1em, 1.5em, 1em),
row-gutter: 0.5em,
[$integral$], [`integral`], [$integral.double$], [`integral.double`],
[$integral.triple$], [`integral.triple`], [$integral.cont$], [`integral.cont`],
[$union.big$], [`union.big`], [$sect.big$], [`sect.big`],
))
= Fences
#align(center, table(
columns: 6,
align: (right, left, right, left, right, left),
column-gutter: (1em, 1.5em, 1em, 1.5em, 1em),
row-gutter: 0.5em,
[$()$], [`()`], [$angle.l angle.r$], [`angle.l angle.r`], [$abs("")$], [`abs("")`],
[$[]$], [`[]`], [$floor("")$], [`floor("")`], [$norm("")$], [`norm("")`],
[${}$], [`{}`], [$ceil("")$], [`ceil("")`],
))
Fix the size with the `lr` function.
#align(center, table(
columns: 2,
column-gutter: 1em,
[$ lr([sum_(k = 0)^n e^(k^2)], size: #50%) $],
[
```
lr([sum_(k = 0)^n e^(k^2)], size: #50%)
```
],
))
To have them grow with the enclosed formula, also use the `lr` function.
#align(center, table(
columns: 2,
column-gutter: 1em,
[$ lr(angle.l i, 2^(2^i) angle.r) $],
[
```
lr(angle.l i, 2^(2^i) angle.r)
```
],
))
Fences scale by default if entered directly as codepoints, and don't scale automatically if entered as symbol notation.
#align(center, table(
columns: 2,
align: (right + horizon, left + horizon),
column-gutter: 1em,
[$ (1 / n^(alpha)) $],
[
```
(1 / n^(alpha))
```
],
[$ paren.l 1 / n^(alpha) paren.r $],
[
```
paren.l 1 / n^(alpha) paren.r
```
],
))
The `lr` function also allows to scale unmatched delimiters and one-side fences.
#align(center, table(
columns: 2,
column-gutter: 1em,
[$ lr(frac(dif f, dif x) |)_(x_0) $],
[
```
lr(frac(dif f, dif x) |)_(x_0)
```
],
))
= Arrays, Matrices
Get a matrix with the `mat` function. You can pass an array to it.
#align(center, table(
columns: 2,
column-gutter: 1em,
[$ mat(a, b; c, d) $],
[
```
$ mat(a, b; c, d) $
```
],
))
In Typst, #link("https://typst.app/docs/reference/types/array")[array] is a sequence of values,
while in #LaTeX, array is a matrix without fences, which is `$mat(delim: #none, ..)$` in Typst.
For the determinant use `|A|`, text operator $det$ `det` or `mat(delim: "|", ..)`.
Definition by cases can be easily obtained with the `cases` function.
#align(center, table(
columns: 2,
column-gutter: 1em,
[
$ f_n = cases(
a &"if" n = 0,
r dot f_(n - 1) &"else"
) $
],
[
```
$ f_n = cases(
a &"if" n = 0,
r dot f_(n - 1) &"else"
) $
```
]
))
= Spacing in mathematics
Improve $sqrt(2) x$ to $sqrt(2) thin x$ with a thin space, as in `sqrt(2) thin x`.
Slightly wider are `medium` and `thick` (the three are in ratio $3 : 4 : 5$).
Bigger space is `quad` for $arrow.r quad arrow.l$, which is useful between parts of a display.
Get arbitrary space with the `h` function.
For example, use `#h(2em)` for `\qquad` in #LaTeX and `#h(-0.1667em)` for `\!`.
= Displayed equations
Display equations in a block level using `$ ... $` with at least one space separating the math content and the `$`.
#align(center, table(
columns: 2,
column-gutter: 1em,
[$ S = k dot lg W $],
[
```
$ S = k dot lg W $
```
],
))
You can break into multiple lines.
#align(center, table(
columns: 2,
column-gutter: 1em,
[
$ sin(x) = x - x^3 / 3! \
+ x^5 / 5! - dots.h.c $
],
[
```
$ sin(x) = x - x^3 / 3! \
+ x^5 / 5! - dots.h.c $
```
],
))
Align equations using `&`
#align(center, table(
columns: 2,
column-gutter: 1em,
[
$ nabla dot bold(D) &= rho \
nabla dot bold(B) &= 0 $
],
```
$ nabla dot bold(D) &= rho \
nabla dot bold(B) &= 0 $
```,
))
(the left or right side of an alignment can be empty).
Get a numbered version by `#set math.equation(numbering: ..)`.
= Calculus examples
The last three here are display style.
#align(center, table(
columns: 2,
column-gutter: 1em,
[$ f: RR -> RR $],
[
```
f: RR -> RR
```
],
[$ "9.8" "m/s"^2 $],
[`"9.8" "m/s"^2` @tricky],
[$ lim_(h->0) (f(x+h)-f(x))/h $],
[
```
lim_(h -> 0) (f(x + h) - f(x)) / h
```
],
[$ integral x^2 dif x = x^3 \/ 3 + C $],
[
```
integral x^2 dif x = x^3 \/ 3 + C
```
],
[$ nabla = bold(i) dif / (dif x) + bold(j) dif / (dif y) + bold(k) dif / (dif z) $],
[
```
nabla = bold(i) dif / (dif x) + bold(j) dif / (dif y) + bold(k) dif / (dif z)
```
],
))
= Discrete mathematics examples
For modulo, there is a symbol $equiv$ from `equiv` and a text operator $mod$ from `mod`.
For combinations the binomial symbol $binom(n, k)$ is from `binom(n, k)`.
This resizes to be bigger in a display.
For permutations use $n^(underline(r))$ from `n^(underline(r))` (some authors use $P(n, r)$, or $""_n P_r$ from `""_n P_r`).
= Statistics examples
#align(center, table(
columns: 2,
column-gutter: 1em,
[$ sigma^2 = sqrt(sum(x_i - mu)^2 \/ N) $],
[
```
sigma^2 = sqrt(sum(x_i - mu)^2 \/ N)
```
],
[$ E(X) = mu_X = sum(x_i - P(x_i)) $],
[
```
E(X) = mu_X = sum(x_i - P(x_i))
```
],
))
The probability density of the normal distribution
$ 1 / sqrt(2 sigma^2 pi) e^(- (x - mu)^2 / (2 sigma^2)) $
comes from this.
#align(center, [
```
1 / sqrt(2 sigma^2 pi)
e^(- (x - mu)^2 / (2 sigma^2))
```
])
= For more
See also the Typst Documentation at #link("https://typst.app/docs").
#block(
line(length: 100%, stroke: headcolor) +
text(headcolor)[johanvx (https://github.com/johanvx) #h(1fr) #date]
)
|
|
https://github.com/thimotedupuch/Template_Rapport_ISMIN_Typst | https://raw.githubusercontent.com/thimotedupuch/Template_Rapport_ISMIN_Typst/main/README.md | markdown | # Template Rapport ISMIN Typst
## Pour celles & ceux qui veulent un beau rapport fait en LaTeX, sans faire en LaTeX
Le fichier `resultat.pdf` est un aperçu PDF du template non modifié.
Il faut bien récupérer les fichiers `slogan.png` et `Nouv_logo_emse_Blanc.svg` pour pouvoir afficher les 2 logos dans la page de garde.
|
|
https://github.com/An-314/Notes-of-Nuclear_Radiation_Physics_and_Detection | https://raw.githubusercontent.com/An-314/Notes-of-Nuclear_Radiation_Physics_and_Detection/main/chap1.typ | typst | #import"@preview/physica:0.9.2":*
#import "template.typ": *
= 原子核的基本性质
*知识准备*
在本课程中，常用$e V$表示能量，用$e V"/"c^2 $表示质量单位。
物质波和波粒二象性
不确定度关系
== 原子核的组成、质量和半径
=== 原子的发现和组成
原子可分：X射线、放射性、电子
Thomson模型：正电荷均匀分布
Rutherford alpha散射实验：核式模型
==== 原子的核式模型
电荷数 < 质量数，且都为整数
==== 中子的发现
原子核=质子+电子？
- 实验验证电子的动能：不确定原理
- 子核自旋$I$的取值与核内粒子数
- 决定原子核是费米子还是玻色子
卢瑟福：预言中子；查德威克：发现中子
$ alpha + "Be" -> n + "C " $
$n$穿透能力很强，质量与质子相近。
*核子*：质子和中子。
$ A = Z + N $
用下面的方式表示一个核子：
$ ""_Z^A X_N = ""^A X $
表示一个特定组成的*核素*。
=== 原子核物理常用术语和意义
==== 核素
*核素*：有一定数目的质子、中子、能态的原子核。
核子数、中子数质子數和能态只要有一个不同就是不同核素。
*元素*：具有相同核电荷数（庐子数）的一类原子的总称，又称化学元素。
==== 同位素(isotope)和同位素丰度
*同位素*：具有相同质子数，但质量数不同的核素所对应的原子称为某元素的同位素。
Z 同， N 不同，在元素周期表中同删立置，具有相同化学性质。
*同位素丰度*：自然界中同位素的相对丰度。
==== 同中异荷素 (isotone)
中子数 N 相同，质子数 Z 不同的核素互称为*同中异荷素*。也称*同中子素*或*同中异位素*。
同中子素之间_符号不同，数字不同_。
==== 同量异位素 (isobar)
质量数相同，质子数 Z 不同的核素互称为*同量异位素*。
同量异位素之间_符号不同，数字相同_。
==== 同质异能素 (isomer)
能态处于*半衰期较长的激发态*的核素称为*基态核素的同质异能素*或*同核异能素*。
同质异能素的质子数和中子数均与基态核素相同。
$
""^(A"m ")X
$
*同质异能态*：同质异能素所处的能态，是半衰期较长的激发态。
==== 偶A核和奇A核
*偶A核*：
- 偶偶(e-e)核：Z 和 N 均为偶数的核素。
- 奇奇(o-o)核：Z 和 N 均为奇数的核素。
*奇A核*：
- 偶奇(e-o)核：Z 为偶数，N 为奇数的核素。
- 奇偶(o-e)核：Z 为奇数，N 为偶数的核素。
==== 镜像核
*镜像核*：质子数和中子数互换的核素。
镜像核$beta$衰变的概率更大。
=== 原子核质量
- $m(Z,A)$：表示原子核的质量
- $M(Z,A)$：表示原子的质量
原子的质量与原子核的质量的关系：
$
M(Z,A) = m(Z,A) + Z dot m_e - B_e/c^2
$
最后一项是电子的静质量能，较小。
=== 原子核的半径
- 原子核：$10^(-15)"m "("fm")$量级
- 原子：$10^(-10)"m "("A ")$量级
原子核的形状作为一级近似可以看作球形。因此，原子核的大小用*原子核的半径*表示。由于原子核有角动量，略呈*旋转椭球*形。
根据测量方法不同，原子核的半径可分为：*核力半径和电荷分布半径*。
$
R = R_0 A^(1/3) prop A^(1/3), V prop A
$
核力半径和电荷分布半径中更大者是*核力半径*。
原子核密度：原子核密度为常数，约为$10^11"kg/cm"^3$。
== 原子核稳定性及核素图
*核素图*：质子数 Z 和中子数 N 为横纵坐标构建的两维图。
横纵坐标相交代表相应组成（质子数和中子数）的核素，可在该位置标示出核素符号以及其稳定性、衰变性质等（用颜色、符号、数据等方式）。
#grid(
columns: (1fr, 1fr),
[#figure(
image("pic/2024-02-29-10-34-03.png", width: 85%),
caption: [
核素图
],
)],
[#figure(
image("pic/2024-02-29-10-53-41.png", width: 90%),
caption: [
$beta$稳定线
],
)]
)
#newpara()
*$beta$稳定线*：A较小时，$"N/Z"->1$；A较大时，$"N/Z">1$。
稳定线下方的核素易发生$beta^+$衰变，稳定线上方的核素易发生$beta^-$衰变。
有经验公式：
$
Z = A/(1.98 + 0.0155 A^(2/3))
$
Z 较小时，库伦排斥作用较小，核力占主导地位，$"N/Z"->1$；Z 较大时，库伦排斥作用较大，核力占主导地位，$"N/Z">1$。库仑力是长程力，核力是短程力。
*稳定核素*的奇偶分类：*偶偶核*稳定核素最多，其次是*偶奇核和奇偶核*，最少的是*奇奇核*稳定核素。
*幻数*：当中子数或者质子数是2、8、20、28、50、82，中子数是126时，核素更稳定。
== 原子核的结合能
=== 原子核的结合能
*质量亏损*：原子核的质量小于其组成核子的质量之和。
*原子核的结合能*：质子中子结合成一个原子核时，由于核力的作用，将释放出一部分能量，表示为
$
B(Z,A) = [Z m_p + N m_n - m(Z,A)] c^2
$
为计算方便，常以原子质量 M 表示，且忽略原子中电子的结合能，即：
$
B(Z,A) = [Z M(""^1H) + N m_n - M(Z,A)] c^2
$
=== 质量亏损和质量过剩
*质量亏损*：原子核的质量总是小于组成它的所有核子的质量之和
$
Delta m(Z,A) = B(Z,A)/c^2
$
则有
$
Delta m(Z,A) = Z m_p + N m_n - m(Z,A)
$
质量亏损和原子核的结合能是同一个物理量的质量能量表示。
所有的核都存在质量亏损。
*质量过剩*：原子核的质量亏损量#footnote[$""^12C$的质量亏损为0，剩下的可正可负]
常用原子质量 M 代替核质量 m，即
$
Delta m(Z,A) = Z M(""^1H) + N m_n - M(Z,A)
$
定义质量过剩，单位为eV
$
Delta (Z,A) = (M(Z,A) - A)dot c^2
$
其中$M(Z,A)$单位为u。
*质量过剩和原子质量*有确定的对应关系，是同一个量的不同表示：
$
M(Z,A) = A + (Delta (Z,A))/931.4940
$
上式左侧单位为eV，右侧单位为u。
可以用质量过剩表示结合能和质量亏损：
$
B(Z,A) &= [Z dot Delta (1,1) + N dot Delta (0,1) - Delta (Z,A)] dot c^2\
Delta m(Z,A) &= Z dot Delta (1,1) + N dot Delta (0,1) - Delta (Z,A)
$
=== 比结合能及比结合能曲线
*比结合能*：原子核的结合能 $B(Z,A)$ 除以核子数$A$，表示为$epsilon(Z,A)$:
$
epsilon(Z,A) = B(Z,A)/A
$
单位是MeV/Nu，其中Nu代表核子。
比结合能的物理意义：比结合能表示核子结合成原子核时，平均每个核子所释放的能量。或者说：原子核被拆散成自由核子时，外界对每个核子所做的最小的平均功。
比结合能的大小表征了原子核结合松紧程度：
- 比结合能大，核子结合紧密，原子核稳定
- 比结合能小，核子结合松散，原子核不稳定
*比结合能曲线*：
#figure(
image("pic/2024-02-29-14-42-45.png", width: 50%),
caption: [
比结合能曲线
],
)
*注*：*同量异位素*中，稳定核素的比结合能未必比不稳定核素大；比较同量异位素的目对稳定性应该比较*原子质量或质量过剩*的大小，*不能比较比结合能*（因为中子和质的质量不同，稳定线附近的核素的结合能大小可能与质量过剩的大小关系不同）。
*例*：_分析的$beta$稳定性，要比较$Delta(Z,A)$与$Delta(Z+1,A)$或$Delta(Z-1,A)$的大小_。
$
B(Z+1,A)-B(Z,A) = Delta(1,1) - Delta(0,1)+ Delta(Z,A) - Delta(Z+1,A)
$
而$Delta(1,1) - Delta(0,1)<0$，不能简单地比较$B(Z+1,A)$和$B(Z,A)$的大小。*质量过剩大就不稳定，质量过剩小就稳定。*
=== 原子核最后一个核子的结合能
一个自由核子与核的其余部分组成原子核时所释放的能量，也是从核外引入一个核子到原子核中所需的能量，称为*最后一个核子的结合能*。#footnote[原子核最后一个核子的结合能不一定大于0]
最后一个质子的结合能：
$
S_P(Z,A) &= (M(""^1H) + M(Z-1,A-1) - M(Z,A)) dot c^2\
&= Delta (1,1) + Delta (Z-1,A-1) - Delta (Z,A)\
&= B(Z,A) - B(Z-1,A-1)
$
可以用结合能表示。
最后一个中子的结合能：
$
S_N(Z,A) &= (M(""^1n) + M(Z,A-1) - M(Z,A)) dot c^2\
&= Delta (0,1) + Delta (Z,A-1) - Delta (Z,A)\
&= B(Z,A) - B(Z,A-1)
$
可以用结合能表示。
*最后一个核子的结合能*反映了：这个原子核相对邻近的那些原子核的稳定程度。
*最后一个$alpha$粒子的结合能*：
$
S_alpha(Z,A) &= Delta (2,4) + Delta (Z-2,A-4) - Delta (Z,A)\
&= B(Z,A) - B(Z-2,A-4) - B(2,4)
$
注意多了一个$B(2,4)$。
*最后一个重离子的结合能*：
$
S(Z,A) = B(Z_1,A_1) + B(Z-Z_1,A-A_1) - B(Z,A)
$
上面的物理量都不一定大于0。
=== 原子核结合能的半经验公式
==== 液滴模型(LDM: Liquid Drop Model)
*液滴模型*：把原子核类比为一个液滴。
根据液滴模型，结合能半经验公式为
$
B = B_V + B_S + B_C + B_"sym" + B_P
$
- 体积能顶（Volume）：结合能中的主导顶，由于核力的饱和性，它正比于核体积伊用。
$
B_V = a_V A
$
- 表面能顶（Surface）：表面核子的核力没有饱和。表面核子结合弱，要从体结合能减去一部分。该部分正比于核的表面积。
$
B_S = - a_S A^(2/3)
$
- 库伦能顶（Coulomb）：核内有 Z 个质子，它们之间存在库仑斥力，使结合能变小，导致核不稳定。
$
B_C = - a_C Z^2/A^(1/3)
$
- 对称能顶（Symmetry）#footnote[如果只有前三项，似乎 Z 越小越稳定，显然不符合实际情况]：反映核内的中子数与质子数是否相等，若它们相等时为零。
$
B_"sym" = - a_"sym" (A/2-Z)^2/A
$
稳定轻核内的中子和质子有对称相处的趋势，即 N = Z
对称能：
- N = Z 时，对称能为零，原子核最稳定;
- N $!=$ Z 时，对称能非零，结合能降低，核不稳定。
- 对能项（Pairing）：由核内 N , Z 的奇偶性确定。核内的中子和质子有各自成对出现的趋势，不同奇偶性的核有不同的对能项。
$
B_P = a_P A^(-1/2) delta
$
其中 $delta$ 为奇偶性因子，当 N 和 Z 都是偶数时，$delta = 1$；当 N 和 Z 都是奇数时，$delta = -1$。
带入就得到了完整的结合能半经验公式：
$
B(Z,A) = a_V A - a_S A^(2/3) - a_C Z^2/A^(1/3) - a_"sym" (A/2-Z)^2/A + a_P A^(-1/2) delta
$
*应用*
1. 求核素的质量
$
m(Z,A) = Z m_p + N m_n - B(Z,A)/c^2
$
计算值与实验结果比较：总体上计算值与实验结果相符，仅当Z=幻数时有偏离，轻核的实验结果与计算差别也较大。——原因：液滴模型给出的是统计的平均结果。
2. 作比结合能曲线
在A固定的时候，对Z作图，得到的曲线是一个二次曲线。
3. 同量异位素质能抛物线
4. 作$beta$稳定线
$
(diff M(Z,A))/(diff A) = 0
$
== 核力和核势垒
=== 核力的一般性质
1. 短程、强相互作用
2. 与电荷无关
3. 具有饱和性
4. 主要是吸引力，在极端程内有排斥芯
5. 与自旋有关
#figure(
image("pic/2024-03-05-14-44-02.png", width: 80%),
caption: [
核子的作用势
],
)
=== 原子核的势垒
#figure(
image("pic/2024-03-05-14-46-06.png", width: 80%),
caption: [
$alpha$粒子与原子核作用过程的势能曲线
],
)
- $r>R$ ： 核力为零，仅为库仑作用，称为*库仑势垒*。
$
V(r) = e^2/(4 pi epsilon_0) (2Z)/r
$
- $r=R$ ： 势垒最高点，称为*库仑势垒高度*。
$
V_c(R) = e^2/(4 pi epsilon_0) (Z_1 Z_2)/(r_0 (A_1^(1/3) + A_2^(1/3)))
$
- $R > r > R_N$：核力大大超过库仑力，势能迅速下降并可能改变符号。
- $r <R_N $：粒子进入靶核，合力为零，势能为常数值——$V_0$。
*隧道效应*(TunneI Effect)：动能 $E$ 小于势垒高度的粒子仍能穿透势垒的现象。
#figure(
image("pic/2024-03-05-14-55-38.png", width: 30%),
caption: [
中子与原子核作用过程的势能曲线
],
)
*中子没有库仑势垒。*
== 原子核的矩
=== 原子核外电子的状态量子数
- 主量子数 $n$：能量量子化 $n = 1, 2, 3, ...(K,L,M,...)$
- 角量子数 $l$：轨道角动量大小量子化 $l = 0, 1, 2, 3, ...(s,p,d,f,...)$
- 磁量子数 $m_l$：角动量空间取向量子化 $m_l = -l, -l+1, ..., 0, ..., l-1, l$
- 自旋角动量量子数 $s$：自旋角动量大小量子化 $s = 1/2$
- 自旋角动量磁量子数 $m_s$：自旋空间取向量子化 $m_s = -s, s$
=== 角动量$arrow(J)$
量子力学中，角动量的大小和空间取向都是量子化的，角动量量子数用_整数或半整数_$I$表示。
角动量大小：
$
|arrow(J)| = sqrt(I(I+1)) hbar
$
角动量空间取向数：
$
2I+1
$
角动量的空间投影
$
arrow(J_z) = m hbar, m = -I, -I+1, ..., 0, ..., I-1, I
$
*角动量耦合*：$arrow(J) = arrow(J_1) + arrow(J_2)$角动量量子数$I$为$I_1 + I_2, I_1 + I_2 - 1, ..., |I_1 - I_2|$
=== 磁矩
==== 带电粒子作圆周运动产生的磁矩
质量为 $m$， 电荷量为 $+q$ 的粒子作圆周运动时，形成环形电流 $i$，产生磁矩 $mu$ 和角动量$L$ 。
$
arrow(mu) = S dot i dot arrow(n_0) = q/2m arrow(L)
$
==== 电子的轨道磁矩
$
arrow(mu_l) = -e/2m_0 arrow(L) = g_l e/2m_0 arrow(L)
$
其中 $g_l$ 为*朗德因子*，$g_l = -1$。
空间投影最大值：
$
mu_l = g_l mu_B l
$
其中 $mu_B = (e hbar)/(2m_0)$ 为*玻尔磁子*。
==== 电子的自旋磁矩
电子自旋运动所对应的磁矩：
$
mu_s = g_s mu_B s
$
其中 $g_s$ 为*朗德因子*，$g_s = -2$。
==== 电子的磁矩
电子的磁矩就是它的轨道磁矩与自旋磁矩之和：
$
arrow(mu) = arrow(mu_l) + arrow(mu_s) = (g_l arrow(L) + g_s arrow(s)) mu_B/hbar
$
其中可以有量子数：
$
|arrow(L)| = sqrt(l(l+1)) hbar, |arrow(s)| = sqrt(s(s+1)) hbar
$
=== 原子核的自旋（Spin）
原子核是一个微观粒子，但它本身又是由多个核子构成的一个微观粒子体系，在原子核内的各个核子都在作自旋和轨道运动。
*原子核的自旋*是*核子轨道、自旋角动量的矢量和*，是核内所有核子的轨道角动量 和 内禀角动量的矢量和。#footnote[同样质子数和中子数的两个原子核，若它们核内核子的
运动状态不同，则它们的自旋可能不同。]
*J - J耦合*：
$
arrow(j_i) = arrow(l_i) + arrow(s_i), arrow(J)=sum_i arrow(j_i)
$
先得到每个核子的总角动量，再耦合得到原子核的自旋。
*L - S耦合*：
$
arrow(L) = sum_i arrow(l_i), arrow(S) = sum_i arrow(s_i), arrow(J) = arrow(L) + arrow(S)
$
先得到总自旋和总轨道角动量，再耦合出原子核的自旋。
*原子核自旋$J$的大小：*
$
|arrow(J)| = sqrt(I(I+1)) hbar, I = 0, 1/2, 1, 3/2, ...
$
$I$为原子核的*自旋量子数*，为整数或半整数。
*原子核自旋$J$的空间投影：*
$
J_z = m_I hbar, m = -I, -I+1, ..., 0, ..., I-1, I
$
$m_I$为原子核自旋的*磁量子数* ，共 $2I+1$个取值。
- *偶 A 核*的自旋（量子数）为*整数*，特别地，*基态偶偶核*的自旋为*零*。
- *奇 A 核*的自旋（量子数）为*半整数*。
核子自旋的测量：原子光谱的超精细结构是由于核的自旋与电子的总角动量的相作用而形成的。可利用原子光谱的超精细结构定出核的自旋。
=== 原子核的磁矩（磁偶极矩 Magnetic Dipole Moments）
==== 核子的自旋磁矩
质子的自旋磁矩：
$
arrow(mu_(p,s)) = g_(p,s) mu_N arrow(S)
$
其中 $mu_N$ 为*核磁子* $mu_N = e hbar/(2m_p)$#footnote[玻尔磁子数量级大于核磁子]，$g_p = 5.5857$。
中子的自旋磁矩：
$
arrow(mu_(n,s)) = g_(n,s) mu_N arrow(S)
$
其中 $g_n = -3.826$。
核子存在*反常自旋磁矩*#footnote[如果核子也像电子一样是点粒子，按狄拉克方程可得出：$g_(p,s) = 2 ,g_(n,s) = 0$；中子由$u u d$构成，质子由$d d u$构成]说明：核子不是点粒子，内部结构具有电荷。
==== 原子核的磁矩
*原子核的磁矩*等于核内：
$
cases(
"所有质子的自旋磁矩、轨道磁矩",
"所有中子的自旋磁矩"
)
$
的矢量和。
$
arrow(mu) = sum_(i=0)^A (g_(N,l) arrow(l_i) + g_(N,s) arrow(s_i)) mu_N
$
其中$g_(N,l) = 0$，中子不带电，轨道磁矩为零。
磁矩是量子化的矢量，与角动量有对应关系：
$
arrow(mu_I) = g_I mu_N arrow(J)
$
$g_I$为*核朗德因子或核的回旋磁比率*，与组成原子核的核子的磁矩，核子在核中的相对运动磁矩都有关系，因此包含了核结构的信息。上式是平行于核自旋方向的磁矩分量。
核磁矩在 $z$ 方向的投影为：
$
mu_(I,z) = g_I mu_N m_I, m_I = -I, -I+1, ..., 0, ..., I-1, I
$
$m_I$为核自旋的磁量子数，共$2I+ 1$个取值。
通常取 $z$ 向投影的最大值表示*核磁矩*：
$
mu_U = g_I mu_N I
$
核子的磁矩像角动量一样可以互相抵消。
可以把核子的状态写成：
$
""^(2s+1)l_I
$
其中 $s$ 为核子的总自旋量子数，$l$ 为核子的总轨道角动量量子数，$I$ 为原子核的自旋角量子数。
#figure(
image("pic/2024-03-07-10-40-13.png", width: 80%),
caption: [
分析氘核（$""^2H$）基态的磁矩
],
)
$s$表示核子的自旋，$l$表示核子的轨道角动量。
=== 原子核的电四极矩 (Electric Quadrupole Moments)
电四极矩反映原子核的形状
- 原子核近似为球形， 但并不严格为球形。
- 多数核的形状是偏离球形不多的轴对称椭球。
- 原子核带电荷$+Z e$， 核内不同的电荷分布会产生不同的电势。
根据电动力学，电荷分布体系产生的电势可以表示为电多极子势的叠加：
$
phi(r) = sum_(l=0)^oo sum_(m=-l)^l (4 pi)/(2l+1) q_(l_m) r^l Y_(l_m)(theta, phi) = sum phi_i
$
其中 $q_(l_m)$ 为电多极矩，$Y_(l_m)(theta, phi)$ 为球谐函数。
特别地，前几个电多极矩为：
$
cases(
phi_0 = 1/(4 pi) (Z e)/z_0,
phi_1 = (1/4 pi) D/z_0^2 "其中" D= q d,
phi_2 = (1/4 pi) e Q/z_0^3 "其中" Q= (2/5) e z_0^2
)
$
原子核*电偶极矩$D = 0$* ,它在对称轴方向所产生的电势可以看作一个*单极子势*和一个四*极子势*之和。
原子核可看作是轴对称椭球，对称轴的半径为 $c$，另外两个半径为 $a$。则，原子核的电四极矩为：
$
Q = (2/5) Z (c^2 - a^2)
$
单位b = $10^(-28) "m"^2$。
- $Q>0$：长椭球形核
- $Q<0$：扁椭球形核
- $Q=0$：球形核
#figure(
image("pic/2024-03-07-10-56-31.png", width: 80%),
caption: [
电四极矩
],
)
*形变参数$epsilon$*：
$
epsilon =( Delta R)/R = (c-R)/R
$
则有
$
Q= 2/5 Z (c^2 - a^2) approx 6/5 Z R^2 epsilon = 6/5 Z r_0^2 A^(2/3) epsilon
$
== 原子核的统计性质
量子力学体系：
- 微观粒子的波函数只反映了出现的概率，无法“任意精确”
- 全同性：同类微观粒子间无法区分
- 只能用统计的方法来描述多个全同粒子组成的体系（如原子核）
*统计性*指的是描述*同类微观粒子体系*某一量子态的*波函数*的*粒子交换对称性*。
两类自旋对应*两类粒子*:
- 自旋为*整数*倍的粒子称为*玻色子*（光子、$pi$介子、偶A核），其波函数在粒子交换下不变。
- 自旋为*半整数*倍的粒子称为*费米子*（电子、中微子、$mu$子、质子、中子、奇A核），其波函数在粒子交换下变号。
=== 交换对称性
对同类微观粒子组成的多粒子体系，设描述此体系某一量子态的波函数为：
$
psi(x_1, x_2, ..., x_i ,..., x_j, ..., x_n)
$
其中$x_i$表示第$i$个粒子的位置和自旋状态。
用$P_(i j)$ 表示体系中第 $i$ 和第 $j$ 个粒子交换的变换算符，即：
$
P_(i j) psi(x_1, x_2, ..., x_i ,..., x_j, ..., x_n) = psi(x_1, x_2, ..., x_j ,..., x_i, ..., x_n)
$
由于微观粒子的*全同性*， 交换前后的波函数应描述体系的同一量子态，它们最多只相差一个*常数$lambda$*倍，即：
$
P_(i j) psi(x_1, x_2, ..., x_i ,..., x_j, ..., x_n) = lambda psi(x_1, x_2, ..., x_j ,..., x_i, ..., x_n)
$
可以得到：
$
P_(i j) P_(i j) psi(x_1, x_2, ..., x_i ,..., x_j, ..., x_n) = lambda^2 psi(x_1, x_2, ..., x_i ,..., x_j, ..., x_n)
$
由于$P_(i j) P_(i j) = 1$，所以$lambda^2 = 1$，即$lambda = +-1$。这是$P$算符的*本征值*。
$lambda$反应了波函数对称性，$lambda = 1$ 时，波函数在粒子交换下不变，即*对称波函数*；$lambda = -1$ 时，波函数在粒子交换下变号，即*反对称波函数*。
=== 费米子与玻色子
*费米子组成的全同粒子体系，其状态波函数交换反对称。*费米子须服从泡利不相容原理:两个全同费米子，不能同处在完全相同的单粒子态中。
*玻色子组成的全同粒子体系，其状态波函数交换对称。*玻色子不受泡利不相容原理的限制。
由奇数个费米子组成的粒子仍然是费米子；由偶数个费米子组成的粒子是玻色子；由任意个玻色子组成的粒子总是玻色子。
== 原子核的宇称
=== 宇称
*宇称*就是波函数在空间反演下的对称性：对称（偶宇称）$psi(-x)=psi(x)$，反对称（奇宇称）$psi(-x)=-psi(x)$。
宇称可能守恒——反应前后的“对称性”不变；也可能不守恒。
宇称是描述*空间反演运算*#footnote[空间反演与镜面反射等价]的物理量。
空间反演、宇称变换：
$
arrow(x) -> -arrow(x), (x, y, z) -> (-x, -y, -z)
$
镜像变换：
$
(x, y, z) -> (x, y, -z)
$
空间反演下物理规律的不变性与它的镜像过程服从相同的物理规律等价。即，将所有实验条件都取镜像，实际过程和镜像过程都遵守相同的物理规律。
宇称的概念是*微观世界中所特有*的，它是微观体系在空间反演变换下具有对称性时，所相应的守恒量。它描写微观体系状态波函数的空间反演对称性。
=== 空间反演不变性与宇称守恒
微观粒子的物理规律由Schödinger方程描述：
$
i hbar (diff psi(arrow(r)))/(diff t) = H(arrow(r)) psi(arrow(r))
$
其中$H$为哈密顿算符，$psi$为波函数。
在空间反演下， 粒子态的波函数为：
$
hat(P) psi(arrow(r)) = psi(-arrow(r))
$
微观粒子在空间反演下遵守物理规律不变，要求：
$
i hbar (diff psi(- arrow(r)))/(diff t) = H(arrow(r)) psi(- arrow(r))
$
即：
$
i hbar (diff psi(arrow(r)))/(diff t) = H(- arrow(r)) psi(arrow(r))
$
从而
$
H(arrow(r)) = H(- arrow(r))
$
即，空间反演变换下物理规律不变等价于$H(arrow(r))$在空间反演变换下不变。
从而：
$
hat(P) H(arrow(r)) psi(arrow(r))= H(arrow(r))hat(P) psi(arrow(r))
$
从而有*对易关系*：
$
[hat(P), H] = 0
$
说明它们有共同的本征函数，且这两个算符所代表的力学量，能量和宇称在该本征函数所描写的状态中，可以同时确定值。
能量具有时间平移不变性，即不随时间改变，则在同样一个波函数描述的状态中，宇称也有这样的性质，即*宇称不随时间改变*。
宇称不随时间改变，宇称量子数$pi$是*好量子数——守恒量*，或者说$H$描写的系统的宇称是不变的，称为*宇称守恒定律*。
*宇称守恒定律*：即一个孤立系统的宇称，奇则永远为奇，偶则永远为偶。若体系发生变化，体系变化前后宇称相同，它的值不随时间改变，即此微观体系的宇称保持不变。
宇称守恒是指*物理规律在空间反演下不变*，这指的是描写运动规律的微分方程不变，并非运动不变。
=== 原子核的宇称
原子核的宇称与核的能量状态有关。
原子核是由中子和质子组成的微观粒子体系(包含A个核子)， 它的状态可以近似地用有心力场中独立运动的各核子波函数的乘积来描写：
$
psi = psi_1 psi_2 ... psi_A
$
==== 轨道宇称
有心场中运动的粒子的波函数（球坐标下）可以表示为：
$
psi_i = R_(n_i l_i)(r) Y_(l_i m_i)(theta, phi) chi_(s_i m_s_i)
$
其中$R_(n_i l_i)(r)$为径向波函数，$Y_(l_i m_i)(theta, phi)$为球谐函数，$chi_(s_i m_s_i)$为自旋波函数。
宇称变换下，径向波函数和球谐函数的变换规律为：
$
R_(n_i l_i)(r) -> R_(n_i l_i)(r), Y_(l_i m_i)(theta, phi) -> (-1)^(l_i) Y_(l_i m_i)(theta, phi)
$
从而有
$
hat(P) psi_i -> (-1)^(l_i) psi_i
$
波函数宇称与$l$的*奇偶性*相同，称为*轨道宇称*。
==== 内禀宇称
微观粒子的内禀宇称与粒子的内部结构有关。
$
cases(
pi = +1 "质子、中子、电子",
pi = -1 pi"介子、光子"
)
$
==== 原子核的宇称
原子核波函数近似为各核子波函数的乘积：
$
psi = psi_1 psi_2 ... psi_A
$
原子核的宇称为各核子波函数的宇称的乘积：
$
pi_N = Pi_(i=1)^A pi_i dot Pi_(i=1)^A (-1)^(l_i) = Pi_(i=1)^A pi_i
$
其中$pi_i$为各核子的内禀宇称，$(-1)^(l_i)$为各核子的轨道宇称。
原子*核宇称*的奇偶性的奇偶性与各核子的*轨道角动量量子数*之和的奇偶性相同。
质量数为 A 的原子核的宇称：
$
pi_N = (-1)^(sum_(i=1)^A l_i)
$
一定的原子核状态具有确定不变的自旋和宇称，表示为：
$
I^pi
$
一定的核状态具有确定的宇称，只有当核状态改变时，即核内中子、质子的运动状态改变（表现在描述相对运动的轨道角动量的变化）时，核的宇称才会发生变化。因此：对原子核宇称的测定可以推知核内核子的运动规律，是研究核结构的重要手段之一。
测量核的宇称也是通过核衰变或核反应使原子核状态发生改变时进行的。
*强相互作用、电磁相互作用宇称守恒；弱相互作用宇称不守恒。*
== 原子核的能态和核的壳层模型
=== 原子核的能态
原子核是由核子组成的微观粒子体系。和原子相似，原子核也有能态结构，原子核有：
- 基态：最低能量态；
- 激发态#footnote[大部分核素有激发态，$""^1H$、$""^2H$、$""^3H$、$""^3H e$没有激发态]：能量高于基态的能态。
轻核的激发能较高；重核的激发能较低。
一般用四个物理量描述原子核的能级特征。
+ *能级能量*
+ *自旋*
+ *宇称*
+ *能级寿命（或能级宽度）*
*衰变纲图*或*核能级图*中，以横线表示原子核的某能级：
- 在横线左上/左边以符号$I^pi$表示该能级的自旋和宇称
- 在横线右上/右边标出该能级的*能级能量*
- 在横线右边标出该能级的*能级寿命（能级宽度）*
#figure(
image("pic/2024-03-12-14-07-28.png", width: 50%),
caption: [
衰变纲图
],
)
=== 幻数的存在与原子核的壳层模型
研究元素的化学性质发现，当*原子序数Z*等于2、10、18、36、54、86时，元素最稳定；这些数称为原子的*幻数*。
$
2(2l+1) "为一个壳层"
$
原子的壳层结构是解释元素周期表的基础，也圆满的解释了原子中出现幻数的原因。
自然界存在着一系列*幻数核*，即当*质子数Z或中子数N*为2、8、20、28、50、82、126时，原子核特别稳定。
虽然核的幻数不同于原子，但稳定性方面却有共同点，*液滴模型*在解释幻数问题上无能为力，促使人们联想到核内是否也有类似原子的*壳层结构*。
参照核外电子的壳层结构，核内要形成壳层结构，必须满足三个条件：
+ 每个核子能级（壳层） 上容纳的核子数目有一定的限制。
核子是*费米子*， 须服从*泡利不相容原理*。
+ 核内存在一平均场。
虽然与原子中存在不变的中心力场不同，但可以看成一个核子在其它核子所形成的平均场中运动，对接近球形的原子核，可以认为这个力场是中心力场。
+ 每个核子在核内的运动是独立的。
核子在核内独立运动。泡利原理既限制了每一核子能级所容纳核子的数目，同时也限制了原子核中核子与核子碰撞的概率。这是由于处于基态的原子核，填充满低核子能级的核子由于碰撞而跃迁到较高核子能级的概率很小，这就使得核子在核内*有较大的自由程*，即单个核子能看成在核内独立运动。
由量子力学，可求得核子在*谐振子势阱*中运动时的能量为：
$
E_n = n_0 hbar omega + 3/2 hbar omega
$
其中$n_0$为*谐振子量子数*：
$
n_0 = 2(nu - 1) + l
$
其中引入量子数：
- *径向量子数* $nu$：$nu = 1, 2, 3, ...$
- *轨道量子数* $l$：$l = 0, 1, 2, ...$(s, p, d, f, ...)
*自旋－轨道耦合项*，使核子能级（除了s态）发生分裂，得到了所有与实验一致的幻数。
- *自旋轨道耦合量子数* $j$：$j = l + 1/2, l - 1/2$
一个核子能级以$nu l_j$表示，每个核子能级上最多放$2j+1$个核子。
#figure(
image("pic/2024-03-12-14-30-03.png", width: 80%),
caption: [
核能级图#footnote[注意和核子能级图区分]
],
)
*主壳层*：两相邻幻数间的各核子能级，形成一个主壳层。
*支壳层*：主壳层内的每一核子能级，叫做支壳层。
质子和中子各自形成自己的壳层（核子能级结构）， 即原子核内存在质子壳层和中子壳层两个壳层结构。
=== 原子核基态的自旋和宇称
原子核的基态是最低能态，它的自旋和宇称是核的基本性质。
*基态*，按原子核的壳层结构模型，指质子和中子都填满最低一些核子能级时原子核的状态，这时，原子核的能量状态最低。
*激发态*，按原子核的壳层结构模型，指核子处于较高核子能级而其较低核子能级未填满时原子核的状态，这时，原子核的能量状态较高。
#grid(
columns: (1fr, 1fr),
[#figure(
image("pic/2024-03-12-14-32-42.png", width: 85%),
caption: [
$""^(16)O$的基态
],
)],
[#figure(
image("pic/2024-03-12-14-32-51.png", width: 85%),
caption: [
$""^(16)O$的激发态
],
)]
)
==== 偶偶核基态的自旋和宇称
*基态*偶偶核：当偶数个核子处于最低那些核子能级时，在每个核子能级上的核子数都是*偶数*。
#figure(
image("pic/2024-03-12-14-36-43.png", width: 20%),
caption: [
偶偶核基态的自旋和宇称
],
)
- 自旋：同一核子能级的所有核子的角动量矢量和为零，则质子壳层和中子壳层都具有等于零的总角动量。
- 宇称：每一核子能级的核子数均为偶数，因此各核子的轨道角动量量子数之和为偶数。
*偶偶核基态的自旋为零，宇称为正。*
==== 奇A核基态的自旋和宇称
基态奇 A 核：由于其余偶数个核子的贡献，相当于一个偶偶核的贡献，因此，奇A核基态的自旋应与*最后一个奇核子的总角动量$arrow(J)$相同*。
#figure(
image("pic/2024-03-12-14-41-13.png", width: 20%),
caption: [
奇A核基态的自旋和宇称
],
)
- 自旋：最后一个奇核子的总角动量$arrow(J)$
- 宇称：最后一个奇核子的轨道角动量量子数$l$的奇偶性
奇A核基态的状态（自旋和宇称）由*单个非成对的核子的状态*（总角动量及轨道角动量）决定。这种模型叫*单粒子模型*。
==== 奇奇核基态的自旋和宇称
奇奇核基态的自旋由最后一个*奇中子和奇质子的角动量耦合而成*。
- 自旋：由于中子和质子的自旋都是$1/2$，而轨道角动量总是整数，因此，耦合结果必定是*整数*。
- 奇奇核基态的宇称由两个奇核子的状态（它们轨道*角动量量子数之和的奇偶性*）决定，奇奇核基态的宇称为：
$
pi = (-1)^(l_n + l_p)
$
#newpara()
*镜像核*的*基态自旋和宇称往往相同*。按壳模型，镜像核质子壳层和中子壳层互换，而两个壳层结构相同，因而得到的基态自旋和宇称是一样的。
==== 同质异能素
同质异能素：寿命长于0.1s的激发态核素。
同质异能态的角动量与基态或较低激发态的角动量之差$Delta I$较大，能量之差一般比较小，因而$gamma$ 跃迁概率比较小。
轻核中没有同质异能素，因为其能级间距大，$gamma$ 跃迁容易发生。
N和A比幻数略小的概率比较大。同质异能素岛：Z, N=50,82,126前。
同质异能素的*寿命较长*；同质异能素的*内转换系数较大*。 |
|
https://github.com/typst/packages | https://raw.githubusercontent.com/typst/packages/main/packages/preview/metro/0.1.0/src/impl/impl.typ | typst | Apache License 2.0 | #import "unit.typ": unit, tothe, raiseto, qualifier
#import "num.typ": num
#import "qty.typ": qty |
https://github.com/polarkac/MTG-Stories | https://raw.githubusercontent.com/polarkac/MTG-Stories/master/stories/049%20-%20The%20Brothers'%20War/003_Episode%203%3A%20Sword%20One.typ | typst | #import "@local/mtgstory:0.2.0": conf
#show: doc => conf(
"Episode 3: Sword One",
set_name: "The Brothers' War",
story_date: datetime(day: 21, month: 10, year: 2022),
author: "<NAME>",
doc
)
#strong[28 AR]
Kroog died on a crimson morning.
