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https://github.com/Myriad-Dreamin/typst.ts | https://raw.githubusercontent.com/Myriad-Dreamin/typst.ts/main/fuzzers/corpora/math/op_00.typ | typst | Apache License 2.0 |
#import "/contrib/templates/std-tests/preset.typ": *
#show: test-page
// Test predefined.
$ max_(1<=n<=m) n $
|
https://github.com/HiiGHoVuTi/requin | https://raw.githubusercontent.com/HiiGHoVuTi/requin/main/template_exo.typ | typst | #import "../lib.typ": *
#show heading: heading_fct
#import "@preview/gloss-awe:0.0.5": gls
#show figure.where(kind: "jkrb_glossary"): it => {it.body}
|
|
https://github.com/ljgago/typst-chords | https://raw.githubusercontent.com/ljgago/typst-chords/main/CHANGELOG.md | markdown | MIT License | # Changelog
All notable changes to this project will be documented in this file.
The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/).
## [v0.4.0](https://github.com/ljgago/typst-chords/compare/v0.3.0...v0.4.0) - 2024-07-09
### Added
- New `background` parameter, now in `chart-chord`, `piano-chord` and `single-chord`. Add a background color on the chord name.
- New `position` parameter in `chart-chord`, `piano-chord`. Now the chart can be below or above of the chord name.
- New `..text-params` in `chart-chord`, `piano-chord` and `single-chord`. It embeds the native text parameters from the standard library of typst.
### Changed
- Renamed `new-chart-chords`, `new-piano-chords` and `new-single-chords` functions by `chart-chord`, `piano-chord` and `single-chord` removing the closure functions. Use the [with](https://typst.app/docs/reference/foundations/function/#definitions-with) property for preset the parameters.
- Renamed `style` parameter by `design` to avoid name collision with the native text parameters. The possible values of `design` are `"sharp"` and `"round"`
- Renamed `fill` parameter by `fill-key` to avoid name collision with the native text parameters.
- Replaced the `styles-measure` syntax by the new [context-measure](https://typst.app/docs/reference/context/) added in Typst v0.11.0.
- Refactored the render and the graphic objects, now each object calculates its own relative position.
### Removed
- Removed `size` as a specific parameter. `size` is included in the native *text* parameters in `..text-params`.
## [v0.3.0](https://github.com/ljgago/typst-chords/compare/v0.2.0...v0.3.0) - 2024-03-01
### Changed
- Renamed `frets` parameter by `frets-amount`.
- Renamed `fret-number` parameter by `fret`.
- Renamed `color` parameter by `fill`.
- Replaced `scale` parameter by `size`. You can use the same functionality using `em` units.
- Replaced new types released in Typst v0.8.0.
## [v0.2.0](https://github.com/ljgago/typst-chords/compare/v0.1.0...v0.2.0) - 2023-08-25
### Added
- New file structure.
- New piano chords.
- Options to scale the graphs.
- New round style.
### Changed
- Renamed new-graph-chords to new-chart-chords.
- Replaced array inputs by string inputs (thanks to `conchord` for the ideas).
### Removed
- Removed dependency of CeTZ, uses only native functions.
## [v0.1.0](https://github.com/ljgago/typst-chords/compare/v0.1.0...v0.1.0) - 2023-07-16
### Added
- Added graph chords.
- Added single chords.
### Changed
- The single chords show the chord name over a specific character or word.
|
https://github.com/ymgyt/blog | https://raw.githubusercontent.com/ymgyt/blog/main/lt/otel-lt/presen.typ | typst | #import "@preview/polylux:0.3.1": *
#import themes.bipartite: *
#show: bipartite-theme.with(aspect-ratio: "16-9")
#show link: underline
#set text(
size: 25pt,
font: (
// "Noto Color Emoji",
// "JetBrainsMono Nerd Font",
"Noto Sans CJK JP",
))
#title-slide(
title: [RustでOpenTelemetry],
subtitle: [tracingと一緒に使ってわかった課題],
author: [ymgyt],
date: [2024-04-10],
)
#west-slide(title: "自己紹介")[
```toml
[speaker]
name = "<NAME>"
x = "@YAmaguchixt"
[company]
name = "FRAIM Inc."
blog = "https://zenn.dev/p/fraim"
```
]
#west-slide(title: "概要")[
- RustにOpenTelemetryを導入して、Traces, Metrics, Logsを取得した
- tracingというlibからOpenTelemetry APIを利用した
]
#west-slide(title: "最初の課題")[
OpenTelemetry APIを直接利用するか\
lib(tracing)経由で利用するか
]
#west-slide(title: "OpenTelemetry APIを直接利用するか")[
#figure(
image("./images/library-design.png", width: 80%,height: 80%, fit: "contain"),
numbering: none,
caption: [#link("https://opentelemetry.io/docs/specs/otel/library-guidelines/")[OpenTelemetry Client Generic Design]]
)
]
#west-slide(title: "OpenTelemetry APIを直接利用するか")[
tracing経由でOpenTelemetryを利用することにした
- 既にtracingを計装済だった
- 利用しているlibの多くがtracingで計装されていた
- #link("https://github.com/tokio-rs/tracing-opentelemetry")[tracing-opentelemetry]が#link("https://github.com/tokio-rs")[tokio]から提供されていた
]
#west-slide(title: "OpenTelemetry APIを直接利用するか")[
RustのOpenTelemetry projectでもtracingとの関係が#link("https://github.com/open-telemetry/opentelemetry-rust/issues/1571")[OpenTelemetry Tracing API vs Tokio-Tracing API for Distributed Tracing]で議論されている
#figure(
image("./images/otel-vs-tracing-ss-2.png", width: 100%,height: 50%, fit: "contain"),
numbering: none,
)
]
#west-slide(title: "Resource")[
#set text(size: 16pt)
#show raw: it => stack(dir: ttb, ..it.lines)
#show raw.line: it => {
box(
width: 100%,
height: 1.3em,
inset: 0.25em,
align(horizon, stack(
dir: ltr,
box(width: 15pt)[#it.number],
it.body,
))
)
}
```rust
use opentelemetry_sdk::{resource::EnvResourceDetector, Resource};
use opentelemetry_semantic_conventions::{
resource::{SERVICE_NAME, SERVICE_NAMESPACE, SERVICE_VERSION},
SCHEMA_URL,
};
pub fn resource(
service_name: impl Into<Cow<'static, str>>,
service_version: impl Into<Cow<'static, str>>,
) -> Resource {
Resource::from_schema_url(
[
(SERVICE_NAME, service_name.into()),
(SERVICE_VERSION, service_version.into()),
(SERVICE_NAMESPACE, "foo".into()),
]
.into_iter()
.map(|(key, value)| KeyValue::new(key, value)),
SCHEMA_URL, // https://opentelemetry.io/schemas/1.21.0
)
.merge(&Resource::from_detectors(
Duration::from_millis(200),
// Detect "OTEL_RESOURCE_ATTRIBUTES" environment variables
vec![Box::new(EnvResourceDetector::new())],
))
}
```
]
#west-slide(title: "Traces")[
#set text(size: 18pt)
```rust
#[tracing::instrument(skip_all, fields(%url))]
async fn fetch_feed(&self, url: Url) -> Result<Feed,Error>
{ /* ... */ }
```
\
関数にSpanを設定するには`#[tracing::instrument]` annotationを利用する\
`fields()`に値を指定するとSpanのattributeになる
]
#west-slide(title: "Traces")[
#figure(
image("./images/trace-ss-1.png", width: 100%,height: 90%, fit: "contain"),
numbering: none,
caption: [Span attributesにurlが記録される]
)
]
#west-slide(title: "Traces")[
```rust
async fn run() {
// ...
info!(
"enduser.id"= user_id,
"operation" = operation,
);
// ...
```
関数の中で行ったlogging(`info`や`error`)はSpanのEventsとして記録される
]
#west-slide(title: "Traces")[
#figure(
image("./images/trace-ss-2.png", width: 100%,height: 90%, fit: "contain"),
numbering: none,
caption: [SpanのEventsに記録される]
)
]
#west-slide(title: "Tracesの課題")[
Context propagationではOpenTelemetryの仕組みを利用するので、OpenTelemetryのContextやBaggageを意識する必要がある。\
(ApplicationがOpenTelemetryをまったく意識しなくていいことにならない)
- inject時は`tracing::Span` -> `opentelemetry::Context` -> `http::Header`
- extract時は`http::Header` -> `opentelemetry::Context` -> `tracing::Span`
]
#west-slide(title: "Tracesの課題")[
OpenTelemetryのtraceは1 layer(plugin)という位置づけなので、samplingしない場合でもtracing側でrespectされない\
あくまでtracing側の機構でspanのsamplingを制御する必要がある\
\
`RUST_LOG=app=info,
lib_b[request{path="foo"}]=trace`\
(一方で、アプリケーションはinfo、lib_bのrequest spanのpathが"foo"はtraceといった制御ができる)
]
#west-slide(title: "Metrics")[
3つの選択肢があった
\
- Prometheus Metrics
- OpenTelemetry Metrics API
- tracing-opentelemetry MetricsLayer
]
#west-slide(title: "Metrics")[
Prometheus Metrics\
\
Applicationからはprometheus形式のmetricsをexportして
OpenTelemetry collectorでOpenTelemetry形式に変換する
#pause => Signalを関連づける重要性が謳われていたので採用しなかった
]
#west-slide(title: "Metrics")[
OpenTelemetry Metrics API\
#set text(size: 20pt)
```rust
fn main() {
let meter = opentelemetry::global::meter("foo");
let counter = meter.u64_counter("counter").init();
counter.add(
10,
&[opentelemetry::KeyValue::new("key","value")],
);
}
```
#pause => tracesとの一貫性を重視して、metricsもtracing経由で操作することにした
]
#west-slide(title: "Metrics")[
tracing-opentelemetry MetricsLayer
#set text(size: 20pt)
```rust
info!(
monotonic_counter.http.server.request = 1,
http.response.status.code = status
);
```
tracingでは、info!のloggingはEventのdispatchになる\
layer側で、`monotonic_counter` prefixがついたeventを受け取ったら、attribute(`http.response.status.code`)を付与して、counter metricsを生成する
]
#west-slide(title: "Metricsの課題")[
Prometheus/Mimirを利用している場合\
OpenTelemetry -> Prometheusの変換を意識する必要がある
]
#west-slide(title: "Metricsの課題")[
例えば、OpenTelemetryのUpDownCounterはPrometheusのGaugeになる
> If the aggregation temporality is cumulative and the sum is non-monotonic, it MUST be converted to a Prometheus Gauge.
#link("https://opentelemetry.io/docs/specs/otel/compatibility/prometheus_and_openmetrics/#sums")
]
#west-slide(title: "Metricsの課題")[
Prometheusとの互換性に関してはPrometheusの
#link("https://prometheus.io/blog/2024/03/14/commitment-to-opentelemetry/")[Our commitment to OpenTelemetry]というブログで互換性向上の取り組みが紹介されていた
- `http.server.request.duration` -> `http_server_request_duration`の変換をなくす
- Native support for resource attributes(prometheusはmetrics attributesとresourceをflatなlabelにする)
- OTLPのsupport
]
#west-slide(title: "Metricsの課題")[
Elastic stack(elasticsearch, kibana)を使っていた際もOpneTelemetryのresourceやattributesが変換されてしまっていたが\
#link("https://opentelemetry.io/blog/2023/ecs-otel-semconv-convergence/")[Announcing the Elastic Common Schema(ECS) and OpenTelemetry Semantic Convention Convergence]で、両者の統合が発表されていた
> The goal is to achieve convergence of ECS and OTel Semantic Conventions into a single open schema that is maintained by OpenTelemetry
]
#west-slide(title: "Metricsの課題")[
Eventのfield(key,value)だけで表現できないmetricsも\
valueにはprimitive型(i64,f64,bool,..)やfmt::Display等の文字列表現しか利用できない \
=> Histogramでboundariesを指定したい場合に対応できない
]
#west-slide(title: "Metricsの課題")[
#set text(size: 15pt)
```rust
use opentelemetry_sdk::metrics::{Instrument, Stream,View};
fn view() -> impl View {
|instrument: &Instrument| -> Option<Stream> {
match instrument.name.as_ref() {
"graphql.duration" => Some(
Stream::new()
.name(instrument.name.clone())
.aggregation(
opentelemetry_sdk::metrics::Aggregation::ExplicitBucketHistogram {
boundaries: vec![
0.005, 0.01, 0.025, 0.05, 0.075, 0.1, 0.25, 0.5, 0.75, 1.0, 2.5,
5.0, 7.5, 10.0,
],
record_min_max: false,
},
)
.unit(Unit::new("s")),
),
_ => {
None
}
}
}
}
```
]
#west-slide(title: "Metricsの課題")[
MetricsのViewという仕組みで、SDK初期化時に変換処理を追加することで対処した\
- Metrics生成箇所とSDK初期化処理でcodeが別れてしまった
- 名前(Instrument.name)で一致させているので型/compile時の保証がない
]
#west-slide(title: "Logs")[
Logsの収集には2つの方法を利用した
- Kubernetes環境ではstdoutに出力したのち、nodeに配置したcollectorからfilelog receiverで収集
- #link("https://github.com/open-telemetry/opentelemetry-rust/tree/main/opentelemetry-appender-tracing")[opentelemetry-appender-tracing]
]
#west-slide(title: "Logs")[
Logsのspec #link("https://opentelemetry.io/docs/specs/otel/logs/")[OpenTelemetry Logging]では\
Tracesやmetricsのように新しいAPIを提供するのではなく\
Logs Bridge APIを用意して、言語ごとの既存のlogging ecosystemに組み込んでもらう方針が説明されている
> Our approach with logs is somewhat different. For OpenTelemetry to be successful in logging space we need to support existing legacy of logs and logging libraries
]
#west-slide(title: "Logs")[
この方針があってか、traces,metricsではtracingが提供しているtracing-opentelemetryでopentelemetryと連携していたが\opentelemetry-appender-tracingはopentelemetry-rustが提供している
]
#west-slide(title: "Logs")[
opentelemetry-appender-tracingを利用すると\
`info!("message")`といったこれまでのloggingがそのまま
OTLPでcollectorに送られる
]
#west-slide(title: "Logsの課題")[
```rust
#[tracing::instrument]
async fn foo() {
info!("message");
}
```
とした場合
- foo Spanのeventに"message"が記録される
- Logのrecordとしても"message"が記録される
]
#west-slide(title: "Logsの課題")[
tracing(tracing_subscriber::FmtLayer)では、
```text
http{method=POST path=/graphql request_id=Fsg3zhkIS4}:
service{query="foo"}:
db{connection=1} "message"
```
のようにlogにspanの情報を埋め込んでくれるのでLog側もtraceの情報を一部保持することになる
#pause traceはsamplingされたりlogとはlifecycleが違うのでlogにどの程度context情報を付与するか悩ましい
]
#west-slide(title: "実際のコード")[
趣味で作っているツールのbackend apiでもOpenTelemetryを利用しました\
本スライドで話した内容の#link("https://github.com/ymgyt/syndicationd/blob/943b9c4d36b3e45a616deb9065f384faf5c193a0/crates/synd_api/src/main.rs#L45")[実際のコード]、#link("https://github.com/ymgyt/mynix/blob/main/homeserver/modules/opentelemetry-collector/config.yaml")[collectorの設定file]、#link("https://ymgyt.grafana.net/public-dashboards/863ebddd82c44ddd9a28a68eaac848ff")[grafana dashboard]を公開しています
#figure(
grid(
columns: 2,
gutter: 10mm,
image("./images/example-ss-1.png", width: 100%,height: 50%, fit: "contain"),
image("./images/dashboard-ss-1.png", width: 100%,height: 50%, fit: "contain"),
)
)
]
#west-slide(title: "まとめ")[
- Rustでtracingを利用してOpenTelemetryの各signalを導入できた
- tracingを通じてOpenTelemetry APIを利用することのメリットもある一方で課題もわかった
]
#west-slide(title: "リンク")[
- #link("https://github.com/tokio-rs")
- #link("https://github.com/tokio-rs/tracing-opentelemetry")
- #link("https://github.com/open-telemetry/opentelemetry-rust/discussions/1032")
- #link("https://github.com/open-telemetry/opentelemetry-rust/issues/1571")[OpenTelemetry Tracing API vs Tokio-Tracing API for Distributed Tracing]
- #link("https://github.com/ymgyt/syndicationd/blob/943b9c4d36b3e45a616deb9065f384faf5c193a0/crates/synd_api/src/main.rs#L45")[OtelLayerのcompose]
]
|
|
https://github.com/jgm/typst-hs | https://raw.githubusercontent.com/jgm/typst-hs/main/test/typ/compiler/ops-invalid-13.typ | typst | Other | // Error: 4-13 cannot divide ratio by length
#( 10% / 5pt )
|
https://github.com/dantevi-other/kththesis-typst | https://raw.githubusercontent.com/dantevi-other/kththesis-typst/main/parts/2-eng-abstract.typ | typst | MIT License | //-- Configurations
#set page(
numbering: "i"
)
//-- Content
= Abstract
#lorem(200) |
https://github.com/MuShann/typst-graph | https://raw.githubusercontent.com/MuShann/typst-graph/main/README.md | markdown | # typst-graph
A typst package of drawing functions.
## Simple graph
```
#d(-5, -5, grid: 0.5, fill: blue)[
#l(0, -5, 0, 5, stroke: blue+1pt, larr: 2, dir: top)[#text(fill: blue, size: 0.5em, $y$)]
#l(-5, 0, 5, 0, stroke: blue+1pt, larr: 2, dir: left)[#text(fill: blue, size: 0.5em, $x$)]
#f(-5, 5, prec: 10, stroke: red.lighten(20%)+1pt)[$4 dot sin x$]
#p(calc.pi, 0, orange)[]
]
```
|
|
https://github.com/sofianedjerbi/ResumeOld | https://raw.githubusercontent.com/sofianedjerbi/ResumeOld/main/modules/projects.typ | typst | Apache License 2.0 | #import "../brilliant-CV/template.typ": *
#let lightbold(str) = text(weight: 501, str)
#let ulink(dest, body) = link(dest, text(blue, underline(body)))
#cvSection("Projets & Détails")
#v(5pt)
#cvEntry(
title: [Ingénieur Recherche et Développement],
society: [Ingenico],
date: [Oct 23 - Maintenant],
location: [Valence, France],
description: par(justify: true)[
Prestation axée sur la création et la maintenance de librairies Java et Kotlin pour la gamme innovante de terminaux Axium, fonctionnant sous #lightbold[Android]. Objectif principal : assurer la compatibilité avec les gammes antérieures #lightbold[Tetra] et permettre la création de logiciels compatible terminaux concurrents, en exploitant efficacement Kotlin KMM.
- #lightbold[Conception de bibliothèques multiplateformes :] Développement et maintenance de librairies Java et Kotlin, spécifiquement adaptées aux besoins des terminaux Axium, garantissant performance et fiabilité. Responsable de la maintenance continue (rôle de mainteneur).
- #lightbold[Kotlin Multiplatform :] Mise en oeuvre de Kotlin KMM, une technologie de pointe pour la programmation multiplateforme, assurant une intégration harmonieuse et efficiente.
- #lightbold[Prise de décisions architecturales :] Engagement dans des décisions architecturales stratégiques, visant à renforcer la modularité, la performance et la facilité de maintenance des librairies.
- #lightbold[Leadership technique en Java & Kotlin :] Référent en Java et Kotlin, offrant expertise technique et coaching à l'équipe pour accélérer le développement et augmenter la qualité du code.
Résultats notables :
- Élaboration d'un framework interne facilitant et accélérant le développement d'applications multiplateformes.
- Simplification de l'ecosysteme existant.
],
tags: ("Java", "Kotlin", "C++", "Gradle", "Jira", "Bitbucket", "KMM", "Linux", "PlantUML")
)
#v(5pt)
#cvEntry(
title: [Architecte et Développeur Java & Rust],
society: [Kaiiju],
date: [Jan 23 - Oct 23],
location: [Valence, France],
description: par(justify: true)[
L'objectif principal de cette mission était de permettre au client de #lightbold[réaliser des économies] en réduisant les coûts liés à l'hébergement, en mettant l'accent sur les ressources liées à la vitesse du processeur (CPU) et à l'espace de stockage.
- #lightbold[Conception d'un nouveau format de stockage optimisé :] Développement d'un format de stockage basé sur l'algorithme ZSTD, réduisant considérablement l'utilisation de l'espace disque et de la RAM. Pour la gestion en RAM, les fichiers ont été compressés à l'aide de LZ4, garantissant une décompression rapide et une utilisation minimale de la RAM. Ce format était accompagné d'un système de flushing multithreadé pour optimiser l'écriture, ainsi que de bibliothèques permettant une manipulation efficace de ce système de stockage.
- #lightbold[Création d'une API] publique, rapide et de haut niveau pour une manipulation aisée de ce nouveau format de stockage. Écrite en Rust, elle prend en charge le chargement et le traitement parallèle des fichiers.
- #lightbold[Désynchronisation du pathfinding :] Mise en place d'un thread-pool asynchrone pour accélérer le processus de pathfinding sans impact sur le thread principal. Utilisation d'un cache pour améliorer la vitesse du pathfinding tout en réduisant la consommation de mémoire.
Résultats notables :
- Réduction de l'utilisation de l'espace disque d'environ #lightbold[63%].
- Augmentation des performances globales d'environ #lightbold[16%].
- Écriture concurrente des fichiers: réduction arbitraire du temps d'écriture.
],
tags: ("Java", "Guava", "Multithreading", "Gradle", "Git", "Rust")
)
#v(5pt)
#cvEntry(
title: [Architecte et Développeur Java & Kotlin],
society: [Elendil],
date: [Jui 23 - Oct 23],
location: [Valence, France],
description: par(justify: true)[
Cette mission consiste à établir une #lightbold[boutique multiplateforme] afin de diversifier les sources de revenus, tout en monitorant les ventes pour identifier les offres les plus rentables.
- #lightbold[Conception intégrale d'une boutique], accessible via diverses plateformes telles que le web, Android et applications PC grâce à Spring et KMM.
- #lightbold[Implémentation d'une tarification en temps réel en fonction de la demande], exploitant une base de données SQL. Les accès à la base de données sont optimisés pour des performances maximales grâce à des méthodes asynchrones avec un cache de type JSON.
- #lightbold[Création d'un système de customisation], avec une documentation complète, incluant des fichiers de configuration de langage. Cette customisation offre la flexibilité d'ajouter ou de supprimer des offres sans nécessiter de compétences en programmation, grâce à un panneau de contrôle facile à utiliser.
- #lightbold[Mise en place d'une interface web] (serveur web Spring Boot) permettant de suivre de près les profits générés par chaque offre, ainsi que les dépenses de chaque client via une API REST. Des graphiques dynamiques et interactifs sont disponibles sur le site pour un suivi complet.
- #lightbold[Développement d'un système d'enchères où les clients peuvent mettre en vente leurs propres objets.] L'administrateur bénéficie d'une interface spéciale pour modérer les offres, garantissant ainsi une expérience sécurisée et transparente pour les utilisateurs.
],
tags: ("Java", "Kotlin", "SQL", "Hibernate", "Spring", "Gson", "Gradle", "JavaScript", "MySQL", "API REST")
)
#pagebreak()
#v(20pt)
#cvEntry(
title: [Développeur Fullstack C++ & SQL],
society: [via Fiverr],
date: [Jan 22 - Jui 22],
location: [Valence, France],
description: par(justify: true)[
Cette mission implique la conception d'un logiciel destiné à répertorier les différentes espèces d'un élevage, à prédire la probabilité de générer les gènes les plus lucratifs, et à compiler un inventaire des espèces et gènes disponibles afin de déterminer les combinaisons les plus rentables.
- #lightbold[Emploi d'Eigen] pour les calculs mathématiques et de Boost pour optimiser la rentabilité des accouplements, en analysant les données stockées.
- #lightbold[Mise en place d'une base de données SQL] pour cataloguer les espèces et gènes, permettant une gestion efficace des informations d'élevage.
- #lightbold[Utilisation de C++ et Qt] pour développer une interface utilisateur, facilitant l'entrée des données d'élevage par les utilisateurs.
- #lightbold[Utilisation de Curl] pour le scrapping de données sur Internet, crucial pour ajuster les stratégies d'élevage aux tendances du marché.
],
tags: ("C++", "SQLite", "Boost", "Eigen", "Qt", "QtCreator", "Curl")
)
#v(5pt)
#cvEntry(
title: [Développeur Linux & Administrateur Système],
society: [Kugge],
date: [Jui 21 - Oct 23],
location: [Grenoble, France],
description: par(justify: true)[
Accompagner et conseiller différents fournisseurs d'hébergement de serveurs (VPS, Pterodactyl..) pour maximiser leurs bénéfices, entretenir les équipements, et proposer des solutions aux problèmes fréquents.
- #lightbold[Création de machines virtuelles] utilisant des technologies telles que Docker, KVM, et LXC. Élaboration de scripts d'installation pour les systèmes d'exploitation Linux, notamment Debian 11, 12, Gentoo, Arch, Ubuntu, et CentOS.
- #lightbold[Développement d'un logiciel de sauvegarde automatisée] visant à garantir des sauvegardes régulières et facilement restaurables. Cette solution permet de réduire considérablement l'utilisation de l'espace disque, pouvant aller jusqu'à une réduction de 90% sur certaines offres d'hébergement, ce qui permet d'offrir des tarifs plus compétitifs.
- #lightbold[Planification de l'évolutivité de l'infrastructure] pour anticiper la croissance future. Une évaluation régulière des besoins et des opportunités d'amélioration est effectuée dans ce cadre.
- Fourniture d'une #lightbold[assistance technique] aux clients et aux utilisateurs des machines virtuelles, y compris la résolution des problèmes et la gestion des demandes de support, qu'elles soient d'ordre commercial ou technique.
],
tags: ("Linux", "Python", "Rust", "SQL", "Docker", "Proxmox", "Flask", "Django", "FastAPI", "Pandas", "Bash")
)
#v(5pt)
#cvEntry(
title: [Développeur Fullstack C++ & Python],
society: [CEA Leti],
date: [Dec 21 - Juin 22],
location: [Grenoble, France],
description: par(justify: true)[
Cette mission consiste à #lightbold[développer un logiciel] pour surveiller en temps réel l'impact des attaques par rayon X sur la RAM et Flash de l'ATMega128, incluant une GUI et une API pour monitorer l'interaction avec la mémoire.
- #lightbold[Développement d'une API haut niveau multiplateforme] dédiée à l'interaction avec les composants électroniques RAM et Flash, prenant en charge les protocoles RS232 et MPSSE USB FTDI. Cette API est accompagnée d'une documentation complète et de tests unitaires.
- #lightbold[Création d'une interface graphique] en utilisant Qt et QtCreator pour afficher et manipuler en temps réel les composants mémoire, permettant de détecter les attaques par rayon X. Cette interface génère des représentations visuelles sous forme de heatmap.
- Gestion complète du projet, y compris la rédaction d'un cahier des charges détaillé, la répartition des tâches au sein de l'équipe, et le suivi du projet en utilisant des outils de gestion de version tels que #lightbold[Git et GitHub]. Présentation du projet ainsi que des résultats obtenus.
],
tags: ("C++", "Python", "Qt", "QtCreator", "FTDI", "ATMega")
)
#v(5pt)
#cvEntry(
title: [Développeur Backend Java],
society: [via Fiverr],
date: [Mars 20 - Août 20],
location: [Grenoble],
description: par(justify: true)[
Développement d'une solution innovante pour l'ajustement dynamique des performances en fonction de l'activité utilisateur et de la charge système. Ce système utilise un algorithme intelligent pour optimiser les ressources en temps réel, réduisant ainsi le temps de réponse et améliorant l'expérience utilisateur.
- #lightbold[Adaptation intelligente :] Implémentation d'un système Java capable d'ajuster les paramètres de rendu en fonction du ping des utilisateurs et de la santé globale du système. Introduction d'un indice de réduction ajusté en temps réel pour optimiser les ressources.
- #lightbold[Amélioration significative de la performance :] Grâce à la gestion adaptative des paramètres, la solution minimise les retards, réduit le temps de réponse et améliore la fluidité de l'expérience utilisateur.
- #lightbold[Configurabilité et contrôle :] Développement d'une interface de configuration complète permettant une personnalisation poussée et un contrôle fin sur le comportement du système selon divers scénarios d'utilisation.
],
tags: ("Java", "Multithreading", "Bash", "Linux", "Maven")
)
#v(5pt)
*Et de nombreux autres projets sont disponibles sur mon GitHub!* \
Lien: #ulink("https://github.com/chaoxel")[https://github.com/chaoxel]
|
https://github.com/PA055/5839B-Notebook | https://raw.githubusercontent.com/PA055/5839B-Notebook/main/Entries/Game_Discussion/pre_reveal.typ | typst | #import "/packages.typ": notebookinator
#import notebookinator: *
#import themes.radial.components: *
#show: create-body-entry.with(
title: "Pre-Rulebook Reveal Thoughts",
type: "identify",
date: datetime(year: 2024, month: 4, day: 17),
author: "<NAME>",
witness: "<NAME>, <NAME>, <NAME>",
)
The reveal of the game made us think we could use some inspiration from the previous over-under season since it reuses a similar elevation endgame mechanic. We will need an intake a lot more than in over-under and it will need to elevate as well in order to reach all of the stakes effectively. It would also be best for the robot to be able be quick, especially because we want to gain control of as many mobile goals as we can. However, it could also be beneficial to be on the heavier side so we can guard the mobile goals in the positive modifer zones at the end.
|
|
https://github.com/Ri0ee/typst-rtu | https://raw.githubusercontent.com/Ri0ee/typst-rtu/master/report.typ | typst | #import "@preview/codelst:2.0.1": *
#import "@preview/tablex:0.0.8": *
#import "template/template.typ": *
#show: project.with(
title: "Laboratory work",
subtitle: "Deducing whether the chicken or the egg",
subject: "Modern Scientology",
authors: (
(
name: "<NAME>",
group: "1. group",
id: "000KEK000",
),
(
name: "<NAME>",
group: "2. group",
id: "000LOL000",
),
),
department: "Faculty of Science and Knowledge",
year: "2023",
lang: "en"
)
= Introduction
You can use bibliography in any section you want, for example, @foo2010 and @shaw1998.
You can also show your code with highlighting and line numbers:
#sourcecode[
```cpp
#include <torch/torch.h>
struct Net : torch::nn::Module {
Net(int64_t N, int64_t M) {
W = register_parameter("W", torch::randn({N, M}));
b = register_parameter("b", torch::randn(M));
}
torch::Tensor forward(torch::Tensor input) {
return torch::addmm(b, input, W);
}
torch::Tensor W, b;
};
int main() {
Net net(4, 5);
for (const auto& p : net.parameters()) {
std::cout << p << std::endl;
}
}
```
]
== Heading level 2
=== Heading level 3
#locate(loc => {
let citation_count = query(ref, loc).filter(e => e.element == none).len()
if citation_count > 0 [#bibliography("./works.bib", style: "ieee")]
}) |
|
https://github.com/typst/packages | https://raw.githubusercontent.com/typst/packages/main/packages/preview/zhconv/0.3.1/zhconv.typ | typst | Apache License 2.0 | #let zhconv-wasm = plugin("./zhconv_typst.wasm")
#let zhconv-str(text, target, wikitext: false) = {
let wikitext-flag = if wikitext { (1,) } else { (0,) }
str(zhconv-wasm.zhconv(bytes(text), bytes(target), bytes(wikitext-flag)))
}
#let is-hans-str(text) = {
zhconv-wasm.is_hans(bytes(text)).at(0) != 0
}
#let zhconv(document, target, wikitext: false) = {
if type(document) == str {
zhconv-str(document, target, wikitext: wikitext)
}
else if type(document) == content and document.has("children") { // container
for child in document.children [
#zhconv(child, target, wikitext: wikitext)
]
}
else if type(document) == content and document.has("text"){ // typical content
zhconv(document.text, target, wikitext: wikitext)
}
else if type(document) == content and document.has("body"){ // e.g. circle, rect, list
let args = document.fields()
let body = zhconv(args.remove("body"), target, wikitext: wikitext)
document.func()(body, ..args)
}
else {
document
}
}
|
https://github.com/LDemetrios/Typst4k | https://raw.githubusercontent.com/LDemetrios/Typst4k/master/src/test/resources/suite/visualize/rect.typ | typst | // Test the `rect` function.
--- rect ---
// Default rectangle.
#rect()
--- rect-customization ---
#set page(width: 150pt)
// Fit to text.
#rect(fill: conifer)[Textbox]
// Empty with fixed width and height.
#block(rect(
height: 15pt,
fill: rgb("46b3c2"),
stroke: 2pt + rgb("234994"),
))
// Fixed width, text height.
#rect(width: 2cm, fill: rgb("9650d6"))[Fixed and padded]
// Page width, fixed height.
#rect(height: 1cm, width: 100%, fill: rgb("734ced"))[Topleft]
// These are inline with text.
{#box(rect(width: 0.5in, height: 7pt, fill: rgb("d6cd67")))
#box(rect(width: 0.5in, height: 7pt, fill: rgb("edd466")))
#box(rect(width: 0.5in, height: 7pt, fill: rgb("e3be62")))}
// Rounded corners.
#stack(
dir: ltr,
spacing: 1fr,
rect(width: 2cm, radius: 30%),
rect(width: 1cm, radius: (left: 10pt, right: 5pt)),
rect(width: 1.25cm, radius: (
top-left: 2pt,
top-right: 5pt,
bottom-right: 8pt,
bottom-left: 11pt
)),
)
// Different strokes.
#set rect(stroke: (right: red))
#rect(width: 100%, fill: lime, stroke: (x: 5pt, y: 1pt))
--- rect-stroke ---
// Rectangle strokes
#rect(width: 20pt, height: 20pt, stroke: red)
#v(3pt)
#rect(width: 20pt, height: 20pt, stroke: (rest: red, top: (paint: blue, dash: "dashed")))
#v(3pt)
#rect(width: 20pt, height: 20pt, stroke: (thickness: 5pt, join: "round"))
--- red-stroke-bad-type ---
// Error: 15-21 expected length, color, gradient, pattern, dictionary, stroke, none, or auto, found array
#rect(stroke: (1, 2))
--- rect-fill-stroke ---
#let variant = rect.with(width: 20pt, height: 10pt)
#let items = for (i, item) in (
variant(stroke: none),
variant(),
variant(fill: none),
variant(stroke: 2pt),
variant(stroke: eastern),
variant(stroke: eastern + 2pt),
variant(fill: eastern),
variant(fill: eastern, stroke: none),
variant(fill: forest, stroke: none),
variant(fill: forest, stroke: conifer),
variant(fill: forest, stroke: black + 2pt),
variant(fill: forest, stroke: conifer + 2pt),
).enumerate() {
(align(horizon)[#(i + 1).], item, [])
}
#grid(
columns: (auto, auto, 1fr, auto, auto, 0fr),
gutter: 5pt,
..items,
)
--- rect-radius-bad-key ---
// Error: 15-38 unexpected key "cake", valid keys are "top-left", "top-right", "bottom-right", "bottom-left", "left", "top", "right", "bottom", and "rest"
#rect(radius: (left: 10pt, cake: 5pt))
--- issue-1825-rect-overflow ---
#set page(width: 17.8cm)
#set par(justify: true)
#rect(lorem(70))
--- issue-3264-rect-negative-dimensions ---
// Negative dimensions
#rect(width: -1cm, fill: gradient.linear(red, blue))[Reverse left]
#rect(width: 1cm, fill: gradient.linear(red, blue))[Left]
#align(center, rect(width: -1cm, fill: gradient.linear(red, blue))[Reverse center])
#align(center, rect(width: 1cm, fill: gradient.linear(red, blue))[Center])
#align(right, rect(width: -1cm, fill: gradient.linear(red, blue))[Reverse right])
#align(right, rect(width: 1cm, fill: gradient.linear(red, blue))[Right])
|
|
https://github.com/typst/packages | https://raw.githubusercontent.com/typst/packages/main/packages/preview/scholarly-tauthesis/0.6.2/template/meta.typ | typst | Apache License 2.0 | /** meta.typ
*
* Defines document metadata. Fill in the information regarding
* your thesis into the commands specified here.
*
***/
//// Common metadata.
#let author = "<NAME>"
#let date = datetime.today()
#let examiners = (
(
title : "Professor",
firstname : "Firstname",
lastname : "Lastname",
),
(
title : "University lecturer",
firstname : "Firstname",
lastname : "Lastname",
),
)
/**
* One of "fi" or "en".
***/
#let language = "fi"
/**
* This allows you to choose a citation style. See
* <https://typst.app/docs/reference/model/bibliography/#parameters-style>
* for possible options.
***/
#let citationstyle = "ieee"
/**
* Set this to false if you are an international student and do
* not need a Finnish abstract.
***/
#let include-finnish-abstract = true
/**
* Set this to true before compiling your document, if you intend
* to print a physical copy of it.
***/
#let physically-printed = false
//// Finnish metadata.
#let alaotsikko = [Alaotsikko] // or none
#let avainsanat = ("avainsana1", "avainsana2")
#let koulu = [Tampereen Yliopisto]
#let tiedekunta = [Tiedekunta]
#let otsikko = [Opinnäytetyöpohja]
#let työntyyppi = [Diplomityö]
#let sijainti = [Tampereella]
//// English metadata.
#let faculty = "Faculty"
#let keywords = ("keyword1", "keyword2")
#let university = [Tampere University]
#let subtitle = [Subtitle] // or none
#let thesistype = "Master's thesis"
#let title = "Thesis template"
#let location = "Tampere"
|
https://github.com/juicebox-systems/ceremony | https://raw.githubusercontent.com/juicebox-systems/ceremony/main/instructions/ceremony.typ | typst | MIT License | #import "data.typ": /*
*/ boot_dvd_sha256, /*
*/ git_commit_hash, /*
*/ known_hashes, /*
*/ read_sha256sums, /*
*/
#import "debug.typ": debug_level, debug_text
#import "exception.typ": exception_sheet
#import "model.typ": /*
*/ assert_card, /*
*/ assert_card_reader, /*
*/ assert_card_reader_connected, /*
*/ assert_component_loaded, /*
*/ assert_computer_on, /*
*/ assert_computer_plugged_in, /*
*/ assert_dvd_drive, /*
*/ assert_hsm_installed, /*
*/ assert_hsm_mode, /*
*/ assert_wrist_strap_connected, /*
*/ boot_dvd, /*
*/ boot_dvd_title, /*
*/ realm_dvd, /*
*/ realm_dvd_title, /*
*/ set_card_reader, /*
*/ set_component_loaded, /*
*/ set_wrist_strap_connected, /*
*/ vendor_dvd, /*
*/ vendor_dvd_title, /*
*/
#import "presentation.typ": /*
*/ appendices, /*
*/ bip39_full, /*
*/ bip39_identifying, /*
*/ blank, /*
*/ blank_mac_address, /*
*/ blank_smartcard_id, /*
*/ blanks, /*
*/ ceremony_doc, /*
*/ checkbox, /*
*/ checkbox_symbol, /*
*/ checkboxes,/*
*/ component_demo, /*
*/ entry_array, /*
*/ fill_color, /*
*/ header_fill, /*
*/ hex_identifying, /*
*/ keys, /*
*/ labeled_blank_bag_id, /*
*/ morse_code, /*
*/ outpath, /*
*/ radio, /*
*/ radio_symbol, /*
*/ ref_step, /*
*/ step, /*
*/ steps, /*
*/ todo, /*
*/
#import "routines.typ": *
#show: body => ceremony_doc(
title: "Juicebox Realm Initialization Ceremony",
author: "<NAME>",
body,
)
This document contains instructions for conducting a key ceremony to initialize
a Juicebox HSM realm.
The source code for this document is available at
#link("https://github.com/juicebox-systems/ceremony")
and identified by the Git commit hash #raw(block: false, git_commit_hash).
Identifying bytes of the SHA-256 hash of the PDF file built from that source
code:
#hex_identifying(bytes: 32)
#block(
width: 50%,
radio[Practice ceremony][Production ceremony]
)
#blanks[Codename][Date][Start time][Location]
#pagebreak(weak: true)
#outline(
indent: auto,
fill: text(
fill: gray,
repeat([.#h(.25em)]),
),
)
= Introduction
The purpose of the ceremony is to create cryptographic keys that may only be
accessed within the trust boundaries of a fixed set of _HSMs_ (Hardware
Security Modules), and only while those HSMs execute a fixed software release.
Additionally, the initialization process will create a single NVRAM file on
each HSM for only the fixed software release to read and write.
One of the cryptographic keys to be generated is an asymmetric key pair used
for encrypted communication with clients. Assuming the private key is indeed
restricted to this software release on these HSMs, clients using the public key
recorded during this ceremony will have certainty that they are communicating
with this software running on the HSMs initialized during this ceremony.
The HSMs used in the ceremony are PCIe expansion cards and thus require a host
computer. The HSMs, software, and ceremony are designed so that secrets are
never accessible to the host computer. However, the security of the realm
depends on the host computer making the correct management requests to the HSMs
and presenting the expected HSM software build to the first HSM to be signed.
The ceremony will use a brand new computer that is never connected to a
network.
The computer's factory Windows OS will be used to verify the hashes of a
publicly auditable #emph(boot_dvd), as well as a vendor-proprietary
#emph(vendor_dvd). Then, the Linux OS on the #boot_dvd will be used for the
main ceremony. See @state_appendix for details on the DVDs and state
management.
Each HSM has an external port for a smartcard reader/writer. The HSMs read and
write secret keys onto smartcards for administrative operations. The ceremony
will utilize two smartcards, referred to as _ACS_ and _OCS_. The smartcards
must be used only as prescribed and must be destroyed during the ceremony.
The ceremony will involve setting up a computer, then using the first HSM to
initialize a _Security World_, write to two smartcards, sign the software, and
create the realm keys. The OCS smartcard will be destroyed after it is used to
sign the software. The keys reside in encrypted form on the host filesystem
(protected by keys that reside on the HSMs and smartcards). As that filesystem
is in volatile memory, the signed software and keys will be burned to a
#emph(realm_dvd) to be accessed later, both during the ceremony and after the
ceremony to set up the production environment.
After completing the Security World and realm initialization process on the
first HSM, the HSM will be reset. Then, each of the five HSMs (including the
first) will be enrolled in the Security World and have its NVRAM file
initialized. After the final HSM has been initialized, the ACS smartcard will
be destroyed.
= Procedures
The following roles are defined for participants of the ceremony:
- The _MC_ introduces the event, keeps it moving, and is the final decision
maker for any exceptions, as explained below.
- The _operator_ executes the steps as instructed in this document. The
operator should be the only person to approach or access the computer, HSMs,
and smartcards during the ceremony. The operator's copy of this document is
the official record.
- Any number of _witnesses_ observe the ceremony.
A small number of other non-participants may also be present for (parts of) the
ceremony, for example to record video.
If, at any point, the instructions are ambiguous, contain an error, fail to
instruct the operator in a particular situation, or must be deviated from, the
operator should write "exception" in the margin and fill out an _exception
sheet_. Several sheets are included at the end of this document
(@exception_sheet_1 through @exception_sheet_5). The participants may then
discuss concerns and options, but the MC ultimately decides how to proceed.
In this document, a checkbox (#checkbox_symbol) denotes a confirmation step
that is not optional. If the operator is unable to meet the requirements to
check a checkbox, that's an exception. A circle (#radio_symbol) is used when
exactly one of multiple mutually exclusive options is required.
The following conventions apply to dates and times hand-written into this
document, unless instructed or annotated otherwise:
- Dates and times should reflect the local time zone.
- Dates should be written as `YYYY-MM-DD`.
- Times should be written as `HH:MM` (24-hour local time with minute
precision).
- The operator's source of time should be the analog clock visible to all
participants.
The ceremony is expected to take about 6 hours. The ceremony instructions
include one break at #ref_step(<intermission>), about halfway through, allowing
(and requiring) the participants to leave the room. If any of the participants
need to leave the room at other times, that should be handled as an exception.
= Participants
#block(
breakable: false,
[
This document is filled out by the following person:
#blanks[Name][Affiliation]
]
)
#v(1em)
#block(
breakable: false,
[
Ceremony participants:
#block(
inset: (x: 2em),
[
#set text(size: 0.9em, weight: "bold")
Do not initial until the completion of the ceremony. By initialing in
this table, you agree that:
- You were present for the entire ceremony (excluding breaks).
- To the best of your knowledge, the instructions in this document were
followed correctly (except as noted elsewhere in this document) and
without deception.
- To the best of your knowledge, this document is a true and accurate
record.
If you do not agree, write "do not agree" instead of your initials and
record an explanation.
]
)
#table(
columns: (auto, 1fr, 1fr, 1in),
align: (center, center, center),
fill: header_fill,
[*Role*], [*Name*], [*Affiliation*],
[*Initials* \ (see above)],
[MC], [], [], [],
[Operator], [], [], [],
..range(10).map(i =>
([Witness], [], [], [])
).flatten()
)
]
)
= Getting Started
== Materials <materials>
#steps(
step(time: "1m", [
Inspect the operator and the environment.
#checkbox[
There is a prominent analog clock with a second hand.
]
#checkbox[
The witnesses confirm that the clock is set to the current local time.
]
#checkbox[
There are two outlets available on the wall or a power strip nearby.
]
]),
step(time: "5m", [
Inspect the materials available to the operator.
#checkbox[
The materials below are available and do not appear tampered with.
]
#checkbox[No other materials are available to the operator.]
]),
)
#let computer_brand = "Lenovo"
#let computer_model = "90T2000SUS"
#checkboxes(
title: [Materials],
[1 antistatic wrist strap],
[1 pair of scissors],
[1 Phillips screwdriver],
[1 rotary tool (to sand through smartcards)],
[1 table number holder (to display smartcards prominently when not in use)],
[2 printouts of this document],
[1 permanent marker],
[1 roll of masking tape],
[
// The ProAmpac GCS9012 tamper-evident bags insist on ballpoint pens.
2 blue ballpoint pens
],
[2 bottles of water],
[2 juice boxes (preferably apple)],
[
1 sealed pack of 100 tamper-evident bags (ProAmpac GCS0912)
// We need these to be secure, with sequential IDs, and large enough to
// fit HSMs, card readers, or this printed document.
//
// The Root DNSSEC KCK Ceremony 50 script declares these bags acceptable:
// AMPAC:
// - GCS1013 (may be discontinued?).
// - GCS0912 (appears to be the ProAmpac Valut Bundle Federal Compliant
// Bags, 9.75x12 size, clear, single-pocket).
// - GCS1216 (appears to be the ProAmpac Valut Bundle Federal Compliant
// Bags, 12.75x16 size, clear, single-pocket).
// MMF Industries (no direct web presence?):
// - 2362010N20
// - 2362011N20
//
// Diego received a sample of ProAmpac GCS0912 bags and determined that
// they are large enough for a smartcard reader and just large enough to
// hold a stack of letter-sized sheets of paper.
],
[1 pre-burned and finalized #boot_dvd],
[1 pre-burned and finalized #vendor_dvd],
[1 sealed spindle of blank DVD-Rs (for the #realm_dvd)],
[
1 computer (#computer_brand #computer_model, including a DVD burner and
keyboard, with the outer box sealed by the purchaser with tamper-evident
tape)
],
[
1 VGA video projector (limited to a low resolution so the text is visible
to all participants)
],
[
1 sealed pack of 10 Entrust smartcards
#v(0.3in) // layout hack
],
[At least 5 of the following Entrust HSMs:
#let hsm_row(sn, esn, packaging) = (
raw(sn, block: false),
raw(esn, block: false),
packaging,
radio_symbol,
radio_symbol,
[\##raw("____")],
)
#table(
columns: 6,
align: center,
fill: header_fill,
[*Serial Number*], [*ESN*], [*Packaging*], [*Present*], [*Absent*], [*Used As*],
..hsm_row("46-X19834", "A114-05E0-D947", [#todo[Bag ID]]),
..hsm_row("46-X20349", "B216-05E0-D947", [#todo[Bag ID]]),
..hsm_row("46-X20517", "3B17-05E0-D947", [#todo[Bag ID]]),
..hsm_row("46-X21267", "341A-05E0-D947", [Factory]),
..hsm_row("46-X21271", "351A-05E0-D947", [Factory]),
..hsm_row("46-X21323", "611A-05E0-D947", [Factory]),
)
The first HSM used in the ceremony should be in factory packaging, which
includes a smartcard reader. Fill in the "Used As" column as you unpack the
HSMs ("\#1", "\#2", etc). The serial number sometimes contains an
additional character after the space (likely `A`), not included here.
],
)
== Set Up the Computer <set_up_computer>
#steps(
step(label: <inspect_computer_packaging>, time: "5m", [
Inspect the computer packaging:
#checkbox[The box does not appear tampered with.]
#checkbox[
The box ends are sealed with customer-applied tamper-evident tape,
on top of somewhat loose #(computer_brand)-branded tape.
]
Inspect the #computer_brand sticker:
- #checkbox[
The model (#outpath[`(31P) M/T Model`]) is
#raw(block: false, computer_model).
]
- Serial Number #outpath[`S(SN)`]:
#entry_array("char", 8, 8)
- Wi-Fi MAC address (#outpath[`WMAC`]):
#blank_mac_address
- #blank[#outpath[`Mfg Date`] (as printed)]
Inspect the shipping sticker(s):
- #blank[#outpath[`SHIP DATE`] (as printed)]
]),
step(time: "4m30s", [
Open the computer box from the top with scissors.
*Outer Box:*
- Remove the small box containing the mouse and power cord from the outer
box.
- Remove the long box containing the keyboard from the outer box.
- Remove the computer, sandwiched by two large pieces of foam, from the
outer box.
- Put away the outer box.
*Desktop:*
- Remove the foam from the desktop, and put away the foam.
- Remove the plastic bag surrounding the desktop (which is not sealed), and
put away the bag.
*Keyboard Box:*
- Open the keyboard box.
- Remove the keyboard from its surrounding plastic (which is not sealed).
- Inspect the keyboard and the label under it.
#blank[Date on label under keyboard (#outpath[`MFG`], as shown)]
- Remove the twist tie on the keyboard's USB cable.
- Put away the keyboard box, plastic bag, and twist tie.
*Mouse and Power Cord Box:*
- Open the mouse and power cord box.
- Remove the power cable from the box.
- Remove the twist tie and plug cover on the power cable, and put away the
tie and cover.
- Remove the mouse (still in a plastic bag) and paperwork from the box,
place them into a tamper-evident bag, and put away the bag. (We don't
expect to need the mouse during this ceremony.)
#labeled_blank_bag_id
- Retain the empty box to prop up the DVD drive later.
#checkbox[The box contents did not appear tampered with or used.]
]),
step(time: "3m", [
Inspect the computer case. Set it down on its right side to inspect the
label on the bottom.
#checkbox[The case does not appear tampered with.]
#checkbox[A Windows sticker is present on the left side panel.]
#checkbox[An Intel Core i5 sticker is present on the front panel.]
#checkbox[
The serial number matches the label on the box
(#ref_step(<inspect_computer_packaging>)).
]
#checkbox[
The manufacturing date (#outpath[`Mfg Date`]) matches the label on the
box (#ref_step(<inspect_computer_packaging>)).
]
]),
step(time: "2m30s", [
Remove the left panel of the case and the front panel:
- Unscrew the two screws holding the left panel in place using the
screwdriver.
- Remove the left panel, and put it away.
- Ground yourself to the unpainted computer chassis with the antistatic
wrist strap. It can be worn on your upper arm or ankle.
- Lift up on the three plastic tabs (top, middle, bottom) to get the left
side of the front panel off.
- Wiggle the front panel off, and put it away.
#checkbox[
The power supply's wattage rating (labeled as
#outpath[`Total output continuous shall not exceed`]) is 260 W.
]
#set_wrist_strap_connected(true)
]),
step(time: "2m30s", [
Remove the SATA drive shelf:
- Brace the DVD drive and press the black and red tab towards the front of
the computer release it. Note: it may eject forcefully.
- Unplug the SATA and power cables from the back of the DVD drive.
- Set the DVD drive nearby on top of the box that the mouse and power cable
came in (since the cables are too short to set the drive down on the
table).
- Unplug the SATA and power cables from the 3.5" hard drive.
- Pull up on the silver and red tab (on the front, left side, middle) to
release the SATA drive shelf.
- Wiggle the SATA drive shelf off (with the 3.5" hard drive attached),
and put away the drive shelf.
- Plug the SATA and power cables back into the DVD drive.
]),
step(time: "3m30s", [
Remove the wireless card and antennas:
- Pull up forcefully on the plastic pin holding the wireless card in place
(near where the DC cables come out of the power supply).
- Remove a small bit of clear plastic that the pin was on.
- Remove the wireless card from the slot.
- Gently pry the two antenna cables from the wireless card.
- Pull forcefully on the front antenna to overcome the adhesive,
then remove any tape holding the cable and pull the cable through.
- Remove the plastic antenna cover on the back of the case by pushing the
tab on top (near the case fan) and wiggling the cover off.
- Pull forcefully on the rear antennas to overcome the adhesive,
then remove any tape holding the cable and pull the cable through.
#checkbox[
The Wi-Fi MAC address (#outpath[`WFM`]) on the wireless card's label
matches the label on the computer box
(#ref_step(<inspect_computer_packaging>)).
]
Place the wireless card, antennas, and plastic bits into a tamper-evident
bag for storage.
#labeled_blank_bag_id
]),
step(time: "1m", [
Prepare the PCIe x16 slot:
- Pull up on the silver and red tab above the placeholder brackets near the
PCIe slots to open the flap.
- Remove the metal placeholder bracket blocking the PCIe x16 slot and put
it away.
- Close the metal flap.
]),
step(time: "3m", [
Open the projector packaging, and put away the packaging.
#checkbox[The packaging does not appear tampered with.]
#checkbox[The projector does not appear tampered with.]
]),
step(time: "30s", [
Plug in the projector power and turn on the projector.
]),
step(time: "30s", [
Plug the USB keyboard and VGA projector into the computer.
]),
boot_into_windows(),
step(time: "1m", [
When the Windows "Out of Box Experience" prompts for input (asking for your
country or region):
- Press #keys(("Shift", "F10")) to open a terminal. (Do not use the
terminal. Opening it switches focus, which enables more hotkeys.)
- Press #keys(("Win", "r")) to open a Run dialog.
- Run `powershell`.
- Press #keys(("Win", "Up")) to maximize the Powershell window.
]),
load_dvd(boot_dvd),
step(time: "1m30s", [
Calculate the SHA-256 hash of the #boot_dvd image.
```powershell
$s = [system.io.file]::open('\\.\e:', 'open', 'read', 'read')
get-filehash -inputstream $s
$s.close()
```
The `get-filehash` command should take about 1 minute.
// This displays 3 column headers and one row:
// Algorithm: SHA256
// Hash: 64 hex characters (uppercase)
// Path: empty
#checkbox[
The #boot_dvd's SHA-256 digest matches
#raw(block: false, boot_dvd_sha256).
]
]),
step(time: "3m", [
Copy the main filesystem image and a small script from the #boot_dvd onto
the NVMe drive.
```powershell
dir
cp -verbose e:\live\filesystem.squashfs
cp -verbose e:\entrust.ps1
dir
```
This will copy the files into `C:\Users\defaultuser0\`. The first copy
command should take about 2 minutes, and the second one should take up to a
few seconds.
]),
load_dvd(vendor_dvd),
step(time: "10m", [
Copy the Entrust-provided files from the #vendor_dvd onto the NVMe drive.
```powershell
cat entrust.ps1
set-executionpolicy -scope process unrestricted
.\entrust.ps1
dir
```
Enter #keys("Y") for yes when setting the policy.
The script verifies the hashes of the files and copies them into
`C:\Users\defaultuser0\`. It should take about 10 minutes. During this
time, review @state_appendix, which discusses the various DVDs and files.
]),
load_dvd(boot_dvd),
power_off(os: "windows"),
boot_into_dvd(uefi_setup: true),
step(time: "2m", [
Display some information about the computer's devices:
```sh
lsblk
lsusb
lspci | nl
```
#checkbox[
`lsblk` reports `loop0` (loopback devices), `sr0` (the DVD drive),
`nvme0n1` with 4 partitions (the Windows disk), and no other block
devices.
]
#checkbox[
`lsusb` reports a "3.0 root hub", a "2.0 root hub", a "Lenovo New
Calliope USB Keyboard", and no other USB devices.
]
#checkbox[
`lspci` reports 24 devices: 22 from Intel, a "Non-Volatile memory
controller" from Samsung Electronics, and an "Ethernet controller" from
Realtek Semiconductor.
]
]),
power_off(),
)
= Realm Creation <realm_creation>
== Prepare the First HSM
#steps(
unpack_hsm(first: true),
boot_into_dvd(),
initialize_hsm(0),
)
== Unpack the Smartcards
#steps(
step(time: "30s", [
Inspect the smartcard packaging.
#checkbox[The packaging does not appear tampered with.]
]),
step(time: "1m", [
Open the smartcard packaging. Take out two cards, and put the rest in a
tamper-evident bag.
#labeled_blank_bag_id
]),
step(time: "1m20s", [
Inspect the first smartcard. Label it "OCS".
#checkbox[The smartcard does not appear tampered with.]
#checkbox[The smartcard has nShield and Entrust trademarks.]
Smartcard ID:
#blank_smartcard_id
]),
step(label: <acs_id>, time: "1m20s", [
Inspect the second smartcard. Label it "ACS".
#checkbox[The smartcard does not appear tampered with.]
#checkbox[The smartcard has nShield and Entrust trademarks.]
Smartcard ID:
#blank_smartcard_id
]),
step(time: "2m", [
Ask a few witnesses to choose a distinctive character or shape, and draw
these on the cards.
]),
step(time: "15s", [
Place the ACS smartcard in the card reader and place the OCS smartcard
visibly in the stand.
#set_card_reader(from: none, to: "ACS")
]),
)
== Create the Security World and Sign the Software
#steps(
step(label: <create_world>, time: "2m", [
Create the HSM Security World, enroll the first HSM in it, and write to the
ACS smartcard. Enter an empty passphrase when prompted.
```sh
ceremony hsm create-world
```
Identifying bytes of `KNSO` hash (#outpath[`hknso`]):
#hex_identifying(bytes: 20)
This command takes about 45 seconds. It writes to the ACS smartcard and
creates encrypted keys on the computer's filesystem.
#assert_card("ACS")
#assert_hsm_mode("initialization")
#assert_component_loaded("secworld", true)
]),
step(label: <display_hkmsw>, time: "1m", [
Display information about the Security World:
```sh
ceremony hsm world-info
```
Identifying bytes of `KMSW` Security World key hash
(#outpath[`World`][`hkm`]):
#hex_identifying(bytes: 20)
#assert_component_loaded("secworld", true)
]),
restart_hsm("operational"),
step(time: "10s", [
Remove the ACS smartcard from the card reader. Place the OCS smartcard in
the card reader and place the ACS smartcard visibly in the stand.
#set_card_reader(from: "ACS", to: "OCS")
]),
step(time: "20s", [
Write to the OCS smartcard. Enter an empty passphrase when prompted.
```sh
ceremony smartcard write-ocs
```
This command should take about 12 seconds.
#assert_hsm_mode("operational")
#assert_card("OCS")
#assert_component_loaded("secworld", true)
]),
step(time: "10s", [
Create a signing key:
```sh
ceremony sign create-key
```
This command should take about 6 seconds. It writes an encrypted key to the
host computer's filesystem.
#assert_card("OCS")
#assert_hsm_mode("operational")
#assert_component_loaded("secworld", true)
]),
step(label: <signing_key_hash>, time: "1m", [
Display information about the signing key:
```sh
ceremony sign key-info
```
Identifying bytes of signing key hash
(#outpath[`Key AppName seeinteg Ident jbox-signer`][`hash`]):
#hex_identifying(bytes: 20)
#assert_component_loaded("secworld", true)
]),
install_codesafe(),
step(time: "40s", [
Build the `entrust_init` tool:
```sh
ceremony build init
```
This command should take about 30 seconds.
#checkbox[
The SHA-256 hash of `entrust_init` encoded as a BIP-39 mnemonic matches:
#bip39_full(bytes: 32, phrase: known_hashes.at("entrust_init_bip39"))
]
#assert_component_loaded("codesafe", true)
#set_component_loaded("entrust_init", true)
]),
step(time: "40s", [
Build the HSM software:
```sh
ceremony build hsm
```
This command should take about 30 seconds.
#checkbox[
Identifying words of the BIP-39 mnemonic encoding of the SHA-256 hash of
`entrust_hsm.elf` match:
#bip39_identifying(
bytes: 32,
phrase: known_hashes.at("entrust_hsm_elf_bip39"),
)
The full mnemonic is checked in the next step when this software is
signed.
]
#assert_component_loaded("codesafe", true)
]),
step(time: "1m", [
Sign the HSM software:
```sh
ceremony sign software
```
This command should take about 2 seconds. It requires the OCS smartcard. It
reads an ELF-format executable from the host computer's filesystem and
writes a signed version of that back to the host computer's filesystem.
#checkbox[
The SHA-256 hash of the input file (`entrust_hsm.elf`) encoded as a
BIP-39 mnemonic matches:
#bip39_full(bytes: 32, phrase: known_hashes.at("entrust_hsm_elf_bip39"))
]
Identifying words of the BIP-39 mnemonic encoding of the SHA-256 hash of
the signed file (`entrust_hsm.sar`):
#bip39_identifying(bytes: 32)
#assert_card("OCS")
#assert_component_loaded("secworld", true)
]),
step(time: "1m", [
Sign the HSM userdata:
```sh
ceremony sign userdata
```
This command should take about 1 second. It requires the OCS smartcard. It
reads the string `dummy` from the host computer's filesystem (the content
is ignored) and writes a signed version of that back to the host computer's
filesystem.
#checkbox[
The input file (`userdata.dummy`) SHA-256 hash encoded as a BIP-39
mnemonic matches:
#bip39_full(
bytes: 32,
// ceremony bip39 encode $(echo -n dummy | sha256sum | cut -d' ' -f1)
phrase: "
remember bind flat patch
banana recall possible tourist
width cycle fringe next
visa people private ready
price tree comic glow
together print annual cash
",
)
]
Identifying words of the BIP-39 mnemonic encoding of the SHA-256 hash of
the signed file (`userdata.sar`):
#bip39_identifying(bytes: 32)
#assert_card("OCS")
#assert_component_loaded("secworld", true)
#set_component_loaded("sar_files", true)
]),
)
== Destroy the OCS Smartcard
#steps(
destroy("OCS")
)
== Create the Realm Keys
#steps(
step(time: "3m", [
Generate the realm keys:
```sh
ceremony realm create-keys
```
Each key's ACL is the same, except for identifiers, having three permission
groups:
- Permission Group 1 allows reading the ACL itself and allows the key to be
duplicated with the same ACL. It should look like:
```
Action: OpPermissions: DuplicateHandle, GetACL
```
- Permission Group 2 allows HSM software signed with the signing key to
read the key (and associated data, which is not used). It should look
like:
```
Requires Cert: hash: ❰SIGNING-KEY-HASH❱ mechanism: Any
Flags: certmech_present
Action: OpPermissions: ExportAsPlain, GetAppData
```
- Permission Group 3 allows the key to be saved as a blob on the host
filesystem, encrypted by the Security World key (`KMSW`), only once. It
should look like (in two lines, wrapped here):
```
Use Limit: Global: max: 1 id: ❰VARYING-40-HEX-CHARS❱
Action: MakeBlob: Flags: AllowKmOnly, AllowNonKm0, kmhash_present kmhash: ❰KMSW-HASH❱
```
#checkbox[
#outpath[`Creating key simple,jbox-mac`...][`Permission Group 2`][`Requires Cert`][`hash`]
matches the signing key hash in #ref_step(<signing_key_hash>).
]
#checkbox[
#outpath[`Creating key simple,jbox-mac`...][`Permission Group 3`][`Action`][`kmhash`]
matches the Security World key hash in #ref_step(<display_hkmsw>).
]
#checkbox[
#outpath[`Creating key simple,jbox-record`...][`Permission Group 2`][`Requires Cert`][`hash`]
shows the same value as the `jbox-mac` permissions.
]
#checkbox[
#outpath[`Creating key simple,jbox-record`...][`Permission Group 3`][`Action`][`kmhash`]
shows the same value as the `jbox-mac` permissions.
]
#checkbox[
#outpath[`Creating key simple,jbox-noise`...][`Permission Group 2`][`Requires Cert`][`hash`]
shows the same value as the `jbox-mac` permissions.
]
#checkbox[
#outpath[`Creating key simple,jbox-noise`...][`Permission Group 3`][`Action`][`kmhash`]
shows the same value as the `jbox-mac` permissions.
]
// Note: does not require smartcard.
#assert_component_loaded("entrust_init", true)
#set_component_loaded("simple_keys", true)
]),
step(time: "1m", [
Verify the ACL on each key no longer allows creating a key blob:
```sh
ceremony realm print-acl mac
ceremony realm print-acl record
ceremony realm print-acl noise
```
#checkbox[
`Permission Group 3` is no longer present for the `jbox-mac` key.
]
#checkbox[
`Permission Group 3` is no longer present for the `jbox-record` key.
]
#checkbox[
`Permission Group 3` is no longer present for the `jbox-noise` key.
]
// Note: does not require smartcard.
#assert_component_loaded("entrust_init", true)
#assert_component_loaded("simple_keys", true)
]),
step(time: "3m", [
Record the public key that clients will use to authenticate this realm.
```sh
ceremony realm noise-public-key
```
The output `Qx` is the X25519 public key encoded in hex.
Identifying bytes of Noise public key (#outpath[`Qx`]):
#hex_identifying(bytes: 32)
Copy and paste the public key into the next command (using the keyboard
shortcuts documented in @tmux_reference):
```sh
ceremony bip39 encode ❰Qx❱
```
Noise public key encoded as a BIP-39 mnemonic phrase:
#bip39_full(bytes: 32)
#assert_component_loaded("simple_keys", true)
#assert_component_loaded("secworld", true)
]),
)
== Write the #realm_dvd_title
#steps(
step(label: <create_realm_dvd_iso>, time: "0s", [
Create the #realm_dvd image:
```sh
ceremony realm-dvd create-iso
```
This command should take less than 1 second. See @state_appendix for
details on which files are included on the image.
Identifying bytes of SHA-256 hash of the #realm_dvd image
(`/root/realm.iso`):
#hex_identifying(bytes: 32)
#assert_component_loaded("entrust_init", true)
#assert_component_loaded("sar_files", true)
#assert_component_loaded("simple_keys", true)
]),
eject_dvd(),
step(time: "30s", [
Inspect the blank DVD packaging.
#checkbox[The packaging does not appear tampered with.]
]),
step(time: "2m", [
Take one blank DVD and label it with:
- "Ceremony #realm_dvd_title",
- the local date and time, and
- the identifying bytes of the SHA-256 hash of the ISO file from
#ref_step(<create_realm_dvd_iso>).
#checkbox[The DVD does not appear tampered with and appears blank.]
Place the remaining spindle in a tamper-evident bag.
#labeled_blank_bag_id
]),
load_dvd(realm_dvd),
step(time: "4m", [
Write the image to the DVD:
```sh
ceremony realm-dvd write
```
This command should take about 4 minutes and should eject the DVD when
completed. Ejecting the DVD is intended to clear any OS or drive caches.
#checkbox[The computer ejected the DVD.]
#set_dvd_drive(from: realm_dvd, to: none)
]),
load_dvd(realm_dvd),
step(time: "1m", [
Verify the files were written to the #realm_dvd correctly:
```sh
ceremony realm-dvd verify
```
#assert_component_loaded("entrust_init", true)
#assert_component_loaded("sar_files", true)
#assert_component_loaded("simple_keys", true)
]),
)
== Clear the First HSM
#steps(
erase_hsm(),
load_dvd(boot_dvd),
power_off(),
)
= HSM Enrollment
== Set up the First HSM
#steps(
boot_into_dvd(),
install_secworld(),
restart_hsm("initialization"),
load_dvd(realm_dvd),
restore_realm_dvd_files(),
enroll_hsm_and_init_nvram(),
load_dvd(boot_dvd),
power_off(),
store_hsm(),
)
== Intermission
#steps(
step(time: "15s", [
Detach the operator end of the antistatic wrist strap, leaving it connected
to the computer chassis.
#set_wrist_strap_connected(false)
]),
step(time: "1m", [
Remove the ACS smartcard from the stand.
Wrap the end of the smartcard with masking tape three times over, covering
the electronics.
Place the ACS smartcard in a tamper-evident bag.
#labeled_blank_bag_id
]),
step(time: "1m", [
Place the card reader in a tamper-evident bag.
#labeled_blank_bag_id
#assert_card_reader(none)
#assert_card_reader_connected(false)
]),
step(time: "30s", [
_MC:_ Decide on an approximate duration for the break.
#blanks[Duration][Resume at (time)]
]),
step(time: "1m", [
Place this document in a tamper-evident bag.
#labeled_blank_bag_id
]),
step(label: <intermission>, time: "30m", [
The operator must step away from the station. Then, everyone (all
participants and anyone else present) should leave the room together.
*No one may enter the room during the break.*
After the break, all participants should reenter the room together. Then,
the operator should return to the station and remove this document from its
bag.
#checkbox[The bag does not appear tampered with.]
#checkbox[The bag ID matches the one recorded above.]
#checkbox[
By a show of hands, each of the participants agrees that, to the best of
their knowledge, no one enter the room during the break.
#blank[Count]
]
]),
step(time: "30s", [
Remove the card reader from its bag.
#checkbox[The bag does not appear tampered with.]
#checkbox[The bag ID matches the one recorded above.]
]),
step(time: "30s", [
Remove the ACS smartcard from the bag, remove the masking tape from it, and
place it visibly in the stand.
#checkbox[The bag does not appear tampered with.]
#checkbox[The bag ID matches the one recorded above.]
#checkbox[The smartcard ID matches #ref_step(<acs_id>).]
]),
step(time: "15s", [
Ground yourself to the unpainted computer chassis with the antistatic wrist
strap. It can be worn on your upper arm or ankle.
#set_wrist_strap_connected(true)
]),
)
#let ordinals = ("First", "Second", "Third", "Fourth", "Fifth")
#let last_hsm = 4
#for i in range(1, last_hsm + 1) [
== Set Up the #ordinals.at(i) HSM
#steps(
unpack_hsm(),
boot_into_dvd(),
initialize_hsm(i),
load_dvd(realm_dvd),
restore_realm_dvd_files(),
if i < last_hsm {(
enroll_hsm_and_init_nvram(leave_acs_in_reader: false),
load_dvd(boot_dvd),
power_off(),
store_hsm(),
)} else {(
// For the last HSM, leave the ACS smartcard in the reader so that it can
// be wiped. The remaining steps are done after the ACS destruction in
// the Conclusion.
enroll_hsm_and_init_nvram(leave_acs_in_reader: true),
)},
)
]
= Conclusion
#steps(
destroy("ACS"),
eject_dvd(),
power_off(),
store_hsm(),
step(time: "1m", [
Place the card reader in a tamper-evident bag.
#labeled_blank_bag_id
]),
step(time: "2m", [
Put away the computer, keyboard, and other materials. Detach both ends of
the antistatic wrist strap.
#set_wrist_strap_connected(false)
]),
step(time: "3m", [
Close out any unused exception sheets.
#blank[Exception sheets used]
]),
step(time: "5m", [
Collect initials from all ceremony participants.
#radio[All participants initialed][Not all participants initialed]
]),
step(time: "5m", [
Display each sheet of this document in sequence to be recorded on video.
]),
)
The ceremony is now complete.
#assert_card_reader(none)
#assert_card_reader_connected(false)
#assert_computer_on(false)
#assert_computer_plugged_in(false)
#assert_dvd_drive(none)
#assert_hsm_installed(false)
#assert_hsm_mode(none)
#assert_wrist_strap_connected(false)
The operator should digitize and publish this document as soon as possible.
Store the paper copy in a tamper-evident bag.
#labeled_blank_bag_id
#show: appendices
= State <state_appendix>
Other than the computer's factory-provided firmware and Windows installation,
the state entering the ceremony is on the public #emph(boot_dvd) (see
@boot_dvd) and the Entrust-confidential #emph(vendor_dvd) (see @vendor_dvd).
In @set_up_computer, several files are copied from the DVDs to the NVMe drive,
to avoid delays from reading DVDs repeatedly during the ceremony. These files
are copied into the primary Windows partition (`C:` or `/dev/nvme0n1p3`, an
NTFS filesystem) into `/Users/defaultuser0`:
+ `/live/filesystem.squashfs` from the #boot_dvd,
+ `/entrust.ps1` from the #boot_dvd,
+ `/CODESAFE.ZIP` from the #vendor_dvd,
+ `/FIRMWARE.ZIP` from the #vendor_dvd, and
+ `/SECWORLD.ZIP` from the #vendor_dvd.
Subsequently, when booting the #boot_dvd, the initial ramdisk will attempt to
mount the Windows partition in read-only mode, validate the copy of the
Squashfs filesystem against the SHA-256 hash found on the #boot_dvd, and boot
into that Squashfs filesystem. If the #boot_dvd cannot validate this hash, it
raises an error.
After booting the #boot_dvd, the Windows partition remains mounted (at
`/run/win`). The ceremony tool verifies the hashes of the copies of the
#vendor_dvd files as found on the Windows partition, then uses those copies
instead of reading the #vendor_dvd.
In @realm_creation, several new files are produced that are burned to a blank
#emph(realm_dvd) (see @realm_dvd). The #realm_dvd is used during the ceremony
and must be retained to set up the realm's production environment.
The HSMs themselves contain some state initialized during the ceremony. Each
will contain the `KMSW` key to decrypt the encryption keys found on the
#realm_dvd, and each will have an empty file allocated on its NVRAM. After the
ceremony, each HSM's key and NVRAM file are only accessible within the trust
boundary of that HSM.
== #boot_dvd_title <boot_dvd>
The #boot_dvd contains only public content, which can be reviewed and
reproduced at #link("https://github.com/juicebox-systems/ceremony/"). The hash
of the ISO 9660 image burned to the DVD is #raw(block: false, boot_dvd_sha256).
The #boot_dvd includes:
- a bootable Linux OS based on Debian 12 (Bookworm),
- an official Rust/Cargo toolchain (pre-installed in binary form),
- Rust's standard library source code (pre-installed in source form),
- Juicebox "ceremony tool" source code (from
#link(
"https://github.com/juicebox-systems/ceremony/tree/" +
git_commit_hash +
"/tool"
), at `/root/ceremony/tool`),
- Juicebox HSM software and tooling source code (from
#link(
"https://github.com/juicebox-systems/juicebox-hsm-realm/tree/" +
known_hashes.at("juicebox_hsm_realm_git_sha1")
), at `/root/juicebox-hsm-realm`),
- source code for Rust dependencies for the above three bullets (at
`/root/crates`), and
- CodeSafe feature activation files received from Entrust for these particular
HSMs (at `/root/features`).
Most of the #boot_dvd contents are stored inside a root filesystem in a
Squashfs file (`/live/filesystem.squashfs`), while the boot loader, kernel,
initial ramdisk, and SHA-256 hashes of all files reside outside of this
filesystem. The #boot_dvd writes all filesystem changes to an in-memory
overlay, which is discarded on shutdown.
== #vendor_dvd_title <vendor_dvd>
The #vendor_dvd consists of three files that are distributed by Entrust to
their nShield HSM customers. We have not found a public location listing these
hashes, and we are not authorized to publish these files. See
#link("https://nshielddocs.entrust.com/") and contact
#link("mailto:<EMAIL>") or
#link("mailto:<EMAIL>") for details.
#let vendor_dvd_file(
path: none,
vendor_filename: none,
sha256: none,
bytes: none,
description,
) = table(
columns: 2,
fill: (col, row) => if col == 0 {
fill_color
} else {
none
},
[Path on #vendor_dvd], raw(path, block: false),
[Entrust filename], raw(vendor_filename, block: false),
[SHA-256 hash], raw(sha256, block: false),
[Size], [#raw(bytes) bytes],
[Description], description,
)
#let vendor_input_hashes = read_sha256sums("../vendor-dvd/sha256sum.inputs.txt")
#vendor_dvd_file(
path: "/CODESAFE.ZIP",
vendor_filename: "Codesafe_Lin64-13.4.3.iso.zip",
sha256: vendor_input_hashes.at("./inputs/Codesafe_Lin64-13.4.3.iso.zip"),
bytes: "586,472,486",
[
Compiler, libraries, and header files used to build source code to run on
the HSM or interface with the HSM
],
)
#vendor_dvd_file(
path: "/FIRMWARE.ZIP",
vendor_filename: "nShield_HSM_Firmware-13.4.4.iso.zip",
sha256: vendor_input_hashes.at("./inputs/nShield_HSM_Firmware-13.4.4.iso.zip"),
bytes: "1,856,501,013",
[Signed HSM firmware images],
)
#vendor_dvd_file(
path: "/SECWORLD.ZIP",
vendor_filename: "SecWorld_Lin64-13.4.4.iso.zip",
sha256: vendor_input_hashes.at("./inputs/SecWorld_Lin64-13.4.4.iso.zip"),
bytes: "678,977,000",
[Host tools, daemons, and driver to manage HSMs],
)
Note that Linux maps the filenames to lowercase when mounting the #vendor_dvd.
The overall hash of the #vendor_dvd ISO 9660 image is \
#raw(block: false,
read_sha256sums("../vendor-dvd/sha256sum.output.txt")
.at("./target/vendor.iso")
).
== #realm_dvd_title <realm_dvd>
These files are copied from the root filesystem overlay to the root directory
of the #realm_dvd:
- Host path: `/opt/nfast/kmdata/local/key_simple_jbox-mac`
A blob of the symmetric key that Juicebox's HSM code uses for HSM-to-HSM
authentication, encrypted by `KMSW`.
- Host path: `/opt/nfast/kmdata/local/key_simple_jbox-noise`
A blob of the asymmetric key used for client-to-HSM communication, encrypted
by `KMSW`.
- Host path: `/opt/nfast/kmdata/local/key_simple_jbox-record`
A blob of the symmetric key that Juicebox's HSM code uses to encrypt its
data, encrypted by `KMSW`.
- Host path: `/opt/nfast/kmdata/local/world`
Contains key blobs for `KMSW` and `KNSO`, encrypted by key(s) encoded in the
ACS smartcard(s), as well as other Security World blobs and information.
- Host path: \
`/root/juicebox-hsm-realm/target/powerpc-unknown-linux-gnu/release/entrust_hsm.sar`
Juicebox's executable program to run within the HSMs, signed by the signing
key.
- Host path: \
`/root/juicebox-hsm-realm/target/powerpc-unknown-linux-gnu/release/userdata.sar`
The string `dummy`, signed by the signing key. This is required to run
software on the HSM, but Juicebox's software does not read the contents.
- Host path: `/root/juicebox-hsm-realm/target/release/entrust_init`
A tool that runs on the host computer to create HSM keys and initialize HSM
NVRAM with appropriate ACLs. This is included on the #realm_dvd to avoid
having to compile it repeatedly.
The #realm_dvd is used during the ceremony and must be retained to set up the
realm's production environment. We have chosen not to publish the #realm_dvd
contents because we are not familiar with the exact file formats and
cryptography used in these files.
= HSM Keys
This appendix describes relevant keys created by the HSM. The authoritative
resource for this information is Entrust (see the Security Manual:
#link("https://nshielddocs.entrust.com/security-world-docs/v13.3/security-manual/intro.html")).
The keys are identified by hashes, encoded as 40 hexadecimal characters. These
hashes are labeled using several conventions but are most commonly prefixed
with an `h` (for example, `hknso` for the hash of the `KNSO` key).
#table(
columns: 2,
fill: header_fill,
[*Name*],
[*Description*],
[`KLTU`],
[
The key that is encoded in the OCS smartcard(s). Its hash is output when
creating a new OCS.
],
[`KMSW` or `KM_sw`],
[
The Security World key that is copied to every HSM in the Security World.
It is generated when the Security World is created. It encrypts application
key blobs in the Security World.
The key is stored within the HSMs that are enrolled in the Security World.
It is also stored as a blob in `/opt/nfast/kmdata/local/world`, encrypted
by a key that's encoded in the ACS smartcard(s).
Although the Security World key is one of multiple "module" keys (`KM`
keys), the hash of `KMSW` is reported by `/opt/nfast/bin/nfkminfo`
(`ceremony hsm world-info`) as `hkm` and in the ACLs as `kmhash`.
],
[`KNSO`],
[
A key that is created and its hash is output when creating a Security
World. When other HSMs are enrolled in the Security World, they output the
same hash.
The key blob is stored in `/opt/nfast/kmdata/local/world`, encrypted by a
key that's encoded in the ACS smartcard(s).
],
)
= Reference
== NATO Alphabet and Morse Code
The NATO alphabet should be used to spell out alphanumeric strings, except
using normal English number pronunciation.
The HSMs have a blue LED that emits error codes in Morse code. Refer to
#link("https://nshielddocs.entrust.com/1/solo-ug/13.3/morse-code-errors") for
the meaning of the error codes. The dashes should have 3 times the duration of
a dot, and the word gap should be 7 times the duration of a dot.
#let alphabet = (
("A", "Alfa", ".-"),
("B", "Bravo", "-..."),
("C", "Charlie", "-.-."),
("D", "Delta", "-.."),
("E", "Echo", "."),
("F", "Foxtrot", "..-."),
("G", "Golf", "--."),
("H", "Hotel", "...."),
("I", "India", ".."),
("J", "Juliett", ".---"),
("K", "Kilo", "-.-"),
("L", "Lima", ".-.."),
("M", "Mike", "--"),
("N", "November", "-."),
("O", "Oscar", "---"),
("P", "Papa", ".--."),
("Q", "Quebec", "--.-"),
("R", "Romeo", ".-."),
("S", "Sierra", "..."),
("T", "Tango", "-"),
("U", "Uniform", "..-"),
("V", "Victor", "...-"),
("W", "Whiskey", ".--"),
("X", "Xray", "-..-"),
("Y", "Yankee", "-.--"),
("Z", "Zulu", "--.."),
("0", "Zero", "-----"),
("1", "One", ".----"),
("2", "Two", "..---"),
("3", "Three", "...--"),
("4", "Four", "....-"),
("5", "Five", "....."),
("6", "Six", "-...."),
("7", "Seven", "--..."),
("8", "Eight", "---.."),
("9", "Nine", "----."),
)
#let alphabet_table(rows) = table(
align: (center + horizon, left + horizon, left + horizon),
columns: 3,
fill: header_fill,
[*Letter*], [*Code Word*], [*Morse Code*],
..rows.map(((letter, word, morse)) => (
raw(letter),
word,
morse_code(morse),
)).flatten()
)
#align(center, grid(
column-gutter: 2em,
columns: 3,
alphabet_table(alphabet.slice(0, 18)),
alphabet_table(alphabet.slice(18)),
))
#pagebreak(weak: true)
== Windows Keyboard Shortcuts
- #keys(("Win", "R")) to open window to launch a program. For example, you can
then run `powershell`.
- #keys(("Win", "Up")) to maximize the current window.
- #keys(("Win", "Down")) to un-maximize the current window if maximized, or to
minimize it otherwise.
- #keys(("Alt", "Tab")) to switch windows.
- #keys(("Alt", "F4")) to close the current window.
== tmux Keyboard Shortcuts <tmux_reference>
#let tmux_prefix = ("Ctrl", "a")
The `tmux` terminal multiplexer is used in the #boot_dvd environment, primarily
to provide scrolling and copy-paste. `tmux` is set to `vi` mode and
#keys(tmux_prefix) is the prefix key.
- #keys(tmux_prefix, "?") for online help (and then #keys("q") or
#keys("Enter") to close the help).
- #keys(tmux_prefix, "[") to enter copy mode.
- #keys(tmux_prefix, "]") to paste.
In copy mode (a scroll indicator will appear on the top-right):
- #keys("Space") to start a visual selection.
- #keys("Enter") to copy the current selection and exit copy mode.
- #keys("Esc") to cancel a selection.
- #keys("q") to exit copy mode.
- Move the cursor with `vi`-like keys or arrows.
- #keys(("Ctrl", "y")) to scroll up by one line and #keys(("Ctrl", "e")) to
scroll down by one line.
- #keys("PageUp") and #keys("PageDown") to scroll by almost one screen.
#for i in range(1, 6) {
exception_sheet(i)
}
#if debug_level >= 2 [
= #debug_text[Component Demo]
#component_demo
]
|
https://github.com/hyrious/typst-syntax-highlight | https://raw.githubusercontent.com/hyrious/typst-syntax-highlight/main/syntax_test_typst.typ | typst | MIT License | // SYNTAX TEST "Packages/Typst/Typst.sublime-syntax"
// foo
// ^ comment.line.double-dash
/**/
// <- comment.block.empty.typst punctuation.definition.comment.typst
// #41
// Nested "//" doesn't count as line comment.
/* // */
// ^ - comment
// #28
/* multiline
/* nested */
comment */
// ^^ comment.block.typst punctuation.definition.comment.end.typst
= Heading
// <- markup.heading.typst punctuation.definition.heading.begin.typst
// ^ markup.heading.typst - punctuation
// <- - entity.name.section
//^^^^^^^ entity.name.section.typst
// ^ meta.whitespace.newline.typst
- foo
- bar
- buzz
//^ markup.list.unnumbered.typst
// ^ markup.list.unnumbered.bullet.typst punctuation.definition.list_item.typst
foo\ bar
// ^ meta.hard-line-break.typst constant.character.escape.typst
foo *bar* _buzz_
// ^^^^^ markup.bold.typst
// ^ punctuation.definition.bold.begin.typst
// ^ punctuation.definition.bold.end.typst
// ^^^^^^ markup.italic.typst
// ^ punctuation.definition.italic.begin.typst
// ^ punctuation.definition.italic.end.typst
foo _*bar*_ _*buzz* buf_ zzz
// ^^^^^^^ markup.italic.typst markup.bold.typst
// ^^^^^^^ markup.italic.typst markup.bold.typst
// ^^^^ markup.italic.typst - markup.bold.typst
foo _bar_buzz_ buf
// ^^^^^^^^^^ markup.italic.typst
// ^ - punctuation.definition.italic
```js
//^ punctuation.definition.raw.code-fence.begin.typst
// ^^ constant.other.language-name.typst
console.log(1)
```
//^ punctuation.definition.raw.code-fence.end.typst
`raw`
// <- markup.raw.inline.typst punctuation.definition.raw.begin.typst
//^^^ markup.raw.inline.typst
// ^ punctuation.definition.raw.end.typst
link: https://example.org?a=%20b
// ^^^^^^^^^^^^^^^^^^^^^^^^^^ markup.underline.link.typst
#1
//^ meta.number.integer.decimal.typst constant.numeric.value.typst
#0xff
//^^^^ meta.number.integer.hexadecimal.typst
//^^ constant.numeric.base.typst
// ^^ constant.numeric.value.typst
#0o10
//^^^^ meta.number.integer.octal.typst
//^^ constant.numeric.base.typst
// ^^ constant.numeric.value.typst
#0b1001
//^^^^^^ meta.number.integer.binary.typst
//^^ constant.numeric.base.typst
// ^^^^ constant.numeric.value.typst
#3.14
//^^^^ meta.number.float.decimal.typst constant.numeric.value.typst
// ^ punctuation.separator.decimal.typst
#1e4
//^^^ meta.number.float.decimal.typst constant.numeric.value.typst
#rect(width: 72pt)
// ^^^^ meta.number.integer.decimal.typst
// ^^ constant.numeric.value.typst
// ^^ constant.numeric.suffix.typst
// ^^^^^ variable.parameter.typst
// ^ punctuation.separator.parameter.typst
#rect(width: 254mm)
// ^^^^^ meta.number.integer.decimal.typst
// ^^^ constant.numeric.value.typst
// ^^ constant.numeric.suffix.typst
#rect(width: 2.54cm)
// ^^^^^^ meta.number.float.decimal.typst
// ^^^^ constant.numeric.value.typst
// ^ punctuation.separator.decimal.typst
// ^^ constant.numeric.suffix.typst
#rect(width: 1in)
// ^^^ meta.number.integer.decimal.typst
// ^ constant.numeric.value.typst
// ^^ constant.numeric.suffix.typst
#rect(width: 2.5em)
// ^^^^^ meta.number.float.decimal.typst
// ^^^ constant.numeric.value.typst
// ^ punctuation.separator.decimal.typst
// ^^ constant.numeric.suffix.typst
#rotate(180deg)[Hello there!]
// ^^^^^^ meta.number.integer.decimal.typst
// ^^^ constant.numeric.value.typst
// ^^^ constant.numeric.suffix.typst
#rotate(3.14rad)[Hello there!]
// ^^^^^^^ meta.number.float.decimal.typst
// ^^^^ constant.numeric.value.typst
// ^ punctuation.separator.decimal.typst
// ^^^ constant.numeric.suffix.typst
#scale(x: 150%)[Scaled apart.]
// ^^^^ meta.number.integer.decimal.typst
// ^^^ constant.numeric.value.typst
// ^ constant.numeric.suffix.typst
Left #h(1fr) Left-ish #h(2fr) Right
// ^^^ meta.number.integer.decimal.typst
// ^ constant.numeric.value.typst
// ^^ constant.numeric.suffix.typst
$ sin pi => 0 $
//^^^^^^^^^^^^^ markup.math.typst
//^^^ support.function.math.typst
// ^^ support.constant.greek.math.typst
// ^^ constant.other.typst
// ^ constant.numeric.value.typst
// ^ markup.math.typst punctuation.definition.math.end.typst
// <- markup.math.typst punctuation.definition.math.begin.typst - markup.math markup.math
$ ( $
// ^ - markup.math
$ frac(1, 2 $
// ^ - markup.math
// #5
#box()[
#table( columns:(1fr,auto,auto),
[#h(1cm) < this causes problems ],[ as you can see ],[ in the for below ],
// ^ punctuation.section.group.begin.typst
// ^ punctuation.section.group.end.typst
[#"hello world".split()],
)]
// <- punctuation.section.group.end.typst
for should not be highlighted here
#let foo = "bar"
//^^^^^^^^^^^^^^^^ meta.expression.typst
//^ punctuation.definition.expression.typst
// ^^^ keyword.declaration.typst
// ^ keyword.operator.typst
// ^^^^^ string.quoted.double.typst
// ^ punctuation.definition.string.begin.typst
// ^ punctuation.definition.string.end.typst
#set heading(numbering: "I.")
// ^^^^^^^^^^^^^^^^^ meta.function-call.arguments.typst
// ^^^^^^^^^ variable.parameter.typst
// ^ punctuation.separator.parameter.typst
#lorem(30)
// ^^^^ meta.function-call.arguments.typst
// The doc on official readme.
#set page(width: 10cm, height: auto)
#set heading(numbering: "1.")
= Fibonacci sequence
The Fibonacci sequence is defined through the
recurrence relation $F_n = F_(n-1) + F_(n-2)$.
It can also be expressed in _closed form:_
$ F_n = round(1 / sqrt(5) phi.alt^n), quad
phi.alt = (1 + sqrt(5)) / 2 $
#let count = 8
#let nums = range(1, count + 1)
#let fib(n) = (
if n <= 2 { 1 }
else { fib(n - 1) + fib(n - 2) }
)
The first #count numbers of the sequence are:
#align(center, table(
columns: count,
..nums.map(n => $F_#n$),
..nums.map(n => str(fib(n))),
))
// #6
#let a-b(a, b) = a + b
// ^^^ support.function.typst
#let a_b(a, b) = a * b
// ^^^ support.function.typst
#a-b(2, 3) #a-b
// ^^^ variable.function.typst
// ^^^^ constant.other.symbol.typst
#a_b(2, 3) #a_b
// ^^^ variable.function.typst
// ^^^^ constant.other.symbol.typst
// #7
+ In list $cal(0)$
Nested content... $E=m c^2$.
$ T eq
cases(
delim: "{",
1 & n lt.eq 1,
2 T lr((log n)) plus 2^(log^ast n) & n gt 1
// ^ punctuation.section.group.begin.typst
// ^ constant.character.parenthesis.typst
// ^ constant.character.parenthesis.typst
// ^ punctuation.section.group.end.typst
) $
and code
```py
def find(arr: list):
pass
```
// #8
This text is properly syntaxed <<<
#h(1cm) foo ```js console.log(1) ```js console.log(2)
// ^^^ punctuation.definition.raw.code-fence.begin.typst
// ^^^^^^^^^^^^^^^^ markup.raw.block.javascript.typst source.js
// ^^^ punctuation.definition.raw.code-fence.end.typst
Evil purple now occurs <<<
// #16
<label>
//^^^^^^^ storage.modifier.label.typst
//^ punctuation.definition.label.begin.typst
// ^^^^^ entity.name.label.typst
// ^ punctuation.definition.label.end.typst
@label
//^^^^^^ constant.other.reference.typst
//^ punctuation.definition.reference.typst
// ^^^^^ - punctuation
$ F_n = round(1 / sqrt(5) phi.alt^n) $
//^ variable.other.math.typst
// ^ variable.other.math.typst
// ^^^^^ support.function.math.typst
// ^^^ support.constant.greek.math.typst
$ foo x $
//^^^ support.function.math.typst
// ^ variable.other.math.typst
#let name = "Typst"
//^^^^^^^^^^^^^^^^^^^ meta.expression.typst
//^ punctuation.definition.expression.typst
// ^^^ keyword.declaration.typst
This is #name's documentation.
// ^^^^^ constant.other.symbol.typst
// ^ punctuation.definition.variable.typst
#include "bar.typ" as baz
//^ punctuation.definition.expression.typst
// ^^^^^^^ keyword.import.typst
// ^^ keyword.control.import.as.typst
// #17
#table(
columns: (1fr, auto),
[1],[stm32f10x_adc.c],
// ^ - punctuation.definition.italic
[2],[stm32f10x_dma.c],
)
// #19
This is _emph_, This is not emph!
// ^^^^^^ markup.italic.typst
// ^ - markup.italic
This is *emph*, This is not emph!
// ^^^^^^ markup.bold.typst
// ^ - markup.bold
// #21
$#[Y] != #[X]$
// ^ - markup.math
=== Sub section B
// #23
#counter(page).update(1).bar
// ^ punctuation.accessor
// ^^^^^^ support.function.typst
// ^ - support.function
// #27
#let f = {
let a = 5
[*bold* _italic_]
// ^^^^^^ markup.bold.typst
// ^^^^^^^^ markup.italic.typst
}
// #29
#let f = (
a-b, a- b, a -b
// ^ - keyword.operator.typst
// ^ - keyword.operator.typst
// ^ keyword.operator.typst
)
// #32
#{
let show-one() = []
let show-two = [asdf]
// ^^^^ - keyword.declaration.typst
let three-show = [jkl]
// ^^^^ - keyword.declaration.typst
let order = [#show-one()]
let mhm = "?"
//^^^ keyword.declaration.typst
// ^^^ string.quoted.double.typst
mhm
}
// ^ - meta.expression.typst
// #34
/ as.df jkl: asdf
// ^ markup.terms.typst punctuation.definition.term.typst
// ^^^^^^^^^ markup.terms.typst entity.name.enum.typst
// foo: bar
// ^^^ - markup.terms.typst
/* foo: bar */
// ^^^ - markup.terms.typst
// #38
/ asdf\: asdf: asdf
// ^ markup.terms.typst punctuation.definition.term.typst
// ^^ constant.character.escape.typst
// ^ markup.terms.typst punctuation.separator.key-value.typst
/ asdf#emph[asdf]: asdf
// ^ markup.terms.typst punctuation.definition.term.typst
// ^^^^^^^^^^^ meta.expression.typst
// ^ markup.terms.typst punctuation.separator.key-value.typst
/ #(a + b): buzz
// ^ markup.terms.typst punctuation.separator.key-value.typst
// ^^^^ - markup.terms.typst
// #39
asdf / asdf:
// ^ - markup.terms.typst
/asdf:
// ^ - markup.terms.typst
// #35
// https://laurmaedje.github.io/posts/types-and-context/
#set text(fill: context text.fill.darken(20%))
// ^^^^^^^ keyword.declaration
#context test(text.lang, "de")
// ^^^^^^^ keyword.declaration
#context {
// ^^^^^^^ keyword.declaration
test(type(rect.stroke), stroke)
test(rect.stroke.paint, red)
}
// #36
#let in-asdf = a in b
// ^^ - keyword
#let and-asdf = a and b
// ^^^ - keyword
#let not-asdf = not a
// ^^^ - keyword
#let or-asdf = a or b
// ^^ - keyword
#let in-asdf()
// ^^ - keyword
#let and-asdf()
// ^^^ - keyword
// #40
#"a,b;c".split(regex("\p{Greek}"))
// ^^^^^^^^^ string.regexp.typst
#show regex("[,;]{2}"): set text(red)
// ^^^^^^^ string.regexp.typst
#regex(`\d+\.\d+(\.\d+)?`.text)
// ^^^^^^^^^^^^^^^^ markup.raw.inline.typst string.regexp.typst
// #42
#let f() = {
let a = ```rs
fn main() -> Result<()> {}
```.text
//^^^ punctuation.definition.raw.code-fence.end.typst
// ^ - raw.code-fence
[Code: #a]
// ^^ meta.expression.typst
}
// ^ - raw.code-fence, meta.expression.typst
// #43
#let x = f("hello", 1)
#let x = f("\"", 1)
#let x = f("she said \"cool\"", 1)
#let x = f("\\", 1)
#let x = f("\\\"", 1)
#let x = f("\\\\", 1)
// ^ - string
#let x = f("\\\\\\", 1)
#let x = f("\"\"", 1)
#let x = f("
multi line \"string\"
ending in slash \
", 1)\
// ^ constant.character.escape.typst
// #48
```//```
// ^^ markup.raw.block.typst
// ^ - comment
asdf
// ^ - comment
`//asdf`
//^^^^^^^^ markup.raw.inline.typst
asdf
// ^ - comment
```js // comment```
// ^ - comment
asdf
// ^ - comment
|
https://github.com/cadojo/vita | https://raw.githubusercontent.com/cadojo/vita/main/src/contact.typ | typst | MIT License | #let contactslist = state("contactslist", ())
#let contact(
name, icon: none,
) = {
let contact = if icon == none {
name
} else {
box(image("../" + icon, height: 1.5em), baseline: 20%)
h(1em)
name
}
contactslist.update(current => current + (contact,))
}
#let contacts() = {
locate(
loc => {
let contactslist = contactslist.final(loc)
if contactslist.len() > 0 {
v(1em)
set text(size: 10pt)
v(1em)
grid(
columns: 2,
contactslist.join(h(0.5em)),
)
}
}
)
}
|
https://github.com/lucafluri/typst-templates | https://raw.githubusercontent.com/lucafluri/typst-templates/master/Project_Report_FHNW_MSE/appendix.typ | typst |
#pagebreak()
#set heading(outlined: true, numbering: none)
= Appendix
|
|
https://github.com/mawkler/cv | https://raw.githubusercontent.com/mawkler/cv/main/cv.typ | typst | MIT License | #import "@preview/fontawesome:0.1.0": *
#let primary_color = rgb("#2b4277") // darker blue
#let secondary_color = rgb("#677fb2") // lighter blue
#let gray_color = rgb("#7c7c7c") // light gray
#let sans_serif_font = "Fira Sans"
#let code_font = "Fira Code"
#let contact_info(services) = {
let glyph(icon) = {
box(baseline: 2.5pt, height: 11pt, text(icon, size: 10pt))
h(3pt)
}
set text(weight: "bold", font: code_font, fill: primary_color, size: 8pt)
services.map(service => {
glyph(service.icon)
if "display" in service.keys() {
link(service.link, service.display)
} else {
link(service.link)
}
}).join(h(10pt))
}
#let header_info(name, links, occupation, tagline, image_path, compiled_date) = {
set text(font: sans_serif_font)
let date = text(size: 8pt, weight: "regular", fill: gray_color, compiled_date)
grid(
columns: (6fr, 1fr),
gutter: 15pt,
align(start + horizon, {
[= #name]
v(2pt)
{
show link: body => text(body, fill: primary_color)
occupation; [ -- ]; text(style: "italic", tagline)
// occupation; text(style: "italic", fill: gray_color, {[ -- ]; tagline})
}
v(-5pt)
date // TODO: try moving date to contact_info
v(0pt)
contact_info(links)
}),
align(end + horizon, image(image_path, height: 8%))
)
}
#let experience(image_path, name, company_name, period, location) = {
set table( inset: 0pt, stroke: none)
set align(horizon)
set text(font: sans_serif_font)
let row_spacing = 4pt
let right_text_font_size = 9pt
v(5pt)
table(
columns: (20pt, 1fr),
column-gutter: 5pt,
image(image_path),
table(
columns: (1fr, auto),
{
set par(justify: false)
text(weight: "bold", name)
},
{
set align(right + bottom)
set text(right_text_font_size, weight: "light")
period; h(3pt); text(fill: secondary_color, fa-calendar(10pt))
},
{
v(row_spacing)
text(style: "italic", company_name)
},
{
set text(right_text_font_size, weight: "light")
set align(right)
v(row_spacing)
location; h(3pt); text(fill: secondary_color, fa-location-dot(10pt))
},
)
)
v(-5pt)
}
#let skill(name, rating) = {
let max_rating = 5
let circles = range(0, max_rating).map(i => {
let color = secondary_color
if i >= rating {
color = rgb("#c0c0c0") // gray
}
box(circle(radius: 4pt, fill: color))
}).join(h(4pt))
name; h(1fr); circles; [\ ]
}
// Produces the LaTeX symbol
#let LaTeX = style(styles => {
set text(font: "Times New Roman") // TODO: look up actual name
let l = measure(text(1em, "L"), styles)
let a = measure(text(0.7em, "A"), styles)
let A = text(0.7em, baseline: a.height - l.height, "A")
let e = measure(text(1em, "E"), styles)
let E = text(1em, baseline: e.height / 4, "E")
box("L" + h(-0.3em) + A + h(-0.1em) + "T" + h(-0.1em) + E + h(-0.125em) + "X")
})
#let bubble(content) = {
box(
fill: secondary_color,
inset: 4pt,
radius: 6pt,
text(weight: "semibold", fill: white, font: sans_serif_font , content)
)
}
#let list_interests(interests) = {
set par(leading: 5pt, justify: false)
interests.map(interest => bubble(interest)).join(h(4pt))
}
#let footer(content) = [
#set align(center)
#set text(6.5pt, fill: gray_color, font: code_font)
#show link: body => underline(text(body, fill: secondary_color, weight: "bold"))
#line(length: 100%, stroke: 0.5pt + gray_color)
#fa-chevron-right() #content
]
#let programming_skills(header, languages_header, other_technologies_header) = {
[== #header]
[=== #languages_header]
skill("Rust", 4)
skill("Go", 3)
skill("TypeScript/JavaScript", 5)
skill("Lua", 4)
skill("Python", 3)
skill("Java", 4)
skill("Haskell", 2)
skill("SQL", 2)
skill("HTML/CSS", 4)
skill("C/C++", 2)
skill("C#", 2)
skill("R", 1)
skill("Typst", 3)
skill(LaTeX, 4)
[=== #other_technologies_header]
skill("Linux", 4)
skill("Neovim/Vim", 5)
skill("Git", 5)
skill("OpenAPI/Swagger", 3)
skill("Jest", 5)
skill("Microsoft Azure", 3)
skill("Serverless (Azure Functions)", 3)
skill("Protobuf", 2)
skill("AWS", 2)
skill("Docker", 2)
skill("Kubernetes", 2)
skill("OAuth 2.0", 1)
skill("HTMX", 1)
skill("Vavr", 2)
}
#let cv(
name: "",
links: (),
occupation: "",
tagline: [],
compiled_date: "",
left_column: [],
right_column_header: "",
languages_header: "",
other_technologies_header: "",
right_column: [],
footer_content: []
) = {
set text(9.8pt, font: "IBM Plex Sans")
set page(margin: (x: 32pt, y: 35pt), footer: footer(footer_content))
set par(justify: true)
show heading.where(level: 2): it => text(fill: primary_color, [
#v(5pt)
#{it.body}
#v(-7pt)
#line(length: 100%, stroke: 1pt + primary_color)
])
show heading.where(level: 4): it => text(fill: primary_color, it.body)
show heading: it => text(font: sans_serif_font, it)
header_info(name, links, occupation, tagline, "images/profile.png", compiled_date)
v(-8pt)
grid(
columns: (1fr, 0.54fr),
gutter: 15pt,
left_column,
{
show link: body => underline(text(body, fill: primary_color))
programming_skills(right_column_header, languages_header, other_technologies_header)
right_column
},
)
}
|
https://github.com/polarkac/MTG-Stories | https://raw.githubusercontent.com/polarkac/MTG-Stories/master/stories/032%20-%20Ixalan/002_A%20Question%20of%20Confidence.typ | typst | #import "@local/mtgstory:0.2.0": conf
#show: doc => conf(
"A Question of Confidence",
set_name: "Ixalan",
story_date: datetime(day: 13, month: 09, year: 2017),
author: "<NAME> & <NAME>",
doc
)
#figure(image("002_A Question of Confidence/01.jpg", width: 100%), caption: [Art by Anna Steinbauer], supplement: none, numbering: none)
Huatli excelled at exactly two things.
She was a knight, and she was an orator.
When demonstrating either, she shined brighter than any other knight in the Sun Empire.
She had never needed to be anything else. And she was certain that finally her emperor would bestow the title of warrior-poet upon her after all these years of ladder-climbing and preparation.
"Let me see it again," her cousin whispered.
Huatli opened her saddlebag. A glint of steel winked back at the two knights.
Inti peeked into the bag, the ghost of a grin on his face. "It's hideous."
Her cousin was maddeningly even-tempered. Huatli had learned over the years how to quantify his enthusiasm, and inferred from his two-word sentence that he was over the moon with pride.
"Whoever made it was clumsy, and the one wielding it was even clumsier." Huatli smiled. Their final victory had been an easy one. No deaths on either side, only superior martial skills and a very convincing offer. The Legion of Dusk had retreated to their ships without weapons or pride.
Huatli looked around the plaza as she and her cousin passed under the arch at the entrance to Pachatupa. Some attendants were setting up for the homecoming ceremony later that day. Some other citizens were purposefully walking across, but by and large the plaza was empty. Only the two knights' mounts (two bright-eyed clawfoots) seemed to care about their presence. Huatli's dinosaur tugged at her reins, eager to get to the stables for a meal.
Huatli and Inti were returning from the Sun Empire's last major campaign on the Sun Coast. Most of the army had already returned, but their squadron had been delayed by one final battle against the Legion of Dusk. And, like all well-earned victories, this one had yielded many spoils all its own.
Inti held out a hand, and Huatli passed him the stolen sword. He rolled his wrist to test its weight and handed it back. "You should have seen their priest," he said.
"Hierophant," Huatli corrected.
"Hierophant? Eww. Anyway, he had fingernails like grandmother's."
Huatli gave an exaggerated nod and an emphatic #emph[hmm] . "The facts line up. Given the evidence, it is more likely than not that Granny is a vampire."
She turned to Inti and counted each piece of evidence on the hand not holding her dinosaur's reins.
"No appetite, vacant stare, #emph[still alive ] despite all odds—"
Inti smirked. Huatli smiled in turn.
The two had grown up together, had gone from battling each other with sticks as children to battling enemies of the Sun Empire as adults.
Inti tapped Huatli's shoulder. Several people were walking toward them with happy, expectant looks on their faces.
"I'll leave you to your fans," he said
Huatli waved farewell to Inti.
"Huatli! Welcome home!" one of the strangers called.
Huatli smiled and bowed her head in recognition.
A girl no older than thirteen broke from the group and ran up to her, eyes wide and breath short. "Warrior-Poet, are you delivering an oration at the homecoming ceremony?"
Huatli hated when people did that. Assumed she had achieved something she hadn't quite yet.
"I am speaking today, but I'm not the warrior-poet #emph[yet] . What is your name, friend?"
"Wayta. I saw you speak at the last equinox festival . . . you were amazing."
"Do you write poetry, Wayta?"
The girl looked down, visibly embarrassed. "It's not good enough to share."
Huatli bent down so the rest of the small (and growing) crowd wouldn't hear. "Would you like to know a secret?"
Wayta looked at Huatli in wonder.
Huatli gave her an honest smile in return. "There are only two types of poems in the world. Poems that are good, and poems that are #emph[honest. ] Poetry that is good is clever, and anyone can be clever if they try hard enough. But poetry that is honest has #emph[magic] in it; the ability to let other people feel what #emph[you feel] is a very powerful magic indeed."
Huatli continued. "If you think your work isn't ready to share, don't try to make it good. Try to make it #emph[honest] ."
She winked.
And Wayta grinned from ear to ear.
#v(0.35em)
#line(length: 100%, stroke: rgb(90%, 90%, 90%))
#v(0.35em)
An hour later, the homecoming ceremony began, and Huatli patiently awaited the moment of her entrance.
While their mission had been small, it represented the end of a larger endeavor to rid the Sun Coast of invaders. To mark this joyous occasion, the Emperor would be speaking to all citizens of Pachatupa, and Huatli would be expected to deliver an oration.
The title of warrior-poet was bestowed to only one person in a generation. They kept the stories and weaved events into words. To earn that title, one must demonstrate excellency in service to the kingdom. Such responsibility ought to have weighed heavily on someone as young as she, but Huatli was not so easily pressured.
All residents of the Sun Empire respected their emperor, but all residents of the Sun Empire #emph[loved ] their warrior-poet. This was surely the last speech she would give before the emperor bestowed the title of warrior-poet upon her, and Huatli wanted nothing more than to prove herself worthy of such admiration.
There were no set qualifications to earn the title of warrior-poet, but the emperor's growing trust in her seemed to signal that the announcement was coming soon. Huatli could sense it in the air like the tang of metal before a storm.
Huatli rolled out her shoulders and inhaled the musty air. The dinosaur beneath her shifted from side to side, anxious to leave the dark shadows of the stable. Huatli lay a hand on her dinosaur's rough hide and willed her to be still.
#emph[Wait] #emph[, ] she urged, sending the scent-memory of #emph[food ] through the connection between her and the beast.
The dinosaur stopped its shuffling as soon as it sensed the promise of a treat. Huatli patted her on the neck. The beast ruffled her feathers and then stilled herself with cold-blooded simplicity, ready for Huatli's next command.
Huatli would be called out to speak at any moment. Huatli never worried about performing anymore. She only worried if she had performed enough#emph[.]
The air of the stable was stuffy and warm.
Distantly, she could hear the emperor's voice echo as he spoke to the citizens of Pachatupa. All who lived in the city would be attending the celebration.
#emph[Perhaps he'll announce it after my oration] , she thought. #emph[Perhaps today is the day he announces that I have done enough to earn the title the city already attaches to my name.]
A figure peeked around the post of the stable and locked eyes with Huatli. He wore the markings of a priest—one of the organizers of this homecoming ceremony—and nodded at Huatli.
#emph[You can do this] , Huatli reminded herself. Her dinosaur cawed in shared excitement.
She squeezed her mount's sides, and the clawfoot took off out of the stable.
The sun was hot as a forge, and the cheers of the crowd were more deafening than any dinosaur's roar.
Thousands of Sun Empire citizens parted to clear the way, applauding Huatli's approach. The city around them shone with amber and the light of the noonday sun. The crowd gathered in the plaza had been facing the Temple of the Burning Sun to hear the emperor speak, but now they all turned to cheer Huatli as she rode at a gallop toward the great stairway that led to the dais.
Huatli's dinosaur ran in a spear-straight line through the parted crowd, underneath archways tall enough for long-necked dinosaurs to pass through uninhibited, and over tile strong enough to withstand even the heaviest of spinetails. Up ahead, Huatli could see the emperor standing at the top of the stairs to the Temple of the Burning Sun. His hand was outstretched in welcome, and even from a distance, Huatli could make out the broad smile on his face.
The crowd began to chant her name.
Huatli beamed, and she sensed that this was the right moment to pull out her prop.
She held aloft a captured sword, and the crowd cheered twice as loud.
The thing was flimsy and thin, meant for quick stabs rather than smooth cuts, and a tacky black rose was welded to one side. To think that these inferior craftsmen thought themselves #emph[conquerors] #emph[.]