To Sanwell, it sounded like a festival day, only the crowds cheered in a minor key, and the booms and reports were not fireworks exploding, and the smoke rising over the city stank of burning industry and steaming bricks.
#figure(image("003_Episode 3: Sword One/01.jpg", width: 100%), caption: [Art by: <NAME>], supplement: none, numbering: none)
The orniary's main yard was abuzz with activity. Technicians and artificers sprinted back and forth hauling anti-armor bolts, powerstones, and avenger swords. Stompers and other autonomous units waited in ready ranks, crowding the plaza. Piles of ammunition, spare parts, and other material stood in hasty stacks. The five student pilots and their instructor stood in front of the canvas-covered supplies, facing a rank of old, refurbished avengers.
The morning sun hung low and hot in the sky, burning away the rest of the night's blood-warm rain. Sanwell, at attention, swayed, lightheaded. His stomach lurched, and he retched on the hot brick between his boots.
"Pilot Sanwell, you will tighten up your constitution," Llora shouted. The cadets' instructor was red-faced and stern, dressed in a crisp and clean uniform despite the early hour and hurried muster.
"Sorry, ma'am," Sanwell said. He spat the last of his sick out onto the hot stone plaza and wiped the back of his hand across his mouth. He had nothing to cough up but water and nerves; the attack had come before breakfast.
"You good, San?" Rica muttered.
Sanwell's face burned with embarrassment. Rica stood unwavering at his side, as stoic as if he was carved from the red brick of Kroog itself.
"Fine," Sanwell said. He wanted to die. "I think I had something sour last night."
Rica did not answer. The warning bells of Kroog rang out across the city. The sound churned Sanwell's stomach almost as much as Rica's stiff non-acknowledgement.
"I'm worried about my brother," Sanwell said. "Rendall is in the capital proper—he's a flyer, he's not cut out for fighting."
"Eyes forward!" Llora barked, interrupting Sanwell's one-sided conversation with Rica. The old Suwwardi paced before the short line of avenger trainees, staring at each one in turn. The woman was tough as new leather and harsh as the lime that cured it, thin as a reed and sharp as needle.
Sanwell felt faint. He was dipping into metaphor, he realized, to get away from the moment.
"You five cadets," Llora began, "have the honor of being the only ground-pounders in the city capable of crewing an avenger while keeping your head on your shoulders." Llora pointed to the ground beneath her boots. "You are being called up, boys. Training is over. Today's the day you save Kroog."
Sanwell looked between his own boots at the crimson bricks, neatly laid in spiraling star patterns. That had taken some getting used to for Sanwell—the Yotians decorated everything. It meant everything from cooking to construction took a little bit longer, but to young Sanwell that was worth it. In Kroog, as in much of Yotia, even the streets were art. Unlike the stoic blocks of his native Penregon, Sanwell could walk with his head low or eyes up, and either way, he would find a little majesty. It was as a city should be, Sanwell came to think: full of little wonders, plainly hidden delights, all watched over by mighty triumphs.
Was he ready to fight to defend it?
Not a theoretical question. Llora had just leaned in, face to face, to ask him.
Sanwell blinked and wavered.
"I said," Llora growled, "are you ready to fight for Kroog?"
"Uh, yes, I am," Sanwell said.
"Yes, #emph[ma'am] ," Llora corrected Sanwell. "You're on the line now, Sanwell. No more training, no more practice. You ready to fight?"
"Yes ma'am," Sanwell said, louder.
Llora nodded. "Show me," she said. She pressed a slim device into Sanwell's hand and stepped back. The four other students—#emph[pilots] , Sanwell corrected. #emph[Mentality. Change your mind, change reality. You're a pilot now] —the four other pilots walked to Llora, taking up relaxed but attentive positions behind the instructor.
Sanwell took the handheld device—a command rod, but a new model—and checked it. It was the length of his forearm, etched on one end for grip, tapered ever so slightly at the smooth opposite end. A small, tactile switch rested under his thumb when he held the rod. Sanwell thumbed the rod on, and a soft hum warmed the tool. A toggle and a trigger rested under his pointer and ring fingers; more controls. Sanwell flipped the toggle and listened to the slight change in the rod's pitch. He pointed the rod at his hand, pulled the trigger, and saw the brief flash of light on his palm.
"Check," Sanwell said. He raised the command rod. Stopped. "Uh, ma'am," he said to Llora. "Which unit am I paired to?"
Llora pointed with her chin. "That one," she said.
Sanwell turned. His jaw dropped.
A new, shining avenger, one of the sword-pattern prototypes, still curled on its transport sledge. Sanwell had only seen the plans for them, passed around the mess during meals. They were larger, lighter, faster, more powerful—unkillable, the artificers bragged. The best they've made to date.
Behind this avenger waited four more. Technicians and artificers hurried to clear the packing debris—straw, canvas sheathes, leather pads, and protective oils—from the waiting machines, preparing them for activation.
Sanwell grinned, nerves momentarily suppressed by excitement.
"You'll find these sword patterns much more intuitive than the units you've been training with—even for prototypes." Llora said. Sanwell thought he could hear the pride in his instructor's voice.
"What's its name?" Sanwell asked Llora.
"Sword One," Llora said.
Sanwell raised his command rod and clicked the transmit button. The rod pitched up.
"Sword One, at attention!"
Sword One unfolded, standing from its sledge. The machine was humanoid, around fifteen feet tall at the shoulder. The prototype avenger looked to Sanwell like a lithe knight animated by magic fire: a mirror-polished cuirass covered its central power core, exhaust apertures fluttering, venting excess heat from its thoracic powerplant. The roar of its power core sent a rush through Sanwell. This was #emph[power] , and it awaited his command.
"Sword One," Sanwell spoke firm and clear, as he had been trained. The command rods themselves were little wonders, able to pick out its operator's voice through the chaos of battle or a crowd. "At the ready!"
The avenger moved in a fluid, silent twist to a low ready stance, positioning one manipulator on the hilt of its primary blade, the other out for balance. Sanwell rocked backward, hair tousled by the rush of air displaced by the speed of Sword One's maneuver.
"Sword One, draw and guard!"
Sword One drew its primary blade, whipping it into a medium guard, one manipulator on the blade shaft to guide it and stabilize against incoming attacks. The blade was larger than a person, eight feet long and a foot wide at the base. Like its cuirass, it was polished to a mirror shine and caught the sun, flashing as it moved.
Sanwell could not suppress his excitement. With one of these, they could turn the tide. With #emph[five] ? He raised the rod one last time.
"Sword One," Sanwell commanded. "To me!"
The avenger darted toward Sanwell, stopping in a defensive crouch above him, sword at the ready.
"Good work, Sanwell." A different speaker.
Sanwell turned and saw Tawnos, Urza's chief apprentice, standing with Llora and the other pilots.
"Sir," Sanwell saluted. He double keyed the command rod and, as with the older stompers, Sword One dropped its defensive stance, resting at ease.
"I see you're acquainted with our new model already," Tawnos said. He spoke with a smile, though Sanwell read through the chief apprentice's brave face.
"It's a dream, Chief," Sanwell said. "Movement fidelity feels one to one—how did Urza do it?"
"Later, son," Tawnos said. He was breathless, as if he had just stopped from a run.
Sanwell realized that was probably the case: the cause for this promotion was not a happy one. Kroog was under attack. He walked over to the group of students and fell in line with them.
"You five are the best of our student corps," Tawnos said, addressing Sanwell, Rica, and the others. "Llora here has told me that each of you possess the skills, temperament, and cleverness necessary to command our sword-pattern avengers, and so it is with great pride that I hereby, officially, promote you to full pilots."
The cadets looked to each other with excitement over having their promotions confirmed—and by Urza's own assistant, no less!
"We can't go through the usual ceremony right now, nor can we bother with unit placement," Tawnos said. He hunched slightly as he spoke, apologetic, a stiff formality about his presentation. He really meant it, Sanwell thought, he really was sorry there could not be any ceremony about the day. Sanwell's heart swelled—Urza may have been the brilliant one, but Tawnos was nearly as smart, and he cared. That made all the difference.
"Kroog is under attack," Tawnos said. "The first waves of Mishra's force have crossed the Mardun; they control the River Wards. The spearhead of their attack is a detachment of dragon engines—large automatons capable of breathing fire. We believe them to be unpiloted."
The students—pilots, Sanwell reminded himself, for #emph[real] this time—exchanged worried looks. Rica, Sanwell knew, was Yotian, and so was Carlo, who was from Kroog's River Wards. Sanwell looked to Carlo and saw he had paled, a bloodless look of fear and worry falling over him. Sanwell put a hand on his back, hoping to steady him.
"Thanks," Carlo said, quietly.
"The city guard and Kroog's garrison have drawn a defensive line around the capital district," Tawnos continued. "Evacuations of the other districts are underway."
"Does that mean we've given up the city?" Carlo said, voice wavering. "What about the River Wards?"
"It means we're defending what we can hold," Tawnos said, ignoring Carlo's second question. "But standing in one place isn't going to win us the day, which is where you and your new avengers come in: we're going to mount a counterattack to buy the evacuations more time." Tawnos motioned to Llora, who hefted a long crate into the middle of the group. She levered the crate open, revealing four command rods packed in straw.
"Each of you take one and pair up," Llora said. "Sanwell, you stick with Sword One." She passed Sanwell an empty holster.
"We need you and your avengers to take down the dragon engines," Tawnos said. "Once the engines are down, we stand a chance to drive Mishra's forces back."
Sanwell listened to Tawnos's briefing as he belted the holster on. The command rod fit snugly in the leather scabbard. That moment made #emph[this] moment real, Sanwell realized. He looked to the other cadets—#emph[pilots] —and watched them pair up with their avengers. Rica took Two, Carlo paired with Three. The others were cadets from a different year, the one just after Sanwell's, and unfamiliar to him. They paired with Four and Five.
"Good," Tawnos said when all the pilots were paired. "I have to go, but I've given instructions here to Llora for your deployment." He looked to the five pilots, hesitating. "We'll have soldiers escort you, so don't worry about being exposed to the fighting," Tawnos said. His voice was hoarse, as if he had been shouting, even though all he did was talk. "With these avengers, visual range will do—anything you say into the command rod, they'll be able to pick up. Don't get too close, aim with the rod, and remember to stay behind your escorts. Good luck, cadets—" Tawnos said. "Pilots," he corrected. "Good luck, pilots. Stay safe, and if you're in danger—don't think, just run. Hench, in the east, is where I have been told the army will gather."
Tawnos's face was a pale mask, graying as if wounded. Sanwell searched for the optimism that usually animated Tawnos but did not find it. A bolt of worry bittered his gut: Tawnos was afraid. Calm and steady Tawnos, the one who came to mess and laughed with the cadets, was afraid. He couldn't even look at them. Worry curdled to fear, a little fear that gnawed at him. How bad was it out there, really? A sudden snap of adrenaline, and Sanwell flinched, moving to raise his hand as if he were still in class.
"Master Tawnos, sir?" Sanwell asked. "My younger brother, Rendall—he's a cadet in the ornithopter corps, stationed at the palace."
"Rendall," Tawnos said, frowning. "I might know him, but don't worry—all of our thopters are deployed with Urza's forces elsewhere or about to depart," Tawnos said. "If he's in the thopter corps, he'll be out of here soon enough."
Sanwell exhaled a long breath he hadn't realized he was holding. He did not have time to thank Tawnos, though, as a sudden and tremendous explosion roared up on the far side of the city along the Mardun, where the fighting was heaviest.
The commotion in the orniary yard stopped as everyone turned to look, even Tawnos and Llora, at the distant calamity.
Roiling crimson smoke leapt into the sky. A whole block of the city rippled with fire. Sanwell could see a darker shape moving in the center of that rising blaze, a conflagration so great that flames swallowed the tops of the belltowers that remained standing. They crumbled as the dark shape moved and another roar split the sky, a gout of smoke and fire lancing through the blocks along the Mardun.
A dragon engine.
Tawnos cursed. He pressed a small order scroll into Llora's hands, with instructions to give them to the captain at their post. He left the yard with a quick salute to the pilots, hurrying just short of running.
"Right," Llora said, watching him go. "Let's get moving—double quick, avengers online and vigilant." Sanwell noticed that Llora had belted on a sword at some point during Tawnos's briefing.
As a unit, the five pilots and their avengers filed out of the yard. Sanwell looked back over his shoulder as they departed; behind, crews hurried to repurpose the transport sledges to haul any goods, materials, chassis, and supplies they could fit. They were preparing to evacuate the orniary.
A shout from Llora. Sanwell was falling behind.
"With me, One," Sanwell said to his avenger. Together, the two of them hurried to catch up with the rest of the pilots as they moved down into the city.
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Kroog was burning, and people choked her streets, fleeing the fire. Sanwell couldn't stop thinking about festival days, where competing parades to the many gods of Yotia snarled the wide brick boulevards and cheering crowds thronged in the side streets. The ringing of festival bells crashed and clamored through the city, a high and bright sound of chaotic joy that propelled and intertwined with the music that filled the air. Sanwell had been overwhelmed during his first festival season in Kroog; by his second year in the city, he fell in love with it. Far from the ponderous ceremonies in Argive, the festivals in Kroog and across Yotia were ebullient, alive. Never in his young life had Sanwell lived in a place where the gods were so close—and never did he imagine himself becoming someone who loved that proximity.
But today, in the blood-slick red brick streets, the gods felt quite distant. This day was a dark mirror to those celebration days, and each block the pilots advanced plunged them deeper into that horrible mirror; the ringing bells today were the same bells that tolled on celebration days, only now they screamed.
"Listen," Llora commanded Sanwell and the rest of the pilots. "Stay close to me and order your avengers to do the same—they will avoid civilians better if you let them navigate the crowd on their own. You focus on staying close to me."
Llora and the pilots hurried through the city streets, shoving their way through the fleeing crowds as they made for the northern district. Sanwell labored under the weight of his pilot kit, donned in haste that morning. Not two blocks into the city proper and his jumpsuit was soaked through with sweat under the light cuirass. The satchels he carried—spare powerstones for Sword One, a brace of tools, small and delicate replacement parts—together felt like an anvil's weight across his shoulders. The few encouraging shouts Sanwell registered from the general pandemonium did nothing to hearten him; to the contrary, they seemed thin and hopeless cries. There was a second, lower tone bubbling through the shoving and rushing crowds, a more terrible fear under their immediate panic. This was not just an attack: this was the beginning of a war, and they were losing. Kroog might die, and with it, all Yotia.
The closer they got to the northern districts, the thinner the crowds were, and the louder the sound of fighting. Fewer bells rang here, but they were still audible, echoing in from the other districts still hurrying to evacuate. The closer the pilots came to the northern district, the more bodies they came across as well. At first, they were the crumpled forms of people who had been trampled in the early rush to flee; by the time the pilots reached their rendezvous point, they started to encounter the bloody and burned dead—soldiers and civilians both.
"Hold here, pilots!" Llora shouted, calling them to a halt. The five pilots and their avengers came to a stop in an abandoned market plaza. Overturned stalls and stands scattered bright sprays of spices, fruits, and vegetables across the ground. A small fire licked the charred ruins of a storefront where a food seller's cart had tipped over, spilling hot coals into the shop's dry interior. People had fled in the middle of their morning routines, leaving everything behind.
At the far end of the plaza was a hasty but substantial barricade defended by at least two dozen Yotian soldiers, soot-stained and bloodied after retaking the plaza. The barricade would not hold off a dragon engine, but it would deter any human soldiers from attacking. The Yotian squadron looked to the avengers with hope, and their pilots with concern. Sanwell tried not to look at the pile of dead Yotians, civilians and soldiers both, that lay in a heap next to the small fountain at the center of the square. Debris fluttered in the hot wind stirred by the raging fires. A scatter of dead Fallaji troopers splayed out unceremoniously on the far end of the plaza, arrow shafts sticking from their bodies.
Llora talked with the ranking officer there—a lieutenant, by his stripes; the captain Tawnos had assigned the pilots to had been killed. Sanwell figured the lieutenant to only be a year or so older than he, though it was hard to tell under his heavy armor.
Sanwell overheard the lieutenant say that this had been a second-line medical post before a bitter fight contested the small plaza. The Yotians now planned to use the plaza as a staging ground for the counterattack: Stacks of firebombs, arrows, and darts stood near the barricade. Occasionally, a runner would come sprinting into the square, haggle with the supply officer, and then run back with a bundle of firebombs tossed over their shoulder or a healer in tow.
"Pilot Sanwell," Llora called, waving him over. "Sanwell, this is <NAME>—" Llora's introduction was drowned out by a roar loud enough to send everyone in the plaza diving for cover. A long, buzzing series of explosions followed moments later, reports echoing out over the city.
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The bells nearby fell silent. Sanwell and the rest of the pilots, Llora included, stayed prone, their avengers watching over them. Some of the soldiers pushed themselves to their feet, gathering up their spears and adjusting their sword belts, peering over the barricade, crawling back to their posts.
The brick was dry and hot. Sanwell clutched the control rod to his chest. The thumping of his heart against the ground matched the rumbling of the nearby dragon engine on the move.
The bells began to ring again and Llora stood, hollering at the pilots to get up. <NAME> bellowed at the rest of his soldiers to get to the walls. Sanwell stood on trembling legs, helped up by Rica and Carlo. The two younger pilots stuck close to Llora and had already sent their avengers to the barricade.
Big, booming explosions crashed through the plaza, sending whistling and skittering shards of metal into the air. Sanwell flinched as a chip of plaza brick leapt up and cut his cheek, flung into him by something pinging off the ground as it flashed past him.
Shrapnel—the Fallaji were attacking!
Sanwell, rooted to the spot, watched as Yotian soldiers hurled firebombs over the barricade toward the charging, unseen Fallaji. Smoke and bright flashes followed, explosions thundering and echoing off the storefronts, raining glass and clouds of dust on the street opposite the barricade. Screams mixed with the rising cry of charging Fallaji as they returned fire, launching heavy crossbow bolts and whistling arrows at the Yotians. Sanwell ducked just in time behind Sword One's extended arm, cringing at every whining ping that rattled off the avenger's armor.
Above it all loomed the dragon engine. Mishra's engine. Sanwell saw through the smoke the heat-warped visage of the titanic machine, reptilian, a beast of artifice and war towering high above the building tops of the northern district. It roared, hungry, cruel, #emph[alive] , and advanced toward them, shrouded once more in the thick smoke.
"Sanwell!" Llora shouted to be heard over the cacophony of combat. "Take Rica and Carlo down that side street," she ordered, pointing with her sword down a narrow alleyway. "Find a way to flank the engine and bring it down, pilot!"
"Yes ma'am!" Sanwell saluted. He started to ask for more direction, but Llora had already hurried toward the wall, a bandolier of firebombs thrown over her shoulder.
"Get your Swords," Sanwell said to Rica and Carlo. "Let's go kill a dragon."
Sanwell led the charge down the side street following Sword One. Rica and Carlo followed behind, Swords Two and Three in tow. The sound of battle at the plaza barricade surely gave their movements some cover. They moved quickly, not quietly.
They made it halfway down the alley before the dragon engine fired a blast into the plaza behind them.
A roar like the sky splitting open, a rippling crescendo of explosions. The boiling red mist scoured the plaza, blasting apart the Yotian barricade and incinerating its defenders.
Sanwell, Rica, and Carlo turned, looking on in horror as the crimson blast swept across their narrow view of the plaza. Llora and the other pilots, <NAME> and their soldiers—gone in a breath.
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The smoke lingered, not moving despite the stinking, howling furnace-blast wind. The air itself sizzled, writhed in pain, crackled with heat-tortured bolts of lightning.
A body staggered into the alleyway from the burning plaza. None of the pilots could tell who it was. The poor soldier bounced off the alley wall, stumbling like a drunk, and collapsed, shattering into ash where they hit the ground. All thoughts of revenge and glory quit Sanwell then; worry stopped gnawing and started consuming.
The plaza echoed with the sound of charging boots: soldiers emerged from the boiling smoke, helms slammed shut against the burning air, their anti-mech spears raised toward Swords Four and Five. Their pilots gone, blasted and heat-warped by the dragon engine's burning breath, the machines nevertheless held their ground, swords flashing. A handful of soldiers died, but the avengers were torn down to cheers. They had slowed Mishra's engine for a moment, and the greater advance of his forces not at all.
A moment. Sanwell remembered the years of training; it bought those other pilots, whose names he never knew, a moment.
Carlo started to scream and neither Sanwell nor Rica could get him to calm down. There was no telling whether the Fallaji could hear them, but they couldn't take the risk. Rica tore open a linen bandage from his medical kit and tied it around Carlo's mouth while Sanwell held him steady. The two of them dragged Carlo away into the darkness of the alley, praying that the dragon engine would not follow.
Their sword avengers followed, ash piled on their armored shoulders.
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Sanwell and Rica, with an alternating mute and screaming Carlo in tow, followed their avengers through the alley into another small and nameless plaza. This one was a crossroads walled in by two- and three-story buildings on all sides. Their alley continued across the plaza; the crossing road was a proper carriageway, wide enough for three carts abreast. At one point in the morning, it had been fortified by a barricade on the northern exit from the plaza, blocking access to the rest of the city against anyone approaching from the Mardun. Now the barricade lay in ruins. Yotian and Fallaji dead splayed across the smoldering wreckage, flies already making meals of them. A stray dog scurried away when the avengers and their pilots came running into the plaza.
Sanwell and Rica ordered their avengers to take up watch on the Mardun side of the crossroads, then staggered to the end of the square opposite the barricade, dragging Carlo with them. His avenger stood still at the end of the alley, awaiting orders. The three of them sat on an overturned cart and caught their breath. The dragon engine hadn't followed them. For the moment, in this quiet corner of besieged Kroog, they were safe.
"What do we do?" Rica asked.
"We can't fight the engine," Sanwell said. "Not even with our Swords—we'd need an army of them to fight that."
"So what do we do?" Rica asked again.
Sanwell looked back down the alleyway they had just emerged from, back toward the scoured plaza. He looked up, at the smoke-darkened sky. The sun, so clear up by the orniary, burned a dim, sick orange. Ash drifted down, black and gray.
"We run," Sanwell said. "Like Tawnos told us—if we're in danger, we run."
Rica took his own survey of their surroundings. "Where?"
The dragon engine bellowed again, deafening, vision-shaking. Sanwell and Rica clapped their hands over their ears, eyes watering at the loudness of the roar. It passed, and like thunder from a moving storm, the two boys listened for its source; it appeared the dragon engine was moving away from them and their avengers, making for the heart of the city.
"Away," Sanwell said, a little too loud as his hearing slowly came back to him. "Anywhere but here. Didn't Tawnos say something about some town? Hinge?"
"Hench," Rica corrected. "Some caravan town, I think. A place for horses to get water."
"Maybe there," Sanwell said.
"We'd have to cross the city," Rica said, chewing his lip. "West might be better—we could run to the western gates and make for the coast, find a ship."
Sanwell hung his head. He thought of his brother, Rendall—was he in the air by now?
"Where would they send the evacuees?" Sanwell asked Rica. "Korlis or Penregon?"
"Korlis is closer," Rica said. "But they're merchants, and they're neutral. Besides, they don't have a standing army, just mercenaries. My guess is Penregon. It's farther, but that's where Urza and—"
A sudden clatter and a shout sounded from northern entrance to the crossroads—the Mardun side where their avengers stood guard.
Sanwell and Rica looked over to see a rank of Fallaji brasscaps approaching the crossroads. Behind them, Sanwell could see what looked like a forest of pikes under which shone the polished brass helms of a whole marching column of soldiers.
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"Sanwell," Rica said, standing. He wasn't calling Sanwell's attention, only uttering. A reflexive gasp, spoken in disbelief at what he saw: the Fallaji army, unimpeded, marching toward them.
"Sword One," Sanwell cried. He stabbed his command rod toward the Fallaji and pressed the trigger. A thin beam of light visible only in the passing smoke dazzled the front rank of the brasscaps. "Attack!"
Sword One bounded toward the Fallaji, followed a second later by Sword Two. Carlo, catatonic, triggered his control rod, flashing the ground at his feet. Sword Three did not move; the machine had dropped into an idle, sword ready but not raised.
The marching soldiers were unable to form a pike wall before the two avengers crashed into them. The front ranks died in chaos, their pikes skittering off the avengers' armor plating. The two avengers worked their great swords with a butcher's efficiency, grinding the Fallaji advance to a halt at the ruined barricade.
Sanwell watched in horror and awe as the avengers cut through the brasscaps. The sound of their swords buzzing through the air, the heavy, wet thunk of the blades meeting and separating flesh, smashing bone, crunching through the proud, bright Fallaji armor as if it were little more than thin foil. Sanwell could only stagger backward, command rod level and aimed, and watch the avenger interpret his most basic command. Sword One cleaved through the soldiers before it with expeditious strikes. Short chops, one manipulator holding the hilt of its sword and one along the blade to guide it.
Rica piloted Two with precision, directing his avenger toward officers and targets that presented a threat to their machines. Soldiers with heavy explosive-tipped lances and crossbows, officers with their command flags and steady voices—Sword Two, under Rica's command, hunted them through the chaos made by Sword One's assault.
Who taught Sword One how to fight?
Sanwell stabbed his control rod toward a pair of brasscaps who had made it around Sword One. He triggered the rod, dazzling its beam across the soldiers, and Sword One immediately interceded, impaling them both with one heavy lunge. Sword One lifted them and swept them off its weapon, sending their bodies tumbling into the still-advancing column.
At some point Sword One had to learn how to move like that, Sanwell thought, keying another target. He backpedaled, retreating with Rica, dragging Carlo with them, putting distance between them and the fight.
Who taught Sword One how to interpret his simple first command and translate it into movements Sanwell could not do himself? He had seen inside the older models as part of his training—they, like Sword One, were not alive. As he understood it, they could not think. They were machines, humanoid assemblies of a thousand complex calculations and delicate complications; thousands of hours of genius and technical acumen and human labor set to a single purpose, achieved with uncanny grace: to swing a sword and end a life.
Brilliance. Madness.
Sword One ejected its dull blade toward the advancing brasscaps, then drew a fresh razor from the magazine on its back. The avenger moved so smoothly that Sanwell could almost believe it was a giant person in armor, a warrior that could not be stopped by fear, pity, or fatigue. Spears and crossbow bolts shattered on Sword One's legs and deflected off its brachial and thoracic armor plates, each glancing blow driving home how indestructible the avenger was.
Another feeling mixing with Sanwell's fear: relief. Relief that the Swords were on #emph[his] side.
An explosion boomed out over Sword Two's upper half, staggering the avenger into Sword One. Sword One gracefully sidestepped its fellow, and Sword Two fell back into the plaza, landing hard enough to crack stone.
Rica swore and Sanwell saw why: a bomb had blown away Two's right arm. Hydraulic fluids and dark oil sprayed from the damaged equipment, pumping into the air until Two's internal systems shut off the flow. Drawing a fresh blade with its remaining arm, Sword Two struggled back to standing—but it was too late. The gap had been made.
The Fallaji brasscaps advanced, driven by their officers behind, cheering, hoarse, heartened by the blow dealt to Sword Two. Sword One tried to intercede but could not hold the road by itself. At first only a handful of brasscaps made it through; Sword Two tried to drive them back, but the Fallaji fired a hail of explosive bolts at its head and legs. The reports boomed on top of each other, pressure waves battering the wounded machine back to the ground. As it fell, soldiers swarmed Sword Two, stabbing bomb-pikes into its joints and between its armor plates, arresting its movement. On the other side of the yard, more brasscaps brought the idle Sword Three to the ground, anti-mech pikes stabbing and slicing vital internals, joints, and mechanisms.
Sanwell screamed something wordless, a mix of terror and fury, stabbing his command rod at the Fallaji, stabbing a dazzling beam at them again and again. No commands, nothing from his training, just giving voice to raw panic as the enemy flooded into the crossroads. Sword One fought on, as it was designed to do.
The brasscaps detonated their bomb lances and killed Sword Two. The avenger's powerstone erupted, a bright flash that blanked the square with white light.
Sanwell went flying, blinded by the blast. Somehow, he held on to his command rod, and as he lay on his back he blinked his vision back from burned to blurry. He could see Carlo laying still, near the overturned cart, uniform smoldering. He watched Rica push himself to his feet, his cheekbones and nose raw and burned. A sandpaper wind whipped through the streets of Kroog, scouring Sanwell's own burned face and hands. He cried out in pain, voice muffled as his hearing was slow to return.
The bells still crashed and rang. Other explosions thumped throughout the city.
Distant, screams.
Distant, the roar of dragon engines.
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Sanwell's world was a haze of cloudy, gray smoke under an ochre sky. The sun above was a dying marigold, fat and close, threatening to slip from the sky, an egg's yolk sloughed from its white. Everything stank of burning wood, burning oil, burning flesh. Ash fell like snow.
When Sanwell was new to Kroog, dispatched with his brother as a child to learn artifice at the orniary, he'd been schooled in Yotian custom and belief. Cultural education, his parents told him. Necessary for any child of the east, for the young scions of civilization to understand the world they were destined to rule; in this education, Sanwell learned that of the many gods of Yotia and their domains, no single one ruled over an underworld or accursed afterlife. A human soul was too myriad to be thrown into hell on the word of one god: damnation for the Yotians was not that simple. One had many souls throughout the course of their life, and each of them was afforded its own judgment.
Sanwell knew now that the Yotians had missed an aspect. They had forgotten a god somewhere in their celebrations: the one who'd damned his living soul to this city of hell. Sanwell imagined that morbid deity flying above the city on torn wings, belching crimson mist down into its burning streets.
"Sword One," Sanwell whispered into the command rod. "To me." Be it hell or nightmare, Sanwell wanted out.
Dark shapes stalked through the haze, though none cut the reassuring profile of Sword One. Lumpen silhouettes bent over their long spears, wide helms turning slowly, listening, searching.
Sanwell moved up to a crouch, slipping further back from the moving shapes. He padded past Rica and hissed for him to follow.
Rica shook his head and held a finger to his lips. He pointed, directing Sanwell's gaze.
Carlo. He crawled toward Sanwell and Rica. The burns across his back and legs were terrible, rendering him into a mess of blistered flesh and melted steel.
"San?" Carlo cried, sobbing. "Rica?"
Rica started toward Carlo, but Sanwell grabbed him and shoved him back.
The dark shapes in the brick haze stopped, listening. Their broad heads turned. Their spears probed the gently falling ash.
"Where are you guys?" Carlo cried again.
A flurry of crossbow bolts thudded into Carlo's back, killing him. A second volley peppered him seconds later, stray bolts pinging and ricocheting off the ash-covered ground. The brasscaps shouted, calling to each other the location of the dead pilot.
"Sword One, kill!" Sanwell shouted into his command rod, his voice cracking. "Kill!"
Rica turned, grabbed Sanwell, and shoved him to a run. Over his shoulder, Sanwell heard Fallaji soldiers screaming in terror under the rising whine of a laboring, wounded machine. He turned, backpedaling for three short steps, and saw Sword One's tall, armored form rising from the darkness.
Sword One was a heat-warped knight in yolk-yellow light, golden death splattered with soot and ash. Though horribly wounded, Sword One was not dead, and until it was, it would obey Sanwell's last order. Blood-splattered, fearless, the terrible machine may have been another forgotten Yotian god: that of war and the crossroads, of machines and the age to come.
Sanwell threw down his control rod. There was nothing left to command.
"San!" Rica's hands clawed at Sanwell's collar, the other boy trying to pull him along. Sanwell stumbled but did not fall.
Together, the two boys ran.
Kroog died on a crimson morning; the war began at sunrise.
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Aiman lay on his back and squinted against the wan light of the marigold sun. The sky was a foul orange tint, deep as the burnt brown of a charred pepper where smoke from still-burning fires belched. Everything stank. Beauty curdled by death, sweet azure sky rusted over, bright bells twisted to screaming.
Aiman needed water.
The thudding thunder of nail-bottomed boots. A stampede of boots. Hundreds, thousands, a million, the whole of the world running by him. One kicked his head hard enough to tumble him over, as the waves once did. Argivian or Fallaji, he could not tell. The strap of his brasscap snapped, and his helm bounced away. Some reinforcements, he thought, running to battle.
To battle!
Kroog, burning city, invaders' city, the city of thieves. Why were they there ? Mishra, the snake-tongue, hungry, jealous. The qadir's greed.
Aiman needed water.
He groaned and tried to move, but when he tried to sit up all strength drained out of him. He coughed, wincing at the pain. He couldn't see well. He looked down his body.
Aiman let slip a weak cry of fear and shock. Three arrows. He'd been hit. One in his upper thigh, one pinning his arm to his chest, and another through his side. Thigh was the deepest, right in the meat. Arm was all the way through, but his arm and breastplate underneath had stopped the arrow from wounding him deeper. Side was little more than a deep cut, trapped in his armor and padded cloth underneath—once the arrow was gone, a clean bandage would be enough. His face throbbed, and a horrible split feeling told him he had been wounded there as well.
Aiman dropped back down.
"I need water," Aiman called out. "Water," he cried, and realized his was only one of many voices adding to a chorus of moaning, weeping, screaming wounded. He looked around, lucidity coming back with the pain.
He was in hell. Bodies packed the space between the buildings, filling the road where they had fought. The gullet of the city, through which soldiers of both kingdoms were ground into meat.
He tried to remember what happened. Some huge golden knight, some bright machine of terror. The column marching forward, shoved by the rear ranks, terrified of death ahead and Mishra's officers behind. Explosions, pain. The boats before that, his hands shaking, the quiet prayer of the soldier next to him, the cold of the river as they charged up the banks, the screams and the screams.
Aiman needed water. He needed to get away. Hands grabbed at him, and a dead man moaned in his ear, begging for his mother. Aiman slapped the hands away with his good arm, gasping for breath. He kicked and scraped, scooting away from the pleading corpse.
Wheezing, Aiman crawled, yelping where the arrow shafts tapped and dragged over the brick. He collapsed against the side of the alley, shaking violently, vision graying.
"Water," Aiman moaned. He was dying. He could feel it. Burning, deep pain throbbed through his leg, his eye, his side—
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Aiman woke up. It was nighttime. He had passed out.
The alley was silent. The dead draped over every surface. Fires lit the night, casting everything in the pit's own ochre glow. No more bells rang, though Aiman could hear the battle still raging in the distant quarters of Kroog.
Aiman moaned when he saw it. A ghost. A revenant, glowing a soft blue as it picked across the fetid alleyway. Aiman started to pray.
The ghost looked over at him.
Aiman's prayer caught in his throat.
The ghost walked toward him, dim blue form tracing an echo through the hot evening air behind it. Death, Aiman knew it. This was death itself, claiming souls to journey with him.
Death crouched above a horribly wounded man. The man's chest rose and fell, hitched, and then deflated. Aiman could hear the rattle from where he hid.
Death stood. His head tracked across the alley, as if taking in the sight. A harvest, Aiman thought. A harvest for this cold reaper.
"Not yet," Death said. He spoke to the empty alley, but Aiman knew Death spoke to him. Death had a strange accent, like something from the far east. As a boy Aiman had tended his father's trading ship, sailing all around the bounds of Terisiare. Penregon's austere harbor had been a regular enough stop, and Aiman had picked up some Argivian; Death's language sounded similar.
"We're too early," Death said. "We're years away, decades at least. It doesn't happen here."
Relief and confusion flooded through him. Aiman let himself hope.
Death sighed, and then Death disappeared.
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Two weeks later, Aiman's fever finally broke. He limped out of the airy medical tent, the right side of his body aching and itching, but healing. He had lost an eye; save for that wound, he would suffer no more than puckered scars where the arrows had pierced him.
The dry desert breeze cooled the sweat on his brow.
Aiman's war was done. His life, he knew for certain, was only beginning. He looked up at the pale blue sky, tracked thin clouds in their heights, and watched the birds wheeling.
Death had told him: not yet.
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https://github.com/kokkonisd/typst-cross | https://raw.githubusercontent.com/kokkonisd/typst-cross/main/README.md | markdown | The Unlicense | # cross
A crossword template for Typst.
## How to install
The template needs to be installed in a special directory, as described [in the
docs](https://github.com/typst/packages?tab=readme-ov-file#local-packages).
The installer in this repo assumes you have `TYPST_LOCAL_PACKAGES` defined to the correct path,
which should be something like `$HOME/.local/share/typst/packages/local` on Linux.
### Stable version
You need to clone this repo, checkout a specific version (tag), and run the install script:
```console
$ git clone <EMAIL>.com:kokkonisd/typst-cross.git
$ git checkout 0.1.0 # `git tag` lists the available tags
$ ./install.sh --offline
```
### Latest (non-stable) version
Here's a one-liner for a Linux installation.
```console
$ bash <(curl -s https://raw.githubusercontent.com/kokkonisd/typst-cross/main/install.sh)
```
## How to use
In the [examples](examples) directory, see a [simple](examples/simple/) and a [more
complex](examples/full/) example.
|
https://github.com/TJ-CSCCG/tongji-undergrad-thesis-typst | https://raw.githubusercontent.com/TJ-CSCCG/tongji-undergrad-thesis-typst/main/init-files/sections/05_conclusion.typ | typst | MIT License | #import "../../paddling-tongji-thesis/tongjithesis.typ": *
= 总结与未来工作展望
本节通常用于对论文进行总结和归纳，并提出未来工作的展望和建议。
在总结部分，需要回顾研究内容和方法，对研究结果进行分析和归纳，并阐述研究工作的贡献。同时，也要对研究过程中存在的问题和不足进行反思和总结，为未来的研究提供参考和启示。
在未来工作展望部分，需要具体提出研究计划和建议，为后续研究提供方向和指导。同时，也要对本文提出的方法和技术进行展望，探索其在未来研究中的应用前景和发展方向。此外，还可以指出当前领域中存在的未解决问题，为未来研究提供新的研究思路和方向。
此外，未来工作展望中还可以对本文研究的局限性进行讨论和说明，提出改进和扩展的方向。同时，也要注意将未来工作展望与本文研究内容相互关联，以确保研究的连续性和完整性。
最后，需要强调本文研究的意义和价值，并对读者进行总结和启示，为相关领域的研究提供借鉴和参考。在撰写总结与未来工作展望时，需要遵循逻辑清晰、表达准确、语言简练的原则，使得整篇论文的结论和建议具有可读性和可信度。
|
https://github.com/drupol/master-thesis | https://raw.githubusercontent.com/drupol/master-thesis/main/src/thesis/extra.typ | typst | Other | #import "imports/preamble.typ": *
#heading("Open Source", level: 1, outlined: false)
This master thesis has been developed exclusively using open-source tools.
Similar to an open-source project, it was maintained in a private `git`
repository #cite(<PolMasterThesis>, form:"normal"). That repository will be made
public after the oral defense and necessary internal cleanup. Automated and
reproducible builds were managed via GitHub Actions
#cite(<ghActions>,form:"normal"), ensuring that a new compiled version was
published at each commit to the project. Additionally, I'm planning to publish
it on Zenodo #cite(<Zenodo>,form: "normal") after the necessary formalities are
completed.
This work is licenced under a dual license: the #gls("CC BY 4.0") and the
#gls("HL3") licences. You are free to share and adapt the material under the
terms of the `CC BY 4.0`, provided you give appropriate credit to the original
author. You must also use the material in accordance with the ethical guidelines
specified in `HL3`, ensuring it is not used to contribute to human rights abuses
or other unethical practices. In case of any conflict between the licences,
`HL3` will take precedence.