Her dinosaur stopped in front of the temple steps, and Huatli dismounted, sword still held aloft.
She looked up to her emperor and ascended the stairs to the temple.
The temple itself had been built on the foundation of an older temple, which had been built over several ruins even older than that. The Sun Empire itself was much the same. It was the latest iteration of a land whose rulers were constantly vying for power, building on top of the old and reaching ever higher with the new. Whereas the River Heralds had once controlled the continent, under the leadership of its new emperor, the Sun Empire had cemented its grip on the land. Apatzec Intli III was responsible not only for the new assertion of control, but also for the current mood of expansionism that had gripped the empire following his mother's death several years before. While the prior emperor had busied herself with conservative busywork, the new emperor yearned to prove himself as the bringer of a glorious new age for the Sun Empire.
Huatli had never met the prior emperor, but she admired Apatzec's determination. He first became aware of her as she moved up the ranks in his guard, and after years of devoted service she had become his most trusted tactical advisor.
At the top of the stairs, Huatli turned and presented the Legion of Dusk sword to the crowd below. They cheered at the display of the spoils of war. Emperor Apatzec approached, flanked by priests on either side, and Huatli gave him the sword.
He clapped Huatli on the shoulder with a smile, and addressed the people of Pachatupa in the plaza below.
"Citizens! I give you the leader of the squadron that successfully deterred the invaders of the Sun Coast. She and her warriors deterred the Legion of Dusk from our shores, and just this morning returned safely home. My words cannot do her victory justice. Listen, and mark the valiant grace of Huatli!"
The crowd roared.
Huatli smiled, held out a steady hand, and lowered her palm with practiced ease. The crowd quieted, and she quickly cast a spell to bring her voice to a commanding volume.
#emph[Just like you practiced. You can do this.]
#figure(image("002_A Question of Confidence/02.jpg", width: 100%), caption: [Art by <NAME>], supplement: none, numbering: none)
"Kinjalli, hear my call!#linebreak The time has come to wake the sleepers,#linebreak To pierce the eastern shadow#linebreak That would darken all our days.
Tilonalli, hear my call!#linebreak Fill your children's hearts with fire#linebreak That we may be the dawn that breaks#linebreak To immolate the Dusk.
With Threefold Sun above us#linebreak And these prayers upon our lips#linebreak Did your proud warriors bring terrible radiance#linebreak To the heathens on your shores.
Astride our clawfoots, platetails, frillhorns,#linebreak We rode for glorious reproof#linebreak To scold the shark-eyed enemy#linebreak That hungers for your birthright.
We met them on the sand,#linebreak Fangs dripping malice, swords aloft,#linebreak But the shadow-bound could not withstand us;#linebreak Soon their vileness fled our shores.
Today we return and beseech you to remember:#linebreak Your Empire is the light.#linebreak Nothing fills the Dusk with terror#linebreak Like the rising of the Sun."
The crowd roared with applause again.
Emperor Apatzec looked at Huatli with an approving grin.
Huatli nodded in gratitude.
The emperor stepped forward and spoke at a volume enhanced by the slight haze of magic. "Today's small victory also marks the beginning of the next stage of our expansion."
The audience quieted. This was important news.
#emph[Does he mean to grant me the mantle now?]
"Driving the Brazen Coalition and the Legion of Dusk from our eastern coast means that we are ready to reclaim the south," Apatzec announced. He spoke with the practiced diction of a ruler and the confidence of a conqueror. "Our warriors have never been more prepared, and with the strength of the Burning Sun, we will banish the Legion of Dusk from our mainland!"
The audience cheered, and Apatzec nodded at Huatli. Her heart sank a bit. If there were ever a time to announce her new title it would have been now. She waved a farewell, turned, and followed the emperor into the temple.
He motioned for the other priests to depart, and shrugged off his ornamental cloak.
Huatli took a seat on a cushion in the center of the room. He sat across from her and smiled.
"Thank you for sharing your gift, Huatli. Our empire needs your voice."
"I am happy to be of service, Emperor Apatzec."
He turned over the Legion of Dusk sword still in his hand and held it aloft, a look of displeasure tugging at his nostrils.
"Gaudy, isn't it?" he noted. "One wonders how they conquered an entire continent with #emph[these] ."
"They used their teeth too, sir." Huatli flashed a broad smile. "Unfortunately for them, ours are much sharper."
"Indeed."
The emperor smiled at Huatli. She sat silently, waiting patiently for him to speak.
Apatzec told her the last thing she expected to hear.
"I am not sending you to fight in the south."
Huatli tried not to show she was hurt.
"I was promised one more mission before I would earn the mantle of warrior-poet." she asked, arranging her face into a neutral expression.
Emperor Apatzec solemnly shook his head. "I knew you'd hate the idea."
"I don't hate the idea," said the woman with a firm-as-steel grip on her own hand.
"The Sun Empire needs you here, in Pachatupa. There may still be invaders yet arriving on our eastern shores."
"Do you know something I do not?"
The emperor frowned. "Only rumors. But I fear a twofold attack by both Brazen Coalition and Legion of Dusk in the near future. You and your squadron will continue to maintain a presence on the coast and deter whatever invaders come while our army is fighting in the south for the next month. You will depart next week for your mission."
"Understood, sir."
The emperor paused and sighed. "I hate what my mother's instructions would have been."
"'Protect the cities and continue the search for the one we lost,' I imagine?"
Apatzec nodded, with a smile tugging at the side of his mouth.
"We would sooner find a flying panther than an entire lost city. It is best to focus on what is real, Huatli. What we can see and hear. Chasing ghosts will only lead us in circles. Prepare your squadron, and be sure to write another good poem while you're gone."
Her heart leapt. She was still in consideration after all.
Apatzec bowed, and Huatli bowed in return.
#v(0.35em)
#line(length: 100%, stroke: rgb(90%, 90%, 90%))
#v(0.35em)
A month later, Huatli caught wind of a rumor.
Scouts reported that a Brazen Coalition ship had appeared just off the coast. Huatli saddled up her mount and bounded into the jungle alongside Inti as soon as she was able.
Flowers towered overhead, and packs of long-necked dinosaurs parted as the two warriors passed on their clawfoot mounts.
#figure(image("002_A Question of Confidence/03.jpg", width: 100%), caption: [Art by <NAME>], supplement: none, numbering: none)
"Reports said they were camped near the outcropping," Inti yelled over the pounding of their dinosaurs' feet.
Vines whipped Huatli's armor as she tore through the jungle. She sat up in her saddle and began a spell to summon some assistance.
She felt her magic alight within her, a little beacon that radiated from her chest. Seconds later, she heard the patter of trotting, two-legged dinosaurs on every side. Within moments, a trickle of dinosaurs had begun riding behind Huatli and Inti. Small egg-eaters were joined by platetails and frillhorns, all of which moved with a sense of purpose, sticking close to the Sun Empire knights' mounts. Huatli instructed the herd to keep following, soothed them with her magic, and assured them they would not be harmed.
"Huatli! Ahead!" Inti was pointing to a clearing ahead where the delta of the river began to meet the sea.
Bright red sails formed an angry mark against the blue sky, and a large pile of crates and supplies were stacked on the beach.
They came to a halt, herd and all, just inside the thick cover of jungle where the trees met the sand. Huatli and Inti looked out at the ship with anticipation.
"No crew," Inti remarked, keeping his voice low.
Huatli nodded. "They must be surveying. I'll destroy the equipment, you flush the pirates down the beach and toward the boat when you see their supplies light up."
"Sounds good," Inti said. He looked at Huatli and nodded. "Stay safe, cousin."
"You too."
Inti took off into the jungle, and Huatli urged her mount out onto the sand, instructing the remaining herd to stay behind in the jungle.
The dinosaur padded silently on the sand, and in a moment, Huatli was positioned near the pile of supplies. She uncorked a flask from her hip and poured its sharp-smelling contents over the boxes of supplies. She then pulled a small dark stone from her armor and struck it against the steel of her blade. Sparks flew onto the dry wood of the crates, and almost instantly they caught flame.
Huatli stowed her blade and ran back into the jungle. She halted where she had begun, at the hidden divide between beach and jungle. A few of the crew were emerging now, panicked by the sight of smoke rising from their rations and gear. But not #emph[enough ] of them were running.
#emph[Chase them onto the beach] #emph[, ] Huatli urged, eyes alight with magic.
The jungle rustled, and a dozen human-and-ogre-and-goblin Brazen Coalition voices screamed as the summoned dinosaurs flushed the remaining crew out onto the sand. The pirates emerged, stumbling and blinking, into the light, only to yelp in surprise at the bonfire before them. They ran forward in desperation, and began whacking at the flames in an attempt to put them out.
Huatli grinned and spotted Inti in the distance. She whistled, and he trotted over. They were hidden from the view of the pirates by thick coastal trees and ferns, and he pulled his mount close.
"We're good here," Huatli said, nodding to the panicked crew already trying to get back to their ship. "Go ahead and scout for freshwater. I could use a drink."
Inti turned and took off ahead into the jungle.
Huatli nudged her mount to a trot and began making her way along the edge of the beach.
Suddenly, something yanked the feet out from under Huatli's clawfoot. Huatli hit the forest floor with a bruising #emph[thud.]
Huatli scurried to her feet just in time to see her dinosaur, feet bound in red-hot chains, cry out in pain, its scaly legs scorched by the heat of the bindings.
The source of the chains came into view, and Huatli gasped with fear.
Emerging from behind a tree was an immensely tall monster.
#figure(image("002_A Question of Confidence/04.jpg", width: 100%), caption: [Art by <NAME>], supplement: none, numbering: none)
He had the body of a blacksmith, but the head of an animal that Huatli had only seen around Legion of Dusk forts—#emph[a bull] ? Heavy iron chains were wrapped around his chest, and he seemed to glow from within like a furnace, a steady flow of steam rising from his snout.
Huatli dove toward the chain in a desperate attempt to help her mount, but her foe snorted in defiant fury as he pulled the chain back from the dinosaur's leg. The metal lifted on its own, then shot out again, wrapping itself around the crying dinosaur's neck. He snapped the chain tight with a sickening crunch, and the beast died instantly.
Huatli leapt to her feet and drew her weapon. She did not bother to hide the disgust on her face—she had known this mount for years. Any monster that would act with such cruelty must surely suffer the consequences.
"What is your name?!" she yelled.
The beast held out his hands. The searing chains snaked back from the dinosaur's legs to around his arms, coiling at the ready for another strike. An unnatural fire burned in the beast's throat, and steam rose from his nostrils.
"I am the dread pirate Angrath," he said, "and I seek the Immortal Sun."
Huatli laughed out loud. "You and everyone else, fool."
His voice had an accent Huatli could not place. "If you will not tell me where the Immortal Sun is, knight, then you will die."
A chain shot out from his right arm. Huatli dodged it, feeling its heat as it passed her face.
Huatli caught her balance and ran toward Angrath, blade at the ready and muscles tensed. She tried to close with him, her semi-circular blade striking low and seeking his tendons, but the pirate burned with a searing heat that was too much to bear at close range. She backtracked, kicking up a spray of dead leaves and dirt as she dodged the chain.
She had backed off just in time to avoid another blow from a chain. A second chain flung out and snagged her foot, and Huatli was yanked to the ground with a ferocity that knocked the air from her lungs.
The chain was white-hot, and she could feel it even through the denseness of her steel greaves. She bent forward, swinging with all the force she could muster to try to break the chain with her blade. Angrath casually walked forward, a furious fire alight in his eyes.
Huatli struggled and shifted, and thankfully, the chain came loose.
No pirate fought with this kind of callous rage. No River Herald would kill with such disregard. And no Legion of Dusk foe was so unpredictable. Huatli felt off-kilter and out of her element, for this foe was unlike any other.
"Huatli?!"
Huatli whipped her head around. Inti must have turned back when he heard the commotion they were making, and was staring back in horror from the thick of the jungle. Angrath turned his head to mark the newcomer, and Huatli hurled herself upright, rushing in for the attack.
Blade tight in one hand, she kept her weight forward, sweeping her leg low, out, and away, to knock the pirate off-balance.
It worked—Angrath hit the ground in a hard thud, and as he tried to stumble to his feet, she sliced a clean line across his chest with her blade.
The bull-headed man roared in pain and launched another length of chain directly at Huatli.
She kept her weight light, dancing her weight from foot to foot, and dodged the attack with sinuous ease. Huatli followed the momentum of her parry, allowing the energy to carry her weight to her other foot, and landed a sharp high kick to his chin.
Angrath buckled, and Huatli called out to Inti, who was watching open-mouthed from the side.
"Inti! I need a mount!"
From behind her, she sensed Inti begin to summon a new dinosaur for her to escape on.
She saw a red-hot chain fly toward her from somewhere on the ground, and dropped low to the ground, sweeping her leg and shifting her weight to avoid the flinging chain. One of her greaves fell off in the process.
Inti yelled, "Behind you!" just in time for Huatli to be struck from behind, falling face-forward into the leafy forest floor.
Angrath was back on his feet, scowling as much as his face would allow.
Huatli heard a yell and watched as Inti was yanked from atop his mount. A second chain suddenly wrapped around the exposed skin of her own leg, and she screamed over the sizzle of flesh.
She suddenly realized this was how both she and her cousin would die.
She tried to stand and face her foe when something deep within her chest #emph[sparked.]
Suddenly, without pain, Huatli began to feel herself coming apart.
Her vision burst into a miasma of color and light, sound rushed through her ears, and she felt her body begin to break away from itself. It was bright and warm and should have been frightening, but it felt like the most natural thing in the world—she felt her head pass forward, deeper into the color and light, and she #emph[saw.]
It was a city that shone with the warmth of gold.
#figure(image("002_A Question of Confidence/05.jpg", width: 100%), caption: [Art by <NAME>], supplement: none, numbering: none)
Bright, shining towers and spires that stretched into the sky. Glimmering metal unlike any she'd seen before, and above it all, pulsing magic that flowed through the clouds like a river.
It was beautiful.
And then it was gone.
Her perception was yanked sharply back, as if some unseen force was pulling her backward to the jungle. Whatever door she peered through had slammed shut, barred her from entry. Everything was flying again through color and light, sound and noise, until her body rearranged itself on the forest floor.
Huatli's blood pounded, and her vision settled on a strange triangle-and-circle symbol hovering with a strange glow above her head.
She tried to catch her breath.
Her fear solidified, and she stopped gasping for air.
Then she realized Angrath was still in front of her.
He was staring in wonder, chains snaking back to his arms and eyes wide with bovine shock.
Inti was dazed, but alive, also staring at both Huatli and the shining symbol fading above her head.
The pirate held out his hand and pointed at Huatli. "You're one too!"
Huatli put a hand on the ground to balance herself. The sigil above her head vanished. She shook her head.
Words dribbled from her mouth without grace or full awareness. "I don't know what just happened."
Angrath was grinning as much as a bull-headed man could grin. "I've never met another one on this wretched plane! We can help each other leave!"
Inti had gotten back on his dinosaur and quickly looped around to stand behind his fellow knight.
"Huatli, get up!" Inti said, holding a hand out to her. She ignored it, staring in shock at Angrath. He, too, was reaching out to her, palms up in an invitation.
She quickly sliced at Angrath with her blade, climbed on Inti's mount, and they ran as Angrath's pained yell echoed through the jungle.
Huatli's mental dialogue was an endless whirl of curses and confusion. This was no time for a pleasant imaginary argument. This was a time for breathless questions.
#emph[My body BROKE APART and there was color and light and was that a seizure was it a hallucination except Angrath saw it too, that DAMNED PIRATE, how dare he think I would ever help him after he killed my dinosaur and tried to kill me, SWEET SUN ABOVE, MY LUNGS DISSOLVED] —
Inti verbalized as many questions as she was thinking.
"Your body! That was magic! How did you do that? Have you been training secretly?! And what was that symbol? Why did the pirate think you would help him?!"
Huatli's response was tangential, brief, and hushed.
"I saw a golden city."
"What?!"
"Inti . . . I think I saw Orazca."
#v(0.35em)
#line(length: 100%, stroke: rgb(90%, 90%, 90%))
#v(0.35em)
Everything Huatli thought was true about the world around her felt like it was coming apart.
Not only had she been attacked by the strangest beast she'd ever seen, but her body had #emph[dissolved] #emph[, ] and for one moment, her consciousness peeked into an open window only to be pulled back to her own world.
It was like trying to stand on a log in the river. Like she was a child spinning in circles and falling to the ground. The ground had left her feet, and Huatli's belief in what was real was #emph[upended] #emph[.]
Night fell as she returned to the city, and Huatli made her way directly to the emperor's residence.
She needed counsel from the one person she knew would not tell a soul what she had seen.
The guards recognized her immediately, and ushered her into the tallest building in Pachatupa with a deep and respectful bow. Their formality put Huatli further on edge.
An attendant led Emperor Apatzec into a formal meeting space. A carving of the sun dominated the largest wall, moonlight glinting off amber embedded in the stone. The emperor looked composed as always, though his usual cape of dinosaur feathers was absent and a less formal robe had taken its place.
"Huatli, what brings you to me at this hour?"
Huatli's heart was still pounding a bruise against the inside of her chest. "I saw something I did not understand."
"A dream?" said the emperor. His sour face betrayed the opinion he held regarding dreams.
"No. I would not believe it myself if I had not seen it with my own eyes."
The emperor lifted a hand to his mouth in thought. "Tell me what happened."
They sat, as friends would sit, and Huatli recounted the incident as best she could.
The emperor listened patiently.
He occasionally sipped from the cup of xocolātl he had summoned when he sensed this story would be a remarkable one, and nodded with understanding at each turn in Huatli's tale.
"What did it feel like?" he asked.
"It felt like I was not allowed to leave. Like I had opened a door, but could only peer my head in before being sucked back."
"Something was keeping you from leaving? And only Inti and I know what happened?"
"Yes, and yes, Emperor."
"'#emph[Apatzec] ,'#emph[ ] please. I don't have the cloak on."
Huatli gave him a tired look.
The emperor shook his head and smiled. "You are remarkably brave, Huatli."
"With all due respect, Emperor, I do not feel it."
Emperor Apatzec sat down his cup and gave her a thoughtful look.
"The Sun expresses itself in three aspects. Creativity, destruction, and sustenance. Your gifts have been lit by the first two, and it seems as if you must explore the last."
"Sir, what do you mean?"
The emperor seemed excited. "My mother was stubborn and old-fashioned. She would rather chase fables in the jungle than secure her power through active means. While I do believe it would be foolish to send our entire army to chase after the power that lies within Orazca, I do not believe it would be unwise to send our most talented knight, especially when destiny summons her anyway."
". . . Emperor . . . ?"
"What you saw is proof of your worthiness to hold that mantle. Huatli of the Sun Empire, the golden city you saw can only be the lost city of Orazca. You must go and find the means to bring growth to our empire with the power that lies within."
Huatli's hands were gripped in worried fists. "But the warrior-poet does not go on #emph[expeditions] , your excellency. #emph[I ] was not meant to go on an expedition!"
"But you did. Therefore, the warrior-poet #emph[does."]
Huatli gasped. Did he mean to imply what he had just said?
The emperor stood, and walked to the other side of the meeting room. He pulled a helm down from a hook on the wall, and walked it over to Huatli.
It was the helm of the warrior-poet.
Huatli's heart began to race.
Apatzec beamed with pride. "Huatli. The title of warrior-poet is yours if you can locate the Golden City of Orazca."
Huatli let out a shaky breath.
Everything she ever wanted hinged on finding a place more myth than reality.
The emperor turned over the helm in his hand. The light from the lamps of the chamber bounced off the amber of the helm, dappling his face with a warm golden glow.
"This is a new era for our empire. No other warrior-poet in our history has foreseen the Golden City." He flashed a broad smile. "That makes my rule a special one."
Huatli grinned and rose to her feet. She straightened her shoulders and looked her emperor in the eye. "I will find Orazca, Emperor, and retrieve the Immortal Sun inside for the glory of the Sun Empire."
Emperor Apatzec smiled in return. "Tomorrow is a new dawn for our empire, Warrior-Poet."
#v(0.35em)
#line(length: 100%, stroke: rgb(90%, 90%, 90%))
#v(0.35em)
The residence for the knights was secluded from the rest of the city by a modest wall. Here she and the other knights trained, ate, slept, and planned the defense of the city. Other regiments were devoted to conquest and the expansion of the empire, but here, the concern was primarily about protecting what the Sun Empire already controlled. Huatli had grown up here, to loving parents who had been knights before her. This was the only home she had ever known, and Huatli had memorized its corners and passages. She slipped through one of these passages now.
"Huatli?"
Inti was looking around the corner. His stern brow was knit with concern. "Did you tell the emperor about what you saw?"
Huatli nodded.
Her cousin, at a loss for what else to do, nodded in return. "That's . . . good. Are you doing all right now?"
Huatli shook her head and shrugged her shoulders, a desperate conglomeration of gestures to reflect her emotional state.
"Yes. No," she confessed.
Inti took her by the shoulder and led her back to the warriors' common room. It was empty and quiet, the rest of the regiment having gone to their bunks hours before. He poured her a drink that smelled rich and sour and was unpleasantly milky in look. If it was good for the soul, as Inti insisted, Huatli was convinced that was all it was good for. Inti waited until she had sipped a bit and regained control of her breathing before starting to prepare a poultice for the burn on her leg.
"Are you sure of what you saw earlier today? When you . . . did the . . ." Inti waved a single hand above his head, alluding as best he could to the event with the sigil from earlier.
Huatli nodded.
"I saw a golden city." She swallowed and glanced at Inti.
He gave her a deadpan look as he smeared the poultice on her ankle. "You saw #emph[a ] golden city?"
Huatli felt her cheeks turn hot. "Yes."
Inti tied a clean bandage around the poultice and sat back, deep in thought. Eventually he broke his own silence. "Was it #emph[the ] Golden City?"
Huatli gave him an apologetic shake of her head. "No one knows what Orazca looks like, so I #emph[assume ] it was #emph[the ] Golden City."
"That's fair."
Inti made a small tutting noise. He wrapped the extra bandage in his hand. "Did the emperor tell you to find it?"
"He told me I will gain the title of warrior-poet if I can locate the city."
Inti was visibly surprised.
He let out a long breath and nodded. "That is quite the reward."
"I'm well aware."
Inti sat back down on the stool. Huatli thrust out her foot and sat before him. He began to unbandage her ankle, revealing the healed skin underneath. All of Inti's practice in medicinal magic had done him good.
Huatli took a deep breath. "Inti, this is a kind of responsibility I've never dealt with before. I don't want to go alone."
"You don't have to," Inti said. "You can take Teyeuh and I. We'll get you there safely."
"I don't know how to get there?" The statement, again tainted by trepidation, came out as a question.
Inti shrugged with a knowing look. "The River Heralds know. Why else would they be so zealous about retaining their territory?"
Huatli's eyes lowered to the ground. "I've trained my whole life to earn this, but going on a voyage to a city more myth than reality wasn't part of the deal."
"Do you #emph[want] to go? Or do you just want the mantle that comes with your success?" he asked.
The answer caught in Huatli's throat, and her gut reaction surprised her, but she gave voice to the thought nonetheless.
"I want to find the city."
Her heart was fluttering. The idea of #emph[explorer ] was a frightening concept, entirely alien to anything she ever thought she could be. And yet, she couldn't hide the excitement she felt when she thought about doing something #emph[other ] than what she was comfortable with.
"I never thought I could be anything other than what I am, Inti. I want to be more than just one of two things."
"You already are, cousin," Inti said, rising to his feet. "I'll find Teyeuh and let her know. We'll be saddled up to leave at sunrise to find a River Herald to guide us."
He began walking toward the armory, paused, and looked over his shoulder.
"Warrior-Poet-#emph[Diviner] ?"
Huatli thought for a moment. "Warrior-Poet-#emph[Voyager] ?" she offered.
Inti weighed the suggestion and countered with another. ". . . Warrior-Poet-Body-Dissolving-Expedition-Leader?"
"They don't make a helm for that, Inti."
"Not yet," he said with a smile.
Inti departed, and Huatli was left alone.
She was terrified. She was excited. She was faced with the most daunting challenge she had ever encountered.
So Huatli smiled.
She wandered, after a while, to her bunk.
As she lay in her hammock and looked upward, she tried to remember the color, light, and sound from earlier. She had felt each piece of herself brighten and break, and though she had seen herself dissolve, not one part of her had been frightened. Rather, Huatli remembered a feeling of elation in that moment. She drew a hand to her chest and closed her eyes, remembering how vividly and clearly the sun had shone against the gold of the city rooftops, how brilliant the rivers of blue and cloud had looked as they curved in the sky above. It was unlike anything she had seen before.
She was not a seer, yet she had seen. She was not a voyager, yet her mission was to voyage. Huatli was #emph[two ] things, and neither seemed connected to the destiny that lay ahead.
Huatli closed her eyes and calmed her busy mind. Her dreams were dappled with gold, shining with the colors of a place beyond her any she had ever seen. The dream shifted, transformed, became more prophecy than dream, and she saw herself as she would someday be.
She was a warrior, and she was an orator.
And now she was an #emph[explorer] .
#figure(image("002_A Question of Confidence/06.jpg", width: 100%), caption: [Art by <NAME>], supplement: none, numbering: none)
|
|
https://github.com/Mc-Zen/quill | https://raw.githubusercontent.com/Mc-Zen/quill/main/examples/fault-tolerant-pi8.typ | typst | MIT License | #import "../src/quill.typ": *
#let group = gategroup.with(stroke: (dash: "dotted", thickness: .5pt))
#quantum-circuit(
group(1, 4, padding: (left: 1.5em)), lstick($|0〉$), nwire(""), $H$, $T$,
ctrl(1), $S X$, rstick($T|ψ〉$), [\ ],
lstick($|ψ〉$), nwire(""), 2, targ(), meter(target: -1),
) |
https://github.com/Myriad-Dreamin/typst.ts | https://raw.githubusercontent.com/Myriad-Dreamin/typst.ts/main/fuzzers/corpora/math/multiline_00.typ | typst | Apache License 2.0 |
#import "/contrib/templates/std-tests/preset.typ": *
#show: test-page
// Test basic alignment.
$ x &= x + y \
&= x + 2z \
&= sum x dot 2z $
|
https://github.com/Myriad-Dreamin/tinymist | https://raw.githubusercontent.com/Myriad-Dreamin/tinymist/main/crates/tinymist-query/src/fixtures/completion/func_params.typ | typst | Apache License 2.0 | // contains: aa,aab,aac,aabc
#let aa(aab, aac, aabc) = {
aac(/* range -2..0 */)
}
|
https://github.com/Vortezz/fiches-mp2i-physique | https://raw.githubusercontent.com/Vortezz/fiches-mp2i-physique/main/tp/wheatstone.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 - PONT DE WHEATSTONE")),
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("Pont de Wheatstone")
= Présentation
Le pont de Wheatstone est un montage électrique utilisé pour mesurer une résistance inconnue. Il est composé de quatre résistances, dont une inconnue, et d'une source de tension. Il est utilisé dans de nombreux domaines, notamment en physique pour mesurer la résistance d'un conducteur, ou en médecine pour mesurer la résistance de la peau.
= Principe
Le principe du pont de Wheatstone est de mesurer la valeur de la résistance inconnue en équilibrant le pont. Pour cela, on utilise un voltmètre pour arriver à l'équilibre. On peut alors déterminer la valeur de la résistance inconnue à partir des valeurs des autres résistances.
= Montage
Le montage du pont de Wheatstone est le suivant :
#figure(
cetz.canvas(length: 1cm, debug: false, {
import cetz.draw: line
import "@local/circuitypst:0.0.1": node, to
to("idealTension", (-3,0), (3,0), label: "")
to("R", (-2,4), (0,4), label: $R_v$)
to("R", (-2,1), (0,1), label: $X$)
to("R", (0,4), (2,4), label: $R_1$)
to("R", (0,1), (2,1), label: $R_2$)
line((-2,4), (-2,1))
line((2,4), (2,1))
to("R", (0,4), (0,2.5), label: "R")
to("voltmeter", (0,2.5), (0,1))
line((-3,0), (-3,2.5))
line((3,0), (3,2.5))
line((-3,2.5), (-2,2.5), label: $U$)
line((2,2.5), (3,2.5), label: $U$)
}),
caption: [Pont de Wheatstone]
)
= Équilibre du pont de Wheatstone
Pour que le pont de Wheatstone soit équilibré, il faut que la tension aux bornes du voltmètre soit nulle. On a alors :
$ frac(R_v,X) = frac(R_1,R_2) $
= Mesure de la résistance inconnue
On peut alors déterminer la valeur de la résistance inconnue à partir des valeurs des autres résistances :
$ X = frac(R_2 R_v, R_1) $ |
|
https://github.com/spherinder/ethz-infk-thesis | https://raw.githubusercontent.com/spherinder/ethz-infk-thesis/master/pages/cover.typ | typst | #let cover_page(
title: "",
document-type: "",
supervisor: "",
tutor: "",
author: none,
timespan: "",
header-logo: none,
sans-font: "CMU Sans Serif",
..rest
) = {
set page(numbering: none, margin: 2.4cm)
set par(
leading: 1em,
first-line-indent: 0em,
justify: false,
)
align(center, header-logo)
v(38mm)
block(
inset: 1.8cm,
align(center)[
#par(leading: 0.3em,
text(font: sans-font, 2.3em, weight: 700, title)
)
#v(0.8em)
#par(leading: 0.6em, text(font: sans-font, 1.3em, weight: "bold", document-type))
#v(-0.4em)
#text(font: sans-font, 1.3em, weight: "bold", "Author: " + author)
// #if (city != none and date != none) [
// \
// #text(font: sans-font, 1.2em, weight: 500, city + ", " + date)
// ]
#v(0.5em)
#text(font: sans-font, "Tutor: " + tutor)
#v(0.5em)
#text(font: sans-font, "Supervisor: " + supervisor)
#v(8em)
#text(font: sans-font, timespan)
])
pagebreak(weak: true)
}
//========================
// #import "../translations.typ": translations
// #let cover_page(
// 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
// {
// upper(text("Bachelor's thesis", 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("Faculty of " + faculty, size: 10pt, weight: "bold"),
// v(2mm),
// // Department
// text("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("<NAME>", size: 9pt, weight: "bold", font: "Open Sans"),
// v(2mm),
// text("Hamburg University of Applied Sciences", size: 9pt, font: "Open Sans"),
// )
// )
// )
// )
// // if true {
// // 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("Bachelor thesis submitted for examination in Bachelor's 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-of-applied-science-hamburg),
// ),
// 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/ukihot/igonna | https://raw.githubusercontent.com/ukihot/igonna/main/article.typ | typst | #import "templates.typ"
#import "@preview/rose-pine:0.1.0": apply
#show: apply(variant: "rose-pine-dawn")
#import "const.typ"
// 環境構築
#show: templates.setup.with(
title: const.title,
author: const.me
)
// 要旨::Abstract
#include "articles/abstract.typ"
// 目次::Contents
#outline(indent: auto, depth: 2)
#set page(columns: 2)
= Console
#include "articles/shell-work/cui.typ"
#include "articles/shell-work/cmd.typ"
#include "articles/shell-work/reg.typ"
= An Introduction to Coding in Rust
#include "articles/rust/syntax.typ"
#include "articles/rust/ownership.typ"
#include "articles/rust/async.typ"
#include "articles/rust/struct.typ"
#include "articles/rust/trait.typ"
#include "articles/rust/exercise.typ"
= Algorithm
#include "articles/algo/order.typ"
#include "articles/algo/sort.typ"
#include "articles/algo/search.typ"
#include "articles/algo/backtracking.typ"
#include "articles/algo/dp.typ"
= Data Analytics
#include "articles/data-science/analytics.typ"
= Category Theory
#include "articles/category/intro.typ"
= An Introduction to Coding in Haskell
#include "articles/haskell/syntax.typ"
= Architecture
#include "articles/design/clean.typ"
#include "articles/design/test.typ"
= Git
#include "articles/git/git.typ"
#include "articles/git/branch.typ"
= Web
#include "articles/web/html.typ"
#include "articles/web/scripts.typ"
#include "articles/web/wasm.typ"
#include "articles/web/deno.typ"
#include "articles/web/jwt.typ"
#include "articles/web/remix.typ"
= Database
#include "articles/database/sql.typ"
#include "articles/database/nosql.typ"
= Network Infrastructure
#include "articles/infra/internet.typ"
#include "articles/infra/data.typ"
= Hardware
#include "articles/computer/pc.typ"
= Technical Writing
#include "articles/technical-writing/sakubun.typ"
= Typst
#bibliography("bib.yml")
#set heading(numbering: none)
#include "appendices.typ"
|
|
https://github.com/lucannez64/Notes | https://raw.githubusercontent.com/lucannez64/Notes/master/Maths_Devoir_Maison_8.typ | typst | #import "@preview/bubble:0.1.0": *
#import "@preview/fletcher:0.4.3" as fletcher: diagram, node, edge
#import "@preview/cetz:0.2.2": canvas, draw, tree
#import "@preview/cheq:0.1.0": checklist
#import "@preview/typpuccino:0.1.0": macchiato
#import "@preview/wordometer:0.1.1": *
#import "@preview/tablem:0.1.0": tablem
#show: bubble.with(
title: "Maths",
subtitle: "Devoir Maison n°8",
author: "<NAME> (Rédacteur) et <NAME>",
affiliation: "<NAME>",
year: "2023/2024",
class: "Terminale B",
)
#set page(footer: context [
#set text(8pt)
#set align(center)
#text("page "+ counter(page).display())
]
)
#set heading(numbering : none)
#show: checklist.with(fill: luma(95%), stroke: blue, radius: .2em)
= Exercice 2
== 1
#block(fill: macchiato.yellow, inset: 8pt, radius: 4pt, [Déterminer les distances AD et CD en fonction de $theta$ et les temps $t_1$ et $t_2$ mis par le lapin et le camion pour parcourir respectivement les distances AD et CD.])
On a $cos(theta) = (A B)/(A D) arrow.l.r.double.long A D = 4/cos(theta) $
et $tan(theta) = (B D)/4 arrow.l.r.double.long B D = 4 tan(theta)$ #linebreak()
De plus $C D = C B + B D$ donc $ C D = 7 + 4 tan(theta)$
$60$ km/h $= 50/3$ m/s
et $30$ km/h $= 25/3$ m/s
$v = d/t$
Ainsi $t_1 = A D times 3/25 = 12/(25 cos(theta))$ et $t_2 = C D times 3/50 = (21+12 tan(theta))/50$
== 2
#block(fill: macchiato.yellow, inset: 8pt, radius: 4pt, [Montrer que le lapin aura traversé la route avant le passage du camion si et
seulement si $f(theta) > 0$.])
Pour que le lapin travserse avant le passage du camion il faut que la relation suivante soit vraie
$ t_1<t_2 $
$ arrow.l.r.double.long (21+12 tan(theta))/50 > 12/(25 cos(theta)) $
$ arrow.l.r.double.long 21 cos(theta) + 12 sin(theta) > 24 $
$ arrow.l.r.double.long 12 tan(theta) - 24/cos(theta) + 21 > 0 $
$ arrow.l.r.double.long 2 tan(theta) - 4/cos(theta) + 7/2 > 0 $
$ arrow.l.r.double.long f(theta) > 0 $
Ainsi pour que le lapin aura traversé la route avant le passage du camion si et seulement si $f(theta) > 0$
== 3
#block(fill: macchiato.yellow, inset: 8pt, radius: 4pt, [Conclure.])
On cherche les variations de $f$ #linebreak()
$ (1/v)' = -v'/v^2 text("avec") v = cos(theta) text("on a") v'(theta) = -sin(theta) $
Ainsi $ (1/cos(theta))' = sin(theta)/cos(theta)^2 $ et
$ f'(theta) = 2/cos(theta)^2 - 4 sin(x)/cos(theta)^2 $
$ f'(theta) = 2/cos(theta)^2 ( 1 - 2 sin(theta)) $
$ f'(theta) > 0 $
$ arrow.l.r.double.long 1 - 2 sin(theta) > 0 text(" car ") 2/cos(theta)^2 > 0 $
$ arrow.l.r.double.long sin(theta) < 1/2 $
$ arrow.l.r.double.long 0 lt.eq theta < pi/6 $
Par conséquent $f$ est croissante sur $ [0; pi/6[$ et décroissante sur $ ]pi/6; pi/2[ $
La fonction $theta arrow.r 1/cos(theta)$ est continue sur l'intervalle $[0;pi/2[$ car c'est la composée de la fonction cosinus (continue sur $[0;pi/2[$) et de la fonction $theta arrow.r 1/x$ (continue sur $[0; pi/2[$). De plus, la fonction $theta arrow.r tan(theta)$ est continue sur l'intervalle $]0,pi/2[$.
La fonction $f$ est donc continue sur l'intervalle $[0,pi/2[$ comme somme et produit de fonctions continues sur cet intervalle.
Sur l'intervalle $[0;pi/6[$
$f$ est continue et strictement croissante
$ f(0) = -1/2$ et $f(pi/6) = (7-4 sqrt(3))/2 approx 0.03 > 0 $ donc $ 0 in [-1/2; (7-4 sqrt(3))/2[ $
Selon le théorème de la bijection $ f(theta) = 0 $ a une solution sur $ [0; pi/6[$ notée $alpha$
Sur l'intervalle $]pi/6;pi/2[$
$f$ est continue et strictement décroissante
$ f(pi/6) = (7-4 sqrt(3))/2 approx 0.03 > 0 $ et $ lim_(theta arrow.r pi/2) f(theta) = lim_(theta arrow.r pi/2) 7/2 + 2 sin(theta)/cos(theta) - 4/cos(theta) = lim_(theta arrow.r pi/2) 1/cos(theta) ( 7/2 cos(theta) + 2 sin(theta) - 4 ) $
$ lim_(theta arrow.r (pi/2)^-) 1/cos(theta) = +infinity $
$ lim_(theta arrow.r (pi/2)^-) cos(theta) = 0 $
$ lim_(theta arrow.r (pi/2)^-) sin(theta) = 1 $
$ lim_(theta arrow.r pi/2) f(theta) = lim_(theta arrow.r pi/2) 1/cos(theta)( 1 - 4 )= lim_(theta arrow.r pi/2) 1/cos(theta) (-3) = lim_(theta arrow.r pi/2) -infinity $
Donc $ 0 in ]-infinity;(7-4 sqrt(3))/2[ $
Selon le théorème de la bijection $ f(theta) = 0 $ a une solution sur $ ]pi/6; pi/2[$ notée $beta$
Ainsi le domaine de la solution est $[alpha; beta]$
On trouve approximativement à l'aide de la calculatrice par balayage $alpha approx 0.395$ et $beta approx 0.644$
Par conséquent le lapin survivra si l'angle $theta$ est entre $0.395$ radians et $0.644$ radians
|
|
https://github.com/fsr/rust-lessons | https://raw.githubusercontent.com/fsr/rust-lessons/master/src/lesson2.typ | typst | #import "slides.typ": *
#show: slides.with(
authors: ("<NAME>", "<NAME>"), short-authors: "H&A",
title: "Wer rastet, der rostet", short-title: "Rust-Kurs Lesson 2", subtitle: "Ein Rust-Kurs für Anfänger",
date: "Sommersemester 2023",
)
#show "theref": $arrow.double$
#show link: underline
#new-section("Basics")
#slide(title: "Funktionen")[
#uncover("2-")[Nutzt aussagekräftige Variablennamen!]
#only(1)[
```rust
fn spass_mit_funktionen() {
let right = 17;
let light = seven();
println!("adding {left} and {right}: {}", add(left, right));
}
fn add(l: u8, r: u8) -> u8 {
return left + right;
}
fn seven() -> u8 {
7 // implicit return
}
```
]
#only("2-")[
```rust
fn spass_mit_funktionen() {
let right = 17;
let left = seven();
println!("adding {left} and {right}: {}", add(left, right));
}
fn add(left: u8, right: u8) -> u8 {
return left + right;
}
fn seven() -> u8 {
7 // implicit return
}
```
]
#uncover(3)[
```rust
let closure = |param1, param2| { /* function body*/ };
```
]
]
#slide(title: "Quiz 3: return", theme-variant: "action")[
Was wird passieren, wenn diese funktionen aufgerufen werden?
```rust
fn add_two_a(a: u32) -> u32 {
return a + 2;
}
fn add_two_b(b: u32) -> u32 {
b + 2;
}
fn add_two_c(c: u32) -> u32 {
c + 2
}
```
#uncover(2)[theref #text(red)[compilation error!]]
]
#slide(title: "Comments")[
```rust
// This is a comment. Multi-line comments
// generally are written this way.
/* You can use this style of comment too. */
/// This is a doc comment.
```
]
#slide(title: "Statements und Expressions")[
#columns(2)[
Statements: \
Instruktionen ohne return Wert
```rust
let a = 2; /*
^^^^^^^^^^ statement */
println!("Hello students!"); /*
^^^^^^^^^^^^^^^^^^^^^^^^^^^^ statement */
fn goodbye() -> () {
println!("Goodbye");
}
```
#uncover("2-")[
```rust
// `-> ()` is implicit
fn goodbye() /* no return */ {
println!("Goodbye");
}
```
]
#colbreak()
#uncover(3)[
Expressions: \
evaluieren zu einem Wert
```rust
fn add_one(a: i32) -> i32 {
a + 1
// ^^^^^ expression
}
let n = add_one(2);
/* ^^^^^^^^^^ expression
^^^^^^^^^^^^^^^^^^^ statement
*/
```
]
]
]
#slide(title: "Statements und Expressions")[
```rust
let a = 3;
let b = {
let a = a + 1;
a * 4
};
```
#uncover(2)[
```rust
let c = if a > 3 { a - 2 } else { a + 4 }; /*
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
|____ expression
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
|____ statement */
```
]
]
#slide(title: "Control flow - branching mit if und else")[
```rust
if students < 10 {
println!("Kein Rust Kurs :(");
} else if students > 30 {
println!("Raum überfüllt!!");
} else {
println!("Rust Kurs findet statt :D");
}
```
]
#slide(title: "Übung 2: Fibonacci", theme-variant: "action")[
Berechne die `n`-te Fibonacci-Zahl mit Hilfe einer rekursiven Funktion. \
Verwende dabei `u16` und ein implicit `return`. \
Zusatz: Verwende gar kein `return`.
Gib deiner Fibonacci-Funktion Zahlen zwischen 0 bis 50. \
Starte dein Programm mit `cargo run`.
Was passiert und warum?
#columns(2, gutter: -20%)[
#uncover("2-")[
```rust
fn fib(n: u16) -> u16 {
if n <= 1 {
return 1;
}
fib(n - 1) + fib(n - 2)
}
```
]
#colbreak()
#uncover(3)[
```rust
fn fib_no_return(n: u16) -> u16 {
if n <= 1 {
1
} else {
fib_no_return(n - 1) + fib_no_return(n - 2)
}
}
```
]
]
]
#slide(title: "Control flow - loops")[
#columns(2)[
Endlosschleife
```rust
loop {
println!("HEYYEYAAEYAAAEYAEYAA");
}
```
#uncover("2-")[
```rust
let mut counter = 0;
let n = loop {
counter += 1;
if counter % 2 == 1 {
println!("yes");
} else if counter % 4 == 3 {
continue;
} else if counter > 20 {
break counter + 2;
}
}
```
]
#colbreak()
#uncover("3-")[
Konditionalschleife
```rust
let mut counter = 5;
while counter >= 0 {
counter -= 1;
println!("no");
}
```
Wieviele "no" gibt das aus? \
]
#uncover(4)[
theref 6
]]
]
#slide(title: "Control flow - loops")[
Über Elemente eines arrays iterieren.
#columns(2)[
`while`-Schleife
```rust
let arr = [1, 2, 3, 4, 5];
let mut idx = 0;
while idx < arr.len() {
println!("{}", arr[idx]);
index += 1;
}
```
#colbreak()
#uncover(2)[
`for`-Schleife
```rust
let arr = [1, 2, 3, 4, 5];
for element in arr {
println!("{element}");
}
```
]]
]
#slide(title: "Quiz 4: Control flow - labeled loops", theme-variant: "action")[
#columns(2)[
Labeled loops
```rust
let mut counter = 0;
let x = 'outer: loop {
'inner: loop {
counter += 2;
if counter > 2 {
break 'outer counter * 4;
} else {
counter -= 1;
}
}
}
```
#colbreak()
#uncover("2-")[
Welchen Wert hat `x` am Ende?
]
#uncover(3)[
theref 12
]]
]
#slide(title: "Control flow - loops")[
Über eine range von Zahlen iterieren.
#columns(2)[
_rechts-offene range_
```rust
for n in 1..4 {
println!("{n}");
}
```
`[1,4)` theref 1, 2, 3
#colbreak()
#uncover(2)[
_rechts-geschlossene range_
```rust
for n in 1..=4 {
println!("{n}");
}
```
`[1,4]` theref 1, 2, 3, 4
]]
]
#slide()[] |
|
https://github.com/HarryLuoo/sp24 | https://raw.githubusercontent.com/HarryLuoo/sp24/main/Physics311/hw9.typ | typst | #show heading: text.with(size: 12pt, weight: 900, font: "Libre Baskerville")
#set text(11pt)
#set page(margin: (x: 1cm, y: 1cm), columns: 1, flipped: false)
#set math.equation(numbering:"(1)")
#show math.equation: set text(13pt)
= 1
#image("assets/2024-04-25-20-58-43.png", width: 70%)
- (a) (b) as graphed above. In order to simulate gravity, $
A = omega^2 R = g => omega = sqrt(g/R) = 0.5 "rad"slash s
$
- (c) effective gravity is $
g_"eff" = omega^2 R prop R\
=> (g_"head" - g_"feet")/(g_"feet") = (R_"head" - R_"feet")/(R_"feet")=(-2)/(40) = -5%
$
#pagebreak()
= 2
- (a) recall EOM for a particle in rotating frame with angular velocity $Omega$, $
m dot.double(arrow(r)) = -m Omega^2 rho + overbrace(2m dot(arrow(r)) times arrow(Omega),F_"cor") + overbrace(m arrow(Omega) times (arrow(r) times arrow(Omega)),F_"centripetal") + F_"buoyancy"
$ noticing that the droplet is relatively stationary with respect to the rotation frame, $F_"cor" = 0, quad F_"centripetal" eq.not 0$
\
- (b) (c)
The direction of $F_g + F_"cent"$ is downward, tengential to the water surface.
The water level is a equipotential surface of the combined potential of gravity and centrifugal force. So for a given height z, $
U = m g z + U_"cent"\
"where" U_"cent" =- integral F_"cent" dif rho = -integral m Omega^2 rho dif rho = -1/2 m Omega^2 rho^2 \
=> U = m g z - 1/2 m Omega^2 rho^2 = "constant" quad \
=> z(rho) = (Omega^2 rho^2)/(2g) + "const"
$
It is obvious that $z(rho)$, i.e. water surface, is a parabola.
#pagebreak()
= 3
we choose the frame to be the following: ${hat(x),hat(y),hat(z)}$, where $hat(x) $ points eastward, $hat(y) $ points northward, and $hat(z) $ points upward. Let particle above earth surface has position $arrow(r)$, whose angle with earth's rotation axis is $theta$.
EOM of particle $
cases(
dot(arrow(v)) = -g hat(z) + 2 arrow(v) times arrow(Omega),
arrow(Omega) = Omega sin theta hat(y) + Omega cos theta hat(z),
arrow(v) = v_x hat(x) + v_y hat(y) + v_z hat(z)
) quad
=> dot(arrow(v)) = - g hat(z) + 2 Omega [(v_y cos theta - v_z sin theta) hat(x) - v_x cos theta hat(y) + v_x sin theta hat(z)] \
$
let $arrow(v)(t) = arrow(v_1) + arrow(v_2)$, with the first term being velocity neglecting rotation, and 2nd term is the correction with rotation.
for $arrow(v)_1, Omega = 0$.
$
=> cases(dot(v)_x = dot(v)_y = 0,
dot(v)_z = -g)
=> quad cases(
arrow(v_1)(t) = arrow(v_0) - g t hat(z),
arrow(r)(t) = arrow(r_0) + arrow(v_0) t - 1/2 g t^2 hat(z)
)
$
Therefore, when recalling the coriolis force, $dot(arrow(v)) = - g hat(z) + 2 arrow(v) times arrow(Omega)$, we have $
dot(arrow(v_1)) + dot(arrow(v_2)) &= -g hat(z) + 2 arrow(v_1) times arrow(Omega) +2 arrow(v_2) times arrow(Omega) \ &&"recognizing" Omega = "small", v_2 = "small" \
& arrow(v_2) approx 2(arrow(v_0) - g t hat(z)) times arrow(Omega)
$
Now consider:
+ free fall from height h, with $v_0=0$ , over a time lapse of $t = sqrt((2h)/g) $
$
dot(arrow(v)) = 2 g t Omega sin theta hat(x) => quad arrow(v) = integral dot(arrow(v)) dif t = g t^2 Omega sin theta hat(x) \
arrow(v) = -g t hat(z) + g t^2 Omega sin theta hat(x)
$
$
arrow(r) = integral arrow(v) dif t = display(mat(1/3g Omega t^3 sin theta ; 0; -1/2 g t^2))
$ Noticing that $t = sqrt((2h)/g) $, displacement on the x-y plane is $
x_f = 1/3 g Omega (sqrt((2h)/g) ) ^3 sin theta
$ <eq.3.1>
+ compare with particle thrown from ground, with $arrow(v_0) = v_0 hat(z), quad t = 2sqrt((2h)/(g)) =(2v_0)/(g)$
$
dot(arrow(v_2)) &= 2(v_0 - g t) hat(z) times arrow(Omega) \
& = 2 (v_0 - g t)hat(z) times (Omega sin theta hat(y) + Omega cos theta hat(z)) \
&= hat(x)[-2 (v_0 - g t )Omega sin theta] \
& = (-2 v_0 Omega sin theta + 2 g t Omega sin theta) hat(x)
$
$
arrow(v_2) = integral arrow(v_2) dif t = (-2 v_0 Omega sin theta t + g Omega sin theta t^2) hat(x) \
=> arrow(v) = arrow(v_1) + arrow(v_2) = display(mat(-2 v_0 Omega sin theta t + g Omega sin theta t^2; 0; v_0 - g t)) $
Considering $t = 2sqrt((2h)/(g)) =(2v_0)/(g)$
$
=> x_t = integral v_x dif t &= -v_0 Omega sin theta t^2 + 1/3 g Omega sin theta t^3 \
& = -v_0 Omega sin theta (2v_0/g)^2 + 1/3 g Omega sin theta (2v_0/g)^3 \
& = -4/3 g Omega (sqrt((2h)/g) ) ^3 sin theta
$ <eq.3.2>
Comparing @eq.3.1 and @eq.3.2, we have $(x_t)slash(x_f) = -4$ , thus showing that the deflection is indeed opposite and 4 times larger when the particle is thrown from the ground.
#pagebreak()
= 4
We propose the following frame: ${hat(x),hat(y),hat(z)}$, where $hat(x) $ points eastward, $hat(y) $ points northward, and $hat(z) $ points upward. Picture a hoop lying on ground with the following illustration:
#image("assets/2024-04-25-23-32-19.png",width: 50%)
Consider the rotation of an infinitesimal element of the hoop over an infinitesimal time interval, across small angle $alpha$.
Find coriolis force $ d F_"cor" = 2 dif m (arrow(v) times arrow(Omega)) $ where $
arrow(v) = omega r display(mat(- sin alpha; cos alpha; 0)), quad arrow(Omega) = Omega display(mat(0;sin theta; cos theta)), quad dif m = m (dif alpha) / (2pi)
$
Torque on said infinitesimal element can be found by $
d tau = arrow(r) times dif F_"cor", quad arrow(r) =r display(mat(cos alpha; sin alpha;0)) \
=> d tau = 2 dif m (arrow(v) (arrow(r) dot arrow(Omega) - arrow(Omega)(arrow(r) dot arrow(v)))) = 2 omega r^2 Omega sin theta dif m display(mat(-sin^2alpha;sin alpha cos alpha; 0))
$
noticing $dif m = m (dif alpha) / (2pi)$ , integrating the above w.r.t. $alpha$ from 0 to $2pi$, $
tau = -(m omega Omega r^2 sin theta) hat(x)
$
The above shows that the torque due to coriolis force is westward with magnitude $m omega Omega r^2 sin theta$
#pagebreak()
= 5
According to the hints in problem statement of Taylor 9.34, we write the puck's position vector, relative to the earth's center O, as $arrow(R) + arrow(r)$, where $arrow(R)$ is the position of thi point P and $arrow(r) = (x,y,0)$ is the puck's position relative to P.
Ignoring centrifugal force, we can write the EOM as the following $
dot.double(arrow(r)) = g_0(r) + 2 dot(arrow(r)) times arrow(Omega) $ <eq.5.1>
$
"where" g_0(r) = -G M (arrow(R) + arrow(r) )/norm((arrow(R) + arrow(r)))^3
= -G M (arrow(R) + arrow(r))/(R^3) (1+ r^2/R^2)^(-3/2) $
recognizing that $r << R$, expanding the above function gives an approximation:
$
g(r) = -G M (arrow(R) + arrow(r))/(R^3) = arrow(g)(0) + g(0) arrow(r)/R
$
putting the above into @eq.5.1, we have $
dot.double(arrow(r)) &= arrow(g)(0) + g(0) arrow(r)/R + 2 dot(arrow(r)) times arrow(Omega) \
& = g(0) display(mat(0;0;1)) -(g)/R display(mat(x;y;0)) + 2 display(mat(dot(y) Omega cos theta - dot(z) Omega sin theta; -dot(x) Omega cos theta;dot(x) Omega sin theta ))
$
The above is set of 2nd order ODEs:
$
dot.double(x) = -g x /R + 2dot(y) Omega cos theta\
dot.double(y) = -g y /R - 2dot(x) Omega cos theta
$
This is the same as Foucault pendulum equation with length of pendulum being $R$.
The oscillation frequency is $omega_0 = sqrt(g/R) approx 1.24 e(-3) space s^(-1) $, frequency of Foucault precession, $Omega_z = Omega cos theta$
|
|
https://github.com/EricWay1024/Scientific-Computation-Notes | https://raw.githubusercontent.com/EricWay1024/Scientific-Computation-Notes/master/main.typ | typst | #import "template.typ": *
#import "theorem.typ": *
#import "algo.typ" : *
#set heading(numbering: "1.a.")
#let lebs = [ $L^2(Omega)$ ]
#let into = [ $integral_Omega$ ]
#let dx = [ $dif x$ ]
#let bd(term) = [ $bold(#term)$]
#let theorem = thmbox(
"theorem",
"Theorem",
fill: rgb("#e8e8f8"),
)
#let lemma = thmbox(
"theorem",
"Lemma",
fill: rgb("#e8e8f8"),
)
#let definition = thmbox(
"theorem",
"Definition",
fill: rgb("#e8f8e8"),
)
#let example = thmbox(
"theorem",
"Example",
stroke: rgb("#ffaaaa") + 1pt,
)
#let method = thmbox(
"theorem",
"Method",
stroke: rgb("#aaaaff") + 1pt,
)
#let problem = thmbox(
"theorem",
"Problem",
stroke: rgb("#aaffaa") + 1pt,
)
#let corollary = thmbox(
"theorem",
"Corollary",
fill: rgb("#e8e8f8"),
)
// #let thm = counter("theorem")
// #let theorem(term, name: "", type: "Theorem") = block(fill: luma(240), inset: 6pt, width: 100%, radius: 2pt)[
// *#type #thm.display()*#if name == "" {} else {[ (#name)]}. #thm.step() #term
// ]
// #let corollary(term, name: "") = theorem(name: name, type: "Corollary")[#term]
// #let lemma(term, name: "") = theorem(name: name, type: "Lemma")[#term]
// #let example(term, name: "") = theorem(name: name, type: "Example")[#term]
// #let definition(term, name: "") = theorem(name: name, type: "Definition")[#term]
#let proof(term) = block(width: 100%)[_Proof._ #term #h(1fr) $qed$]
// Take a look at the file `template.typ` in the file panel
// to customize this template and discover how it works.