For the purpose of the @chapter3, an open-source project
#cite(<r13yBuildScenarios>,form:"normal") was created to provide a full
transparency on the results shown in that chapter.
|
https://github.com/Toniolo-Marco/git-for-dummies | https://raw.githubusercontent.com/Toniolo-Marco/git-for-dummies/main/book/components/multi-label.typ | typst | #import "@preview/fletcher:0.4.4" as fletcher: diagram, node, edge, draw
#import "utils.typ" : calc_width
#let cell(..texts, stroke) = {
let texts = texts.pos()
let columns = texts.map(((_, len)) => len)
let texts = texts.map(((text, _)) => text)
let anchor_pos = {
let anchor_pos = ()
let width = 0pt
for i in range(0, texts.len()) {
let text = texts.at(i)
if text == none {
anchor_pos.push(width + columns.at(i) / 2)
}
width += columns.at(i)
}
anchor_pos = anchor_pos.map((x) => x - width / 2)
anchor_pos
}
let n = columns.len()
let tbl = table(
columns: columns,
stroke: (x, y) => if x != 0 and x != n - 1 { (x: stroke) },
..texts,
)
(node: tbl, anchors: anchor_pos)
}
#let multi_label(array, stroke) = {
let separator = ("", 0mm);
// Transform each element of the array into a tuple with length.
let items = array.map((x) => (x, calc_width(x)));
// Interleave items and separators.
let output = range(0, items.len() * 2 - 1).map(i => {
if calc.rem(i,2) == 0 {
items.at(calc.quo(i,2))
} else {
separator
}
});
cell(..output, stroke)
} |
|
https://github.com/SWATEngineering/Docs | https://raw.githubusercontent.com/SWATEngineering/Docs/main/src/2_RTB/PianoDiProgetto/sections/PreventivoSprint/TerzoSprint.typ | typst | MIT License | #import "../../const.typ": Re_cost, Am_cost, An_cost, Ve_cost, Pr_cost, Pt_cost
#import "../../functions.typ": prospettoOrario, prospettoEconomico, glossary
== Terzo #glossary[sprint]
*Inizio*: Venerdì 08/12/2023
*Fine*: Giovedì 14/12/2023
#prospettoOrario(sprintNumber: "3")
#prospettoEconomico(sprintNumber: "3") |
https://github.com/typst/packages | https://raw.githubusercontent.com/typst/packages/main/packages/preview/unichar/0.1.0/ucd/block-1780.typ | typst | Apache License 2.0 | #let data = (
("KHMER LETTER KA", "Lo", 0),
("KHMER LETTER KHA", "Lo", 0),
("KHMER LETTER KO", "Lo", 0),
("KHMER LETTER KHO", "Lo", 0),
("KHMER LETTER NGO", "Lo", 0),
("KHMER LETTER CA", "Lo", 0),
("KHMER LETTER CHA", "Lo", 0),
("KHMER LETTER CO", "Lo", 0),
("KHMER LETTER CHO", "Lo", 0),
("KHMER LETTER NYO", "Lo", 0),
("KHMER LETTER DA", "Lo", 0),
("KHMER LETTER TTHA", "Lo", 0),
("KHMER LETTER DO", "Lo", 0),
("KHMER LETTER TTHO", "Lo", 0),
("KHMER LETTER NNO", "Lo", 0),
("KHMER LETTER TA", "Lo", 0),
("KHMER LETTER THA", "Lo", 0),
("KHMER LETTER TO", "Lo", 0),
("KHMER LETTER THO", "Lo", 0),
("KHMER LETTER NO", "Lo", 0),
("KHMER LETTER BA", "Lo", 0),
("KHMER LETTER PHA", "Lo", 0),
("KHMER LETTER PO", "Lo", 0),
("KHMER LETTER PHO", "Lo", 0),
("KHMER LETTER MO", "Lo", 0),
("KHMER LETTER YO", "Lo", 0),
("KHMER LETTER RO", "Lo", 0),
("KHMER LETTER LO", "Lo", 0),
("KHMER LETTER VO", "Lo", 0),
("KHMER LETTER SHA", "Lo", 0),
("KHMER LETTER SSO", "Lo", 0),
("KHMER LETTER SA", "Lo", 0),
("KHMER LETTER HA", "Lo", 0),
("KHMER LETTER LA", "Lo", 0),
("KHMER LETTER QA", "Lo", 0),
("KHMER INDEPENDENT VOWEL QAQ", "Lo", 0),
("KHMER INDEPENDENT VOWEL QAA", "Lo", 0),
("KHMER INDEPENDENT VOWEL QI", "Lo", 0),
("KHMER INDEPENDENT VOWEL QII", "Lo", 0),
("KHMER INDEPENDENT VOWEL QU", "Lo", 0),
("KHMER INDEPENDENT VOWEL QUK", "Lo", 0),
("KHMER INDEPENDENT VOWEL QUU", "Lo", 0),
("KHMER INDEPENDENT VOWEL QUUV", "Lo", 0),
("KHMER INDEPENDENT VOWEL RY", "Lo", 0),
("KHMER INDEPENDENT VOWEL RYY", "Lo", 0),
("KHMER INDEPENDENT VOWEL LY", "Lo", 0),
("KHMER INDEPENDENT VOWEL LYY", "Lo", 0),
("KHMER INDEPENDENT VOWEL QE", "Lo", 0),
("KHMER INDEPENDENT VOWEL QAI", "Lo", 0),
("KHMER INDEPENDENT VOWEL QOO TYPE ONE", "Lo", 0),
("KHMER INDEPENDENT VOWEL QOO TYPE TWO", "Lo", 0),
("KHMER INDEPENDENT VOWEL QAU", "Lo", 0),
("KHMER VOWEL INHERENT AQ", "Mn", 0),
("KHMER VOWEL INHERENT AA", "Mn", 0),
("KHMER VOWEL SIGN AA", "Mc", 0),
("KHMER VOWEL SIGN I", "Mn", 0),
("KHMER VOWEL SIGN II", "Mn", 0),
("KHMER VOWEL SIGN Y", "Mn", 0),
("KHMER VOWEL SIGN YY", "Mn", 0),
("KHMER VOWEL SIGN U", "Mn", 0),
("KHMER VOWEL SIGN UU", "Mn", 0),
("KHMER VOWEL SIGN UA", "Mn", 0),
("KHMER VOWEL SIGN OE", "Mc", 0),
("KHMER VOWEL SIGN YA", "Mc", 0),
("KHMER VOWEL SIGN IE", "Mc", 0),
("KHMER VOWEL SIGN E", "Mc", 0),
("KHMER VOWEL SIGN AE", "Mc", 0),
("KHMER VOWEL SIGN AI", "Mc", 0),
("KHMER VOWEL SIGN OO", "Mc", 0),
("KHMER VOWEL SIGN AU", "Mc", 0),
("KHMER SIGN NIKAHIT", "Mn", 0),
("KHMER SIGN REAHMUK", "Mc", 0),
("KHMER SIGN YUUKALEAPINTU", "Mc", 0),
("KHMER SIGN MUUSIKATOAN", "Mn", 0),
("KHMER SIGN TRIISAP", "Mn", 0),
("KHMER SIGN BANTOC", "Mn", 0),
("KHMER SIGN ROBAT", "Mn", 0),
("KHMER SIGN TOANDAKHIAT", "Mn", 0),
("KHMER SIGN KAKABAT", "Mn", 0),
("KHMER SIGN AHSDA", "Mn", 0),
("KHMER SIGN SAMYOK SANNYA", "Mn", 0),
("KHMER SIGN VIRIAM", "Mn", 0),
("KHMER SIGN COENG", "Mn", 9),
("KHMER SIGN BATHAMASAT", "Mn", 0),
("KHMER SIGN KHAN", "Po", 0),
("KHMER SIGN BARIYOOSAN", "Po", 0),
("KHMER SIGN CAMNUC PII KUUH", "Po", 0),
("KHMER SIGN LEK TOO", "Lm", 0),
("KHMER SIGN BEYYAL", "Po", 0),
("KHMER SIGN PHNAEK MUAN", "Po", 0),
("KHMER SIGN KOOMUUT", "Po", 0),
("KHMER CURRENCY SYMBOL RIEL", "Sc", 0),
("KHMER SIGN AVAKRAHASANYA", "Lo", 0),
("KHMER SIGN ATTHACAN", "Mn", 230),
(),
(),
("KHMER DIGIT ZERO", "Nd", 0),
("KHMER DIGIT ONE", "Nd", 0),
("KHMER DIGIT TWO", "Nd", 0),
("KHMER DIGIT THREE", "Nd", 0),
("KHMER DIGIT FOUR", "Nd", 0),
("KHMER DIGIT FIVE", "Nd", 0),
("KHMER DIGIT SIX", "Nd", 0),
("KHMER DIGIT SEVEN", "Nd", 0),
("KHMER DIGIT EIGHT", "Nd", 0),
("KHMER DIGIT NINE", "Nd", 0),
(),
(),
(),
(),
(),
(),
("KHMER SYMBOL LEK ATTAK SON", "No", 0),
("KHMER SYMBOL LEK ATTAK MUOY", "No", 0),
("KHMER SYMBOL LEK ATTAK PII", "No", 0),
("KHMER SYMBOL LEK ATTAK BEI", "No", 0),
("KHMER SYMBOL LEK ATTAK BUON", "No", 0),
("KHMER SYMBOL LEK ATTAK PRAM", "No", 0),
("KHMER SYMBOL LEK ATTAK PRAM-MUOY", "No", 0),
("KHMER SYMBOL LEK ATTAK PRAM-PII", "No", 0),
("KHMER SYMBOL LEK ATTAK PRAM-BEI", "No", 0),
("KHMER SYMBOL LEK ATTAK PRAM-BUON", "No", 0),
)
|
https://github.com/Pablo-Gonzalez-Calderon/showybox-package | https://raw.githubusercontent.com/Pablo-Gonzalez-Calderon/showybox-package/main/lib/sections.typ | typst | MIT License | /*
* ShowyBox - A package for Typst
* <NAME> and Showybox Contributors (c) 2023
*
* lib/sections.typ -- The package's file containing all the
* internal functions for drawing sections.
*
* This file is under the MIT license. For more
* information see LICENSE on the package's main folder.
*/
#import "func.typ": *
/*
* Function: showy-get-title-props()
*
* Description: Returns the title's properties
*
* Parameters:
* + sbox-props: Showybox properties
*/
#let showy-get-title-props(sbox-props) = {
/*
* Properties independent of `boxed`
*/
let props = (
spacing: 0pt,
fill: sbox-props.frame.title-color,
inset: showy-section-inset("title", sbox-props.frame)
)
/*
* Properties dependent of `boxed`
*/
if sbox-props.title-style.boxed-style != none {
props = props + (
width: auto,
radius: sbox-props.title-style.boxed-style.radius,
stroke: showy-stroke(sbox-props.frame),
)
} else {
props = props + (
width: 100%,
radius: (
top-left: showy-value-in-direction("top-left", sbox-props.frame.radius, 5pt),
top-right: showy-value-in-direction("top-right", sbox-props.frame.radius, 5pt),
bottom: 0pt
),
stroke: showy-stroke(sbox-props.frame, bottom: sbox-props.title-style.sep-thickness)
)
}
return props
}
/*
* Function: showy-title()
*
* Description: Returns the title's block
*
* Parameters:
* + sbox-props: Showybox properties
*/
#let showy-title(sbox-props) = block(
..showy-get-title-props(sbox-props),
align(
sbox-props.title-style.align,
text(
sbox-props.title-style.color,
weight: sbox-props.title-style.weight,
sbox-props.title
)
)
)
/*
* Function: showy-body()
*
* Description: Returns the body's block
*
* Parameters:
* + sbox-props: Showybox properties
* + body: Body content
*/
#let showy-body(sbox-props, ..body) = block(
width: 100%,
spacing: 0pt,
breakable: sbox-props.breakable,
inset: showy-section-inset("body", sbox-props.frame),
align(
sbox-props.body-style.align,
text(
sbox-props.body-style.color,
body.pos()
.map(block.with(spacing:0pt, width: 100%, breakable: sbox-props.breakable))
.join(
block(
spacing: sbox-props.sep.gutter,
align(
left, // Avoid alignment errors
showy-line(sbox-props.frame)(
stroke: (
paint: sbox-props.frame.border-color,
dash: sbox-props.sep.dash,
thickness: sbox-props.sep.thickness
)
)
)
)
)
)
)
)
/*
* Function: showy-footer()
*
* Description: Returns the footer's block
*
* Parameters:
* + sbox-props: Showybox properties
* + body: Body content
*/
#let showy-footer(sbox-props, footer) = block(
width: 100%,
spacing: 0pt,
inset: showy-section-inset("footer", sbox-props.frame),
fill: sbox-props.frame.footer-color,
stroke: showy-stroke(sbox-props.frame, top: sbox-props.footer-style.sep-thickness),
radius: (
bottom-left: showy-value-in-direction("bottom-left", sbox-props.frame.radius, 5pt),
bottom-right: showy-value-in-direction("bottom-right", sbox-props.frame.radius, 5pt),
top: 0pt
),
align(
sbox-props.footer-style.align,
text(
sbox-props.footer-style.color,
weight: sbox-props.footer-style.weight,
footer
)
)
) |
https://github.com/sitandr/typst-examples-book | https://raw.githubusercontent.com/sitandr/typst-examples-book/main/src/packages/presentation.md | markdown | MIT License | # Presentations
## Polylux
> See [polylux book](https://polylux.dev/book/)
```typ
// Get Polylux from the official package repository
#import "@preview/polylux:0.3.1": *
// Make the paper dimensions fit for a presentation and the text larger
#set page(paper: "presentation-16-9")
#set text(size: 25pt)
// Use #polylux-slide to create a slide and style it using your favourite Typst functions
#polylux-slide[
#align(horizon + center)[
= Very minimalist slides
A lazy author
July 23, 2023
]
]
#polylux-slide[
== First slide
Some static text on this slide.
]
#polylux-slide[
== This slide changes!
You can always see this.
// Make use of features like #uncover, #only, and others to create dynamic content
#uncover(2)[But this appears later!]
]
```
## Slydst
> See the documentation [there](https://github.com/glambrechts/slydst?ysclid=lr2gszrkck541184604).
Much more simpler and less powerful than polulyx:
```typ
#import "@preview/slydst:0.1.0": *
#show: slides.with(
title: "Insert your title here", // Required
subtitle: none,
date: none,
authors: (),
layout: "medium",
title-color: none,
)
== Outline
#outline()
= First section
== First slide
#figure(rect(width: 60%), caption: "Caption")
#v(1fr)
#lorem(20)
#definition(title: "An interesting definition")[
#lorem(20)
]
``` |
https://github.com/TypstApp-team/typst | https://raw.githubusercontent.com/TypstApp-team/typst/master/tests/typ/bugs/table-row-missing.typ | typst | Apache License 2.0 | // Test that a table row isn't wrongly treated like a gutter row.
---
#set page(height: 70pt)
#table(
rows: 16pt,
..range(6).map(str).flatten(),
)
|
https://github.com/flavio20002/typst-kaobook-template | https://raw.githubusercontent.com/flavio20002/typst-kaobook-template/main/README.md | markdown | Apache License 2.0 | A Typst implementation of https://github.com/fmarotta/kaobook/tree/master/examples
See the example pdf in the Release section of this project
To compile the example:
typst watch ./example/example.typ --root . --font-path fonts
This template was realized with the help of:
|
https://github.com/Isaac-Fate/booxtyp | https://raw.githubusercontent.com/Isaac-Fate/booxtyp/master/src/theorems/new-plain-template.typ | typst | Apache License 2.0 | #import "../colors.typ": color-schema
#import "../counters.typ": exercise-counter
#let new-plain-template(
identifier,
title-color: color-schema.green.dark,
title-prefix: none,
body-text-style: "normal",
template-counter: none,
) = (body) => {
locate(loc => {
// Get the current template number
let number = if template-counter != none {
// Increament the template counter
template-counter.step(level: 3)
numbering("1.1", ..template-counter.at(loc))
} else {
none
}
figure(block()[
// Something to add before the title
#title-prefix
// Render the template title
#if number != none {
text(fill: title-color)[*#identifier #number*]
} else {
text(fill: title-color)[*#identifier*]
}
// Add some space
#h(0.0em)
// Main content
#text(style: body-text-style)[#body]
], kind: identifier, supplement: identifier)
})
} |
https://github.com/SWATEngineering/Docs | https://raw.githubusercontent.com/SWATEngineering/Docs/main/src/2_RTB/VerbaliEsterni/VerbaleEsterno_231221/meta.typ | typst | MIT License | #let data_incontro = "21-12-2023"
#let inizio_incontro = "15:30"
#let fine_incontro = "16:00"
#let luogo_incontro = "Chiamata Google Meet"
#let company = "Sync Lab" |
https://github.com/Functional-Bus-Description-Language/Specification | https://raw.githubusercontent.com/Functional-Bus-Description-Language/Specification/master/src/functionalities/status.typ | typst | == Status
The status represents data that is produced by the provider and is only read by the requester.
The status functionality has following properties:
*`atomic`*` bool (true) {definitive}`
#pad(left: 1em)[
The atomic property defines whether an access to the status must be atomic.
If atomic is true, then the provider must guarantee that any change of the status value is seen as an atomic change by the requester.
This is especially important when a status spans more than single register, as in case of single register read the change is always atomic.
]
*`read-value`*` bit string (None) {definitive}`
#pad(left: 1em)[
The read-value property defines the value that must be returned by the provider on the status read after the first read.
If the read-value property is set, then the actual value of the status can be read only once.
]
*`width`*` integer (bus width) {definitive}`
#pad(left: 1em)[
The width property defines the bit width of the status.
]
The code generated for the requester must provide a mean for reading the status.
|
|
https://github.com/Shuenhoy/modern-zju-thesis | https://raw.githubusercontent.com/Shuenhoy/modern-zju-thesis/master/pages/outline.typ | typst | MIT License | #import "./template-individual.typ": template-individual
#import "../dependency/i-figured.typ"
#let main-outline(
title: "目录",
titlelevel: 2,
outlined: false,
..args,
) = {
template-individual(outlined: outlined, titlelevel: titlelevel, title, outline(depth: 3, title: none, ..args))
}
#let figure-outline(
title: "图目录",
titlelevel: 2,
outlined: false,
..args,
) = {
template-individual(
outlined: outlined,
titlelevel: titlelevel,
title,
i-figured.outline(depth: 3, title: none, target-kind: image, ..args),
)
}
#let table-outline(
title: "表目录",
titlelevel: 2,
outlined: false,
..args,
) = {
template-individual(
outlined: outlined,
titlelevel: titlelevel,
title,
i-figured.outline(depth: 3, title: none, target-kind: table, ..args),
)
}
) |
https://github.com/01mf02/jq-lang-spec | https://raw.githubusercontent.com/01mf02/jq-lang-spec/main/spec.typ | typst | #import "@preview/ctheorems:1.1.0"
#import "common.typ": *
#show: ctheorems.thmrules
#set heading(numbering: "1.1")
#let title = [A formal specification of the jq language]
#set document(title: title)
#text(size: 20pt, weight: "bold", title)
#set raw(lang: "jq")
= Introduction
`jq` is a tool that provides a programming language
to efficiently process JSON data.
We call this programming language the "jq language".
This text aims to give a precise, mathematical description of the jq language, similar to
the "WebAssembly Core Specification" for WebAssembly @WebAssemblyCoreSpecification2.
It is intended to complement the user manual @jq-manual.
In some places, the behaviour described in this text diverges from `jq`.
We try to point out such differing behaviour whenever it occurs.
The first and foremost goal of this text is to allow users to
_precisely predict what their jq programs will output_.
On the other hand, this text does not try to describe how
to implement a performant interpreter for the jq language --- the focus is not
on _how_ a jq interpreter executes a jq program, but
on _what_ a jq program outputs.
This differentiates this text from the jq language description @jq-description,
which draws much stronger on the implementation of `jq` to describe the jq language.
This text does not cover all parts of the jq language;
in particular, it does not cover the module system.
However, most of the programs that use features not covered by this specification
can be translated into programs that are completely covered by this specification.
For example, a program made of several modules can be
transformed into a program that does not use modules.
/*
Note that this text only aims to specify
the behaviour of jq filters that have special syntax, such as `|`;
it does not attempt to specify
the behaviour of particular named filters, such as `reverse`.
*/
This text is structured as follows:
@tour gives an introduction to the jq language.
@syntax specifies the syntax treated in this text and transforms it to a simpler subset.
@values defines values.
@semantics defines the output of jq programs, and
@updates defines the output of jq updates.
In the appendix,
@json defines JSON values as well as some operations on them used in jq.
#include "tour.typ"
#include "syntax.typ"
#include "values.typ"
#include "semantics.typ"
#let appendix(body) = {
set heading(numbering: "A.1", supplement: [Appendix])
counter(heading).update(0)
body
}
#show: appendix
#include "json.typ"
#bibliography("literature.bib")
|
|
https://github.com/gongke6642/tuling | https://raw.githubusercontent.com/gongke6642/tuling/main/Math/attach.typ | typst | #set text(
size:10pt,
)
#set page(
paper:"a5",
margin:(x:1.8cm,y:1.5cm),
)
#set par(
justify: true,
leading: 0.52em,
)
= 附加
下标、上标和限制。
附件可以显示为下标/上标或限制。Typst 会根据基数自动决定哪个更合适，但您也可以使用 scripts 和 limits 函数手动控制它。
= 例
#image("10.png")
= 语法
此函数还具有用于基数后附件的专用语法：使用下划线表示下标，即底部附件，使用帽子 （^） 表示上标，即顶部附件。
= 功能
= 附加
带有可选附件的底座。
#image("11.png")
= 基座
事物所附着的底座。
= t
顶部附件，巧妙地放置在底座的右上方或上方。
您可以用limits()或者scripts()将底座包裹起来以此覆盖智能定位。
默认：none
= b
底部附件，巧妙地放置在底座的右下角或下方。
您可以用limits()或者scripts()将底座包裹起来以此覆盖智能定位。
默认：none
= tl
左上角的附件（在底座之前）。
默认：none
= bl
左下角的附件（在底座之前）。
默认：none
= tr
右上角的附件（在底座之后）。
默认：none
= br
右下角的附件（在底座之后）。
默认：none
= 脚本
强制底座将附件显示为脚本。
#image("12.png")
= 内容
要将脚本附加到底座。
= 限制
强制底座将附件显示为限制。
#image("13.png")
= 内容
要将脚本附加到底座。
= 内联
是否也要在内联方程中强制限制。
全局应用限制时（例如，通过显示规则），通常最好禁用此限制。
默认：true |
|
https://github.com/Myriad-Dreamin/typst.ts | https://raw.githubusercontent.com/Myriad-Dreamin/typst.ts/main/fuzzers/corpora/math/frac_01.typ | typst | Apache License 2.0 |
#import "/contrib/templates/std-tests/preset.typ": *
#show: test-page
// Test parenthesis removal.
$ (|x| + |y|)/2 < [1+2]/3 $
|
https://github.com/HynDuf/typst-cv | https://raw.githubusercontent.com/HynDuf/typst-cv/master/template/modules_en/education.typ | typst | Apache License 2.0 | // Imports
#import "../../lib.typ": cvSection, cvEntry, hBar
#let metadata = toml("../metadata.toml")
#let cvSection = cvSection.with(metadata: metadata)
#let cvEntry = cvEntry.with(metadata: metadata)
#cvSection("Education")
#cvEntry(
title: [Bachelors in Information Technology (Specialized program)],
society: [University of Engineering and Technology - Vietnam National University],
date: [2021 - 2025],
location: [Vietnam],
logo: image("../src/logos/UET.png"),
description: list(
[*GPA*: 3.89 / 4.0],
[*Courses*: #h(3pt) Database Systems #hBar() Computer Networks #hBar() Software Engineering #hBar() Artificial Intelligence],
),
)
|
https://github.com/EpicEricEE/typst-plugins | https://raw.githubusercontent.com/EpicEricEE/typst-plugins/master/equate/assets/example-local.typ | typst | #import "../src/lib.typ": equate
#set text(size: 14pt)
#set par(justify: true)
#set page(
width: 11cm,
height: auto,
margin: 1em,
background: pad(0.5pt, box(
width: 100%,
height: 100%,
radius: 4pt,
fill: white,
stroke: white.darken(10%),
)),
)
// 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.
|
|
https://github.com/almarzn/portfolio | https://raw.githubusercontent.com/almarzn/portfolio/main/templates/typst/.template/experiences.typ | typst |
#import "@preview/splash:0.3.0": tailwind
#import "@preview/cmarker:0.1.0"
#import "./shared/flex.typ": *
#let experience-block(
content
) = block(
inset: 24pt,
radius: 16pt,
fill: tailwind.slate-100,
)[
#flex(
gap: 24pt,
[
#flex(gap: 18pt)[
#grid(
column-gutter: 12pt,
columns: (1fr, auto),
text(fill: tailwind.orange-500)[=== #content.name],
align(bottom, text(baseline: -1pt, content.dates))
)
#block(
heading(level: 4, content.title)
)
#set par(justify: true)
#content.description
]
#flex(gap: 18pt)[
==== Réalisations
#for el in content.work [
#flex(gap: 12pt)[
===== #el.title
#cmarker.render(el.content)
]
]
]
#flex(
direction: row,
gap: 6pt,
for el in content.skills {
box(
inset: 6pt,
fill: white,
radius: 2pt,
el
)
}
)
]
)
] |
|
https://github.com/jgm/typst-hs | https://raw.githubusercontent.com/jgm/typst-hs/main/test/typ/compiler/ops-prec-01.typ | typst | Other | // Assignment binds stronger than boolean operations.
// Error: 2:3-2:8 cannot mutate a temporary value
#let x = false
#(not x = "a")
|
https://github.com/xdoardo/co-thesis | https://raw.githubusercontent.com/xdoardo/co-thesis/master/thesis/chapters/imp/analysis/index.typ | typst | == Analyses and optimizations<section-analysis_optimization>
We chose to demonstrate the use of coinduction in the definition of operational
semantics implementing transformations on the code itself, then showing proofs
regarding the result of the execution of the program. The main inspiration for
these transformations is @concrete-semantics, and they are _source to source_,
that is, they transform Imp programs to (pontentially untouched) Imp programs.
#include "./dia.typ"
#include "./fold.typ"
|
|
https://github.com/Ttajika/class | https://raw.githubusercontent.com/Ttajika/class/main/seminar2024/cetz.typ | typst | #import "@preview/cetz:0.2.2"
#show: align.with(center)
#set page(width: auto, height:auto, margin:5mm)
#cetz.canvas({
import cetz.draw: *
//情報集合
hobby((2-0.2, 0.1), (5, -.8), (6.2, 0.2), omega: 0, stroke: (paint: red.lighten(20%), thickness: 14pt, cap: "round"))
hobby((2-0.2, 0.1), (5., -.8), (6.2, 0.2), omega: 0, stroke:(paint: red.lighten(100%), thickness: 8pt, cap: "round"))
hobby((-0.1, -0.1), (1, 1), (4, -0.), (5.2, 1), (8.1, -0.1), omega: 0, stroke: (paint: blue.lighten(20%), thickness: 14pt, cap: "round"))
hobby((-0.1, -0.1), (1, 1), (4.0, -0.), (5.2, 1), (8.1, -.1), omega: 0, stroke: (paint: blue.lighten(100%), thickness: 8pt, cap: "round"))
line((0,0),(10,0), mark:(end:"straight"))
for i in range(5){
line((2*i,0),(2*i,-1.5), mark:(end:"straight"))
circle((2*i,0),radius: 1mm, fill:white)
let name = {
if calc.odd(i+1) {1} else {2} }
let payoff1 = {
i+2 - 2*name
}
let payoff2 = {
i + 3- 4/name
}
content((2*i,0),[#box(fill:white.transparentize(10%))[P#name]],padding:(y:4mm), anchor:"south")
content((2*i+1,-0.2),[#box(fill:white.transparentize(10%))[C]],padding:(y:4mm), anchor:"south")
content((2*i +.2,-1.2),[D],padding:(y:4mm), anchor:"south")
content((2*i,-2.5),[$(#payoff1, #payoff2)$],padding:(y:4mm), anchor:"south")
}
content( (10,0), [$(3,5)$], anchor:"west",padding:(x:2mm))
}
) |
|
https://github.com/Myriad-Dreamin/typst.ts | https://raw.githubusercontent.com/Myriad-Dreamin/typst.ts/main/fuzzers/corpora/text/stroke_00.typ | typst | Apache License 2.0 |
#import "/contrib/templates/std-tests/preset.typ": *
#show: test-page
#set text(size: 20pt)
#set page(width: auto)
测试字体 #lorem(5)
#text(stroke: 0.3pt + red)[测试字体#lorem(5)]
#text(stroke: 0.5pt + red)[测试字体#lorem(5)]
#text(stroke: 0.7pt + red)[测试字体#lorem(5)]
#text(stroke: 1pt + red)[测试字体#lorem(5)]
#text(stroke: 2pt + red)[测试字体#lorem(5)]
#text(stroke: 5pt + red)[测试字体#lorem(5)]
#text(stroke: 7pt + red)[测试字体#lorem(5)]
#text(stroke: (paint: blue, thickness: 1pt, dash: "dashed"))[测试字体#lorem(5)]
#text(stroke: 1pt + gradient.linear(..color.map.rainbow))[测试字体#lorem(5)] // gradient doesn't work now
|
https://github.com/floriandejonckheere/utu-thesis | https://raw.githubusercontent.com/floriandejonckheere/utu-thesis/master/thesis/figures/08-case-study/link.typ | typst | #import "@preview/cetz:0.2.2"
#set text(font: "Fira Sans", size: 9pt)
#cetz.canvas(length: 1cm, {
import cetz.draw: *
set-style(
content: (padding: .2),
stroke: black
)
line((0, 0), (10, 0), stroke: (paint: gray, dash: "dashed"))
content((0.5, 0.5), align(left, text(gray, "Cloud")))
content((0.90, -0.5), align(left, text(gray, "On-premise")))
rect(
(4.5, 1), (5.5, 2),
radius: 0.5,
fill: blue.lighten(80%),
stroke: (paint: blue.lighten(40%)),
name: "nephroflow")
content("nephroflow.north", text(blue.darken(20%), align(center, [NephroFlow\ Cloud#v(5em)])))
rect(
(4.5, -1), (5.5, -2),
radius: 0.5,
fill: orange.lighten(80%),
stroke: (paint: orange.lighten(40%)),
name: "link")
content("link.south", text(orange.darken(20%), align(center, [#v(5em)NephroFlow\ Link])))
content((4, 0.5), text(gray, align(center, [HTTPS])))
rect(
(4.25, -0.25), (5.75, 0.25),
radius: 0.05,
fill: red.lighten(80%),
stroke: (paint: red.lighten(40%)),
name: "firewall")
content("firewall.north-east", text(red.darken(20%), align(center, [#h(5em)Firewall#v(2em)])))
line((5.1, -0.9), (5.1, 0.9), stroke: gray, mark: (start: ">", fill: gray))
line((4.9, -0.9), (4.9, 0.9), stroke: gray, mark: (end: ">", fill: gray))
rect(
(2, -1), (3, -2),
radius: 0.5,
fill: yellow.lighten(80%),
stroke: (paint: yellow.lighten(40%)),
name: "ehr")
content("ehr.south", text(yellow.darken(20%), align(center, [#v(5em)Electronic Health\ Record])))
content((3.8, -1), text(gray, align(center, [HL7])))
line((3.1, -1.4), (4.4, -1.4), stroke: gray, mark: (start: ">", fill: gray))
line((3.1, -1.6), (4.4, -1.6), stroke: gray, mark: (end: ">", fill: gray))
rect(
(7, -0.5), (7.5, -1),
radius: 0.5,
fill: green.lighten(80%),
stroke: (paint: green.lighten(40%)),
name: "dialysis_1")
line((6.9, -0.85), (5.6, -1.35), stroke: green.lighten(40%), mark: (end: ">", fill: green.lighten(40%)))
rect(
(7, -1.25), (7.5, -1.75),
radius: 0.5,
fill: green.lighten(80%),
stroke: (paint: green.lighten(40%)),
name: "dialysis_2")
line((6.9, -1.5), (5.6, -1.5), stroke: green.lighten(40%), mark: (end: ">", fill: green.lighten(40%)))
rect(
(7, -2), (7.5, -2.5),
radius: 0.5,
fill: green.lighten(80%),
stroke: (paint: green.lighten(40%)),
name: "dialysis_3")
line((6.9, -2.15), (5.6, -1.65), stroke: green.lighten(40%), mark: (end: ">", fill: green.lighten(40%)))
content("dialysis_2.east", text(green.darken(20%), align(center, [#h(8em)Dialysis\ #h(8em)machines])))
content((6.5, -2.8), text(green.darken(20%), align(center, [TCP/serial])))
})
#v(2em)
|
|
https://github.com/xhalo32/constructive-logic-course | https://raw.githubusercontent.com/xhalo32/constructive-logic-course/master/slides/01-logiikka.typ | typst | #import "@preview/touying:0.4.2": *
#import "slidetheme.typ"
#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 => block(
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: [1 – Lauselogiikka],
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
== Tällä tunnilla
TODO tunnin oppimistavoitteet
- Ymmärtää logiikan perusteet
- Filosofiaa: totuus, erilaiset logiikat, päättely, loogiset paradoksit
- Lauseet, väitteet, aksioomat, syy ja seuraus, hypoteesit, totuusarvot, ristiriidat, tautologiat
- Tietää mitä ovat informaali ja formaali logiikka
- Ymmärtää lauselogiikan perusmääritelmät ja notaation
- Osaa lukea ja muodostaa totuusatauluja
== Yleisiä loogisia virheitä
- Korrelaatio on kausaatio (implikaatio vs. ekvivalenssi)
- Kehäpäätelmä
- Argumentointivirheet
- TODO
== Logiikka
TODO tarkemmin mitä logiikka on
== Formaali logiikka
#slide(composer: (1fr, auto))[
- Miten eroaa epäformaalista logiikasta?
- Mitä tarkoittaa formaali kieli?
- Nollannen asteen logiikkaa kutsutaan nimellä lauselogiikka
][
$ (p quad p -> q) / q $
]
== Lauselogiikka
#slide(composer: (1fr, auto))[
- Totuusarvot
- Tosi, $top$, $1$
- Epätosi, $bot$, $0$
- Atomisilla lauseilla on totuusarvot
- Lauseita usein merkitään kirjaimilla $p, q, r, s, t$
- Logiikkaan ei kuulu muuttujia (onko tarpeellista kertoa?)
- Mutta lauseissa voi esiintyä _metamuuttujia_
][
$ p -> (q or r -> (r -> not p)) $
]
== Lean
```lean4
import Mathlib
def divides (n m : Nat) : Prop := ∃ k, n * k = m
def prime (n : Nat) : Prop := ∀ m, m < n ∧ m ≠ 1 → divides m n ∧ n < 10
def primes : Set Nat := {n | prime n}
-- TODO implement prime number algorithm
#check ((((((1))))))
def nth_prime : Nat → primes := sorry
-- instance : Decidable (n ∈ primes) := by
-- rw [primes]
-- #eval 10 ∈ primes
def prime_id : primes → Nat := by
rw [primes]
intro x
cases' x with n
exact n
def countable_primes : Countable primes := by
use prime_id
intro a b h
cases' a with a ah
cases' b with b bh
simp [prime_id] at h
subst b
rfl
```
== "Judgement"
- Filosofinen väite
== Implikaatio
== Ekvivalenssi
== "Hypothetical Judgement"
- Matematiikan vahvuus on siinä, että väitteiden totuus ei riipu puhujasta tai kuulijasta, vaan oletuksista
- $arrow$ Tarvitaan judgement jossa esitetään myös oletukset |
|
https://github.com/DashieTM/ost-5semester | https://raw.githubusercontent.com/DashieTM/ost-5semester/main/compiler/weeks/week3.typ | typst | #import "../../utils.typ": *
#section("Parser")
Turns tokens into a parse tree, meaning it can check syntax. -> type must be
before variable. Note that it does not offer semantic checking, aka will it
compile etc. It only offers what clangd offers in templates, aka syntax only.
- creates syntax tree
- must be valid
- only one tree possible, otherwise syntax ambiguous
#columns(
2,
[
*Parse tree / Concrete syntax tree* | complete view of tokens as syntax tree
#align(
center,
[#image("../../Screenshots/2023_10_02_08_17_28.png", width: 80%)],
)
#colbreak()
*Abstract syntax tree* | Simplified view, everything unnecessary removed
#align(
center,
[#image("../../Screenshots/2023_10_02_08_18_06.png", width: 80%)],
)
],
)
#columns(2, [
*Top Down Parsing*
#align(
center,
[#image("../../Screenshots/2023_10_02_08_20_20.png", width: 100%)],
)
#colbreak()
*Bottom Up Parsing*
#align(
center,
[#image("../../Screenshots/2023_10_02_08_20_51.png", width: 100%)],
)
])
#subsection("Recursive Descent parser code")
```cs
// Expression = Term { ( "+" | "-" ) Term }.
void ParseExpression() {
ParseTerm();
while (Is(Tag.PLUS) || Is(Tag.MINUS)) {
_stream.Next();
ParseTerm();
}
}
```
Recursive descent defines a function for every non-terminal token, this makes it
easy to parse said tokens. Also note that these tokens need to be recursive as
their name implies that you need to go through it multiple times to receive
terminal tokens.
#subsection("Predictive Direct vs Backtracking")
Predictive direct makes it clear which function(which token will be parsed) will
be called when, backtracking on the other hand will try a random parser until it
fails, then goes to the next parser to try again. (Backtracking is used for the
lexer, for the parser we don't want this since we have only one tree either way,
otherwise the syntax is wrong and we can't make a real parser either way!!)
#subsection("Lookahead")
Many tokens require multiple specific tokens in a row to be valid, for these we
need lookahead for tokens. For this we need a way to view tokens without calling
Next(), which would take these tokens away.
#subsubsection("Multi lookahead")
Sometimes multiple tokens have the same next token, which means we will have to
lookahead further than just one token. In this case we can *reform* the tokens
with new tokens that will make it possible to use 1 lookahead.
#columns(2, [
#align(
center,
[#image("../../Screenshots/2023_10_02_08_56_46.png", width: 100%)],
)
#colbreak()
#align(
center,
[#image("../../Screenshots/2023_10_02_08_43_28.png", width: 80%)],
)
])
#subsection("Left-recursion vs EBNF-Repetition")
//typstfmt::off
#columns(2, [
```cs
// Sequence = Sequence ["s"].
void ParseSequence() {
ParseSequence();
if (!_stream.IsEnd) {
if (_stream.Current == ‘s’) {
_stream.Next();
} else {
Error();
}
}
}
```
#text(red)[Problem: endless recursion possible!]
#colbreak()
```cs
// Sequence = {"s"}.
void ParseSequence() {
while (!_stream.IsEnd()) {
if (_stream.Current == ‘s’) {
_stream.Next();
} else {
Error();
break;
}
}
}
```
#text(green)[better]
])
//typstfmt::on
#subsection("Class syntax tree")
#columns(2, [
#align(center, [#image("../../Screenshots/2023_10_02_08_53_30.png", width: 100%)])
#colbreak()
#align(center, [#image("../../Screenshots/2023_10_02_08_54_17.png", width: 100%)])
])
#subsection("Statement syntax tree")
#align(center, [#image("../../Screenshots/2023_10_02_08_53_57.png", width: 80%)])
#subsection("Creation of Parse Nodes")
//typstfmt::off
```cs
ExpressionNode ParseFactor() {
if (IsOperator(UNARY_OPERATORS)) {
return ParseUnaryExpression();
} else if (Is(Tag.OPEN_PARENTHESIS)) {
int start = currentStart;
_stream.Next();
var expression = ParseExpression();
Check(Tag.CLOSE_PARENTHESIS);
if (IsIdentifier()) {
return ParseTypeCast(start, expression);
} else {
return expression;
}
} else {
return ParseOperand();
}
}
```
//typstfmt::on
#subsubsection("Errors in tokens")
//typstfmt::off
```cs
if (Is(Tag.RIGHT_PARENTHESIS)) {
_stream.Next();
} else {
Error(") missing");
}
```
//typstfmt::on
#subsubsection("Skippable errors")
Sometimes errors make it impossible to parse something, in that case we might want to just move to the next top token, for example a class and try to parse that again. -> Compiler should be fast
//typstfmt::off
```cs
Expression ParseTerm() {
if (!IsNumber() || !Is(Tag.LEFT_PARENTHESIS)) {
Error("invalid term");
while (!IsNumber() && !Is(Tag.LEFT_PARENTHESIS)
&& canSkip()) {
_stream.Next();
}
}
```
//typstfmt::on
|
|
https://github.com/cadojo/correspondence | https://raw.githubusercontent.com/cadojo/correspondence/main/src/rolo/src/names.typ | typst | MIT License | #let name(
given: none,
family: none,
literal: none,
dropping-particle: none,
non-dropping-particle: none,
) = (
given: given,
family: family,
literal: literal,
dropping-particle: dropping-particle,
non-dropping-particle: non-dropping-particle,
)
#let fullname(name) = {
if name == none {
none
} else if type(name) == "string" {
name
} else {
if name.literal != none {
name.literal
} else {
(name.given, name.family).filter(v => v != none).join(" ")
}
}
}
#let nickname(name) = {
if name == none {
none
} else {
if type(name) == "string" {
name
}
else if name.literal != none {
name.literal
} else {
name.given
}
}
} |
https://github.com/Mouwrice/thesis-typst | https://raw.githubusercontent.com/Mouwrice/thesis-typst/main/conclusion.typ | typst | = Conclusion <conclusion>
In this thesis, we have presented a method to compare body tracking data from a computer vision model with a motion capture system. Using the method, we have shown that an average accuracy of 5-10 mm can be achieved with MediaPipe Pose for the movements relative to the camera. We have shown that the accuracy of the depth estimation is a low lower and suffers from major instability. MediaPipe Pose can track the movements of the body in real-time with a frame rate of around 30 frames per second on consumer hardware. And reaching up to 45 fps on a powerful GPU. During the measurements, a jitter phenomenon was observed in the signal which appears to be caused by overlapping body parts such as crossed arms.
We have also shown that the signal stability can be increased by using a simple prediction model combined with an interpolation method between the predicted and the measured value. This method reduces the jitter and noise in the signal. However, the signal is still not perfect. Future work could focus on increasing the signal stability even further.
A drum application was built to demonstrate the capabilities of the system. The application uses the body pose estimation to track the movements of the user and translate these movements to drum sounds. The application was able to track the movements of the user in real-time and play the drum sounds accordingly. The simple yet very effective procedure for detecting drum hits has been described as well. The application technology stack consists of MediaPipe Pose for the body pose estimation, PyGame for the visualisation and sound, and Python for the application logic. The application and its source code have been made publicly available for download and can be found on GitHub.
The future of body pose estimation is promising. The accuracy and performance are shown to already be sufficient to construct a simple real-time air drumming application. The application of body pose estimation is not limited to drumming. It can be used in various applications, such as in medical rehabilitation, virtual reality, and human-computer interaction. Future work could focus on increasing the signal stability, improving the depth estimation, and finding new applications for body pose estimation. We have seen that body pose estimation can bring the expensive and complex technology of motion capture to consumer hardware. This opens up a whole new world of possibilities for applications that require body tracking.
|
|
https://github.com/typst/packages | https://raw.githubusercontent.com/typst/packages/main/packages/preview/cetz/0.2.0/gallery/plot.typ | typst | Apache License 2.0 | #import "@preview/cetz:0.2.0": canvas, plot
#set page(width: auto, height: auto, margin: .5cm)
#let style = (stroke: black, fill: rgb(0, 0, 200, 75))
#canvas(length: 1cm, {
plot.plot(size: (8, 6),
x-tick-step: none,
x-ticks: ((-calc.pi, $-pi$), (0, $0$), (calc.pi, $pi$)),
y-tick-step: 1,
{
plot.add(
style: style,
domain: (-calc.pi, calc.pi), calc.sin)
plot.add(
hypograph: true,
style: style,
domain: (-calc.pi, calc.pi), calc.cos)
plot.add(
hypograph: true,
style: style,
domain: (-calc.pi, calc.pi), x => calc.cos(x + calc.pi))
})
})
|
https://github.com/Mufanc/hnuslides-typst | https://raw.githubusercontent.com/Mufanc/hnuslides-typst/master/templates/title.typ | typst | #import "/configs.typ"
#import "/utils/colors.typ"
#import "/utils/fonts.typ": font
#import "/utils/background.typ": bg
#let count = counter("chapters")
#let image-1 = [
#place(
dx: 0%, dy: 18%,
center + bottom,
image(width: 60%, "/assets/images/title-01.png")
)
]
#let image-2 = [
#place(
dx: -1%, dy: 5%,
left + bottom,
image(width: 56%, "/assets/images/title-02.png")
)
]
#let image-3 = [
#place(
dx: -3%, dy: 0%,
right + bottom,
image(width: 47%, "/assets/images/title-03.png")
)
]
#let image-4 = [
#place(
dx: 2%, dy: 10%,
center + bottom,
image(width: 60%, "/assets/images/title-04.png")
)
]
#let image-select = context {
let style = calc.rem(count.get().at(0), 4)
if style == 0 {
bg(image-1)
} else if style == 1 {
bg(image-2)
} else if style == 2 {
bg(image-3)
} else {
bg(image-4)
}
}
#let title(title, description: "") = {
set align(center)
image-select
count.step()
v(25%)
stack(dir: ltr, spacing: 3em)[
// 计数超过 10 个 title 会出问题，但与此同时目录也会出问题，所以先不管（
#let number = text(size: 6em, font: font.MSYH, fill: colors.primary)[
#count.display("01")
]
#number
// 数字镂空效果，没想到啥好办法，用背景图遮一下
#context {
place(dy: -2em, box(
width: measure(number).width, height: 1.2em,
fill: pattern(image("/assets/images/bg-common.png"))
))
}
][
#let no-desc = description.len() == 0
#set align(if no-desc { center } else { left })
#show heading: set text(
size: if no-desc { 1.8em } else { 1.33em },
font: font.HYSH
)
#let header = heading(level: 1, title)
#let line-color = colors.primary.transparentize(50%)
#header <title>
#if no-desc {
v(-0.5em)
context {
line(length: measure(header).width + 2em, stroke: (paint: line-color, dash: "dashed"))
}
} else {
line(length: 18em, stroke: line-color)
v(-0.8em)
text(font: font.FZKT, fill: colors.secondary.transparentize(25%), description)
}
]
pagebreak()
}
|
|
https://github.com/TheRiceCold/resume | https://raw.githubusercontent.com/TheRiceCold/resume/main/src/fontawesome.typ | typst | /*
typst-fontawesome
https://github.com/duskmoon314/typst-fontawesome
generated by typst-fontawesome helper python script
*/
#let FA_VERSION = state("fa-version", "Font Awesome 6")
#let FA_SET = state("fa-set", "Free")
#let fa-icon(
name,
fa-version: FA_VERSION,
fa-set: FA_SET,
..args
) = {
locate(loc => {
let fa-version = if type(fa-version) == "string" {
fa-version
} else {
fa-version.at(loc)
}
let fa-set = if type(fa-set) == "string" {
fa-set
} else {
fa-set.at(loc)
}
text(
font: fa-version + " " + fa-set,
name,
..args
)
})
}
#let fa-0 = fa-icon.with("\u{30}")
#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-4 = fa-icon.with("\u{34}")
#let fa-5 = fa-icon.with("\u{35}")
#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-42-group = fa-icon.with("\u{e080}")
#let fa-innosoft = fa-icon.with("\u{e080}")
#let fa-500px = fa-icon.with("\u{f26e}")
#let fa-a = fa-icon.with("\u{41}")
#let fa-accessible-icon = fa-icon.with("\u{f368}")
#let fa-accusoft = fa-icon.with("\u{f369}")
#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-algolia = fa-icon.with("\u{f36c}")
#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-alipay = fa-icon.with("\u{f642}")
#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-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-angellist = fa-icon.with("\u{f209}")
#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-angle-up = fa-icon.with("\u{f106}")
#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-angrycreative = fa-icon.with("\u{f36e}")
#let fa-angular = fa-icon.with("\u{f420}")
#let fa-ankh = fa-icon.with("\u{f644}")
#let fa-app-store = fa-icon.with("\u{f36f}")
#let fa-app-store-ios = fa-icon.with("\u{f370}")
#let fa-apper = fa-icon.with("\u{f371}")
#let fa-apple = fa-icon.with("\u{f179}")
#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-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-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-long = fa-icon.with("\u{f175}")
#let fa-long-arrow-down = fa-icon.with("\u{f175}")
#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-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-long = fa-icon.with("\u{f177}")
#let fa-long-arrow-left = fa-icon.with("\u{f177}")
#let fa-arrow-pointer = fa-icon.with("\u{f245}")
#let fa-mouse-pointer = fa-icon.with("\u{f245}")
#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-bracket = fa-icon.with("\u{f08b}")
#let fa-sign-out = fa-icon.with("\u{f08b}")
#let fa-arrow-right-long = fa-icon.with("\u{f178}")
#let fa-long-arrow-right = fa-icon.with("\u{f178}")
#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-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-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-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-a-z = fa-icon.with("\u{f15e}")
#let fa-sort-alpha-up = fa-icon.with("\u{f15e}")
#let fa-arrow-up-from-bracket = fa-icon.with("\u{e09a}")
#let fa-arrow-up-from-ground-water = fa-icon.with("\u{e4b5}")
#let fa-arrow-up-from-water-pump = fa-icon.with("\u{e4b6}")
#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-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-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-arrows-down-to-line = fa-icon.with("\u{e4b8}")
#let fa-arrows-down-to-people = fa-icon.with("\u{e4b9}")
#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-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-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-eye = fa-icon.with("\u{e4bf}")
#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-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-audible = fa-icon.with("\u{f373}")
#let fa-audio-description = fa-icon.with("\u{f29e}")
#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-award = fa-icon.with("\u{f559}")
#let fa-aws = fa-icon.with("\u{f375}")
#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-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-bag-shopping = fa-icon.with("\u{f290}")
#let fa-shopping-bag = fa-icon.with("\u{f290}")
#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-ban = fa-icon.with("\u{f05e}")
#let fa-cancel = fa-icon.with("\u{f05e}")
#let fa-ban-smoking = fa-icon.with("\u{f54d}")
#let fa-smoking-ban = fa-icon.with("\u{f54d}")
#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-barcode = fa-icon.with("\u{f02a}")
#let fa-bars = fa-icon.with("\u{f0c9}")
#let fa-navicon = fa-icon.with("\u{f0c9}")
#let fa-bars-progress = fa-icon.with("\u{f828}")
#let fa-tasks-alt = fa-icon.with("\u{f828}")
#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-basket-shopping = fa-icon.with("\u{f291}")
#let fa-shopping-basket = fa-icon.with("\u{f291}")
#let fa-basketball = fa-icon.with("\u{f434}")
#let fa-basketball-ball = fa-icon.with("\u{f434}")
#let fa-bath = fa-icon.with("\u{f2cd}")
#let fa-bathtub = fa-icon.with("\u{f2cd}")
#let fa-battery-empty = fa-icon.with("\u{f244}")
#let fa-battery-0 = fa-icon.with("\u{f244}")
#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-quarter = fa-icon.with("\u{f243}")
#let fa-battery-2 = fa-icon.with("\u{f243}")
#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-pulse = fa-icon.with("\u{f487}")
#let fa-procedures = fa-icon.with("\u{f487}")
#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-slash = fa-icon.with("\u{f1f6}")
#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-bimobject = fa-icon.with("\u{f378}")
#let fa-binoculars = fa-icon.with("\u{f1e5}")
#let fa-biohazard = fa-icon.with("\u{f780}")
#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-black-tie = fa-icon.with("\u{f27e}")
#let fa-blackberry = fa-icon.with("\u{f37b}")
#let fa-blender = fa-icon.with("\u{f517}")
#let fa-blender-phone = fa-icon.with("\u{f6b6}")
#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-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-lightning = fa-icon.with("\u{e0b7}")
#let fa-bomb = fa-icon.with("\u{f1e2}")
#let fa-bone = fa-icon.with("\u{f5d7}")
#let fa-bong = fa-icon.with("\u{f55c}")
#let fa-book = fa-icon.with("\u{f02d}")
#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-bookmark = fa-icon.with("\u{e0bb}")
#let fa-book-journal-whills = fa-icon.with("\u{f66a}")
#let fa-journal-whills = fa-icon.with("\u{f66a}")
#let fa-book-medical = fa-icon.with("\u{f7e6}")
#let fa-book-open = fa-icon.with("\u{f518}")
#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-book-skull = fa-icon.with("\u{f6b7}")
#let fa-book-dead = fa-icon.with("\u{f6b7}")
#let fa-book-tanakh = fa-icon.with("\u{f827}")
#let fa-tanakh = fa-icon.with("\u{f827}")
#let fa-bookmark = fa-icon.with("\u{f02e}")
#let fa-bootstrap = fa-icon.with("\u{f836}")
#let fa-border-all = fa-icon.with("\u{f84c}")
#let fa-border-none = fa-icon.with("\u{f850}")
#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-droplet = fa-icon.with("\u{e4c4}")
#let fa-bottle-water = fa-icon.with("\u{e4c5}")
#let fa-bowl-food = fa-icon.with("\u{e4c6}")
#let fa-bowl-rice = fa-icon.with("\u{e2eb}")
#let fa-bowling-ball = fa-icon.with("\u{f436}")
#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-open = fa-icon.with("\u{f49e}")
#let fa-box-tissue = fa-icon.with("\u{e05b}")
#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-braille = fa-icon.with("\u{f2a1}")
#let fa-brain = fa-icon.with("\u{f5dc}")
#let fa-brazilian-real-sign = fa-icon.with("\u{e46c}")
#let fa-bread-slice = fa-icon.with("\u{f7ec}")
#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-water = fa-icon.with("\u{e4ce}")
#let fa-briefcase = fa-icon.with("\u{f0b1}")
#let fa-briefcase-medical = fa-icon.with("\u{f469}")
#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-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-bug-slash = fa-icon.with("\u{e490}")
#let fa-bugs = fa-icon.with("\u{e4d0}")
#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-ngo = fa-icon.with("\u{e4d7}")
#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-bullhorn = fa-icon.with("\u{f0a1}")
#let fa-bullseye = fa-icon.with("\u{f140}")
#let fa-burger = fa-icon.with("\u{f805}")
#let fa-hamburger = fa-icon.with("\u{f805}")
#let fa-buromobelexperte = fa-icon.with("\u{f37f}")
#let fa-burst = fa-icon.with("\u{e4dc}")
#let fa-bus = fa-icon.with("\u{f207}")
#let fa-bus-simple = fa-icon.with("\u{f55e}")
#let fa-bus-alt = fa-icon.with("\u{f55e}")
#let fa-business-time = fa-icon.with("\u{f64a}")
#let fa-briefcase-clock = fa-icon.with("\u{f64a}")
#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-cable-car = fa-icon.with("\u{f7da}")
#let fa-tram = fa-icon.with("\u{f7da}")
#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-calculator = fa-icon.with("\u{f1ec}")
#let fa-calendar = fa-icon.with("\u{f133}")
#let fa-calendar-check = fa-icon.with("\u{f274}")
#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-minus = fa-icon.with("\u{f272}")
#let fa-calendar-plus = fa-icon.with("\u{f271}")
#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-camera = fa-icon.with("\u{f030}")
#let fa-camera-alt = fa-icon.with("\u{f030}")
#let fa-camera-retro = fa-icon.with("\u{f083}")
#let fa-camera-rotate = fa-icon.with("\u{e0d8}")
#let fa-campground = fa-icon.with("\u{f6bb}")
#let fa-canadian-maple-leaf = fa-icon.with("\u{f785}")
#let fa-candy-cane = fa-icon.with("\u{f786}")
#let fa-cannabis = fa-icon.with("\u{f55f}")
#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-car-battery = fa-icon.with("\u{f5df}")
#let fa-battery-car = fa-icon.with("\u{f5df}")
#let fa-car-burst = fa-icon.with("\u{f5e1}")
#let fa-car-crash = fa-icon.with("\u{f5e1}")
#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-car-side = fa-icon.with("\u{f5e4}")
#let fa-car-tunnel = fa-icon.with("\u{e4de}")
#let fa-caravan = fa-icon.with("\u{f8ff}")
#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-carrot = fa-icon.with("\u{f787}")
#let fa-cart-arrow-down = fa-icon.with("\u{f218}")
#let fa-cart-flatbed = fa-icon.with("\u{f474}")
#let fa-dolly-flatbed = fa-icon.with("\u{f474}")
#let fa-cart-flatbed-suitcase = fa-icon.with("\u{f59d}")
#let fa-luggage-cart = fa-icon.with("\u{f59d}")
#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-cash-register = fa-icon.with("\u{f788}")
#let fa-cat = fa-icon.with("\u{f6be}")
#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-cent-sign = fa-icon.with("\u{e3f5}")
#let fa-centercode = fa-icon.with("\u{f380}")
#let fa-centos = fa-icon.with("\u{f789}")
#let fa-certificate = fa-icon.with("\u{f0a3}")
#let fa-chair = fa-icon.with("\u{f6c0}")
#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-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-column = fa-icon.with("\u{e0e3}")
#let fa-chart-gantt = fa-icon.with("\u{e0e4}")
#let fa-chart-line = fa-icon.with("\u{f201}")
#let fa-line-chart = fa-icon.with("\u{f201}")
#let fa-chart-pie = fa-icon.with("\u{f200}")
#let fa-pie-chart = fa-icon.with("\u{f200}")
#let fa-chart-simple = fa-icon.with("\u{e473}")
#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-chess = fa-icon.with("\u{f439}")
#let fa-chess-bishop = fa-icon.with("\u{f43a}")
#let fa-chess-board = fa-icon.with("\u{f43c}")
#let fa-chess-king = fa-icon.with("\u{f43f}")
#let fa-chess-knight = fa-icon.with("\u{f441}")
#let fa-chess-pawn = fa-icon.with("\u{f443}")
#let fa-chess-queen = fa-icon.with("\u{f445}")
#let fa-chess-rook = fa-icon.with("\u{f447}")
#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-chevron-up = fa-icon.with("\u{f077}")
#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-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-arrow-down = fa-icon.with("\u{f0ab}")
#let fa-arrow-circle-down = fa-icon.with("\u{f0ab}")
#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-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-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-exclamation = fa-icon.with("\u{f06a}")
#let fa-exclamation-circle = fa-icon.with("\u{f06a}")
#let fa-circle-h = fa-icon.with("\u{f47e}")
#let fa-hospital-symbol = fa-icon.with("\u{f47e}")
#let fa-circle-half-stroke = fa-icon.with("\u{f042}")
#let fa-adjust = fa-icon.with("\u{f042}")
#let fa-circle-info = fa-icon.with("\u{f05a}")
#let fa-info-circle = fa-icon.with("\u{f05a}")
#let fa-circle-left = fa-icon.with("\u{f359}")
#let fa-arrow-alt-circle-left = fa-icon.with("\u{f359}")
#let fa-circle-minus = fa-icon.with("\u{f056}")
#let fa-minus-circle = fa-icon.with("\u{f056}")
#let fa-circle-nodes = fa-icon.with("\u{e4e2}")
#let fa-circle-notch = fa-icon.with("\u{f1ce}")
#let fa-circle-pause = fa-icon.with("\u{f28b}")
#let fa-pause-circle = fa-icon.with("\u{f28b}")
#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-question = fa-icon.with("\u{f059}")
#let fa-question-circle = fa-icon.with("\u{f059}")
#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-stop = fa-icon.with("\u{f28d}")
#let fa-stop-circle = fa-icon.with("\u{f28d}")
#let fa-circle-up = fa-icon.with("\u{f35b}")
#let fa-arrow-alt-circle-up = fa-icon.with("\u{f35b}")
#let fa-circle-user = fa-icon.with("\u{f2bd}")
#let fa-user-circle = fa-icon.with("\u{f2bd}")
#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-city = fa-icon.with("\u{f64f}")
#let fa-clapperboard = fa-icon.with("\u{e131}")
#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-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-rotate-left = fa-icon.with("\u{f1da}")
#let fa-history = fa-icon.with("\u{f1da}")
#let fa-clone = fa-icon.with("\u{f24d}")
#let fa-closed-captioning = fa-icon.with("\u{f20a}")
#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-bolt = fa-icon.with("\u{f76c}")
#let fa-thunderstorm = fa-icon.with("\u{f76c}")
#let fa-cloud-meatball = fa-icon.with("\u{f73b}")
#let fa-cloud-moon = fa-icon.with("\u{f6c3}")
#let fa-cloud-moon-rain = fa-icon.with("\u{f73c}")
#let fa-cloud-rain = fa-icon.with("\u{f73d}")
#let fa-cloud-showers-heavy = fa-icon.with("\u{f740}")
#let fa-cloud-showers-water = fa-icon.with("\u{e4e4}")
#let fa-cloud-sun = fa-icon.with("\u{f6c4}")
#let fa-cloud-sun-rain = fa-icon.with("\u{f743}")
#let fa-cloudflare = fa-icon.with("\u{e07d}")
#let fa-cloudscale = fa-icon.with("\u{f383}")
#let fa-cloudsmith = fa-icon.with("\u{f384}")
#let fa-cloudversify = fa-icon.with("\u{f385}")
#let fa-clover = fa-icon.with("\u{e139}")
#let fa-cmplid = fa-icon.with("\u{e360}")
#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-code-pull-request = fa-icon.with("\u{e13c}")
#let fa-codepen = fa-icon.with("\u{f1cb}")
#let fa-codiepie = fa-icon.with("\u{f284}")
#let fa-coins = fa-icon.with("\u{f51e}")
#let fa-colon-sign = fa-icon.with("\u{e140}")
#let fa-comment = fa-icon.with("\u{f075}")
#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-medical = fa-icon.with("\u{f7f5}")
#let fa-comment-slash = fa-icon.with("\u{f4b3}")
#let fa-comment-sms = fa-icon.with("\u{f7cd}")
#let fa-sms = fa-icon.with("\u{f7cd}")
#let fa-comments = fa-icon.with("\u{f086}")
#let fa-comments-dollar = fa-icon.with("\u{f653}")
#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-compress = fa-icon.with("\u{f066}")
#let fa-computer = fa-icon.with("\u{e4e5}")
#let fa-computer-mouse = fa-icon.with("\u{f8cc}")
#let fa-mouse = fa-icon.with("\u{f8cc}")
#let fa-confluence = fa-icon.with("\u{f78d}")
#let fa-connectdevelop = fa-icon.with("\u{f20e}")
#let fa-contao = fa-icon.with("\u{f26d}")
#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-cotton-bureau = fa-icon.with("\u{f89e}")
#let fa-couch = fa-icon.with("\u{f4b8}")
#let fa-cow = fa-icon.with("\u{f6c8}")
#let fa-cpanel = fa-icon.with("\u{f388}")
#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-critical-role = fa-icon.with("\u{f6c9}")
#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-crow = fa-icon.with("\u{f520}")
#let fa-crown = fa-icon.with("\u{f521}")
#let fa-crutch = fa-icon.with("\u{f7f7}")
#let fa-cruzeiro-sign = fa-icon.with("\u{e152}")
#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-cuttlefish = fa-icon.with("\u{f38c}")
#let fa-d = fa-icon.with("\u{44}")
#let fa-d-and-d = fa-icon.with("\u{f38d}")
#let fa-d-and-d-beyond = fa-icon.with("\u{f6ca}")
#let fa-dailymotion = fa-icon.with("\u{e052}")
#let fa-dashcube = fa-icon.with("\u{f210}")
#let fa-database = fa-icon.with("\u{f1c0}")
#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-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-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-next = fa-icon.with("\u{e476}")
#let fa-diagram-predecessor = fa-icon.with("\u{e477}")
#let fa-diagram-project = fa-icon.with("\u{f542}")
#let fa-project-diagram = fa-icon.with("\u{f542}")
#let fa-diagram-successor = fa-icon.with("\u{e47a}")
#let fa-diamond = fa-icon.with("\u{f219}")
#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-d20 = fa-icon.with("\u{f6cf}")
#let fa-dice-d6 = fa-icon.with("\u{f6d1}")
#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-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-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-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-dong-sign = fa-icon.with("\u{e169}")
#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-left-and-up-right-to-center = fa-icon.with("\u{f422}")
#let fa-compress-alt = fa-icon.with("\u{f422}")
#let fa-down-long = fa-icon.with("\u{f309}")
#let fa-long-arrow-alt-down = fa-icon.with("\u{f309}")
#let fa-download = fa-icon.with("\u{f019}")
#let fa-draft2digital = fa-icon.with("\u{f396}")
#let fa-dragon = fa-icon.with("\u{f6d5}")
#let fa-draw-polygon = fa-icon.with("\u{f5ee}")
#let fa-dribbble = fa-icon.with("\u{f17d}")
#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-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-bite = fa-icon.with("\u{f6d7}")
#let fa-drupal = fa-icon.with("\u{f1a9}")
#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-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-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-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-eject = fa-icon.with("\u{f052}")
#let fa-elementor = fa-icon.with("\u{f430}")
#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-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-envelope = fa-icon.with("\u{f0e0}")
#let fa-envelope-circle-check = fa-icon.with("\u{e4e8}")
#let fa-envelope-open = fa-icon.with("\u{f2b6}")
#let fa-envelope-open-text = fa-icon.with("\u{f658}")
#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-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-exclamation = fa-icon.with("\u{21}")
#let fa-expand = fa-icon.with("\u{f065}")
#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-low-vision = fa-icon.with("\u{f2a8}")
#let fa-low-vision = fa-icon.with("\u{f2a8}")
#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-dizzy = fa-icon.with("\u{f567}")
#let fa-dizzy = fa-icon.with("\u{f567}")
#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-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-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-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-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-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-tear = fa-icon.with("\u{f5b4}")
#let fa-sad-tear = fa-icon.with("\u{f5b4}")
#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-wink = fa-icon.with("\u{f4da}")
#let fa-smile-wink = fa-icon.with("\u{f4da}")
#let fa-face-surprise = fa-icon.with("\u{f5c2}")
#let fa-surprise = fa-icon.with("\u{f5c2}")
#let fa-face-tired = fa-icon.with("\u{f5c8}")
#let fa-tired = fa-icon.with("\u{f5c8}")
#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-fan = fa-icon.with("\u{f863}")
#let fa-fantasy-flight-games = fa-icon.with("\u{f6dc}")
#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-ferry = fa-icon.with("\u{e4ea}")
#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-circle-check = fa-icon.with("\u{e5a0}")
#let fa-file-circle-exclamation = fa-icon.with("\u{e4eb}")
#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-excel = fa-icon.with("\u{f1c3}")
#let fa-file-export = fa-icon.with("\u{f56e}")
#let fa-arrow-right-from-file = fa-icon.with("\u{f56e}")
#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-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-medical = fa-icon.with("\u{f477}")
#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-powerpoint = fa-icon.with("\u{f1c4}")
#let fa-file-prescription = fa-icon.with("\u{f572}")
#let fa-file-shield = fa-icon.with("\u{e4f0}")
#let fa-file-signature = fa-icon.with("\u{f573}")
#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-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-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-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-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-first-order = fa-icon.with("\u{f2b0}")
#let fa-first-order-alt = fa-icon.with("\u{f50a}")
#let fa-firstdraft = fa-icon.with("\u{f3a1}")
#let fa-fish = fa-icon.with("\u{f578}")
#let fa-fish-fins = fa-icon.with("\u{e4f2}")
#let fa-flag = fa-icon.with("\u{f024}")
#let fa-flag-checkered = fa-icon.with("\u{f11e}")
#let fa-flag-usa = fa-icon.with("\u{f74d}")
#let fa-flask = fa-icon.with("\u{f0c3}")
#let fa-flask-vial = fa-icon.with("\u{e4f3}")
#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-florin-sign = fa-icon.with("\u{e184}")
#let fa-fly = fa-icon.with("\u{f417}")
#let fa-folder = fa-icon.with("\u{f07b}")
#let fa-folder-blank = fa-icon.with("\u{f07b}")
#let fa-folder-closed = fa-icon.with("\u{e185}")
#let fa-folder-minus = fa-icon.with("\u{f65d}")
#let fa-folder-open = fa-icon.with("\u{f07c}")
#let fa-folder-plus = fa-icon.with("\u{f65e}")
#let fa-folder-tree = fa-icon.with("\u{f802}")
#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-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-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-franc-sign = fa-icon.with("\u{e18f}")
#let fa-free-code-camp = fa-icon.with("\u{f2c5}")
#let fa-freebsd = fa-icon.with("\u{f3a4}")
#let fa-frog = fa-icon.with("\u{f52e}")
#let fa-fulcrum = fa-icon.with("\u{f50b}")
#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-gamepad = fa-icon.with("\u{f11b}")
#let fa-gas-pump = fa-icon.with("\u{f52f}")
#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-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-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-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-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-gift = fa-icon.with("\u{f06b}")
#let fa-gifts = fa-icon.with("\u{f79c}")
#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-water = fa-icon.with("\u{e4f4}")
#let fa-glass-water-droplet = fa-icon.with("\u{e4f5}")
#let fa-glasses = fa-icon.with("\u{f530}")
#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-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-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-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-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-grip = fa-icon.with("\u{f58d}")
#let fa-grip-horizontal = fa-icon.with("\u{f58d}")
#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-gripfire = fa-icon.with("\u{f3ac}")
#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-gulp = fa-icon.with("\u{f3ae}")
#let fa-gun = fa-icon.with("\u{e19b}")
#let fa-h = fa-icon.with("\u{48}")
#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-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-dots = fa-icon.with("\u{f461}")
#let fa-allergies = fa-icon.with("\u{f461}")
#let fa-hand-fist = fa-icon.with("\u{f6de}")
#let fa-fist-raised = fa-icon.with("\u{f6de}")
#let fa-hand-holding = fa-icon.with("\u{f4bd}")
#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-medical = fa-icon.with("\u{e05c}")
#let fa-hand-lizard = fa-icon.with("\u{f258}")
#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-point-left = fa-icon.with("\u{f0a5}")
#let fa-hand-point-right = fa-icon.with("\u{f0a4}")
#let fa-hand-point-up = fa-icon.with("\u{f0a6}")
#let fa-hand-pointer = fa-icon.with("\u{f25a}")
#let fa-hand-scissors = fa-icon.with("\u{f257}")
#let fa-hand-sparkles = fa-icon.with("\u{e05d}")
#let fa-hand-spock = fa-icon.with("\u{f259}")
#let fa-handcuffs = fa-icon.with("\u{e4f8}")
#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-hands-clapping = fa-icon.with("\u{e1a8}")
#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-praying = fa-icon.with("\u{f684}")
#let fa-praying-hands = fa-icon.with("\u{f684}")
#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-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-hat-cowboy = fa-icon.with("\u{f8c0}")
#let fa-hat-cowboy-side = fa-icon.with("\u{f8c1}")
#let fa-hat-wizard = fa-icon.with("\u{f6e8}")
#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-mask = fa-icon.with("\u{e063}")
#let fa-head-side-virus = fa-icon.with("\u{e064}")
#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-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-pulse = fa-icon.with("\u{f21e}")
#let fa-heartbeat = fa-icon.with("\u{f21e}")
#let fa-helicopter = fa-icon.with("\u{f533}")
#let fa-helicopter-symbol = fa-icon.with("\u{e502}")
#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-highlighter = fa-icon.with("\u{f591}")
#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-puck = fa-icon.with("\u{f453}")
#let fa-holly-berry = fa-icon.with("\u{f7aa}")
#let fa-hooli = fa-icon.with("\u{f427}")
#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-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-hospital-user = fa-icon.with("\u{f80d}")
#let fa-hot-tub-person = fa-icon.with("\u{f593}")
#let fa-hot-tub = fa-icon.with("\u{f593}")
#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-hourglass = fa-icon.with("\u{f254}")
#let fa-hourglass-empty = fa-icon.with("\u{f254}")
#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-chimney = fa-icon.with("\u{e3af}")
#let fa-home-lg = fa-icon.with("\u{e3af}")
#let fa-house-chimney-crack = fa-icon.with("\u{f6f1}")
#let fa-house-damage = fa-icon.with("\u{f6f1}")
#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-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-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-signal = fa-icon.with("\u{e012}")
#let fa-house-tsunami = fa-icon.with("\u{e515}")
#let fa-house-user = fa-icon.with("\u{e1b0}")
#let fa-home-user = fa-icon.with("\u{e1b0}")
#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-hurricane = fa-icon.with("\u{f751}")
#let fa-i = fa-icon.with("\u{49}")
#let fa-i-cursor = fa-icon.with("\u{f246}")
#let fa-ice-cream = fa-icon.with("\u{f810}")
#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-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-portrait = fa-icon.with("\u{f3e0}")
#let fa-portrait = fa-icon.with("\u{f3e0}")
#let fa-images = fa-icon.with("\u{f302}")
#let fa-imdb = fa-icon.with("\u{f2d8}")
#let fa-inbox = fa-icon.with("\u{f01c}")
#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-infinity = fa-icon.with("\u{f534}")
#let fa-info = fa-icon.with("\u{f129}")
#let fa-instagram = fa-icon.with("\u{f16d}")
#let fa-instalod = fa-icon.with("\u{e081}")
#let fa-intercom = fa-icon.with("\u{f7af}")
#let fa-internet-explorer = fa-icon.with("\u{f26b}")
#let fa-invision = fa-icon.with("\u{f7b0}")
#let fa-ioxhost = fa-icon.with("\u{f208}")
#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-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-js = fa-icon.with("\u{f3b8}")
#let fa-jsfiddle = fa-icon.with("\u{f1cc}")
#let fa-jug-detergent = fa-icon.with("\u{e519}")
#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-key = fa-icon.with("\u{f084}")
#let fa-keybase = fa-icon.with("\u{f4f5}")
#let fa-keyboard = fa-icon.with("\u{f11c}")
#let fa-keycdn = fa-icon.with("\u{f3ba}")
#let fa-khanda = fa-icon.with("\u{f66d}")
#let fa-kickstarter = fa-icon.with("\u{f3bb}")
#let fa-kickstarter-k = fa-icon.with("\u{f3bc}")
#let fa-kip-sign = fa-icon.with("\u{e1c4}")
#let fa-kit-medical = fa-icon.with("\u{f479}")
#let fa-first-aid = fa-icon.with("\u{f479}")
#let fa-kitchen-set = fa-icon.with("\u{e51a}")
#let fa-kiwi-bird = fa-icon.with("\u{f535}")
#let fa-korvue = fa-icon.with("\u{f42f}")
#let fa-l = fa-icon.with("\u{4c}")
#let fa-land-mine-on = fa-icon.with("\u{e51b}")
#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-language = fa-icon.with("\u{f1ab}")
#let fa-laptop = fa-icon.with("\u{f109}")
#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-laravel = fa-icon.with("\u{f3bd}")
#let fa-lari-sign = fa-icon.with("\u{e1c8}")
#let fa-lastfm = fa-icon.with("\u{f202}")
#let fa-layer-group = fa-icon.with("\u{f5fd}")
#let fa-leaf = fa-icon.with("\u{f06c}")
#let fa-leanpub = fa-icon.with("\u{f212}")
#let fa-left-long = fa-icon.with("\u{f30a}")
#let fa-long-arrow-alt-left = fa-icon.with("\u{f30a}")
#let fa-left-right = fa-icon.with("\u{f337}")
#let fa-arrows-alt-h = fa-icon.with("\u{f337}")
#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-life-ring = fa-icon.with("\u{f1cd}")
#let fa-lightbulb = fa-icon.with("\u{f0eb}")
#let fa-line = fa-icon.with("\u{f3c0}")
#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-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-linkedin = fa-icon.with("\u{f08c}")
#let fa-linkedin-in = fa-icon.with("\u{f0e1}")
#let fa-linode = fa-icon.with("\u{f2b8}")
#let fa-linux = fa-icon.with("\u{f17c}")
#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-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-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-location-arrow = fa-icon.with("\u{f124}")
#let fa-location-crosshairs = fa-icon.with("\u{f601}")
#let fa-location = fa-icon.with("\u{f601}")
#let fa-location-dot = fa-icon.with("\u{f3c5}")
#let fa-map-marker-alt = fa-icon.with("\u{f3c5}")
#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-lock = fa-icon.with("\u{f023}")
#let fa-lock-open = fa-icon.with("\u{f3c1}")
#let fa-locust = fa-icon.with("\u{e520}")
#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-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-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-plus = fa-icon.with("\u{f00e}")
#let fa-search-plus = fa-icon.with("\u{f00e}")
#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-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-ventilator = fa-icon.with("\u{e524}")
#let fa-masks-theater = fa-icon.with("\u{f630}")
#let fa-theater-masks = fa-icon.with("\u{f630}")
#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-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-megaport = fa-icon.with("\u{f5a3}")
#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-message = fa-icon.with("\u{f27a}")
#let fa-comment-alt = fa-icon.with("\u{f27a}")
#let fa-meta = fa-icon.with("\u{e49b}")
#let fa-meteor = fa-icon.with("\u{f753}")
#let fa-microblog = fa-icon.with("\u{e01a}")
#let fa-microchip = fa-icon.with("\u{f2db}")
#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-microscope = fa-icon.with("\u{f610}")
#let fa-microsoft = fa-icon.with("\u{f3ca}")
#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-minus = fa-icon.with("\u{f068}")
#let fa-subtract = fa-icon.with("\u{f068}")
#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-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-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-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-bills = fa-icon.with("\u{e1f3}")
#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-monument = fa-icon.with("\u{f5a6}")
#let fa-moon = fa-icon.with("\u{f186}")
#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-mountain-sun = fa-icon.with("\u{e52f}")
#let fa-mug-hot = fa-icon.with("\u{f7b6}")
#let fa-mug-saucer = fa-icon.with("\u{f0f4}")
#let fa-coffee = fa-icon.with("\u{f0f4}")
#let fa-music = fa-icon.with("\u{f001}")
#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-neos = fa-icon.with("\u{f612}")
#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-directional = fa-icon.with("\u{e530}")
#let fa-nfc-symbol = fa-icon.with("\u{e531}")
#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-not-equal = fa-icon.with("\u{f53e}")
#let fa-notdef = fa-icon.with("\u{e1fe}")
#let fa-note-sticky = fa-icon.with("\u{f249}")
#let fa-sticky-note = fa-icon.with("\u{f249}")
#let fa-notes-medical = fa-icon.with("\u{f481}")
#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-group = fa-icon.with("\u{f247}")
#let fa-object-ungroup = fa-icon.with("\u{f248}")
#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-well = fa-icon.with("\u{e532}")
#let fa-old-republic = fa-icon.with("\u{f510}")
#let fa-om = fa-icon.with("\u{f679}")
#let fa-opencart = fa-icon.with("\u{f23d}")
#let fa-openid = fa-icon.with("\u{f19b}")
#let fa-opera = fa-icon.with("\u{f26a}")
#let fa-optin-monster = fa-icon.with("\u{f23c}")
#let fa-orcid = fa-icon.with("\u{f8d2}")
#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-p = fa-icon.with("\u{50}")
#let fa-padlet = fa-icon.with("\u{e4a0}")
#let fa-page4 = fa-icon.with("\u{f3d7}")
#let fa-pagelines = fa-icon.with("\u{f18c}")
#let fa-pager = fa-icon.with("\u{f815}")
#let fa-paint-roller = fa-icon.with("\u{f5aa}")
#let fa-paintbrush = fa-icon.with("\u{f1fc}")
#let fa-paint-brush = fa-icon.with("\u{f1fc}")
#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-panorama = fa-icon.with("\u{e209}")
#let fa-paper-plane = fa-icon.with("\u{f1d8}")
#let fa-paperclip = fa-icon.with("\u{f0c6}")
#let fa-parachute-box = fa-icon.with("\u{f4cd}")
#let fa-paragraph = fa-icon.with("\u{f1dd}")
#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-paypal = fa-icon.with("\u{f1ed}")
#let fa-peace = fa-icon.with("\u{f67c}")
#let fa-pen = fa-icon.with("\u{f304}")
#let fa-pen-clip = fa-icon.with("\u{f305}")
#let fa-pen-alt = fa-icon.with("\u{f305}")
#let fa-pen-fancy = fa-icon.with("\u{f5ac}")
#let fa-pen-nib = fa-icon.with("\u{f5ad}")
#let fa-pen-ruler = fa-icon.with("\u{f5ae}")
#let fa-pencil-ruler = fa-icon.with("\u{f5ae}")
#let fa-pen-to-square = fa-icon.with("\u{f044}")
#let fa-edit = fa-icon.with("\u{f044}")
#let fa-pencil = fa-icon.with("\u{f303}")
#let fa-pencil-alt = fa-icon.with("\u{f303}")
#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-group = fa-icon.with("\u{e533}")
#let fa-people-line = fa-icon.with("\u{e534}")
#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-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-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-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-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-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-drowning = fa-icon.with("\u{e545}")
#let fa-person-falling = fa-icon.with("\u{e546}")
#let fa-person-falling-burst = fa-icon.with("\u{e547}")
#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-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-shelter = fa-icon.with("\u{e54f}")
#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-snowboarding = fa-icon.with("\u{f7ce}")
#let fa-snowboarding = fa-icon.with("\u{f7ce}")
#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-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-flip = fa-icon.with("\u{f879}")
#let fa-phone-alt = fa-icon.with("\u{f879}")
#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-photo-film = fa-icon.with("\u{f87c}")
#let fa-photo-video = fa-icon.with("\u{f87c}")
#let fa-php = fa-icon.with("\u{f457}")
#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-piggy-bank = fa-icon.with("\u{f4d3}")
#let fa-pills = fa-icon.with("\u{f484}")
#let fa-pinterest = fa-icon.with("\u{f0d2}")
#let fa-pinterest-p = fa-icon.with("\u{f231}")
#let fa-pix = fa-icon.with("\u{e43a}")
#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-lock = fa-icon.with("\u{e558}")
#let fa-plane-slash = fa-icon.with("\u{e069}")
#let fa-plane-up = fa-icon.with("\u{e22d}")
#let fa-plant-wilt = fa-icon.with("\u{e5aa}")
#let fa-plate-wheat = fa-icon.with("\u{e55a}")
#let fa-play = fa-icon.with("\u{f04b}")
#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-minus = fa-icon.with("\u{e43c}")
#let fa-podcast = fa-icon.with("\u{f2ce}")
#let fa-poo = fa-icon.with("\u{f2fe}")
#let fa-poo-storm = fa-icon.with("\u{f75a}")
#let fa-poo-bolt = fa-icon.with("\u{f75a}")
#let fa-poop = fa-icon.with("\u{f619}")
#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-print = fa-icon.with("\u{f02f}")
#let fa-product-hunt = fa-icon.with("\u{f288}")
#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-piece = fa-icon.with("\u{f12e}")
#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-r = fa-icon.with("\u{52}")
#let fa-r-project = fa-icon.with("\u{f4f7}")
#let fa-radiation = fa-icon.with("\u{f7b9}")
#let fa-radio = fa-icon.with("\u{f8d7}")
#let fa-rainbow = fa-icon.with("\u{f75b}")
#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-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-ad = fa-icon.with("\u{f641}")
#let fa-ad = fa-icon.with("\u{f641}")
#let fa-rectangle-list = fa-icon.with("\u{f022}")
#let fa-list-alt = fa-icon.with("\u{f022}")
#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-red-river = fa-icon.with("\u{f3e3}")
#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-registered = fa-icon.with("\u{f25d}")
#let fa-renren = fa-icon.with("\u{f18b}")
#let fa-repeat = fa-icon.with("\u{f363}")
#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-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-retweet = fa-icon.with("\u{f079}")
#let fa-rev = fa-icon.with("\u{f5b2}")
#let fa-ribbon = fa-icon.with("\u{f4d6}")
#let fa-right-from-bracket = fa-icon.with("\u{f2f5}")
#let fa-sign-out-alt = fa-icon.with("\u{f2f5}")
#let fa-right-left = fa-icon.with("\u{f362}")
#let fa-exchange-alt = fa-icon.with("\u{f362}")
#let fa-right-long = fa-icon.with("\u{f30b}")
#let fa-long-arrow-alt-right = fa-icon.with("\u{f30b}")
#let fa-right-to-bracket = fa-icon.with("\u{f2f6}")
#let fa-sign-in-alt = fa-icon.with("\u{f2f6}")
#let fa-ring = fa-icon.with("\u{f70b}")
#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-rocket = fa-icon.with("\u{f135}")
#let fa-rocketchat = fa-icon.with("\u{f3e8}")
#let fa-rockrms = fa-icon.with("\u{f3e9}")
#let fa-rotate = fa-icon.with("\u{f2f1}")
#let fa-sync-alt = fa-icon.with("\u{f2f1}")
#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-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-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-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-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-s = fa-icon.with("\u{53}")
#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-salesforce = fa-icon.with("\u{f83b}")
#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-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-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-screenpal = fa-icon.with("\u{e570}")
#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-scribd = fa-icon.with("\u{f28a}")
#let fa-scroll = fa-icon.with("\u{f70e}")
#let fa-scroll-torah = fa-icon.with("\u{f6a0}")
#let fa-torah = fa-icon.with("\u{f6a0}")
#let fa-sd-card = fa-icon.with("\u{f7c2}")
#let fa-searchengin = fa-icon.with("\u{f3eb}")
#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-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-arrow-turn-right = fa-icon.with("\u{f064}")
#let fa-mail-forward = fa-icon.with("\u{f064}")
#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-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-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-dog = fa-icon.with("\u{e573}")
#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-virus = fa-icon.with("\u{e06c}")
#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-shirtsinbulk = fa-icon.with("\u{f214}")
#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-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-shopify = fa-icon.with("\u{e057}")
#let fa-shopware = fa-icon.with("\u{f5b5}")
#let fa-shower = fa-icon.with("\u{f2cc}")
#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-shuttle-space = fa-icon.with("\u{f197}")
#let fa-space-shuttle = fa-icon.with("\u{f197}")
#let fa-sign-hanging = fa-icon.with("\u{f4d9}")
#let fa-sign = fa-icon.with("\u{f4d9}")
#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-signature = fa-icon.with("\u{f5b7}")
#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-simplybuilt = fa-icon.with("\u{f215}")
#let fa-sink = fa-icon.with("\u{e06d}")
#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-sketch = fa-icon.with("\u{f7c6}")
#let fa-skull = fa-icon.with("\u{f54c}")
#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-sleigh = fa-icon.with("\u{f7cc}")
#let fa-sliders = fa-icon.with("\u{f1de}")
#let fa-sliders-h = fa-icon.with("\u{f1de}")
#let fa-slideshare = fa-icon.with("\u{f1e7}")
#let fa-smog = fa-icon.with("\u{f75f}")
#let fa-smoking = fa-icon.with("\u{f48d}")
#let fa-snapchat = fa-icon.with("\u{f2ab}")
#let fa-snapchat-ghost = fa-icon.with("\u{f2ab}")
#let fa-snowflake = fa-icon.with("\u{f2dc}")
#let fa-snowman = fa-icon.with("\u{f7d0}")
#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-solar-panel = fa-icon.with("\u{f5ba}")
#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-spaghetti-monster-flying = fa-icon.with("\u{f67b}")
#let fa-pastafarianism = fa-icon.with("\u{f67b}")
#let fa-speakap = fa-icon.with("\u{f3f3}")
#let fa-speaker-deck = fa-icon.with("\u{f83c}")
#let fa-spell-check = fa-icon.with("\u{f891}")
#let fa-spider = fa-icon.with("\u{f717}")
#let fa-spinner = fa-icon.with("\u{f110}")
#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-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-square = fa-icon.with("\u{f0c8}")
#let fa-square-arrow-up-right = fa-icon.with("\u{f14c}")
#let fa-external-link-square = fa-icon.with("\u{f14c}")
#let fa-square-behance = fa-icon.with("\u{f1b5}")
#let fa-behance-square = fa-icon.with("\u{f1b5}")
#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-dribbble = fa-icon.with("\u{f397}")
#let fa-dribbble-square = fa-icon.with("\u{f397}")
#let fa-square-envelope = fa-icon.with("\u{f199}")
#let fa-envelope-square = fa-icon.with("\u{f199}")
#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-full = fa-icon.with("\u{f45c}")
#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-instagram = fa-icon.with("\u{e055}")
#let fa-instagram-square = fa-icon.with("\u{e055}")
#let fa-square-js = fa-icon.with("\u{f3b9}")
#let fa-js-square = fa-icon.with("\u{f3b9}")
#let fa-square-lastfm = fa-icon.with("\u{f203}")
#let fa-lastfm-square = fa-icon.with("\u{f203}")
#let fa-square-minus = fa-icon.with("\u{f146}")
#let fa-minus-square = fa-icon.with("\u{f146}")
#let fa-square-nfi = fa-icon.with("\u{e576}")
#let fa-square-odnoklassniki = fa-icon.with("\u{f264}")
#let fa-odnoklassniki-square = fa-icon.with("\u{f264}")
#let fa-square-parking = fa-icon.with("\u{f540}")
#let fa-parking = fa-icon.with("\u{f540}")
#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-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-reddit = fa-icon.with("\u{f1a2}")
#let fa-reddit-square = fa-icon.with("\u{f1a2}")
#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-share-nodes = fa-icon.with("\u{f1e1}")
#let fa-share-alt-square = fa-icon.with("\u{f1e1}")
#let fa-square-snapchat = fa-icon.with("\u{f2ad}")
#let fa-snapchat-square = fa-icon.with("\u{f2ad}")
#let fa-square-steam = fa-icon.with("\u{f1b7}")
#let fa-steam-square = fa-icon.with("\u{f1b7}")
#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-up-right = fa-icon.with("\u{f360}")
#let fa-external-link-square-alt = fa-icon.with("\u{f360}")
#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-whatsapp = fa-icon.with("\u{f40c}")
#let fa-whatsapp-square = fa-icon.with("\u{f40c}")
#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-youtube = fa-icon.with("\u{f431}")
#let fa-youtube-square = fa-icon.with("\u{f431}")
#let fa-squarespace = fa-icon.with("\u{f5be}")
#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-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-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-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-staylinked = fa-icon.with("\u{f3f5}")
#let fa-steam = fa-icon.with("\u{f1b6}")
#let fa-steam-symbol = fa-icon.with("\u{f3f6}")
#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-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-slash = fa-icon.with("\u{e071}")
#let fa-strava = fa-icon.with("\u{f428}")
#let fa-street-view = fa-icon.with("\u{f21d}")
#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-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-plant-wilt = fa-icon.with("\u{e57a}")
#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-swatchbook = fa-icon.with("\u{f5c3}")
#let fa-swift = fa-icon.with("\u{f8e1}")
#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-large = fa-icon.with("\u{f009}")
#let fa-th-large = fa-icon.with("\u{f009}")
#let fa-table-columns = fa-icon.with("\u{f0db}")
#let fa-columns = fa-icon.with("\u{f0db}")
#let fa-table-list = fa-icon.with("\u{f00b}")
#let fa-th-list = fa-icon.with("\u{f00b}")
#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-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-tablet-screen-button = fa-icon.with("\u{f3fa}")
#let fa-tablet-alt = fa-icon.with("\u{f3fa}")
#let fa-tablets = fa-icon.with("\u{f490}")
#let fa-tachograph-digital = fa-icon.with("\u{f566}")
#let fa-digital-tachograph = fa-icon.with("\u{f566}")
#let fa-tag = fa-icon.with("\u{f02b}")
#let fa-tags = fa-icon.with("\u{f02c}")
#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-teamspeak = fa-icon.with("\u{f4f9}")
#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-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-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-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-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-arrow-turn-left = fa-icon.with("\u{e580}")
#let fa-tent-arrows-down = fa-icon.with("\u{e581}")
#let fa-tents = fa-icon.with("\u{e582}")
#let fa-terminal = fa-icon.with("\u{f120}")
#let fa-text-height = fa-icon.with("\u{f034}")
#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-the-red-yeti = fa-icon.with("\u{f69d}")
#let fa-themeco = fa-icon.with("\u{f5c6}")
#let fa-themeisle = fa-icon.with("\u{f2b2}")
#let fa-thermometer = fa-icon.with("\u{f491}")
#let fa-think-peaks = fa-icon.with("\u{f731}")
#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-ticket = fa-icon.with("\u{f145}")
#let fa-ticket-simple = fa-icon.with("\u{f3ff}")
#let fa-ticket-alt = fa-icon.with("\u{f3ff}")
#let fa-tiktok = fa-icon.with("\u{e07b}")
#let fa-timeline = fa-icon.with("\u{e29c}")
#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-slash = fa-icon.with("\u{e072}")
#let fa-toilet-portable = fa-icon.with("\u{e583}")
#let fa-toilets-portable = fa-icon.with("\u{e584}")
#let fa-toolbox = fa-icon.with("\u{f552}")
#let fa-tooth = fa-icon.with("\u{f5c9}")
#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-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-light = fa-icon.with("\u{f637}")
#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-tram = fa-icon.with("\u{e5b4}")
#let fa-transgender = fa-icon.with("\u{f225}")
#let fa-transgender-alt = fa-icon.with("\u{f225}")
#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-tree = fa-icon.with("\u{f1bb}")
#let fa-tree-city = fa-icon.with("\u{e587}")
#let fa-trello = fa-icon.with("\u{f181}")
#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-trophy = fa-icon.with("\u{f091}")
#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-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-front = fa-icon.with("\u{e2b7}")
#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-ramp-box = fa-icon.with("\u{f4de}")
#let fa-truck-loading = fa-icon.with("\u{f4de}")
#let fa-tty = fa-icon.with("\u{f1e4}")
#let fa-teletype = fa-icon.with("\u{f1e4}")
#let fa-tumblr = fa-icon.with("\u{f173}")
#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-up = fa-icon.with("\u{f3bf}")
#let fa-level-up-alt = fa-icon.with("\u{f3bf}")
#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-twitch = fa-icon.with("\u{f1e8}")
#let fa-twitter = fa-icon.with("\u{f099}")
#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-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-uncharted = fa-icon.with("\u{e084}")
#let fa-underline = fa-icon.with("\u{f0cd}")
#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-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-long = fa-icon.with("\u{f30c}")
#let fa-long-arrow-alt-up = fa-icon.with("\u{f30c}")
#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-upload = fa-icon.with("\u{f093}")
#let fa-ups = fa-icon.with("\u{f7e0}")
#let fa-usb = fa-icon.with("\u{f287}")
#let fa-user = fa-icon.with("\u{f007}")
#let fa-user-astronaut = fa-icon.with("\u{f4fb}")
#let fa-user-check = fa-icon.with("\u{f4fc}")
#let fa-user-clock = fa-icon.with("\u{f4fd}")
#let fa-user-doctor = fa-icon.with("\u{f0f0}")
#let fa-user-md = fa-icon.with("\u{f0f0}")
#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-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-minus = fa-icon.with("\u{f503}")
#let fa-user-ninja = fa-icon.with("\u{f504}")
#let fa-user-nurse = fa-icon.with("\u{f82f}")
#let fa-user-pen = fa-icon.with("\u{f4ff}")
#let fa-user-edit = fa-icon.with("\u{f4ff}")
#let fa-user-plus = fa-icon.with("\u{f234}")
#let fa-user-secret = fa-icon.with("\u{f21b}")
#let fa-user-shield = fa-icon.with("\u{f505}")
#let fa-user-slash = fa-icon.with("\u{f506}")
#let fa-user-tag = fa-icon.with("\u{f507}")
#let fa-user-tie = fa-icon.with("\u{f508}")
#let fa-user-xmark = fa-icon.with("\u{f235}")
#let fa-user-times = fa-icon.with("\u{f235}")
#let fa-users = fa-icon.with("\u{f0c0}")
#let fa-users-between-lines = fa-icon.with("\u{e591}")
#let fa-users-gear = fa-icon.with("\u{f509}")
#let fa-users-cog = fa-icon.with("\u{f509}")
#let fa-users-line = fa-icon.with("\u{e592}")
#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-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-v = fa-icon.with("\u{56}")
#let fa-vaadin = fa-icon.with("\u{f408}")
#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-square = fa-icon.with("\u{f5cb}")
#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-vial-virus = fa-icon.with("\u{e597}")
#let fa-vials = fa-icon.with("\u{f493}")
#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-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-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-virus-slash = fa-icon.with("\u{e075}")
#let fa-viruses = fa-icon.with("\u{e076}")
#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-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-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-walkie-talkie = fa-icon.with("\u{f8ef}")
#let fa-wallet = fa-icon.with("\u{f555}")
#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-watchman-monitoring = fa-icon.with("\u{e087}")
#let fa-water = fa-icon.with("\u{f773}")
#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-wave-square = fa-icon.with("\u{f83e}")
#let fa-waze = fa-icon.with("\u{f83f}")
#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-whatsapp = fa-icon.with("\u{f232}")
#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-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-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-wikipedia-w = fa-icon.with("\u{f266}")
#let fa-wind = fa-icon.with("\u{f72e}")
#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-wine-bottle = fa-icon.with("\u{f72f}")
#let fa-wine-glass = fa-icon.with("\u{f4e3}")
#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-wrench = fa-icon.with("\u{f0ad}")
#let fa-x = fa-icon.with("\u{58}")
#let fa-x-ray = fa-icon.with("\u{f497}")
#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-xmarks-lines = fa-icon.with("\u{e59a}")
#let fa-y = fa-icon.with("\u{59}")
#let fa-y-combinator = fa-icon.with("\u{f23b}")
#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-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/felsenhower/kbs-typst | https://raw.githubusercontent.com/felsenhower/kbs-typst/master/latex-logo.typ | typst | MIT License | #let LaTeX = {
let A = (
offset: (
x: -0.33em,
y: -0.3em,
),
size: 0.7em,
)
let T = (
x_offset: -0.12em
)
let E = (
x_offset: -0.2em,
y_offset: 0.23em,
size: 1em
)
let X = (
x_offset: -0.1em
)
[L#h(A.offset.x)#text(size: A.size, baseline: A.offset.y)[A]#h(T.x_offset)T#h(E.x_offset)#text(size: E.size, baseline: E.y_offset)[E]#h(X.x_offset)X]
}
|
https://github.com/adam-zhang-lcps/papers | https://raw.githubusercontent.com/adam-zhang-lcps/papers/main/seminar-letter-to-next-year.typ | typst | Creative Commons Attribution Share Alike 4.0 International | #set page(paper: "us-letter")
#set text(font: ("New Computer Modern", "Twitter Color Emoji"))
/* Requirements:
- A “welcome to AP Seminar” introductory paragraph.