#show: project.with(
title: "Notes for MATH3036 Scientific Computation and Numerical Analysis",
authors: (
"Notes by <NAME>",
"Lectures by <NAME>"
),
date: "March 23, 2023",
)
This document serves as an unofficial companion for the module MATH3036, _Scientific Computation and Numerical Analysis_, at the University of Nottingham. The material presented here is based on the available lecture slides from the academic year 2022-23. It is important to note that there might be slight variations in notation and the order of topics covered. As the course evolves, the content itself may also undergo changes at the instructor's discretion in subsequent academic years. Please be aware that this current version is provided with the caveat that it may contain typos, errors or inaccuracies. Your valuable contributions to enhance this resource are greatly appreciated. Feel free to get in touch by email at #link("mailto:<EMAIL>")[#underline[<EMAIL>]] or by submitting an issue or pull request on #link("https://github.com/EricWay1024/Scientific-Computation-Notes")[#underline[GitHub]].
#outline(indent: true)
#pagebreak()
= FEM for PDEs I
== Problem statement
Let $Omega subset RR$ be an open interval. We always take $Omega = (0, 1)$ as an example.
#definition(name: "Sobolev spaces")[
Define the _Sobolev spaces_
$ H^1(Omega) &= {v : Omega -> RR | v, v' in L^2 (Omega)} \
H_0^1(Omega) &= { v in H^1(Omega) | v(0) = v(1) = 0} \
H_(\(0)^1(Omega) &= { v in H^1(Omega) | v(0) = 0} \
H_(0\))^1(Omega) &= { v in H^1(Omega) | v(1) = 0} $
where $L^2(Omega)$ is the Lebesgue space.
]
#problem(name: "Two-point boundary value problem, strong form")[Given $f in lebs$, the _strong form_ of a _two-point boundary value problem_ is to find $u in H_0^1(Omega)$ such that
$ -u'' = f $]
#problem(name: "Two-point boundary value problem, weak form")[
Given $f in lebs$, the _weak form_ of a _two-point boundary value problem_ is to find $u in H_0^1(Omega)$ such that for all $v in H_0^1(Omega)$
$ integral_0^1 u' v' dif x = integral_0 ^1 f v dif x $
<weak-form>
]
#theorem[
Any solution $u in H_0^1(Omega)$ to the strong form also solves the weak form.
]
#proof[
Let $u$ solve the strong form. Then take any $v in H_0^1(Omega)$, we have $ -u'' v = f v $ Integrate over $Omega$ and use the boundary conditions to obtain
$ integral_0^1 u' v' dif x = integral_0 ^1 f v dif x $
Thus $u$ also solves the weak form.
]
== Petrov-Galerkin discretization
#problem(name: "Abstract weak form")[
Let $U, V$ be function spaces. Given a bilinear form $b: U times V -> RR$ and a linear functional $l : V -> RR$,
find $u in U$ such that for all $v in V$ $ b(u, v) = l(v) $
]
#method(name: "Petrov-Galerkin discretization")[
Given discrete subspaces $U_h subset U$ and $V_h subset V$ with $dim U_h = dim V_h$, find $u_h in U_h$ such that for all $v_h in V_h$ $ b(u_h, v_h) = l(v_h) $
This method is called _Petrov-Galerkin discretization_ and specially, when $U_h = V_h$, _Galerkin discretization_.
]
#definition(name: "Finite element mesh")[
A _finite element mesh_ is a partition of $Omega$ into non-overlapping subsets.
]
In Petrov-Galerkin discretization, $U_h$ and $V_h$ are the span of basis functions which are defined with respect to a finite element mesh.
#example[
Let $U_h = "span"{x, x^2}$ and $V_h = "span"{1, x}$. Then $u_h = u_1 x + u_2 x^2$ where $u_1, u_2$ are to be determined. Setting $v_h(x) = 1$ and $v_h(x) = x$ gives two equations for $u_1$ and $u_2$. We then compute $u_1$ and $u_2$ to obtain $u_h(x)$.
]
== Finite element spaces in 1-D
Consider $Omega subset RR$ with finite element mesh $ {(x_0, x_1), (x_1, x_2), dots, (x_(N-1), x_N)} $
#definition(name: ['Hat' basis functions])[
Define for $j = 0, 1, dots, N$, $ phi _j (x_i) = cases(1 quad "if " i = j, 0 quad "if " i != j) $
and $phi_j$ is linearly interpolated elsewhere.
]
#definition[
Define for $i = 1, dots, N$, $ psi_i(x) = cases(1 quad "if " x in (x_(i-1), x_i), 0 quad "otherwise") $
]
Then $U_h = "span"{ phi_j } _(j = 0) ^ N$ is the space of continuous piecewise linear polynomials, and $V_h = "span"{ psi_i } _(i = 1) ^ N $ is the space of discontinuous piecewise constant polynomials.
#example[
Given $f$, find $u$ such that $u' = f$ for $x in (0, 1)$ and $u(0) = 0$.
]
#proof[
Multiply $v$ on both sides of $u' = f$ and integrate over $[0, 1]$, we see that
$ integral_0^1 f v dx = integral_0^1 u' v dx = [u v ]_0^1 - integral_0^1 u v' dx $
We now derive two weak forms.
#list(
block(width: 100%)[ A weak form where no $v'$ appear: find $u in H_(\(0)^1(Omega)$ such that $ integral_0^1 f v dx = integral_0^1 u' v dx $ for any $v in L^2(Omega)$.],
[ A weak form where no $u'$ appear: find $u in lebs$ such that $ integral_0^1 f v dx = - integral_0^1 u v' dx $ for any $v in H_(0\))^1(Omega)$.]
)
We now apply Petrov-Galerkin discretization to the first weak form: find $u_h in U_h subset U = H_(\(0)^1$ such that
$ integral_0^1 f v_h dx = integral_0^1 u_h' v_h dx $
for any $v_h in V_h subset V = lebs$.
With a finite element mesh of $N$ intervals, we define $U_h = "span"{phi_j : j = 1, 2, dots, N}$.
// Note that $phi_0$ is not included since $u(0) = 0$.
Thus $ u_h = sum_(j=1)^N u_j phi_j(x) $ for $u_j in RR$, $j = 1, dots, N$. We define $V_h = "span"{psi_i : i = 1, dots, N}$ and pick $v_h = psi_i$ for $i = 1, dots, N$.
We now need to find $bd(u) = vec(u_1, dots, u_N) in RR^N$ such that
$ sum_(j=1)^N u_j integral_0^1 phi_j'(x) psi_i(x) dx = integral_0^1 f(x) psi_i(x) dx $
Define $A in RR^(N times N)$ where $ A_(i, j) = integral_0^1 phi_j'(x) psi_i(x) dx = cases(1 &"if " i = j, -1 &"if " i = j + 1, 0 &"otherwise") $ and $bd(b) in RR^N$ where
$ b_i = integral_0^1 f(x) psi_i(x) dx = integral_(x_(i-1))^(x_i) f(x) dx $
Then the problem is reduced to solving an algebraic system $A bold(u) = bold(b)$, where $ A = mat(
1, 0, 0, ..., 0;
-1, 1, 0, ..., 0;
0, -1, 1, ..., 0;
0, 0, -1, ..., 0;
dots.v, dots.v, dots.v, dots.down, dots.v;
0, 0, 0, ..., 1
) quad "and" quad bold(b) = vec(
integral_(x_0) ^ (x_1) f(x) dif x,
integral_(x_1) ^ (x_2) f(x) dif x,
dots.v,
integral_(x_(N-1)) ^ (x_N) f(x) dif x,
)
$
]
#pagebreak()
= FEM for PDEs II
== Hilbert space
#definition(name: [Inner product space])[
An inner product space is written as $(V, angle.l dot.c, dot.c angle.r _V)$ where $V$ is a linear vector space over $RR$ and $angle.l dot.c, dot.c angle.r _V : V times V -> RR$ is a inner product. The inner product induces a norm $|| dot.c || _V$ on the space.
]
#definition(name: [Hilbert space])[
A _Hilbert space_ is a complete inner product space.
]
#example(name: $RR^n$)[$angle.l x, y angle.r = sum_i x_i y_i$ and $|| x || _ (RR ^ n) = sqrt(sum_i x_i^2)$.]
#example(name: $L^2(Omega)$)[$angle.l f, g angle.r = integral_Omega f g dif x$ and $|| f || _(L^2(Omega)) = sqrt(integral_Omega f^2 dif x)$.]
== Well-posedness
#definition(name: "Well-posedness")[ A PDE problem is _well-posed_ if
- a unique solution exists and
- it satisfies continuous dependence (small changes in the problem lead to small changes in the solution).]
Main idea: if the weak form is well-posed (usually by the following Lax-Milgram Theorem) and the data is regular, then the strong form is also well-posed and the solution to the weak form also solves the strong form.
#theorem(name: "Lax-Milgram Theorem")[Let $V$ be a Hilbert space, $b(dot.c, dot.c): V times V -> RR$ a bilinear form, and $l(dot.c) : V -> RR$ a linear functional. Assume:
$
|b(w, v)| <= c_b || w || _V || v || _V quad & forall w, v in V quad &"Continuity of " b \
|l(v)| <= c_l || v || _V quad & forall v in V &"Continuity of " l\
b(w, w) >= alpha || w || ^2 _V quad & forall w in V &"Coercivity"
$
for some $c_b, c_l, alpha > 0$.
Then the following problem is well-posed:
- Find $u in V$ such that $b(u, v) = l(v)$ for all $v in V$.]
// == Poincare-Friedrichs inequality
#theorem(name: "Poincare-Friedrichs inequality")[
For all $w in H_0^1(Omega)$, there exists $c_"PF" > 0$ such that $ || w ||_(L^2(Omega)) <= c_"PF" || w' ||_(L^2(Omega)) $]
#corollary[
$ || w || _(H^1(Omega)) = sqrt(|| w' ||_(L^2(Omega))^2 + || w ||_(L^2(Omega))^2) $ and $|| w' || _(lebs)$ are equivalent norms on $H^1(Omega)$ and thus on $H_0^1(Omega)$.]
#proof[
By Poincare-Friedrichs inequality,
$ || w' ||_(L^2(Omega))^2 <= || w' ||_(L^2(Omega))^2 + || w ||_(L^2(Omega))^2 <= (1 + c^2_"PF") || w' ||_(L^2(Omega))^2 $
Taking the square root yields the result.
]
// == Main example
#example[#thmref(<weak-form>)[The weak form defined in Problem] is well-posed.]
#proof[
Here $b(u, v) = integral_0^1 u' v' dif x$ and $l(v) = integral_0 ^1 f v dif x$.
$V = H_0^1(Omega)$ with inner product $angle.l w, v angle.r_V = integral_0^1 w' v' dif x$ is a Hilbert space with induced norm $ || w || _V = sqrt(integral_Omega (w')^2 dif x) $
#list(
[Clearly $b(u, v) = integral_0^1 u' v' dif x = angle.l u, v angle.r _ V$ is bi-linear and $l(v) =integral_0 ^1 f v dif = angle.l f, v angle.r _ lebs $ is linear. ],
[Continuity of $b$: For all $u, v in V$, by Cauchy-Schwartz inequality on $V$,
$ |b(u, v)| = |angle.l u, v angle.r_V| <= norm(u)_V norm(v)_V $
Thus we can take $c_b = 1$.],
[Continuity of $l$: For all $v in V$,
$ |l(v)| = |angle.l f, v angle.r_lebs | <= norm(f)_lebs norm(v)_lebs <= norm(f)_lebs (c_"PF" norm(v')_lebs) = (c_"PF" norm(f)_lebs) norm(v)_V $
The first inequality is due to Cauchy-Schwartz inequality on $lebs$ and the second is due to Poincare-Friedrichs inequality. Thus we can take $c_l = c_"PF" norm(f)_lebs$.
],
[
Coersivity of $b$: For all $w in V$,
$ b(w, w) = angle.l w, w angle.r_V = norm(w)_V^2 $
Thus we can take $alpha=1$.],
)
By Lax-Milgram Theorem, the problem is well-posed.
]
== Weak derivative
#definition[
$ C^oo(Omega) &= {phi.alt: Omega -> RR | phi.alt, phi.alt', phi.alt'', dots "are continuous"} \ C^oo_0(Omega) &= {phi.alt: Omega -> RR | phi.alt, phi.alt', phi.alt'', dots "are continuous and 0 on the boundary"} $
]
#definition(name: "Weak derivative")[
Let $v in #lebs$. If for all $phi.alt in C_0^oo (Omega)$, there exists $w in #lebs$ such that $ integral_Omega w phi.alt dif x = integral_Omega - v phi.alt' dif x $ where $phi.alt'$ is the classical derivative of $phi.alt$, then we define the _weak derivative_ of $v$ as $w$.
]
Not every function has a weak derivative.
#example(name: "Main trivial example")[
Assume $v in C^1(overline(Omega))$. Then $ integral_Omega v' phi.alt dif x = integral_Omega - v phi.alt' dif x + [v phi.alt ]_0 ^ 1 = integral_Omega - v phi.alt' dif x $ for any $phi.alt in C_0^oo (Omega)$. Thus the classical derivative of $v$ is its weak derivative.
]
#example(name: "Main non-trivial example")[Let $ v(x) = cases(2x quad x in [0, 1/2], 2 - 2x quad x in [1/2, 1]) $
Then $ w(x) = cases(2 quad x in (0, 1/2), -2 quad x in (1/2, 1)) $ is the weak derivative of $v$.
The value of $w$ at $x = 1/2$ is arbitrary.
]
#example[The solution to the weak form also solves the strong form, assuming $f in C(overline(Omega))$.]
#proof[Given $ integral_Omega u' phi.alt' dif x = integral_Omega f phi.alt dif x $ for all $phi.alt in H_0^1(Omega) supset C_0^oo(Omega) $. Hence $u'$ has weak derivative $u'' = -f in L^2 (Omega)$. Next, assume $f in C(overline(Omega)) subset #lebs$, then $u'' in C(overline(Omega))$ and thus $u in C^2(overline(Omega))$. Thus $-u''(x) = f(x)$ for all $x in Omega$.]
== Convergence of FEM
#lemma(name: "Galerkin orthogonality")[For all $v_h in V_h$,
$ angle.l u - u_h, v_h angle.r_V = into (u' - u_h')v_h' dx = 0 $
]
#proof[
Take $v = v_h in V_h subset V$ in the weak form:
$ into u'v_h' dx = into f v_h dx $
Also we have the Galerkin discretization:
$ into u_h' v_h' dx = into f v_h dx $
Subtracting second equation from the first gives the result.
]
#lemma(name: "Interpolation error estimate")[
Given $w in H^2(Omega)$, let $I_h(w) in V_h$ denote the linear interpolant of $w$ on the finite element mesh, namely for $i = 0, 1, dots, N$,
$ I_h(w)(x_i) = x_i $
Then there exists $C > 0$ such that
$ norm(w' - I_h(w)')_lebs <= C h $
]
#proof[
Define for $x in Omega$, $ e(x) = w(x) - I_h(w)(x) $
Fix $i in {1, dots, N}$. Since $e(x_(i-1)) = e(x_i) = 0$, by Rolle's Theorem, there exists $xi_i in (x_(i-1), x_i)$ such that $e'(xi_i) = 0$.
For $x in (x_(i-1), x_i)$, $ |e'(x)| = |e'(xi_i) + integral_(xi_i)^x e''(t) dif t | = |integral_(xi_i)^x w''(t) dif t| <= sqrt(h) sqrt(integral_(x_(i-1))^(x_i) (w''(t))^2 dif t) $
by C-S inequality. Then
$ norm(e')^2_lebs &= sum_(i=1)^N integral_(x_(i-1))^(x_i) (e'(x))^2 dif x \
&<= sum_(i=1)^N integral_(x_(i-1))^(x_i) (h integral_(x_(i-1))^(x_i) (w''(t))^2 dif t) dx \
&= sum_(i=1)^N h^2 (integral_(x_(i-1))^(x_i) (w''(t))^2 dif t) \
&= h^2 norm(w'')^2_lebs
$
where we take $C^2 = norm(w'')^2_lebs $. Taking the square root yields the result.
]
#theorem(name: "A priori error analysis")[For all $v_h in V_h$,
// $ ||u - u_h|| _V = || u' - u_h' || _#lebs <= || u' - v_h' || _#lebs = ||u - v_h|| _V $
$ ||u - u_h|| _V <= ||u - v_h|| _V $
This implies that $u_h$ is the best possible approximation for $u$ in $V_h$.]
// #proof[
// $
// norm(u' - u_h')_lebs^2 &= into (u' - u_h') (u' - u_h') dx \
// &= into (u' - u_h') u' dx \
// &= into (u' - u_h') (u' - v_h') dx \
// &<= norm(u' - u_h')_lebs norm(u' - v_h')_lebs
// $
// Thus $norm(u' - u_h')_lebs <= norm(u' - v_h')_lebs$.
// ]
#proof[
Apply Galerkin orthogonality twice (the first time with $u_h = v_h$) and use C-S inequality:
$
norm(u - u_h)_V^2 &= angle.l u - u_h, u - u_h angle.r_V \
&= angle.l u - u_h, u angle.r_V - angle.l u - u_h, u_h angle.r_V - angle.l u - u_h, v_h angle.r_V \
&= angle.l u - u_h, u - v_h angle.r_V \
&<= norm(u-u_h)_V norm(u-v_h)_V
$
Cancelling $norm(u - u_h)_V$ on both sides gives the result.
]
#corollary[
There exists $C > 0$ such that $ || u' - u_h' || _#lebs <= C h $
]
#proof[
Take $v_h$ as the linear interpolant of $u$ in the previous theorem.
]
The corollary implies that as $h -> 0$, $u_h -> u$ and the order of convergence is linear.
#pagebreak()
= FEM for PDEs III
== Poisson problem
#definition(name: "Laplacian")[$ Delta = nabla dot.c nabla = diff^2/(diff^2 x) + diff^2/(diff^2 y) = (dot.c)_(x x) + (dot.c)_(y y) $]
Let $Omega subset RR^2$ be an open subset.
#definition[
$ #lebs &= { v: Omega -> RR | norm(v)_#lebs < oo } \
H^1(Omega) &= {v in #lebs | v_x, v_y in #lebs} \
H_0^1(Omega) &= {v in H^1(Omega) | v = 0 "on" diff Omega} $
]
#problem(name: "Poisson problem, strong form")[
Given $f in lebs$, find $u in H_0^1(Omega)$ such that $ -Delta u = f $
]
#problem(name: "Poisson problem, weak form")[
Given $f in lebs$, find $u in H_0^1(Omega)$ such that for all $v in H_0^1(Omega)$, $ integral_Omega nabla u dot.c nabla v dif x = integral_Omega f v dif x $
]
== Galerkin FEM method for triangulations
#definition[
A _2-D mesh_ for $Omega$ is a triangulation of $Omega$.
]
#definition(name: [2-D hat basis functions])[
$ phi_j(bold(x)) = cases(
1 quad bold(x) = bold(x)_j,
0 quad bold(x) = bold(x)_i "where" i != j,
"linearly interpolated elsewhere"
) $
]
#method(name: [Galerkin FEM])[
Define $U_h = V_h = "span"{phi_j}_(j=1)^N$. Then
$ V_h = {w_h: Omega -> RR | w_h "is continuous", w_h = 0 "on" diff Omega, lr(w_h |) _T in PP^1(T) quad forall T "in mesh"} $
where $lr(w_h |) _T in PP^1(T)$ is equivalent to $w_h(x, y) = c_0 + c_1 x + c_2 y$ for $(x, y) in T$. In other words, $V_h$ the set of continuous piecewise-linear functions defined on $Omega$ that vanish on $diff Omega$.
Now, find $u_h in V_h$ such that for all $v_h in V_h$,
$ integral_Omega nabla u_h dot.c nabla v_h dif x = integral_Omega f v_h dif x $
$u_h = sum_(j=1)^N u_j phi_j$ where $u_j$ are coeffients. Pick $v_h = phi_i$ for all $i = 1, dots, N$ to obtain $A bold(u) = bold(b)$, where
$ A_(i j) = integral_Omega nabla phi_j dot.c nabla phi_i dif x quad "and" quad b_i = integral_Omega f phi_i dif x $
]
#example[
$ u_t - u_(x x) = f $ for all $(t, x) in (0, T) times Omega$, where $Omega = (0, 1)$.
- Initial condition: $u(0, x) = u_0(x)$ for all $x in Omega$.
- Boundary condition: $u(t, 0) = u(t, 1) = 0$ for all $t in (0, T)$.
]
#proof[
Write the weak form:
$ integral_Omega u_t v dif x + integral_Omega u_x v_x dif x = integral_Omega f v dif x $ for all $v$ such that $v(t, 0) = v(t, 1) = 0$. Also $ u_h(t, x) = sum_(j=1)^(N-1) u_j(t) phi_j(x) $
Take $v = phi_i$ for all $i = 1, dots, N-1$, we have
$ M bold(dot(u))(t) + K bold(u)(t) = bold(b)(t) $
where
$ M_(i j) = integral_Omega phi_j phi_i dif x$, $K_(i j) = into phi_j' phi_i' dx $, and $b_i(t) = into f(t, x) phi_i(x) dx$.
]
#pagebreak()
= Linear Systems: Advanced Methods I
== Vector norms and matrix norms
#definition[
A _vector norm_ on $RR^n$ is a function $RR^ n -> RR$ with:
- $norm(bold(x)) >= 0$,
- $norm(bold(x)) = 0$ if and only if $bold(x) = bold(0)$,
- $norm(alpha x) = |alpha| norm(bold(x))$,
- $norm(bold(x) + bold(y)) <= norm(bd(x)) + norm(bd(y))$.
]
#definition[
A _matrix norm_ on $RR^(n times n)$ is a function $RR^(n times n) -> RR$ with:
- $norm(A) >= 0$,
- $norm(A) = 0$ if and only if $A = O$,
- $norm(alpha A) = |alpha| norm(A)$,
- $norm(A+B) <= norm(A) + norm(B)$,
- $norm(A B) <= norm(A) norm(B)$.
]
#definition[
The _induced/subordinate/natural_ matrix norm for a given vector norm is defined as
$ norm(A)
=max_(bd(x) != bd(0)) (norm(A bd(x)))/ (norm(bd(x)))
=max_(norm(bd(x)) = 1) norm(A bd(x)) $
]
#example[ Let
$ A = mat(1, 1/3; 1/3, 1) $
We now compute $norm(A)_2$. Take $bd(x) = vec(a, b) != bd(0)$, then
$ A bd(x) = vec(a + b/3, a/3 + b)$. Then
$ (norm(A bd(x))_2 / norm(bd x)_2) ^2 = (10/9 (a² + b²) + 4/3 a b) / (a² + b²) = 10/9 + 2/3 (2a b) / (a² + b²) <= 10/9 + 2/3 = 16 / 9 $
The maximum is obtained when $a = b$. Thus
$ norm(A)_2 = 4/3 $
Although in practice, we use a later theorem to find $norm(A)_2 = sqrt(rho(A^t A))$.
]
#theorem[ For a vector norm and its induced matrix norm,
$ norm(A bd(x)) <= norm(A) norm(bd(x)) $ <matrix-norm>
]
#proof[
This follows directly from the definition of induced matrix norm.
]
#definition[
For a non-singular square matrix $A$,
$ kappa(A)=norm(A) norm(A^(-1)) $ is the _condition number_ of $A$.
]
#lemma[
For a symmetric matrix $A in RR^(n times n)$, the eigenvalues are real and we can choose a set of orthonormal eigenvectors that span $RR^n$. <symmetric-eigen>
]
#definition[
A matrix $B in RR^(n times n)$ is _positive definite_ if $bd(x)^t B bd(x) > 0$ for any $bd(x) != bd(0)$.
]
#lemma[
The eigenvalues of a positive definite matrix are positive. <pd-eigenvalue>
]
#definition[
For a square matrix $A$,
$rho(A) = max_k | lambda_k |$ where $lambda_k$ are eigenvalues of $A$.
]
#theorem[For a non-singular square matrix $A$,
$
norm(A)_2 = sqrt( rho (A^t A))
$
]
#proof[
$A^t A$ is clearly symmetric. $A^t A$ is also positive definite because for any $bd(x) != bd(0)$, $bd(x)^t (A^t A) bd(x) = norm(A bd(x))^2_2 > 0$ since $A$ is non-singular. By #thmref(<pd-eigenvalue>)[Lemma], the eigenvalues $mu_j$ of $A^t A$ are positive. By #thmref(<symmetric-eigen>)[Lemma], we can choose a set of orthonormal eigenvectors $bd(w)_j$ that span $RR ^ n$. Namely, for all $j, k = 1 , dots , N$,
$ A^t A bd(w)_j &= mu_j bd(w)_j \
bd(w)_j dot.c bd(w)_k &= delta_(j k) $ and for all $bd(x) in RR^n$, there exist $x_1, dots, x_n$ such that $bd(x) = sum_(j=1)^n x_j bd(w)_j$.
Then $ norm(A)_2^2 &= max_(norm(bd(x)) = 1) bd(x)^t A^t A bd(x) \
&= max_(norm(bd(x)) = 1) (sum_(i=1)^n x_i bd(w)^t_i) A^t A (sum_(j=1)^n x_j bd(w)_j) \
&= max_(norm(bd(x)) = 1) (sum_(i=1)^n x_i bd(w)^t_i)(sum_(j=1)^n x_j mu_j bd(w)_j) \
&= max_(norm(bd(x)) = 1) sum_(i=1)^n sum_(j=1)^n x_i x_j mu_j bd(w)^t_i bd(w)_j \
&= max_(norm(bd(x)) = 1) sum_(i=1)^n x_i^2 mu_i \
&<= max_(norm(bd(x)) = 1) sum_(i=1)^n x_i^2 max_j |mu_j| \
&= max_j |mu_j|
$
If $k = "argmax"_j|mu_j|$, then the maximum is obtained when $x_i = delta_(i, k)$. This proves the result.
]
== Error estimates
Given $A in RR ^ (n times n), bold(b) in RR^n$. Assume there exists $bold(x) in RR^n$ such that $A bold(x) = bold(b)$. Given $hat(bold(x))$, an approximation to $bold(x)$, estimate the upper bound for the error $norm(bold(x) - bold(hat(x)))$. The main idea is to use $bold(hat(r)) = bold(b) - A bold(hat(x))$ and $norm(bold(hat(r)))$.
// Let $A, bd(b), bd(x), bd(hat(x))$ be such that $A bd(x) = bd(b)$ and $bold(hat(r)) = bold(b) - A bold(hat(x))$.
#theorem(name: "Absolute error estimate")[
$ norm(bd(x) - bd(hat(x))) <= norm(A^(-1)) norm(hat(bd(r))) $ <error-1>
]
#proof[
$
norm(bd(x) - bd(hat(x)))
&= norm(A^(-1)bd(b) - bd(hat(x))) \
&= norm(A^(-1)(bd(b) - A bd(hat(x)))) \
&= norm(A^(-1) hat(bd(r))) \
&<= norm(A^(-1)) norm(hat(bd(r)))
$
The last inequality is due to #thmref(<matrix-norm>)[Theorem].
]
#theorem(name: "Relative error estimate")[
For any $bd(x) != bd(0)$,
$ norm(bd(x) - bd(hat(x))) / norm(bd(x)) <= kappa(A) norm(bd(hat(r))) / norm(bd(b)) $
<error-2>
]
#proof[
By #thmref(<matrix-norm>)[Theorem],
$
norm(bd(b)) = norm(A bd(x)) <= norm(A) norm(bd(x))
$
Thus for $bd(x) != bd(0)$,
$
1 / norm(bd(x)) <= norm(A) / norm(bd(b))
$
Then by #thmref(<error-1>)[Theorem],
$
norm(bd(x) - bd(hat(x))) / norm(bd(x)) <=norm(A) norm(A^(-1)) norm(bd(hat(r))) / norm(bd(b)) = kappa(A) norm(bd(hat(r))) / norm(bd(b))
$
]
#theorem(name: "Perturbation Theorem")[
Let $A bd(x) = bd(b)$ and $(A + delta A) hat(bd(x)) = bd(b) + delta bd(b)$, where $delta A$ and $delta bd(b)$ are perturbations. Assume $norm(delta A) < 1/norm(A^(-1))$. Then
$ norm(bd(x) - hat(bd(x))) / norm(bd(x)) <= kappa(A) / (1 - kappa(A) norm(delta A) / norm(A)) (norm(delta bd(b)) / norm(bd(b)) + norm(delta A) / norm(A) ) $
]
#proof[
From $A bd(x) = bd(b)$ and $(A + delta A) hat(bd(x)) = bd(b) + delta bd(b)$ we can deduce that
$
A(bd(x) - bd(hat(x))) = - delta bd(b) + delta A bd(hat(x)) = - delta bd(b) + delta A bd(x) - delta A (bd(x) - bd(hat(x)))
$
Thus $bd(x) - bd(hat(x)) = A^(-1)(- delta bd(b) + delta A bd(x) - delta A (bd(x) - bd(hat(x))))$ and by triangle inequality and #thmref(<matrix-norm>)[Theorem],
$
norm(bd(x) - bd(hat(x))) <= norm(A^(-1)) (norm(delta bd(b)) + norm(delta A) norm(bd(x)) + norm(delta A) norm(bd(x) - bd(hat(x))))
$
From $1/norm(bd(x)) <= norm(A) / norm(bd(b))$ and $kappa(A) = norm(A) norm(A^(-1)) $ we deduce that
$
norm(bd(x) - hat(bd(x))) / norm(bd(x)) <= kappa(A) (norm(delta bd(b)) / norm(bd(b)) + norm(delta A) / norm(A) + norm(delta A) / norm(A) norm(bd(x) - hat(bd(x))) / norm(bd(x)))
$
Thus
$
(1 - kappa(A) norm(delta A) / norm(A)) norm(bd(x) - hat(bd(x))) / norm(bd(x)) &<= kappa(A) (norm(delta bd(b)) / norm(bd(b)) + norm(delta A) / norm(A)) $
When $norm(delta A) < 1/norm(A^(-1))$, we have that $1 - kappa(A) norm(delta A) / norm(A) > 0$ and thus
$
norm(bd(x) - hat(bd(x))) / norm(bd(x)) &<= kappa(A) / (1 - kappa(A) norm(delta A) / norm(A)) (norm(delta bd(b)) / norm(bd(b)) + norm(delta A) / norm(A))
$
]
#pagebreak()
= Linear Systems: Advanced Methods II
#definition[
$Q in RR^(n times n)$ is said to be an _orthognal_ or _orthonormal_ matrix when $Q^t Q = I$.
]
#theorem(name: "QR factorisation")[
Let $A in RR^(n times n)$. Then there exist an orthognal matrix $Q in RR^(n times n)$ and an upper triangular matrix $R in RR^(n times n)$ such that $A = Q R$.
]
#corollary[
If $A bd(x) = bd(b)$, then $R bd(x) = Q^t bd(b)$.
]
We can easily solve $R bd(x) = Q^t bd(b)$ using backwards substitution.
#example(name: "Over-determined systems")[
Consider $A bd(x) = bd(b)$, where $A in RR^(m times n), bd(x) = RR^n, bd(b) in RR^m$ and $m > n$. Then there is generally no solution to $bd(x)$. We would then like to find the least-squares solution, which is to find $bd(x) = RR^n$ that minimises $1/2 norm(bd(b) - A bd(x))^2_2$. Differentiating using matrix calculus gives $ A^t A bd(x) = A^t bd(b) $
It is not advisable to compute $B = A^t A$ and then use Gaussian elimination on $B bd(x) = A^t bd(b)$. Instead, factorise $A$ as $A = Q R$ and $ (R^t Q^t) (Q R) bd(x) = (R^t Q^t) bd(b) $
Since $Q^t Q = I$, pre-multiplying $R^(-t)$ gives
$ R bd(x) = Q^t bd(b) $
Thus we see that QR factorisation solves the least-squares problem.
]
#definition[
The _projection operator_ defined on an inner product space is $ "proj"_(bd(u))(bd(v)) = (angle.l bd(v), bd(u) angle.r)/(angle.l bd(u), bd(u) angle.r) bd(u) $
This operator projects $bd(v)$ orthogonally onto the line spanned by vector $bd(u)$. Specially, when $norm(bd(u)) = 1$, $ "proj"_(bd(u))(bd(v)) = angle.l bd(v), bd(u) angle.r bd(u) $
]
To QR factorise any given matrix $A$, we apply the Gram-Schmidt algorithm.
#method(name: "Gram-Schmidt algorithm")[
Let $bd(a)_1, dots, bd(a)_n$ be the $n$ columns of a given matrix $A$. Define $r_(1, 1) = norm(bd(a)_1)$, $bd(q)_1 = bd(a)_1 \/r_(1, 1)$, and for all $1 <= i < j <= n$, define
$
r_(i, j) &= angle.l bd(a)_j, bd(q)_i angle.r \
bd(v)_j &= bd(a)_j - sum_(i=1)^(j-1) "proj"_(bd(q)_i) bd(a)_j = bd(a)_j - sum_(i=1)^(j-1) r_(i, j) bd(q)_i \
bd(q)_j &= bd(v)_j / r_(j, j) quad "with" quad r_(j, j) = norm(bd(v)_j)
$
Then $Q$ defined by its $n$ columns $bd(q)_j$ and $R$ defined by its entries $r_(i, j)$ satisfy $A= Q R$.
]
The classical implementation given below is not stable.
#algo(title: "Classical Gram-Schmidt algorithm")[
for $j <- 1$ to $n$ #i\
$bd(v)_j <- bd(a)_j$ \
for $i <- 1$ to $j - 1$ #i\
$r_(i, j) <- bd(q)_i^t bd(a)_j$ \
$bd(v)_j <- bd(v)_j - r_(i, j) bd(q)_i$ #d\
end\
$r_(j, j) <- norm(bd(v)_j)_2$\
$bd(q)_j <- bd(v)_j / r_(j, j)$ #d\
end\
]
To find an orthognal (instead of orthonormal) basis $bd(q)_1, dots, bd(q)_n$ for $"span"{bd(a)_1, dots, bd(a)_n}$ (such that for all $i != j$, $angle.l bd(q)_i, bd(q)_j angle.r = 0$), the following simplified process can be used.
#method(name: "Gram-Schmidt algorithm")[
Let $bd(a)_1, dots, bd(a)_n$ be the $n$ columns of a given matrix $A$. Define $bd(q)_1 = bd(a)_1 $, and for all $2 <= j <= n$, define
$
bd(q)_j &= bd(a)_j - sum_(i=1)^(j-1) "proj"_(bd(q)_i) bd(a)_j
$
<gs-simp>
]
#pagebreak()
= Linear Systems: Advanced Methods III
#problem[
Given $A in RR^(n times n)$ and $bd(b) in RR^n$, solve for $bd(x)$ in $A bd(x) = bd(b)$, where $A$ is symmetric positive definite (SPD for short).
]
== Stationary iterative methods
#method(name: "Stationary iterative methods")[
Iterate from an initial guess $bd(x)_0$ using
$ bd(x)_(k+1) = T bd(x)_k + bd(c) $ for some $T$ and $bd(c)$ such that $rho(T) < 1$ and $bd(x)_k -> bd(x)$ as $k -> oo$. Note that $T$ is fixed here for all $k$ (hence the name).
]
Now write $A = D - L - U$ where $D$ is a diagnoal matrix, $L$ is lower triangular and $U$ is upper triangular.
#method(name: "Jacobi method")[
The Jacobi method is a stationary iterative method with
$ T &= D^(-1) (L+U) \ bd(c) &= D^(-1) bd(b) $
]
#method(name: "Gauss-Seidel method")[
The Gauss-Seidel method is stationary iterative method with $ T&=(D-L)^(-1) U \ bd(c) &= (D - L)^(-1) bd(b) $
]
== Non-stationary methods: Steepest-descent method
#method(name: "Steepest-descent method")[Iterate from an initial guess $bd(x)_0$ using
$ bd(x)_(k+1) = bd(x)_k + alpha_k bd(r)_k $
where $bd(r)_k = bd(b) - A bd(x)_k$ and $ alpha_k = (bd(r)^t_k bd(r)_k) / (bd(r)^t_k A bd(r)_k) $
]
#theorem[
Every two consecutive steps in the steepest-descent method are orthognal, i.e. $bd(r)_k dot.c bd(r)_(k+1) = 0$.
]
#proof[
$ bd(r)_k dot.c bd(r)_(k+1) &= bd(r)_k^t (bd(b) - A bd(x)_(k+1)) \
&= bd(r)_k^t (bd(b) - A (bd(x)_k + alpha_k bd(r)_k)) \
&= bd(r)_k^t (bd(r)_k - alpha_k A bd(r)_k) \
&= bd(r)_k^r bd(r)_k - alpha_k bd(r)_k^t A bd(r)_k \
&= 0
$
]
== Non-stationary methods: The conjugate gradient method
#theorem[
Let $A$ be a symmetric positive definite matrix. Then $ angle.l bd(u), bd(v) angle.r_A = bd(u)^t A bd(v) $ defines an inner product. <matrix-ip>
]
#definition(name: [$A$-norm])[ The _$A$-norm_ is the induced norm of the inner product defined in #thmref(<matrix-ip>)[Theorem]:
$ norm(bd(x))_A = sqrt(bd(x)^t A bd(x)) $
]
#definition(name: "Conjugate directions")[
Two vectors $bd(u)$ and $bd(v)$ are _conjugate_ if and only if they are orthogonal with respect to the inner product defined in #thmref(<matrix-ip>)[Theorem], i.e. $ angle.l bd(u), bd(v) angle.r_A = bd(u)^t A bd(v) = 0 $
]
#method(name: "Conjugate gradient method")[Iterate from an initial guess $bd(x)_0$ with $ bd(x)_(k+1) = bd(x)_k + alpha_k bd(p)_k $ where we define $bd(p)_0 &= bd(r)_0 = bd(b) - A bd(x)_0$ and $
alpha_j &= (bd(p)_j^t bd(r)_0) / (bd(p)_j^t A bd(p)_j) \
bd(r)_k &= bd(b) - A bd(x)_k \
bd(p)_k &= bd(r)_k - sum_(i=0)^(k-1) c_(k i) bd(p)_i quad "with" quad
c_(k i) = (bd(p)_i^t A bd(r)_k) / (bd(p)_i^t A bd(p)_i ) \
$
]
#theorem[
In the conjugate gradient method, ${bd(p)_i}$ are conjugate directions, i.e. for all $i != j$, $ bd(p)_j^t A bd(p)_i = 0 $ <cg-conjugate>
]
#proof[
For any given $k$,
${bd(p)_0, dots, bd(p)_k}$ are obtained exactly by applying #thmref(<gs-simp>)[Method] to ${bd(r)_0, dots, bd(r)_k}$ with respect to the inner product defined in #thmref(<matrix-ip>)[Theorem].
]
#theorem[In the conjugate gradient method, for all $0 <= j <= k - 1$,
$ bd(p)_j dot.c bd(r)_k = bd(p)_j^t (bd(b) - A bd(x)_k) = 0 $
]
#proof[ From the recursive relation we obtain
$ bd(x)_k = bd(x)_0 + sum_(i=1)^(k-1) alpha_i bd(p)_i $
Thus
$
bd(p)_j dot.c bd(r)_k = bd(p)_j^t (bd(b) - A bd(x)_k) &= bd(p)_j^t (bd(b) - A (bd(x)_0 + sum_(i=1)^(k-1) alpha_i bd(p)_i ) ) \
&= bd(p)_j^t (bd(r)_0 - sum_(i=1)^(k-1) alpha_i A bd(p)_i ) \
&= bd(p)_j^t bd(r)_0 - sum_(i=1)^(k-1) alpha_i bd(p)_j^t A bd(p)_i \
&= bd(p)_j^t bd(r)_0 - alpha_j bd(p)_j^t A bd(p)_j \
&= 0
$
where $ sum_(i=1)^(k-1) bd(p)_j^t A bd(p)_i = bd(p)_j^t A bd(p)_j$ due to #thmref(<cg-conjugate>)[Theorem].
]
// Let $ bd(x)_k = bd(x)_0 + sum_(i=0)^(k-1) alpha_i bd(p)_i $ with ${bd(p)_i}$ are conjugate directions $ bd(p)_j^t A bd(p)_i = 0 $ for any $i != j$. Equivalently, $ bd(x)_(k+1) = bd(x)_k + alpha_k bd(p)_k $
// Denote $bd(r)_k = b - A bd(x)_k$. Then we want $ bd(p)_j dot.c bd(r)_k = bd(p)_j^t (bd(b) - A bd(x)_k) = 0 $ for all $j = 0, dots, k - 1$. Then $ alpha_j = (bd(p)_j^t bd(r)_0) / (bd(p)_j^t A bd(p)_j) $
// Compute conjugate directions: $A$-orthogonal Gram-Schmidt:
// $ bd(p)_k = bd(r)_k - sum_(i=0)^(k-1) c_(k i) bd(p)_i $
// where $ c_(k i) = (bd(p)_i^t A bd(r)_k) / (bd(p)_i^t A bd(p)_i ) $ are obtained from the constraint of conjugate directions.
// === Minimisation of $A$-norm of the error
== Error analysis of the conjugate gradient method
#definition(name: ["Krylov" subspace])[
$ cal(K)_k = "span"{bd(p)_0, dots, bd(p)_(k-1)} = "span"{bd(r)_0, dots, bd(r)_(k-1)} $
]
#theorem[
Let $bd(x)_k$ be given by the conjugate gradient method applied to $A bd(x) =bd(b)$ with $bd(x)_0 = bd(0)$. Assume at the $k$-th step the method is not yet converged, namely $bd(r)_(k-1) != bd(0)$, then $bd(x)_k$ is the unique minimiser of $bd(y) |-> norm(bd(x) - bd(y)) _ A$ in $cal(K)_k$ .
]
#proof[
Consider an arbitrary $bd(y) in cal(K)_k$. We would like to show that $norm(bd(x) -bd(y))_A >= norm(bd(x) - bd(x)_k)_A$. Let $bd(e) = bd(x) - bd(y)$ and $bd(e)_k = bd(x) - bd(x)_k$. Then $A bd(e)_k = A(bd(x) - bd(x)_k) = bd(b)-A bd(x)_k = bd(r)_k$.
Further let $bd(delta x) = bd(x)_k - bd(y) $. Note that $bd(delta x) in cal(K)_k$ is a linear combination of $bd(p)_0, dots, bd(p)_(k-1)$ and $bd(r)_k^t bd(p)_j = 0$ for all $j = 0, dots, k - 1$. Thus $bd(delta x)^t bd(r)_k = 0$.
From $bd(e) = bd(e)_k + bd(delta x)$ we deduce
$ norm(bd(e))_A^2 &= (bd(e)_k + bd(delta x))^t A (bd(e)_k + bd(delta x)) \
&= bd(e)_k^t A bd(e)_k + bd(delta x)^t A bd(e)_k + bd(e)_k^t A bd(delta x) + bd(delta x)^t A bd(delta x) \
&= bd(e)_k^t A bd(e)_k + 2 bd(delta x)^t A bd(e)_k + bd(delta x)^t A bd(delta x) \
&= bd(e)_k^t A bd(e)_k + 2 bd(delta x)^t bd(r)_k + bd(delta x)^t A bd(delta x) \
&= bd(e)_k^t A bd(e)_k + bd(delta x)^t A bd(delta x)
$
which is minimised exactly when $bd(delta x) = bd(0)$ since $A$ is positive definite.
]
#theorem[
Assume $bd(r)_k != 0$, then $bd(p)_k != 0$.
]
#proof[ From how we calculate $bd(p)_k$,
$ bd(p)_k^t bd(r)_k = bd(r)_k^t bd(r)_k - sum_(i=0)^(k-1) c_(k i) bd(p)_i^t bd(r)_k = bd(r)_k^t bd(r)_k >0 $
The result thus follows.
]
#corollary[
The conjugate gradient method converges in at most $n$ steps.
]
#proof[
$dim cal(K)_n = n$ and therefore $cal(K)_n = RR^n$. Thus $bd(x)_n = bd(x)$.
]
#theorem[
When $n$ is large,
$ (norm(bd(e)_k)_A) / (norm(bd(e)_0)_A) <= 2 ((sqrt(kappa) - 1) / (sqrt(kappa) + 1))^k -> abs(1 - 2 / sqrt(kappa)) $ as $k -> oo$, where $kappa = kappa(A)$ is the conditional nubmer of $A$.
]
#pagebreak()
= Low-Rank Approximation I
== The power method and Rayleigh quotient
#problem[
Given $A in RR^(m times m)$ and $A = A^t$. Find its dominant eigenvalue-eigenvector pair $bd(v), lambda$, where $ A bd(v) = lambda bd(v) $ for the largest $abs(lambda)$.
]
#method(name: [Power method])[
Given $bd(v)^((0))$ where $norm(bd(v)^((0))) = 1$. For $k = 1, 2, dots$, let $ bd(w) &= A bd(v)^((k-1)) \ bd(v)^((k)) &= (bd(w))/ (norm(bd(w))) \ lambda^((k)) &= (bd(v)^((k)))^t A bd(v)^((k)) $
]
#theorem[In the power method,
$ bd(v)^((k)) -> plus.minus bd(q)_1 quad "and" quad lambda^((k)) -> lambda_1 quad "as " k -> oo $
]
#proof[
$A$ is real symmetric, so all eigenvalues of $A$ are real and $A$ has a set of orthonormal eigenvectors which span $RR^(m)$ by #thmref(<symmetric-eigen>)[Lemma].
For the eigenvalues of $A$, suppose $|lambda_1| > |lambda_2| >= dots >= |lambda_m| >= 0 $ and let $
bd(v)^((0)) = sum_(i=1)^m a_i bd(q)_i
$
Then by the recursive relation, $
bd(v)^((k)) &= c_k A^k bd(v)^((0)) \
&= c_k ( sum_(i=1)^m a_i A^k bd(q)_i) \
&= c_k ( sum_(i=1)^m a_i lambda_i^k bd(q)_i) \
&= c_k lambda_1^k (a_1 bd(q)_1 + sum_(i=2)^m a_i (lambda_i / lambda_1)^k bd(q)_i)
$
where $c_k$ are normalising coefficients.
Since $|lambda_i| < |lambda_1|$, for all $i = 2, dots, m$, $ (lambda_i / lambda_1)^k -> 0 $ Thus $ bd(v)^((k)) -> c_k lambda_1^k a_1 bd(q)_1 $ But $norm(bd(v)^((k))) = norm(bd(q)_1) = 1$ thanks to the normalising effect of $c_k$, thus
$bd(v)^((k)) -> plus.minus bd(q)_1 $. Then $ lambda^((k)) = (bd(v)^((k)))^t A bd(v)^((k)) -> bd(q)_1^t A bd(q)_1 = lambda_1 bd(q)_1^t bd(q)_1 = lambda_1 $
]
// #example[
// Power Rank: the dominant eigenvalue is $1$.
// ]
== The power method: Convergence analysis
#definition(name: "Rayleigh Quotient")[
Define Rayleigh quotient of vector $bd(x)$ as $ r(bd(x)) = (bd(x)^t A bd(x)) / (bd(x)^t bd(x)) $
]
#lemma[
$ nabla r = vec(diff/(diff x_1), dots, diff / (diff x_m)) r(bd(x)) = 2 / (bd(x)^t bd(x)) (A bd(x) - r(bd(x)) bd(x)) $
]
#lemma[
$ r(bd(y)) = r(bd(x)) + nabla r dot.c (bd(y) - bd(x)) + O(norm(bd(y)-bd(x))^2) $
]
#theorem[
Suppose $|lambda_1| > |lambda_2| >= dots >= |lambda_m| >= 0 $ and $bd(q)_1^t bd(v)^((0)) != 0$. Then the power method converges and $
norm(bd(v)^((k)) - (plus.minus bd(q)_1)) &= O(abs((lambda_2) / (lambda_1))^k) \
|lambda^((k)) - lambda_1| &= O(abs((lambda_2) / (lambda_1))^(2k))
$
as $k -> oo$. They both convergence linearly.
]
#proof[
$ norm(bd(v)^((k)) - c_k lambda_1^k a_1 bd(q)_1) = norm(c_k lambda_1^k sum_(i=2)^m a_i (lambda_i / lambda_1)^k) -> O(abs((lambda_2) / (lambda_1))^k) $
as $k -> oo$.
By definition,
$r(bd(q)_1) = lambda_1 $ and $r(bd(v)^((k))) = lambda^((k))$. Thus
$
lambda^((k)) - lambda_1 = r(bd(v)^((k))) - r(bd(q)_1) = nabla r (bd(q)_1)(bd(v)^((k)) - bd(q)_1) + O(norm(bd(v)^((k)) - bd(q)_1)^2)
$
But $nabla r (bd(q)_1) = 0$. Thus
$ |lambda^((k)) - lambda_1| &= O(abs((lambda_2) / (lambda_1))^(2k)) $
]
== Inverse iteration
Let $lambda$ and $bd(v)$ be a pair of eigenvalue and eigenvector of matrix $A$, then $ A bd(v) = lambda bd(v) $ Then since $ lambda^(-1) bd(v) = A^(-1) bd(v) $ we see that $lambda^(-1)$ is an eigenvalue of $A^(-1)$ for the same eigenvector $bd(v)$. To find the eigenvalue with the smallest absolute value of $A$, we only need to find the one with the largest absolute value for $A^(-1)$. In general, since for $mu != lambda$,
$ (A - mu I) bd(v) &= (lambda - mu) bd(v) \
1/(lambda - mu) bd(v) &= (A - mu I)^(-1) bd(v)
$ we have the following.
#method(name: "Inverse iteration")[Suppose $mu$ is not an eigenvalue of $A$. To find the eigenvalue $lambda$ of $A$ which is the closest to $mu$, we only need to find the largest-magnitude eigenvalue $lambda'$ of $B = (A - mu I)^(-1)$ and $ lambda = mu + 1 / (lambda') $
In practice, we solve a linear system at each step instead of actually computing the inverse matrix of $A - mu I$.]
#theorem[
Suppose $lambda_J$ and $lambda_K$ are the closest and second closest eigenvalue of $A$ to $mu$ and $bd(q)_J^t bd(v)^((0)) != 0$. Then the inverse iteration method converges, with
$ norm(bd(v)^((0)) - bd(q)_J^t) &= O(abs( (mu - lambda_J) / (mu - lambda_K) )^k) \
abs(lambda^((k)) - lambda_J) &= O(abs( (mu - lambda_J) / (mu - lambda_K) )^(2k))
$
]
== Simultaneous iteration
#method(name: "Simultaneous iteration, unnormalised version")[
Suppose $A in RR^(m times m)$, where $m >= n$. Take $ V^((0)) = mat( bd(v)_1^((0)), dots, bd(v)_n^((0)); ) $ where $bd(v)_i in RR^m$. For $k = 1, 2, dots$, $ V^((k)) = A V^((k-1)) = mat(A bd(v)_1^((k-1)), dots, A bd(v)_n^((k-1)) ; ) $
With QR factorisation of $V^((k))$, we expect that $Q^((k)) -> mat(bd(q)_1, dots, bd(q)_n; )$ where $ Q^((k)) R^((k)) = V^((k)) $ and $ Q^((k)) in RR^(m times n)$.
]
#method(name: "Simultaneous iteration, normalised version")[
Pick $Q^((0)) in RR^(m times n)$ with orthonormal columns. For $k = 1, 2, dots$,
$ Z&= A Q^((k-1)) \ Q^((k)) R^((k)) &= Z $ which is the reduced QR factorisation of $Z$.
]
#theorem[
Suppose $|lambda_1| > |lambda_2| > dots > |lambda_n| > |lambda_(n+1)| >= dots >= |lambda_m|$ and all leading principal submatrices of $Q^T V^((0))$ are nonsingular with $Q=mat(bd(q)_1, dots, bd(q)_n; )$. Then
$ Q^((k)) -> Q $ linearly with $ norm(bd(q)_j^((k)) - (plus.minus bd(q)_j)) = O(alpha^k) $ where $alpha = max_(1<=k<=n) (lambda_(k+1)) / (lambda_k)$.
]
#pagebreak()
= Low-Rank Approximation II
== Single value decomposition
#theorem(name: "Matrix diagonalisation")[
Suppose $A in RR^(n times n)$ with $n$ linearly independent eigenvalues. Then $ A = X Lambda X^(-1) $ where each column $bd(x)_i$ of $X$ is an eigenvector of $A$ and $lambda_i$ is the corresponding eigenvalue.
]
#definition(name: "Orthogonal matrices")[
A matrix $Q in RR^(n times n)$ is _orthogonal_ if $ Q^t = Q^(-1) $
]
#theorem(name: "Spectral theorem")[
Suppose $A in RR^(n times n)$ is symmetric, then $ A = Q Lambda Q^t $ where $lambda_i in RR$ and $Q$ is an orthogonal matrix.
]
#definition[
The _column (row) space_ of a matrix is the vector space spanned by its columns (rows).
]
#definition[
The _rank_ of a matrix is the dimension of its column space (or equally, its row space).
]
We would like to decompose a matrix into two sets of vectors $bd(u)_i$ and $bd(v)_i$ satisfying
$ A bd(v)_i = sigma_i bd(u)_i $ where $bd(v)_i$ is the $i$-th right singular vector, $sigma_i$ is the $i$-th singular value, and $bd(u)_i$ is the $i$-th left singular vector. Further, $A^t A$ and $A A^t$ are symmetric matrices which satisfy
$ A^t A bd(u)_i &= sigma_i^2 bd(u)_i \
A A^t bd(v)_i &= sigma_i^2 bd(v)_i $
We then write $ A = U Sigma V^t $ where $bd(u)_i$ is the $i$-th column of $U$, $bd(v)_i$ is the $i$-th column of $V$, and $sigma_i$ is the $i$-th entry of the diagonal matrix $Sigma$. Equivalently, $ A = sum_(i=1)^r sigma_i bd(u)_i bd(v)_i^t $
where $r <= min{m, n}$ is the rank of $A$.
#definition(name: "Unitary matrices")[
A matrix $U in RR^(m times n)$ is _unitary_ if $ U^t U = I_(n times n) $
]
We see that unitary matrices are a generalisation of orthogonal matrices.
#definition(name: "Singluar value decomposition")[
Consider matrix $A in RR^(m times n)$ (not necessarily full rank). Then a _singular value decomposition_ of $A$ is
$ A = U Sigma V^t $
where
$U in RR^(m times n)$ is a unitary matrix, $Sigma in RR^(n times n)$ is a diagonal matrix
with non-negative entries, and $V in RR^(n times n)$ is an orthogonal matrix.
]
#theorem[
An SVD always exists with $sigma_i$ unique, which are called the _singular values_ of $A$ and are the non-negative square roots of the eigenvalues of $A^t A$.
If $A$ is square, then $bd(u)_i$ and $bd(v)_i$ are unique up to its sign.
]
If $A = U Sigma V^t$, then
$ A^t A = V Sigma^t Sigma V^t $
where $ Sigma^t Sigma = "diag"(sigma_1^2, dots, sigma_n^2) $This is the spectral theorem for $A^t A$.
Since $ A V &= U Sigma \ A^t U &= V Sigma $
we have that
$
underbrace(mat(O, A^t; A, O), H) underbrace(mat(V, V; U, -U), Q) = underbrace(mat(V, V; U, -U), Q) underbrace(mat(Sigma, O; O, -Sigma), Lambda)
$
Hence by computing the eigenvalues and eigenvectors of $H$ we can get the SVD of $A$.
== Low rank approximation
#definition(name: "Low rank approximation")[
Let $sigma_1 >= sigma_2 >= dots >= sigma_r >= 0$ be the singular values of $A$, then for $1 <= k <= r$, the _best rank-$k$ approximation_ of $A$ is
$ A_k = sum_(j=1)^k sigma_j bd(u)_j bd(v)_j^t $
]
#lemma[Let $sigma_1$ be the largest singular value of $A$, then
$ norm(A)_2 = sigma_1 $
<singular-norm>
]
#proof[
This directly follows from $ norm(A)_2 = sqrt(rho(A^t A))$ and how we compute $sigma_1$.
]
#theorem(name: "The Eckart-Young Theorem")[
$ norm(A-A_k) = min_(B in RR^(m times n), "rank" B <= k) norm(A - B) $
where $norm(dot)$ is either $ norm(A)_2 = max_(bd(x)) (norm(A bd(x))_2 / norm(bd(x))_2) $ or
the Frobenius norm $ norm(A)_F = sqrt(sum_(i=1)^m sum_(j=1)^n |a_(i j)|^2) $
Further, $ norm(A - A_k)_2 = sigma_(k+1) $ and $ norm(A - A_k)_F = sqrt(sum_(i=k+1)^n sigma_i^2) $
]
#proof[We only prove for the $2$-norm.