- A summary of your personal experiences in taking this course.
- A “helpful hints” section that describes what study skills are most effective, how to organize your time, additional resources you would recommend, etc.
- A “what to avoid” section that describes mistakes you made that may have impacted your success in the class, common practices of many AP Seminar students that will prove to NOT be helpful or constructive to the students’ success in AP Seminar, etc.
- A concluding paragraph that contains “words of encouragement” to next year’s students. */
Dear future AP Seminar students,
Welcome to AP Seminar! In case you have no idea what this class is, and just signed up for it because why not---as I did---this is a class about research, writing, and presentation. If that's not what you signed up for---well, hopefully Mr. Sakole shows this to you early enough that you can still drop the course if you so choose. If you're still with us, then great---let's talk about what you're getting yourself into.
#show "AP": [AP#super(emoji.reg)]
This is an AP class. I'm sure you already knew that, and everything that comes with the package---the GPA boost, the end of year assessment, and all that. However, I want to emphasize a difference from the other number of AP classes dedicated juniors like you are inevitably taking: this class is *not* all about the AP exam. The exam is important---but only 45%-of-your-score important---it is a _minority_ of your score.
"Well then," I hear you asking. "Where is the other 55%?"
I'm glad you asked. Throughout the year, you will complete two "performance tasks". I'm sure you're familiar with "project-based assessments", probably from a social science course you've taken#footnote([I would be willing to bet you took AP World History, and have done the four PBAs that I did.])---think of performance tasks as PBAs, but scaled up by an order of magnitude. Rather than being relatively quick projects (that, admittedly, are just grade padding), these "performance tasks" are multi-month projects that will end up being a part of your AP score. I'm sure you can guess what these projects involve... if you guessed "research, writing, and presentation", congratulations, gold star for you.star.
If that sounds a bit scary, don't worry---honestly, it's not as bad as it sounds. In fact, grade-wise, this is probably the easiest AP class you could ever take; if you turn everything in on time, I can near-guarantee that you'll end every quarter with an A+. While I wouldn't go as far as to say this class is _easy_, it is definitely not as demanding as most AP classes. However, I do say this with a word of warning---the experience of the year is truly what *you* make of it. Personally, I found large portions of this class to be unenjoyable, but I don't fault the class for that; the main reason for my issues was my own tendencies to not stay on top of things, _especially_ the big deliverables#footnote([Of which, if you're curious, there are six.]). However, in retrospect, even with the stressful days and long nights that I had as a result of this class, I am still grateful for the skills that I have acquired from this class. No class that you can take#footnote([With the exception of AP Research, but you can't take that without taking this class first anyway.])---not even AP Lang---will prepare you better for _real-world_ writing and presentation than this class will.
That leads me into my next topic of interest---I want to prevent you from making the same mistakes that I did, because, trust me, I made many. If you take _nothing_ else away from this letter#footnote([I wouldn't blame you, I have already reached the word count requirement for this assignment and have plenty left to say; I know reading is hard sometimes, especially when you see walls of text.]), then please just take this word of advice and caution: *do not procrastinate*. Yes, this is coming from a chronic procrastinator, and yes, I know it is hard, and yes, I know it's not what you want to hear. But these are not your middle-school or freshman-year papers; as someone that left them until the last minute, trust me when I say you do *not* want to leave them until the last minute. These are papers that take genuine effort, genuine research, genuine thought, not something that you can bull\*\*\*\* your way through on the day before it's due---at least, not if you want a good AP score; and yes, that is coming from someone that did exactly that, and I can assure you that my papers were _not_ good.
I know writing papers is hard sometimes, and preparing for presentations is even harder---it feels like a monolith, a mountain that is hard to take the first step upon. My advice to you there is to break the mountain apart into small, surmountable hills. Mr. Sakole is a great teacher, and he will hand you the climbing boots, the ropes, and the picks, and show you the trail---in the forms of assignments like outlines and check-ins, designed to ensure that you're making progress. However, in the end, like I said---this class is ultimately in *your* hands. You have to take the first step onto the hill, and from there, you have to keep walking. Take small steps---climb the small hills. Perhaps you'll find some articles one night, put together an introduction the next night. Then you have to skip two nights, because you've got an AP US History exam coming up---that's alright. But remember to pick back up afterwards. Again, the absolute *worst* thing you can do is put it all off till the last night---you can't climb Mount Everest in a night#footnote([In fact, an average expedition takes around two months---which is, funnily enough, probably around the amount of time you'll have for a single performance task.]), no matter how much caffeine you have.
Another way to make it easier to not procrastinate is to *write about something you're interested in*. You'll have three opportunities to choose a research question throughout the year. Two of them will be with groups, so compromises will have to be made, and the third will be limited in the topic, so, again, compromises will have to be made. But don't be afraid to think outside of the box---choose a topic that interests you, that you won't hate spending weeks researching and writing about. The second-easiest way to make yourself miserable (after procrastination, of course) is to force yourself to spend hours learning about a topic you couldn't care less about.
I hate to say it, and I know you're tired of hearing it, but your junior year is going to be hard. That's okay---every function has a maximum, and I'm confident that you'll find your way through. Hopefully, when you reach the end of your year, and you find yourself in the position that I am in now---#strike([putting in way too much effort for a small, single-class assignment]) writing _your_ letter to the class of 2027---you can look back on the year, and feel proud of how far you've come. Remember, your junior year is going to be long---don't look up at the peak of the mountain. Only look down---look at how far you've come, and focus on the moment, on what you're doing *now*. Forget about the endless futures---all you can change is in the present moment.
Have an amazing year,
<NAME>
|
https://github.com/DaAlbrecht/thesis-TEKO | https://raw.githubusercontent.com/DaAlbrecht/thesis-TEKO/main/content/Verification.typ | typst | == Verification plan
#[
#show regex("\w"): it => [#sym.zws;#it]
#figure(
table(
columns: (auto, auto, auto, auto,auto),
rows: auto,
align: (center+horizon, center+horizon, left, left ,center + horizon),
[*ID*],
[*From*],
[*Test case*],
[*Should be*],
[*Is*],
[VER-1],
[REQ-1],
[Check the time of the last commit of the amqp library],
[Last commit is newer than 01.01.2022],
text(fill: rgb(34,139,34))[OK],
[VER-2],
[REQ-2],
[Check the source code of the microservice],
[The microservice is written in rust, go or java],
text(fill: rgb(34,139,34))[OK],
[VER-3],
[REQ-3],
[The container is a docker image],
[The container is a docker image],
text(fill: rgb(34,139,34))[OK],
[VER-4],
[REQ-4],
[Start the container and use the command `top` to see the resources used by the container],
[The container uses less than 500MB of RAM and less than 0.5 cpu cores],
text(fill: rgb(34,139,34))[OK],
[VER-5],
[REQ-5],
[Check the source code of the microservice for an openapi specification],
[The microservice has an openapi specification],
text(fill: rgb(34,139,34))[OK],
[VER-6],
[REQ-6],
[Enable metrics and start the microservice. Use the endpoint `/metrics` to get the metrics.],
[The metrics are in the prometheus format],
text(fill: rgb(34,139,34))[OK],
[VER-7],
[REQ-7],
[Start the microservice and check for stdout logs],
[The microservice logs to stdout],
text(fill: rgb(34,139,34))[OK],
[VER-8],
[REQ-8],
[Start the microservice and visit the endpoint `/health`],
[The endpoint `/health` returns a 200 status code],
text(fill: rgb(34,139,34))[OK],
[VER-9],
[REQ-9, REQ-10, REQ-14, REQ-15, REQ-16],
[Run `cargo test` in the microservice directory],
[All tests pass],
text(fill: rgb(34,139,34))[OK],
[VER-9],
[REQ-11],
[Visit the repository at #link("https://github.com/DaAlbrecht/rabbit-revival")],
[The repository is public and provides a contribution guide],
text(fill: rgb(34,139,34))[OK],
[VER-10],
[REQ-12],
[Visit the repository at #link("https://github.com/DaAlbrecht/rabbit-revival"), a readme is present],
[A readme is present],
text(fill: rgb(34,139,34))[OK],
)
)
]
#pagebreak()
|
|
https://github.com/csimide/SEU-Typst-Template | https://raw.githubusercontent.com/csimide/SEU-Typst-Template/master/seu-thesis/utils/show-appendix.typ | typst | MIT License | #import "states.typ": part-state
#import "numbering-tools.typ": chinese-numbering
#import "packages.typ": i-figured
#let show-appendix-bachelor(
it,
table-numbering: "A.1",
image-numbering: "A-1",
equation-numbering: "(A.1)",
) = {
part-state.update("附录")
counter(heading).update(0)
counter(heading.where(level: 1)).update(0)
set heading(numbering: chinese-numbering.with(in-appendix: true))
show figure: i-figured.show-figure.with(numbering: image-numbering)
show figure.where(kind: table): i-figured.show-figure.with(numbering: table-numbering)
show math.equation.where(block: true): i-figured.show-equation.with(numbering: equation-numbering)
it
}
#let show-appendix-degree(
it,
table-numbering: "A-1",
image-numbering: "A-1",
equation-numbering: "(A-1)",
) = {
show: show-appendix-bachelor.with(
table-numbering: table-numbering,
image-numbering: image-numbering,
equation-numbering: equation-numbering,
)
it
} |
https://github.com/EpicEricEE/typst-plugins | https://raw.githubusercontent.com/EpicEricEE/typst-plugins/master/outex/README.md | markdown | # outex
A package for styling outlines similar to LaTeX.
## Usage
Applying this style is as simple as adding a show rule to your document. The `outex` function comes with a few options that can be used to customize the style of the outline:
| Option | Description | Default |
| --- | --- | --- |
| `gap` | The gap between numbering and section title | `1em` |
| `fill-pad` | The padding around the "fill" line | `(left: 0.5em, right: 1em)` |
| `bold` | Whether the first-level titles should be bold | `true` |
| `space` | Whether to add block-spacing before fist-level titles | `true` |
The package also comes with a custom `repeat` function to allow for easier customization of the fill line. The function allows setting a `gap` and whether to `justify` the items to fill the width. Be careful when importing this function, as it will override the default `repeat` function!
```typ
#import "@local/outex:0.1.0": outex
#set heading(numbering: "1.1 i")
#show heading: set block(below: 1em)
#show: outex
#outline(title: "Table of Contents")
// ...
```
|
|
https://github.com/QuadnucYard/pavemat | https://raw.githubusercontent.com/QuadnucYard/pavemat/main/README.md | markdown | MIT License | # Pavemat
<div style="text-align: center">
<img src="./examples/logo.svg"/>
<p><strong> pavement + matrix </strong></p>
</div>
## Introduction
The pavemat is a versatile tool for creating styled matrices with custom paths, strokes, and fills. It allows users to define how paths should be drawn through the matrix, apply different strokes to these paths, and fill specific cells with various colors. This function is particularly useful for visualizing complex data structures, mathematical matrices, and creating custom grid layouts.
## Key Features
- Custom Paths: Define paths through the matrix using directional characters.
- Stroke Styles: Customize the appearance of path lines with different dash patterns, thicknesses, and colors.
- Cell Fills: Fill specific cells with colors, making certain parts of the matrix stand out.
- Custom Direction Characters: Override default directional characters to suit different notations.
- Debug Mode: Visualize hidden lines and debug the path layout.
## Examples
The logo example:
```typst
#{
set math.mat(row-gap: 0.25em, column-gap: 0.1em)
set text(size: 2em)
pavemat(
pave: (
"SDS(dash: 'solid')DDD]WW",
(path: "sdDDD", stroke: aqua.darken(30%))
),
stroke: (dash: "dashed", thickness: 1pt, paint: yellow),
fills: (
"0-0": green.transparentize(80%),
"1-1": blue.transparentize(80%),
"[0-0]": green.transparentize(60%),
"[1-1]": blue.transparentize(60%),
),
delim: "[",
)[$mat(P, a, v, e; "", m, a, t)$]
}
```
More examples can be found in `examples/examples.typ`.
## Manual
See `docs/manual.typ`.
|
https://github.com/Error-418-SWE/Documenti | https://raw.githubusercontent.com/Error-418-SWE/Documenti/src/3%20-%20PB/Documentazione%20interna/Verbali/24-02-25/24-02-25.typ | typst | #import "/template.typ": *
#show: project.with(
date: "25/02/24",
subTitle: "Meeting di retrospettiva e pianificazione",
docType: "verbale",
authors: (
"<NAME>",
),
reviewers: (
"<NAME>",
),
timeStart: "15:10",
timeEnd: "16:10",
);
= Ordine del giorno
- Valutazione del progresso generale;
- Analisi retrospettiva;
- Pianificazione.
= Valutazione del progresso generale <avanzamento>
Lo Sprint 16 ha visto le task assegnate completate nei tempi previsti, non sono stati riscontrati rallentamenti o problematiche significative.
Il giorno giovedì 22/02/2024 si è svolto il meeting esterno con il Proponente, come pianificato, per aggiornare riguardo lo stato dei lavori.
== Modifiche di carattere generale
Predisposta la repository per contenere materiali inerenti la PB.
Aggiornati riferimenti di vari documenti, espanso il glossario e aggiornate le automazioni.
== #ndp
Le #ndp hanno visto completati i lavori:
- redazione capitolo Technical processes/Design Definition process;
- redazione capitolo Technical processes/Architecture Definition process;
- aggiornamento capitolo 4.6.3 per quanto riguarda il contenuto dei verbali interni;
- aggiornamento capitolo 4.6.4 per quanto riguarda l'introduzione di variabili Typst per l'uso di termini ricorrenti;
- redazione paragrafo inerente l'utilizzo di Figma tra gli strumenti utilizzati;
- descrizione versionamento del codice;
- definizione metriche di prodotto.
== #pdp
Il #pdp ha visto completati i lavori:
- inclusione nel documento del contenuto presente in #ris;
- estensione #ris;
- codificazione dei rischi;
- codificazione metodi di risoluzione dei rischi;
- estensione sezione di monitoraggio;
- redazione consuntivo sprint 15.
== #pdq
Il #pdq ha visto completati i lavori:
- aggiornamento grafici delle metriche per lo sprint 15;
- definizione metriche di prodotto.
= Analisi retrospettiva
Lo Sprint 16 è terminato con il raggiungimento di tutti gli obiettivi prefissati, il cui rendimento positivo è sostenuto dalle principali metriche esposte dal #pdq\:
- CPI di progetto cresce passando da 0.98 a 1.02;
- EAC diminuisce passando da € 13.292,70 a € 12.777,29;
- $"SEV" >= "SPV"$.
Maggiori dettagli in merito al valore delle metriche alla loro analisi sono reperibili all'interno dei documenti #pdq_v e #pdp_v.
== Keep doing <keep-doing>
Come nello sprint precedente viene riconosciuto il ruolo del Verificatore che ha saputo offrire review precise e tempestive.
Come nello Sprint precedente il gruppo ha saputo mantenere una modalità di lavoro e di comunicazione asincrona.
== Improvements <improvements>
Non sono state riscontrate criticità.
= Pianificazione <pianificazione>
Viene pianificata una riunione interna in data 26/02 alle ore 15:00 per discutere del design che il sistema software dovrà implementare.
#let table-json(data) = {
let keys = data.at(0).keys()
table(
align: left,
columns: keys.len(),
..keys,
..data.map(
row => keys.map(
key => row.at(key, default: [n/a])
)
).flatten()
)
}
#figure(caption: [Task pianificate per lo Sprint 17.],
table-json(json("tasks.json"))
) |
|
https://github.com/maucejo/cnam_templates | https://raw.githubusercontent.com/maucejo/cnam_templates/main/template/main_rapport.typ | typst | MIT License | #import "../src/cnam-templates.typ": *
#show: cnam-rapport.with(
toc: true,
sec-number: true,
config-titre: (
titre: none,
composante: "lmssc",
// composante: "cnam",
alignement: "center",
// alignement: "irreg",
surtitre: ("Guide", "pratique"),
// logo: (image("../src/resources/logo/new/ccr-bretagne.png"), image("../src/resources/logo/new/ccr-ge.png"), image("../src/resources/logo/new/lmssc.png"))
// logo: image("../src/resources/logo/new/lmssc.png")
)
)
= Introduction
= Objectifs
== Sous-objectifs
#pagebreak()
= Méthodologie |
https://github.com/jgm/typst-hs | https://raw.githubusercontent.com/jgm/typst-hs/main/test/typ/math/multiline-04.typ | typst | Other | // Test mixing lines with and some without alignment points.
$ "abc" &= c \
&= d + 1 \
= x $
|
https://github.com/howardlau1999/sysu-thesis-typst | https://raw.githubusercontent.com/howardlau1999/sysu-thesis-typst/master/chapters/appendix01.typ | typst | MIT License | #import "../functions/allinone.typ": *
= 关于 Typst <about>
== 在附录中插入图片和公式等
附录中也可以插入图片，如 @web1。
#figure(
image("../images/chapter1/1-writing-app.png", width: 100%),
caption: "Typst 网页版界面",
) <web1>
附录中也可以插入公式，如 @appendix-eq。
#tablex(
columns: (1fr, 1fr),
[
#set align(center)
代码
],
[
#set align(center)
渲染结果
],
```typ
$ S = pi r^2 $ <appendix-eq>
$ mat(
1, 2, ..., 10;
2, 4, ..., 20;
3, 6, ..., 30;
dots.v, dots.v, dots.down, dots.v;
10, 20, ..., 100
) $
$ cal(A) < bb(B) < frak(C) < mono(D) < sans(E) < serif(F) $
$ bold(alpha < beta < gamma < delta < epsilon) $
$ upright(zeta < eta < theta < iota < kappa) $
$ lambda < mu < nu < xi < omicron $
$ bold(Sigma < Tau) < italic(Upsilon < Phi) < Chi < Psi < Omega $
```,
[
$ S = pi r^2 $ <appendix-eq>
$ mat(
1, 2, ..., 10;
2, 4, ..., 20;
3, 6, ..., 30;
dots.v, dots.v, dots.down, dots.v;
10, 20, ..., 100
) $
$ cal(A) < bb(B) < frak(C) < mono(D) < sans(E) < serif(F) $
$ bold(alpha < beta < gamma < delta < epsilon) $
$ upright(zeta < eta < theta < iota < kappa) $
$ lambda < mu < nu < xi < omicron $
$ bold(Sigma < Tau) < italic(Upsilon < Phi) < Chi < Psi < Omega $
]
)\
@complex 是一个非常复杂的公式的例子：
#tablex(
columns: (1fr, 1fr),
[
#set align(center)
代码
],
[
#set align(center)
渲染结果
],
```typ
$ vec(overline(underbracket(underline(1 + 2) + overbrace(3 + dots.c + 10, "large numbers"), underbrace(x + norm(y), y^(w^u) - root(t, z)))), dots.v, u)^(frac(x + 3, y - 2)) $ <complex>
```,
[
$ vec(overline(underbracket(underline(1 + 2) + overbrace(3 + dots.c + 10, "large numbers"), underbrace(x + norm(y), y^(w^u) - root(t, z)))), dots.v, u)^(frac(x + 3, y - 2)) $ <complex>
]
)\
附录中也可以插入代码块，如 @appendix-code。
#codeblock(
```rust
fn main() {
println!("Hello, world!");
}
```,
caption: "一个简单的 Rust 程序",
outline: true,
) <appendix-code>
== Typst 的开发者 <developers>
办苦手心标得，深海者到度我以星？
果自还如杂小素里家给人欢文告再的都场选推工结负？ 量到做都大明设个人知师。 理回么节以不到育放来加...... 的平红思道社。 事大制气一变议经以元比港心大委陆阿城需心我器候因具书光画感下外假，层动么因。 消出力我回她水简心、我速子局都上请文不除么识年孩化过我，古器直面林息每子打意证省花入，游民希法：安坡们回钱小是都舞数惊野加员进绝关闻就了单必环如...... 话现教野。 有面在信军全地八得市感里大人试孩任化我展小古了现声来由有又导分我族量。 制的上病还在; 又业色来过，游入用不老三种灯能交年！ 会主策火的资排然黄突开湾高。 们益别间否，园员！
他术问但起和间公合。
还出无过年兴变质竟的个天主明自外就微，认无书、类车文，我电着光一客场...... 中不心友定送成一然不，的人营功！ 们书表女成，争罗打客，写问道亲这杂座灵正么让，主事歌也在的党买报变用试往处早多的优，争我大子到方力妈业以证之公间们地; 进人制服新苦半如！ 民第等、实助要报万随诗处更级运定音子毒生，然面布一皮相快外美一，所白心上是成轻斯长。 体技的台军红去头己？ 待台解爸期体经天赛兴业一香化西日花同。
不手来，资这那声此其上公音他有太了后看轻决。 头几同！ 台基名气边专包成静制一少学毛会星我事我房他久。 出者的。 河分及明古、得上这和又安，上子精还由皮排生着起物看的不打放么知一国生诉老像家台科无们体很...... 所的望正子。 声业汽妈有亲有时它日因下中，多难又日选、好国和发次作，放同可告; 洲传直，人儿子呢也所运。 种查任发，台部上到的合视有平西然个大最奖眼：治人结态说而建人终！
己式于师者他多环清济电！ 位妈长前口动改里数：无不知病这能卖起，一过连造，去再处公好亲比的。 家得说因老运城点教了她会星会我是里了实位兰！
加一量的感也过进一失的必为自希头有，家可虽作惊法轻要形生大、其要的：就名开了？ 不看地笔远馆之光行父政首半母城长远人表，来市台样强只到北景以有商太以策妈好，原生看国多论李别的会收。 物人小变问每进是主音罗使民资政区子人读市经而医排父毛回清热事决！ 地入家外因车王、教长此一终向效形一眼台不直近们人电温一展; 的民期定简人民来！ 他重在成同里保基怕原眼多利全成是交如心的; 来导儿主; 权才快业直人要把下巴长实我光价自运自当早但世会、为看以。 质生艺画业，力女元叶妈那请利台！ 案教平告进，会被任爱，斯发还财化远化奇屋的童心师老，失面孩反因界血山长德十作纪落，空世感去细家花，得父只股是离止些本只必布，别动华民长不：医说列政这的官中到了备来精案对一、异展工约算于企位排你着价见上加争叶亲不欢小，做养纸，决放所得车史善？ 保于不提队根海黄不专！ 往想车企哥于夜立老不但不再水衣每少儿二在三是东; 解人市地了土便着过族后不交上去他信治马中成业分怀来长常家古建明我候星除常和入着总？ |
https://github.com/sitandr/typst-examples-book | https://raw.githubusercontent.com/sitandr/typst-examples-book/main/src/snippets/external.md | markdown | MIT License | # Use with external tools
Currently the best ways to communicate is using
1. Preprocessing. The tool should generate Typst file
2. Typst Query (CLI). See the docs [there](https://typst.app/docs/reference/meta/query#command-line-queries).
3. WebAssembly plugins. See the docs [there](https://typst.app/docs/reference/foundations/plugin/).
In some time there will be examples of successful usage of first two methods. For the third one, see [packages](../packages/index.md).
|
https://github.com/jgm/typst-hs | https://raw.githubusercontent.com/jgm/typst-hs/main/test/typ/visualize/line-02.typ | typst | Other | // Test errors.
// Error: 12-19 point array must contain exactly two entries
#line(end: (50pt,))
|
https://github.com/AugustinWinther/structured-uib | https://raw.githubusercontent.com/AugustinWinther/structured-uib/main/lib.typ | typst | MIT License | // Original frontpage design by <NAME> (<EMAIL>), made
// in LaTeX originaly, converted to Typst by <NAME> (https://winther.io).
// TEMPLATE FUNCTION
#let report(
task-no: none,
task-name: none,
authors: none,
mails: none,
group: none,
date: none,
supervisor: none,
body
) = {
// DOCUMENT METADATA
set document(title: [PHYS114 - Laboppgave #task-no - Gruppe #group],
author: authors.map(author => author),
date: datetime.today())
// DOCUMENT LANGUAGE
set text(lang: "nb")
// CREATE MAIL LINK ARRAY
let mail-links = mails.map(mail => link("mailto:" + mail))
// DOCUMENT FONTS
set text(font: "STIX Two Text", size: 12pt)
show math.equation: set text(font: "STIX Two Math")
// FRONT PAGE
set page(paper: "a4", margin: (left: 27mm, right: 20mm, top: 20mm, bottom:30mm))
v(10mm)
line(length: 16cm, stroke: 0.1cm)
v(2mm)
h(5mm)
text(size: 48pt, weight: "bold", "PHYS114")
h(45mm)
box(image("media/uib-emblem.svg", width: 20%, fit: "contain"), baseline: 18mm)
v(-12mm)
line(length: 11cm, stroke: 0.1cm)
v(12mm)
h(5mm)
box(text(size: 36pt, [*Grunnleggende målevitenskap og eksperimentalfysikk*]))
v(12mm)
align(center, text(size: 20pt, [*Laboratorierapport*]))
table(
columns: 2,
stroke: none,
align: left,
row-gutter: 4mm,
[*Lab.oppgave:*], [#task-no: #task-name],
[*Navn (alle i lab.gruppen):*], [#authors.join(", ")],
[*Epost (alle i lab.gruppen):*], [#mail-links.join(" ")],
[*Lab.gruppe\#:*], [#group],
[*Dato utført:*], [#date],
[*Veileder:*], [#supervisor],
[*Godkjent:*], []
)
line(length: 16cm, stroke: 0.1cm)
v(4mm)
h(5mm)
text(size: 18pt, [*Institutt for fysikk og teknologi*])
linebreak()
h(5mm)
text(size: 18pt, [*Det matematisk-naturvitenskapelige fakultet*])
pagebreak()
// PAGE SETUP FOR REST OF DOCUMENT
set page(
paper: "a4",
margin: (left: 27mm, right: 20mm, top: 20mm, bottom:30mm),
numbering: "1",
header: align(center, text(size: 10pt, [PHYS114 - Laboppgave #task-no - Gruppe #group])),
)
counter(page).update(1) // Skip first page in numbering
// PARAGRAPH SETUP
set par(justify: true,)
show par: set block(spacing: 0.65em)
show par: it => {
it
v(15pt, weak: true)
}
// HEADING SETUP
set heading(numbering: "1.1.1 -")
show heading: it => {
v(5mm)
text(weight: "semibold", it)
v(2mm)
}
// LIST SETUP
set enum(indent: 10pt, body-indent: 9pt)
set list(indent: 10pt, body-indent: 9pt)
// EQUATION SETUP
set math.equation(numbering: "(1)")
show math.equation: set block(spacing: 0.65em)
// FIGURE SETUP
show figure: it => {
align(center,
if it.kind == image or it.kind == raw {
it.body
v(-6pt)
text(10pt, [*#it.supplement #it.counter.display(it.numbering)*: _ #it.caption.body _])
} else if it.kind == table {
text(10pt, [*#it.supplement #it.counter.display(it.numbering)*: _ #it.caption.body _])
v(-6pt)
it.body
})
v(15pt, weak: true)
}
// TABLE SETUP
set table(fill: (_, row) => if row == 0 { luma(220) } else { white })
show table: it => {
set par(justify: false,)
set align(center)
it
}
// LINK SETUP
show link: it => {
text(fill: rgb("#00F"), it)
}
// REFERENCE SETUP
show ref: it => {
text(fill: rgb("#00F"), it)
}
// FOOTNOTE SETUP
show footnote: it => {
text(fill: rgb("#00F"), it)
}
// OUTLINE SETUP
set outline(indent: auto, depth: 2)
show outline.entry: it => {
let heading = it.element
// Adds "Appendiks " prefix to level 1 chapters if it is an appendix
// and overwrites link color to black from blue.
if heading.level == 1 {
v(12pt, weak: true)
if heading.supplement == [Appendiks] {
link(heading.location(), text(fill: rgb("#000"),
[*Appendiks #it.body #box(width: 1fr, it.fill) #it.page*]))
} else {
link(heading.location(), text(fill: rgb("#000"),
[*#it.body #box(width: 1fr, it.fill) #it.page*]))
}
}
// Do not show appendiks level 2 in outline, replace with vertical space.
// Show other level 2 chapters tho.
if heading.level == 2 {
if heading.supplement == [Appendiks] {
v(-38pt)
} else {
it
}
}
}
// BIBLIOGRAPHY SETUP
set bibliography(title: "Referanser")
// DISPLAY CONTENT
body
}
// APPENDIX FUNCTION
#let appendices(body) = {
// Reset heading counter as appendicies uses own number system
counter(heading).update(0)
set heading(numbering: "A.1 -", supplement: "Appendiks")
show heading: it => {
v(19pt)
if it.level == 1 {
text(weight: "semibold")[Appendiks #counter(heading).display() #it.body]
}
else {
text(weight: "semibold")[#counter(heading).display() #it.body]
}
}
// Include content
body
}
|
https://github.com/BoostCookie/systemd-tshirtd | https://raw.githubusercontent.com/BoostCookie/systemd-tshirtd/main/src/tshirtd.origlogo.black.typ | typst | #set page(fill: rgb("#201a26"))
#include "common.origlogo.typ"
|
|
https://github.com/Myriad-Dreamin/tinymist | https://raw.githubusercontent.com/Myriad-Dreamin/tinymist/main/crates/tinymist-query/src/fixtures/goto_definition/import_alias.typ | typst | Apache License 2.0 | // path: base.typ
#let f() = 1;
-----
#import "base.typ": f as one
#(/* position after */ one);
|
https://github.com/tingerrr/typst-test | https://raw.githubusercontent.com/tingerrr/typst-test/main/docs/book/src/guides/ci.md | markdown | MIT License | # Setting Up CI
Continuous integration can take a lot of manual work off your shoulders.
In this chapter we'll look at how to run `typst-test` in your GitHub CI to continuously test your code and catch bugs before they get merged into main.
We start off by creating a `.github/workflows` directory in our project and place a single `ci.yaml` file in this directory.
The name is not important, but should be something that helps you distinguish which workflow you're looking at.
<div class="warning">
If you simply want get CI working without any elaborate explanation, skip ahead to the bottom and copy the full file.
There's a good chance that you can simply copy and paste the workflow as is and it'll work, but the guide should give you an idea on how to adjust it to your liking.
</div>
First, we configure when CI should be running:
```yml
name: CI
on:
push:
branches: [ main ]
pull_request:
branches: [ main ]
```
The `on.push` and `on.pull_request` fields both take a `branches` fields with a single pattern matching our main branch, this means that this workflow is run on pull requests and pushes to main.
We could leave out the `branches` field and it would apply to all pushes or pull requests, but this is seldom useful.
If you have branch protection, you may not need the `on.push` trigger at all, if you're paying for CI this may save you money.
Next, let's add the test job we want to run, we'll let it run on `ubuntu-latest`, that's a fairly common runner for regular CI.
More often than not, you won't need matrix or cross platform tests for Typst projects as Typst takes care of the OS differences for you.
Add this below the job triggers:
```yml
# ...
jobs:
tests:
runs-on: ubuntu-latest
steps:
- name: Checkout
uses: actions/checkout@v3
```
This adds a single step to our job (called `tests`), which checks out the repository, making it available for the following steps.
For now, we'll need `cargo` to download and install `typst-test`, so we install it and cache the installation with a package cache action.
And then we install `typst-test` straight from Github using the `ci-semi-stable` tag, this tag does not yet have features like test set expressions, but it works just the same otherwise.
```yml
steps:
# ...
- name: Probe runner package cache
uses: awalsh128/cache-apt-pkgs-action@latest
with:
packages: cargo
version: 1.0
- name: Install typst-test from github
uses: baptiste0928/[email protected]
with:
crate: typst-test
git: https://github.com/tingerrr/typst-test.git
tag: ci-semi-stable
```
Because the `typst-test` version at `ci-semi-stable` does not yet come with it's own Typst compiler, it needs a Typst installation in the runner. Add the folllowing with your prefferred Typst version:
```yml
steps:
# ...
- name: Setup typst
uses: yusancky/setup-typst@v2
with:
version: 'v0.11.1'
```
Then we're ready to run our tests, that's as simple as adding a step like so:
```yml
steps:
# ...
- name: Run test suite
run: typst-test run
```
CI may fail for various reasons, such as
- missing fonts
- system time dependent test cases
- or otherwise hard-to-debug differences between the CI runner and your local machine.
To make it easier for us to actually get a grasp at the problem we should make the results of the test run available.
We can do this by using an upload action, however, if `typst-test` fails the step will cancel all regular steps after itself, so we need to ensure it runs regardless of test failure or success by using `if: always()`.
We upload all artifacts since some tests may produce both references and output on-the-fly and retain them for 5 days:
```yml
steps:
# ...
- name: Archive artifacts
uses: actions/upload-artifact@v4
if: always()
with:
name: artifacts
path: |
tests/**/diff/*.png
tests/**/out/*.png
tests/**/ref/*.png
retention-days: 5
```
And that's it, you can add this file to your repo, push it to a branch and open a PR, the PR will already start running the workflow for you and you can adjust and debug it as needed.
> The full workflow file:
>
> ```yml
> name: CI
> on:
> push:
> branches: [ main ]
> pull_request:
> branches: [ main ]
>
> jobs:
> tests:
> runs-on: ubuntu-latest
> steps:
> - name: Checkout
> uses: actions/checkout@v3
>
> - name: Probe runner package cache
> uses: awalsh128/cache-apt-pkgs-action@latest
> with:
> packages: cargo
> version: 1.0
>
> - name: Install typst-test from github
> uses: baptiste0928/[email protected]
> with:
> crate: typst-test
> git: https://github.com/tingerrr/typst-test.git
> tag: ci-semi-stable
>
> - name: Setup typst
> uses: yusancky/setup-typst@v2
> with:
> version: 'v0.11.1'
>
> - name: Run test suite
> run: typst-test run
>
> - name: Archive artifacts
> uses: actions/upload-artifact@v4
> if: always()
> with:
> name: artifacts
> path: |
> tests/**/diff/*.png
> tests/**/out/*.png
> tests/**/ref/*.png
> retention-days: 5
> ```
|
https://github.com/polarkac/MTG-Stories | https://raw.githubusercontent.com/polarkac/MTG-Stories/master/stories/028%20-%20Kaladesh/001_Homesick.typ | typst | #import "@local/mtgstory:0.2.0": conf
#show: doc => conf(
"Homesick",
set_name: "Kaladesh",
story_date: datetime(day: 29, month: 08, year: 2016),
author: "<NAME>",
doc
)
#emph[Five Planeswalkers allied as the Gatewatch. From Kaladesh, the pyromancer <NAME>. From Theros, the hieromancer <NAME>. From Zendikar, the elven animist <NAME>. From someplace he no longer remembers, the telepath <NAME>. From Dominaria, the necromancer <NAME>. With the aid of Tamiyo, a soratami scholar of Kamigawa, they defeated the eldritch titan Emrakul, sealing the entity within Innistrad's silver moon.]
#emph[Three months have passed.]
#v(0.35em)
#line(length: 100%, stroke: rgb(90%, 90%, 90%))
#v(0.35em)
She knocked again, louder.
From the far side of the door came a thump and a muttered obscenity. After long seconds of fabric rustling this way and that, accompanied by sotto voce imprecations against #emph[these] blankets in particular, bedding in #emph[general] , and the entire profession of weaving #emph[by] #emph[extension] , the sounds of unsteady feet on hardwood lurched and swayed towards the door.
"Yeah. What. What?" a sleep-thick feminine voice mumbled from the other side.
"It's almost noon. You need to get up."
"Can't be noon. It's still too heavy out."
"Could you open the door?"
"No." A moment of silence, a sigh, then long seconds of loose-limbed scrabbling against the door lock. A final pause. "Wait. Didn't lock it. #emph[You] open it."
She pushed gently, and the door creaked open, the movement of air rustling the dark silk of her dress. The woman collapsing against the doorframe on the far side was a chin-level explosion of sleep-mussed copper hair in a baggy nightshirt, its neckline untied and sliding off one shoulder. The light from the hall fell across one sunburnt and freckled cheek. She groaned and squeezed amber eyes shut. "Morning, Liliana," she mumbled into the door frame.
"Oh my," Liliana said. "You look terrible, Chandra."
Chandra smeared night sand out of one eye with the hand she wasn't leaning on. "Oh yeah? Well you look..." She dropped her hand and squinted at her blearily. Her eyelid twitched. "...Great, actually." There was a definite unspoken "damn it" at the end of the sentence.
"Why, thank you."
The only light beyond Chandra's shoulder was a sliver of blinding sun slicing between the heavy folds of drawn curtains. The bedroom seemed to have been ransacked by hasty goblins. Or possibly a bear had taken up residence. The blankets on the four-post bed were pulled off and trailing across the lacquered hardwood, leaving behind only a shambling fortress-pile of overstuffed pillows in the center of the mattress.
The desk was covered with dried-out paint bottles in several lurid colors, and one oversized, half-eaten cookie. There were piles of wadded-up clothes in two different corners. In the gloom, Liliana couldn't tell which was the clean pile. Assuming either was. In a third corner lay the charred remnants of at least two easels.
"I trust the evening was worth it?" Liliana asked. A breeze kicked through the hall, carrying the scents of sun-baked bricks and frying food, the susurration of crowds and the tinkling of bands in the square below. A strand of wayward orange hair wavered in the summer wind and fell across Chandra's eye. Liliana reached out and tucked it behind the girl's ear, tsking. It was dry as straw, the ends split. To be expected, perhaps, given its tendency to burst into flame.
"Stop that," Chandra said, waving away her hands. "I wasn't doing anything last night. Just went to watch..." she hesitated, amber eyes squinting off into the gloom of her bedroom. "Uh, some minstrels. Yeah. A tavern in—on Tin Street. They had, like...fiddles."
Liliana had met many terrible liars over the centuries, but impressively few could rival Chandra. She folded her arms across her chest and allowed one corner of her mouth to tilt upwards. "You went to see the Izzet air races."
"#emph[No!] ...Yes." She yawned. "So you gonna yell at me, or what?"
She laughed lightly. "Why on earth should I? Do what you want." She waved over her shoulder, the gesture encompassing the sun-baked hall, the quiet, book-stacked rooms of Jace's sanctum, and the preposterous band of freelance do-gooders she'd found herself walking two steps behind and shaking her head at. "Nobody here has a right to tell you what to do. That's certainly not what #emph[I] signed up for."
"You didn't #emph[sign] anything."
"Never do, sweetie. Best to live unfettered." She tapped a finger against her lips. "Air races are dangerous for most. But after Emrakul, the perils of goblins with rockets strapped to their backs seems distinctly...non-perilous for you."
#figure(image("001_Homesick/01.jpg", width: 100%), caption: [Goblin Test Pilot | Art by <NAME>], supplement: none, numbering: none)
"One of them had rockets in his #emph[boots] . But he blew up. #emph[Boof!] " Chandra's hands cupped and spread apart, describing an expanding cloud of yuck. "Chunks #emph[everywhere] . #emph[Super] gross."
"Charming. Did you enjoy your evening?"
The younger woman grinned, the freckles on her cheeks scrunching up into an adorable mess. "#emph[Yeah!] I love air races. I haven't seen once since—" her mouth hung a moment, and she blinked twice, rapidly. "Not for a while, anyways. Not big with the monks," she said, with an unconvincing laugh.
Liliana studied the fall of the noon sun across Chandra's hair, remembering the brittle feel of it between her fingers. "Beefslab wants everyone downstairs in an hour. We have a guest."
"Who?"
"I'm sure I didn't ask."
"What? No, I mean...#emph[Beefslab?] "
Liliana let the corner of her mouth slide up again, placed one hand on her hip, and waited for it.
"#emph[Oh!] " Chandra snorted a laugh. "Gids."
She waved pale fingers in the air and rolled her eyes, theatrically. "Surely you've thought the same? It feels like I have to ask him to put a shirt on every other day."
Chandra rubbed her left eye and yawned again. "Hey, I don't mind the view. I wanna get breakfast on the way. Lunch. Whatever. You coming with?"
She moved to brush past Liliana, who stopped her with a hand to her exposed shoulder. The skin was radiantly, unnaturally warm, as if she'd been lying in the sun. She'd noticed that on the rare occasions Chandra sat still for five minutes, her lap inevitably attracted a small pile of drowsy cats.
"Before we go downstairs, sweetie," she said, "you might wish to put on pants."
"What are you, my m—aunt?" Chandra grumped. She turned and wobbled toward one of the piles of laundry, toes curling up at the cold of the hardwood. That settled the question of which pile was the clean. Hopefully.
Liliana silvered a laugh into the air. "I'd rather you think of me as...a sibling, shall we say?"
Chandra pulled a pair of leggings out of the pile, sniffed, and tossed them over her shoulder with a grimace. "I don't have any siblings. Anyways, aren't you like two hundred or something?"
"Ah, but two hundred going on twenty-nine."
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"Not wearing armor today?" Liliana asked as they walked to the stairs.
"Around the house? Nah. You think maybe I should for this meeting?" Chandra was looking down at the lacing of her shirt. She'd been trying to work out a knot, but only managed to get a thumb caught. "I left it downstairs, in that room Jace keeps all his cloaks." A puzzled frown bent her lips. "He's got an #emph[awful] lot of them. Hold on."
She paused by one of the open bedroom doors to work her thumb free. It was Nissa's room, theoretically. The curtains were pulled wide, letting noontime sun fall on undisturbed bedding and a dusty bureau. Chandra glanced in. "We've been here like three months, but I've barely seen Nissa since Innistrad."
"You won't find her in there. Let me see that." Liliana turned and batted Chandra's free hand away from her shirt's lacing. The other hand was now connected by the thumb and an additional finger. "The first morning you all were here, she stumbled out looking like death warmed over."
Chandra brightened and opened her mouth.
"Yes, yes," Liliana sighed. "I'd know best what that looks like."
"Aw..."
"Sweet girl, trust me. I #emph[have] heard all the necromancer jokes." Liliana sucked in her lower lip as she dug in her fingernail to tease a knot free. "Nissa mumbled something like, 'Can't sleep. Too many angles.' She's been staying in the roof garden ever since."
"Weird." Chandra watched dust motes swirl in the air. "What about you?"
"What #emph[about] me?" Liliana pulled at another knot.
With her free hand, Chandra pushed her goggles further back on her forehead. "Jace offered you a room too. Right? Like the rest of us? But you went and got your own place, even when everything's so expensive here."
A final, firm tug, and Chandra's hand was free. "I mislike relying on the mercy of others," Liliana said, forcing lightness into her voice. It had the virtue of being true, if not the #emph[entire] truth. "Now let me tie this for you properly."
Sleeping under a roof that #emph[Jace] paid for? Not just "no," but "hell no."
"There." She patted the lacing on Chandra's shirt. "Don't touch it again. Next time you'll probably get a toe caught."
"Thanks," Chandra grinned, then wrapped one warm arm up around Liliana's bare shoulders and squeezed. "I'm so hungry I could eat an Eldrazi. Maybe even one of the gooey ones." She launched herself toward the stairs. "They don't get breakfast on Ravnica at #emph[all] . It's like they get it all #emph[backwards] . Big dinners, long lunches, skipped breakfasts. Crusty bread with butter? For #emph[breakfast?] " Chandra made a lemon-pucker face. "Come the hell #emph[on] ."
"Is that why you can't get up in the morning here?" Liliana asked, mildly.
Chandra slugged her in the arm. "#emph[Jerk] ." She was taken so off guard she staggered. Chandra walked obliviously ahead as Liliana rubbed the potential bruise. Her steps quickened as she warmed to her topic and gestured to an audience only she could see. "#emph[Listen] . A real breakfast starts with methi thepla. With ginger, chilis, and some yogurt in the mix. When you wake up to that smell—" she paused; swallowed; shook her head. "With pickled mango! Mango is the best. Anyone who says otherwise should be pitied for their tragic and inescapable wrongness."
Liliana shook her head. "I have no idea what mango is."
"A fruit." Chandra said. "Nothing else tastes like it in the multiverse. At least in the parts I've been. When it's perfectly ripe and you take a bite..." she cupped both hands under her mouth. "...the juice just runs down your chin. Sweet and tangy at the same time—and sharp in the back of your nose. Like the way juniper smells, a little. They're like a sunrise in your mouth. So big and bright it spills out."
"They sound...messy," Liliana allowed.
"I guess. Sometimes. But #emph[so] worth it," Chandra grinned. "For the #emph[second] course, do you know what a chickpea—#emph[oh] ." They had turned into a hall that opened over a courtyard on one side, open to the sky and brimming over with green. Chandra's forward momentum trickled to a halt as she drifted toward the balustrade.
"We've got time for one more go before the meeting. Whenever you're ready." The booming voice of Gideon. "Let's do this!" An echoing clap of meaty hands.
She moved to stand beside Chandra. Below, Mancake settled into what was probably a Theros wrestling stance, braced as if expecting a blow. Across from him, the willowy Zendikari elf stood with one hand gripping her opposing shoulder, looking like she wanted to fold into herself and disappear.
"Are you sure?" she asked the grass. Her voice was uneven, scratchy with disuse.
His laugh echoed off the stonework. Liliana was fairly certain she heard distant glassware vibrating. "If I know it's coming, I'm indestructible. The whole point's to see how far #emph[you] can go. #emph[Trust] yourself, Nissa. And if you don't...trust #emph[me] . I can absolutely take it."
"But..."
"#emph[Indestructible,] " he repeated cheerfully, flashing perfect teeth.
"All right." Nissa closed her pine-shadow eyes. "There's not much here to work with."
"We could do this in the garden."
"I meant...never mind." She breathed in, and raised a hand.
The bushes exploded into bloom. Lavender-and-white petals swirled on a sudden wind, filling the air with thick sweetness. Ivy shot up the walls, emerald leaves swelling and unfurling, coating every surface. The grass stretched and bent, whispering in the breeze, lovingly wrapping itself around Nissa's hiking boots.
Chandra took an involuntary step back, inhaling sharply as greenery embraced the balustrade.
Branches swelled and twined, weaving into a single four-legged shape. Maybe some Zendikari beast? Liliana had visited some decades before, but found the place too dull to stay long. The bushes pulled themselves free of the ground, flicking dirt from their root-feet like a fastidious cat.
The bush-beast—more a tree now—reared back, creaking and groaning like the world's largest rocking chair. It shed pastel petals in a constant rain, motes of pollen swirling in the noontime sun. Its front limbs interlaced into a single fist, which it drove down on Gideon like an avalanche.
His flesh shone with liquid gold.
Then he was driven down into the earth, up to his chest.
Nissa gasped. With a wave of her hand, the tree-beast jumped back away from him, landing with a reverberating impact that left Liliana clutching the ivy-clad railing for support. Somewhere in the house, she heard porcelain shatter. Several somewheres, actually.
Gideon laughed uproariously. "That was #emph[incredible!] " He braced his hands on either side of the crater, and with a grunt uprooted himself. He rolled up on to his feet and brushed black earth off his trousers, a grin lighting his face. "You can't hurt #emph[me] , but I didn't even #emph[think] about the floor."
The tree-beast keened at Nissa like a scolded puppy. "Shh," the elf whispered, bending to rest her forehead against the monster's wooden brow. "My fault, my fault."
"Nicely done," Gideon laid a massive hand on Nissa's thin shoulder. She twitched and inhaled sharply. The tree-beast swung toward him and shook itself, leaves rattling a feline hiss.
He stepped back, hands in the air. "Easy, big fella. Not attacking mom."
Nissa laid a stilling hand on the beast. "Thank you. Rest now." It dug its wooden fingers and toes into the earth, groaned, and settled back into mere topiary. Nissa stood alone again, the beast's last pale blossom petals tumbling down around her.
Gideon rubbed his prickly jaw. "Hope Jace is all right with us landscaping."
Liliana glanced at Chandra. She was up on her toes, leaning forward over the rail with a dazzled little smile. "Careful you don't fall off."
Chandra hopped back down, and stuck out her tongue. "Like I would. Come on, I'm hungry."
Liliana smiled and followed. Behind her, Gideon's voice echoed from the courtyard bricks. "Nissa, before you go. That thing I do, where I clap people on the shoulder? Does that make you uncomfortable?"
Liliana paused at the door, listening. If the elf responded, her words weren't audible.
"I'm sorry. I hadn't realized. I won't do it again." Liliana couldn't imagine his expression, but his tone dripped such brown-eyed-shaggy-dog sincerity her lips twitched with irritation.
"Thank you." Barely more than a whisper of wind on leaves.
"If anything makes you uncomfortable, let me know, all right? #emph[Especially] if it's me."
Liliana set her mouth in a hard line and followed after Chandra, boots clicking on the hardwood, silk hem swishing in her wake. If she listened to any more she might vomit. Of course the #emph[elf] gets apologies and promises. Two hundred years ago, #emph[she'd] had to learn to break fingers.
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There were a dozen ways into Jace's library, not counting the hidden passages her shades had found. Three stories of overflowing floor-to-ceiling bookshelves, all in alphabetical order by author, and arranged by subject. After a few weeks, she'd started taking random books and placing them on other shelves. It would drive him #emph[insane] when he noticed.
The marble table at the center was normally covered with Jace's neatly squared stacks of notes. He'd moved that into a private office; the library had become a common room because the table was the only one in the house large enough to accommodate them all. He'd visibly twitched when they started taking meals there.
#figure(image("001_Homesick/02.jpg", width: 100%), caption: [Jace's Sanctum | Art by <NAME>], supplement: none, numbering: none)
Today the table held only a pitcher of water and six glasses. Jace was already here, of course, pacing, frowning, flipping through a bundle of notes, and trying to keep clear of Lavinia, who'd stationed herself by the exterior door and stared pragmatically into the middle distance. You could almost see checklists and formation marches lockstepping behind her eyes, taking up cycles while she waited for something important to happen.
Liliana had seen her sort a thousand times. Dutiful, observant, entirely unimaginative. If she had a favored tavern, which seemed unlikely, her usual was a mug of room-temperature water.
Lavinia was almost certainly standing by the door to keep Jace from bolting out on some adventure. Of course, if he really wanted to leave, he just needed to be alone for a few minutes. She knew that now; with four Planeswalkers living here (and one availing herself of the amenities, thank you very much), it had been necessary to explain. Jace had invoked some Guildpact bylaw of subsection of article as amended and ratified by who the hell cares to swear her to secrecy.
Liliana smiled to herself as she scraped a chair out from under the table, imagining the guard banging on the door of the privy; "Are you still in there, Guildpact? Respond at #emph[once!] "
Jace looked up at the noise of her chair. "You're early?" He sounded aghast. She was professionally affronted.
"No. Everyone else is later than me." She cast a critical eye up and down his form. Firm, fit, alert, hair combed. She mentally called bull on it. "You can drop the glamour, dear. No one cares."
He sighed, and shimmered as his illusion dropped. #emph[There] was the real Jace; paler, hair rumpled, eyes sunken from late nights, and his chin tinted by the adorable peach fuzz that almost counted as a someday-maybe beard.
"Vanity?" she said. "That's not like you."
He raked a hand back through his hair, which did nothing to calm its random angles. "I should be at my best for team meetings. Project leadership. Confidence. The idea that I know what the hell I'm doing. And why am I telling #emph[you] this?" He looked annoyed at himself.
She raised one ivory shoulder in a careless shrug. "Who else knows you well enough to understand?" Liliana leaned back in her chair and placed her feet up on the table, one ankle crossed over the other. The hem of her dress fell away from her boots in a rustle of silk.
"That's rude," Jace frowned.
"Mm."
His eyebrows collapsed into fuzzy perpendiculars of irritation. "And distracting."
Liliana favored him with a lazy, indolent smile. "I'll remember." She turned her attention to scanning the book spines nearby, and imagined his fuming.
Gideon thundered down the stairs, taking them two at a time as he yanked a shirt down over his various bulges, ripples, and throbbing bits. "Oh, good. You remembered today," she said.
He blinked at her. "What?"
"Nothing." She waved a careless half-salute in his direction. "Carry on, Sir General sir."
Jace set his notes down as Gideon pulled out the chair across from her. "That's nearly all of us, so I'll start. We can catch Chandra up when she gets here."
Liliana blinked and scanned the room. What about—oh. Nissa was sitting cross-legged in a chair under the shadow of the bookshelves, several steps removed from the table. She wondered how long the elf had been there.
"The short of it is," Jace continued, "I'm still tied up with Guildpact work, and will be for a while. When I got back from Innistrad, my desk was covered. Actually, the whole office was a maze of stacked papers and books. It took me five minutes to #emph[reach] the desk."
A faint smile tugged the corner of Lavinia's mouth. Liliana revised her estimate of the woman's creativity upward.
Jace leaned on the table with the tips of his fingers. "I've put word out through—"
Bits of armor clattered and rang across the table. Jace glared up at Chandra. The pyromancer's arms swept up the pile of her spilled equipment. "Sowwy," she said around the pastry she held in her mouth. It dripped cinnamon icing on the marble. She collapsed in the chair beside Liliana, bit off a piece, and started strapping on pieces of armor. "Wha' wersh you shayin'?" she asked from the side of her mouth.
"I was saying," Jace said, with exaggerated patience, "that I've put word out through Tamiyo that the Gatewatch is ready to help. She and other Planeswalkers pass information to each other. They collect news and stories in their travels. The way bards work, but they carry word from other planes instead of the next town over."
"How many are they?" Gideon asked, resting his chin in one hand. "How often do they meet?"
Jace shook his head. "They're not organized like we are. It's informal. Practically gossip. But they move around often, and talk to many people. If someone wants help, they'll mention us. If someone needs help, they'll get word to us." He paused, and looked at each of them. "This has already borne fruit. Someone's sought us out. He's waiting outside."
Gideon grinned and sat straighter in his chair, which creaked at the shift in weight. "Outstanding work, Jace."
Jace nodded. "Our guest is <NAME>. He's Minister of Inspections for some kind of inventors' festival on Kaladesh." Warmth bloomed to Liliana's right. "Lavinia, could you see him in please?"
Minister. Hmm. Liliana took her feet off the table, sat up straight, and crossed her legs, brushing the folds of her dress into smoothness. A ripple passed over Jace; he'd re-summoned the neat and tidy illusion he'd been wearing when she entered.
Across the table from her, Gideon eyed their mutual preparations thoughtfully.
Chandra slumped further down in her chair, pulled her goggles down over her eyes, and folded her arms tight across her chest.
#figure(image("001_Homesick/03.jpg", width: 100%), caption: [Art by <NAME>], supplement: none, numbering: none)
The vedalken man was tall, thin as dueling blade, blue-skinned, and impeccably dressed. His suit was partially encased in whorls and filigrees of brass, bits of which hissed and ticked faintly. He descended the stairs with brisk, precise motions, hands clasped behind his back, and Liliana wondered how he managed it. Surely the bits of metal covering his sleeves would get tangled?
He paused as he passed a painting, frowned, and reached out to nudge it upward on one side.
"Minister Baan," Jace said. "These are my colleagues Nissa, Gideon, Chandra, and Liliana."
As she was introduced, Liliana unfolded from her chair and applied a pleasant smile. She curtseyed, keeping her eyes locked on Baan's as she bobbed. His were a fevered, restless fuchsia. A fascinating contrast from his cool demeanor. "Charmed, Minister." Her form was rusty, but she doubted he'd be familiar with the particulars of Dominarian court manners.
Baan laid an arm across his stomach and bowed to her from the waist, lowering his eyes to the floor before her. "Likewise, <NAME>."
"I hope your wait was comfortable?" Jace asked, indicating an empty chair at the far end of the table.
Baan glanced at it with momentary puzzlement, but made no move to sit. "The accommodations were tolerable."
Jace's projected face gave no hint of the discomfort Liliana's suspected lay beneath it. "Good. Well. What can the Gatewatch do for you?"
"I have come to inquire with regard to the matter discussed in my previous correspondence."
After a moment of silence, doubtless spent unpacking Baan's baroque grammar, Gideon cleared his throat. "Excuse us, Minister. Not everyone here has seen your letter."
Baan inhaled slowly. "Ah. Very well. I will recapitulate." Clasping his hands behind his back, he began to pace at the end of the table.
"I have the honor of coming before you as an officially and duly designated representative of the Consulate of Kaladesh. I have, of course, educated myself on the means of governance on Ravnica; your system of competing 'guilds.'" Baan pronounced the word with delicacy, as if it were some rare sweet he'd never encountered before. "Our Consulate stands in contrast. It is unified; centralized; meritocratic. All resources are administered and distributed by the rational and equal application of the law. We have achieved a society in which no one #emph[wants] ."
Liliana's right arm felt sunburned. She glanced at Chandra. A shimmer of heat-haze danced over the younger woman's head. Stray wisps of copper hair rose and wavered in the updraft. But she was silent, rigid, the muscles of her jaw rippling as she clenched her teeth.
Liliana quietly slid her chair to the left.
"Six months ago," Baan continued, "the Consulate scheduled an Inventors' Fair in the capital city of Ghirapur. It is to begin on the morning following. There are to be expositions of artifice in a variety of fields. Award of grants for exceptional work."
Baan allowed the corners of his mouth to turn up, ever so slightly. "It has been my pleasure to personally inspect all submissions for safety of visitors. If I may be forgiven for saying so, I believe the judges have many difficult choices to make. I am confident that at least one of our luminaries has managed to create an entirely new order of artifice."
He paused at the books stacked along the wall, and tapped the brass of his shoulder piece. An array of lenses whirred into place before his left eye. He peered through them for a moment, frowned, and drew one slim finger across the surface of the shelf.
"In recent weeks," he continued, pulling a handkerchief from his pocket as he turned on his heel, "preparations have been repeatedly disrupted by vandals and malcontents. My safety arrangements have thus far prevented any casualties." He wiped his finger with the handkerchief, carefully folded the cloth into quarters, and slid it back into a pocket. "However, efforts to discover and eliminate the source of this unrest have been less successful."
Baan's lens array ticked back into a storage position over his shoulder plate. "That is all."
Gideon cleared his throat. "So, to be clear, you want the Gatewatch to provide...security?"
"To root out the source of these attacks?" Jace suggested.
Baan looked from one to the other, and inhaled as if he'd smelled something from the bottom of a shoe. "Just so," he said. "As stated in my original correspondence."
"Who are these people?" Gideon asked. "Why do they want to disrupt a #emph[festival] #emph[?] "
Baan inclined his head. "A logical question, Mister Gideon. I regret there is no logical #emph[answer] for your query. The renegades' grievances largely exist in the fevered space between their own ears. The most significant objection they can muster is that equal distribution to all by the Consulate is somehow 'unfair' to them personally. Put simply, they feel they are entitled to more than their fair share. When the Consulate declines to indulge their selfish desires, they resort to sabotage of government property and theft of resources appropriated for the common good."
Chandra's chair tilted over backward as she bolted to her feet. Liliana snapped out an arm and kept it from clattering to the floor as she stomped away, trailing heat-blurred air and sparks.
"What are you—?" Gideon began, but flinched away from Chandra's flickering hands as she passed him. She vaulted up the stairs two at a time, snarling eye-watering obscenities.
Baan's eyes followed her, his eyebrows arching skyward. "I trust she is aware that is not anatomically possible?"
Jace cleared his throat, too loudly. "Minister Baan?" The vedalken turned back to the table as the massive library doors slammed shut. "Are any of your renegades #emph[Planeswalkers?] "
"Not to my knowledge."
Gideon shook his head, "Then I don't see how we can help. I'm sorry, but—"
"Wait." Jace leaned forward. "He said he doesn't #emph[know] . We can prove one way or the other."
Baan closed his fever-bright eyes and pinched the bridge of his nose between thin fingers. "Gentlemen, forgive my presumption. Which of you is making decisions for this group?"
Jace and Gideon looked at each other.
"Well..."
"Uh..."
"Gideon is the battlefield commander..."
"Jace is the administrator..."
"But we both..."
"But neither of us..."
Baan was clutching his head as if he had a migraine.
"Minister Baan," Liliana interrupted. She rose in an ostentatious swish of silk and lace, and affected her most disarming smile. "What troubles my...colleagues is the focus of our group. The Gatewatch was formed to stop people like us—Planeswalkers—from interfering with others. Problems from #emph[without] , in other words. It sounds like your problems come from #emph[within] . In which case," she gestured with feigned helplessness, "our hands are tied."
Baan released a slow, relieved breath. "Ah. Thank you, <NAME>. Your position is abundantly clear to me to now. I did not fully comprehend the strictures you operate under. Of course I cannot expect you to violate the laws that bind your organization." He bowed to her again. "My sincerest apologies. In the future I will endeavor to be more thorough in my research. If you will permit me, I shall take my leave."
Jace stared at Liliana open-mouthed, annoyance and astonishment warring across his face. #emph[Priceless] .
"Uh, hold on," Gideon jumped to his feet. "Minister, you should at least stay for dinner."
Baan looked at him as if he'd grown several additional heads. "<NAME>, even if I considered it acceptable to further impose upon your hospitality, I am sorely needed on Kaladesh. I have no doubt that since I departed, there have been several acts of sabotage."
Gideon grinned at Baan. "Planeswalks can be taxing, and you've already done one today. We couldn't let you go on an empty stomach. Rules of hospitality, let's say. While we get that made, I could give you a tour of Jace's hou—of our headquarters."
Baan stared down his nose at him. "I assure you, my fitness is within acceptable boundaries for one of my age and profession, though I do not believe the matter to be any of your concern. Still. If it is your custom to provide sustenance to a departing guest, I will respect it."
"Outstanding!" He moved to clap the Minister on the shoulder, but stopped himself and disguised the instinct as an awkward stretch.
Lavinia cleared her throat. "Guildpact. Before your associates leave. The other business?"
Gideon paused. "Other business?"
Jace grimaced. "While I was away on Zendikar and Innistrad, a few influential members in the Azorius Senate were...eliminated."
"Certainly a concern," Gideon said. "But what does that have to—"
"You said 'eliminated,'" Liliana interjected. "Not 'killed.'"
Jace nodded. "They were #emph[petrified] . Turned to stone." He hesitated. Liliana raised her brows. Jace speechless? How intriguing. "About a year ago, there was a gorgon assassin operating on Ravnica. A #emph[planeswalking] gorgon, with a grudge against the Azorius. I stopped her, but...irritated her."
"You have such a way with ladies," Liliana said.
"The point is," Jace said, "she swore she'd be back someday."
Gideon rubbed his jaw, eyes flickering to Lavinia. "Huh. Any leads?"
"Not yet," Lavinia said.
Jace turned to Gideon. "I'd like you to investigate this."
He shook his head. "You're the best choice, Jace. Look into it and report back to me."
Liliana's eyes flickered from one to the other. #emph[So] glad she had her own place. Though if things ever came to a group vote, this made it easier to tilt things in whatever direction she wished.
"You have #emph[no] idea how much I'd like to handle this myself," Jace said. There was a faint creak of leather as Lavinia's gloved hand tightened on her scabbard. "I have #emph[paperwork] ." He spat it like an obscenity. "Gideon, I'm not going to...it's not an #emph[order] , all right? It's just something that needs to be done. I can't do it myself, and I think you'd work well with the Azorius. Better than Liliana would, at any rate."
"Oh, he's right about that," Liliana said, mildly. She was fairly certain they would still have her wanted posters up from four years ago, when she and Jace had worked for Tezzeret's criminal Consortium. Odd to consider how much had changed since then. Now Jace was the one the Azorius appealed to for aid, and she was more powerful than the guild could possibly deal with.
She laid a hand over the hidden pocket where she kept the Chain Veil. Not that she needed to assure herself of its presence. She could feel the icy sprawl of it against her thigh, and when her concentration lapsed, the whispers of the Onakke spirits possessing it rasped from the darker corners of the room.
"That makes sense," Gideon said, nodding slowly. "All right. Lavinia, I'd like a summary of what the Azorius know."
The guard looked scandalized. "A #emph[summary?] Captain Jura, the witness statements alone total several thousand—"
"I'm new here." He gave her an easy smile. "I need to rely on your expertise. I know it's a lot to ask, but could you get something for me by tonight? Even a little would be great."
Lavinia flustered under his gaze. "Absolutely, sir."
"Thank you, Lavinia," Gideon gestured to Baan, and moved toward the door on the far end of the room. "Jace's kitchen staff is incredible. Perk of being Guildpact, apparently. What's your interest?"
Jace dropped his illusion of calm and glared into Liliana's smile.
"I am content with a loaf of unleavened bread, a thin cut of meat, and water."
A booming laugh. "We can do better than that!" They turned down a hallway.
Lavinia tromped off, making notes on a small pad.
They were alone again.
Liliana placed herself between the table and the door to Jace's office as he gathered his paperwork. He scowled to see her waiting, lowered his chin, and marched past her looking into the distance. She smiled benignly. #emph[Magnanimously] . "In the future, my dear, maybe you should leave the talking to me?"
"I hate it when you do that," Jace said, low and colder than she thought she'd earned. "When you walk in and take over. Like you own everything and everyone. Then expect me to #emph[thank] you." He turned his shoulder to her and brushed past.
Her words came out by reflex, unbidden; pain for pain. She breathed into the collapsing space between them, "I remember when you #emph[enjoyed] that."
Then he was gone, leaving behind only his angry words, each a nail of ice pounded into her heart.
Well, damn it. There went her good mood. She swiped a hand beneath one eye (just being sure, nothing would ever be there), then squared her shoulders and lifted her chin. To Grixis with him, then. Let's see where Chandra stormed off to. That could be fun.
She turned toward the stairs, and noticed Nissa's chair was empty. The elf had left as unobtrusively as she'd arrived.
It was only when she was halfway to the second floor that Liliana realized Nissa hadn't said a single word through the entire meeting.
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I keep throwing punches.
The jolts pass up my arms, irregular, staccato. Gids's punchy-kicky bag of sand swings and wobbles under the blows.
If he were here, he'd be telling me to pace myself, keep my arms straight, use short and controlled jabs, so I guess it's just too bad for me he's listening to that Consulate #emph[butt] instead.
Inventors' Fair? The hell. They #emph[killed] the best damn inventors on Kaladesh. Baan and his sort. The #emph[Consuls] and their damn stupid #emph[rules] .
Now they're trying to hunt down somebody else. Someone else's kid. Maybe someone else's—
The canvas of Gids's punchybag bursts into flames.
"Oh crap!"
There's gotta be—he's gotta have water in here. He's like the king of eight glasses a day. I scan the room. Weights. Wrestle-y floor-pillow dealies. Big ball I'm not supposed to throw at Jace again. More weights. Rack of weird stuff he never explained. More different weights. There!
I slide across the table and grab for the bucket below the window. It smells funny. Maybe he soaks his head in it, I don't know. Just need the water.
Behind me, the canvas bursts, and sand hisses across the floor.
Oh, #emph[damn it] .
I pour the bucket over flaming scraps of fabric.
That's a big pile of mud. I wonder if it will ruin the floor? I stick the toe of my boot in and trace a line across the mess. Maybe I should make a sand castle.
I hate this. I hate the me that breaks nice people's crap. Even if Gids #emph[is] being nice to one of the people who killed my—
My eyes are stinging again. I drop the bucket and rub them. Sparks and embers drift away.
Maybe Gids totally deserves it. Screw his punchybag.
Why am I even here? I don't belong here.
I should go back to Regatha. Do that stupid ritual where you spend all night watching a log burn. Bit by bit it starts to glow. Red, orange, yellow, crawling up the bark. Flaring and fading down again. Then it turns grey and falls into ash. "This is what it means to be consumed by divinity," <NAME> said. "Transformed." Old life falls away and blah blah blah.
Which divinity? The Eldrazi? The guys who screwed over Gids? I can't believe in a god that burns everyone they touch. A god's gotta be better than that.
I remember the pool.
Behind the power that shook the strength from my legs.
It was there. I saw it. I #emph[swear] I saw it.
She was floating in green and I could breathe there.
That's where I want to be.
I #emph[need] to be there.
It's an itch I gotta scratch. Crawling up my spine and under my hair. Gotta go #emph[now] .
My feet have already taken me to the door. No, stop. Can't just barge in and...I mean, #emph[weird] , right? #emph[Rude] . I don't want her to think I'm the sort that just breaks in and...all right, maybe I #emph[am] the sort who does that, but I'm trying #emph[real hard] to be polite now. I just need to take a few minutes to—
Damn it, I'm already up the stairs. And I'm stomping down the hall like a #emph[big freak] because my legs are shaking and my brain is sizzling. This is #emph[stupid] . I'm going to stop putting one foot in front of the other. I'm going to turn around. I'm going to tiptoe down the stairs real quiet, like a little baby mouse. Any second now. Damn it, Chandra, don't open that door. Stop gawping at the ginormous flowers that weren't here a month ago. Bad Chandra, no cinnamon pastry. Just turn around, go back downstairs, and never think of doing this agai—
"Chandra?"
#emph[FFFFFFFFF...]
"H-hey. Nissa? You in here?" Yeah, that's it. Casual. #emph[Smooth] . Be all nonchalant, like Liliana. Nothing gets to Liliana.
"I mean, heh, 'course you're in here. 'Cause you just talked. I mean, uh, you got a minute? Maybe?" #emph[All right you can stop talking now] .
"Yes. I'm behind the kass—behind the purple flowers."
My hands are shaking. I push branches aside and walk toward her voice. The leaves feel like sandpaper. Just a little farth—
She's sitting cross-legged on a patch of moss. Dark hair unbound, spilling in waves over her shoulders, trailing across her lap. She's woven little flowers around the crown of her head. Butterflies are dancing around her. She pays them no mind. A shaft of light through the leaves paints her in golden sun. She smells like anyone's best childhood memory.
She hasn't taken her eyes off me. Just sits. Listens. Waits. It's making me itchy and I think I'm sweating.
When was the last time I took a bath? Aren't elves supposed to have super dog noses or something?
Also, I'm standing bent over under a branch, holding leaves out of my face like a freaking idiot. "Uh. Can I sit?" I'm breathing through my mouth, fighting for air, struggling not to be loud about it.
"Please." She gestures. Her arm moves like water. Just sorta #emph[flows] .
Then I manage to trip and fall on my face.
"Oh!" she reaches out, but her fingers seem to bounce off an invisible bubble a handspan away from me. "There's a root..." She pulls her hand back, cradles it with her other arm.
"I'm fine!" I blurt into the dirt, then roll on to my knees and grab my head to make sure I really am. Bleeding from my face would be super embarrassing during this conversation. "Are you fine?"
She cocks her head to the side. "I..."
"Ha-ha-ha! 'Course you are. Sorry. I'm the one who fell on her face." #emph[SHUT UP SHUT UP] .
I try to sit like she is, but the armor on my shins digs into my thighs. I lean against a tree, stretch out my legs, cross them at the ankles.
Wait! My feet are almost touching her knees. I shouldn't do that. She might not like that. I shift my weight, point them off to one side.
Great. Now I have a root jabbing into my butt.
She just watches me. Silent. Patient.
I giggle and try to push the hair off my sweaty forehead. I'm steaming under her gaze, skin gone molten. "I think I'm crushing your flowers."
"They'll be fine." Her eyes are so deep. When I was a kid, there was this quarry outside Ghirapur. It had filled with water, and moss and floaty green stuff grew all over it. Deep, black, still. If you fell in, you'd never reach the bottom. That's what they said, anyways. I'm standing at the edge, too scared to jump.
She clears her throat. "Can I help with something?"
I swallow, but my throat's dried up and it takes a few tries. "I—I just thought that...You know that time on Zendikar, when our minds touched? I felt Zendikar's anger, right? The power of a whole world. #emph[Your] world. And it was #emph[amazing] . The most incredible thing #emph[ever] . But behind Zendikar, behind the anger and the power, I felt #emph[you] . Your mind. And it was real tranquil, you know? You kinda...centered me, I guess. You were all calm and connected-y."
Then my brain shuts off, but my mouth keeps walking over a cliff.
"When I touched that part of you, it was like when you're swimming, and you just lie back and float, looking up at the sky. Nothing below. Just blue and air above, and everything's cool and still. You can see forever, and don't have to worry..."
#emph[WHAT IS COMING OUT OF MY FACE?]
I run a hand back through my sweaty hair. "Ha ha, wow. You must think this is dumb, huh? I come in here and start spouting bad poetry—"
The tiniest of smiles. "I thought it eloquent."
I grab a strand of my hair and yank until it hurts. That will keep me focused, I bet. "Anyways. I was thinking there are times when I get super pi—uh, real angry, and usually something blows up. But I think I'd rather be able to touch that place again. What your mind felt like. Calm. #emph[Grounded] . I mean..." I make the mistake of looking up and her eyes are just #emph[there] , watching, and all the air in my throat jams up and refuses to move.
I struggle to pull in a breath. "I think #emph[Jace] would prefer that. So I don't wreck his house. I mean, he's got this expensive stuff all over."
"I can teach you to meditate, if you wish."
"Uh, yeah." Let's go with that. Sounds good.
Her pencil-sketch eyebrows go all bendy. "Are you unwell? You seem anxious."
The entire garden is full of floaty sparkly silver things, I spent the last hour trying not to blow up Jace's house, and my heart's slamming against my ribcage like I just ran a marathon. #emph[I'M GREAT THANKS FOR ASKING.]
Instead I blurt, "It's just, you've been staring at me this whole time."
"You're speaking to me. Should I not pay attention?" I swear her lip trembles. "Is this not—not polite on your world?" She looks away for the first time, and one hand tugs a grass-stem ear. The snow of her cheek is brushed with sunset color.
#emph[WHAT THE HELL DID I JUST SAY?]
"Wha—uh, no! I mean...Sorry!"
I'm on my feet, slamming my head into a low branch. "Ow! S-sorry. This was dumb." I back away, clutching my head, pulling in my elbows to hide my burning eyes, stumbling over the #emph[same damn root] , shaking, panting for breath, stomach churning. What did I do, what did I do, what did I do?
She's on her feet in the turn of a breath. "Wait."
"I made you feel weird. I should go. I'm just gonna go. Sorry. Bye. Sorry."
"Chandra, please..."
I turn and run, trailing sparks, trees and flowers smearing around me, banging through the door.
...I think I'm gonna puke.
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"What a disaster," Liliana murmured. She leaned one hip against the door into Beefslab's gymnasium. After the scene downstairs, she'd expected fire damage. The sandcastle was a surprise.
Gideon's voice boomed from the stairs behind her, "Up here's where I exercise. I've been trying to train up Chandra and Jace, get everyone able to handle an actual weapon. You know. Just in case."
"I have every confidence it will prove equally fascinating as the rest of your facility," Baan replied, wearily.
#emph[BANG.]
She startled, turning in time to see Chandra hurtle down past Baan and Gideon, a red-haired comet trailing embers from her eyes.
"#emph[SorryIblewupyourthingy] ," she said in passing, the words floating up from underwater.
Then she was gone, the thunder of her feet rumbling down the stairs.
"Careful! You might fall!" Gideon yelled down after her.
Liliana stepped into the stairwell and glanced upwards. Nissa looked down with hands clasped and fretting at her chest, lips parted with unvoiced confusion, long ears drooping.
Liliana shook her head and started down the stairs. Someone had to clean up the mess. Chandra was easy to read. #emph[Too ] easy. Yet she commanded incredible power. A convenient combination.
The sun was westering, settling down into a long, hot afternoon. Low slate clouds to the east promised evening rain, the kind that would make the summer air thicker instead of cooler.
Not that heat bothered her greatly. Necromantic powers had benefits seldom mentioned in brochures. For example, a body temperature low enough to alarm healers. It made summers far more pleasant, and her breath frigid instead of warm. Jace had been preternaturally sensitive to it. The slightest puff of air on his neck had been enough to wake him from sleep.
She frowned and firmly pushed the memory out of mind.
Chandra wasn't hard to find. Setting aside the fact that she had a tendency to knock into people and objects when running flat out, her hair was smoking, in a subtly different color from the food carts scattered around the plaza. Liliana didn't even need to summon a shade to help search.
She was crouched halfway down an alley three blocks from Jace's home, its entrance hidden behind a hoarse food vendor whose cart smelled of cheap pork and overboiled cabbage. Curled up knees to chin, back to a brick wall, she tugged on handfuls of her copper hair.
Sibilant whispers echoed from the alley mouth; "Stupid, stupid, stupid..."
This wouldn't do at all. Liliana swept imperiously around the corner, careful to lift her skirts clear of the rainbow-skimmed puddles. "Why, Chandra, here you are."
She bolted to her feet, wiping under her nose with the back of a shaky hand. "Uh, hey. What—what are you doing here?"
"I was on my way to do some shopping," Liliana extemporized. She'd probably believe that. Big Sis Liliana, leading the glamorous lifestyle and whatnot.
She sniffed and gave a skeptical look. "In an #emph[alley?] "
"We don't all shop in the same places," Liliana said. "Care to join me?"
Chandra looked over her shoulder, down at the other end of the alley, where crowd-shadows flickered and danced across the afternoon light. "Anyone with you? Gids?"
"Goodness, no. He wouldn't be caught dead shopping with me."
She grinned. "But if he #emph[was] , you'd raise him to carry your bags!" She paused. "Did you just let me have a necromancer joke?"
"Just this once. Because I like you." The stiffness in Chandra's shoulders relaxed, just slightly. Good.
Chandra wiped under her nose again, then absently rubbed the hand clean on the shawl tied around her waist. "So what are you even shopping for?"
"Oh, nothing terribly important," Liliana said, airily. "A bottle of wine, a half-dozen dead cats—seven to ten days decomposed, by preference—lavender-scented candles, a twelve-inch bone saw..."
Chandra's mouth worked for a moment before the words came. "I...can't tell if you're joking?"
"Then I suppose you'll have to come along and see. We can talk on the way."
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All was dark. Cold. Silent. Dampness encased her. A distant warmth filtered down, the lightest breath on the small of her back. She'd waited an eternity, sleeping under moons of cracking ice and pounding rain, feeling the press of quick lives passing overhead.
It was time to move.
Slowly she unwound, pushing back against the softness that pressed in on her. Her limbs stretched, creaking and quaking from an eternity spent huddled in the dark. All around she could feel her siblings stirring. The warmth on her back was drumming into them all, calling. It was time to meet, at last.
...Nissa...
She pushed against the weight above her. Strained. Pale, thin toes sank into the velvet depths below her belly, down where the long cold still lurked and growled, stretching knives of clearest crystal through unknown spaces. She shuddered with the strain.
Maybe she couldn't do it. Maybe she'd be down here forever. Lost, collapsing back into a forgotten husk. Not dead, but never-lived.
...Nissa?
The darkness broke over her.
She shuddered, aching, unsteady legs pushing up, arms shaking as they unfolded from her torso. Every move was agony. The heat beat down, making cold-choked blood flow, filling her limbs with strength and color. Her head lifted into the light, hair spreading into radiance.
#emph["Nissa?"]
#figure(image("001_Homesick/04.jpg", width: 100%), caption: [Art by <NAME>], supplement: none, numbering: none)
The word cracked across her from a thousand leagues away.
She was yanked away in the span of a breath.
The world flashed past. Jumbles of wood and fungus growing over and through one another, breathing together; wastelands of hissing dust, patiently eating stone; ranks of muttering clouds opening themselves to the earth below; ranks of axe-blade stone clawing open the sky; waters deep, cold, and empty.
She blinked at Gideon, momentarily baffled by his grunting beast-sounds—#emph[words] , some part of her corrected—and by the club-shapes—#emph[fingers] —waving before eyes that suddenly saw light instead of heat. "I..."
#emph[I'm not a seed.]
#emph[Nissa. I'm Nissa again] .
He looked at her expectantly. Rain tapped against the windows of Jace's library. Her words came out broken and creaking, "I'm sorry, Gideon. What did you say?"
He showed his teeth. A grin. "Thought you'd fallen asleep for a minute."
"I was..." A flower struggling out of spring tundra half a world away, delighting in the first touch of the sun. She searched his kind and open face, but found no capacity for understanding. No context she could appeal to. No words that could explain.
"...I was just thinking." She looked down at her lap, where a bowl of food sat untouched.
He speared a hunk of meat from his plate with a utensil—#emph[fork] , she remembered—that was all but lost between his thick, calloused fingers. "I was telling Minister Baan what you did on Zendikar. You and Chandra."
Chandra. The blood surging hot through her freckled cheeks, the sharp, swift movements of her hands. They'd moved like birds.
Nissa fed birds sometimes, in the garden. They would peer at the seeds cupped in her hand, hungry and needing, but fluttered off when she moved the wrong way.
She'd moved the wrong way, and Chandra had flown.
All her senses and instincts were off.
Ravnica had beaten against her since she arrived, the hot, constant breath of a beast on the back of her neck. The sun was blinding white, the smells thick and unpleasant. Every surface seemed to have edges made to cut and tear.