It is easy to see that $norm(A - A_k)_2 = sigma_(k+1)$ by #thmref(<singular-norm>)[Lemma].
Assume that there exists $B in RR^(m times n)$ with $"rank" B <= k$ such that $ norm(A-B)_2 < norm(A - A_k)_2 = sigma_(k+1) $
There exists $W_1 subset RR^n$ such that $dim W_1 = n - k$ and
$B bd(w)_1 = bd(0)$
for all $bd(w)_1 in W_1$, since $"rank" B <= k$.
Then
$
norm(A bd(w)_1)_2 = norm((A-B)bd(w)_1)_2 <= norm(A-B)_2 norm(bd(w)_1)_2 < sigma_(k+1) norm(bd(w)_1)_2
$
There exists $W_2 subset RR^n$ such that $W_2 = "span" {bd(v)_1, dots, bd(v)_(k+1)}$ and $dim W_2 = k + 1$. Then $ norm(A bd(w)_2)_2 >= sigma_(k+1) norm(bd(w)_2)_2 $
Then $dim (W_1 sect W_2) >= 1$ and for $w in W_1 sect W_2$ we have both $norm(A bd(w))_2 < sigma_(k+1) norm(bd(w))_2$ and $norm(A bd(w))_2 >= sigma_(k+1) norm(bd(w))_2$, which is a contradiction.
]
// #proof[
// Assume $m >= n$. Since $A^t A in RR^(n times n)$ is positive semi-definite, we can find a spectral decomposition of it:
// $ A^t A = V D V^t $
// Let $Sigma = sqrt(D)$ but of size $m times n$ (pad with zero rows). Then $
// (Sigma V^t)^t (Sigma V^t) = V Sigma^t Sigma V^t = V D V^t = A^t A
// $
// Then by the unitary freedom of PSD decompositions, there exists unitary $U$ such that $
// A = U Sigma V^t
// $
// ]
|
|
https://github.com/maxgraw/bachelor | https://raw.githubusercontent.com/maxgraw/bachelor/main/apps/document/src/0-base/2-abstract.typ | typst | #set align(start + horizon)
#set heading(numbering: none, supplement: [Abschnitt])
= Abstract
This thesis addresses the conception and development of an augmented reality construction environment for furniture systems based on WebXR. The primary goal is to validate the suitability of WebXR for the development of an augmented reality application and to investigate user experience and application possibilities in the furniture industry. Following an analysis of the current use of augmented reality in the furniture industry and the technical fundamentals of WebXR and augmented reality, a concept for the application was developed and implemented. The user experience was evaluated using the User Experience Questionnaire method in an online study, which yielded positive feedback for the application. However, the results must be critically examined due to observed high variance. Nevertheless, the application can be considered a functional basis for further studies and developments.
#pagebreak() |
|
https://github.com/RaphGL/ElectronicsFromBasics | https://raw.githubusercontent.com/RaphGL/ElectronicsFromBasics/main/DC/chap1/2_insulators_and_electron_flow.typ | typst | Other | #import "../../core/core.typ"
=== Conductors, insulators and electron flow
The electrons of different types of atoms have different degrees of freedom to move around. With some types of materials, such as metals, the outermost electrons in the atoms are so loosely bound that they chaotically move in the space between the atoms of that material by nothing more than the influence of room-temperature heat energy. Because these virtually unbound electrons are free to leave their respective atoms and float around in the space between adjacent atoms, they are often called _free electrons_.
In other types of materials such as glass, the atoms' electrons have very little freedom to move around. While external forces such as physical rubbing can force some of these electrons to leave their respective atoms and transfer to the atoms of another material, they do not move between atoms within that material very easily.
This relative mobility of electrons within a material is known as electric _conductivity_. Conductivity is determined by the types of atoms in a material (the number of protons in each atom's nucleus, determining its chemical identity) and how the atoms are linked together with one another. Materials with high electron mobility (many free electrons) are called _conductors_, while materials with low electron mobility (few or no free electrons) are called _insulators_.
Here are a few common examples of conductors and insulators:
#table(
columns: (auto, auto),
stroke: none,
align: left,
table.header(
[*Conductors*], [*Insulators*]
),
[silver], [glass],
[copper], [rubber],
[gold], [oil],
[aluminum], [asphalt],
[iron], [fiberglass],
[steel], [porcelain],
[brass], [ceramic],
[bronze], [quartz],
[mercury], [(dry) cotton],
[graphite], [(dry) paper],
[dirty water], [(dry) wood],
[concrete], [plastic],
[], [air],
[], [diamond],
[], [pure water],
)
It must be understood that not all conductive materials have the same level of conductivity, and not all insulators are equally resistant to electron motion. Electrical conductivity is analogous to the transparency of certain materials to light: materials that easily "conduct" light are called "transparent," while those that don't are called "opaque." However, not all transparent materials are equally conductive to light. Window glass is better than most plastics, and certainly better than "clear" fiberglass. So it is with electrical conductors, some being better than others.
For instance, silver is the best conductor in the "conductors" list, offering easier passage for electrons than any other material cited. Dirty water and concrete are also listed as conductors, but these materials are substantially less conductive than any metal.
Physical dimension also impacts conductivity. For instance, if we take two strips of the same conductive material -- one thin and the other thick -- the thick strip will prove to be a better conductor than the thin for the same length. If we take another pair of strips -- this time both with the same thickness but one shorter than the other -- the shorter one will offer easier passage to electrons than the long one. This is analogous to water flow in a pipe: a fat pipe offers easier passage than a skinny pipe, and a short pipe is easier for water to move through than a long pipe, all other dimensions being equal.
It should also be understood that some materials experience changes in their electrical properties under different conditions. Glass, for instance, is a very good insulator at room temperature, but becomes a conductor when heated to a very high temperature. Gases such as air, normally insulating materials, also become conductive if heated to very high temperatures. Most metals become poorer conductors when heated, and better conductors when cooled. Many conductive materials become perfectly conductive (this is called _superconductivity_) at extremely low temperatures.
While the normal motion of "free" electrons in a conductor is random, with no particular direction or speed, electrons can be influenced to move in a coordinated fashion through a conductive material. This uniform motion of electrons is what we call _electricity_, or _electric current_. To be more precise, it could be called _dynamic_ electricity in contrast to static electricity, which is an unmoving accumulation of electric charge. Just like water flowing through the emptiness of a pipe, electrons are able to move within the empty space within and between the atoms of a conductor. The conductor may appear to be solid to our eyes, but any material composed of atoms is mostly empty space! The liquid-flow analogy is so fitting that the motion of electrons through a conductor is often referred to as a "flow."
A noteworthy observation may be made here. As each electron moves uniformly through a conductor, it pushes on the one ahead of it, such that all the electrons move together as a group. The starting and stopping of electron flow through the length of a conductive path is virtually instantaneous from one end of a conductor to the other, even though the motion of each electron may be very slow. An approximate analogy is that of a tube filled end-to-end with marbles:
#image("static/marbles-in-tube.png")
The tube is full of marbles, just as a conductor is full of free electrons ready to be moved by an outside influence. If a single marble is suddenly inserted into this full tube on the left-hand side, another marble will immediately try to exit the tube on the right. Even though each marble only traveled a short distance, the transfer of motion through the tube is virtually instantaneous from the left end to the right end, no matter how long the tube is. With electricity, the overall effect from one end of a conductor to the other happens at the speed of light: a swift 186,000 miles per second!!! Each individual electron, though, travels through the conductor at a _much_ slower pace.
If we want electrons to flow in a certain direction to a certain place, we must provide the proper path for them to move, just as a plumber must install piping to get water to flow where he or she wants it to flow. To facilitate this, _wires_ are made of highly conductive metals such as copper or aluminum in a wide variety of sizes.
Remember that electrons can flow only when they have the opportunity to move in the space between the atoms of a material. This means that there can be electric current only where there exists a continuous path of conductive material providing a conduit for electrons to travel through. In the marble analogy, marbles can flow into the left-hand side of the tube (and, consequently, through the tube) if and only if the tube is open on the right-hand side for marbles to flow out. If the tube is blocked on the right-hand side, the marbles will just "pile up" inside the tube, and marble "flow" will not occur. The same holds true for electric current: the continuous flow of electrons requires there be an unbroken path to permit that flow. Let's look at a diagram to illustrate how this works:
#align(center)[
#linebreak()
#line(length: 30%)
]
A thin, solid line (as shown above) is the conventional symbol for a continuous piece of wire. Since the wire is made of a conductive material, such as copper, its constituent atoms have many free electrons which can easily move through the wire. However, there will never be a continuous or uniform flow of electrons within this wire unless they have a place to come from and a place to go. Let's add an hypothetical electron "Source" and "Destination:"
#image("static/electron-flow.png")
Now, with the Electron Source pushing new electrons into the wire on the left-hand side, electron flow through the wire can occur (as indicated by the arrows pointing from left to right). However, the flow will be interrupted if the conductive path formed by the wire is broken:
#image("static/broken-electron-flow.png")
Since air is an insulating material, and an air gap separates the two pieces of wire, the once-continuous path has now been broken, and electrons cannot flow from Source to Destination. This is like cutting a water pipe in two and capping off the broken ends of the pipe: water can't flow if there's no exit out of the pipe. In electrical terms, we had a condition of electrical _continuity_ when the wire was in one piece, and now that continuity is broken with the wire cut and separated.
If we were to take another piece of wire leading to the Destination and simply make physical contact with the wire leading to the Source, we would once again have a continuous path for electrons to flow. The two dots in the diagram indicate physical (metal-to-metal) contact between the wire pieces:
#image("static/broken-electron-flow-2.png")
Now, we have continuity from the Source, to the newly-made connection, down, to the right, and up to the Destination. This is analogous to putting a "tee" fitting in one of the capped-off pipes and directing water through a new segment of pipe to its destination. Please take note that the broken segment of wire on the right hand side has no electrons flowing through it, because it is no longer part of a complete path from Source to Destination.
It is interesting to note that no "wear" occurs within wires due to this electric current, unlike water-carrying pipes which are eventually corroded and worn by prolonged flows. Electrons do encounter some degree of friction as they move, however, and this friction can generate heat in a conductor. This is a topic we'll explore in much greater detail later.
#core.review[
- In conductive materials, the outer electrons in each atom can easily come or go, and are called free electrons.
- In insulating materials, the outer electrons are not so free to move.
- All metals are electrically conductive.
- Dynamic electricity, or electric current, is the uniform motion of electrons through a conductor.
- Static electricity is an unmoving (if on an insulator), accumulated charge formed by either an excess or deficiency of electrons in an object. It is typically formed by charge separation by contact and separation of dissimilar materials.
- For electrons to flow continuously (indefinitely) through a conductor, there must be a complete, unbroken path for them to move both into and out of that conductor.
]
|
https://github.com/Tran-Thu-Le/typst-collection | https://raw.githubusercontent.com/Tran-Thu-Le/typst-collection/main/state-in-typst/tool.typ | typst | #let __param = state("param", 0)
#let init(param: 0) = {
__param.update(param)
}
#let sentence = context{[The current value of parameter is #__param.get()]} |
|
https://github.com/Toniolo-Marco/git-for-dummies | https://raw.githubusercontent.com/Toniolo-Marco/git-for-dummies/main/slides/practice/checkout.typ | typst | #import "@preview/touying:0.5.2": *
#import themes.university: *
#import "@preview/numbly:0.1.0": numbly
#import "@preview/fletcher:0.5.1" as fletcher: node, edge
#let fletcher-diagram = touying-reducer.with(reduce: fletcher.diagram, cover: fletcher.hide)
#import "../components/gh-button.typ": gh_button
#import "../components/git-graph.typ": branch_indicator, commit_node, connect_nodes, branch
#grid(
columns: (3fr,2fr), column-gutter: 5%,
[
During the development of git, several features were developed and over time almost all of them have been added to the `git checkout` command.
Currently the git team, is working on separating these features into separate commands.
We will find different commands that serve the same purpose. We will try to cover both versions for completeness; however, it is advisable to use the newer commands.
To immediately give an example of this problem, let us look at the case where we want to see the current state we are in:
],
figure(
image("../img/graphical-representation-git-checkout.png"),
caption: [Graphical representation of the `git checkout` command]
)
) |
|
https://github.com/dyc3/senior-design | https://raw.githubusercontent.com/dyc3/senior-design/main/harness-design.typ | typst | = Test Harness Design
The test harness utilizes Rust's libtest to aggregate and run tests. For each test function, we add a setup and teardown step to spin up and tear down the Balancer (as provided by the `test-context` #cite(<crate-test-context>) crate), and then we run the test function. The test function is responsible for creating emulated Monoliths and Clients, and sending/receiving messages from the Balancer. The test function is also responsible for making assertions about what the Balancer should do.
This allows us to utilize Rust's testing framework and take advantage of the reporting and test discovery features it provides.
#figure(
image("figures/harness/harness-test-runner-topology.svg"),
caption: [The Topology of a `TestRunner` inside the Harness, and how it relates to the Balancer and the `Test` being executed.]
) <Figure::harness-test-runner-topology>
== Auth Tokens
Auth tokens must be present in all the places they would normally be, but they do not need to be verified in a testing environment. Therefore, all HTTP requests that would have auth tokens should have them, but they should be ignored by the Balancer, and emulated Monoliths.
== Emulated Monoliths
Emulated Monoliths are not actual Monoliths, they merely act like them. To that end, each emulated Monolith needs to listen on 2 ports each (one for normal http traffic, and one for the balancer websocket connections). This also means that there needs to be a service discoverer that the harness can use to convey the correct ports to the Balancer. (@Section::HarnessMonolithDiscovery)
== Emulated Clients
Emulated Clients are similar to emulated Monoliths, but they do not need to listen on any ports. They merely need to be able to connect to the Balancer, and send/receive messages. They should behave like a normal client, and they should optionally be able to keep track of the room state they are connected to.
== Conveying Emulated Monoliths to Balancer <Section::HarnessMonolithDiscovery>
When emulated Monoliths are created, they need to convey their existence to the Balancer. To that end, the `TestRunner` should also manage a `DiscoveryProvider` that connects to the Balancer and tells it about the emulated Monoliths that are running. For the harness to connect, the balancer first needs a port to listen on. Assuming the port binds correctly, the discoverer will listen until a harness connects, and then store references to all emulated Monoliths given by the discovery provider. To handle connecting to the Balancer, the harness uses the `DiscoveryProvider` mentioned earlier. The provider takes in a set of emulated Monoliths, and connects to the same port the discoverer is listening on.
|
|
https://github.com/liamrosenfeld/resume | https://raw.githubusercontent.com/liamrosenfeld/resume/main/resume.typ | typst | #import "template.typ": *
#show: resume.with(
name: "<NAME>",
contactInfo: (
link("mailto://<EMAIL>")[<EMAIL>],
link("https://liamr.dev")[liamr.dev],
"407-864-0452"
)
)
#let isDigital = true
== Skills
#skillsTable(
content: (
strong("Languages"),
"Swift, Rust, Objective-C, C++, C, Python, ARM & AVR Assembly, Typescript, SQL, VHDL",
strong("Frameworks"),
"SwiftUI, AppKit, UIKit, Accelerate, Axum, Vue, Svelte",
strong("Tools"),
"macOS, Linux, Git, Xcode Instruments, Docker, MongoDB, LaTeX"
)
)
== Education
*BS in Computer Engineering*, University of Florida
#h(1fr) Class of 2025 #linebreak()
GPA: 3.98, Minor in Mathematics, Honors Program
== Work History
#workItem(
role: "Software Engineering Intern",
company: "Apple",
when: "Summer 2023",
description: [
- On the Productivity Apps team responsible for canvas, editing, and core infrastructure
- Built a highly requested feature for Keynote, Pages, and Numbers on macOS, iOS, and Web
- Wrote a specification to define the behavior of the feature and its implementation
- Debugged a complex UI framework
]
)
#workItem(
role: "Backend Software Engineer",
company: "Parametic Capital",
when: "Summer 2022",
description: [
- Built a server to collect, aggregate, and serve time series metrics to a visualization frontend using Rust
]
)
== Research
#projectItem(
name: "Lilypad",
when: "2021-Present",
writeup: link("https://ieeexplore.ieee.org/document/10305659")[First Paper],
description: [
- Building a text-based visual code editor to improve programming education
- First author for showpiece paper in the 2023 IEEE Symposium on Visual Languages and Human-Centric Computing
- Building using Rust to run native and in Web Assembly
]
)
== Select Projects
#if not isDigital [
#v(weak: true, 4pt)
Writeups on my website
#v(weak: true, 8pt)
]
#projectItem(
name: "NaviGator",
when: "Released 2023",
writeup: "",
description: [
- Mobile app for the Gainesville RTS (bus system)
- Built in a team of two, my responsibility is the live map (built with MapKit) and data fetching
- Thousands of downloads with hundreds of daily active users
],
isDigital: isDigital
)
#projectItem(
name: "UF Cat Tracker",
when: "Built 2022",
writeup: "",
description: [
- Website so students can crowdsouce the location of friendly campus cats to pet
- Built in a team of four using Rust, React, and PostgreSQL for ease of development and stability
],
isDigital: isDigital
)
#projectItem(
name: "Iconology",
when: "Released 2020",
writeup: link("https://liamrosenfeld.com/projects/iconology")[Writeup],
description: [
- macOS app to stream-line the process of icon generation with 6.5k downloads
- Built using AppKit, CoreGraphics, and SwiftUI
],
isDigital: isDigital
)
#projectItem(
name: "Raspberry Pi OS",
when: "Built 2022",
writeup: link("https://liamrosenfeld.com/projects/rustos/")[Writeup],
description: [
- A kernel and basic operating system for a Raspberry Pi built in Rust
- Implemented booting, GPIO, UART, chainloading, allocation, and a Fat32 filesystem
],
isDigital: isDigital
)
#projectItem(
name: "WWDC Accepted Scholarship Playgrounds",
when: "2019, 2020",
writeup: [
#link("https://liamrosenfeld.com/projects/fourier-artist/")[2019 Writeup,]
#link("https://liamrosenfeld.com/projects/stfourier-explainer/")[2020 Writeup]
],
description: [
- My 2019 submission visualized the Fourier transform as rotating circles drawing a path
- My 2020 submission taught applying the Fourier transform to digital signal processing using Accelerate vDSP
- I had an opportunity to discuss my projects with <NAME>
],
isDigital: isDigital
)
#projectItem(
name: "Image To ASCII Art",
when: "Released 2017",
writeup: link("https://liamrosenfeld.com/projects/ascii-art/")[Writeup],
description: [
- iOS and macOS app on the App Store with 17k downloads
- Interface built using SwiftUI, UIKit, and AppKit and generation uses Accelerate vImage
],
isDigital: isDigital
)
== Teaching
*Advanced Programming Fundamentals (COP 3504C) TA* #h(1fr) Fall 2022
|
|
https://github.com/gongke6642/tuling | https://raw.githubusercontent.com/gongke6642/tuling/main/可视化/线/xian.typ | typst | = line 元素
从一个点到另一个点的线。
#image("1.png")
#image("2.png") |
|
https://github.com/j10ccc/algorithm-analysis-homework-template-typst | https://raw.githubusercontent.com/j10ccc/algorithm-analysis-homework-template-typst/main/README.md | markdown | # Algorithm-analysis-homework-template-typst
For Algorithm Analysis And Design course homework.
## Usage
> Before use this template, you should learn a bit
> [typst](https://typst.app) language syntax, like function
> call, text render syntax. It is some different from LaTeX.
Clone the repository.
Before build output file, you should create your
own homework document, use template also :).
Create a `.typ` file with casual name in "workspace"
directory. There has been a example file in that directory,
maybe you can refer it.
### Prefix Snippet
The document source code should contains below prefix snippet.
Those code include the whole paper template, and include the
important function `question`.
```typst
#import "../main.typ": template
#import "../layout/question.typ": question
#let config = (
homework_id: [0],
date: [2023.9.04],
time_consume: [xxx],
deadline: [2023.9.24 : 6 PM],
intro: [本次习题主要涉及递归算法以及递归函数求解。请用 LATEX 编辑所有解答。所有问题请给出简洁的回答，任何冗余的回答可能会得低分。提交文件格式为 PDF。]
)
#show: doc => template(doc, config)
```
### `question` function
This function receives two arguments.
| arg | comments |
|-----|----------|
|`body`| the question body, rendered in the next line after the question title. (maybe it is not exist) |
|`homework_id`| the number of this homework, it appears like `Question <homework_id>_<question_id>`. this can be omitted. |
|`title`| the question title, rendered in the same line with the question number. |
```typst
#question(
homework_id: "0",
title: [
// question title
Your first problem is that..
])[
// question body, if unnecessary, leave it empty
There is some cases..
]
// Type your answer here.
// Create a new page if needed.
#pagebreak()
```
**NOTE**: You don't need to pay any attention to the number of
questions, just declare them, the template will handle it.
### Code block
If you need to write some code, use
[codelst](https://github.com/typst/packages/tree/main/packages/preview/codelst).
````typst
#sourcecode(frame: none)[
```typst
hello *world*
```
]
````
### Frontmatter
About homework meta data, id, name, edit these in `config.typ`.
### Compile
#### For single file
In the root directory of the repo, run this command to compile.
```sh
$ typst compile workspace/<YOUR_DOC_NAME>.typ --root ..
```
The output pdf file will be generated in workspace with the
same name of source code file.
#### For multiple files
All pdf document files will be compiled in `/output` after running
the command.
```
$ make
```
## Design Principle
If you are interested in the structure of the template of
**Typst**, you can read the design principle.
Define components or layout in single file and a directory.
In a directory, there is always a `index.typ`. It declare a
identical name variable(`content`) to combine all components
in it's directory. You can declare components order or mixin
atom components.
```typst
import "layout/divider.typ": divider
#divider
// or
import "layout/headers/index.typ": headers
#headers
// it is not recommend to use a inner layout component
import "layout/headers/title.typ": title
#title
```
## Font
The font family used in compile are declared in
`constants/fonts.typ`. The two **Fandol font**(mostly used
in _ctex_) can be download in this
[repo](https://www.ctan.org/tex-archive/fonts/fandol). The
`default` font, you can update to your favorite font available
in you os.
## Examples
A real compile example `workspace/ps0.typ` is created.
## Roadmap
- Style
- Adjust `raw` block colorset
## Contribution
You can point out all of layout or render logical bugs(if there is)
or advice in issue.
If you want to modify code, you should pull a
request for further contribution. It is better to use **git flow**
as your contribution standard. |
|
https://github.com/CL4R3T/QFT_homework | https://raw.githubusercontent.com/CL4R3T/QFT_homework/main/HW1/HW1_Sol.typ | typst | #import "@preview/problemst:0.1.0": pset
#import "@preview/physica:0.9.3": *
#show: pset.with(
class: "QFT",
student: read("../.authorinfo"),
title: "Homework 1",
date: datetime(year: 2024, month: 9, day: 26),
)
#set heading(numbering: (..nums) => {
nums = nums.pos()
nums.at(0) -= 1
if nums.len() == 1 {
[Problem #nums.at(0):]
} else {
numbering("1.1.a.i", ..nums)
}
})
#let vec3(letter) = math.upright(math.bold(letter))
#let cre(letter) = $a^dagger (vec3(letter))$
#let ann(letter) = $a(vec3(letter))$
#let veclen(k) = math.abs(vec3(k))
=
The energy of boson $omega_vec3(k)$ is
$
E_vec3(k) = mel(vec3(k), H, vec3(k)) = bra(vec3(k)) H cre(k) ket(0)
= bra(vec3(k)) cre(k) H ket(0) + mel(vec3(k), [H, cre(k)], 0)
= mel(vec3(k), [H, cre(k)], 0)
$
here
$
[H, cre(k)] &= [integral (d^3 l) / ((2 pi)^3 2) cre(l) ann(l) + "const", cre(k)]\
&= integral (d^3 l) / ((2 pi)^3 2) (cre(l) [ann(k), ann(l)] + [cre(l), cre(k)] ann(l))\
&= integral (d^3 l) / ((2 pi)^3 2) cre(l) (2 pi)^3 2 omega_vec3(k) delta(vec3(k)-vec3(l))\
&= omega_vec3(k) cre(k)
$
then
$ E_vec3(k) = mel(vec3(k), omega_vec3(k) cre(k), 0) = mel(vec3(k), omega_vec3(k), vec3(k)) = omega_vec3(k) $
=
== Problem 2.9c)
Since we have
$
tensor((S^(mu nu)_upright(V)),+rho,-tau) eq.triple hbar / i (
g^(mu rho) tensor(delta,+nu,-tau)-g^(nu rho) tensor(delta,+mu,-tau)
)
$
then
$ (i S^12_upright(V)) / hbar = mat(0,0,0,0;0,0,+1,0;0,-1,0,0;0,0,0,0,) $
Differential of $Lambda$ gives
$
dv(Lambda,theta) = mat(0,0,0,0;0,-sin theta,-cos theta,0;0,cos theta,-sin theta,0;0,0,0,0) = - (i S^12_upright(V)) / hbar Lambda
$
while
$ tensor(Lambda,+mu,-nu)|_(theta=0) = tensor(delta,+mu,-nu) $
which gives
$ Lambda = exp(-i theta S^12_upright(V)\/hbar) $
== Problem 2.9d)
Since we have
$
tensor((S^(mu nu)_upright(V)),+rho,-tau) eq.triple hbar / i (
g^(mu rho) tensor(delta,+nu,-tau)-g^(nu rho) tensor(delta,+mu,-tau)
)
$
then
$ (i S^30_upright(V)) / hbar = mat(0,0,0,+1;0,0,0,0;0,0,0,0;+1,0,0,0,) $
Differential of $Lambda$ gives
$
dv(Lambda,eta) = mat(sinh eta,0,0,cosh eta;0,0,0,0;0,0,0,0;cosh eta,0,0,sinh eta) = + (i S^30_upright(V)) / hbar Lambda
$
while
$tensor(Lambda,+mu,-nu)|_(eta=0) = tensor(delta,+mu,-nu)$
which gives
$ Lambda = exp(-i eta S^30_upright(V)\/hbar) $
=
Using eqs. (3.29) we get
$
[H, cre(k)] &= [integral (d^3 l) / ((2 pi)^3 2) cre(l) ann(l) + "const", cre(k)]\
&= integral (d^3 l) / ((2 pi)^3 2) (cre(l) [ann(k), ann(l)] + [cre(l), cre(k)] ann(l))\
&= integral (d^3 l) / ((2 pi)^3 2) cre(l) (2 pi)^3 2 omega_vec3(k) delta(vec3(k)-vec3(l))\
&= omega_vec3(k) cre(k)
$
then
$
H ket(k_1 k_2 dots k_n) &= H cre(k_1) cre(k_2) dots cre(k_n) ket(0)\
&= ([H, cre(k_1)] + cre(k_1) H) cre(k_2) dots cre(k_n) ket(0)\
&= omega_1 cre(k_1) cre(k_2) dots cre(k_n) ket(0) + cre(k_1) H cre(k_2) dots cre(k_n) ket(0)\
&= (omega_1 + dots + omega_n) cre(k_1) cre(k_2) dots cre(k_n) ket(0) + cre(k_1) cre(k_2) dots cre(k_n) H ket(0)\
&= (omega_1 + dots + omega_n) ket(k_1 k_2 dots k_n)
$
So $ket(k_1 k_2 dots k_n)$ is an eigenstate of $H$ with eigenvalue $omega_1 + dots + omega_n$.
=
#let ftphi = $tilde(phi)_a (k)$
$
[H, ftphi] &= [H, integral d^4x e^(-i k dot x) phi_a (x)]\
&= integral dd(x,4) e^(-i k dot x) [H, phi_a (x)]\
&= -i integral dd(x,4) e^(-i k dot x) pdv(phi_a (x),t)\
&= -i integral dd(x,3) e^(- vec3(k) dot vec3(x)) integral dd(t) e^(i k^0 t) pdv(phi_a (x),t)\
&= i integral dd(x,3) e^(- vec3(k) dot vec3(x)) integral dd(t) phi_a (x) pdv(e^(i k^0 t),t)\
&= - k^0 integral dd(x,4) e^(- k dot x) phi_a (x)\
&= - k^0 ftphi
$
Similarly,
$ [P^i, ftphi] = - k^i ftphi $
Hence,
$
H ftphi ket(Psi) &= [H, ftphi] ket(Psi) + ftphi H ket(Psi)\
&= (E-k^0) ftphi ket(Psi)
$
and
$
P^i ftphi ket(Psi) &= [P^i, ftphi] ket(Psi) + ftphi P^i ket(Psi)\
&= (p^i-k^i) ftphi ket(Psi)
$
then the state $ftphi ket(Psi)$ have energy $E' = E - k^0$ and momentum $vec3(p)' = vec3(p) - vec3(k)$.
=
== Evaluation of the integral
It is obvious that $C(x)$ is only related to $x^0$ and $veclen(x)$, so it is proper to assume that $vec3(x)= (veclen(x),0,0)$, in order to make the integral easier.
Introducing variants $eta in [0,+infinity), theta in [0,pi], phi in [0,2 pi)$ satisfying the relation below:
$ vec3(k) eq.triple (k^1, k^2, k^3) eq.triple omega_0 eta (cos theta, sin theta cos phi, sin theta sin phi) $
then
$ omega_vec3(k) = sqrt(omega_0^2+veclen(k)^2) = omega_0 sqrt(1 + eta^2) $
and
$
tilde(dd(k)) eq.triple dd(k,3) / ((2 pi)^3 2 omega_vec3(k))
= (omega_0^2 eta^2 sin theta dd(eta) dd(theta) dd(phi)) / ((2 pi)^3 2 sqrt(1 + eta^2))
$
So we get
$
C(x) &= -i c_+ integral (omega_0^2 eta^2 sin theta dd(eta) dd(theta) dd(phi)) / ((2 pi)^3 sqrt(1 + eta^2))
sin(omega_0 x^0 sqrt(1 + eta^2))e^(i omega_0 veclen(x) eta cos theta )\
&= -(i c_+ omega_0^2) / (2 pi)^2 integral_0^(+infinity)dd(eta)
integral_(-1)^(+1)dd((cos theta))
eta^2 / sqrt(1 + eta^2) sin(omega_0 x^0 sqrt(1 + eta^2))e^(i omega_0 veclen(x) eta cos theta )\
&= -(2i c_+ omega_0) / ((2 pi)^2 veclen(x)) integral_0^(+infinity)dd(eta) eta / sqrt(1 + eta^2) sin (
omega_0 veclen(x) eta
)sin(omega_0 x^0 sqrt(1 + eta^2))\
$
Using eq.3.876(1) from _Table of Integrals, Series, and Products (Seventh Edition)_ by Gradshteyn and Ryzhik:
$
integral_0^infinity sin(p sqrt(x^2+a^2)) / sqrt(x^2+a^2)cos(b x)dd(x) = cases(pi/2 J_0(abs(a) sqrt(p^2-b^2)) " " &[0<b<p],0 &[0<p<b]) " "[
a>0
]
$
which equals to
$
integral_0^infinity sin(p sqrt(x^2+a^2)) / sqrt(x^2+a^2)cos(b x)dd(x) = sgn(p)theta(p^2-b^2)pi / 2 J_0(
abs(a) sqrt(p^2-b^2)
)
$
Differential of both sides with respect to $b$ gives
$
-integral_0^infinity sin(p sqrt(x^2+a^2)) / sqrt(x^2+a^2)x sin(b x)dd(x) = sgn(p)(
(pi abs(a) b) / (2 sqrt(p^2-b^2)) theta(p^2-b^2)J_1(abs(a) sqrt(p^2-b^2)) - pi b delta(p^2-b^2)
)
$
Taking $x=eta, a=1, b=omega_0 veclen(x), p=omega_0 x^0$ gives
$
C(x)&=(2i c_+ omega_0) / ((2 pi)^2 veclen(x)) sgn(omega_0 x^0) (
(pi omega_0 veclen(x)) / (2 omega_0 tau) theta(omega_0^2 tau^2) J_1(
omega_0 tau
)-pi omega_0 veclen(x) delta(omega_0^2 tau^2)
)\
&=c_+sgn(x^0)(i omega_0 theta(tau^2) (J_1(omega_0 tau)) / (4 pi tau) - i / (2pi) delta(tau^2))
$
here $tau = sqrt((x^0)^2-veclen(x)^2) = sqrt(-x^2)$.
With the commutator relation $[phi(x), phi(y)] = C(x-y)$, we have
$
[phi(x), phi(y)] = c_+ sgn(x^0-y^0)(i omega_0 theta(tau^2) (J_1(omega_0 tau)) / (4 pi tau) - i / (2pi) delta(tau^2))
$
here $tau = sqrt(-(x-y)^2)$.
== spacelike intevals
If $-tau^2=(x-y)^2>0$, then $theta(tau^2)=delta(tau^2)=0$, which will give $[phi(x),phi(y)]=0$.
== $0<tau^2<<omega_0^(-2)$
Since $J_1(x) = 1/2 x+ o(x^3)$, we have
$
[phi(x), phi(y)] = c_+ sgn(x^0-y^0)(i omega_0^2) / (8 pi)+o(tau^2)
$
== $tau^2 >> omega_0^2$
The approximation of $J_1(x)$ when $x->infinity$ is
$
J_1(x) tilde sqrt(2/(pi x)) cos(x-3/4 pi)
$
So we have
$
[phi(x), phi(y)] &= c_+ sgn(x^0-y^0)(i omega_0) / (4 pi tau)sqrt(2/(pi omega_0 tau)) cos(omega_0 tau - 3/4 pi)\
&=c_+ sgn(x^0-y^0)(i omega_0^(1 / 2)) / (2 pi tau)^(3 / 2) cos(omega_0 tau- 3/4 pi)
$
== Dirac $delta$ term
If $t eq.triple x^0-y^0>0$, the second term is
$
-(i c_+) / (2pi) delta(tau^2) &= -(i c_+) / (2pi) delta(veclen(x-y)^2-t^2)\
&= -(i c_+) / (2pi) delta((veclen(x-y)+t)(veclen(x-y)-t))\
&= -(i c_+) / (2pi (veclen(x-y)+t)) delta(veclen(x-y)-t)\
&= -(i c_+) / (2pi (t+t))delta(veclen(x-y)-t)\
&= -(i c_+) / (4pi) t^(-1) delta(veclen(x-y)-t)\
$
Thus the constant $alpha=1$
== the dimension
Since $sgn(x)$ is dimensionless and $delta(x)$ have the dimension of $[x]^(-1)$, the dimension of $C(x)$ is
$ [C(x)] = [c_+ delta(tau^2)] = [tau]^(-2) = ("length")^(-2) $
Then we have
$ [phi(x)] = [C(x)]^(1 / 2) = ("length")^(-1) $
|
|
https://github.com/linhduongtuan/BKHN-Thesis_template_typst | https://raw.githubusercontent.com/linhduongtuan/BKHN-Thesis_template_typst/main/contents/appendix.typ | typst | Apache License 2.0 | = How to train large langugue models
#lorem(100)
= How to train very huge image-language datasets
#lorem(100) |
https://github.com/mangkoran/utm-thesis-typst | https://raw.githubusercontent.com/mangkoran/utm-thesis-typst/main/03_declaration_supervisor.typ | typst | MIT License | #import "@preview/tablex:0.0.7": tablex, colspanx
#import "utils.typ": empty
#let content(
degree: empty[degree],
supervisor: (
empty[supervisor 1],
empty[supervisor 2],
),
) = [
#set align(center + horizon)
"We hereby declare that we have read this thesis and in our opinion
this thesis is sufficient in terms of scope and quality
for the award of the degree of #degree"
#tablex(
auto-lines: false,
columns: (auto, 40%),
..(for i in range(supervisor.len()) {(
..(if i != 0 {(
colspanx(2)[], (),
colspanx(2)[], (),
colspanx(2)[], (),
)}),
[Signature of Supervisor #(i+1)], [:],
colspanx(2)[], (),
colspanx(2)[], (),
colspanx(2)[], (),
[Name of Supervisor #(i+1)], [: #upper[#supervisor.at(i)]],
[Date], [: #datetime.today().display()],
)})
)
#pagebreak(weak: true)
]
#content()
|
https://github.com/jgm/typst-hs | https://raw.githubusercontent.com/jgm/typst-hs/main/test/typ/compiler/spread-13.typ | typst | Other | // Spread in the middle.
#{
let f(a, ..b, c) = (a, b, c)
test(repr(f(1, 2)), "(1, (), 2)")
test(repr(f(1, 2, 3, 4, 5)), "(1, (2, 3, 4), 5)")
}
|
https://github.com/denizenging/site | https://raw.githubusercontent.com/denizenging/site/master/page/links/index.en.typ | typst | #import "@local/pub-page:0.0.0": *
#show: template(
title: "Links",
menu: (4, "link"),
links: (
(
"ORCID iD",
"ORCID iD is a unique identifier for researchers and their publications.",
"https://orcid.org/0009-0004-9445-8502",
"img/orcid.webp",
),
(
"GitHub",
"GitHub is a software forge where I host most of my software projects.",
"https://github.com/denizenging",
"img/github.webp",
),
(
"LinkedIn",
"LinkedIn is a professional networking site for career connections.",
"https://linkedin.com/in/denizenging/",
"img/linkedin.webp",
),
(
"X/Twitter",
"X/Twitter is a social media platform, primarily for news and opinions.",
"https://x.com/denizenging",
"img/x.webp",
),
(
"YouTube",
"YouTube is a video/music streaming service where I have many good playlists!",
"https://www.youtube.com/@denizenging",
"img/youtube.webp",
),
(
"Instagram",
"Instagram is a social media app, where you can see pictures of mine!",
"https://instagram.com/denizenging/",
"img/instagram.webp",
),
(
"Goodreads",
"Goodreads is a social network for keeping track of books and reviews.",
"https://goodreads.com/denizenging/",
"img/goodreads.webp",
),
(
"Letterboxd",
"Letterboxd is a social platform for sharing film reviews and ratings.",
"https://letterboxd.com/denizenging/",
"img/letterboxd.webp",
),
(
"Duolingo",
"Duolingo is an app for learning languages through interactive lessons.",
"https://www.duolingo.com/profile/denizenging",
"img/duolingo.webp",
),
),
)
The list of links of the platforms I use, where you can reach me and say hi!
|
|
https://github.com/TechnoElf/mqt-qcec-diff-thesis | https://raw.githubusercontent.com/TechnoElf/mqt-qcec-diff-thesis/main/content/implementation/algorithms.typ | typst | #import "@preview/fletcher:0.5.1": diagram, node, edge
#import "@preview/gentle-clues:0.9.0": example, code
#import "@preview/lovelace:0.3.0": pseudocode-list
== Algorithms
This section provides an overview of the implemented diff algorithms.
Initially, research was done to determine suitable algorithms for the task.
A variety of algorithms was found, but only a limited representative set was chosen for implementation due to their similarity and the given time constraints.
The chosen algorithms are: Djikstra's algorithm (for its simplicity) @djikstra1959shortest, Myers' algorithm (for its ubiquity) @myers1986diff and the patience algorithm (for its relative novelty) @cohen2010patience.
=== Djikstra's Algorithm
Djikstra's algorithm is an @sssp algorithm @djikstra1959shortest.
This means that it solves the problem of finding the shortest distance from a node of a graph to any other node.
It can thus be trivially applied as a diff algorithm by finding the shortest path across an edit graph.
@djikstras_algorithm_abstract presents a slightly modified form of the original algorithm that more closely matches modern programming languages.
#figure(
block(
pseudocode-list[
+ *def* $"djikstra"(G, s, e)$
+ create a list of remaining nodes $N$ containing all nodes in $G$
+ set the distance for all nodes in $N$ to infinity
+ set the parent for all nodes in $N$ to none
+ set the distance for the starting node $s$ in $N$ to $0$
+ *while* there are nodes left ($N$ is not empty)
+ take node $c$ with the lowest distance from $N$
+ *if* $c$ is the end node $e$
+ *break*
+ *end*
+ *for* each child node $n$ of of the current node $c$
+ *if* the current distance is shorter than the stored distance in $n$
+ set the current distance as the distance of $n$
+ set the current node $c$ as the parent of $n$
+ *end*
+ *end*
+ *end*
+ *return* a path through the graph found by traversing the parent nodes of the end node $e$
+ *end*
],
width: 100%
),
caption: [Djikstra's algorithm.]
) <djikstras_algorithm_abstract>
Essentially, Djikstra's algorithm functions by greedily following the current shortest path from a starting node until the end node of the graph is reached.
To implement this, a set $N$ of all unvisited nodes is created and each node assigned a path length (where unvisited or unreachable nodes have a distance of infinity).
The starting node has its distance set to 0 to ensure it will be picked first.
In each iteration, the node with the shortest path is then removed from the set $N$ and the distance of all neighbouring nodes is updated.
This is performed repeatedly until the end node is found.
In this pseudocode implementation, the inner loop corresponds to Step 1 and the outer loop to Step 2 from the original description @djikstra1959shortest.
The list $N$ corresponds to sets $B$ and $C$ and the nodes removed from $N$ correspond to the set $A$.
Given the constraints of the edit graph, it is possible to simplify the algorithm.
Firstly, the edges have no assigned weight and are therefore assumed to uniformly have a weight of $1$ for this algorithm.
Secondly, the graph is always a @dag.
Djikstra's algorithm hereby essentially reduces to a breadth-first search over the graph.
The implementation is thus as follows:
#figure(
block(
pseudocode-list[
+ *def* $"djikstra_modified"(v)$
+ create a list of remaining nodes containing only $v$
+ *while* the list of remaining nodes is not empty
+ take the lowest element from the list of remaining nodes
+ *if* the current element is the last node
+ *break*
+ *end*
+ *for* each child node $c$ of of the current element
+ *if* $c$ has no parent
+ set the current element as the parent of $c$
+ add $c$ to the list of remaining nodes
+ *end*
+ *end*
+ *end*
+ find a path through the edit graph by traversing the parent nodes of the final node
+ *return* the edit script found by taking the reverse of the path
+ *end*
],
width: 100%
),
caption: [Modified Djikstra's algorithm.]
) <mod_djikstras_algorithm_abstract>
#example[
@example_djikstra shows an example instance of the modified Djikstra's algorithm shown in @mod_djikstras_algorithm_abstract.
The edge labels specify the order in which the nodes are visited.
Child nodes are iterated over from top right to bottom left in this case, however the order is not important for the functionality of the algorithm.
The red edges highlight the final path found by the algorithm after traversing the parent nodes from the final node in reverse order.
#figure(
diagram(
spacing: 1cm,
node-stroke: .1em,
for y in range(0, 5) {
for x in range(0, 5) {
node((x, y), radius: 1em)
}
},
edge((3, 0), (4, 1), [12], "->", stroke: 1.5pt),
edge((0, 1), (1, 2), [4], "->", stroke: 1.5pt + red),
edge((2, 1), (3, 2), [14], "->", stroke: 1.5pt),
edge((0, 2), (1, 3), "->"),
edge((2, 2), (3, 3), [15], "->", stroke: 1.5pt + red),
edge((1, 3), (2, 4), [17], "->", stroke: 1.5pt),
edge((0, 0), (1, 0), [0], "->", stroke: 1.5pt),
edge((1, 0), (2, 0), [2], "->", stroke: 1.5pt),
edge((2, 0), (3, 0), [6], "->", stroke: 1.5pt),
edge((3, 0), (4, 0), [11], "->", stroke: 1.5pt),
edge((0, 1), (1, 1), "->"),
edge((1, 1), (2, 1), "->"),
edge((2, 1), (3, 1), "->"),
edge((3, 1), (4, 1), "->"),
edge((0, 2), (1, 2), "->"),
edge((1, 2), (2, 2), [8], "->", stroke: 1.5pt + red),
edge((2, 2), (3, 2), "->"),
edge((3, 2), (4, 2), "->"),
edge((0, 3), (1, 3), "->"),
edge((1, 3), (2, 3), "->"),
edge((2, 3), (3, 3), "->"),
edge((3, 3), (4, 3), [21], "->", stroke: 1.5pt + red),
edge((0, 4), (1, 4), "->"),
edge((1, 4), (2, 4), "->"),
edge((2, 4), (3, 4), "->"),
edge((3, 4), (4, 4), "->"),
edge((0, 0), (0, 1), [1], "->", stroke: 1.5pt + red),
edge((0, 1), (0, 2), [5], "->", stroke: 1.5pt),
edge((0, 2), (0, 3), [10], "->", stroke: 1.5pt),
edge((0, 3), (0, 4), [19], "->", stroke: 1.5pt),
edge((1, 0), (1, 1), [3], "->", stroke: 1.5pt),
edge((1, 1), (1, 2), "->"),
edge((1, 2), (1, 3), [9], "->", stroke: 1.5pt),
edge((1, 3), (1, 4), [18], "->", stroke: 1.5pt),
edge((2, 0), (2, 1), [7], "->", stroke: 1.5pt),
edge((2, 1), (2, 2), "->"),
edge((2, 2), (2, 3), [16], "->", stroke: 1.5pt),
edge((2, 3), (2, 4), "->"),
edge((3, 0), (3, 1), [13], "->", stroke: 1.5pt),
edge((3, 1), (3, 2), "->"),
edge((3, 2), (3, 3), "->"),
edge((3, 3), (3, 4), [22], "->", stroke: 1.5pt),
edge((4, 0), (4, 1), "->"),
edge((4, 1), (4, 2), [20], "->", stroke: 1.5pt),
edge((4, 2), (4, 3), "->"),
edge((4, 3), (4, 4), [23], "->", stroke: 1.5pt + red),
),
caption: [Modified Djikstra's algorithm on an example edit graph.]
) <example_djikstra>
]
It was also considered whether to implement another @spsp algorithm such as A\* @hart1968astar.
This was, however, deemed unnecessary, as there exist better solutions tailored specifically to edit graphs.
=== Myers' Algorithm
Myers' algorithm in its original form only solves the @lcs problem without producing an edit script for transforming one input sequence into the other @myers1986diff.
The version presented here has been extended to provide this functionality.
It does so by using the edit graph traversal of the original algorithm to find a point that must be part of the shortest edit script and then recursively applying the algorithm to the two remaining sub graphs @elder2017myers.
@myers_algorithm_abstract presents the pseudocode for this procedure.
#figure(
block(
pseudocode-list[
+ *def* $"myers"()$
+ find a central connecting snake between the top left and bottom right of the edit graph
+ *if* the edit graph is trivial
+ *return* the trivial solution
+ *else*
+ run $"myers"()$ on the top left sub graph recursively
+ run $"myers"()$ on the bottom right sub graph recursively
+ *return* the combined edit scripts from the recursive calls and the central snake
+ *end*
+ *end*
],
width: 100%
),
caption: [Myers' algorithm.]
) <myers_algorithm_abstract>
The following example visually demonstrates how the edit graph is split up by the recursive calls in the algorithm.
#example(breakable: true)[
Applying the first step of the abstract Myers' algorithm to the sample edit graph from @example_edit_graph yields the connecting snake marked in red in @example_snake. The algorithm then saves this snake as part of the edit script and continues working on the resulting sub graphs, as shown in @example_recursion. It will then combine the edit scripts from these with the connecting snake to form a final edit script.
#figure(
diagram(
spacing: 1cm,
node-stroke: .1em,
for y in range(0, 5) {
for x in range(0, 5) {
node((x, y), radius: 1em)
}
},
edge((3, 0), (4, 1), "->"),
edge((0, 1), (1, 2), "->", stroke: 2pt),
edge((2, 1), (3, 2), "->"),
edge((0, 2), (1, 3), "->"),
edge((2, 2), (3, 3), "->"),
edge((1, 3), (2, 4), "->", stroke: 2pt + red),
edge((0, 0), (1, 0), "->"),
edge((1, 0), (2, 0), "->"),
edge((2, 0), (3, 0), "->"),
edge((3, 0), (4, 0), "->"),
edge((0, 1), (1, 1), "->"),
edge((1, 1), (2, 1), "->"),
edge((2, 1), (3, 1), "->"),
edge((3, 1), (4, 1), "->"),
edge((0, 2), (1, 2), "->"),
edge((1, 2), (2, 2), "->"),
edge((2, 2), (3, 2), "->"),
edge((3, 2), (4, 2), "->"),
edge((0, 3), (1, 3), "->"),
edge((1, 3), (2, 3), "->"),
edge((2, 3), (3, 3), "->"),
edge((3, 3), (4, 3), "->"),
edge((0, 4), (1, 4), "->"),
edge((1, 4), (2, 4), "->"),
edge((2, 4), (3, 4), "<-", stroke: 2pt),
edge((3, 4), (4, 4), "<-", stroke: 2pt),
edge((0, 0), (0, 1), "->", stroke: 2pt),
edge((0, 1), (0, 2), "->"),
edge((0, 2), (0, 3), "->"),
edge((0, 3), (0, 4), "->"),
edge((1, 0), (1, 1), "->"),
edge((1, 1), (1, 2), "->"),
edge((1, 2), (1, 3), "->", stroke: 2pt),
edge((1, 3), (1, 4), "->"),
edge((2, 0), (2, 1), "->"),
edge((2, 1), (2, 2), "->"),
edge((2, 2), (2, 3), "->"),
edge((2, 3), (2, 4), "->"),
edge((3, 0), (3, 1), "->"),
edge((3, 1), (3, 2), "->"),
edge((3, 2), (3, 3), "->"),
edge((3, 3), (3, 4), "->"),
edge((4, 0), (4, 1), "->"),
edge((4, 1), (4, 2), "->"),
edge((4, 2), (4, 3), "->"),
edge((4, 3), (4, 4), "->"),
),
caption: [Snake found by the algorithm after the first iteration.]
) <example_snake>
#figure(
diagram(
spacing: 1cm,
node-stroke: .1em,
for y in range(0, 5) {
for x in range(0, 5) {
node((x, y), radius: 1em)
}
},
edge((0, 1), (1, 2), "->"),
edge((0, 2), (1, 3), "->"),
edge((0, 0), (1, 0), "->"),
edge((0, 1), (1, 1), "->"),
edge((0, 2), (1, 2), "->"),
edge((0, 3), (1, 3), "->"),
edge((2, 4), (3, 4), "->"),
edge((3, 4), (4, 4), "->"),
edge((0, 0), (0, 1), "->"),
edge((0, 1), (0, 2), "->"),
edge((0, 2), (0, 3), "->"),
edge((1, 0), (1, 1), "->"),
edge((1, 1), (1, 2), "->"),
edge((1, 2), (1, 3), "->"),
),
caption: [Remaining sub graphs to recursively apply the algorithm to.]
) <example_recursion>
]
This algorithm was implemented in both Kaleidoscope and @qcec.
As such, the implementation was extended and reworked several times to optimise it for quantum circuit equivalence checking.
The discussion on diff visualisation in the following sections explores some of the improvements made to the algorithm.
The version presented here is the final version that was integrated into @qcec.
#code(breakable: true)[
The actual implementation of Myers' algorithm uses a slightly different procedure, where the sub graphs are checked for triviality instead of the input graph.
This would be slower when the entire edit graph is trivial, however, this edge case will almost never occur when applying this algorithm to equivalence checking of quantum circuits.
The following functions use the global lists $A$ and $B$ to access the structure of the input circuits.
These contain some sort of representation of the gates in the circuits that can be checked for equivalence.
Recursion is implemented with the parameters $x$, $y$, $m$, and $n$.
These specify the subsection of the circuits being processed and must be set to $0$, $0$ and the length of the two sequences respectively for the first call.
#block(
pseudocode-list[
+ *def* $"myers"(x, y, m, n)$
+ $("snake_start_x", "snake_start_y", "snake_end_x", "snake_end_y") = "find_snake"(x, y, m, n)$
+ $"result" = {}$
+ $"result" = "result" + "process_subgraph"(x, y, "snake_start_x", "snake_start_y", m, n)$
+ $"result" = "result" + ("snake_end_x" - "snake_start_x", "snake_end_x" - "snake_start_x")$
+ $"result" = "result" + "process_subgraph"(x + "snake_end_x", y + "snake_end_y", m - "snake_end_x", n - "snake_end_y", m, n)$
+ *return* $"result"$
+ *end*
],
width: 100%
)
#block(
pseudocode-list[
+ *def* $"process_subgraph"(x, y, w, h, m, n)$
+ *if* $(w = 0 and h != 0) or (w != 0 and h = 0)$
+ *return* $(w, h)$
+ *else if* $w = m and h = n$
+ *if* $w > h$
+ *return* ${(h, h), (w - h, 0)}$
+ *else*
+ *return* ${(w, w), (0, h - w)}$
+ *end*
+ *else*
+ *return* $"myers"(x, y, w, h)$
+ *end*
+ *end*
],
width: 100%
)
#block(
pseudocode-list[
+ *def* $"find_snake"(x, y, m, n)$
+ $"best_x_forward"$ *is* $"array"((m + n) * 2 + 1)$
+ $"best_x_backward"$ *is* $"array"((m + n) * 2 + 1)$
+ *for* operations *in* $0$ *to* $m + n$
+ *for* diagonal *in* $-("operations" - 2 * max(0, "operations" - m))$ *to* $"operations" - 2 * max(0, "operations" - m)$
+ $"calculate_best_x_forward"("best_x_forward", "diagonal", m, n)$
+ $"snake_start" = "follow_snake_forward"("best_x_forward", "diagonal", x, y, m, n)$
+ *if* $"overlap_forward"()$
+ $"snake_start_x" = "snake_start"$
+ $"snake_start_y" = "snake_start" - "diagonal"$
+ $"snake_end_x" = "best_x_forward"[m + n + "diagonal"]$
+ $"snake_end_y" = "best_x_forward"[m + n + "diagonal"] - "diagonal"$
+ *return* $("snake_start_x", "snake_start_y", "snake_end_x", "snake_end_y")$
+ *end*
+ *end*
+ *for* diagonal *in* $-("operations" - 2 * max(0, "operations" - m))$ *to* $"operations" - 2 * max(0, "operations" - m)$
+ $"calculate_best_x_backward"("best_x_forward", "diagonal", m, n)$
+ $"snake_end" = "follow_snake_backward"("best_x_backward", "diagonal", x, y, m, n)$
+ *if* $"overlap_backward"()$
+ $"snake_start_x" = m - "best_x_forward"[m + n + "diagonal"]$
+ $"snake_start_y" = n - "best_x_forward"[m + n + "diagonal"] + "diagonal"$
+ $"snake_end_x" = m - "snake_end"$
+ $"snake_end_y" = n - "snake_end" + "diagonal"$
+ *return* $("snake_start_x", "snake_start_y", "snake_end_x", "snake_end_y")$
+ *end*
+ *end*
+ *end*
+ *end*
],
width: 100%
)
The implementations of the $"_backward"$ functions used in the `find_snake()` function are analogous to the $"_forward"$ functions shown in the following code blocks.
#block(
pseudocode-list[
+ *def* $"calculate_best_x_forward"("best_x_forward", "diagonal", m, n)$
+ *if* $"diagonal" = -"operations"$
+ $"best_x_forward"[m + n + "diagonal"] = "best_x_forward"[m + n + "diagonal" + 1]$
+ *else if* $"diagonal" = "operations"$
+ $"best_x_forward"[m + n + "diagonal"] = "best_x_forward"[m + n + "diagonal" - 1]$
+ *else*
+ *if* $"best_x_forward"[m + n + "diagonal" - 1] > "best_x_forward"[m + n + "diagonal" + 1]$
+ $"best_x_forward"[m + n + "diagonal"] = "best_x_forward"[m + n + "diagonal" - 1]$
+ *else*
+ $"best_x_forward"[m + n + "diagonal"] = "best_x_forward"[m + n + "diagonal" + 1]$
+ *end*
+ *end*
+ *end*
],
width: 100%
)
#block(
pseudocode-list[
+ *def* $"follow_snake_forward"("best_x_forward", "diagonal", x, y, m, n)$
+ $"snake_start" = "best_x_forward"[m + n + "diagonal"]$
+ *while* $"best_x_forward"[m + n + "diagonal"] < m and "best_x_forward"[m + n + "diagonal"] < n and A[x + "best_x_forward"[m + n + "diagonal"]] == B[y + "best_x_forward"[m + n + "diagonal"] - "diagonal"]$
+ $"best_x_forward"[m + n + "diagonal"] = "best_x_forward"[m + n + "diagonal"] + 1$
+ *end*
+ *return* $"snake_start"$
+ *end*
],
width: 100%
)
#block(
pseudocode-list[
+ *def* $"overlap_forward"("best_x_forward", "best_x_backward", "diagonal", x, y, m, n)$
+ *return* $(-2n < "diagonal") and ("diagonal" < 2m) and ("best_x_forward"[m + n + "diagonal"] != -1) and ("best_x_backward"[2m + "diagonal"] != -1) and ("best_x_forward"[m + n + "diagonal"] + "best_x_backward"[2m + "diagonal"] >= m)$
+ *end*
],
width: 100%
)
]
=== Patience Algorithm
The patience algorithm is based around a divide-and-conquer approach that splits up the input sequences into many sub ranges, which the algorithm is then recursively run on.