An endless array of faces milled and circled the streets, strange and terrifying. More faces than she thought could ever exist. They melted into one another, became a single monstrosity with a thousand heads that jostled past her. A walk around the building left her sweaty and trembling. She had to crouch and study the lone flowers that struggled through the cracked cobbles, had to ignore the milling, noisy shapes that shoved and kicked and poked.
There was no silence. Discordant anvils rang by day. Endless banquets hissed and roared from a thousand ovens. The wail of sirens and the crackle of mana by night. A million voices constantly yelling and screaming, crying in pain and grief, lust and anger, overlapping in babble. She hadn't heard the shush of wind through trees for three months. She hadn't heard #emph[nothing] .
The faces. The noise. The million and one unfamiliar smells that settled in the back of her throat to gag her. When it was too much to bear, she'd curl up in the garden, cover her ears, and the trees would hold her safe.
Everything here was hard, and bright, and sharp.
Chandra. Eyes like sunrises. Every passing thought writ bold across her face. Fearless.
#emph[Oh, Zendikar, how did I offend her? What did I do?]
But her friend—her #emph[best] friend, her constant companion for two score years—couldn't answer. The corner of her mind where Zendikar had lived was silent and empty. #emph[There's so much I don't understand. I wish you could be here.]
She'd never been among so many, and never been so alone.
"Nissa?"
"Yes." She lifted a small red fruit from her bowl. #emph[Tomato] , Jace called it. Taut skin flush with water, smelling faintly of acid. "What did you want to know?"
Baan laid his utensils across the edges of his plate at an angle so precise it hurt her eyes, then steepled his fingers. "Indulge my curiosity, if you will, Miss...Nissa." He frowned as the title made him hiss. "I am given to understand you have the ability to perceive and manipulate naturally occurring patterns of magic. Through the land, I believe?"
The golden filigree over his coat was ticking softly, a counterpoint to the clock on the far side of the room. She could hear energy within it sizzling and snapping, imperceptible to Gideon, and perhaps to Baan; his ears were as small as a human's.
"Leylines," she said. "Yes."
His nostrils pinched as he inhaled sharply. "A fascinating inversion. On my world, similar energies stream through the upper reaches of the #emph[sky] . Aether, it is called. We siphon this power—on mountaintops or from thopters—store it within mechanical devices, and release it for various productive uses. Do people do the same on your world?"
#emph[Dagger-blade stones floating in the air, bending the world. A web, a cage...a lattice.]
A wave of nausea passed through her.
"No," she said to her bowl, shoulders drawing inwards. "Some did, but they..." The tales piled up against the back of her teeth. Where could she even begin? "The land isn't—we ask. We don't take."
"Ask?" Baan echoed, turning the word sideways in his mouth. "Ask #emph[whom?] Your leylines are naturally occurring phenomena, surely?" His voice thinned with saline contempt. The shape of his eyes changed, tissues settling into harsh angles. "Would you ask the mountain for its kind permission to shape the iron at its root? Would you beg the tree for the fruit that sustains you?"
"Yes," she said, and nothing more. She placed the tomato in her mouth and bit down. The water flooded out—#emph[the sharp light of a white sun beating down, rows of dark earth spiced with the remains of those gone before; gently tilled lanes, the hush of elves and dryads swaying among them; tilting cans to set brief, borrowed rains tapping and shivering down leaves] .
A lifetime carried in a mouthful of sweet flesh. Months of patience. #emph[Thank you] , she thought, and swallowed.
Gideon shifted in his chair, leaning forward, subtly placing himself between them. "Minister, things are...different on Nissa's world."
The heavy door at the far end of the room opened, and Jace trudged out looking drained. Lavinia drifted into his wake. When he muttered, "I could really use drink," she pushed a mug of tea into his hand, its steam fragrant with lemon, hibiscus, and several herbs Nissa didn't recognize. He blinked. "How did you know to...?"
"It's my job to anticipate you, Guildpact," she said, crisply. "Should I get someone to reheat your dinner?"
"No. Thanks, Lavinia." He pulled a chair out—old oak, dark and worn from years of sun. Nissa wondered where the chair had come from. It was far older than the house. The life it had held was just a whisper now, a shadow cast on a cloudy day.
Jace's plate contained some yellow-white mass involving cheese and grains. Even cold, she could smell it from the far side of the room. He frowned. "Did they put #emph[broccoli] in this?"
"You need iron," Lavinia said.
"I hate—"
"You won't even notice it's there." Her voice brooked no argument.
Baan regarded him coolly. "You were bullied as a child."
Jace coughed on his first mouthful of food and struggled to swallow. "I, uh, don't remember my childhood." A dozen unvoiced thoughts flickered behind his eyes.
The Kaladeshi raised his brows. "One need not consciously recollect an event to fall into habitual behaviors determined by the experience. It is not inconceivable that one could forget their entire life. I would safely wager that were that the case, the subject would still tend to make similar lapses of judgement, and would be drawn to associate with the same sorts of people." He waved a hand, the swish of an ox's tail dismissing flies. "The nature of mortals is not so malleable as some would naively suppose. A person of religious inclination will always find something greater than themselves to place their faith in. A criminal will forever remain a criminal."
Jace put his fork down. "That's a very...deterministic point of view, Minister."
Baan blinked, first one eye, then the other. Not a wink, but some form of body language unique to him, unlike any Nissa had seen before. "The mortal corpus, even the mind, is merely a series of sophisticated mechanisms. It is simplicity itself to observe a mechanism in action, and draw appropriate conclusions."
There was a moment of silence. Jace cleared his throat. "Did you enjoy the tour?"
Nissa looked down at her food. She plucked out a piece of steamed fish with her fingers and let the flavor melt across her tongue. #emph[Quicksilver bodies flickering under green shadows. The grit of suspended peat, the faint tang of metal.] It was not her first language, but there all the same. #emph[Thank you,] she thought. #emph[I will use what you've given with wisdom.]
Baan's chair creaked as he settled back. "There are a number of structural and organizational deficiencies I believe it best you be made aware of. The load-bearing beams on the lowest levels are cracked. Application of sufficient force would cause them to give way. The arrangement of furniture in most of the bedrooms is inefficient, leaving many "pockets"—if you will excuse the imprecision of the term—of floor space too small to make practical use of. There are seventeen books that were returned to incorrect shelves in this library. A number of lamps on the second floor lack appropriate protection from drafts..."
"Maybe I should write this down," Gideon said, with a lopsided smile.
"I'll remember it all," Jace said.
Baan paused. "I am given to understand that the incident within Mister Gideon's gymnasium was the responsibility of a pyromancer in your employ?"
"'Employ' might be too strong a word."
"Regardless of the particulars of your arrangement, the lack of appropriate precautionary measures is deplorable. You possess a library of admirable scope and selection. To a pyromancer, this is merely so much kindling. If a conflagration were to start in here—"
"I have...differences with Chandra, but I trust her to..." Jace paused. "Where #emph[is] Chandra?"
Nissa looked up. Chandra's usual seat at the table was empty.
Gideon shrugged. "I've been looking for her myself. We need to have a talk about proper care of other people's equipment. Last I saw, she was running down from the roof—"
Her breath caught.
"—and Liliana was following her."
Jace looked up sharply. Lavinia, standing watch by the door, cleared her throat. "Guildpact. Permission to report?"
"What? Yes!" Jace turned entirely around in his chair. "You know where they are?"
Lavinia straightened, almost imperceptibly. "Some time ago, <NAME> requested I have someone follow <NAME> when she leaves."
Jace glared at Gideon, who shrugged. "Necromancer. Only prudent." He put another forkful of steak in his mouth.
Lavinia shifted weight to her other foot, setting her armor to humming, a tone no one else in the room could hear. "She contacted <NAME>—"
Baan leaned forward in his chair. His eyes narrowed.
"They spent the afternoon wandering the market district, then, ah...planeswalked."
"#emph[Together?] " Jace asked.
"Yes, sir."
Gideon put down his fork. "Where to?"
"No way for us to know, sir."
"#emph[Nalaar,] " Baan said, softly. He pronounced it with the same enunciation Chandra used, and none of the others had ever quite managed to reproduce. "You must excuse my consternation. That is a name I have not heard for many years."
Jace pushed his plate aside and laid his hands on the table. "I need you to explain that."
"I would not say it is my pleasure to do so, but I do believe it is my obligation." Baan folded his hands in his lap. "Pia and <NAME> were early luminaries of the renegade movement. They were criminals, I regret to say, engaged in the theft and unlawful redistribution of Consulate aether resources."
"They're relatives of Chandra's?" Gideon asked. "I didn't even know she was from Kaladesh..."
"Her parents, unless I greatly miss my guess. Twelve years ago, they compelled their daughter—her name was not recorded—to assist in their smuggling operations. I am not familiar with the details, but the girl escaped custody when she manifested dangerous pyromantic abilities. The Nalaars attempted to hide in the countryside. A manhunt brought them to ground in Bunarat, but during the attempt to take them into custody, the village was set ablaze. All three were reported dead by the officer in charge."
"Twelve years?" Gideon said, aghast. "But she's only—!"
"She would have been a #emph[child] ," Nissa said, softly.
Baan opened his mouth, closed it again, and looked inward, tapping his fingers on the filigree covering his sleeve. "Please understand," he said at last. "This was performed under the authority of a previous administration. Even then, these actions were considered...extraordinary. The officer in charge of the investigation pursued despite an official recall. I believe formal charges were brought against him for the expense."
"#emph[For the expen—!] " Jace sputtered.
"I don't know what her parents did," Gideon said, his mouth a hard line. "I don't much care, either. Whatever #emph[their] sins were, they had #emph[nothing] to do with Chandra." His eyes narrowed. "Is she impulsive? Sure. I'd be stupid not to say that. But her heart's the size of the moon."
Baan laced his fingers and rested his chin on them. "Mister Gideon, aether is in the very air we breathe. It is in the rain that falls to earth, and in the leaves of the trees. We only dare touch such power through the gloves of artifice; a million pieces of instrumentality, each safely performing its assigned function. By rigorous adherence to this method, we avoid 87.4% of the accidents provoked by mages drawing upon mana directly. If you will forgive me for saying so, pyromancers are particularly prone to...collateral damage." Baan inhaled slowly, fuchsia eyes darting around some image that only existed in his thoughts. "In the past, pyromancers have precipitated...terrible tragedies. Not always by their intent, but universally by their nature."
"So have you outlawed #emph[matches?] " Gideon asked, with a severity Nissa hadn't heard from him before.
Baan lowered his eyes. "May I assume, based upon your reactions, that <NAME> never spoke to you of this?"
"Not a word," Gideon said. He stared at his unfinished meal, one hand curling into a fist.
Jace looked at him sympathetically, "She didn't confide in #emph[any] of us."
Gideon shook his head slightly. "But she should have felt that she #emph[could] ."
"That was her choice to make. Not ours," Nissa murmured. She laid a fingertip along the rim of her bowl and slid it down, setting the pottery to ringing. "We all have scars we don't want others to touch."
Chandra had sat across from her, cheeks burning, twisting flower-stems around her fingers, asking for nothing more than a moment of peace. For something that could slow the frantic, bird-like stammer of her heart. But she'd moved the wrong way. Chandra had fluttered and flown.
"If I may inquire," Baan said, "Where do you suppose she might have gone? Surely she could not be so rash as to depart for Kaladesh."
Nissa looked up. Jace and Gideon were exchanging a look. Both glanced at her.
They stood as one.
Jace turned toward the coat room. "I'll head to Kaladesh. It should be easy for me to—"
Lavinia appeared in his path, one hand resting on the pommel her sword. "Again?" she said, in a weary, disappointed tone.
He frowned up at her. "You can't expect me to sit here and do paperwork!"
She nodded to Gideon and Nissa. "They can find <NAME>. They can't be the Guildpact."
Gideon laid a meaty hand on Jace's shoulder. "She's not wrong. Think of the bigger picture, Jace. I can take this one. Although," he winced, "I'm not looking forward to it. You know how she gets when someone tells her what to do..."
Kaladesh. Ghirapur. A city of brass and industry. Like Ravnica, a place that never slept, where the wind smelled of metal and cracking energies, and ceaseless tides of mortal faces buffeted to and fro. An ocean of strangers, gawping and whispering at her. Staring. Pointing. Shoving.
"I'll go." The words had flown before she'd thought them.
Gideon turned to her. "Are you sure?" His eyes drifted down to her trembling fingers. "Nissa, you don't have to go alone."
She balled her hands into fists, stilling them. "I #emph[will] go to Kaladesh. Baan can guide me. I'll..."
What?
Bring Chandra home? She #emph[was] home.
Get her out of trouble? She was a woman grown. She could do as she pleased.
Protect her? Chandra's heart was a baloth. She needed no champion.
"...I'll stand with her."
It felt right.
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https://github.com/Favo02-unimi/reti-di-calcolatori | https://raw.githubusercontent.com/Favo02-unimi/reti-di-calcolatori/main/Teoria/Dispensa.typ | typst | #import "@preview/gentle-clues:0.8.0": *
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#text(3em)[*Reti di calcolatori*]\
#text(1.5em)[Università degli studi di Milano - Informatica]
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_Reti di calcolatori_
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/ Autori: #link("https://github.com/Favo02")[<NAME>] _(indice)_, #link("https://github.com/???")[???] _(chi li finirà per Settembre???)_
/ Ringraziamenti: #link("https://github.com/LucaCorra02")[<NAME>] _(appunti)_, #link("https://github.com/michelebolis")[<NAME>] _(appunti)_, #link("https://github.com/alsacchi")[<NAME>] _(revisione)_
/ Sorgente e Licenza: #link("https://github.com/Favo02/reti-di-calcolatori")[github.com/Favo02/reti-di-calcolatori] (#link("https://creativecommons.org/licenses/by/4.0/")[CC-BY-4.0])
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= Introduzione
== Cos'è una rete
=== Commutazione
È la scelta di un percorso (inteso come linea di ingresso-uscita) al fine di inviare un messaggio.
==== Commutazione di circuito
==== Commutazione di messaggio
Il messaggio viene inviato per intero sulla rete.
Svantaggi:
- Il messaggio può raggiungere grandi dimensioni
- Difficile gestione nei nodi (ordine di instradamento, precendenze tra i messaggi)
- Difficoltà nell'allocare memoria data la variabilità della dimensione
- Se corrotto va reinviato interamente
==== Commutazione di pacchetto
Il messaggio viene inviato tramite pacchetti di dimensione standard.
Svantaggi:
- È necessaria una decomposizione e poi ricomposizione del messaggio
- Intestazioni ripetute su ogni pacchetto
- Tempo di arrivo e ordine non predicibile
=== Tipologie di rete
- LAN
- MAN
- WAN
=== Topologie di rete
- Reti magliate
- Reti broadcast
=== Commutazione
- Di messaggio
- A pacchetto
=== Rete affidabile
Per garantire affidabilità di una trasmissione è necessario soddisfare tre proprietà:
- ogni pacchetto deve essere *corretto*
- garantire l'*ordine originale* dei pacchetti
- *assenza* di pacchetti *duplicati*
È possibile utilizzare due approcci garantire affidabilità:
- ogni *coppia di nodi* rende affidabile il link che li collega
- i *nodi agli estremi* rendeono affidabile l'intera trasmissione
== Composizione di una rete
=== Dispositivi di rete
Porte PISO (Parallel In Serial Our) / SIPO (Serial In Parallel Out)
==== Hub (livello 1)
#informalmente[
Ripetitore stupido di quello che gli arriva da una porta a tutte le porte (broadcast)
]
==== Bridge (livello 2)
#informalmente[
Separa tipicamente due domini di collisione (le collisioni possono comunque avvenire nelle singole aree). È intelligente ed ha una tabella di forwarding
]
#nota[
Lavora in modo software
]
==== Switch (livello 2)
#informalmente[
Ogni porta (interfaccia) ha un suo dominio di collisione. È intelligente ed ha una tabella di forwarding
]
Tabella di forwarding:
- riceve qualcosa
- mittente
- già in tabella: non succede nulla
- non in tabella: aggiunge il suo MAC e la porta a cui è connesso
- destinataorio:
- già in tabella: manda il frame solo a quella porta
- non in tabella: manda in flooding a tutte le porte tranne la sorgente
#attenzione[
se un dispositivo non manda mai pacchetti (ma riceve e basta) non verrà mai associato il suo MAC alla sua porta
]
#nota[
Lavora in modo hardware, molto più efficiente di un bridge
]
==== Router (livello 3)
Ogni nodo della rete è un *router*, collegati tra loro attraverso dei *link*. Ogni router ha al suo interno almeno un'*interfaccia di rete*, a sua volta composta da *due code* (buffer): una d'ingresso e una d'uscita.
Il router funziona grazie a tre processi:
- *scheduler*: si occupa di gestire quando e quali messaggi esaminare
- *interprete*: esamina i messaggi e li passa al processo di routing
- *routing*: determina in quale coda d'uscita mandare il pacchetto, attraverso la consultazione delle *tabelle di routing* (instradamento)
=== Mezzi trasmissivi (cavi)
- Rame/Coassiale/Telefono: $2 dot 10^8 space b p s$
- Fibra: $3 dot 10^8 space b p s$
== Regole di una rete: protocolli
Un protocollo è un algoritmo distribuito, che organizza la comunicazione tra entità:
- realizza le *macchine a stati finiti* che governano le entità
- impone una *serie di convenzioni* sui messaggi scambiati
=== Modello ISO/OSI
- Livello 1: Fisico
- Livello 2: Data link
- Livello 3: Rete
- Livello 4: Trasporto
- Livello 5: Sessione
- Livello 6: Presentazione
- Livello 7: Applicazione
#informalmente[
Modello teorico non davvero usato
]
=== Stack TCP/IP
- Livello 1 (1+2 ISO/OSI): Data link
- Livello 2 (3 ISO/OSI): Rete
- Livello 3 (4 ISO/OSI): Trasporto
- Livello 4 (5+6+7 ISO/OSI): Applicazione
#informalmente[
Standard de facto
]
== Unità di misura
Utilizzeremo soprattutto $s$ (secondi), $b$ (bit) e $B$ (byte), con relativi multipli:
- $T$ tera: $10^12$
- $G$ giga: $10^9$
- $M$ mega: $10^6$
- $K$ kilo: $10^3$
- $m$ milli: $10^(-3)$
- $mu$ micro: $10^(-6)$
- $n$ nano: $10^(-9)$
= Livello 2: Data Link _(Livello 1 TCP/IP)_
Unità: frame
#informalmente[
Gestisce logicamente l'accesso al canale fisico (livello inferiore), evitando collisioni.
]
== Multiple Access Control (MAC)
#informalmente[
Parte "bassa" del livello: gestice l'accesso fisico al canale
]
=== Tempi di trasmissione
Tempi di accesso/scrittura al canale fisico
==== Velocità di trasmissione $V_x$ (banda/bitrate)
Misurato in $b p s$ (bit per second)
#informalmente[
Quanto velocemente si riesce ad "infilare" bit nel cavo
]
#nota[
Il clock è limitato dalla larghezza di banda
]
==== Tempo di trasmissione $t_x$
#informalmente[
Tempo che ci mettono i dati da mandare ad essere "inseriti" nel cavo
]
Misurato in $s$ (secondi):
$ t_x = N/V_x $
Dove $N$ è il numero di bit da inviare e $V_x$ è la banda (velocità di trasmissione) del cavo utilizzato
==== Velocità di propagazione $V_p$
Misurato in $m\/s$ (metri al secondo)
#informalmente[
Velocità alla quale il segnale (elettrico o luce) si propaga nel cavo
]
==== Tempo di propagazione $t_p$
#informalmente[
Tempo che ci mette il dato ad arrivare all'altra estremita del cavo
]
Misurato in $s$ (secondi):
$ t_p = L / V_p $
Dove $L$ è la lunghezza del cavo e $V_p$ è la velocità di propagazione
==== Rount trip time $R T T$
#informalmente[
Tempo che ci mette il dato ad *andare* e *tornare* al mittente
]
Misurato in $s$ (secondi):
$ R T T = 2 t_p $
==== Retrasmission timeout $R T O$
#informalmente[
Tempo prima di reinviare ancora un certo dato, tipicamente perchè non si è ricevuto un ACK
]
==== Efficienza della rete $U$
#informalmente[
Quanto il canale è occupato, ovvero se stiamo continuamente "infilando" dati nel canale o stiamo aspettando tanto tempo per la propagazione
]
Misura adimensionale, tra $0$ e $1$:
$ U = t_x / (t_x + 2 t_p) $
#attenzione[
Nei protocolli a finestra (con finestra $k$) diventa:
$ U = k dot t_x / (t_x + 2 t_p) $
]
==== Jitter
#informalmente[
Due pacchetti non possono metterci lo stesso tempo a viaggiare dato che la rete è complessa e possono accadere innumerevoli problemi. Il jitter è la varianza tra i vari tempi di trasmissione
]
==== Latenza
Tempo totale impegato dal pacchetto per essere spedito e ricevuto.
$ T = t_"coda" + t_"elaborazione" + t_"trasmissione" + t_"propagazione" $
- $t_"coda"$: (generalmente trascurabile) tempo di permanenza nella coda di invio
- $t_"elaborazione"$: (generalmente trascurabile) tempo impegato dal nodo per decidere come inoltrare il pacchetto
- $t_"trasmissione"$: $"dimensione pacchetto"/"bitrate"$ tempo necessario per trasferire i dati dal dispositivo al mezzo fisico
- $t_"propagazione"$: $"distanza"/"velocità mezzo"$ tempo che impega l'informazione ad arrivare da un capo all'altro del mezzo fisico
=== Codifiche
I dati quando vengono trasmessi sono codificati. La classica codifica è $1$ alto, $0$ basso.
==== Codifica di Manchester
#informalmente[
Viene trasferito anche il clock insieme ai dati, codifica autosincronizzante
]
==== Codifica Non Return to Zero Inverted (NRZI)
#informalmente[
$0$ mantiene lo stesso segnale che lo precedeva, $1$ lo inverte.
Si lavora sempre con cambi di fronte (come nella codifica Manchester)
]
=== Frammentazione
#informalmente[
Non è possibile mandare file interi, vengono frammentati in tanti frame (livello 2), pacchetti (livello 3) o segmenti (livello 4)
]
== Logical Link Layer (LLC)
#informalmente[
Gestione logica del livello, controllo di flusso ed errori
]
=== Livello 2 best-effort
#informalmente[
Ci prova a trasmettere senza errori, ma possono accadere e non vengono controllati o corretti
]
==== Character stuffing
#informalmente[
Differenziare caratteri di controllo da caratteri nel payload. Vengono aggiunti dei caratteri appositi (per disambiguare) quando nel payload si incontrano determinati caratteri riservati al controllo
]
- $"DELSTX" -> "Inizio frame"$
- $"DELETX" -> "Fine frame"$
Sostituisco tutti i $"DEL"$ singoli con:
- $"DEL" -> "DELDEL"$
#informalmente[
Quando leggo un DEL non susseguito da un altro DEL allora so che quello è controllo
]
==== Bit stuffing
#informalmente[
Stesso principio del character stuffing ma con i bit
]
Disambiguare $01111110$ da tanti $1$ nel payload:
- ogni cinque $1$ inserisco uno $0$
In lettura se leggo sei $1$ allora è la flag, altrimenti posso scartare lo $0$ dopo il quinto $1$.
=== Livello 2 affidabile: High-Level Data Link Control (HDLC) e (Point-to-Point) PPP
#informalmente[
Protocolli affidabili: controllano e correggono la perdita di messaggi, attraverso dei messaggi di ACK
]
Per fare ciò usano dei meccanismi come:
==== Idle RQ
#informalmente[
Fino a quando non ricevo un ACK per l'ultimo segmento mandato aspetto. Quando scade il timer di ritrasmissione ($R T O$) allora lo reinvio e aspetto ancora l'ACK
]
#nota[
Identificatori distinti: $1$
]
==== Protocolli a finestra (Continuous RQ)
#informalmente[
Mandano più frame prima di aspettare (non solo uno come Idle RQ)
]
#attenzione[
Cambia l'utilizzo del canale, dipende anche la finestra $k$
]
===== Go back-N
#informalmente[
Il mittende continua a mandare i $k$ frame successivi all'ultimo frame convalidato. Il destinatario scarta tutto ciò che è fuori sequenza
]
#nota[
Identificatori distinti: $k+1$
]
===== Selective repeat
#informalmente[
Il mittente manda $k$ frame. Il destinatario tiene in un buffer tutti i frame ricevuti (non duplicati), anche quelli fuori sequenza. Manda come ACK l'ultimo frame in sequenza, il mittente rimanderà solo il primo senza ACK, credendo che tutti gli altri siano stati ricevuti
#attenzione[
Se $k = 3$ e vengono persi i frame $2, 3$ allora il destinatario farà ACK di $1$, il mittente manderà solo $2$ e dopo l'ACK di $2$ allora manderà $3$. Questo perchè solo a finestra "completa" vengono mandati tutti, dopo ne manda solo quello "richiesto", essendo ottimista che gli altri siano ricevuti anche se fuori sequenza
]
]
#nota[
Identificatori distinti: $2k$
]
====== ACK selettivo
#informalmente[
Un ACK valida solo il frame specificamente validato
]
====== ACK cumulativo
#informalmente[
Un ACK valida tutti i frame minori o uguali al frame validato
]
#attenzione[
Spesso è conveniente usare un approccio misto: mittente Go back N, destinatario Selective repeat
]
== Reti broadcast
#informalmente[
Reti che comunicano mandando ogni frame a tutte le stazioni, poi solo il destinatario la terrà, gli altri scartano
]
=== Local Area Network (LAN)
IEEE 802.3
=== Virtual Local Area Network (VLAN)
IEEE 802.1Q
=== Accesso al canale: collisioni
#informalmente[
Se si usa un canale condiviso, possono avvenire delle collisioni: più stazioni trasmettono sullo stesso cavo e i dati si "schiacciano a vicenda", diventano illeggibili
]
==== Algoritmi deterministici
===== Round robin
#informalmente[
Viene dato un tot di tempo ad ogni stazione, molto inefficiente (anche se non hai da comunicare usi il tuo tempo)
]
===== Token-ring
#informalmente[
Solo chi ha il token può comunicare, se non hai nulla da dire fai girare il token velocemente. Prolemi:
- se il token si perde?
- se chi ha il token non lo cede più?
]
==== Algoritmi probabilistici
===== ALOHA
#informalmente[
Appena si ha da trasmettere si trasmette, se avviene una collisione si aspetta tempo randomico $t$ (calcolato basandosi su una Poisson). Non ci si ferma appena avviene una collisione ma si trasmette comunque tutto
]
Algoritmo *probabilistico* per gestire reti broadcast, cercando di limitare le collisioni.
Viene designato un _centro_, a cui tutti i dispositivi trasmettono, chiamato _satellite_. Il satellite ritrasmette in _maniera passiva_ a tutte le stazioni collegate ad esso.
Le regole del protocollo sono molto _banali_:
- Se hai dati da mandare, *mandali* _(*senza* controllare che nessun altro stia trasmettendo)_
- Se stai mandando dati e ricevi dati da un'altra stazione, allora c'è stata una collisione. Tutte le stazioni dovranno ritrasmettere *più tardi*
La parte importante del protocollo è il _"più tardi"_ in caso di collisioni, ovvero la parte _probabilistica_ dell'algoritmo, basato su delle assunzioni:
- tutti i frame hanno la stessa lunghezza
- tutte le stazioni hanno un solo frame da mandare alla volta _(non sono presenti code)_
- le stazioni che provano a trasmettere seguono una #link("https://en.wikipedia.org/wiki/Poisson_distribution")[distribuzione di Poisson]
Viene calcolato un *tempo randomico* $T$ _(sfruttando queste assunzioni)_ e viene riprovata la trasmissione.
L'efficienza dell'algoritmo ALOHA è calcolata del *18.4%*, ovvero solo il 18% del tempo totale è utilizzato per trasmissioni con successo.
===== Carrier Sense Multiple Access with Collision Detection (CSMA-CD)
#informalmente[
Si effettua CS: se il canale è vuoto si trasmette, altrimenti si aspetta.
Quando avviene una collisione, allora si interrompe subito la trasmissione e si aspetta tempo randomico che aumenta esponenzialmente (BEB, spiegato sotto) (per 15 volte, dopo si abortisce la comunicazione)
]
Protocollo (ormai obsoleto) utilizzato su ethernet non #link("https://en.wikipedia.org/wiki/Duplex_(telecommunications)")[full-duplex]. Permette una migliore efficienza rispetto all'ALOHA.
Funzionamento del protocollo:
- se il cavo non è _IDLE_, allora aspetta
- se il cavo è _IDLE_, allora inizia a trasmettere
- se avviene una collisione (quello che viene inviato è diverso da quello che si riceve), allora:
- trasmetti un segnare di JAM fino a garantire la grandezza minima del frame (garantire che tutte le stazioni rilevano la collisione)
- incrementa il _Retrasmission counter_
- se il _Retrasmission counter_ ha raggiunto il numero massimo di tentativi, allora annulla la trasmissione
- altrimenti, aspetta il tempo calcolato usando il _Random backoff period_ e riprova
Per garantire che tutte le stazioni rilevino la collisione, è necessario che il *tempo di trasmissione* sia maggiore di *due volte il tempo di propagazione* $t_x > 2 t_p$. Questo è garantito dallo standard *IEEE 802.3*, che impone dei vincoli sulla _lunghezza dei cavi_ (massimo 2500 metri) e la _grandezza dei frame_ (minimo 64 Byte).
#informalmente[
Per rilevare una collisione vengono confrontati i dati in _uscita_ con quelli in _entrata_. Questo è possibile solo se i dati _"di ritorno"_ (natura broadcast della rete) sono abbastanza veloci a tornare *prima* che l'*invio del frame sia finito*. Questo è descritto da: $ t_x > 2 t_p $
Di conseguenza, se il cavo è troppo lungo (o il frame è troppo piccolo), allora questo meccanismo non funziona, in quanto l'host non riscirà a capire se la frame che ha colliso fosse sua oppure no.
]
Una volta rilevata una _collisione_, allora gli host _aspettano_ generando un *tempo randomico di backoff*. Questo tempo è *esponenziale* rispetto al _numero di tentativi falliti_ (*retrasmission counter*).
- 1P: carrier sense persistente, appena si libera trasmetto
- 0P (termine non standard): carrier sense a intervalli randomici, se libero trasmetto, altrimenti aspetto tempo random
*Standard IEEE 802.3:*
- $10 M b p s$
- Grandezza minima frame: $t_x >= 51.2 mu s$, $64 B$
- Lunghezza cavo: $<= 2500 m$
- $1 G b p s$
- Grandezza minima frame: $t_x >= 512 n s$, $512 B$
- Lunghezza cavo: $<= 200 m$
====== Binary Exponential Backoff (BEB)
#informalmente[
Ogni volta che avviene una collisione si aspetta tempo random che aumenta in manieta esponenziale con l'aumentare delle collisioni. Alla 16 collisione si abortisce la comunicazione
]
= Livello 3: Rete _(Livello 2 TCP/IP)_
Unità: pacchetto
#informalmente[
Fanno comunicare delle sottoreti "distanti" che formano internet
]
== Addressing
#informalmente[
Fornire un indirizzo univoco ad ogni host presente in internet, in modo che è possibile comunicarci
#attenzione[
Non è del tutto vero, molto molto molto spesso tanti host hanno un unico IP pubblico (quello della LAN) e tanti IP privati
]
]
=== Internet Protocol Version 4 (IPv4)
==== Header pacchetto
#figure(caption: "Header pacchetto IP")[#image("imgs/ip-header.png", width: 80%)]
===== Frammentazione
Quando viene frammentato un dato in tanti pacchetti IP gli header importanti sono:
- *Identification (ID)*: identificatore (uguale in tutti i pacchetti che formano il dato diviso)
- *More fragments (MF)*: se ci sono altri frammenti dopo il corrente
- *Fragment offset*: quando è spostato il frammento corrente rispetto al totale del dato (vengono contati 8 Byte alla volta)
- *Total size*: grandezza totale del dato da trasmettere
- *Payload size*: grandezza del payload di questo pacchetto
==== Subnet mask
#informalmente[
Separa la parte che identifica la rete da quella che identifica gli host, maschera binaria di 32 bit
]
==== Suddivisione indirizzi pubblici
===== Classi NetID
#informalmente[
Classi "statiche" con numero di host fissi
]
- Classe A: 8 bit di subnet mask
- Classe B: 16 bit di subnet mask
- Classe C: 24 bit di subnet mask
- Classi D ed E: riservate per scopi speciali
===== Classless Inter-Domain Routing (CIDR)
#informalmente[
Il numero di bit di rete non è più per forza 8, 16 o 24 ma può essere qualsiasi numero. Si indica con \<IP>/\<numero di 1 nella subnet>, ad esempio 172.16.58.3/23
]
==== Suddivisione indirizzi privati: subnetting
#informalmente[
È possibile suddividere la parte privata di una rete in tante altre sottoreti, effettuando del subnetting
]
==== Comunicazione
===== Network Address Translation (NAT)
#informalmente[
Serve per limitare l'uso di IPv4, ogni rete ha un solo IP pubblico e tanti privati. Traduce le richieste effettuate dall'interno della rete da IP privato a IP pubblico.
#attenzione[
Per fare ciò ha bisogno anche di informazioni di livello 4, ovvero la porta
]
]
Formato tabella:
- IP sorgente
- Porta sorgente
- IP destinazione
- Porta destinazione
- Porta NAT
===== Address Resolution Protocol (ARP / RARP)
#informalmente[
All'interno di una LAN è necessario parlare a livello 2, quindi utilizzano i MAC address (non IP). ARP serve per tradurre un indirizzo IP ad un indirizzo MAC, inviando una richiesta il broadcast
]
- Se in ARP cache: allora si ha già il MAC
- Altrimenti si manda in broadcast una richiesta con:
- IP dell'host di cui ci serve il MAC
- Nostro IP
- Nostro MAC
- L'host che stiamo cercando risponde al nostro MAC con suo il MAC
#attenzione[
La cache ARP ha un timeout, scadono le entry
]
#informalmente[
RARP fa la stessa cosa ma al contrario, dato un MAC restituisce un IP (molto molto poco usato)
]
===== Dynamic Host Configuration Protocol (DHCP)
#informalmente[
Quando un host di connette ad una rete non ha (ancora) un IP (privato), qualcuno glielo deve fornire, questo qualcuno è il server DHCP
#attenzione[
Ce ne possono essere più di uno in una rete
]
]
- Discover: il dispositivo manda in broadcast (src: 0.0.0.0, dst: 255.255.255.255) una richiesta con un certo transaction ID
- Offer: i server DHCP rispondono in broadcast (ma con stesso transaction ID) offrendo un IP
- Request: il dispositivo (sempre con src 0.0.0.0 e dst 255.255.255.255) ne accetta una
- ACK: il server risponde in broadcast con ACK, da questo momento il client ha un IP
===== Internet Control Message Protocol (ICMP)
#informalmente[
Informazioni di controllo del flusso di internet, ad esempio segnalazione problemi, congestione o ping
]
=== Internet Protocol Version 6 (IPv6)
#informalmente[
Nuova versione del protocollo, con molti (mooolti) più indirizzi disponibili di IPv4 (128 bit), questi non finiscono
]
==== Header pacchetto
#figure(caption: "IPv6 header")[#image("imgs/ipv6-header.png", width: 60%)]
#informalmente[
Sono stati snelliti di molto gli header, ora sono come una lista concatenata, il next header punta ad un campo opzionale che può essere presente tra la fine degli header ed il payload. A sua volta ogni next header può puntare ad un successivo, fino all'ultimo che fa da "tappo"
]
===== Source routing (esatto ed approssimato)
#informalmente[
Il source routing permette di far viaggiare il pacchetto seguendo un percorso prestabilito (e non deciso dai router)
- esatto: vengono specificati tutti i router da cui passare (tramite header opzionali)
- approssimato: vengono specificati solo alcuni punti chiave (tramite header opzionali)
]
Certo, ecco dei rapidi riassunti per ogni header:
===== Source routing (esatto ed approssimato)
#informalmente[
Il source routing permette di specificare il percorso esatto che un pacchetto deve seguire attraverso la rete, piuttosto che lasciare che i router decidano il percorso.
- *Esatto:* Viene definito ogni singolo router attraverso cui deve passare il pacchetto (tramite header opzionali).
- *Approssimato:* Vengono definiti solo alcuni punti chiave del percorso (tramite header opzionali).
]
===== Frammentazione
#informalmente[
A differenza di IPv4, la frammentazione può avvenire solo al nodo sorgente e NON lungo il percorso (cosa fatitbile il IPv4). Questo scarica overhead dai router lungo il cammino, ma non permette al pacchetto di passare da link il cui MTU (Maximum Trasmissiun Unit) è maggiore della grandezza del pacchetto
#nota[
Vengono mandati dei pacchetti MTU discoveri attraverso ICMP per sapere se un pacchetto può passare o meno
]
]
==== Compatibilità con IPv4
Soluzioni:
- *Tunneling*: incapsulare pacchetto IPv6 in un pacchetto IPv4, ad esempio per connettere reti IPv6 isolate
- *Dual stack*: dispositivi che hanno sia un'interfaccia IPv4 che IPv6 in modo da poter comunicare con entrambi i protocolli
- *NAT*: utilizzo di NAT che trasformano indirizzi IPv4 in IPv6 o viceversa per far comunicare reti che utilizzano protocolli diversi
== Routing
#informalmente[
Instradare i pacchetti per raggiungere la loro destinazione, facendo possibilmente il percorso migliore (numero di HOP o tempo)
]
=== Distance Vector (DV)
#informalmente[
- Gli host mantengono una tabella con:
- Nodo da raggiungere
- Distanza
- Primo HOP per raggiungerlo
- Ogni tot tempo viene propagato questo Distance vector (SOLO nodo + distanza, senza link utilizzato) ai propri adiacenti
- Gli adiacenti aggiornano le distanze
]
==== Trigger update
#informalmente[
Al posto di aspettare che scada il timer e poi propagare, viene propagato appena c'è un cambiamento
#attenzione[
Non risolve il count to infinity o l'effetto bouncing in quanto il pacchetto si può perdere
]
]
==== Problematiche
===== Count to infinity ed Effetto bouncing
#informalmente[
Dato che non viene propagato quale link si usa per raggiungere un nodo, allora se ad esempio di rompe un link e si perde il pacchetto che aggiorna in negativo, allora si forma un circolo vizioso dove l'adiacente comunica al nodo su cui si è rotto il link che in realtà è raggiungbile, senza accorgersi che passa attraverso di lui (quindi si inizia a rimbalzare e si arriva a distanza infinita)
]
===== Split Horizon
#informalmente[
Si condivide sul link che si vuole utilizzare distanza infinita, in modo da non poter causare problemi
]
==== Routing Information Protocol (RIP)
#informalmente[
Usa i distance vector
]
=== Link State (LS)
#informalmente[
Ogni nodo condivide con tutto il resto della rete (in flooding) le informazioni sui suoi adiacenti, in modo che ogni nodo della rete potrà avere un idea chiara di tutta la rete (ognuno costruisce il grado completo) ed ognuno può calcolare il percorso migliore.
Vengono aggiunti anche gli ACK e i sequence number, per evitare che le informazioni di un nodo arrivino ad un altro attraverso percorsi diversi e continuino a viaggiare all'infinito
]
==== Open Shortest Path First (OSPF)
#informalmente[
Usa i Link state
]
==== Spanning tree broadcast
=== Path Vector
#informalmente[
Simile ai distance vector, ma è presente tutta la path che deve percorrere, per evitare di causare problemi come il count to infinity. Ogni nodo condivide con i suoi adiacenti tutto il percorso per raggiungere altri nodi
]
==== Border Gateway Protocol (BGP)
#informalmente[
Usa i Path vector
]
=== Multi Packet Label Switching (MPLS)
#informalmente[
Per aumentare l'efficienza, spesso nelle aree0 e grandi reti, al posto che fare routing IP si effettua routing basato su etichette.
I router agli estremi dell'area incapsulano il pacchetto in dei pacchetti apposta dotati di un'etichetta. I router interni alla rete in base all'etichetta e alla porta in ingresso, smistano il pacchetto cambiando etichetta e porta in uscita
#nota[
I router agiscono come dei grandi switch, senza aprire il pacchetto IP e calcoalre il percorso. Molto efficiente
]
]
=== Architettura ottimizzata
==== Autonomous system (AS)
#informalmente[
Grandi reti gestite da una singola organizzazione (spesso internet service provider ISP), ed utilizzano una certa politica di routing.
Tanti AS sono connessi tra loro attraverso la internet backbone formano tutta internet. Vengono etichettati da IANA (Internet Assigned Numbers Authority)
]
==== Designated router e Software Defined Network (SDN)
#informalmente[
Spesso, in grandi reti, sono presenti dei router designati a calcolare i percorsi migliori e comunicarli, centralizzando le operazioni di calcolo.
Quando questa funzione è spostata in cloud (per evitare singolo punto di failure e garantire maggiore affidabilità) si parla di Software defined network
]
== Schedulazione e priorità: Quality of Service (QoS)
#informalmente[
In base ai servizi utilizzati, alcuni pacchetti possono avere una priorità maggiore rispetto ad altri (come streaming rispetto ad email).
Per assecondare queste richieste, esiste la Quality of Service, che staibilisce appunto una priorità ai vari pacchetti, che viene comunicata ai router (che attuano delle politiche per adattarsi)
]
=== Weighted Fair Queuing (WFQ)
#informalmente[
Un router possiede più code, ognuna con un certo peso. I pacchetti in ingresso vengono distribuiti sulle varie code in base alla loro priorità e viene assegnata ad ogni pacchetto una quantità di banda proporzionale in base alla priorità di quella coda
]
=== Call Admission
#informalmente[
Quando tanti pacchetti al alta priorità devono viaggiare (come in una chiamata VoIP), allora viene effettuata una Call Admission: viene controllato se sono presenti abbastanza risorse per gestire questa call.
Se queste risorse sono presenti la call viene avviata, altrimenti viene rifiutata
]
=== Token Bucket
#informalmente[
Limita il numero di pacchetti che possono viaggiare:
- vengono generati ad intervallo costante dei token
- quando arriva un pacchetto controlla se sono presenti sufficienti token per passare
- in caso positivo li preleva e passa
- altrimenti viene scartato o viene messo in coda fino a quando non sono presenti abbastanza token
]
=== Tail drop e Random Early Detection (RED)
#informalmente[
Tail drop:
- quando c'è spazio nella coda di un router allora viene ammesso tutto
- quando la coda è piena viene droppato tutto
Random early detection:
- quando si è sotto una certa soglia minima: viene accettato tutto
- quando si è sopra una certa soglia massima: viene droppato tutto
- quando si è tra le due soglie: alcuni pacchetti random vengono droppati (proporzionalmente a quanto è piena la coda)
]
= Livello 4: Trasporto _(Livello 3 TCP/IP)_
Unità: fragment
== Transmission Control Protocol (TCP)
#informalmente[
Protocollo affidabile, stabilisce una connessione logica
]
=== Header e Pseudoheader TCP
#figure(caption: "Header TCP")[#image("imgs/tcp-header.png", width: 70%)]
#informalmente[
Il pacchetto viaggia da un IP:porta ad un altro IP:porta, ma gli IP sono già nel pacchetto IP, inutile duplicarli nell'header TCP.
Però il checksum viene effettuato anche andando ad estrarre i dati dal pacchetto IP, prendendo il nome di pseudoheader
]
=== Fasi della connessione
- Apertura
- Comunicazione
- Chiusura
==== Apertura: three way handshake
#figure(caption: "Header TCP")[#image("imgs/tcp-apertura.png", width: 60%)]
==== Comunicazione
#informalmente[
Scambio di dati tra i due host
]
===== Controllo del flusso
====== Window Size $W_s$
#attenzione[
Viene chiamata anche _Advertised window_
]
#informalmente[
La finestra di ricezione viene negoziata tra il client ed il server quando viene stabilita la connessione.