Specifically, it seeks to find elements that occur only once in each sequence and match these up to produce as many `keep` operations as possible.
Unlike the Myers' algorithm, the patience algorithm does not, in fact, solve the @lcs problem.
Instead, it only aims to produce valid edit scripts, that are qualitatively superior for human use.
It was designed as an alternative to the Myers' algorithm for the version control software `git` with the aim of generating more sensible diffs when code is refactored @cohen2010patience.
For this purpose it is simply not necessary and sometimes even detrimental to produce an optimal edit script.
Whether or not this approach also positively affects the performance of the equivalence checking process is explored in the benchmark results presented in this thesis.
An abstract description of the algorithm is given in @patience_algorithm_abstract.
#figure(
block(
pseudocode-list[
+ *def* $"patience"()$
+ find unique elements common to both $A$ and $B$
+ *if* there are no unique elements
+ *return* the results of another diff algorithm (for example $"myers"()$)
+ *end*
+ apply patience sort to the unique common elements to find the longest increasing sequence
+ *for* each range between the elements of the sequence produced by the patience sort
+ *if* the range is trivial
+ append the trivial result to the edit script
+ *else*
+ run $"patience"()$ recursively on the range and append the result to the edit script
+ *end*
+ append $(1, 1)$ to the edit script
+ *end*
+ *return* the edit script
+ *end*
],
width: 100%
),
caption: [The patience algorithm.]
) <patience_algorithm_abstract>
While most of these steps are trivial, the patience sort procedure requires some elaboration.
This sorting algorithm finds the longest possible sequence of matching element pairs in the two sequences, where the indices in both are monotonically increasing @alfedenzo2008patience.
It does this by creating a list of piles of elements that grow vertically, and where horizontal connections represent valid increasing sequences.
@patience_sort_abstract provides additional details on the algorithm.
#figure(
block(
pseudocode-list[
+ *def* $"patience_sort"("matches")$
+ ensure $"matches"$ is sorted by the indices into the first string (this is already the case in the patience algorithm)
+ create a list of piles (which are just lists) of elements that consist of an index into each input string and a reference to another element, and which is initially empty
+ create a new pile containing the first entry in $"matches"$ with an empty reference
+ *for* each subsequent unique matching element in $"matches"$
+ find the first pile where the index into the second string of the topmost element is greater than the index into the second string of the current element
+ *if* such a pile exists
+ add the current element to the top of the pile
+ *else*
+ create a new pile with the current element
+ *end*
+ add a reference to the current element pointing to the topmost element on the previous pile
+ *end*
+ follow the references backwards from the topmost element of the last pile
+ *return* the reverse of the found path
+ *end*
],
width: 100%
),
caption: [The patience sorting algorithm.]
) <patience_sort_abstract>
The following example illustrates the functionality of the patience diff algorithm and the patience sort graphically.
#example(breakable: true)[
To run the patience algorithm on a pair of input sequences, pairs of unique common must first be found.
In this example, the already established strings "hxhy" and "yhhx" will be used.
@example_unique_common shows the unique common elements for these strings.
#figure(
diagram(
spacing: 1cm,
node-stroke: .1em,
node((0, 0), radius: 1em, "h", shape: rect),
edge((0, 0), (1, 0), "->"),
node((1, 0), radius: 1em, "x", shape: rect),
edge((1, 0), (2, 0), "->"),
node((2, 0), radius: 1em, "h", shape: rect),
edge((2, 0), (3, 0), "->"),
node((3, 0), radius: 1em, "y", shape: rect),
node((0, 2), radius: 1em, "y", shape: rect),
edge((0, 2), (1, 2), "->"),
node((1, 2), radius: 1em, "h", shape: rect),
edge((1, 2), (2, 2), "->"),
node((2, 2), radius: 1em, "h", shape: rect),
edge((2, 2), (3, 2), "->"),
node((3, 2), radius: 1em, "x", shape: rect),
edge((1, 0), (3, 2), "<->", stroke: 1.5pt),
edge((3, 0), (0, 2), "<->", stroke: 1.5pt)
),
caption: [Finding unique common elements.]
) <example_unique_common>
The unique common elements are "x" (at indices 1 and 3) and "y" (at indices 3 and 0).
In this case, the longest increasing sequence of these elements is obviously either "x" or "y".
To illustrate the patience sort, the pair of strings "a\_b\_c\_d\_" and "\_ca\_bd" will therefore be used instead.
@example_unique_common_long visualises the unique common elements of the two strings.
#figure(
diagram(
spacing: 1cm,
node-stroke: .1em,
node((0, 0), radius: 1em, "a", shape: rect),
edge((0, 0), (1, 0), "->"),
node((1, 0), radius: 1em, "_", shape: rect),
edge((1, 0), (2, 0), "->"),
node((2, 0), radius: 1em, "b", shape: rect),
edge((2, 0), (3, 0), "->"),
node((3, 0), radius: 1em, "_", shape: rect),
edge((3, 0), (4, 0), "->"),
node((4, 0), radius: 1em, "c", shape: rect),
edge((4, 0), (5, 0), "->"),
node((5, 0), radius: 1em, "_", shape: rect),
edge((5, 0), (6, 0), "->"),
node((6, 0), radius: 1em, "d", shape: rect),
edge((6, 0), (7, 0), "->"),
node((7, 0), radius: 1em, "_", shape: rect),
node((1, 2), radius: 1em, "_", shape: rect),
edge((1, 2), (2, 2), "->"),
node((2, 2), radius: 1em, "c", shape: rect),
edge((2, 2), (3, 2), "->"),
node((3, 2), radius: 1em, "a", shape: rect),
edge((3, 2), (4, 2), "->"),
node((4, 2), radius: 1em, "_", shape: rect),
edge((4, 2), (5, 2), "->"),
node((5, 2), radius: 1em, "b", shape: rect),
edge((5, 2), (6, 2), "->"),
node((6, 2), radius: 1em, "d", shape: rect),
edge((0, 0), (3, 2), "<->", stroke: 1.5pt),
edge((2, 0), (5, 2), "<->", stroke: 1.5pt),
edge((4, 0), (2, 2), "<->", stroke: 1.5pt),
edge((6, 0), (6, 2), "<->", stroke: 1.5pt)
),
caption: [Unique common elements of a more complex pair of sequences.]
) <example_unique_common_long>
Possible increasing sequences of matching pairs in this case include "cd", "ab", "bd" and "abd".
This pattern lends itself to a visual analogy: A valid sequence must not contain crossings when the strings are graphed as in @example_unique_common_long.
Using the patience sort algorithm, the longest sequence that satisfies this condition can be found.
#figure(
diagram(
spacing: 1cm,
node-stroke: .1em,
node((0, 0), radius: 1em, "a", shape: rect),
node((1, 0), radius: 1em, "b", shape: rect),
node((0, 0.5), radius: 1em, "c", shape: rect),
node((2, 0), radius: 1em, "d", shape: rect),
edge((1, 0), (0, 0), "->"),
edge((2, 0), (1, 0), "->"),
),
caption: [Piles constructed by the patience sort algorithm.]
) <example_patience_sort>
The matching pairs are iterated over in the order they appear in the first string.
Initially, a pile with the element "a" is created and its index in the second string is recorded.
Next, the element "b" is added.
As its index in the second string is greater than that of "a", a new pile is created.
Again, the index is recorded and a reference to the topmost element of the previous pile is added.
The next element to be added is "c".
Its index in the second string is lower than that of "a", so it is added to the top of the pile.
Finally, "d" is added.
The index of "d" in the second string is greater than any of the indices of the topmost elements of all existing piles, so, a new pile is created again.
A reference to the topmost element of the previous pile, "b", is also added.
Tracing all the references from the topmost element of the last pile produces the longest increasing sequence of unique common elements: "abd".
For the first example shown in @example_unique_common, the algorithm would have produced a single pile with "y" stacked on top of "x", thus giving "y" as the longest increasing sequence.
The sequence can then be converted into a list of indices into the input strings, which, in turn, can be converted into a list of ranges between these indices, as shown in @example_unique_ranges.
#figure(
grid(
columns: (4fr, 1fr, 4fr, 1fr, 4fr),
align(horizon)[$"a" \ "b" \ "d"$],
align(horizon)[$->$],
align(horizon)[$(0, 2) \ (2, 4) \ (6, 5)$],
align(horizon)[$->$],
align(horizon)[$("none", 0 "to" 1) \ (1 "to" 1, 3 "to" 3) \ (3 "to" 5, "none") \ (7 "to" 7, "none")$]
),
caption: [Converting the sequence of unique elements to a sequence of sub ranges of the input strings.]
) <example_unique_ranges>
The sub ranges are then iterated over to generate the edit script.
For the ranges found in @example_unique_ranges, only $(1 "to" 1, 3 "to" 3)$ must be evaluated recursively, while the others are trivial as they only contain elements from one of the two input strings.
The edit script would therefore be $[$`+_`, `+c`, `keep a`, `keep _`, `keep b`, `-_`, `-c`, `-_`, `keep d`, `-_`$]$.
For the strings "hxhy" and "yhhx" the final edit script would thus be $[$`-h`, `-x`, `-h`, `keep y`, `+h`, `+h`, `+x`$]$.
This is clearly not a solution to the @lcs problem, however, as discussed, the patience algorithm does not actually seek to fully solve this problem.
It is only guaranteed to produce valid edit scripts, not optimal ones.
The effect of this will be investigated using the benchmark results produced in this work.
]
The following code block discusses the final implementation that was created for @qcec.
#code(breakable: true)[
As with the Myers' algorithm, the implementation of the Patience algorithm differs slightly from the abstract representation.
In all of the following functions, it is assumed that the input circuits are accessible through the global variables $A$ and $B$.
These contain some sort of representation of the gates in the circuits which must be useable as an index into a map (for example by providing a hash function).
$x$, $y$, $m$, and $n$ are there to provide the recursive functionality of the function.
These specify the subsection of the circuits being processed and must be set to $0$, $0$ and the length of the two sequences respectively.
#set text(size: 11.8pt)
#block(
pseudocode-list[
+ *def* $"patience"(x, y, m, n)$
+ $"index_matches" = "find_index_matches"(x, y, m, n)$
+ *if* $"index_matches"$ *is empty*
+ *return* $"myers"(x, y, m, n)$
+ *end*
+ $"increasing_matches" = "patience_sort"("index_matches")$
+ *append* $(m, n)$ *to* $"increasing_matches"$
+ $"edit_script"$ *is* $"vector of" ("integer", "integer")$
+ $("prev_a_index", "prev_b_index") = (0, 0)$
+ *for* $("a_index", "b_index")$ *in* $"increasing_matches"$
+ $("a_delta", "b_delta") = ("a_index" - "prev_a_index", "b_index" - "prev_b_index")$
+ *if* $"a_delta" > 0 and "b_delta" > 0$
+ *append* $"patience"("prev_a_index", "prev_b_index", "a_delta", "b_delta")$ *to* $"edit_script"$
+ *else if* $"a_delta" > 0$
+ *append* $("a_delta", 0)$ *to* $"edit_script"$
+ *else if* $"b_delta" > 0$
+ *append* $(0, "b_delta")$ *to* $"edit_script"$
+ *end*
+ *if* $"a_index" = m and "b_index" = n$
+ *return* $"edit_script"$
+ *end*
+ *if* $($*last element of* $"edit_script")[0] = ($*last element of* $"edit_script")[1]$ {
+ $($*last element of* $"edit_script")[0] = ($*last element of* $"edit_script")[0] + 1$
+ $($*last element of* $"edit_script")[1] = ($*last element of* $"edit_script")[1] + 1$
+ *else*
+ *append* $(1, 1)$ *to* $"edit_script"$
+ *end*
+ $("prev_a_index", "prev_b_index") = ("a_index" + 1, "b_index" + 1)$
+ *end*
+ *end*
],
width: 100%
)
#block(
pseudocode-list[
+ *def* $"find_index_matches"(x, y, m, n)$
+ $"a_count"$ *is* $"map of gates to integers"$
+ $"a_index"$ *is* $"map of gates to integers"$
+ $"b_count"$ *is* $"map of gates to integers"$
+ $"b_index"$ *is* $"map of gates to integers"$
+ *for* i *in* 0 *to* m
+ $"a_count"[A[x + i]] = "a_count"[A[x + i]] + 1$
+ $"a_index"[A[x + i]] = i$
+ *end*
+ *for* i *in* 0 *to* n
+ $"b_count"[B[x + i]] = "b_count"[B[x + i]] + 1$
+ $"b_index"[B[x + i]] = i$
+ *end*
+ $"index_matches"$ *is* $"map of integers to integers"$
+ *for* $("gate", "count")$ *in* $"a_count"$
+ *if* $"count" = 1 and "b_count"["gate"] = 1$
+ $"index_matches"["a_index"["gate"]] = "b_index"["gate"]$
+ *end*
+ *end*
+ *return* $"index_matches"$
+ *end*
],
width: 100%
)
#block(
pseudocode-list[
+ *def* $"patience_sort"("index_matches")$
+ $"piles"$ *is* $"vector of vector of" ("integer", "integer", "integer")$
+ *for* $("a_index", "b_index")$ *in* $"index_matches"$
+ *if* $"piles"$ *is empty*
+ *append* $("a_index", "b_index", 0)$ *to* $"piles"$
+ *else*
+ *for* $i$ *in* 0 *to* *length of* $"piles"$ {
+ *if* $i =$ *length of* $"piles"$ {
+ *append* $("a_index", "b_index", ($*length of* $"piles"[i - 1]) - 1)$ *to* $"piles"$
+ *break*
+ *end*
+ *if* $($*last element of* $"piles"[i])[1] > "b_index"$
+ *append* $("a_index", "b_index", ($*length of* $"piles"[i - 1]) - 1)$ *to* $"piles"$
+ *break*
+ *end*
+ *end*
+ *end*
+ *end*
+ $"increasing_matches"$ *is* $"vector of" ("integer", "integer")$
+ $"prev_pile_element" =$ *length of* $($*last element of* $"piles") - 1$
+ *for* $"pile"$ *in* *reverse* $"piles"$
+ $"element" = "piles"["prev_pile_element"]$
+ *append* $("element"[0], "element"[1])$ *to* $"increasing_matches"$
+ $"prev_pile_element" = "element"[2]$
+ *end*
+ *return* $"increasing_matches"$
+ *end*
],
width: 100%
)
]
=== Adaptation of Diff Algorithms for QCEC
All of these algorithms had a common issue, however.
For a diff algorithm to be useful as an application scheme for @qcec, it must output a list of pairs of numbers describing the quantity of gates to apply from either circuit.
As demonstrated in the background and state of the art sections, the @dd\-based equivalence checker functions by alternating between applying a certain number of gates from the first circuit and the second circuit until all gates have been added and the identity @dd is once again produced.
A heuristic approach therefore needs to be able to determine how many gates to apply from either circuit in a single step.
This is contrary to the typical requirement of an edit script that describes insert, remove and keep operations.
These operations, however, correspond directly to the application:
- A removal operation in the edit script is analogous to the application of a gate from the left of the first circuit, expanding the @dd.
- An insertion operation in turn is analogous to the inverse application of a gate from the right of the second circuit, theoretically bringing the @dd closer to the identity again.
- Finally, A keep operation causes both applications simultaneously, which should leave the @dd unchanged.
Furthermore, the specifications of the actual gates that are being applied are redundant once the edit script has been found.
Only the application order is significant to the algorithm.
This results in a sequence consisting only of the operations "apply first", "apply second" and "apply both".
Sequences of identical operations can also be combined into a single operation as this does not affect the application order.
Each application operation can then be represented by a tuple of two values $(r, l)$, the first of which specifies the gates to be applied from the first circuit, and the other those from the second.
Additionally, the order of the gates in the second circuit must be inverted before calculating the edit script.
This is due to the "socks and shoes" rule of matrix inversion: For the product of two matrices $A$ and $B$ the equation $(A B) ^ (-1) = B ^ (-1) A ^ (-1)$ must hold.
The inversion of the product may be calculated by taking the inverse of each matrix and multiplying them in reverse order.
By induction the same is true for the product of any number of matrices.
As quantum gates and circuits are representations of matrices, the same rule applies to them as well.
The @dd\-based alternating equivalence checker therefore not only inverts each gate in the second circuit, but reverses their application order as well.
This means that the second circuit must also be reversed before applying the diff algorithm in order to find structural similarities between the first circuit and the inverse of the second circuit.
The following example illustrates these concepts graphically.
#example[
Keeping the same sequence as used in the previous examples, "hxhy" and "yhhx", @example_edit_script_conversion demonstrates the conversion of an edit script as produced by the discussed diff algorithms into a form useable by @qcec.
The edit script used is identical to the one found in @example_path.
#figure(
grid(
columns: (4fr, 2fr, 4fr, 2fr, 4fr),
align(horizon)[`+y` \ `+h` \ `=h` \ `=x` \ `-h` \ `-y`],
align(horizon)[$->$ \ convert],
align(horizon)[$(0, 1) \ (0, 1) \ (1, 1) \ (1, 1) \ (1, 0) \ (1, 0)$],
align(horizon)[$->$ \ simplify],
align(horizon)[$(0, 2) \ (2, 2) \ (2, 0)$]
),
kind: image,
caption: [Sample transformation of edit script operations into a sequence of gate applications.]
) <example_edit_script_conversion>
In this example, the second circuit is assumed to have been inverted beforehand.
The original circuit would have been "xhhy".
]
|
|
https://github.com/Robotechnic/alchemist | https://raw.githubusercontent.com/Robotechnic/alchemist/master/lib.typ | typst | MIT License | #import "@preview/cetz:0.2.2"
#import "src/default.typ": default
#import "src/utils.typ"
#import "src/drawer.typ"
#import "src/drawer.typ" : skeletize, draw-skeleton
#import "src/links.typ" : *
#import "src/molecule.typ" : *
#let transparent = color.rgb(100%,0,0,0)
/// === Molecule function
/// Build a molecule group based on mol
/// Each molecule is represented as an optional count followed by a molecule name
/// starting by a capital letter followed by an optional indice
/// #example(```
/// #skeletize({
/// molecule("H_2O")
/// })
///```)
/// It is possible to use an equation as a molecule. In this case, the spliting of the equation uses the same rules as in the string case. However, you can use parenthesis to group elements together.
/// #example(```
/// #skeletize({
/// molecule($C(C H_3)_3$)
/// })
///```)
/// - name (content): The name of the molecule. It is used as the cetz name of the molecule and to link other molecules to it.
/// - links (dictionary): The links between this molecule and previous molecules or hooks. The key is the name of the molecule or hook and the value is the link function.
///
/// Note that the antom-sep and angle arguments are ignored
/// - mol (string, equation): The string representing the molecule or an equation of the molecule
/// - vertical (boolean): If true, the molecule is drawn vertically
/// #example(```
/// #skeletize({
/// molecule("ABCD", vertical: true)
/// })
///```)
/// -> drawable
#let molecule(name: none, links: (:), vertical: false, mol) = {
let atoms = if type(mol) == str {
split-string(mol)
} else if mol.func() == math.equation {
split-equation(mol, equation: true)
} else {
panic("Invalid molecule content")
}
(
(
type: "molecule",
name: name,
atoms: atoms,
links: links,
vertical: vertical,
count: atoms.len(),
),
)
}
/// === Hooks
/// Create a hook in the molecule. It allows tu connect links to the place where the hook is.
/// Hooks are placed at the end of links or at the beginning of the molecule.
/// - name (string): The name of the hook
/// -> drawable
#let hook(name) = {
(
(
type: "hook",
name: name,
),
)
}
/// === Branch and cycles
/// Create a branch from the current molecule, the first element
/// of the branch has to be a link.
///
/// You can specify an angle argument like for links. This angle will be then
/// used as the `base-angle` for the branch.
///
/// #example(```
/// #skeletize({
/// molecule("A")
/// branch({
/// single(angle:1)
/// molecule("B")
/// })
/// branch({
/// double(angle: -1)
/// molecule("D")
/// })
/// single()
/// double()
/// single()
/// molecule("C")
/// })
///```)
#let branch(..args) = {
if args.pos().len() != 1 {
panic("Branch takes one positional argument: the body of the branch")
}
((type: "branch", draw: args.pos().at(0), args: args.named()),)
}
/// Create a regular cycle of molecules
/// You can specify an angle argument like for links. This angle will be then
/// the angle of the first link of the cycle.
///
/// The argument `align` can be used to force align the cycle according to the
/// relative angle of the previous link.
///
/// #example(```
/// #skeletize({
/// cycle(5, {
/// single()
/// double()
/// single()
/// double()
/// single()
/// })
/// })
///```)
#let cycle(..args) = {
if args.pos().len() != 2 {
panic("Cycle takes two positional arguments: number of faces and body")
}
let faces = args.pos().at(0)
if faces < 3 {
panic("A cycle must have at least 3 faces")
}
(
(
type: "cycle",
faces: faces,
draw: args.pos().at(1),
args: args.named(),
),
)
}
|
https://github.com/mismorgano/UG-DifferentialGeometry23 | https://raw.githubusercontent.com/mismorgano/UG-DifferentialGeometry23/main/Tareas/Tarea-04/Tarea-04.typ | typst | #let title = [
Geometría Diferencial\
Tarea 4
]
#let author = [
<NAME>
]
#let book = [
Differential Geometry of Curves and Surfaces
]
#set text(font: "New Computer Modern", size: 12pt)
#set enum(numbering: "a)")
#align(center, text(17pt)[
*#title*\
#author
])
Del libro *#book*.
== Problema 1
Muestra que la superficie $S = {(x, y, z) in RR^3: x^2 + y^2 -z^2 =0}$ no es regular.
*Demostración:*
Supongamos que $S$ es regular y consideremos una parametrización $X$ en $p=(0, 0, 0) in S$.
Entonces por la proposición 3 tenemos que existe una vecindad $V$ de $p$ en $S$ tal que es la gráfica de una
función diferenciable que tiene una de las siguientes tres formas $z=f(x, y)$, $y = g(x, z)$ o $x=h(y, z).$
Podemos notar $g$ y $h$ se pueden descartar pues la proyección de $S$ sobre
los planos $x z$ y $y z$ no son inyectivos. Entonces si existiera $f$ debería
coincidir con $z = plus.minus (x^2 + y^2)$ la cual no es siquiera una función.
Por lo tanto $S$ no es una superficie regular.
Otro argumento podría ser el siguiente:
Supongamos que $sigma: U -> S sect W$ es un homeomorfismo y sea $a = sigma^(-1)(p)$, podemos suponer que $U$ es una bola abierta con centro en $a$, pues $U$
es abierto. Entonces $W$ debe contener puntos $q_1$ con $z>0$ y $q_2$ con $z<0$, sean $b = sigma^(-1)(q_1)$ y $c = sigma^(-1)(q_2)$ y sea $gamma$ una curva en $U$ que una $b$ y $c$ y no pase por $a$ entonces la imagen de $gamma$ bajo $sigma$ esta contenida en $S$ y no pasa por $p$ ,lo cual no es posible.
== Problema 2
Sea $f(x, y, z) = (x+y+z-1)^2$.
+ Encuentra los puntos y valores críticos de $f$.
+ ¿Para qué valores de $c$ es el conjunto $f(x, y, z) = c$ una superficie regular?
+ Responde las preguntas a) y b) para la función $f(x, y, z) = x y z^2$.
*Solución:*
+ En este caso tenemos que dado $p = (x, y, z) in RR^3$ se cumple que $ dif f_p = nabla f(p) &= ((diff f)/(diff x)(p), (diff f)/(diff y)(p), (diff f)/(diff z)(p)) \
&= (2(x+y+z-1), 2(x+y+z-1), 2(x+y+z-1)) \
&= 2(x+y+z-1) dot vec(1, 1, 1), $
de donde podemos notar que $dif f_p$ es sobre si y solo si $2(x+y+z-1) != 0$
y por tanto $p$ es un punto critico si y solo si $2(x+y+z-1) = 0$, es decir,
si $x+y+z-1 = 0.$
Entonces si $p$ es un punto critico se cumple que $f(p) = 0$, lo cual
implica que $0$ es el único valor critico el cual corresponde al plano
$ {(x, y, z) in RR^3 | x+y+z-1 = 0}. $
+ Primero notemos que $f >= 0$ y además es sobre, por el inciso anterior $0$ es
el único valor critico, entonces si $c>0$ por la proposición 2
tenemos que $f^(-1)(c)$ es una superficie regular.
+ En este caso, si $p=(x, y, z) in RR^3$ tenemos que
$ dif f_p = nabla f(p) &= ((diff f)/(diff x)(p), (diff f)/(diff y)(p), (diff f)/(diff z)(p)) \
&= (y z^2, x z^2, 2x y z)\
&= z(y z, x z , 2x y), $
entonces $p$ es un punto critico si $ y z^2 = 0quad, x z^2 = 0 quad, 2x y z = 0, $
es decir, si y solo si $z = 0$ o $x=y=0$.
De lo anterior tenemos que los puntos críticos de $f$ son:
$ {(x, y, 0) in RR^3} union {(0, 0, z) in RR^3}. $
Podemos notar que si $p$ es un punto critico entonces $f(p) = 0.$
En este caso $f(RR^3) = RR$, por lo anterior $0$ es el único punto critico,
por lo cual si $c in RR minus{0}$, la proposición 2 nos dice que $f^(-1)(c)$
es una superficie regular.
== Problema 3
Encuentra una parametrización del hiperboloide de dos mantas ${(x, y, z) in RR^3: -x^2 -y^2 +z^2 = 1} $.
*Solución:*
Sea $ S = {(x, y, z) in RR^3: -x^2 -y^2 +z^2 = 1}, $
sabemos que $S$ es una superficie regular y consideremos las siguientes
parametrizaciones $sigma_plus.minus: RR^2 -> RR^3$ dadas por:
$ sigma_plus.minus (u, v) = (u, v, plus.minus sqrt(1+u^2+v^2)), $
podemos notar que $sigma_plus.minus$ son diferenciables, pues
tienen derivadas parciales continuas de todos los ordenes.
Además, dado $ p = (u, v) in RR^2$ tenemos que
$ dif sigma_(plus.minus ) (p) = mat((diff x)/(diff u), (diff x)/(diff v);
(diff y)/(diff u), (diff y)/(diff v); (diff z)/(diff u), (diff z)/(diff v))
= mat(1, 0;
0, 1;
plus.minus (2u)/sqrt(1+u^2+v^2), plus.minus (2v)/sqrt(1+u^2+v^2)), $
y se puede ver que las columnas son linealmente independientes para todo $p$,
entonces se cumple que $dif sigma_(plus.minus ) (p)$ es inyectiva.
Más aún podemos notar que $sigma_plus.minus$ son inyectivas, luego
por la por la proposición 4 tenemos que $sigma_plus.minus ^(-1)$ son continuas
y por tanto $sigma_plus.minus$ son parametrizaciones que cubren a $S$. |
|
https://github.com/jassielof/typst-templates | https://raw.githubusercontent.com/jassielof/typst-templates/main/apa7/template/main.typ | typst | MIT License | // #import "@preview/apa7:0.1.0": *
#import "../lib.typ": *
#show: apa7.with(
title: [American Psychological Association (APA) Style Template for Typst],
// // authors with different affiliations
// authors: (
// (
// name: [Author Name 1],
// affiliations: ("AF-1", "AF-2"),
// ),
// (
// name: [Author Name 2],
// affiliations: ("AF-3",),
// ),
// (
// name: [Author Name 3],
// affiliations: ("AF-4", "AF-5", "AF-6"),
// ),
// ),
// affiliations: (
// (
// id: "AF-1",
// name: [Affiliation Department 1],
// ),
// (
// id: "AF-2",
// name: [Affiliation Department 2],
// ),
// (
// id: "AF-3",
// name: [Affiliation Department 3],
// ),
// (
// id: "AF-4",
// name: [Affiliation Department 4],
// ),
// (
// id: "AF-5",
// name: [Affiliation Department 5],
// ),
// (
// id: "AF-6",
// name: [Affiliation Department 6],
// )
// ),
// authors with shared affiliations
authors: (
(
name: [Author Name 1],
affiliations: ("AF-1", "AF-2", "AF-3"),
),
(
name: [Author Name 3],
affiliations: ("AF-1", "AF-2", "AF-3"),
),
),
affiliations: (
(
id: "AF-1",
name: [Affiliation Department 1],
),
(
id: "AF-2",
name: [Affiliation Department 2],
),
(
id: "AF-3",
name: [Affiliation Department 3],
)
),
// custom-authors: [Author Name],
// custom-affiliations: [Affiliation Department, Affiliation Name],
// Student-specific fields
course: [Course Code: Course Name],
instructor: [Instructor Name],
// At the moment only supports English
due-date: datetime.today().display(),
// Professional-specific fields
running-head: [running head],
author-notes: [
#include-orcid([Author Name], "0000-0000-0000-0000")
#lorem(50)
],
keywords: ("APA", "template", "Typst"),
abstract: [
#lorem(100)
],
// Common fields
font-family: "Libertinus Serif",
font-size: 12pt,
region: "us",
language: "en",
paper-size: "us-letter",
implicit-introduction-heading: true, // wether to repeat the paper title as the introduction heading
toc: true,
)
#include "sections/introduction.typ"
#pagebreak()
#include "sections/lists.typ"
#pagebreak()
#include "sections/quotes.typ"
#pagebreak()
#include "sections/computer-code.typ"
#pagebreak()
#bibliography(
"bibliography/bibliography.bib",
full: true,
title: auto,
)
#pagebreak()
#include "sections/footnote.typ"
#pagebreak()
#include "sections/tables.typ"
#pagebreak()
#include "sections/figures.typ"
#show: addendum.with(
heading-numbering: "A.1.1.",
supplement: "Appendix",
)
#include "sections/appendix.typ" |
https://github.com/dead-summer/math-notes | https://raw.githubusercontent.com/dead-summer/math-notes/main/notes/Analysis/ch1-measures/construct-of-measures.typ | typst | #import "/book.typ": book-page
#import "../../../templates/conf.typ": *
#import "@preview/mitex:0.2.4": *
#show: thmrules.with(qed-symbol: $square$)
#show: book-page.with(title: "Construct of Measures")
= Construct of Measures
#def[
Let $#mi("\mathcal{A} \subset \mathcal{P}(X) ")$ be an algebra.
A function $#mi("\mu_0: \mathcal{A} \\to [0, +\infty]")$ is a premeasure iff
- $mu_0(#sym.emptyset.rev) = 0$,
- if ${A_j }_1^infinity subset.eq cal(A)$ is disjoint,
s.t. $union.big_1^infinity in cal(A)$ .
]
The goal of this section is to start
from $(X, cal(A), mu_0)$ to construct a measure on $sigma (A)$
that extends $mu_0$
#def[
An outer measure on $X$ is a function $mu^*: cal(P) -> [0, +infinity]$
s.t.
- $mu^* (diameter) = 0$,
- $mu^* (A) <= mu^*(B)$ if $A subset.eq B$,
- $mu^* (union.big _1^infinity A_j) <= sum_1^infinity mu^*(A_j)$.
(*$sigma$-subadditivity*)
]
It arises from approximately a set of "from the outside".
#prp[
Let $(X, cal(A), mu_0)$ be a premeasure space, then $forall E in X$,
$
mu^*(E) := inf{sum_(j=1)^infinity mu_0(A_j): A_j in cal(A), union.big _(j=1)^infinity A_j supset E}
$
defines an outer measure.
]
#def[
Say $A subset X$ satisfies separation condition [C] of Caratheodory iff
$
mu^*(E) = mu^*(E sect A) + mu^*(E without A), forall E subset X
$
where $mu^*$ is an outer measure.
]
#thm("Caratheodory's Theorem")[
Let $mu^*$ be an outer measure on $X$ . Then
$
cal(F) := {A subset X: mu^*(E) = mu^*(E sect A) + mu^*(E without A), forall E subset X}
$
is a $sigma$-algebra, and $mu^*|_cal(F)$ is a complete measure.
] |
|
https://github.com/r8vnhill/apunte-bibliotecas-de-software | https://raw.githubusercontent.com/r8vnhill/apunte-bibliotecas-de-software/main/Unit2/open_closed.typ | typst | == Clases Abiertas y Cerradas
=== Problema de la Base Frágil (Fragile Base Class Problem)
Este problema surge cuando cambios en una clase base causan que las clases derivadas dejen de funcionar correctamente.
Una causa común es la sobreescritura no intencionada de miembros de la clase base, lo que puede alterar el comportamiento esperado de las clases derivadas.
<NAME>, en su obra "Effective Java", resume este desafío con la frase: “Design and document for inheritance or else prohibit it”.
Esto sugiere que las clases deberían diseñarse con la herencia en mente o, de lo contrario, limitar quién puede extender de ellas para prevenir problemas.
=== Clases Abiertas y Cerradas
- *Clase Abierta:* En Kotlin, una clase es abierta a la extensión (puede ser heredada) solo si se marca explícitamente con la palabra clave `open`.
- *Clase Cerrada o Final:* Una clase es cerrada o final si no permite extensión. Esta es la configuración por defecto en Kotlin para evitar el problema de la base frágil inadvertidamente.
==== Métodos en Clases Abiertas
Los métodos en una clase abierta que se pueden sobreescribir deben ser marcados también como `open`.
Por el contrario, los métodos en una clase cerrada no necesitan esta marca, ya que no pueden ser heredados.
==== Clases y Métodos Abstractos
Las clases y métodos abstractos son intrínsecamente abiertos porque esperan ser completados en las clases derivadas.
=== Ejemplos de Clases Abiertas y Cerradas
*Clase Abierta:*
```kotlin
// Esta clase es abierta, así que puede ser heredada.
open class UniversityStudent(
name: String,
val university: String
) : AbstractStudent(name) {
override fun study() {
println("Studying at $university")
}
open fun party() {
println("Partying at $university")
}
}
```
*Clase Cerrada:*
```kotlin
// Esta clase es cerrada, así que no puede ser heredada.
class PhDStudent(
name: String,
university: String,
val thesisTopic: String
) : UniversityStudent(name, university) {
override fun study() {
println("I'm studying a lot!")
}
override fun party() {
println("I'm too busy to party!")
}
}
```
En el ejemplo de `PhDStudent`, se demuestra cómo una clase derivada puede sobrescribir métodos de su clase base abierta, pero al mismo tiempo, se declara como final para prevenir más herencia.
|
|
https://github.com/mrtz-j/typst-thesis-template | https://raw.githubusercontent.com/mrtz-j/typst-thesis-template/main/template/chapters/typst-basics.typ | typst | MIT License | #import "../utils/symbols.typ": LaTeX
This chapter will go into some basic features of the typst typesetting system, and how to use them in conjunction with this thesis template. Note that you should supplement this with the official guides on the typst website #footnote()[see #link("https://typst.app/docs/tutorial/")].
== Headings <subsec:headings>
We've already used headings a number of times in this template, and they are intuitive and easy to write. The syntax is markdown-like with `=` instead of `#` serving as its symbol. Chapters are the lowest depth headings, and this template styles them distinctly with a large graphic and new page, like we see here in @chp:typst_basics.
=== An even deeper heading <subsubsec:deepheading>
We can also create sections of various depths.
==== Super deep heading <subsubsubsec:superdeep>
@subsubsubsec:superdeep is an example of heading of depth 4. Note that we can also easily give headings labels and reference them anywhere in the document: We can for instance refer to @chp:introduction from here. The same applies to any kind of figure. We should also mention that the prefix in for instance `<subsec:headings>` is only a suggestion to keep your labels organized, you can call it whatever you want.
== Lists <subsec:lists>
As with headings, typst has syntactic sugar for lists so that we can use simple markdown-like syntax to create them. This goes for both ordered lists:
- One list item
- Another list item
- A sub-item
...as well as ordered lists:
1. A numbered list item
2. Another one
- Sub-items can go here too
== Other Nifty Features <subsec:nifty>
Creating *bold*, _italic_ and _*bold italic*_ text segments is also easily available with markdown-like syntax along with `inline code blocks`. In addition to this, a number of functions are available to achieve most of the textual styling. We can add #strike[strikethrough to our text], easily add #text(orange)[color] to it. We get subscripts#sub[like this] and superscripts#super[like this]. Typst also makes it easy to move characters around, for example to create the #LaTeX symbol (Take a look in the function in utils to see how it's achieved).
Footnotes #footnote()[These are useful for clickable links: #link("https://typst.app/docs/reference/model/footnote/")] are another useful feature natively supported in typst. Note that any function that takes content (anything inside `[brackets]`) allows us to use other functions in the content we give it. Look for example at this footnote #footnote()[_We can do *all sorts*_ of stuff in #text(blue)[here]]
For further reference, the typst official library reference, tutorial and guides along with the unofficial _Typst Examples Book_ found here #footnote()[see #link("https://sitandr.github.io/typst-examples-book/book/about.html")] are great resources.
#pagebreak(weak: true)
== Citing References <subsec:citing>
We can cite references defined in our bibliography file easily @QayyumY-sac2022. Once a reference is cited, it will appear in the bibliography at the end of the thesis.
|
https://github.com/VisualFP/docs | https://raw.githubusercontent.com/VisualFP/docs/main/SA/design_concept/content/poc/options_ui_haskellgi.typ | typst | #import "../../../acronyms.typ": ac
= Haskell-gi
#ac("GTK") is a widget toolkit that allows the creation of #ac("UI")s that work on
many popular operating systems. GTK widgets can be created programmatically or
with an XML #ac("UI") definition. @gtk_project
Haskell-gi is a Haskell library that offers bindings to GTK. The library allows
widget creation in a rather imperative style.
There also is a library that supports widget creation in a functional style
called 'gi-gtk-declarative'
#footnote("https://github.com/owickstrom/gi-gtk-declarative"), but that library
is still experimental. @haskell_gi
Using Haskell-gi to create the #ac("UI") of VisualFP would allow the frontend and
backend logic to be implemented in Haskell.
The downside to Haskell-gi is that #ac("GTK") is unknown to both authors and it
doesn't seem to be used as much as web-based frameworks, which could impact the
availability of documentation and examples.
|
|
https://github.com/jgm/typst-hs | https://raw.githubusercontent.com/jgm/typst-hs/main/test/typ/compiler/import-18.typ | typst | Other | // Error: 26-29 unexpected string
#import "module.typ": a, "b", c
|
https://github.com/TypstApp-team/typst | https://raw.githubusercontent.com/TypstApp-team/typst/master/tests/typ/layout/page-marginals.typ | typst | Apache License 2.0 | #set page(
paper: "a8",
margin: (x: 15pt, y: 30pt),
header: {
text(eastern)[*Typst*]
h(1fr)
text(0.8em)[_Chapter 1_]
},
footer: align(center)[\~ #counter(page).display() \~],
background: counter(page).display(n => if n <= 2 {
place(center + horizon, circle(radius: 1cm, fill: luma(90%)))
})
)
But, soft! what light through yonder window breaks? It is the east, and Juliet
is the sun. Arise, fair sun, and kill the envious moon, Who is already sick and
pale with grief, That thou her maid art far more fair than she: Be not her maid,
since she is envious; Her vestal livery is but sick and green And none but fools
do wear it; cast it off. It is my lady, O, it is my love! O, that she knew she
were! She speaks yet she says nothing: what of that? Her eye discourses; I will
answer it.
#set page(header: none, height: auto, margin: (top: 15pt, bottom: 25pt))
The END.
|
https://github.com/fathonix/praktikum_alpro | https://raw.githubusercontent.com/fathonix/praktikum_alpro/master/README.md | markdown | MIT License | # Laporan Praktikum Algoritme Pemrograman ITK
This repository holds a [Typst](https://typst.app) markup file
that is consist of the template and contents, with the
compiled PDF included.
The Typst layouting replicates the original .docx file layout
provided by ITK.
## Building
To build the template, only Make and Typst are needed. Run
`make prakalpro1.pdf` to build. Run `make dev` to have Typst
recompile when there is a file change. To build with the front
cover, you need [GhostScript](https://www.ghostscript.com)
installed to merge the PDFs. Simply run `make` to build it.
## TODOs
- Split template and contents into multiple files
- Replicate the front cover in Typst
## License
The template and build script are licensed under The MIT
License. The contents, however, remain proprietary. |
https://github.com/Sematre/typst-kit-thesis-template | https://raw.githubusercontent.com/Sematre/typst-kit-thesis-template/main/README.md | markdown | # typst-kit-thesis-template
A template for creating Master and Bachelor theses for students.
This projects tries to be close to the [original LaTeX version](https://www.overleaf.com/read/mvnctgvbnsrf).
However this is not an official template and this project is not affiliated with the KIT.
This template is not guaranteed to comply with the current KIT guidelines.
## Preview ([PDF version](https://raw.githubusercontent.com/wiki/Sematre/typst-kit-thesis-template/main.pdf))
| Title page | Outline |
|--------------------------------------------------------------------------------------------------------------|---------------------------------------------------------------------------------------------------------------|
|  |  |
| Content | |
|  |  |
| Bibliography | Appendix |
|  |  |
|
|
https://github.com/cetz-package/cetz-venn | https://raw.githubusercontent.com/cetz-package/cetz-venn/master/doc/style.typ | typst | Apache License 2.0 | #import "example.typ": example
#import "/src/lib.typ"
#import "@preview/tidy:0.1.0"
#import "@preview/t4t:0.3.2": is
#let show-function(fn, style-args) = {
[
#heading(fn.name, level: style-args.first-heading-level + 1)
#label(style-args.label-prefix + fn.name + "()")
]
let description = if is.sequence(fn.description) {
fn.description.children
} else {
(fn.description,)
}
let parameter-index = description.position(e => {
e.func() == heading and e.body == [parameters]
})
description = description.map(e => if e.func() == heading {
let fields = e.fields()
let label = fields.remove("label", default: none)
heading(level: style-args.first-heading-level + 1 + fields.remove("level"), fields.remove("body"), ..fields); [#label]
} else { e })
if parameter-index != none {
description.slice(0, parameter-index).join()
} else {
description.join()
}
set heading(level: style-args.first-heading-level + 2)
block(breakable: style-args.break-param-descriptions, {
heading("Parameters", level: style-args.first-heading-level + 2)
(style-args.style.show-parameter-list)(fn, style-args.style.show-type)
})
for (name, info) in fn.args {
let types = info.at("types", default: ())
let description = info.at("description", default: "")
if description == [] and style-args.omit-empty-param-descriptions { continue }
(style-args.style.show-parameter-block)(
name, types, description,
style-args,
show-default: "default" in info,
default: info.at("default", default: none),
)
}
if parameter-index != none {
description.slice(parameter-index+1).join()
}
}
#let show-parameter-block(name, types, content, show-default: true, default: none, in-tidy: false, ..a) = {
if type(types) != array {
types = (types,)
}
stack(dir: ttb, spacing: 1em,
// name <type> Default: <default>
block(breakable: false, width: 100%, stack(dir: ltr,
[#text(weight: "bold", name + [:]) #types.map(tidy.styles.default.show-type).join(" or ")],
if show-default {
align(right)[
Default: #raw(
lang: "typc",
// Tidy gives defaults as strings but outside of tidy we pass defaults as the actual values
if in-tidy { default } else { repr(default) }
)
]
}
)),
// text
block(inset: (left: .4cm), content)
)
}
#let show-type = tidy.styles.default.show-type
#let show-outline = tidy.styles.default.show-outline
#let show-parameter-list = tidy.styles.default.show-parameter-list
#let style = (
show-function: show-function,
show-parameter-block: show-parameter-block.with(in-tidy: true),
show-type: show-type,
show-outline: show-outline,
show-parameter-list: show-parameter-list
)
#let parse-show-module(path) = {
tidy.show-module(
tidy.parse-module(
read(path),
scope: (
example: example,
show-parameter-block: show-parameter-block,
cetz: lib
)
),
show-outline: false,
sort-functions: none,
style: style
)
}
|
https://github.com/0x1B05/nju_os | https://raw.githubusercontent.com/0x1B05/nju_os/main/lecture_notes/content/17_Linux进程的地址空间.typ | typst | #import "../template.typ": *
#pagebreak()
= Linux 进程的地址空间
== Linux 进程的地址空间
两个很基本 (但也很困难) 的问题
以下程序的 (可能) 输出是什么?
```c
printf("%p\n", main);
```
何种指针访问不会引发 segmentation fault?
```c
char *p = random();
*p; // 什么时候访问合法?
```
=== 查看进程的地址空间
pmap (1) - report memory of a process
- Claim: pmap 是通过访问 procfs (/proc/) 实现的
- 如何验证这一点?`strace`
查看进程的地址空间
- 等程序运行起来后 (gdb)，使用 `pmap` 命令查看地址空间
- 地址空间是若干连续的 “内存段”
- “段” 的内存可以根据权限访问
- 不在段内/违反权限的内存访问 触发 SIGSEGV
gpt 回答:what kind of tools can help me print out the address space of a linux
process?
- pmap
- cat /proc/[pid]/maps
- gdb
- readelf
- objdump
- lsof
- nm
==== minimal
```sh
❯ gcc -c minimal.S && ld minimal.o -o minimal && ./minimal
Hello, OS World
```
立刻执行完毕, 那应该怎么直接看地址空间呢?
1. 可以找个不会终止的程序, 例如 shell
2. 在 minimal 里面加个死讯和
3. gdb 来暂停, 在暂停的时候查看地址空间
```
starti -> 使得程序进入execve加载程序后的初始状态
layout asm -> 显示汇编
info inferiors-> 得到pid
!pmap pid
```
> `!`可以在 gdb 里面执行命令, 就像 vim 里面一样
```
(gdb) !pmap 6726
6726: .../minimal
0000000000400000 4K r---- minimal
0000000000401000 4K r-x-- minimal
00007ffff7ff9000 16K r---- [ anon ]
00007ffff7ffd000 8K r-x-- [ anon ]
00007ffffffde000 132K rw--- [ stack ]
total 164K
```
#image("images/2023-12-06-13-18-58.png")
这就解答了一开始的问题, 即哪些地址可以访问.
使用`cat /proc/[pid]/maps`
```
(gdb) !cat /proc/6726/maps
00400000-00401000 r--p 00000000 08:20 220712 .../minimal
00401000-00402000 r-xp 00001000 08:20 220712 .../minimal
7ffff7ff9000-7ffff7ffd000 r--p 00000000 00:00 0 [vvar]
7ffff7ffd000-7ffff7fff000 r-xp 00000000 00:00 0 [vdso]
7ffffffde000-7ffffffff000 rw-p 00000000 00:00 0 [stack]
```
`pmap`是通过`proc/[pid]/maps`实现的, 怎么证明? `strace pmap [pid]`,
可以发现里面有一段
```
openat(AT_FDCWD, "/proc/6726/maps", O_RDONLY) = 3
newfstatat(3, "", {st_mode=S_IFREG|0444, st_size=0, ...}, AT_EMPTY_PATH) = 0
read(3, "00400000-00401000 r--p 00000000 "..., 1024) = 515
write(1, "0000000000400000 4K r---- m"..., 390000000000400000 4K r---- minimal
) = 39
write(1, "0000000000401000 4K r-x-- m"..., 390000000000401000 4K r-x-- minimal
) = 39
write(1, "00007ffff7ff9000 16K r---- "..., 4200007ffff7ff9000 16K r---- [ anon ]
) = 42
write(1, "00007ffff7ffd000 8K r-x-- "..., 4200007ffff7ffd000 8K r-x-- [ anon ]
) = 42
write(1, "00007ffffffde000 132K rw--- "..., 4300007ffffffde000 132K rw--- [ stack ]
) = 43
read(3, "", 1024) = 0
close(3) = 0
```
`man 5 proc`手册获取更多信息.
==== hello
`gcc hello.c -static -o hello && gdb hello`
```gdb
(gdb) starti
Starting program: .../hello
Program stopped.
0x0000000000401650 in _start ()
(gdb) info inferiors
Num Description Connection Executable
* 1 process 8303 1 (native) .../hello
(gdb) !pmap 8303
8303: .../hello
0000000000400000 4K r---- hello
0000000000401000 604K r-x-- hello
0000000000498000 164K r---- hello
00000000004c1000 28K rw--- hello
00000000004c8000 20K rw--- [ anon ]
00007ffff7ff9000 16K r---- [ anon ]
00007ffff7ffd000 8K r-x-- [ anon ]
00007ffffffde000 132K rw--- [ stack ]
total 976K
(gdb) !cat /proc/8303/maps
00400000-00401000 r--p 00000000 08:20 220725 .../hello
00401000-00498000 r-xp 00001000 08:20 220725 .../hello
00498000-004c1000 r--p 00098000 08:20 220725 .../hello
004c1000-004c8000 rw-p 000c0000 08:20 220725 .../hello
004c8000-004cd000 rw-p 00000000 00:00 0 [heap]
7ffff7ff9000-7ffff7ffd000 r--p 00000000 00:00 0 [vvar]
7ffff7ffd000-7ffff7fff000 r-xp 00000000 00:00 0 [vdso]
7ffffffde000-7ffffffff000 rw-p 00000000 00:00 0 [stack]
```
猜测:
- 第一段是 ro 的 4KB -> elf 头
- 第二段 rx -> code
- 第三段 ro -> rodata
- 第四段 rw -> data
如何验证呢?
=== 操作系统提供查看进程地址空间的机制
RTFM: /proc/[pid]/maps (man 5 proc)
- 进程地址空间中的每一段
- 地址 (范围) 和权限 (rwxsp)
- 对应的文件: offset, dev, inode, pathname
- TFM 里有更详细的解释
- 和 readelf (-l) 里的信息互相验证
- 好的本能：做一些代码上的调整，观察 address space 的变化
- 堆 (bss) 内存的大小
- 栈上的大数组 v.s. memory error
在 hello.c 里面增加:
```c
#define MB * 1048576
char mem[64 MB];
```
`gcc hello.c -static -o hello && gdb hello`
```gdb
21197: .../hello
0000000000400000 4K r---- hello
0000000000401000 604K r-x-- hello
0000000000498000 164K r---- hello
00000000004c1000 28K rw--- hello
00000000004c8000 65556K rw--- [ anon ]
00007ffff7ff9000 16K r---- [ anon ]
00007ffff7ffd000 8K r-x-- [ anon ]
00007ffffffde000 132K rw--- [ stack ]
total 66512K
(gdb) !cat /proc/21197/maps
00400000-00401000 r--p 00000000 08:20 220725 .../hello
00401000-00498000 r-xp 00001000 08:20 220725 .../hello
00498000-004c1000 r--p 00098000 08:20 220725 .../hello
004c1000-004c8000 rw-p 000c0000 08:20 220725 .../hello
004c8000-044cd000 rw-p 00000000 00:00 0 [heap]
7ffff7ff9000-7ffff7ffd000 r--p 00000000 00:00 0 [vvar]
7ffff7ffd000-7ffff7fff000 r-xp 00000000 00:00 0 [vdso]
7ffffffde000-7ffffffff000 rw-p 00000000 00:00 0 [stack]
```
=== 更完整的地址空间映象
如果改成动态链接呢?
```gdb
21592: .../hello
0000555555554000 4K r---- hello
0000555555555000 4K r-x-- hello
0000555555556000 4K r---- hello
0000555555557000 8K rw--- hello
0000555555559000 65536K rw--- [ anon ]
00007ffff7fbd000 16K r---- [ anon ]
00007ffff7fc1000 8K r-x-- [ anon ]
00007ffff7fc3000 8K r---- ld-linux-x86-64.so.2
00007ffff7fc5000 168K r-x-- ld-linux-x86-64.so.2
00007ffff7fef000 44K r---- ld-linux-x86-64.so.2
00007ffff7ffb000 16K rw--- ld-linux-x86-64.so.2
00007ffffffde000 132K rw--- [ stack ]
total 65948K
(gdb) bt
#0 0x00007ffff7fe3290 in _start () from /lib64/ld-linux-x86-64.so.2
#1 0x0000000000000001 in ?? ()
#2 0x00007fffffffe121 in ?? ()
#3 0x0000000000000000 in ?? ()
```
在这个进程状态机被创建的一瞬间, 还没有`printf`, 而 pc 位于`/lib64/ld-linux-x86-64.so.2`.
静态链接初始化之后, pc 是 elf 文件里标记的 entry, 而动态链接实际上有个
interpreter, 这个解释器就是`/lib64/ld-linux-x86-64.so.2`.(用另外一个程序来执行当前的程序.所以他就是一个加载器
loader.)
在 main 上面打个断点再 continue 查看.
```gdb
(gdb) !pmap 22293
22293: .../hello
0000555555554000 4K r---- hello
0000555555555000 4K r-x-- hello
0000555555556000 4K r---- hello
0000555555557000 4K r---- hello
0000555555558000 4K rw--- hello
0000555555559000 65536K rw--- [ anon ]
00007ffff7d80000 12K rw--- [ anon ]
00007ffff7d83000 160K r---- libc.so.6
00007ffff7dab000 1620K r-x-- libc.so.6
00007ffff7f40000 352K r---- libc.so.6
00007ffff7f98000 16K r---- libc.so.6
00007ffff7f9c000 8K rw--- libc.so.6
00007ffff7f9e000 52K rw--- [ anon ]
00007ffff7fbb000 8K rw--- [ anon ]
00007ffff7fbd000 16K r---- [ anon ]
00007ffff7fc1000 8K r-x-- [ anon ]
00007ffff7fc3000 8K r---- ld-linux-x86-64.so.2
00007ffff7fc5000 168K r-x-- ld-linux-x86-64.so.2
00007ffff7fef000 44K r---- ld-linux-x86-64.so.2
00007ffff7ffb000 8K r---- ld-linux-x86-64.so.2
00007ffff7ffd000 8K rw--- ld-linux-x86-64.so.2
00007ffffffde000 132K rw--- [ stack ]
total 68176K
```
libc 归来! 使用 strace
查看动态链接和静态链接的程序发现两者的差距很大.静态链接很快就开始执行代码,
但是动态链接有很多操作, 这很多操作都是为了把需要的库搬到地址空间.
更改 hello.c:
```c
```
```gdb
(gdb) !pmap 22909
22909: .../hello
0000555555554000 4K r---- hello
0000555555555000 4K r-x-- hello
0000555555556000 4K r---- hello
0000555555557000 8K rw--- hello
00007ffff7fbd000 16K r---- [ anon ]
00007ffff7fc1000 8K r-x-- [ anon ]
00007ffff7fc3000 8K r---- ld-linux-x86-64.so.2
00007ffff7fc5000 168K r-x-- ld-linux-x86-64.so.2
00007ffff7fef000 44K r---- ld-linux-x86-64.so.2
00007ffff7ffb000 16K rw--- ld-linux-x86-64.so.2
00007ffffffde000 132K rw--- [ stack ]
total 412K
(gdb) !cat /proc/22909/maps
555555554000-555555555000 r--p 00000000 08:20 220726 .../hello
555555555000-555555556000 r-xp 00001000 08:20 220726 .../hello
555555556000-555555557000 r--p 00002000 08:20 220726 .../hello
555555557000-555555559000 rw-p 00002000 08:20 220726 .../hello
7ffff7fbd000-7ffff7fc1000 r--p 00000000 00:00 0 [vvar]
7ffff7fc1000-7ffff7fc3000 r-xp 00000000 00:00 0 [vdso]
7ffff7fc3000-7ffff7fc5000 r--p 00000000 08:20 59431 /usr/lib/x86_64-linux-gnu/ld-linux-x86-64.so.2
7ffff7fc5000-7ffff7fef000 r-xp 00002000 08:20 59431 /usr/lib/x86_64-linux-gnu/ld-linux-x86-64.so.2
7ffff7fef000-7ffff7ffa000 r--p 0002c000 08:20 59431 /usr/lib/x86_64-linux-gnu/ld-linux-x86-64.so.2
7ffff7ffb000-7ffff7fff000 rw-p 00037000 08:20 59431 /usr/lib/x86_64-linux-gnu/ld-linux-x86-64.so.2
7ffffffde000-7ffffffff000 rw-p 00000000 00:00 0 [stack]
```
问 gpt `vvar`和`vdso`是什么?
In a Linux process memory space, `vvar` and `vdso` are two special regions that
serve important system-level functions:
1. vvar: `vvar` stands for "virtual dynamic shared object section." It is a small
region of memory reserved for the kernel to store certain variables that are
used by the process but need to be kept separate from the process's own data.
These variables include the thread-local storage (TLS) pointer, which points to
the thread-specific data area (TSD) used by the thread-local storage mechanism.
The `vvar` region is mapped into the process's memory space when the process is
started, and its address is fixed at `0xffffffffff600000`. This address is
outside the normal user-space address range and is reserved for kernel use.
- The current time(`time_t`)
- The page size of the system
- The process's CPU clock frequency
- ....
2. vdso: `vdso` stands for "virtual dynamic shared object." It is another special
region of memory that contains a set of system call wrappers implemented in
userspace, allowing user applications to directly access some frequently used
kernel functions without having to switch to kernel mode via the `syscall` instruction.
This method is faster and more efficient than traditional system call
invocation, as it avoids expensive context switches between user and kernel
modes. The `vdso` region is also mapped into the process's memory space at a
fixed address (`0x7fffb5f77000` on x86-64 architectures), and it is loaded into
the process's memory by the kernel during process startup. The contents of `vdso` are
updated dynamically by the kernel to reflect changes in the kernel's
implementation of system calls, so they always match the running kernel version.
- `gettimeofday()`
> 即不进入内核的系统调用.
=== RTFM (5 proc): 我们发现的宝藏
vdso (7): Virtual system calls: 只读的系统调用也许可以不陷入内核执行。
无需陷入内核的系统调用
- 例子: `time (2)`
- 时间：内核维护秒级的时间 (所有进程映射同一个页面)
- 例子: `gettimeofday (2)`
- [ RTFSC
](https://elixir.bootlin.com/linux/latest/source/lib/vdso/gettimeofday.c#L49)
(非常聪明的实现)
- 更多的例子：问 GPT 吧！
- 计算机系统里没有魔法！我们理解了进程地址空间的全部！
可以调试一下, 了解更多细节(如何实现不进入内核的系统调用). 例如可以看到`vdso`地址附近都是系统调用:
#image("images/2023-12-06-16-39-15.png")
== 进程地址空间管理
=== 地址空间 = 带访问权限的内存段
操作系统应该提供一个修改进程地址空间的系统调用
```c
// 映射
// 增加一段
void *mmap(void *addr, size_t length, int prot, int flags,
int fd, off_t offset);
// 删除一段
int munmap(void *addr, size_t length);
// 修改映射权限
int mprotect(void *addr, size_t length, int prot);
```
本质：在状态机状态上增加/删除/修改一段可访问的内存
- `mmap`: 可以用来申请内存 (`MAP_ANONYMOUS`)，也可以把文件 “搬到” 进程地址空间中
=== 把文件映射到进程地址空间?
Everything is a (file|descriptor); file is a descriptor.
文件描述符是操作系统对象的指针. 那`mmap`就可以把文件的实在内容搬到内存里面取.
在一定的限度下, 文件里的内容和内存里的数据是可以同步的.
它们的确好像没有什么区别
- 文件 = 字节序列 (操作系统中的对象)
- 内存 = 字节序列
- 操作系统允许映射好像挺合理的……
- 带来了很大的方便
- ELF loader 用 `mmap` 非常容易实现
- 解析出要加载哪部分到内存，直接 `mmap` 就完了
- 我们的 loader 的确是这么做的 (strace)
=== 使用 mmap
==== Example 1: 申请大量内存空间
```c
#include <unistd.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <sys/mman.h>
#define GiB * (1024LL * 1024 * 1024)
int main() {
volatile uint8_t *p = mmap(NULL, 8 GiB, PROT_READ | PROT_WRITE,
MAP_ANONYMOUS | MAP_PRIVATE, -1, 0);
printf("mmap: %lx\n", (uintptr_t)p);
if ((intptr_t)p == -1) {
perror("cannot map");
exit(1);
}
*(p + 2 GiB) = 1;
*(p + 4 GiB) = 2;
*(p + 7 GiB) = 3;
printf("Read get: %d\n", *(p + 4 GiB));
printf("Read get: %d\n", *(p + 6 GiB));
printf("Read get: %d\n", *(p + 7 GiB));
}
```
- 瞬间完成内存分配
- 只是在操作系统里面*标记*分配的连续的 8G 内存是属于该进程的.
并没有实际分配.第一次进行内存访问的时候, 处理器会发生一个异常(内存不存在,
因为没有分配.), 异常交给 OS 执行, 由于之前`mmap`已经声明了, 于是可以分配 1 page
的内存.然后进程就可以继续运行了. > 用多少内存, 就分配多少内存.
- `mmap`/`munmap` 为 `malloc`/`free` 提供了机制
- `libc` 的大 `malloc` 会直接调用一次 `mmap` 实现
- 不妨 `strace`/`gdb` 看一下
==== Example 2: Everything is a file
- 映射大文件, 只访问其中的一小部分
```c
with open('/dev/sda', 'rb') as fp:
mm = mmap.mmap(fp.fileno(),
prot=mmap.PROT_READ, length=128 << 30)
hexdump.hexdump(mm[:512])
```
映射磁盘的 128G 内存, 把前 512 字节打印出来.可以看到末尾的`55AA`说明是个可启动的磁盘.
=== Memory-Mapped File: 一致性
但我们好像带来了一些问题……
- 如果把页面映射到文件
- 修改什么时候生效?
- 立即生效：那会造成巨大量的磁盘 I/O
- `unmap` (进程终止) 时生效：好像又太迟了……
- 若干个映射到同一个文件的进程?
- 共享一份内存?
- 各自有本地的副本?
请查阅手册，看看操作系统是如何规定这些操作的行为的
- 例如阅读 `msync` (2)
- 这才是操作系统真正的复杂性
== 🌶️ 入侵进程地址空间
=== Hacking Address Spaces
进程 (M,R 状态机) 在 “无情执行指令机器” 上执行
- 状态机是一个封闭世界
- 但如果允许一个进程对其他进程的地址空间有访问权?
- 意味着可以任意改变另一个程序的行为
- 听起来就很 cool
一些入侵进程地址空间的例子
- 调试器 (gdb)
- gdb 可以任意观测和修改程序的状态
- Profiler (perf)
- 合理的需求，操作系统就必须支持 → Ask GPT!
=== 入侵进程地址空间 (0): 金手指
如果我们能直接物理劫持内存，不就都解决了吗?
- 听起来很离谱，但 “卡带机” 时代的确可以做到！
#image("images/2023-12-06-18-50-20.png")
> ROM 只能 load, RAM 可以 load/store
Game Genie: 一个 Look-up Table (LUT)
- 当 CPU 读地址 a 时读到 x，则替换为 y
- [ NES Game Genie Technical Notes
](https://tuxnes.sourceforge.net/gamegenie.html) ([ 专利
](https://patents.google.com/patent/EP0402067A2/en), [ How did it work?
](https://www.howtogeek.com/706248/what-was-the-game-genie-cheat-device-and-how-did-it-work/))
- 今天我们有 [ Intel Processor Trace
](https://perf.wiki.kernel.org/index.php/Perf_tools_support_for_Intel®\_Processor_Trace)
> 物理外挂, 简单稳定有效.
=== 入侵进程地址空间 (1): 金山游侠
在进程的内存中找到代表 “金钱”, “生命” 的重要属性并且改掉
包含非常贴心的 “游戏内呼叫” 功能
- 它就是游戏的 (阉割版) “调试器”
- 我们也可以在 Linux 中实现它 (man 5 proc)
> 第一次扫描内存里的金钱数, 会有许多匹配. 减少/增加了钱数, 再扫描相应的钱数, 就可以直接找到相应的存储金钱的地址.
=== 入侵进程地址空间 (2): 按键精灵
大量重复固定的任务 (例如 2 秒 17 枪)
这个简单，就是给进程发送键盘/鼠标事件
- 做个驱动 (可编程键盘/鼠标)
- 利用操作系统/窗口管理器提供的 API
- #link("https://github.com/jordansissel/xdotool")[ xdotool ] (我们用这玩意测试 vscode
的插件)
- #link("https://www.kernel.org/doc/html/latest/input/input.html")[ evdev ]
(按键显示脚本；主播常用)
=== 入侵进程地址空间 (3): 变速齿轮
调整游戏的逻辑更新速度
比如某[ 神秘公司
](https://baike.baidu.com/item/台湾天堂鸟资讯有限公司/8443017)慢到难以忍受的跑图和战斗
本质：程序是状态机
#image("images/2023-12-06-19-04-32.png")
- 除了 syscall，是不能感知时间的
- 只要 “劫持” 和时间相关的 syscall，就能改变程序对时间的认识
- 原则上程序仍然可以用间接信息 “感知” 的 (就想表调慢了一样)
=== 定制游戏外挂
“劫持代码” 的本质是 debugger 行为
游戏也是程序，也是状态机 外挂就是 “为这个游戏专门设计的 gdb” 修改 API 调用的值
```c
set_alarm(1000 / FPS); // 希望改成 100 / FPS
```
锁定生命值
- 最简单的生命值锁定是 spin modify
- 还是可能出现 hp < 0 的判定 (尤其是一刀秒的时候)
```c
hp -= damage; // 希望 “消除” 此次修改
if (hp < 0) game_over();
```
=== 代码注入 (hooking)
用一段代码 “勾住” 程序的执行
技术，无论是计算机系统、编程语言还是人工智能，都是给人类带来福祉的。但越强大的技术就也有越 “负面” 的用途。使用游戏外挂破坏游戏的平衡性、利用漏洞入侵计算机系统，或是用任何技术占他人之先、损害他人的利益，都是一件可耻的事情。
|
|
https://github.com/bennyhandball/PA1_LoB_Finance | https://raw.githubusercontent.com/bennyhandball/PA1_LoB_Finance/main/PA/supercharged-dhbw/2.1.0/check-attributes.typ | typst | #let check-attributes(
title,
authors,
language,
at-university,
confidentiality-marker,
type-of-thesis,
type-of-degree,
show-confidentiality-statement,
show-declaration-of-authorship,
show-table-of-contents,
show-acronyms,
show-list-of-figures,
show-list-of-tables,
show-code-snippets,
show-appendix,
show-abstract,
show-header,
show-title-in-header,
show-left-logo-in-header,
show-right-logo-in-header,
show-header-divider,
numbering-alignment,
toc-depth,
acronym-spacing,
abstract,
appendix,
acronyms,
university,
university-location,
supervisor,
date,
city,
bibliography,
bib-style,
logo-left,
logo-right,
logo-size-ratio,
) = {
if (title == none or title == "") {
panic("Title is missing. Specify a title in the 'title' attribute of the template.")
}
let boolean-attributes = (
at-university: at-university,
show-confidentiality-statement: show-confidentiality-statement,
show-table-of-contents: show-table-of-contents,
show-acronyms: show-acronyms,
show-declaration-of-authorship: show-declaration-of-authorship,
show-list-of-figures: show-list-of-figures,
show-list-of-tables: show-list-of-tables,
show-code-snippets: show-code-snippets,
show-appendix: show-appendix,
show-abstract: show-abstract,
show-header: show-header,
show-title-in-header: show-title-in-header,
show-left-logo-in-header: show-left-logo-in-header,
show-right-logo-in-header: show-right-logo-in-header,
show-header-divider: show-header-divider,
)
for (key, attribute) in boolean-attributes {
if (type(attribute) != bool) {
panic("Attribute '" + key + "' is invalid. Specify 'true' or 'false' in the '" + key + "' attribute of the template.")
}
}
let string-attributes = (
university: university,
university-location: university-location,
)
for (key, attribute) in string-attributes {
if (type(attribute) != str or attribute.len() == 0) {
panic("Attribute '" + key + "' is missing. Specify a " + key + " in the '" + key + "' attribute of the template.")
}
}
let optional-string-attributes = (
type-of-thesis: type-of-thesis,
type-of-degree: type-of-degree,
bib-style: bib-style,
)
for (key, attribute) in optional-string-attributes {
if (attribute != none and (type(attribute) != str or attribute.len() == 0)) {
panic("Attribute '" + key + "' is invalid. Specify a string in the '" + key + "' attribute of the template.")
}
}
if (type(confidentiality-marker) != none) {
if (
type(confidentiality-marker) != dictionary or
"display" not in confidentiality-marker or
type(confidentiality-marker.display) != bool
) {
panic("Confidentiality marker is invalid. Specify a dictionary in the 'confidentiality-marker' attribute of the template containing a 'display' attribute with a boolean value.")
}
}
let length-attributes = (
acronym-spacing: acronym-spacing,
)
if ("offset-x" in confidentiality-marker) {
length-attributes.insert("offset-x (confidentiality-marker)", confidentiality-marker.offset-x)
}
if ("offset-y" in confidentiality-marker) {
length-attributes.insert("offset-y (confidentiality-marker)", confidentiality-marker.offset-y)
}
if ("size" in confidentiality-marker) {
length-attributes.insert("size (confidentiality-marker)", confidentiality-marker.size)
}
if ("title-spacing" in confidentiality-marker) {
length-attributes.insert("title-spacing (confidentiality-marker)", confidentiality-marker.title-spacing)
}
for (key, attribute) in length-attributes {
if (type(attribute) != length) {
panic("Attribute '" + key + "' is invalid. Specify a length in the '" + key + "' attribute of the template.")
}
}
if (authors == none or authors == ()) {
panic("Author is missing. Specify authors in the 'authors' attribute of the template.")
}
let max-authors = if at-university {
8
} else {
6
}
if (
(type-of-thesis != none and type-of-thesis != "") or
(type-of-degree != none and type-of-degree != "") or
(confidentiality-marker.display == true)
) {
max-authors -= 2
}
if (authors.len() > max-authors) {
panic("Too many authors. Specify a maximum of " + str(max-authors) + " authors in the 'authors' attribute of the template. To increase the maximum number of authors (max. 8), change one of the following attributes: 'at-university', 'type-of-thesis', 'type-of-degree'. (See the package documentation for more information.)")
}
for author in authors {
if (
"name" not in author or
author.name == none or
author.name == ""
) {
panic("Author name is missing. Specify a name for each author in the 'authors' attribute of the template.")
}
if (
"student-id" not in author or
author.student-id == none or
author.student-id == ""
) {
panic("Student ID of '" + author.name + "' is missing. Specify a student ID for each author in the 'authors' attribute of the template.")
}
if (
"course" not in author or
author.course == none or
author.course == ""
) {
panic("Course of '" + author.name + "' is missing. Specify a course for each author in the 'authors' attribute of the template.")
}
if (
"course-of-studies" not in author or
author.course-of-studies == none or
author.course-of-studies == ""
) {
panic("Course of studies of '" + author.name + "' is missing. Specify a course of studies for each author in the 'authors' attribute of the template.")
}
if (at-university) {
if ("company" in author) {
panic("Company of '" + author.name + "' is not allowed. Remove the 'company' object from the author.")
}
if (type(city) != str or city == "") {
panic("City is invalid. Specify a string containing a city in the 'city' attribute.")
}
} else {
if (type(city) == str) {
panic("Remove the City attribute. When 'at-university' is true the city inside the company object is used.")
}
if ("company" not in author) {
panic("Author '" + author.name + "' is missing a company. Add the 'company' object to the author.")
}
}
}
if (language != "en" and language != "de") {
panic("Language is invalid. Specify 'en' for English or 'de' for German in the 'language' attribute of the template.")
}
if (type(numbering-alignment) != alignment) {
panic("Numbering alignment is invalid. Specify a alignment in the 'numbering-alignment' attribute of the template.")
}
if (type(toc-depth) != int) {
panic("TOC depth is invalid. Specify an integer in the 'toc-depth' attribute of the template.")
}
if (type(date) != datetime and (type(date) != array or date.len() != 2 or type(date.at(0)) != datetime or type(date.at(1)) != datetime)) {
panic("Date is invalid. Specify a datetime in the 'date' attribute of the template to display a specific date or use a array containing two datetime elements to display a date range.")
}
let image-attributes = (
logo-left: logo-left,
logo-right: logo-right
)
for (key, attribute) in image-attributes {
if (type(attribute) != content and attribute != none) {
panic("Attribute '" + key + "' is invalid. Specify an image in the '" + key + "' attribute of the template.")
}
}
if (type(logo-size-ratio) != str or logo-size-ratio.len() == 0) {
panic("Logo size ratio is missing. Specify a ratio in the 'logo-size-ratio' attribute of the template.")
}
let ratio = logo-size-ratio.split(":")
if (ratio.len() != 2) {
panic("Invalid ratio. Specify a ratio in the format 'x:y' in the 'logo-size-ratio' attribute of the template.")
}
if (type(bibliography) != content and bibliography != none) {
panic("Bibliography is invalid. Specify a bibliography in the 'bibliography' attribute of the template.")
}
if (type(supervisor) != dictionary or
("company" not in supervisor or supervisor.company == none or supervisor.company == "") and
("university" not in supervisor or supervisor.university == none or supervisor.university == "")
) {
panic("Supervisor(s) is/are invalid. Specify a supervisor either for the company and/or the university in the 'supervisor' attribute of the template.")
}
} |
|
https://github.com/Myriad-Dreamin/typst.ts | https://raw.githubusercontent.com/Myriad-Dreamin/typst.ts/main/fuzzers/corpora/text/raw_11.typ | typst | Apache License 2.0 |
#import "/contrib/templates/std-tests/preset.typ": *
#show: test-page
//
// // Unterminated.
// // Error: 1-2:1 unclosed raw text
// `endless |
https://github.com/EpicEricEE/typst-marge | https://raw.githubusercontent.com/EpicEricEE/typst-marge/main/tests/parameter/format/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(3)
#sidenote(format: it => [(#it.counter.display(it.numbering)) #it.body])[
Sidenote with parenthesized number.
]
#lorem(10)
#sidenote(format: it => smallcaps(it.default))[
Small caps sidenote.
]
#lorem(10)
#sidenote(format: it => text(red, it.default))[
Sidenote with red text and number.
]
#lorem(5)
|
https://github.com/frectonz/the-pg-book | https://raw.githubusercontent.com/frectonz/the-pg-book/main/book/035.%20usa.html.typ | typst | usa.html
Made in USA
November 2004(This is a new essay for the Japanese edition of
Hackers
& Painters.
It tries to explain why Americans make some things well
and others badly.)A few years ago an Italian friend of mine travelled by train from
Boston to Providence. She had only been in America for a
couple weeks and hadn't seen much of the country yet. She arrived
looking astonished. "It's so ugly!"People from other rich countries can scarcely imagine
the squalor of the man-made bits of America. In travel books
they show you mostly natural environments: the Grand Canyon,
whitewater rafting, horses in a field. If you see
pictures with man-made things in them, it will be either a
view of the New York skyline shot from a discreet distance,
or a carefully cropped image of a seacoast town in Maine.How can it be, visitors must wonder. How can the richest country
in the world look like this?Oddly enough, it may not be a coincidence. Americans are good
at some things and bad at others. We're good at making
movies and software, and bad at making cars and cities.
And I think we may be good at what we're good at for the same
reason we're bad at what we're bad at. We're impatient.
In America, if you want to do something, you don't worry that
it might come out badly, or upset delicate social balances, or
that people might think you're getting above yourself. If you
want to do something, as Nike says, just do it.This works well in some fields and badly in others. I suspect
it works in movies and software because they're both messy
processes. "Systematic"
is the last word I'd use to describe the way
good programmers write software.
Code is not something they assemble painstakingly after
careful planning, like the pyramids. It's something they
plunge into, working fast and constantly changing their minds,
like a charcoal sketch.In software, paradoxical
as it sounds, good craftsmanship means working fast.
If you work slowly and meticulously,
you merely end up with a very fine implementation of your initial,
mistaken idea.
Working slowly and meticulously is
premature optimization. Better to get a
prototype done fast, and see what new ideas
it gives you.It sounds like making movies works a lot like making software.
Every movie is a Frankenstein, full of imperfections
and usually quite different from what was originally envisioned.
But interesting, and finished fairly quickly. I think we get away with this in movies and software
because they're both malleable mediums. Boldness pays.
And if at the last minute two parts don't quite
fit, you can figure out some hack that will at least conceal
the problem.Not so with cars, or cities. They are all too physical.
If the car business worked like software or movies, you'd
surpass your competitors by making a car that weighed only
fifty pounds, or folded up to the size of a motorcycle when
you wanted to park it. But with physical products there are
more constraints. You don't win by dramatic innovations
so much as by good taste and attention to detail.The trouble is, the very word "taste"
sounds slightly ridiculous to American ears.
It seems pretentious, or frivolous, or even effeminate.
Blue staters think it's "subjective," and red staters
think it's for sissies. So anyone in America
who really cares about design will be sailing upwind.Twenty years ago we used to hear that the problem with
the US car industry was the workers.
We don't hear that any more now that Japanese companies
are building cars in the US. The problem with
American cars is bad design. You can see that just by
looking at them.All that extra sheet metal on the AMC Matador wasn't
added by the workers. The problem
with this car, as with American cars today, is that it was
designed by marketing people instead of designers.Why do the Japanese make better cars than us? Some say it's
because their culture encourages cooperation. That may come
into it. But in this case it seems more to the point that
their culture prizes design and craftsmanship.For centuries the Japanese have made finer things than we
have in the West. When you look at swords they
made in 1200, you just can't believe the date on the label
is right.
Presumably their cars fit together more
precisely than ours for the same reason their joinery always has.
They're obsessed with making things well.Not us.
When we make something in America, our aim is just to get the
job done. Once we reach that point, we take one of two routes.
We can stop there, and have something crude but
serviceable, like a Vise-grip. Or we can improve it,
which usually means encrusting it with gratuitous ornament.
When we want to make a car "better,"
we stick tail fins on it, or make it
longer, or make the
windows smaller, depending on the current fashion.Ditto for houses. In America you can have either a flimsy box banged
together out of two by fours and drywall, or a McMansion-- a
flimsy box banged together out of two by fours and drywall,
but larger, more dramatic-looking, and full of expensive fittings.
Rich people don't get better design or craftsmanship;
they just get a larger, more conspicuous version of the
standard house.We don't especially prize design or craftsmanship here. What
we like is speed, and we're willing to do something in an ugly
way to get it done fast. In some
fields, like software or movies, this is a net win.
But it's not just that software and movies are malleable mediums.
In those businesses, the designers (though they're
not generally called that) have more power.
Software companies, at least successful ones, tend to be run
by programmers. And in the film industry, though producers
may second-guess directors, the director controls most of
what appears on the screen.
And so American software and movies, and Japanese cars, all
have this in common: the people in charge care about
design-- the former because the designers are in charge, and the latter
because the whole culture cares about design.I think most Japanese executives would be horrified at
the idea of making a bad car. Whereas American executives,
in their hearts, still believe the most important thing about
a car is the image it projects.
Make a good car? What's "good?" It's so subjective.
If you want to know how to design a car, ask a focus group.Instead of relying on their own internal design compass
(like <NAME> did),
American car companies try to make what marketing people
think consumers want. But it isn't working. American cars continue
to lose market share. And the reason is that the customer
doesn't want what he thinks he wants.Letting focus groups design your cars for you
only wins in the short term. In the long term, it pays
to bet on good design. The focus group may say they want the
meretricious feature du jour, but what they want even more is
to imitate sophisticated buyers, and they, though a
small minority, really do care about good design.
Eventually the
pimps and drug dealers notice that the doctors and lawyers
have switched from Cadillac to Lexus, and do the same.Apple is an interesting counterexample to the general
American trend. If you want to buy a nice CD player, you'll
probably buy a Japanese one. But if you want to buy an
MP3 player, you'll probably buy an iPod. What happened?
Why doesn't Sony dominate MP3 players? Because Apple is
in the consumer electronics business now, and unlike
other American companies, they're obsessed with good design.
Or more precisely, their CEO is.I just got an iPod, and it's not just nice. It's
surprisingly nice. For it to surprise me, it must be
satisfying expectations I didn't know I had. No focus
group is going to discover those. Only a great
designer can.Cars aren't the worst thing we make in America.
Where the just-do-it model fails most dramatically is in our cities-- or
rather, exurbs.
If real estate developers operated on a large enough scale, if
they built whole towns, market forces would compel
them to build towns that didn't suck. But they only build a
couple office buildings or suburban streets at a time, and the
result is so depressing that the inhabitants consider it a great
treat to fly to Europe and spend a couple weeks living what
is, for people there, just everyday life. [1]But the just-do-it model does have advantages. It seems the clear
winner for generating wealth and technical innovations
(which are practically the same thing). I think speed is the reason.
It's hard to create wealth by making a commodity. The
real value is in things that are new, and if you want to
be the first to make something, it helps to work fast.
For better or worse, the just-do-it model is fast,
whether you're <NAME> writing the prototype of VisiCalc in
a weekend, or a real estate developer
building a block of shoddy condos in a month.If I had to choose between the just-do-it model and the
careful model, I'd probably choose just-do-it.
But do we have to choose? Could we have it both ways?
Could Americans have nice
places to live without undermining the impatient, individualistic spirit
that makes us good at software? Could other countries
introduce more individualism into their technology companies
and research labs without having it metastasize as strip malls?
I'm optimistic. It's harder to
say about other countries, but in the US, at least, I think
we can have both.Apple is an encouraging example. They've managed to preserve
enough of the impatient, hackerly spirit you need to write
software. And yet when
you pick up a new Apple laptop, well, it doesn't
seem American. It's too perfect. It seems as if it
must have been made by a Swedish or a Japanese company.In many technologies, version 2 has higher resolution. Why
not in design generally? I think we'll gradually see
national characters superseded
by occupational characters: hackers in Japan will be allowed
to behave with a willfulness
that would now seem unJapanese,
and products in America will be designed with an
insistence on taste that would now seem unAmerican.
Perhaps the most successful countries, in the future, will be
those most willing to ignore what are now considered
national characters, and do each kind of work in the way
that works best. Race you.Notes[1] Japanese cities are ugly too, but for different reasons.
Japan is prone to earthquakes, so buildings are traditionally
seen as temporary; there is no grand tradition of city planning
like the one Europeans inherited from Rome. The other cause is
the notoriously corrupt relationship between the government
and construction companies.Thanks to <NAME>, <NAME>, <NAME>,
<NAME>, <NAME>, <NAME>, <NAME>,
and <NAME>
for reading drafts of this.American GothicThe John Rain Books
|
|
https://github.com/i-am-wololo/cours | https://raw.githubusercontent.com/i-am-wololo/cours/master/main/parties_i23/CalculBool.typ | typst | #import "../templates.typ": *
#title("logique de boole")
= Algebre de boole
soit $BB$ un enssemble munit d'une structure algebrique, on l'appelle algebre de boole.
#definition(title:"")[on appelle booleen toute variable defini sur un ensemble a deux elements]
Pour simplifier l'ecriture des expressions logique, l'operande $not$ peut etre ecrit de cette facon: $macron(x)$. et on a
#table(columns: (auto, auto, auto),
$x$, $0$, $1$,
$macron(x)$, $1$, $0$
)
dans le cadre de l'algebre de Boole, un litterale designe la aussi une variable $x$ (litteral positif) ou sa negation $macron(x)$ (litteral negatif)
== Proprietes de calcul
on dispose des nombreuses proprietess suivantes heritees du calcul propositionnel:
#text[#set enum(numbering:"1.")
+ associativite: $(a+b)+C = a+(b+c) = a+b+c$
+ commutativite $a+ b = b+a$
+ distributivite $a(b+c) = a b+(a c)$
+ idempotence: $a+a+a+a...=a$ et $a a a.... = a$
+ element neutre: $a+0=0+a=a$ et $a 1=1 a =a$
+ absorption $0 a = a$ et $1 + a = 1$
+ simplifcication: $a + macron(a) b = a+b$ et $a (macron(a) + b)= a b$
+ redondance: $a b +macron(a) c = a b + macron(a) c + b c$ et $(a+b)(macron(a)+c)=(a+b)(tilde(a)+c)(b+c)$
+ DeMorgan: $macron(a b) = macron(a) + macron(b)$
+ Involution: $macron(macron(a))= a$
+ tiers exclu: $macron(a) + a =1$
+ non contradiction: $a macron(a) = 0$
]
on retrouve les cinq autres operateur binaire, implication, equifvvalence, disjonction exclusive, non conjenction et non disjonction:
$ a => b = tilde(a) +b, \
a <=> b = (tilde(a) + b) (a+ tilde(b)) \
a xor b = ( a+b)(tilde(a)+tilde(b)) \
a arrow.t b = tilde(a b) \
a arrow.b b = tilde(a + b) \
$
qui ont les tables de verite:
#table( columns: ( auto, auto, auto),
$=>$, $0$, $1$,
$0$, $1$, $1$,
$1$, $0$, $1$
)
#table( columns: ( auto, auto, auto),
$<=>$, $0$, $1$,
$0$, $1$, $0$,
$1$, $0$, $1$
)
#table( columns: ( auto, auto, auto),
$xor$, $0$, $1$,
$0$, $0$, $1$,
$1$, $1$, $0$
)
#table( columns: ( auto, auto, auto),
$arrow.t$, $0$, $1$,
$0$, $1$, $1$,
$1$, $1$, $0$
)
#table( columns: ( auto, auto, auto),
$arrow.b$, $0$, $1$,
$0$, $1$, $0$,
$1$, $0$, $0$
)
= Definitions:
#definition(title:"antilogie")[L'antilogie est le cas ou une formule repond toujours faux, a l'inverse de la tautologie qui répond toujours vrai]
= Code Gray
#definition(title:"Code Gray")[]
= Minterme, maxterme
#definition(title:"Minterme, Maxterme")[on appelle Minterme toute fonction d'ordre n, prenant une seule fois la valeur 1]
|
|
https://github.com/haxibami/haxipst | https://raw.githubusercontent.com/haxibami/haxipst/main/src/resume/resume.typ | typst | #import "../lib/set-metadata.typ": *
#import "../lib/better-indent.typ": *
#import "../lib/better-heading.typ": *
#let resume(
pdf-title: none,
pdf-author: (),
pdf-keywords: (),
pdf-date: auto,
title: none,
author: [],
date: [],
size: "a4",
pagenum: true,
header: [],
indent: true,
lang: "ja",
region: "JP",
font-serif: (
"Linux Libertine",
"Latin Modern Math",
"Latin Modern Roman",
"Noto Serif CJK JP",
"serif",
),
font-sans: (
"Liberation Sans",
"Noto Sans CJK JP",
),
font-emoji: (
"Twitter Color Emoji",
),
font-mono: (
"Liberation Mono",
"Noto Sans Mono CJK JP",
"monospace",
),
font-size: 10pt,
spacing: 1.5em,
tight: false,
heading-inset: none,
body,
) = {
// set PDF metadata
show: set-metadata.with(
pdf-title: if (
pdf-title == none
) {
title
} else {
pdf-title
},
pdf-author: pdf-author,
pdf-keywords: pdf-keywords,
pdf-date: pdf-date,
)
// language, font family & size
set text(
lang: lang,
region: region,
size: font-size,
font: (
..font-serif,
..font-sans,
..font-emoji,
),
)
set enum(indent: 1em)
set table(inset: 0.8em)
set list(marker: (
[•],
[▹],
[»],
[--],
))
// page size
set page(paper: size)
// header
set page(header: [
#set text(8pt)
#header
]) if header != []
set page(numbering: "1") if pagenum
// heading
show: better-heading.with(
font: font-sans,
tight: tight,
inset-y: heading-inset,
)
// title, date, author
align(
center,
text[
#set text(font: font-sans)
#title
#v(0.5em)
],
)
align(
right,
text[
#date
],
)
align(
right,
text[
#author
],
)
// inline code style
show raw.where(block: false): it => {
set text(font: font-mono)
box(
fill: luma(240),
inset: (
x: 3pt,
y: 0pt,
),
outset: (
y: 3pt,
),
radius: 2pt,
)[#it]
}
// code block style
show raw.where(block: true): it => {
set text(font: font-mono)
block(
fill: luma(240),
inset: 10pt,
radius: 4pt,
)[#it]
}
// code block style
// show raw.where(block: true): block.with(
// fill: luma(240),
// inset: 10pt,
// radius: 4pt,
// )
// link style
show link: it => {
underline(
offset: 3pt,
text(
blue,
it,
),
)
}
// paragraph style
show par: set block(spacing: spacing)
set par(leading: 1em)
show: better-indent.with(
indent: indent,
length: 1em,
spacing: spacing,
font-size: font-size,
)
body
}
|
|
https://github.com/katamyra/Notes | https://raw.githubusercontent.com/katamyra/Notes/main/Personal%20Notes/DeepLearning/Modules/Introduction.typ | typst | #import "../../../template.typ": *
= Introduction
*Machine Learning* is the study of algorithms that can learn from experience, typically in the form of observational data or interactions with an environment, its performance improves.
Core components that follow us around, no matter what kind of machine learning we tackle:
+ The _data_ that we can learn from
+ A _model_ of how to transform the data
+ An _objective function_ that quantifies how well (or badly) the model is doing
+ An _algorithm_ to adjust the model's parameters to optimize the objective function
#note[
*Data*
Each data point/instance consists of a set of attributes called _features_ (or co-varies/inputs)/
In supervised learning, our goal is the predict the value of a special attribute, called the _label/target_ which is not part of the model's input.
In cases when every example is characterized by the same number of numerical features, we say that the inputs are fixed-length vectors and we call the constant length of the vectors the _dimensionality_ of the data. However, often we have to work with varying lengths of data.
]
By *model*, we denote the computational machinery for ingesting data of one type, and spitting out predictions of a possibly different type. Specifically, we are interested in _statistical models_ that can be estimated from data.
_Deep learning is differentiated from the classical approaches principally by the set of power models that it focuses on_. We often chain many successive transformations of the data from top to bottom.
#note[
In order to develop a formal mathematical system for learning machines, we need to have objective functions to see how good or bad our models our. We often define objective functions so that lower is better by convention, which is why we call them _loss functions_.
When trying to predict numerical values, we can often use _squared error_ as a loss function, but for classification, the most common objective function is to minimize error rate (% of wrong predictions). *During optimization, we think of the loss as a function of the model's parameters, and treat the training dataset as a constant*. We will learn the best values of our model's parameters by minimize the loss incurred on a set consisting of some number of examples collected for training.
]
We typically want to split the available data into a _training dataset_ and a _test set_ which is held for evaluation. When a model performs well on the training set but fails to generalize unseen data, we say that it is *overfitting* on training data.
Now, once we have a data source, a model, and a well defined objective function, we need an algorithm capable of searching for the best possible parameters for minimizing the loss function. Popular optimization algorithms for deep learning are based on an approach known as *gradient descent*
#definition[
*Gradient Descent*: an optimization algorithm where the method check to see (at each step) for each parameter, how that training set would change if you perturbed that parameter by just a small amount. It then updates the parameter in a direction that lowers the loss.
Neural Networks and other complicated models often have many hundreds or thousands of inputs, so using calculus/statistics to find the minimum is often not feasible. Instead, we start at any old input and find the slope of the function where you are, and shift towards the direction that minimizes the loss.
However, there are many local minimums we can land in (see below) and we might not actually get the most minimum.
#image("../Images/LocalMinimums.png", width: 90%)
]
This carries over to neural networks, and its really hard to find the absolute minimum.
Note: if you make your step sizes proportional to the slope, then as your slope flattens out your steps get smaller and smaller to help you from overshooting.
When we add more inputs, we instead want to use the idea of *gradient*, which is the direction of the steepest increase and also tells us just how steep it is. We can use this to move our parameters in the opposite direction of the steepest increase and know how much to move it.
Steps:
+ Compute #sym.triangle.stroked.b C
+ Small step in - #sym.triangle.stroked.b C direction
+ Repeat
#sym.triangle.stroked.b C is a vector that tells us how to "nudge" all weights and biases to cause the most rapid decrease to the cost function. The sign of each value in the vector tells us which direction to move it.
== Kinds of Machine Learning
*Supervised learning* describes tasks where we are given a dataset containing both features and labels and asked to produce a model that predicts the labels when given input features.
The supervision comes into play because for choosing parameters we produce the model with a dataset consisting of labeled examples. We are interested in estimating the conditional probability of a label given input features.
When labels take on arbitrary numerical values (even if its within some interval), we consider this to be a *regression problem*.
In most our chapters, we will try to learn models that minimize the squared error loss function.
In *classification*, we want our model to look at features and predict which category/class it belongs to.
*Reinforcement learning* gives a very general statement of a problem in which an agent interacts with an environment over a series of time steps. At each step, the agent receives some _observation_ from the environment and must chose an _action_ that is subsequently transmitted back into the environment leading to some reward by the ML model. |
|
https://github.com/vEnhance/1802 | https://raw.githubusercontent.com/vEnhance/1802/main/r14.typ | typst | MIT License | #import "@local/evan:1.0.0":*
#show: evan.with(
title: [Notes for 18.02 Recitation 14],
subtitle: [18.02 Recitation MW9],
author: "<NAME>",
date: [23 October 2024],
)
#quote(attribution: [Lemony Snicket, in A Series of Unfortunate Events])[The world is quiet here.]
This handout (and any other DLC's I write) are posted at
#url("https://web.evanchen.cc/1802.html").
= Reading
You should read section 21 of LAMV for the full details, which don't fit on the page.
The following are just excerpts for quick reference.
= Recipes
#recipe(title: [Recipe for integrating over a rectangle])[
To integrate something of the form $int (int dif y) dif x$:
1. Evaluate the inner integral as in 18.01, treating $x$ as constant.
2. You should get something only depending on $x$. Integrate it as in 18.01.
]
#recipe(title: [Recipe for converting to $x y$-integration])[
1. Draw a picture of the region as best you can.
2. Write the region as a list of inequalities.#footnote[I don't
think other sources always write the inequalities the way I do.
But I think this will help you a lot with making sure bounds go the right way.]
3. Pick _one_ of $x$ and $y$, and use your picture to describe all the values it could take.
4. Solve for the _other_ variable in all the inequalities.
]
= Pictures for the example from Poonen's notes
#sample[
Show both ways of setting up an integral of a function $f(x,y)$
over the region bounded by $y-x=2$ and $y=x^2$.
]
Here the region would be described as $y >= x^2$ and $y-x <= 2$.
#align(center)[
#image("figures/ints-pararegion.png", width: 50%)
]
#align(center)[
#table(
columns: 2,
align: left,
stroke: none,
[#image("figures/ints-para-vert.png", width: 90%)],
[#image("figures/ints-para-horiz.png", width: 90%)],
),
]
= Recitation questions from official course
/ 1.: Calculate the double integral of the function $f (x , y) = 6 x^2 + 2 y$
over the rectangle $R = [0 , 2] times [- 1 , 1]$. Use both vertical and
horizontal slicings and check you get the same answer.
/ 2.: Let $R$ be the first-quadrant region bounded by the two curves
$y = sqrt(x)$ and $y = x^3$. Compute in two different ways the double
integral $ iint_R x y^2 dif A . $
/ 3.: Let $R$ be the (bounded) region between the parabola $y^2 = x$ and the
line through $(2 , 0)$ having slope $1$. Find the points where the
curves intersect and describe the region $R$ in terms of horizontal
slices and vertical slices. Express the double integral
$ iint_R f (x , y) dif A$ as an iterated integral in both
ways, using both horizontal and vertical slicings.
In the second case, you will have to write the integral in two pieces.
|
https://github.com/GYPpro/Java-coures-report | https://raw.githubusercontent.com/GYPpro/Java-coures-report/main/Report/3.typ | typst | #set text(font:("Times New Roman","Source Han Serif SC"))
#show raw.where(block: false): box.with(
fill: luma(240),
inset: (x: 3pt, y: 0pt),
outset: (y: 3pt),
radius: 2pt,
)
// Display block code in a larger block
// with more padding.
#show raw.where(block: true): block.with(
fill: luma(240),
inset: 10pt,
radius: 4pt,
)
#set math.equation(numbering: "(1)")
#set text(
font:("Times New Roman","Source Han Serif SC"),
style:"normal",
weight: "regular",
size: 13pt,
)
#set page(
paper:"a4",
number-align: right,
margin: (x:2.54cm,y:4cm),
header: [
#set text(
size: 25pt,
font: "KaiTi",
)
#align(
bottom + center,
[ #strong[暨南大学本科实验报告专用纸(附页)] ]
)
#line(start: (0pt,-5pt),end:(453pt,-5pt))
]
)
#show raw: set text(
font: ("consolas", "Source Han Serif SC")
)
= UID管理器
\
#text("*") 实验项目类型：设计性\
#text("*")此表由学生按顺序填写\
#text(
font:"KaiTi",
size: 15pt
)[
课程名称#underline[#text(" 面向对象程序设计/JAVA语言 ")]成绩评定#underline[#text(" ")]\
实验项目名称#underline[#text(" UID管理器 ")]指导老师#underline[#text(" 干晓聪 ")]\
实验项目编号#underline[#text(" 1 ")]实验项目类型#underline[#text(" 设计性 ")]实验地点#underline[#text(" 数学系机房 ")]\
学生姓名#underline[#text(" 郭彦培 ")]学号#underline[#text(" 2022101149 ")]\
学院#underline[#text(" 信息科学技术学院 ")]系#underline[#text(" 数学系 ")]专业#underline[#text(" 信息管理与信息系统 ")]\
实验时间#underline[#text(" 2023年10月27日上午 ")]#text("~")#underline[#text(" 2023年10月27日中午 ")]\
]
#set heading(
numbering: "一、"
)
#set par( first-line-indent: 1.8em)
= 实验目的
\
#h(1.8em)熟悉基础的面向对象知识，包括成员变量、方法，访问控制与构造函数
= 实验环境
\
#h(1.8em)计算机：PC X64
操作系统：Windows
编程语言：Java
IDE：Visual Studio Code
= 程序原理
\
#h(1.8em)提供三种类型的UID生成、申请与维护。
+ 基于日期的UID，例如2022101149
+ 完全无序的类激活码，例如AA2CA-STBS3-AED2P-RDGSSP
+ 按顺序发放的序列，可选固定位数，例如00001,00002
#h(1.8em)可以保证所有UID不会重复。
类中储存所有UID对应的引用。
申请复杂度O(1)，引用复杂度O(log(n))
测试用例的控制台规则：
中括号内为需要填入字符串，尖括号为可选参数，默认为列表第一个。
#figure(
table(
columns: 2,
align: left+horizon,
[```shell-unix-generic
getUID <type: "date" | "code" | "seq"> [name]
```],[申请对应类型的新UID，并与一个引用名称name绑定],
[```shell-unix-generic
secUID <type: "date" | "code" | "seq"> [UID]
```],[查找UID对应的引用名称]
)
)
= 程序代码
文件：`sis2\UIDmanager.java`实现了`UIDmanager`类
```java
package sis2;
import java.text.SimpleDateFormat;
import java.util.Date;
import java.util.HashMap;
import java.util.Random;
public class UIDmanager {
private HashMap<String,Object> dateHM = new HashMap<String, Object>();
private HashMap<String,Object> codeHM = new HashMap<String, Object>();
private HashMap<String,Object> seqHM = new HashMap<String, Object>();
final Random rd = new Random();
final Integer DATENUM_LENGTH;
final Integer SEQ_LENGTH;
final Integer CODE_LENGTH;
private Integer nextDataNum = 0;
private Integer nextSeq = 0;
private char getRandChar()
{
int flg = rd.nextInt(26+10);
if(flg < 10) return (char)(48+flg);
else return (char)(55+flg);
}
public UIDmanager()
{
DATENUM_LENGTH = 4;
SEQ_LENGTH = 10;
CODE_LENGTH = 5;
}
public UIDmanager(int _SEQ_LENGTH,int _DATENUM_LENGTH,int _CODE_LENGTH)
{
DATENUM_LENGTH = _DATENUM_LENGTH;
SEQ_LENGTH = _SEQ_LENGTH;
CODE_LENGTH = _CODE_LENGTH;
}
public String nextDate(Object c)
{
Date date = new Date();
SimpleDateFormat sf = new SimpleDateFormat("yyMMdd");
String s = sf.format(date);
nextDataNum++;
Integer tmp = nextDataNum;
StringBuffer sb = new StringBuffer();
for(int i = 0;i < DATENUM_LENGTH;i ++)
{
sb.append(tmp % 10);
tmp /= 10;
}
String rt = s + sb.reverse().toString();
dateHM.put(rt, c);
return rt;
}
public String nextDate()
{
Date date = new Date();
SimpleDateFormat sf = new SimpleDateFormat("yyMMdd");
String s = sf.format(date);
nextDataNum++;
Integer tmp = nextDataNum;
StringBuffer sb = new StringBuffer();
for(int i = 0;i < DATENUM_LENGTH;i ++)
{
sb.append(tmp % 10);
tmp /= 10;
}
String rt = s + sb.reverse().toString();
return rt;
}
public String nextCode(Object c)
{
StringBuffer rt = new StringBuffer();
for(int k = 0;k < 4;k ++)
{
for(int i = 0;i < CODE_LENGTH;i ++)
{
rt.append(getRandChar());
}
if(k != 3)rt.append('-');
}
codeHM.put(rt.toString(), c);
return rt.toString();
}
public String nextCode()
{
StringBuffer rt = new StringBuffer();
for(int k = 0;k < 4;k ++)
{
for(int i = 0;i < CODE_LENGTH;i ++)
{
rt.append(getRandChar());
}
if(k != 3)rt.append('-');
}
return rt.toString();
}
public String nextSeq(Object c)
{
StringBuffer rt = new StringBuffer();
nextSeq ++;
Integer tmp = nextSeq;
for(int i = 0;i < SEQ_LENGTH;i ++)
{
rt.append(tmp % 10);
tmp /= 10;
}
seqHM.put(rt.reverse().toString(), c);
return rt.toString();
}
public String nextSeq()
{
StringBuffer rt = new StringBuffer();
nextSeq ++;
Integer tmp = nextSeq;
for(int i = 0;i < SEQ_LENGTH;i ++)
{
rt.append(tmp % 10);
tmp /= 10;
}
return rt.reverse().toString();
}
public Object secDate(String uid) throws Exception
{
return dateHM.get(uid);
}
public Object secCode(String uid) throws Exception
{
return codeHM.get(uid);
}
public Object secSeq(String uid) throws Exception
{
return seqHM.get(uid);
}
public void bindUID(String uid,Object c) throws Exception
{
if(uid.length() == 4 + DATENUM_LENGTH) dateHM.put(uid, c);
else if(uid.length() == 4 + CODE_LENGTH * 4) codeHM.put(uid, c);
else if(uid.length() == SEQ_LENGTH) seqHM.put(uid, c);
else throw new Exception("UID格式错误\n");
}
}
```
文件：`sis2\test.java`用于实现指令交互的测试
```java
package sis2;
import java.util.Scanner;
public class Test {
public static void main(String[] args) {
UIDmanager uidm = new UIDmanager();
try (Scanner sc = new Scanner(System.in)) {
for(;;)
{
String cmd = sc.next();
if(cmd.equals("getUID"))
{
String type = sc.next();
if(type.equals("date"))
{
String name = sc.next();
System.out.println(uidm.nextDate(name));
}
else if(type.equals("code"))
{
String name = sc.next();
System.out.println(uidm.nextCode(name));
}
else if(type.equals("seq"))
{
String name = sc.next();
System.out.println(uidm.nextSeq(name));
}
}
else if(cmd.equals("secUID"))
{
String type = sc.next();
if(type.equals("date"))
{
String uid = sc.next();
System.out.println(uidm.secDate(uid));
}
else if(type.equals("code"))
{
String uid = sc.next();
System.out.println(uidm.secCode(uid));
}
else if(type.equals("seq"))
{
String uid = sc.next();
System.out.println(uidm.secSeq(uid));
}
} else break;
}
sc.close();
} catch (Exception e) {
e.printStackTrace();
}
}
}
```
= 出现的问题、原因与解决方法
\
#h(1.8em)编码过程十分顺利
= 测试数据与运行结果
#figure(
table(
align: left + horizon,
columns: 3,
[*输入*],[*输出*],[*解释*],
[`getUID date GYP`],[`2312150001`],[生成了一个基于当前日期的UID并且与GYP绑定],
[`getUID code program_by_GYP`],[`7EFBG-GM1E6-8KFL9-7MU08`],[生成一个随机串并与program_by_GYP绑定],
[`getUID seq seq1`],[`0000000001`],[生成一个顺序编号的ID并与seq1绑定],
[`getUID seq seq2`],[`0000000002`],[生成一个顺序编号的ID并与seq2绑定],
[`secUID date ??`],[`UID格式错误`],[查询UID时使用了错误格式],
[`secUID date 2312150001`],[`GYP`],[查询到2312150001所绑定的数据为GYP],
[`secUID code 7EFBG-GM1E6-8KFL9-7MU08`],[`program_by_GYP`],[查询到7EFBG-GM1E6-8KFL9-7MU08所绑定的数据为program_by_GYP]
)
) |
|
https://github.com/jgm/typst-hs | https://raw.githubusercontent.com/jgm/typst-hs/main/test/typ/text/features-00.typ | typst | Other | // Test turning kerning off.
#text(kerning: true)[Tq] \
#text(kerning: false)[Tq]
|
https://github.com/EvanLuo42/rcore-notes | https://raw.githubusercontent.com/EvanLuo42/rcore-notes/main/Chapter%201/main.typ | typst | #import "template.typ": *
#show: project.with(
title: "应用程序与基本执行环境"
)
= 操作系统启动流程
== 第一阶段
加电后 PC 寄存器（Program Counter；用于执行汇编指令）被设置为 ROM 的物理地址。随后会运行 ROM 当中存储的程序，即固件（Firmware）。固件被用于初始化 CPU 状态，如各寄存器的初始值，以及从硬盘中加载 bootloader 程序。最后将 PC 设置为 bootloader 程序的地址，并跳转以转移控制权。
== 第二阶段
bootloader 和固件所做的事情相似。它同样会初始化一些寄存器状态，并将操作系统代码从硬盘中取出，最后把 PC 寄存器设置为操作系统地址，移交控制权。
== 第三阶段
操作系统将会承担后续控制步骤。
= 程序内存布局与编译流程
== 程序内存布局
#figure(
image("figures/memory-layout.png", width: 70%),
caption: [内存布局]
) <memory-layout>
一个程序被编译成可执行文件后，可执行文件大致分为两部分：代码与数据。代码为一条条可以被 CPU 执行的命令，数据则是一些可以被 CPU 读取的内存空间。在 @memory-layout 中，代码只占 `.text` 这一小部分，其余的部分全部为数据部分。数据部分可以根据功能被分为更小的单位：*段*（Section）。不同的段被放置在不同的位置上，这构成了程序的*内存布局*（Memory Layout）。
其中，@memory-layout 中的几个段分别用于以下几个功能：
- 程序当中以初始化的全局数据为 `.rodata` 与 `.data`。前者用于存放只读的全局数据，如常数、常量、字符串等。后者用于存放可修改的全局数据。
- 未初始化数据段 `.bss` 用于保存程序中未初始化的全局数据。通常 `.bss` 会被程序加载者进行零初始化，即将该区域字节全部设置为零。
- 堆（Heap）用于存放程序运行时动态存放的数据。它向高地址增长。
- 栈（Stack）用于存放函数调用时的上下文以及函数中的局部变量。它向低地址增长。
== 编译流程
从源代码到可执行文件的编译流程大致有以下几个阶段：
+ 编译器（Compiler）将每个源文件从某门高级编程语言转化为汇编语言，注意此时源文件仍然是一个 ASCII 或其他编码的文本文件。
+ 汇编器（Assembler）会将上一步生成文件中的汇编指令转化为机器码，得到一个二进制的目标文件（Object File）。
+ 链接器（Linker）会将上一步获得的所有目标文件以及一些外部的目标文件链接在一起形成一个完整的可执行文件。
#figure(
image("figures/link-sections.png", width: 70%),
caption: [链接器工作原理]
) <link-sections>
链接器会做如下几件事情：
+ 将来自不同目标文件的段在目标内存布局中重新排列，一般按照段功能排列。
+ 将符号替换为具体地址。在模块化编程中，我们会暴露给其他模块一些函数以及全局变量。他们的名字被称作符号。在源代码级别，我们只需要知道对应的符号即可访问对应的函数和变量。而在机器码级别，我们并不能通过符号来寻找对应的函数和变量。因此在链接过程中我们需要把符号转化为对应的地址。
|
|
https://github.com/Coekjan/typst-upgrade | https://raw.githubusercontent.com/Coekjan/typst-upgrade/master/tests/exception2/entry.incompat.typ | typst | MIT License | #strong[
#import "@preview/pack1:1.1.1": pack
here is strong text, #pack.
]
#import "@preview/pack3:3.0.0": pack3
#syntax-error-node-here(
|
https://github.com/typst/packages | https://raw.githubusercontent.com/typst/packages/main/packages/preview/unichar/0.1.0/ucd/block-1F600.typ | typst | Apache License 2.0 | #let data = (
("GRINNING FACE", "So", 0),
("GRINNING FACE WITH SMILING EYES", "So", 0),
("FACE WITH TEARS OF JOY", "So", 0),
("SMILING FACE WITH OPEN MOUTH", "So", 0),
("SMILING FACE WITH OPEN MOUTH AND SMILING EYES", "So", 0),
("SMILING FACE WITH OPEN MOUTH AND COLD SWEAT", "So", 0),
("SMILING FACE WITH OPEN MOUTH AND TIGHTLY-CLOSED EYES", "So", 0),
("SMILING FACE WITH HALO", "So", 0),
("SMILING FACE WITH HORNS", "So", 0),
("WINKING FACE", "So", 0),
("SMILING FACE WITH SMILING EYES", "So", 0),
("FACE SAVOURING DELICIOUS FOOD", "So", 0),
("RELIEVED FACE", "So", 0),
("SMILING FACE WITH HEART-SHAPED EYES", "So", 0),
("SMILING FACE WITH SUNGLASSES", "So", 0),
("SMIRKING FACE", "So", 0),
("NEUTRAL FACE", "So", 0),
("EXPRESSIONLESS FACE", "So", 0),
("UNAMUSED FACE", "So", 0),
("FACE WITH COLD SWEAT", "So", 0),
("PENSIVE FACE", "So", 0),
("CONFUSED FACE", "So", 0),
("CONFOUNDED FACE", "So", 0),
("KISSING FACE", "So", 0),
("FACE THROWING A KISS", "So", 0),
("KISSING FACE WITH SMILING EYES", "So", 0),
("KISSING FACE WITH CLOSED EYES", "So", 0),
("FACE WITH STUCK-OUT TONGUE", "So", 0),
("FACE WITH STUCK-OUT TONGUE AND WINKING EYE", "So", 0),
("FACE WITH STUCK-OUT TONGUE AND TIGHTLY-CLOSED EYES", "So", 0),
("DISAPPOINTED FACE", "So", 0),
("WORRIED FACE", "So", 0),
("ANGRY FACE", "So", 0),
("POUTING FACE", "So", 0),
("CRYING FACE", "So", 0),
("PERSEVERING FACE", "So", 0),
("FACE WITH LOOK OF TRIUMPH", "So", 0),
("DISAPPOINTED BUT RELIEVED FACE", "So", 0),
("FROWNING FACE WITH OPEN MOUTH", "So", 0),
("ANGUISHED FACE", "So", 0),
("FEARFUL FACE", "So", 0),
("WEARY FACE", "So", 0),
("SLEEPY FACE", "So", 0),
("TIRED FACE", "So", 0),
("GRIMACING FACE", "So", 0),
("LOUDLY CRYING FACE", "So", 0),
("FACE WITH OPEN MOUTH", "So", 0),
("HUSHED FACE", "So", 0),
("FACE WITH OPEN MOUTH AND COLD SWEAT", "So", 0),
("FACE SCREAMING IN FEAR", "So", 0),
("ASTONISHED FACE", "So", 0),
("FLUSHED FACE", "So", 0),
("SLEEPING FACE", "So", 0),
("DIZZY FACE", "So", 0),
("FACE WITHOUT MOUTH", "So", 0),
("FACE WITH MEDICAL MASK", "So", 0),
("GRINNING CAT FACE WITH SMILING EYES", "So", 0),
("CAT FACE WITH TEARS OF JOY", "So", 0),
("SMILING CAT FACE WITH OPEN MOUTH", "So", 0),
("SMILING CAT FACE WITH HEART-SHAPED EYES", "So", 0),
("CAT FACE WITH WRY SMILE", "So", 0),
("KISSING CAT FACE WITH CLOSED EYES", "So", 0),
("POUTING CAT FACE", "So", 0),
("CRYING CAT FACE", "So", 0),
("WEARY CAT FACE", "So", 0),
("SLIGHTLY FROWNING FACE", "So", 0),
("SLIGHTLY SMILING FACE", "So", 0),
("UPSIDE-DOWN FACE", "So", 0),
("FACE WITH ROLLING EYES", "So", 0),
("FACE WITH NO GOOD GESTURE", "So", 0),
("FACE WITH OK GESTURE", "So", 0),
("PERSON BOWING DEEPLY", "So", 0),
("SEE-NO-EVIL MONKEY", "So", 0),
("HEAR-NO-EVIL MONKEY", "So", 0),
("SPEAK-NO-EVIL MONKEY", "So", 0),
("HAPPY PERSON RAISING ONE HAND", "So", 0),
("PERSON RAISING BOTH HANDS IN CELEBRATION", "So", 0),
("PERSON FROWNING", "So", 0),
("PERSON WITH POUTING FACE", "So", 0),
("PERSON WITH FOLDED HANDS", "So", 0),
)
|
https://github.com/Enter-tainer/typstyle | https://raw.githubusercontent.com/Enter-tainer/typstyle/master/tests/assets/unit/comment/line-comment.typ | typst | Apache License 2.0 | #{
// test
/*
if direction == "bottom" {
draw.line(a, (rel: (0, -grow/3)), ((), "-|", b), b)
} else if direction == "up" {
draw.line(a, (rel: (0, grow/3)), ((), "-|", b), b)
} else if direction == "left" {
draw.line(a, (rel: (-grow/3, 0)), ((), "|-", b), b)
} else if direction == "right" {
draw.line(a, (rel: (grow/3, 0)), ((), "|-", b), b)
}
*/
}
|
https://github.com/pedrofp4444/BD | https://raw.githubusercontent.com/pedrofp4444/BD/main/report/content/%5B0%5D%20Resumo/main.typ | typst | #let resumo = {
heading(numbering: none, outlined: false)[Resumo]
[
Ao longo deste projeto foi desenvolvido um sistema de gestão de base de dados, direcionado para a empresa _Lusium_, com o intuito de melhorar a segurança em Vizela. Este sistema seria aplicado especificamente na gestão dos roubos relacionados com minérios _edium_ e _nunium_, onde seriam avaliadas informações sobre os terrenos e os seus trabalhadores, bem como os casos ativos.