#nota[
In realtà è scelta dal server e comunicata
]
È quanto spazio il server ha disponibile per ricevere dati. Inizialmente sarà grande come la grandezza del buffer, mano a mano che riceve dati si riduce, comunicandolo al client.
#attenzione[
In realtà entrano in gioco altri controlli e va gestista anche la *congestione*
]
#nota[
Quando è grande più di 1MSS, allora significa che il client può mandare più segmenti senza aspettare il relativo ACK prima di mandarne di nuovi (protocollo a finestra)
]
]
====== Persistent timer
#informalmente[
Salvaguarda il client.
In caso che il client riceva una $W_s = 0$, allora deve aspettare fino ad una nuova notifica di finestra più grande per poter mandare dati. Ma se questo pacchetto si perde?
Allora il client fa partire un timer, quando scade manda un _*Window probe*_ al server, richiedendo esplicitamente al server l'ACK
#nota[
In caso il server non risponda ai window probe viene chiusa la connessione
]
]
====== Keep alive timer
#informalmente[
Salvaguarda il server.
In caso il server non riceva nulla per un timer di tempo, allora manda un _*Keep alive probe*_ per controllare che il client non si sia disconnesso senza comunicarlo (ad esempio spento il PC). Se non risponde dopo un numero di probe, allora chiude la connessione
]
====== Silly Window Syndrome
#informalmente[
Quando un estremo della connessione TCP è molto lento a produrre/consumare i dati da inviare/ricevuti, allora si avrà un graduale restringimento della finestra e l'invio di segmenti sempre più piccoli, causando un utilizzo inefficiente del canale.
#attenzione[
Può avvenire in entrambi i sensi, sia con client veloce e server lento che viceversa. In base al caso si utilizzano due soluzioni diverse _(descritte sotto)_
]
]
======= Algoritmo di Clark
Caso in cui il consumatore (server) è molto lento a leggere i dati dal buffer.
#informalmente[
Il server è molto lento, quindi il buffer si svuota molto lentamente (ad esempio 1B alla volta). Per evitare di mandare tantissimi ACK con Window size minuscole (cresce di solo 1B), allora viene adottata la soluzione di Clark:
si aspetta a mandare una nuova Window size fino a quando non è almeno:
$ min(1/2 "bufferSize", "MSS") $
#nota[
MSS = Maximum Segment Size, la grandezza massima di un singolo segmento che può transitare sulla rete
]
]
======= Algoritmo di Nagle (Delayed ACK)
Caso in cui il produttore (client) è molto lento a produrre dati.
#informalmente[
Il client è molto lento a produrre dati, ad esempio produce un byte alla volta (ad esempio una connessione netcat, ogni carattere premuto).
Il problema è quindi mandare tanti piccoli messaggi con tanto overhead (20B IP + 20B TCP) per pochissimo payload (1B). La soluzione è usare l'algoritmo di Nagle e il *Timer di piggybacking*.
Il server quando gli arriva un solo segmento più piccolo rispetto al MSS e alla Window size, allora aspetta o la ricezione di altri messaggi o un timer (di piggybacking) prima di mandare l'ACK.
In questo tempo di "attesa" i messagi sul client si accumuleranno, mandando un unico frammento più grande
]
===== Gestione degli errori
#informalmente[
Quando vengono persi degli ACK o dei fragment
]
====== Retrasmission Timeout (RTO)
#informalmente[
Come a livello 2 affidabile, quando viene mandato un messaggio si fa partire un timer (RTO), se non arriva un ACK prima della fine del timer, allora viene rimandato lo stesso messaggio
]
======= Calcolo RTO
#nota[
- RTT = Sampled rount trip time
- Var = Varianza RTT
- SRTT = Smoothed RTT
]
Tempo 0:
- RTO = 3 sec (da RFC è stato modificato a 1 sec)
Tempo 1:
- $S R T T = R T T$
- $R T T"Var" = (R T T) / 2$
- $R T O = S R T T + 4 dot R T T"Var"$
Tempo 2 o più:
- $S R T T = (1 - alpha) S R T T_"old" + alpha R T T$
- $R T T"Var" = (1 - beta) R T T"Var"_"old" + beta |R T T - S R T T_"old"|$
- $R T O = S R T T + 4 dot R T T"Var"$
======= Retransmission ambiguity: politica di Karn
#informalmente[
Se viene perso un messaggio e scatta l'RTO, allora viene rimandato lo stesso messaggio. Il tempo di ritorno dell'ACK (RTT) deve venir usato per calcolare il prossimo RTO.
Ma come faccio a sapere se l'ACK che ho ricevuto è solo stato molto lento ma del primo segmento che ho mandato o se si era perso e quindi l'ACK è del secondo segmento?
Non viene scelto nessuno dei due, viene usata la *politica di Karn*, semplicemente il nuovo RTO è dimezzato:
$ R T O = (R T O_"old") / 2 $
]
====== Fast retrasmission
#informalmente[
Abbiamo detto che un segmento è rimandato quando scatta il suo RTO. Ma se stiamo mandando tanti segmenti alla volta e riceviamo tanti ACK cumulativi duplicati vuol dire che tanti segmenti fuori sequenza sono stati ricevuti.
Quindi il problema non è la lentezza della rete, ma è molto probabile se si sia perso (dato che gli altri sono stati ricevuti), quindi è inutile aspettare il timer di RTO ma possiamo rimandare subito il segmento. Questo meccanismo scatta con 3 ACK cumulativi duplicati
#nota[
Fast retrasmit perchè appunto non aspetta lo scadere dell'RTO ma rimanda prima
]
]
====== Timestamp
#informalmente[
All'interno dell'header TCP vengono inseriti dei timestamp, in modo che non si possano creare ambiguità (Retrasmission ambiguity) e sia più facile calcolare RTT (sottrazione tra timestamp invio e tempo alla ricezione)
]
===== Controllo della congestione: finestra di congestione $W_c$
#informalmente[
Non basta gestire la finestra che il server può ricevere (window size), bisogna anche tenere conto della congestione della rete.
Per fare ciò si utilizza la finestra di congestione, che è sempre limitata superiormente dalla window size.
Si inizia con una finestra di congestione piccola e la sin ingrandisce fino a quando non ci sono dei problemi (o si raggiunge la Window size)
]
====== Slow start
#informalmente[
Si inizia mandano poco alla volta: di solito 1MSS.
Per ogni ACK ricevuto allora si ingrandisce la finestra di 1, effettivamente *duplicando* la grandezza della finstra ogni volta.
$ C_w = 2 dot C_w $
Questo avviene fino al ragguingimento della *Slow Start Treshold (SST)*
]
====== Congestion avoidance
#informalmente[
Si inizia a rallentare: per ogni finestra completa tutta validata (non per ogni segmento, per ogni finestra completa) si *aumenta di 1* la grandezza della finestra, effettivamente facendo crescere linearmente la finestra
$ C_w = 1 + C_w $
]
====== Fase costante
#informalmente[
Quando si raggiunge la Window size allora non si può più aumentare (ovviamente), quindi si continua in modo costante (se non ci sono errori ovviamente)
$ C_w = C_w $
]
#figure(caption: "Slow start treshold")[#image("imgs/congestion-window.png", width: 80%)]
====== Errori
In caso avvengano degli errori:
- Fast retrasmit:
- $S S T = C_w / 2$
- $C_w = S S T_"new"$
#figure(caption: "Errore: fast retrasmit")[#image("imgs/congestion-window-fast-retrasmit.png", width: 80%)]
- Scadenza del timer RTO:
- $S S T = C_w / 2$
- $C_w = 1 M S S$
#figure(caption: "Errore: scandeza RTO")[#image("imgs/congestion-window-rto.png", width: 80%)]
==== Chiusura
#informalmente[
La chiusura è asimmetrica, ovvero uno dei due host comunica la chiusura quando l'altro può ancora star comunicando/ha ancora da comunicare
]
===== Four way close
Viene usata la primitiva `close()`
#informalmente[
Chiusura da standard completa senza problemi, entrambi accettano la fine e nessuno dei due ha da trasmettere
]
#figure(caption: "TCP 4 way close")[#image("imgs/tcp-four-way-close.png", width: 40%)]
===== Three way close
Viene usata la primitiva `close()`
#informalmente[
Il client chiede la chiusura ma il server ha ancora degli ACK da mandargli, quindi viene accorpato in un unico messaggio gli N ack mancanti, l'ACK del FIN e il FIN (quindi le due freccie centrali del grafico sono unite)
#attenzione[
Client e server sono interscambiabili, uno ha ancora ACK da mandare mentre l'altro chiude la connessione
]
]
===== Half close
Viene usata la primitiva `shutdown()`
#informalmente[
Il client chiede di chiudere la connessione ma il server vuole ancora inviare dati
]
#figure(caption: "TCP Half close")[#image("imgs/tcp-half-close.png", width: 80%)]
== User Datagram protocol (UDP)
= Livello 7: Applicazione _(Livello 4 TCP/IP)_
== Domain Name System (DNS)
=== Risoluzione iterativa
=== Risoluzione ricorsiva
== File Transfer Protocol (FTP)
== Hyper Text Transfer Protocol (HTTP)
Versione in-band (sia controllo che dati su un'unica connessione TCP) del FTP
https://www.digitalocean.com/community/tutorials/http-1-1-vs-http-2-what-s-the-difference
=== HTTP/1.0
=== HTTP/1.1
==== Pipelining e Head-of-Line Blocking
==== Resource Inlining
=== HTTP/2
==== Streams
==== Server push
==== Compressione
=== HTTP/3
==== QUIC (over UDP)
=== HTTPS
== Email
=== User Agent (UA)
=== Message Transfer Agent (MTA)
=== Invio: Simple Mail Transport Protocol (SMTP)
=== Ricezione
==== Internet Message Access Protocol (IMAP)
==== Post Office Protocol (POP 3)
=== Codifica Base64
== Content Delivery Network (CDN)
== Dynamic Adaptive Streaming over HTTP (DASH)
== Session Initiation Protocol (SIP) e Voice over IP (VoIP)
// numerazione appendici
#set heading(numbering: "A.1.")
#counter(heading).update(0)
= Lista acronimi
/ AS: Autonomous System
/ BEB: Binary Exponential Backoff
/ BGP: Border Gateway Protocol
/ CIDR: Classless Inter-Domain Routing
/ CSMA-CD: Carrier Sense Multiple Access with Collision Detection
/ DASH: Dynamic Adaptive Streaming over HTTP
/ DHCP: Dynamic Host Configuration Protocol
/ DNS: Domain Name System
/ DV : Distance Vector
/ FQDN: Fully Qualified Domain Name
/ FTP: File Transfer Protocol
/ HDLC: High-Level Data Link Control
/ HTTP: Hyper Text Transfer Protocol
/ HTTPS: Hyper Text Transfer Protocol Secure
/ IANA: Internet Assigned Numbers Authority
/ ICMP: Internet Control Message Protocol
/ IMAP: Internet Message Access Protocol
/ IP: Internet Protocol
/ IPv4: Internet Protocol Version 4
/ IPv6: Internet Protocol Version 6
/ ISP: Internet Service Provider
/ LAN: Local Area Network
/ LLC: Logical Link Control
/ LS: Link State
/ MAC: Multiple Access Control and Media Access Control
/ MAN: Metropolitan Area Network
/ MPLS: Multi Packet Label Switching
/ MSS: Maximum Segment Size
/ MTA: Message Transfer Agent
/ MTU: Maximum Transmission Unit
/ NAT: Network Address Translation
/ NRZI: Non Return to Zero Inverted
/ OSPF: Open Shortest Path First
/ PISO: Parallel In Serial Out
/ POP3: Post Office Protocol
/ PPP: Point-to-Point Protocol
/ QoS: Quality of Service
/ RED: Random Early Detection
/ RIP: Routing Information Protocol
/ RARP: Reverse Address Resolution Protocol
/ RTD: Round Trip Delay
/ RTO: Retrasmission Timeout
/ RTT: Round Trip Time
/ SDN: Software Defined Network
/ SIPO: Serial In Parallel Out
/ SIP: Session Initiation Protocol
/ SMTP: Simple Mail Transfer Protocol
/ SNMP: Simple Network Management Protocol
/ SST: Slow Start Threshold
/ TCP: Transmission Control Protocol
/ UA: User Agent
/ UDP: User Datagram Protocol
/ VLAN: Virtual Local Area Network
/ VoIP: Voice over IP
/ WAN: Wide Area Network
/ WFQ: Weighted Fair Queuing
= Esercizi
- Massimizzare grandezza finestra:
- calculare $U$ (senza $k$)
- trovare $k$ che lo fa avvicinare a $1$
- _parte non sicura, non è detto che serva_: questo $k$ è rappresentabile con dei bit (quindi a potenza di 2)?:
- in base a se è gobackn ($N+1$) o selective repeat ($2N$), allora capire quanti indentificati diversi servono
- se il numero di identificatori è multiplo di 2 allora ok, altrimenti spiegare perchè si sprecherebbero dei bit
- Calcolare grandezza minima frame:
- imporre $t_x > 2t_p$
- sostituire $t_x$ con $N / "banda"$
- isolare $N$ e risolvere
- in caso ci siano ripetitori che danno aggiungono ritardo, sommarli a $t_p$
- Esercizi in generali sui tempi di propagazione:
- sostituire tutti i dati che abbiamo e isolare l'incognita
- Frammentare un pacchetto IP in modo che possa passare da una LAN ethernet
- massima dimensione per rete ethernet: 1500B (1480 payload + 20 header IP)
- header importanti:
- identification: uguale in tutti i nuovi pacchetti
- more fragments: tutti a 1 tranne l'ultimo
- fragment offset: somma dei pacchetti precedenti / 8 (è un offset a gruppi di 8 Byte
- payload size: grandezza totale prima di essere frammentato
- fragment size: grandezza del payload di questo pacchetto
|
|
https://github.com/npujol/npujol.github.io | https://raw.githubusercontent.com/npujol/npujol.github.io/main/Me/chuli-cv/cv-es.typ | typst | #import "@local/chuli-cv:0.1.0": *
#import "@preview/fontawesome:0.1.0": *
#show: cv
#let icons = (
phone: fa-phone(),
homepage: fa-home(fill: colors.accent),
linkedin: fa-linkedin(fill: colors.accent),
github: fa-github(fill: colors.accent),
xing: fa-xing(),
mail: fa-envelope(fill: colors.accent),
book: fa-book(fill: colors.accent),
cook: fa-utensils(fill: colors.accent),
bike: fa-biking(fill: colors.accent),
game: fa-gamepad(fill: colors.accent),
robot: fa-robot(fill: colors.accent),
bed: fa-bed(fill: colors.accent),
write: fa-pen-to-square(fill: colors.accent),
talk: fa-comments(fill: colors.accent),
code: fa-code(fill: colors.accent),
paint: fa-paintbrush(fill: colors.accent),
music: fa-music(fill: colors.accent),
friends: fa-users(fill: colors.accent),
beer: fa-beer(fill: colors.accent),
)
#header(
full-name: [<NAME>],
job-title: [Ingeniera de Software],
socials: (
(
icon: icons.github,
text: [npujol],
link: "https://github.com/npujol"
),
(
icon: icons.mail,
text: [<EMAIL>],
link: "mailto://<EMAIL>"
),
(
icon: icons.linkedin,
text: [<NAME>],
link: "https://linkedin.com/in/npujolm/"
),
(
icon: icons.homepage,
text: [Berlin, Alemania],
link: "#"
),
),
profile-picture: image("media/avatar.jpeg")
)
#show: body => columns(2, body)
#section("Experiencia Profesional")
#entry(
title: "Desarrolladora de Software",
company-or-university: "InterContent Group",
date: "2021 - Today",
location: "Berlin, Germany",
logo: image("media/intercontent.jpeg"),
description: list(
[Desarrollo de aplicaciones web con Django y Golang],
[Desarrollo de APIs RESTful con Python y Django],
[Desarrollo de APIs GraphQL con Python y Django],
[Desarrollo de APIs GraphQL con GraphQL-Playground y React],
[Desarrollo de APIs GraphQL con Apollo-Client y React],
[Desarrollo de APIs GraphQL con Apollo-Server y React],
[Desarrollo de APIs GraphQL con Hasura y React],
[Desarrollo de APIs GraphQL con GraphQL-Playground y React],
[Desarrollo de APIs GraphQL con Apollo-Client y React],
[Desarrollo de APIs GraphQL con Apollo-Server y React],
[Desarrollo de APIs GraphQL con Hasura y React]
)
)
#entry(
title: "Especialista en ciencias informáticas",
company-or-university: "Universidad de las Ciencias Informáticas",
date: "2014 - 2019",
location: " La Habana, Cuba",
logo: image("media/universidad_de_las_ciencias_informaticas_logo.jpeg"),
description: list(
[Desarrollo del sitio de gestión de actividades de posgrado de la universidad. Utilizando Python, Django, PostgreSQL, RESTful WebServices],
[Testing of websites following the TDD process and according to the planned schedules],
[Identificación de los problemas descubiertos por las pruebas o por los comentarios de los clientes, y la corrección de los problemas o la remisión de los mismos al personal apropiado para su corrección],
[Automatización de las tareas de limpieza de datos y identificación de errores utilizando Celery y Redis],
[ Análisis de datos, búsqueda de patrones, y desarrollo de predicción utilizando Jupyter, scikit-learn, NumPy y Pandas]
)
)
#section("Educación")
#education-entry(
title: "Máster en Informática Avanzada",
company-or-university: "Universidad de las Ciencias Informáticas",
date: "05/2016 - 12/2018",
location: "La Habana, Cuba",
logo: image("media/universidad_de_las_ciencias_informaticas_logo.jpeg"),
gpa: "4.82",
gpa-total: "5.0"
)
#education-entry(
title: "Ingeniería en Ciencias Informáticas",
company-or-university: "Universidad de las Ciencias Informáticas",
date: "09/2009 - 07/2014",
location: "La Habana, Cuba",
logo: image("media/universidad_de_las_ciencias_informaticas_logo.jpeg"),
gpa: "4.71",
gpa-total: "5.0"
)
#section("Proyectos Personales")
#entry(
title: "anki_wiktionary",
company-or-university: "Personal Project",
date: "2020 - 2024",
location: "",
logo: image("media/github_avatar.jpeg"),
description: list(
[Desarrollado un proyecto para importar datos de Wiktionary y crear una baraja de Anki, para aprender nuevas palabras de una manera más eficaz],
[Usando Python, Beautiful Soup, y Anki API para crear el proyecto],
[Implementacion de funciones como buscar palabras, añadir nuevas palabras, eliminar palabras y actualizar palabras existentes],
[Desarrollado un bot de telegram para ser utilizado para obtener nuevas tarjetas de anki],
[Integrado con APIs externas para proporcionar recursos y orientación para el apoyo a la salud mental basado en las respuestas de los usuarios]
)
)
#entry(
title: "tts_stories",
company-or-university: "Personal Project",
date: "2021 - 2024",
location: "",
logo: image("media/github_avatar.jpeg"),
description: list(
[Desarrollado un proyecto para crear historias de voz de una manera más eficaz],
[Usando diferentes fuentes de procedencia de las historias, tanto online como local],
[Desarrollado un bot de telegram para ser utilizado para salvar las historias de voz generadas]
)
)
#section("Habilidades e Intereses")
#skill(
skills: ("python", "django", "terraform", "golang", "aws", "azure", "devops", "docker", "javascript", "postgresql", "celery", "redis", "github actions", "yaml", "latex", "pandas", "pydantic", "git", "linux", "postman", "sentry", "bash", "typst"),
)
#section("Idiomas")
#language(
name:"Español",
label:"Nativo",
nivel:5,
)
#language(
name:"Alemán",
label:"Medio",
nivel:3,
)
#language(
name:"Inglés",
label:"Medio",
nivel:3,
)
#section("Mi tiempo libre")
#piechart(
activities: (
(
name: icons.friends,
val: 0.01
),
(
name: icons.book,
val: 0.01
),
(
name: icons.talk,
val: 0.01
),
(
name: icons.code,
val: 0.01
),
(
name: icons.robot,
val: 0.009
),
(
name: icons.music,
val: 0.009
),
(
name: icons.game,
val: 0.008
),
(
name: icons.write,
val: 0.008
),
(
name: icons.bike,
val: 0.007
),
(
name: icons.cook,
val: 0.007
),
(
name: icons.paint,
val: 0.003
),
(
name: icons.beer,
val: 0.002
)
)
) |
|
https://github.com/rxt1077/otc-2024 | https://raw.githubusercontent.com/rxt1077/otc-2024/main/success.typ | typst | #import "@preview/polylux:0.3.1": *
#import themes.bipartite: *
#show: bipartite-theme
#show link: it=> {
set text(blue)
underline(it)
}
#set text(size: 25pt)
#let cc-image(file: none, title: none, url: none, author: none, width: 50%) = [
#align(center, [
#block(width: width, below: 5pt, [
#image(width: 100%, file)
])
#text(8pt, [
#link(url)["#title"] by #author is licensed under #link("https://creativecommons.org/licenses/by/2.0/?ref=openverse")[CC BY 2.0.]
])
])
]
#let fairuse-image(file: none, title: none, url: none, width: 50%) = [
#align(center, [
#block(width: width, below: 5pt, [
#image(width: 100%, file)
])
#text(8pt, [
#link(url)[#title] is used under fair use
])
])
]
#title-slide(
author: [<NAME>],
title: [Computer Systems Security],
subtitle: [A Success Story],
date: [2024-09-27],
)
#split-slide[
#align(center, [
What is the project?
#image("cover.svg")
])
][
- An undergraduate, introductory cybersecurity textbook
- #link("https://web.njit.edu/~rt494/security")[Computer Systems Security: Planning for Success]
- #link("https://researchguides.njit.edu/opentextbooks")[NJIT OER Grant] for scope and sequence
- #link("https://opennj.net/otc")[OTC Grant] for the book itself
]
#east-slide(title: [What does it take?])[
#cc-image(
file: "openness_collaboration.png",
title: "Openness and Collaboration",
url: "https://www.flickr.com/photos/45581782@N00/1805374441",
author: "psd",
width: 40%,
)
#align(left, [
- Many _people_ working together
- Content knowledge experts, instructional designers, technologists, editors, enthusiasts, promoters, testers, learners...
])
]
#west-slide(title: [How do you do it?])[
#fairuse-image(
file: "asciidoctor-logo.png",
title: "AsciiDoctor logo",
url: "https://asciidoctor.org/",
width: 25%,
)
- Technically: AsciiDoctor and git #link("https://web.njit.edu/~rt494/open_source_for_oer/slides/")[(OEGlobal 2023 presentation)]
- Check-ins every two weeks
- Publish, test, revise, rewrite, re-publish...
- Incorporate into educational praxis
]
#east-slide(title: [How do people find it?])[
#cc-image(
file: "magnifying-glass.jpg",
title: "Magnifying glass",
url: "https://www.flickr.com/photos/46864401@N07/10120260443",
author: "<NAME>",
)
#align(left, [
- #link("https://oercommons.org/")[OER Commons]
- #link("https://www.merlot.org/merlot/index.htm")[MERLOT]
- #link("https://open.umn.edu/opentextbooks/")[Open Textbook Library]
- #link("https://opennj.net/otc")[OTC]
])
]
#west-slide(title: [Do people actually use it?])[
#cc-image(
file: "classroom.jpg",
title: "BYU Observation Classroom",
url: "https://www.flickr.com/photos/46935248@N00/2089556006",
author: "Cherice"
)
- IT 230 at NJIT averages three sections a semester
- A few emails every semester from professors (Middle Tennessee State University, Berea College)
- At least one "intensive summer course taught abroad"
- People contribute question banks and labs
]
#split-slide[
#align(center)[
What does the future hold?
]
#cc-image(
file: "ai.jpg",
title: "Artificial Intelligence & AI & Machine Learning",
url: "https://creativecommons.org/licenses/by/2.0/?ref=openverse",
author: "mikemacmarketing",
width: 100%
)
][
- Computer Systems Security has already been used to train two AI models: #link("https://arxiv.org/abs/2312.15838")[SecQA], #link("https://dl.acm.org/doi/abs/10.1145/3626772.3657855")[TriviaHG]
- #link("https://oersi.org/resources/pages/en/about/")[Open Educational Resources Search Index (OERSI)]
- #link("https://typst.app/")[Typst]
- #link("https://pretextbook.org/")[PreTeXt?]
]
|
|
https://github.com/dainbow/MatGos | https://raw.githubusercontent.com/dainbow/MatGos/master/themes/6.typ | typst | #import "../conf.typ": *
= Исследование функций одной переменной при помощи первой и второй производных на монотонность, локальные экстремумы, выпуклость. Необходимые условия, достаточные условия.
== Необходимые и достаточные условия монотонности функции
#theorem(
"Предельный переход в неравенстве",
)[
Пусть заданы две последовательности $seq(x), seq(y)$.
Если $lim_(n -> oo) x_n = a, lim_(n -> oo) y_n = b$ и, начиная с некоторого $N: forall n > N : x_n <= y_n$,
то $a <= b$.
]
#theorem[
Пусть $f$ дифференцируема на $(a, b)$. Тогда
+ $forall x in (a, b) : f'(x) >= 0 <=> f - "неубывающая на" (a, b)$
+ $forall x in (a, b) : f'(x) <= 0 <=> f - "невозрастающая на" (a, b)$
+ $forall x in (a, b) : f'(x) > 0 => f - "возрастающая на" (a, b)$
+ $forall x in (a, b) : f'(x) < 0 => f - "убывающая на" (a, b)$
]
#proof[
+ $f'(x) >= 0 =>$ По теореме Лагранжа:
#eq[
$forall x_1, x_2 : a < x_1 < x_2 < b: exists xi in (x_1, x_2) : f(x_2) - f(x_1) = f'(xi)(x_2 - x_1) >= 0$
]
То есть для произвольных $x_1 < x_2: f(x_1) <= f(x_2)$.
Обратно, пусть $f(x)$ неубывающая. Тогда
#eq[
$forall x_0 in (a, b) : forall Delta x : "sign" (f(x_0 + Delta x) - f(x_0)) = "sign" Delta x $
]
Ну и тогда при $abs(Delta x) < min(x_0 - a, b - x_0)$:
#eq[
$(f(x_0 + Delta x) - f(x_0)) / (Delta x) >= 0$
]
Совершим предельный переход в неравенстве и получим требуемое.
+ Аналогично предыдущему пункту
+ Контрпримером для $arrow.l.double$ является $f(x) = x^3$ в точке 0
+ Контрпримером для $arrow.l.double$ является $f(x) = -x^3$ в точке 0
]
== Достаточные условия локальных экстремумов
#theorem(
"Первое достаточное условие экстремума функции",
)[
Пусть $f$ непрерывна в $U_delta_0 (x_0)$ и дифференцируема в $dot(U)_delta_0 (x_0), delta_0 > 0$:
+ Если $exists delta > 0 : forall x in (x_0 - delta, x_0) : f'(x) > 0$ и $forall x in (x_0, x_0 + delta) : f'(x) < 0$,
то $x_0$ -- точка строгого локального максимума $f$
+ Если $exists delta > 0 : forall x in (x_0 - delta, x_0) : f'(x) < 0$ и $forall x in (x_0, x_0 + delta) : f'(x) > 0$,
то $x_0$ -- точка строгого локального минимума $f$
]
#proof[
По сути просто заменили в определении локального экстремума монотонность на
достаточное условие знакопостоянности производной из предыдущей теоремы.
]
#theorem(
"Второе достаточное условие локального экстремума",
)[
Если $f$ $n$ раз дифференцируема в точке $x_0$, $f^((n))(x_0) != 0, forall k = overline("1, n-1"): f^((k))(x_0) = 0$,
то
+ Если $n$ чётно, то $f$ имеет в точке $x_0$ локальный минимум при $f^((n))(x_0) > 0$ и
локальный максимум при $f^((n))(x_0) < 0$.
+ Если $n$ нечётное, то $f$ не имеет локального экстремума в точке $x_0$.
]
#proof[
+ Воспользуемся разложением в Тейлора с остаточным членом в форме Пеано (учитывая
факт нулевых производных):
#eq[
$f(x) = f(x_0) + (f^((n))(x_0)) / n! (x - x_0)^n + o((x - x_0)^n), x -> x_0$
]
Так как $n$ чётно, то $n = 2m$:
#eq[
$(f(x) - f(x_0)) / (x - x_0)^(2m) = (f^((n))(x_0)) / n! + o(1), x -> x_0$
]
Левая часть в некоторой окрестности точки $x_0$ имеет тот же знак, что и правая.
Тогда в силу чётной степени в знаменателе левой части получаем, что разность $f(x) - f(x_0)$ одного
знака с $n$-ой производной.
+ Рассмотрим $f(x) = x^3$.
]
== Необходимые и достаточные условия выпуклости
#definition[
$f$ называется *выпуклой (вниз) (вогнутой вверх)* на $(a, b)$, если её график
лежит не выше хорды, стягивающей любые две точки этого графика над $(a, b)$.
$f$ называется *выпуклой (вверх) (вогнутой вниз)* на $(a, b)$, если её график
лежит не ниже хорды, стягивающей любые две точки этого графика над $(a, b)$.
]
#definition[
Для числовой функции выпуклость вверх (вниз) можно определить как выполнение
*неравенства Йенсена*:
#eq[
$forall x, y : forall t in [0, 1] : f(t x + (1 - t) y) >= (<=) space t f(x) + (1 - t) f(y)$.
]
]
#theorem[
Пусть $f$ дважды дифференцируема на $(a, b)$:
+ $f$ выпукла вниз на $(a, b) <=> forall x in (a, b) : f''(x) >= 0$.
+ $f$ выпукла вверх на $(a, b) <=> forall x in (a, b) : f''(x) <= 0$
+ $f$ строго выпукла вниз на $(a, b) arrow.l.double forall x in (a, b) : f''(x) > 0$.
+ $f$ строго выпукла вверх на $(a, b) arrow.l.double forall x in (a, b) : f''(x) < 0$
]
#proof[
+ $arrow.l.double$ Рассмотрим эквивалентное определение выпуклости:
#eq[
$forall x_0, x_1 : a < x_0 < x_1 < b : forall t in [0, 1] : \
x_t := t x_0 + (1 - t) x_1 : space f(x_t) <= t f(x_0) + (1 - t) f(x_1)$
]
Разложим $f$ в формулу Тейлора с остаточным членом в форме Лагранжа с центром в
точке $x_t$:
#eq[
$exists xi_1 in (x_0, x_t) : f(x_0) = f(x_t) + f'(x_t)(x_0 - x_t) + (f''(xi_1)) / 2! (x_0 - x_t)^2 \
exists xi_2 in (x_1, x_t) : f(x_1) = f(x_t) + f'(x_t)(x_1 - x_t) + (f''(xi_2)) / 2! (x_1 - x_t)^2$
]
Из-за знакопостоянности второй производной из этих равенств следуют следующие
неравенства:
#eq[
$f(x_0) >= f(x_t) + f'(x_t)(x_0 - x_t) \
f(x_1) >= f(x_t) + f'(x_t)(x_1 - x_t) $
]
Умножим первое на $t$, второе на $1 - t$ и сложим их:
#eq[
$t f (x_0) + (1 - t) f(x_1) >= f(x_t) + underbrace(f'(x_t)(t x_0 + (1 - t) x_1 - x_t), 0)$
]
$=>$ Рассмотрим произвольную точку $x_0 in (a, b)$ и достаточно малую
окрестность $delta := min(x_0 - a, b - x_0)$. Тогда
#eq[
$forall u in (-delta, delta) : x_0 = 1 / 2 (x_0 - u) + 1/2 (x_0 + u) : space f(x_0) <= 1 / 2 f(x_0 - u) + 1 / 2 f(x_0 + u )$
]
Применим формулу Тейлора с остаточным членом в форме Пеано:
#eq[
$f(x_0 plus.minus u) = f(x_0) plus.minus f'(x_0) u + (f''(x_0)) / 2 u^2 + o(u^2), u -> 0$
]
В прошлой строчке мы записали сразу два равенства благодаря $plus.minus$,
давайте умножим каждое на $1 / 2$ и сложим их:
#eq[
$1 / 2 f(x_0 - u) + 1 / 2 f(x_0 + u) = f(x_0) + (f''(x_0)) / 2 u^2 + o(u^2), u -> 0$
]
Тогда при достаточно малых $u$ $(f''(x_0)) / 2 u^2$ обязано будет стать такого
же знака, как и $1 / 2 f(x_0 - u) + 1 / 2 f(x_0 + u) - f(x_0) >= 0$
+ Аналогично
+ $arrow.l.double$ аналогично только со строгими неравенствами, а $=>$ вообще
говоря не верно, например, для $f(x) = x^4$
+ $arrow.l.double$ аналогично только со строгими неравенствами, а $=>$ вообще
говоря не верно, например, для $f(x) = -x^4$
]
|
|
https://github.com/LilNick0101/Bachelor-thesis | https://raw.githubusercontent.com/LilNick0101/Bachelor-thesis/main/thesisHeader.typ | typst |
#let script-size = 7.97224pt
#let footnote-size = 8.50012pt
#let small-size = 9.24994pt
#let normal-size = 10.00002pt
#let large-size = 11.74988pt
#import "@preview/glossarium:0.2.0": make-glossary
#let mainPage(
summary,
specialThanks,
doc
) = {
let data = yaml("./metadata.yaml")
align(center,[
#set document(
title: data.title,
author: data.student
)
#show: make-glossary
#figure(
image("./resources/images/unipd-logo.png", width: 35%)
)
#align(center)[
*#data.university*
#line(length: 75%)
#data.department
#data.degree
#align(center + horizon,
text(18pt)[
*#data.title*
]
)
]
#align(center + bottom)[
#grid(
columns: (1fr, 1fr),
align(center)[
Laureando \
#data.student \
Matricola \
2008088
],
align(center)[
Relatore \
#data.relator \
]
)
#line(length: 75%)
Anno accademico #data.ay
]
])
counter(page).update(0)
set page(
paper: "a4",
margin: (x: 1.8cm, y: 1.6cm),
number-align: right,
numbering: "I"
)
set text(
lang: "it",
size: normal-size,
font: "New Computer Modern"
)
set par(
leading: 1.5em
)
if summary != [] {
summary
}
if specialThanks != [] {
specialThanks
}
pagebreak()
outline(
title: [Tabella dei contenuti]
)
outline(
title: [Lista delle tabelle],
target: figure.where(kind: table),
)
outline(
title: [Tabella delle figure],
target: figure.where(kind: image),
)
counter(heading).update(0)
counter(page).update(0)
set page(
paper: "a4",
margin: (x: 1.8cm, y: 1.6cm),
number-align: right,
header: locate(loc => {
let elems = query(
selector(heading.where(level:1)).before(loc,inclusive: true),
loc,
)
if elems == () {
[]
} else {
align(right, emph(elems.last().body))
}}
),
header-ascent: 30%,
numbering: "1"
)
show link: it => underline(text(style: "italic",[#it]))
show heading: it => {
// Create the heading numbering.
let number = if it.numbering != none {
counter(heading).display(it.numbering)
h(7pt, weak: true)
}
// Level 1 headings are centered and smallcaps.
// The other ones are run-in.
if it.level == 1 {
let styled = strong
set text(size: 14pt, weight: 400)
[
#v(15pt, weak: true)
#number
#styled(it.body)
#v(normal-size, weak: true)
]
} else {
v(11pt, weak: true)
number
let styled = if it.level == 2 { strong } else { emph }
styled(it.body)
h(7pt, weak: true)
}
}
doc
} |
|
https://github.com/OrangeX4/typst-talk | https://raw.githubusercontent.com/OrangeX4/typst-talk/main/examples/touying.typ | typst | #import "@preview/touying:0.3.2": *
#let s = themes.aqua.register(aspect-ratio: "16-9", lang: "en")
#let s = (s.methods.info)(
self: s,
title: [Title],
subtitle: [Subtitle],
author: [Authors],
date: datetime.today(),
institution: [Institution],
)
#let (init, slides, touying-outline, alert) = utils.methods(s)
#show: init
#show strong: alert
#let (slide, title-slide, outline-slide, focus-slide) = utils.slides(s)
#show: slides
= The Section
== Slide Title
#slide[
#lorem(40)
]
#focus-slide[
Another variant with primary color in background...
]
== Summary
#align(center + horizon)[
#set text(size: 3em, weight: "bold", s.colors.primary)
THANKS FOR ALL
] |
|
https://github.com/hemmrich/CV_typst | https://raw.githubusercontent.com/hemmrich/CV_typst/master/modules/projects.typ | typst | // Imports
#import "../template/template.typ": cvSection, cvEntry
#let metadata = toml("../metadata.toml")
#let cvSection = cvSection.with(metadata: metadata)
#let cvEntry = cvEntry.with(metadata: metadata)
#cvSection("Research Projects")
#cvEntry(
title: [Oral Premalignancy Progression Prediction | PI: <NAME>, MD, PhD],
society: [University of Chicago Department of Hematology and Oncology],
date: [2024-current],
location: [Chicago, IL],
description: list(
[Building model to predict progression of oral premalignant lesions based on deep learning of histopathology],
[Combined datasets from UChicago, University of Iowa, Brazil, and the NIH]
),
)
#cvEntry(
title: [Oral Cavity Resection Margins | PI: <NAME>, MD],
society: [Endeavor Health / NorthShore University Health System],
date: [2024-current],
location: [Chicago, IL],
description: list(
[First prospective study to assess impact of resection margins on recurrence rate of cT1 and cT2 oral cavity SCC],
[Submitted IRB and created REDCap database for HIPAA-compliant data storage],
[Patient enrollment currently ongoing]
),
)
#cvEntry(
title: [COPD Readmission Prediction | PI: <NAME>, MD, MPH],
society: [University of Chicago Department of Medicine],
date: [2018-2021],
location: [Chicago, IL],
description: list(
[PI: <NAME>, MD, MPH],
[Built machine learning model using electronic health record data to predict risk of readmission after COPD excerbation],
[Disseminated findings at international, national, and regional conferences],
[Received Healthcare Delivery Science Award for research excellence at 2018 Pritzker Summer Research Forum],
[Received Health Service Research Abstract Award at 2019 American Thoracic Society International Conference],
),
)
#cvEntry(
title: [Head & Neck Cancer Recurrence Database | PI: <NAME>, MD, PhD],
society: [University of Chicago Department of Medicine],
date: [2020-2021],
location: [Chicago, IL],
description: list(
[Built natural language processing classifier to extract tumor data from radiology notes],
[Data will be combined with content extracted from pathology notes to build a recurrence database to assess efficacy of treatment modalities and determine predictors of recurrence],
),
)
#cvEntry(
title: [COVID-19 Natural History | PI: <NAME>, MD],
society: [University of Chicago Department of Medicine],
date: [2020-2021],
location: [Chicago, IL],
description: list(
[Chart reviews of first 413 COVID patients at UChicago Medical Center],
[Literature review for subgroup analysis of COVID in young and obese patients],
[Poster accepted at HIV Glasgow 2020 conference]
),
) |
|
https://github.com/csimide/SEU-Typst-Template | https://raw.githubusercontent.com/csimide/SEU-Typst-Template/master/seu-thesis/pages/title-page-degree-cn-fn.typ | typst | MIT License | #import "../utils/packages.typ": fakebold, show-cn-fakebold
#import "../utils/fonts.typ": 字体, 字号, chineseunderline, justify-words
#let title-cn-conf(
author: (CN: "王东南", EN: "<NAME>", ID: "012345"),
thesis-name: (
CN: "硕士学位论文",
EN: [
A Thesis submitted to \
Southeast University \
For the Academic Degree of Master of Touching Fish
],
heading: "东南大学硕士学位论文",
),
title: (
CN: "摸鱼背景下的Typst模板使用研究",
EN: "A Study of the Use of the Typst Template During Touching Fish",
),
advisors: (
(CN: "湖牌桥", EN: "<NAME>", CN-title: "教授", EN-title: "Prof."),
(
CN: "苏锡浦",
EN: "<NAME>",
CN-title: "副教授",
EN-title: "Associate Prof.",
),
),
school: (
CN: "摸鱼学院",
EN: "School of Touchingfish",
),
major: (
main: "摸鱼科学",
submajor: "计算机摸鱼",
),
date: (
CN: (
defend-date: "2099年01月02日",
authorize-date: "2099年01月03日",
finish-date: "2024年01月15日",
),
EN: (
finish-date: "Jan 15, 2024",
),
),
thanks: "本论文受到摸鱼基金委的基金赞助（123456）",
anonymous: false,
) = page(
margin: (top: 3cm, bottom: 2cm, left: 2cm, right: 2cm),
numbering: none,
header: none,
footer: none,
{
set align(center)
set par(first-line-indent: 0pt)
image("../assets/vi/seu.png", width: 180pt)
block(fakebold(text(font: 字体.标题宋体, size: 字号.小初, thesis-name.CN)))
v(40pt)
block(text(font: 字体.黑体, size: 字号.一号, weight: "bold", title.CN))
v(40pt)
set text(font: 字体.宋体, size: 字号.小二, weight: "bold")
grid(
columns: (5em, 1em, 10em),
row-gutter: 3em,
text(font: 字体.黑体, "专业名称".clusters().join(h(1em / 3))),
"：",
chineseunderline(major.main),
text(font: 字体.黑体, "研究生姓名"),
"：",
chineseunderline(author.CN),
text(font: 字体.黑体, "导师姓名".clusters().join(h(1em / 3))),
"：",
chineseunderline(advisors.map(it => it.CN + " " + it.CN-title).join("\n")),
)
if thanks != none {
place(bottom + left, text(font: 字体.宋体, size: 字号.小四, thanks))
}
},
)
#title-cn-conf(
author: (CN: "王东南", EN: "<NAME>", ID: "012345"),
thesis-name: (
CN: "硕士学位论文",
EN: [
A Thesis submitted to \
Southeast University \
For the Academic Degree of Master of Touching Fish
],
heading: "东南大学硕士学位论文",
),
title: (
CN: "摸鱼背景下的Typst模板使用研究",
EN: "A Study of the Use of the Typst Template During Touching Fish",
),
advisors: (
(CN: "湖牌桥", EN: "<NAME>", CN-title: "教授", EN-title: "Prof."),
(
CN: "苏锡浦",
EN: "<NAME>",
CN-title: "副教授",
EN-title: "Associate Prof.",
),
),
school: (
CN: "摸鱼学院",
EN: "School of Touchingfish",
),
major: (
main: "摸鱼科学",
submajor: "计算机摸鱼",
),
date: (
CN: (
defend-date: "2099年01月02日",
authorize-date: "2099年01月03日",
finish-date: "2024年01月15日",
),
EN: (
finish-date: "Jan 15, 2024",
),
),
thanks: "本论文受到摸鱼基金委的基金赞助（123456）",
anonymous: false,
) |
https://github.com/Jollywatt/typst-fletcher | https://raw.githubusercontent.com/Jollywatt/typst-fletcher/master/tests/edge-mark-shorthands/test.typ | typst | MIT License | #set page(width: auto, height: auto, margin: 1em)
#import "/src/exports.typ" as fletcher: diagram, node, edge
$
#for i in (
"->",
"<-",
">-<",
"<->",
"<=>",
"<==>",
">==<",
"|->",
"|=>",
">->",
"<<->>",
">>-<<",
">>>-}>",
"hook-hook",
"hook'--hook'",
"|=|",
"||-||",
"|||-|||",
"/--\\",
"\\=\\",
"/=/",
"x-X",
">>-<<",
"harpoon-harpoon",
"harpoon'-<<",
"<--hook'",
"|..|",
"hooks--hooks",
"o-o",
"O-o",
"*-@",
"o==O",
"||->>",
"<|-|>",
"|>-<|",
"-|-",
"hook-/->",
"<{-}>",
) {
$ #block(inset: 2pt, fill: white.darken(5%), raw(repr(i)))
&= #align(center, box(width: 15mm, diagram(edge((0,0), (1,0), marks: i), debug: 0))) \ $
}
$
|
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