Este projeto engloba várias etapas que, de forma sucinta, podem ser divididas em definição do sistema, levantamento e análise dos requisitos, modelação concetual, modelação lógica e implementação física. Estas etapas, e a sua posterior validação, tornam-se essenciais para a construção de um sistema de gestão de base de dados bem estruturado.
Após uma ponderação sobre as melhores ferramentas a utilizar, optamos pelo uso do "BrModelo" para a modelação concetual, do "MySQL Workbench" para a modelação lógica e implementação física e do "RelaX" para abordar a componente de álgebra linear, dada a sua eficácia e capacidade de lidar com desafios específicos de um sistema de gestão de bases.
*Área de Aplicação*: Análise, planeamento, modelação, arquitetura e implementação de um sistema de gestão de base de dados.
*Palavras-Chave*: Sistema de gestão de base de dados, _Lusium_, Casos, Requisitos, Modelação Concetual, Modelação Lógica, Implementação Física.
]
}
|
|
https://github.com/jhnko/umu-templates | https://raw.githubusercontent.com/jhnko/umu-templates/main/report/template.typ | typst | The Unlicense | #import "@preview/tablex:0.0.6": tablex
#let TABLE_STROKE = 0.5pt + black
#show terms: it => {
it
.children
.map(child => [
#strong[#child.term]
#block(inset: (left: 1.5em, top: -0.4em))[#child.description]
])
.join()
}
#let swedish_month(month_num) = {
let months = (
"januari",
"februari",
"mars",
"april",
"maj",
"juni",
"juli",
"augusti",
"september",
"oktober",
"november",
"december",
)
let month = months.at(month_num - 1)
return month
}
#let format_date(date, lang: none) = {
if lang == "sv" [
#date.day() #swedish_month(date.month()) #date.year()
] else {
date.display("[month repr:long] [day padding:none], [year]")
}
}
#let is_outline_page = state("is_outline_page", false)
#let last_outline_page = state("last_outline_page", false)
#let page_header(
subtitle: none, // Text in the top-left corner
skip_chapter_numbers_for: () // A list of chapter names to skip numbering for
) = (
context {
let page_number = counter(page).get().first()
// In this context, a "chapter" would be a level 1 heading
let chapter_headings = query(heading.where(level: 1)).rev()
let chapter_heading = chapter_headings.find(h => h.location().page() <= here().page())
if (chapter_heading == none) {
return
}
let chapter_number = counter(heading).at(chapter_heading.location()).first()
if page_number > 0 {
if chapter_heading != none {
let numbering_scheme = if chapter_heading.numbering != none {
chapter_heading.numbering
} else {
"1."
}
let chapter = (
name: chapter_heading.body,
number: chapter_number,
)
let can_number_chapter = (not is_outline_page.get()) and chapter_number != none
let should_number_chapter = not skip_chapter_numbers_for.contains(chapter.name.text)
let num_text = if can_number_chapter and should_number_chapter {
numbering(numbering_scheme, chapter_number)
} else {
none
}
block(below: 0.5em)[
#smallcaps(subtitle) #h(1fr) #num_text #chapter.name
]
line(length: 100%)
}
}
}
)
#let pagefooter(date: none, lang: none) = (
context {
let pagenumber = counter(page).get().first()
if pagenumber != 0 [
#line(length: 100%)
#columns(3)[
// #author.name, #username
#colbreak()
#set align(center)
#if is_outline_page.get() or last_outline_page.get() {
counter(page).display("i")
} else {
counter(page).display()
}
#colbreak()
#set align(right)
#format_date(date, lang: lang)
]
]
}
)
#let title_page(
title: none,
subtitle: none,
authors: none,
graders: (),
graders_label: none,
date: none,
lang: none,
) = {
set table(stroke: TABLE_STROKE)
columns(2)[
// Empty top left corner.
#colbreak()
#set align(right)
*#format_date(date, lang: lang)*
]
v(4cm)
if title != none {
align(center)[
#block(
inset: 1em,
above: 4em,
width: 75%,
below: 1em,
)[
#text(size: 24pt)[
#title
]
]]
}
if subtitle != none {
align(
center,
block(
inset: 1em,
text(
weight: "thin",
size: 20pt,
)[
#subtitle
],
),
)
}
// The DOA template had labels for name and username
// let name_label = if lang == "sv" [Namn] else [Name]
// let username_label = if lang == "sv" [Användarnamn] else [Username]
if authors != none {
align(
center,
block(
inset: 1em,
grid(
columns: array.range(authors.len()).map(n => auto),
row-gutter: 1.5em,
column-gutter: 3em,
..authors.map(author => {
[
#set align(center)
#set text(size: 14pt)
#author.name
]
}),
..authors.map(author => block(if "email" in author {
let link_title = if "username" in author {
author.username
} else {
author.email
}
let email_link = "mailto:" + author.email
link(email_link)[#raw(link_title)]
} else {
if "username" in author {
raw(author.username)
}
}))
),
),
)
}
v(1fr)
let graders_label = if graders_label != none {
graders_label
} else {
if lang == "sv" [Labrättare] else [Graders]
}
if graders.len() > 0 {
align(
center,
block()[
#text(size: 14pt)[
*#graders_label*
] \
#text(size: 12pt)[
#graders.join(pagebreak())
]
],
)
}
}
// Call this function to use the template
#let conf(
title: none,
authors: none,
subtitle: none,
date: datetime.today(),
graders: (),
graders_label: none,
skip_chapter_numbers_for: ("References", "Referenser"),
abstract: none,
cols: 1,
margin: (x: 1.25in, y: 1.25in),
paper: "a4",
lang: "sv",
region: "SE",
font: (),
fontsize: 12pt,
outline: outline(indent: true),
doc,
) = {
show figure.where(kind: table): set figure.caption(position: top)
// Decimal comma for Swedish
show math.equation: it => if lang == "sv" {
show regex("\d+\.\d+"): it => {
show ".": {
"," + h(0pt)
}
it
}
it
} else {
it
}
show heading: it => {
set text(weight: "regular")
let above = if it.level > 1 {
2em
} else {
1em
}
block(
above: above,
it,
)
}
counter(page).update(0)
set page(
paper: paper,
margin: margin,
header: page_header(
subtitle: subtitle,
skip_chapter_numbers_for: skip_chapter_numbers_for,
),
footer: pagefooter(
date: date,
lang: lang,
),
)
set text(
lang: lang,
region: region,
font: font,
size: fontsize,
)
title_page(
title: title,
subtitle: subtitle,
authors: authors,
graders: graders,
graders_label: graders_label,
date: date,
lang: lang,
)
set par(justify: true)
set heading(numbering: "1.1")
if (outline != none) {
is_outline_page.update(true)
pagebreak()
counter(page).update(1)
outline
last_outline_page.update(true)
is_outline_page.update(false)
pagebreak()
last_outline_page.update(false)
}
set page(numbering: "1")
counter(page).update(1)
if cols == 1 {
doc
} else {
columns(cols, doc)
}
}
|
https://github.com/Otto-AA/definitely-not-tuw-thesis | https://raw.githubusercontent.com/Otto-AA/definitely-not-tuw-thesis/main/template/content/appendix.typ | typst | MIT No Attribution | = Overview of Generative AI Tools Used
(Lorem Ipsum is no AI tool, it's a clever algorithm as described in @lorem-ipsum-alg)
= Samples from Lorem Ipsum
== 5 words lorem
#lorem(5)
== 10 words lorem
#lorem(10)
== Long ipsum
#lorem(300)
#lorem(300) |
https://github.com/typst/packages | https://raw.githubusercontent.com/typst/packages/main/packages/preview/scholarly-tauthesis/0.4.0/template/meta.typ | typst | Apache License 2.0 | /** meta.typ
*
* Defines document metadata. Fill in the information regarding
* you thesis into the commands specified here.
*
***/
//// Common metadata.
#let author = "<NAME>"
#let date = datetime.today()
#let examiners = (
(
title : "Professor",
firstname : "Firstname",
lastname : "Lastname",
),
(
title : "University lecturer",
firstname : "Firstname",
lastname : "Lastname",
),
)
#let language = "fi"
#let citationstyle = "ieee"
//// Finnish metadata.
#let alaotsikko = "T<NAME>"
#let avainsanat = ("avainsana1", "avainsana2")
#let koulu = "<NAME>"
#let tiedekunta = "Tiedekunta"
#let otsikko = "Opinnäytetyöpohja"
#let työntyyppi = "Diplomityö"
#let sijainti = "Tampereella"
//// English metadata.
#let faculty = "Faculty"
#let keywords = ("keyword1", "keyword2")
#let university = "Tampere University"
#let subtitle = "Tampere University"
#let thesistype = "Master's thesis"
#let title = "Thesis template"
#let location = "Tampere"
|
https://github.com/Wh4rp/Presentacion-Typst | https://raw.githubusercontent.com/Wh4rp/Presentacion-Typst/master/ejemplos/10_set.typ | typst | #set text(font: "Ubuntu Mono")
#set text(fill: blue)
#set par(justify: true)
#lorem(20) |
|
https://github.com/polarkac/MTG-Stories | https://raw.githubusercontent.com/polarkac/MTG-Stories/master/stories/002%20-%20Return%20to%20Ravnica/012_Rogue’s Passage.typ | typst | #import "@local/mtgstory:0.2.0": conf
#show: doc => conf(
"Rogue’s Passage",
set_name: "Return to Ravnica",
story_date: datetime(day: 21, month: 11, year: 2012),
author: "<NAME>",
doc
)
Tanek awoke lying shirtless on his back. The smoke-masked sun was already high in the sky, and the exhaust pipe next to him blasted a long jet of steam.
He looked around—the others who slept on the rooftop were long gone. He checked his left pocket for his coin purse, felt behind his head for his balled-up shirt and through the hole in his right pocket for the razor tied to his leg. Everything still there. Good.
#figure(image("012_Rogue’s Passage/02.jpg", width: 100%), caption: [Plains | Art by Richard Wright], supplement: none, numbering: none)
The roof had been a lucky find. In good weather, it was much better than sleeping on the ground, and when it rained there was enough of an overhang to curl up under. Those who slept on the rooftop occasionally traded tricks, although not too often. He liked it there. It felt safe. Or at least as safe as one could get.
Tanek’s stomach growled and he felt lightheaded. Paying for food was always disappointing, but working on an empty stomach was too dangerous. He sat up, pulled on his ash-stained shirt, and dumped his ratty coin purse out onto the rooftop. Someone had shaved the edges of his Boros-made five zino coin, but not enough that most people would notice. He was saving that one for an emergency. The three one-zino coins were of Azorius mint and a relatively new design. The symbol extended higher off the face than it did on the older coins; someone with a sharp knife and a steady hand could probably shave it down, although he hadn’t seen anyone try it yet. There were also a few fifty and twenty-five zib pieces. He could get a stick of grilled meat and an apple for forty zibs. That would have to be enough for the morning.
He descended a broken ladder off the side of the rooftop, jumped to an awning a few feet away, and climbed down to the street. It was amazing that most people didn’t think to try to get up there, but then again, most people didn’t know that alley existed. He trotted down the alley to a dead end, crawled through a hole in the wall just above ground level, squeezed between two bushes, and emerged onto the street.
#figure(image("012_Rogue’s Passage/04.jpg", width: 100%), caption: [Rogue’s Passage | Art by <NAME>], supplement: none, numbering: none)
Tanek made his way through the busy streets to the smelting district marketplace. An onslaught of sounds and smells, the marketplace served as both a place for the guildless metalworkers to sell their wares and a place where their hired help could buy lunch. It was also something of a thief’s paradise, although there weren’t so many pickpockets around that the authorities paid attention. Tanek knew most of them, and a few who lived on the rooftop with him were already at work. Migen was talking to a tall man while Erika darted away holding something. Ivo crouched in a nearby shadow, watching. Tanek smiled and melted into the crowd.
It wasn’t quite lunchtime, but some workers on break were already there. A pack of jabbering goblins in brown uniforms mobbed around a pastry vendor and a hulking minotaur in an ash-stained smock haggled with a woman selling whole, roasted chickens. There were also a few guild members present, although in this unaligned part of the city they stood out like spires in the skyline. An elf wearing green and white spoke with a swordsmith and a stuffy-looking vedalken woman in Azorius colors negotiated with a jeweler. There were also a few Boros patrolmen—at least three Tanek could see. They were observing someone. Tanek prepared to bolt, but they weren’t looking at him.
#figure(image("012_Rogue’s Passage/06.jpg", width: 100%), caption: [Armory Guard | Art by Karl Kopinski], supplement: none, numbering: none)
As Tanek pushed his way through the crowd, the object of the patrol’s attention came into focus. Two chunky Orzhov thugs with shaved heads were harassing Busa, Tanek’s favorite chicken vendor. All three men were talking in raised voices, their arms flailing, but Busa was clearly on the defensive. Someone with an uncovered basket of fruit paused while walking by, distracted by the row. Tanek grabbed an apple off the top and pocketed it, then slid toward the racket.
The toadies had moved on by the time Tanek got there, but the rest of the crowd was still leaving Busa a wide berth. Tanek approached with a sheepish smile. "One stick."
"Twenty-five zibs. Actually paying today, eh?"
He shrugged. "I can’t work on an empty stomach." Busa put a stick of nearly cooked chicken on the grill. "And besides, I like your food. What was that about?"
Busa’s face fell. "Ambroz’s thugs again."
Tanek screwed his face up as he handed Busa a coin. "I think you mean <NAME>’s thugs."
Busa laughed, but his eyes betrayed fear. "They’re getting braver. Today they doubled the rate and said they’d cut my daughter’s toes off if I didn’t pay on time. And they’re not just doing it to me." They both looked a few stalls over, where the same two thugs were having the same conversation with a candy seller. "I can’t imagine this is good for your type either, with the Boros around."
Tanek took the stick of meat. "Nope. Wish I could do something about it." A pair of viashino with hungry eyes sauntered toward them. "Well, see you later."
He sat down on the curb and began to eat, savoring each bite with half-closed eyes. As he finished the meat and started into the apple, a practiced voice pierced the noise of the crowd. "Make way, make way!"
The crowd parted. An armored guard in an Orzhov surcoat came first, followed by a fat man in black and white silk robes, followed again by a beautiful and barely dressed woman who held an umbrella over him. A balding servant brought up the rear and approached the fat man, gesturing with an open hand. "<NAME>, the pastry merchant you were inquiring about is this way."
#figure(image("012_Rogue’s Passage/08.jpg", width: 100%), caption: [Orzhov Pontiff | Art by Adam Rex], supplement: none, numbering: none)
The fat man threw his head back. "Lead me to him."
The procession of pristine black and white walked past Tanek. At the baker’s stand, Benakov stood perusing the pastries on display for two whole minutes before selecting one. He took a too-large bite, and the cream filling squirted down his chubby face. His umbrella holder dabbed it off with a cloth as he chewed, nearly getting it on his ridiculous high collar. "Oh my, this is quite good." He took another bite. "You should harve one," he said to the servant, his mouth full. "It’s farntarstic."
The man bowed like a puppet. "I am not hungry, but thank you."
"Very well. Let us return to my office." The guard turned around, leading the way back through the crowd. Benakov turned as well, and the drape of his robes revealed to Tanek a small bag-shaped bulge hanging at his right hip.
There was a stray board on the street a few feet from Tanek. He grabbed the board, reached through the hole in his pocket for the razor, and palmed the it. He turned to judge the alleyway behind him. If he remembered correctly, there were two dogleg turns, then a dead end. The wall there would be tough to climb, but not impossible. He turned back to the street, waiting to pounce.
Just as Benakov was about to pass in front of him, Tanek tossed the board in the way. The fat man tripped, falling flat onto his face. Tanek was on him in an instant, cutting the right side of the man’s robe and the string that held his coin purse in place. Benakov yelled. Tanek grabbed the purse and darted into the alleyway, but caught a flash of white and red behind him. As he rounded the first corner, he heard footsteps closing in. He ran as fast as his legs could carry him. He managed to slip the pouch into his left pocket before he hit the second corner, but nearly tripped over a bucket of water as he rounded it.
The back wall of the alley was twenty feet high, and there were fewer handholds in the black and gray stone than he remembered. He dropped the razor and began to climb. The footsteps behind him kept coming. A bucket of water bounced off the wall above him, dousing him and the smooth stone. He tried to keep climbing, found no purchase, and fell onto his back. In an instant, the heel of the man’s boot was on his neck, followed by the point of his sword.
#figure(image("012_Rogue’s Passage/10.jpg", width: 100%), caption: [Art by <NAME>], supplement: none, numbering: none)
The man sneered. "The money."
Tanek’s eyes went wide. "I… don’t have it."
The sword’s point pushed into Tanek’s neck just enough to draw blood. "The money."
"Okay, okay." He reached into his pocket and handed over the pouch.
The pressure on Tanek’s neck loosened, and the man’s face relaxed. "Why did you do this?"
"That lump of a man threatened my friends."
"Your friends?"
"Busa the chicken vendor. And others, too. Those thugs you were watching are <NAME>’s men. You may be watching now, but you won’t stop them when they come back in the dark. They’re mean. They torture you and cut your kids’ toes off. Anything to get your money."
The Boros legionnaire shook the coin pouch. "And you thought taking this would stop him?"
Tanek thought. "I… I don’t know. I didn’t think—"
"I can tell." The legionnaire pocketed the pouch and took his foot off Tanek’s neck, but kept the sword at his throat. "What else do you know?"
"Benakov didn’t show up until a few weeks ago. No one paid him until the pastry seller’s wife disappeared, and everyone has since then. He just doubled the protection rate today. Between them, and now you, things are way too dangerous."
The man sheathed his sword and almost smiled. "I don’t normally like parasites, but you’re not so bad." He reached down with one hand. Tanek grasped it, and the man pulled him to his feet. "I’m Radomir of the Boros Legion. It’s too bad you weren’t such a good climber, but at least I got the money back."
Tanek blinked. The Boros man smiled. "Can you write?" Tanek nodded. "If you find out more, drop a note in the empty planter on the roof of the goblin forge. I pay well, and I’d rather not see someone whose heart could be in the right place stealing from his ‘friends.'"
Radomir turned on his heel and began to walk away. Tanek took one step after him. "Are you paying me for today?"
"Oh. Good point." Radomir took the purse from his pocket, dug out two coins, and tossed them back toward Tanek; the coins clattered onto the ground between them. "I suppose most of the money will have to be good enough."
Tanek scrambled to pick them up. They were both ten-zino pieces, of Orzhov mint, with pristine milled edges still intact. His eyes went wide. By the time he thought to thank the man, Radomir was already gone.
#figure(image("012_Rogue’s Passage/12.jpg", width: 100%), caption: [Conjured Currency | Art by Steve Argyle], supplement: none, numbering: none)
Twenty zinos. Not a great haul, but enough to live on comfortably for a week or two. Maybe enough for a new shirt, too. Tanek put the coins into his pocket, retrieved the razor, climbed a different wall, and went rooftop to rooftop until he was far enough away from the marketplace that descending to the street level was safe. From there, he made his way back to the two bushes, crawled through the hole in the wall, and climbed up to the rooftop.
Erika and Migen were already back. "Hi Tanek," Migen chirped.
"You’re wet. Did that guy catch you?" Erika asked.
Tanek thought for a moment. "No, but I dropped the money."
"Aww. We did great today!" said Migan.
"It’s amazing what you can take from people when they’re distracted by a sad little girl," said Erika with a gleam in her eye.
Who had they stolen from? Hopefully not Busa. Tanek had stolen from Busa before, but that was a long time ago. Could he do it again? He wasn’t sure.
"I need to go. I’ll see you later." Tanek turned away.
"Okay," they said in unison. He climbed down from the rooftop. He wouldn’t see them again for a while. Definitely not today, at least. He needed a different rooftop. One with more space to think. And hopefully one closer to the goblin forge.
|
|
https://github.com/ivaquero/book-control | https://raw.githubusercontent.com/ivaquero/book-control/main/12-非线性控制器.typ | typst | #import "@local/scibook:0.1.0": *
#show: doc => conf(
title: "非线性控制器",
author: ("ivaquero"),
header-cap: "现代控制理论",
footer-cap: "github@ivaquero",
outline-on: false,
doc,
)
= 自适应控制器
<自适应控制器>
对系统
$ dot(x) = a x^2 + u $
其中，$a$为常量（或一定时间内几乎不变）。
令$e = x_d - x$，则
$ dot(e) = dot(x)_d - dot(x) = dot(x)_d - a x^2 - u $
当$a$已知，可采用反馈线性化，求得 Lyapunov
函数$V(x)$；当$a$未知，则有
$ V(e, tilde(a)) = 1 / 2 e^2 + 1 / 2 a ̃^2 $
其中，
- 测量误差$e = x_d - x$
- 估计误差$tilde(a)= a - a ̂$
求导，得
$
dot(V)(e, tilde(a)) = e dot(e) + tilde(a)tilde(dot(a)) &= e (x_d - a x^2 - u) - tilde(a)hat(dot(a))\
&= -k e^2 - tilde(a)(e x^2 + hat(dot(a)))
$
#tip[
不难得出，$tilde(dot(a)) = dot(a) - hat(dot(a)) = -hat(dot(a))$
]
显然，$-k e^2$半负定，若使$dot(V)(e, tilde(a))$半负定，可以使$e x^2 + hat(dot(a)) = 0$。
由$dot(V)(e, tilde(a)) = -k e^2 ≤ - (k e^2)$，令$g(t) = k e^2$，得
$ dot(V)(e, tilde(a)) ≤ - g(t) $
此时，$dot(g)(t) = 2 k e e ̇$有界，于是
$ lim_(t → ∞) k e^2 = 0 $
由上，可得
$ u = dot(x)_d + x^2 ∫_0^t e x^2 dd(t) + k e $
#theorem("Barbalat 引理")[
若函数$V$和$g(t)$满足
- $V ≥ 0$
- $dot(V)≤ - g(t)$，其中，$g(t) ≥ 0$
- $dot(g)(t) ∈ L_x$
则
$ lim_(t → ∞) g(t) = 0 $
]
#pagebreak()
= 鲁棒控制
<鲁棒控制>
=== 滑模控制
<滑模控制>
对系统
$ dot(x) = f(x) + u $
有
$ dot(e) = dot(x)_d - dot(x) = dot(x)_d - f(x) - u $
令
$ u = dot(x)_d + k e + u_(a u x) = dot(x)_d + k e + ρ|e| / e $
其中，
$ |e| / e = "sign"(e) cases(delim: "{", 1 & e > 0, 0 & e = 0, - 1 & e < 0) $
#tip[
$e = x_d - x$，则$lim_(t → ∞) e = 0$
]
于是
$ dot(e) = -k e - f(x) - ρ(x) e / |e| $
其中，
- $-k e$为平衡项
- $f(x)$为系统项
- $ρ(x) e/|e|$为控制器项
- $|f(x)| < ρ(x)$
后两项的作用是，使输出回归到第一项上。
对系统
$ dot(x) = a x^2 + u $
其中，$a$为变量。则
- $|a| ≤ |a ̄|$
- $|f(x)| = |a| x^2 ≤ |a ̄| x^2 < |a|(x^2 + 0.1)$
于是，可以设计
$ u = k e + dot(x)_d + |a ̄|(x^2 + 0.1) |e| / e $
=== 高增益鲁棒控制
<高增益鲁棒控制>
对上述问题，采用高增益鲁棒控制，使用足够大的输入来抵消不确定性
令
- $u_(a u x 2) = 1 / ɛ⋅ρ^2 e$
- $V = 1 / 2 e^2$
则
$
dot(V)= e dot(e) &= e (dot(x)_d - f(x)) - k e - dot(x)_d - 1 / ɛ p^2 e\
&= -e f(x) - k e^2 - 1 / ɛ ρ^2 e^2
$
于是有
$ dot(V)≤ - k e^2 + p|e|(1 - 1 / ɛ ρ|e|) $
- 当$ρ|e| > ɛ$，$dot(V)≤ - k e^2$
- 当$ρ|e| ≤ ɛ$，$dot(V)≤ 2 k V + ɛ$
最终有
$ lim_(t → ∞) e ≤ sqrt(ɛ/k) $
=== 高频鲁棒控制
<高频鲁棒控制>
对上述问题，采用高频鲁棒控制，平滑滑膜控制
令
- $u_(a u x 3) = frac(ρ^2 e, ρ|e| + ɛ)$
- $V = 1 / 2 e^2$
$
dot(V)= e dot(e) ≤ - k e^2 + ρ|e| - e frac(ρ^2 e, ρ|e| + ɛ) = -k e^2 + ɛ (frac(ρ|e|, p|e| + ɛ))
$
其中，$0 ≤ frac(ρ|e|, p|e| + ɛ) ≤ 1$，即
$ dot(V)≤ - k e^2 + ɛ $
类似$u_(a u x 2)$，最终有
$ lim_(t → ∞) e ≤ sqrt(ɛ/k) $
#figure(
table(
columns: 7,
align: center + horizon,
inset: 4pt,
stroke: frame(rgb("000")),
[Name], [$u_(a u x)$], [$ɛ$], [稳态误差], [收敛速度], [瞬态输入], [稳态输入],
[Sliding Mode], [$ρ e\/norm(e)$], [N/A], [5], [4], [2], [1],
[High Gain], [$1\/ɛ ρ^2 e$], [0.1], [4], [5], [1], [2],
[High Gain], [$1\/ɛ ρ^2 e$], [1], [2], [3], [3], [4],
[High Freq], [$(ρ^2 e)\/(ρ norm(e) + ɛ)$], [0.1], [3], [2], [4], [3],
[High Freq], [$(ρ^2 e)\/(ρ norm(e) + ɛ)$], [1], [1], [1], [5], [5],
),
caption: [高频鲁棒控制],
supplement: "表",
kind: table,
)
|
|
https://github.com/typst/packages | https://raw.githubusercontent.com/typst/packages/main/packages/preview/pyrunner/0.1.0/example.typ | typst | Apache License 2.0 | #import "@preview/pyrunner:0.1.0" as py
#let compiled = py.compile(
```python
def find_emails(string):
import re
return re.findall(r"\b[a-zA-Z0-9._%+-]+@[a-zA-Z0-9.-]+\.[a-zA-Z]{2,}\b", string)
def sum_all(*array):
return sum(array)
def add(a, b):
return f'{a+b=}'
```)
#let txt = "My email address is <EMAIL> and my friend's email address is <EMAIL>."
#py.call(compiled, "find_emails", txt)
#py.call(compiled, "sum_all", 1, 2, 3)
#py.block(```
import sys
sys.version, sys.path
```)
#py.block(
```python
[1, True, {"a": a, 5: "hello"}, None]
```,
globals: (a: 3))
#py.call(compiled, "add", 1, 2)
#py.call(compiled, "add", "1", "2")
|
https://github.com/polarkac/MTG-Stories | https://raw.githubusercontent.com/polarkac/MTG-Stories/master/stories/021%20-%20Battle%20for%20Zendikar/008_Revelation%20at%20the%20Eye.typ | typst | #import "@local/mtgstory:0.2.0": conf
#show: doc => conf(
"Revelation at the Eye",
set_name: "Battle for Zendikar",
story_date: datetime(day: 14, month: 10, year: 2015),
author: "<NAME>",
doc
)
#emph[<NAME> is not a fighter. His immediate goal in coming to Zendikar was to solve a puzzle: the question of how the plane's floating stone hedrons had contained the Eldrazi, and how they might be used to capture—or kill—the titan Ulamog, who remains on Zendikar.]
#emph[With all the scholarship on the subject destroyed in ] the fall of Sea Gate#emph[, Jace was forced to undertake ] a dangerous journey#emph[ to the Eye of Ugin, the center of the hedron network. Jace had been there once before, when he inadvertently helped release the Eldrazi. Now, he must return to the Eye and unravel the puzzle of Zendikar's hedrons.]
#emph[If he can live that long.]
#v(0.35em)
#line(length: 100%, stroke: rgb(90%, 90%, 90%))
#v(0.35em)
<NAME> wedged his boot against a jagged rock, pushed, and stretched, barely wrapping his aching fingers around the next handhold.
He was not exactly in his element. The wind whipped his cloak around him. He didn't look down.
He wasn't afraid of heights, not more than the average person. But he knew how high up the cliff face he was, and looking added no useful information. And anyway, a certain amount of wariness seemed rational, given that a fall from this height would certainly kill him, splattering him against the . . .
He didn't look down.
#figure(image("008_Revelation at the Eye/01.jpg", width: 100%), caption: [Looming Spires | Art by <NAME>], supplement: none, numbering: none)
At the top of this cliff, if the mental map he'd pulled out of Jori En's mind was accurate, was what passed for even ground in Akoum, a vast expanse of jagged volcanic rocks and treacherous canyons. The Tuktuk tribe of goblins lived somewhere in this area, or had before the Eldrazi rose. The landscape had been rearranged when the three Eldrazi progenitors physically emerged from the mountain range known as the Teeth of Akoum, and neither Jace's prior experience nor Jori's knowledge could guide him. He needed help. He needed Tuktuk and his tribe.
Inch by inch, handhold by handhold, Jace pulled himself up the rock face. At last, hands aching, he hauled himself over the lip of the cliff—
—and straight into an Eldrazi.
It was small, as Eldrazi went—perhaps as big as he was—and its blank, bone-white face was just a few feet from his. He stumbled backwards but caught himself, one boot dangling out over the abyss. He rolled sideways and got to his hands and knees out of easy reach of the thing.
#figure(image("008_Revelation at the Eye/02.jpg", width: 100%), caption: [Salvage Drone | Art by Slawomir Maniak], supplement: none, numbering: none)
The Eldrazi was looking at him, its eyeless face swiveling to follow his movement. It lunged.
Jace pushed himself to his feet, summoning an illusionary guardian. The Eldrazi's mind was as blank as its face, and none of his usual tricks seemed to work on them. Sleep magic did nothing against things that didn't sleep. Invisibility was useless against monsters without eyes. Even his illusions seemed to falter against these otherworldly adversaries.
The Eldrazi tore through his illusion like it was paper and kept coming.
With more time, Jace could have conjured up a more solid illusion. With more time, he might have been able to confuse the creature long enough to get away—to try out tactile or auditory illusions that might misdirect it. He was out of time, and exhausted from the climb, and all he could do was try to wedge himself between two of the sharp rocks and hope he could get a few good kicks in.
There was a #emph[thwack] , and a flash of bright blue light. The Eldrazi reeled. Jace blinked. What . . . ?
"Down, foul thing!" came a voice from his left.
The Eldrazi swiveled its bony face to look—or the eyeless equivalent—just as a heavy club came down on its blank white head. There was a sound like shattering porcelain and a splatter of meaty goo, and the Eldrazi dropped.
Jace peeked around the rock next to him to see a squat goblin grinning from ear to ear. Like most of the goblins he'd seen since his return, she had a heavy metallic growth on the top of her skull. She had a heavy basket on her back and a stone club—no, not a club, he realized, and not a basket. A pestle and a mortar. The goblin stood only as tall as his waist, but she had to be monstrously strong to lug those around.
#figure(image("008_Revelation at the Eye/03.jpg", width: 100%), caption: [Zada, Hedron Grinder | Art by <NAME>allis], supplement: none, numbering: none)
"Hello!" said the goblin with, it seemed to him, undue cheer. "Not safe, traveling alone."
She wiped her pestle on a rock, scraping off bits of bone and whatever passed for an Eldrazi's brain. Jace didn't want to go rooting around in her head just yet. That had a way of hindering potential good relations.
"Thanks for the save," he said. "How did you do that? To the Eldrazi?"
"Oh, their skulls bust just as easily as yours," said the goblin. She rapped the top of her head, which clanged. "Bit easier than mine."
"Before that," said Jace. "The spell, or whatever it was."
By way of response, she looked around as though she'd lost something, then shouted "Aha!" and scrambled to pick up what looked to Jace like a small rock. No—not a rock. A shard of one of Zendikar's magical stone hedrons.
"A hedron holds magic for a thousand years," she said. "Or less, if need be. This one's mostly spent, but I'll grind out what I can."
She cackled, tossed the hedron into her mortar, and started absentmindedly pounding away at it. There were sparks and pops.
"The size of 'em doesn't tell you much," said Zada. "Every hedron's like a deep, dark hole. Could be filled with good stuff. Could be empty. Only way to know for sure is to dive in."
"I see," he said. "Uh . . . I'm Jace, by the way."
"Zada of Slab Haven," said the goblin, as though that explained everything.
"I'm looking for Tuktuk," said Jace. "Do you know him?"
For some reason this made Zada roar with laughter.
"He's dead," she said. "Stone dead, you might say."
She started laughing again, but at Jace's blank expression, she managed to wheeze out, "He was made of rocks, you know."
"What happened?" asked Jace.
"I ate him," said Zada.
Jace spent a moment imagining horrific cannibal rites until he remembered what she'd just said about Tuktuk, which pushed her claim from horrifying to merely improbable.
"You what?"
Zada grinned again, showing off rows of enormous pitted teeth.
"<NAME>."
"I thought you said he was made of rocks," said Jace.
"Yep," said Zada. "You don't know much about goblins, do you?"
"I really don't," said Jace. "Why did you . . . eat him?"
"When we find hedrons and other magic rocks, we grind 'em up and eat 'em," said Zada. "Makes us stronger. Tuktuk had us doing it. But then I figured, Tuktuk was the most magic rock of all . . ."
She shrugged and patted her belly.
"That . . . makes a weird kind of sense."
"Thank you!" said Zada.
"Uh . . . anyway," said Jace, "what I'm really looking for is the Eye of Ugin. I've been there before, but everything seems to have changed."
"Why?" said Zada.
"To stop the Eldrazi," said Jace. "I need to learn more about the hedron network, and the Eye of Ugin is its center."
"Was," said Zada. "A scrambled mess doesn't have a center."
She sighed.
"But I suppose I'll show you the way, if you think it's important," she said, gesturing for him to follow. "Not sure what all the fuss is about, though. We're getting along fine up here . . ."
#v(0.35em)
#line(length: 100%, stroke: rgb(90%, 90%, 90%))
#v(0.35em)
It was a few hours' hard walking to the Eye, as Zada picked a winding path through the precarious spires of Akoum. Twice they had to double back to avoid Eldrazi, and even Zada seemed a bit lost in the tumultuous landscape. All the while she nattered on about the nature of hedrons. Jace hadn't realized they actually stored energy, or that their energy could still be directed against the Eldrazi, so at least he was learning.
Eventually Zada pointed him at a cave entrance and bade him farewell.
"You're not coming in?" said Jace.
"Nope," replied Zada. "Nobody goes in there. Bad magic. Certain death. Good luck!"
She bounded away over the rocks, and Jace turned to the ominous, angular mouth of a cave that certainly was not natural stone.
He descended carefully, picking his way among enormous fallen hedrons. The place was silent, lifeless, devoid of the thrumming power that had suffused it on his last visit. His illusionary light threw strange shadows through the vast and ruined space. If the Eye was dead, if whatever power had animated it was now gone, he might not learn anything after all.
#figure(image("008_Revelation at the Eye/04.jpg", width: 100%), caption: [Sanctum of Ugin | Art by James Paick], supplement: none, numbering: none)
A cold, blue-white glow shone up ahead—were his eyes playing tricks? He snuffed his light. Yes. A glow. That meant—what? Some life remained in the Eye after all? Or someone else was already here?
He stepped carefully now, with so little light, down the path of jagged hedron shards. As he walked, the stones around him became more orderly—their faces and runes repaired, their alignments corrected.
"Welcome back," said a voice. It was smooth and powerful, seeming to thunder from the stone around him. "I hope you didn't come alone. My preparations are nearly complete."
A shape unfolded itself from the shadows of the enormous cavern. Horns glinted and wings unfurled, and an enormous dragon made a short glide toward him. Jace took a step back, heart racing. Bolas?
No. Not Bolas. This dragon was glowing from within with the soft light Jace had seen earlier.
The enormous shape settled before him, wings outstretched.
"Hmm," said the dragon, frowning. "You're not who I was expecting."
"I could say the same," said Jace. "Who are you?"
The dragon regarded him.
"Do you know the name of this place?"
"I do," said Jace. "But I'm not going to let you claim to be what I'm expecting. What's your name?"
The dragon smiled, keeping his teeth hidden.
"Fair enough," said the dragon. "My name is Ugin. I helped build this place, long ago."
Jace had assumed Ugin was long dead, if indeed Ugin had ever been a person at all. Yet here he was, in the luminous flesh. Jace tried to read the great being's mind, to verify his story, but found it as smooth and dazzling as a wall of crystal.
#figure(image("008_Revelation at the Eye/05.jpg", width: 100%), caption: [Ugin, the Spirit Dragon | Art by Chris Rahn], supplement: none, numbering: none)
"My name is <NAME>. I'm here to learn about the hedron network. I didn't imagine I'd find one of its builders."
"You've been here before," said Ugin. It was, unfortunately, not a question.
"Ah," said Jace. "Yes. Once. It . . . didn't go well."
"You released the Eldrazi," said Ugin.
"I—" said Jace. "Yes. There were three of us. We fought. The chamber—"
"I know," said Ugin. "You, a pyromancer, and a dragonspeaker. Planeswalkers all. You opened the Eye."
#emph[How did he know that?]
"It wasn't our fault," said Jace. "We were—"
"Manipulated, yes," said Ugin. "By another dragon Planeswalker, a rival of mine—"
"Oh, no."
"—<NAME>. You know him?"
"We're acquainted," said Jace. "This wouldn't be the first time he's manipulated me."
"It is his nature," said Ugin.
"Why?" said Jace. "Why would he want the Eldrazi released?"
"That," said Ugin, "is an excellent question, one I will devote considerable resources to answering. At the moment, however, we must do, in all likelihood, exactly what Bolas wants us to do, and that is focus on the Eldrazi."
"We'd better hurry," said Jace. "One of the Eldrazi titans is headed for Sea Gate right now."
"Sea Gate?" said Ugin.
Jace froze.
Mighty Ugin, creator of the Eye . . . didn't know Zendikar's greatest city?
"How long have you been away?" said Jace.
"Ages," said Ugin, with a tone that suggested the literal meaning of the word. "I was detained. Sea Gate?"
"A center of civilization and learning on the coast of Tazeem. They had scholarship on the hedrons, but it was lost to the Eldrazi. Now Ulamog is headed toward it to devour the survivors gathered there."
"Do not assume," said Ugin, "that you know anything of the minds of the Eldrazi. Ulamog goes where he does and does what he must."
"But they're drawn to concentrations of life, aren't they? There is a logic to their movements."
"They are and there is," said Ugin. "If survivors have congregated at this Sea Gate, then Ulamog could be seeking them out."
"We've got to stop him," said Jace. "Incapacitate him, kill him—whatever it takes."
"You cannot kill Ulamog," said Ugin.
"Stop him, then. Whatever we do, we need to do it now. People are dying. We have to do something, and thanks to your hedrons, we've got all the plane's leylines at our disposal. What do you suggest?"
Jace began to gather mana, a sensation like the rush of knowledge and a deep, cool current.
"I have allies, ancient and powerful ones," said Ugin. "The two who helped me imprison the Eldrazi on this world thousands of years ago . . . they can help. You've begun to understand the hedrons' true purpose. The Eldrazi can be imprisoned."
"And how did that work out last time?"
#figure(image("008_Revelation at the Eye/06.jpg", width: 100%), caption: [Hedron Archive | Art by <NAME>], supplement: none, numbering: none)
The dragon shifted. Rose. He felt it too, then, that nagging sensation that they might not be on the same side after all.
"Perfectly," said Ugin. "Until you and your cohorts let them out."
"You'll forgive me," said Jace, "if I take cold comfort in knowing that three people who knew next to nothing about any of this were able to overwhelm your security measures by #emph[accident] ."
"It was not an accident," said Ugin. "It was carefully orchestrated. Don't make the mistake of thinking your plans are the only ones that matter."
"Didn't you make the same mistake? You thought no one would want the Eldrazi released from their prison. But Bolas does. And if he wants them out, he can orchestrate them right back out again."
"You're still making assumptions," said Ugin. "Whatever Bolas wants, it's entirely possible he's already achieved it. And as you say, people are dying. We would be fools to pursue the impossible simply because you believe the achievable is flawed."
"Impossible is a hell of a word, coming from you," snapped Jace. "You know a lot more about the hedrons than I do, but all you can talk about is what we can't get done. You must have a better idea. Well? I'm listening!"
A rush of mana, a spell from the great dragon—but not an attack. An illusion. A network of scattered nodes and gently curving lines drawn in bright white light. Jace let it come.
"The hedron network," said Ugin, "as it was."
The dragon's voice was amplified, booming, echoing from within every one of the angular stones that made up the chamber's walls. The diagram grew larger and larger, a bright ring in the center looming balefully—the Eye of Ugin. Jace tried to take it in, but it was too much—too vast, too complicated, a knot he couldn't hope to untangle in a hundred lifetimes. A knot that Ugin had #emph[made] .
Then it changed. Nodes drifted; some vanished. The curves of the leylines—certainly, they were leylines—began to change. Within a few seconds, the network was disordered, chaotic.
"The Lithomancer who made these hedrons has been gone a long time," said Ugin. More illusions flared around the dragon, multiplied images of a kor woman with a broad smile and fierce eyes. Then she vanished. "Gone, or careless. Without her, the hedrons drifted. Then . . . you arrived. The Eldrazi were awakened, their brood lineages unleashed upon Zendikar. But my fail-safes remained in place. The Eldrazi were not yet free."
More change. Order. The network reasserted itself. Nodes arranged themselves back into curves, then into lines. What had been gentle, looping, a sort of cosmic finger-trap, became rigid, binding, strong. Jace stood rooted in one spot, unable to turn away from the abstract vision of a nightmare.
#figure(image("008_Revelation at the Eye/07.jpg", width: 100%), caption: [Island | Art by <NAME>], supplement: none, numbering: none)
"The network tried to contain the Eldrazi, just as it was designed to," said Ugin. "Without further interference, it might have succeeded. Then someone—or was that you too?—opened the last lock, dismantled the final fail-safe."
The diagram fractured. The nodes scattered. The lines went haywire. The Eye at the center went dark, so that Jace could see Ugin himself through it.
"The hedron network as it stands," said Ugin. "This is what we have to work with, Beleren. If three Planeswalkers at the height of our power could not kill the Eldrazi titans with the hedrons in full working order, what makes you think you and I can do it with this sad remnant?"
Jace gritted his teeth. Enough of this. Enough.
"You're speaking in abstractions," he said.
He fired off a counterspell to tear through Ugin's illusion, and sent up a few of his own. Sea Gate at its height, when Jace had visited it shortly after the Eldrazi rose. The survivors' camp when he'd been there weeks ago, where the same scholars, now diminished in number and in hope, huddled around campfires. Gideon, standing tall, inspiring people. Nissa communing with the land.
#figure(image("008_Revelation at the Eye/08.jpg", width: 100%), caption: [Dispel | Art by Chase Stone], supplement: none, numbering: none)
"Zendikar isn't a puzzle to be solved," said Jace. "It's a #emph[place] . It's somebody's home. And those people are out there, right now, fighting for their world and wondering if anybody's going to help them kill what's killing them."
He showed scenes of suffering, then—of families mourning the lost, of landscapes ravaged by Ulamog, of even the skies and seas teeming with the Eldrazi menace.
Ugin cocked his head. The hedron architecture of the chamber seemed to melt and flow, became a pattern of tessellating dragons mocking him from the walls.
"So certain," said Ugin, "and so young."
The diagram sprang back, crowding out Jace's images. Then it changed again—restored, as much as its current state allowed. It had fewer nodes, more sharply curving lines. A pattern. A glyph—circular, with three points at equal intervals around the circumference. He'd never seen the glyph before, but immediately he understood it. Leylines. If the leylines of Zendikar could be coaxed into this shape . . .
"The Eldrazi can be imprisoned," Ugin said again. "You speak of killing them as though they were houseflies. You shouldn't—and you can't."
"Don't tell me about #emph[can't] ," said Jace. "Tell me about #emph[will] or #emph[won't] . Kill them, trap them . . . it's irrelevant. All of it. I came here to stop them. So did you. Right?"
Jace's illusions flowed and changed without his willing it, became enveloped by the vast abstraction of the hedron network.
"Your knowledge of the hedrons," said Jace. "My knowledge of Zendikar on the ground. Of a place called Sea Gate. Of the people here and why they're worth saving."
"Do not lecture me about what is worth saving," said Ugin, his voice booming. "There is more than this world at stake—certainly more than the people who happen to be alive here at the moment. You come to me speaking of the threat of Ulamog. But do not forget: They came as three. With the Eldrazi at large, the entire Multiverse is at risk. That is what I am here to save, Beleren. The Multiverse, in all its vastness of time and space. Not the people you shared a cookfire with."
Dragon and diagram became one, luminous and looming. Lines and nodes, wings and horns, the shapes of hedrons, and at the center one glowing, glowering Eye. Jace faltered under its gaze.
"Tell me what to do, Ugin. Tell me how to help."
The Eye pulsed. Jace's consciousness began to fade.
Then it was gone. Ugin's illusions, Jace's, all of it. Only the chamber and the dragon remained.
"You truly want to help?"
"That's why I came here," said Jace. "I did have a hand in releasing the Eldrazi. If I can take part in stopping them, I will."
"I said earlier that you weren't who I was expecting," said Ugin. "My allies, the two who helped me imprison the Eldrazi thousands of years ago . . . are not here. One is missing. I sent the other after her. I've heard from neither since. They are needed here, urgently. Have you heard of a Planeswalker named <NAME>?"
#figure(image("008_Revelation at the Eye/09.jpg", width: 100%), caption: [Art by <NAME>], supplement: none, numbering: none)
"No," said Jace. "Should I have?"
"Only because of his connection to this place," said Ugin. "He is my erstwhile ally, self-proclaimed lord of his home plane of Innistrad."
One of Liliana's favorite haunts, though Jace had never been there.
"That I've heard of," said Jace. "You could say I have an ally there myself."
#emph[You'd be kidding yourself] , he thought, #emph[but you could say that.]
"Good," said Ugin. "Sorin is crucial to our efforts. If you want to help, then seek him out, bring him here, but . . . do not trust him."
"What does that mean?"
"It means," said Ugin, "that although he speaks of the greater good, he is a selfish creature. He fought the Eldrazi not out of compassion for Zendikar, but out of a very long-minded sense of self-preservation. If more urgent matters have consumed his attention, his priorities may not align with our own."
Jace wasn't sure if it was the longevity or the power, but he'd noticed that ancient Planeswalkers had something in common: They were all completely insane.
"What about your other ally?" said Jace.
"Nahiri, called the Lithomancer," said Ugin. "A kor of Zendikar, and its guardian. I do not know why she would leave this world, and I cannot imagine that she would stay away if she could possibly return. Something has happened to her. If you cannot find Sorin, find her."
"I'm not abandoning Zendikar," said Jace. "I've got friends here." Friends. Yes. Close enough, at any rate. "They're relying on me to return with information about the hedron network. Unless you want to go to Sea Gate and tell them yourself?"
"No," said Ugin. "I am needed here, at the Eye. I must rebuild the central chamber so that my associates can restore the network to its full function and trap the Eldrazi once more."
"Then I'm afraid your allies will have to sort themselves out," said Jace. "What can I do here?"
"The hedron network is damaged," said Ugin. "I will need Ulamog corralled. Contained, within a circle of hedrons. Will these friends of yours help imprison an Eldrazi titan, rather than try to kill it?"
"I think so," said Jace, though in fact he was far from certain. "But only if I can convince them it's the only option. They've seen plenty of Eldrazi die. And you still haven't told me why we can't kill Ulamog."
"The Eldrazi titans do not dwell in physical space," said Ugin. "They are creatures of the Blind Eternities, and it is in the Eternities that they remain."
"Until they manifest physically, you mean?"
"No," said Ugin. "I meant what I said. Ulamog remains in the Eternities."
"Then what did I see heading toward Sea Gate?"
"You saw a portion of him," said Ugin. "A projection. Imagine that you reach your hand into a pond. The fish below the surface sees a five-headed monster, and cannot perceive the man attached to it. It mistakes a hangnail for an eye because the truth is beyond its imagining. You see?"
"And when you trapped them . . ."
"Like driving a spike through the hand," said Ugin. "The man will not die, but neither will he trouble other ponds. 'Killing' Ulamog's physical form would be like cutting off the hand. The man might be diminished, but he would survive—and he would be freed."
"But the hedrons don't just direct leylines," said Jace, thinking fast. "They store energy. Vast amounts of it. That's how they pulled the Eldrazi in to begin with, isn't it?"
It was a guess, but it seemed a reasonable one.
"Correct," said Ugin. "Your point?"
Jace's mind raced.
If the hedrons could pull, then couldn't they pull harder? With enough power, couldn't they be used to draw the Eldrazi fully into the physical realm? If you had a spike through a man's hand, you could do a lot more than hold him there. You could pull him into the pond. And then . . .
"I . . . no, never mind," said Jace. "Sorry. Still wrapping my head around all this."
The dragon had made his position on killing Ulamog quite clear, and Jace himself wasn't at all sure it was a good idea. He understood the hedrons now. He'd seen the glyph. If Ugin would help them imprison the Eldrazi, then that was, at the very least, a good first step. And if the opportunity arose to do more . . . he'd be ready. And Ugin might not be.
"Of course," said Ugin. "Considering your inexperience, you're keeping up better than I'd expect."
It was intended as a compliment. Jace decided to take it as such.
"This . . . hand metaphor," said Jace. "It's describing the three titans. What about all the others? Does killing them free them too? Are there thousands of Eldrazi loose in the Eternities now?"
"Suppose the man reaches his other hand into the pond," said Ugin. "Does the fish face one monster, or two?"
Jace's patience for this method of imparting information was minimal, but he tried to give the dragon's question-answers due consideration.
"The fish sees two beings," he said, after a moment. "But they're part of one whole."
"Suppose the man has a hundred hands," said Ugin. "Or a million."
Understanding dawned. A wave of nausea overtook him.
"You're saying they're connected. Ulamog's brood aren't really spawn. They're . . . appendages."
"More like cells," said Ugin. "Organs, in the case of some of the larger ones. But all of them are replaceable—sub-lives that come into being, fulfill their function, and die or a reabsorbed, without diminishing the whole."
"So killing them does nothing, other than keeping them from killing you."
"Ultimately, no," said Ugin.
Jace ran a hand through his hair.
"All right," he said. "That's enough information. I'll present your plan to my friends at Sea Gate. I'll try to convince them that imprisoning Ulamog is the right course of action."
#figure(image("008_Revelation at the Eye/10.jpg", width: 100%), caption: [Ulamog, the Ceaseless Hunger | Art by <NAME>], supplement: none, numbering: none)
"You must do more than try," said Ugin. "With the hedron network damaged and the fail-safe removed, the titans are free to leave the plane. If Ulamog is wounded, you could drive him away from Zendikar entirely. Away from the hedron network, and our best chance of stopping him. You understand why that would be a disaster. But it may not seem that way to the people of Zendikar. You must dissuade your friends from attacking Ulamog directly—and, if necessary, you must stop them."
"Understood," said Jace. "I'll tell them."
"Do not let them drive Ulamog away from Zendikar," said Ugin. "The consequences would be grave, and that justifies whatever means are necessary to stop it."
"You've made yourself clear," said Jace. "I won't let Ulamog escape."
#emph[One way or another] , he thought.
"Good fortune, <NAME>. I will make sure my preparations are complete."
"I'll be ready," said Jace.
Jace turned, walked out of the Eye of Ugin, and stepped into the sunlight. He had a plan. He had a destination. He #emph[was] ready.
One way or another.
|
|
https://github.com/LaurenzV/simplecv | https://raw.githubusercontent.com/LaurenzV/simplecv/main/src/main.typ | typst | MIT License | #import "simplecv.typ": template, education_entry, work_entry, skill_entry
// Change the theme color of the cv.
#let color = green
// Change to your name.
#let name = "<NAME>"
// Change the shown contact data. You can also change the order of the elements so that they will show up in a different order. Currently, only these five elements are available with icons, but you can add new ones by editing the template.
#let contact_data = (
(
"service": "linkedin",
"display": "<NAME>",
"link": "https://www.linkedin.com/in/JohnDoe"
),
(
"service": "email",
"display": "<EMAIL>",
"link": "mailto://<EMAIL>"
),
(
"service": "phone",
"display": "+1 123 456 789",
"link": "tel:+1 123 456 789"
),
(
"service": "github",
"display": "JohnDoe",
"link": "https://github.com/JohnDoe"
),
(
"service": "website",
"display": "mywebsite.com",
"link": "https://mywebsite.com"
),
)
#show: doc => template(name, contact_data, color, doc)
// Starting from here, you can add as much content as you want. This represents the main content of the cv.
= Education
#education_entry("Computer Science", "Stanford University",
degree_title: "BSc.", start_date: "Sep 2012", end_date: "Jul 2016",
description: lorem(12), location: "California, USA")
= Experience
#work_entry("Senior Software Engineer", "Microsoft", start_date: "Since Nov 2021", tasks: (
lorem(7),
lorem(13),
lorem(9)
),
location: "Seattle, USA")
#work_entry("Senior Software Engineer", "Apple", start_date: "Jan 2020", end_date: "Oct 2021", tasks: (
lorem(4),
lorem(6),
lorem(14)
),
location: "California, USA")
#work_entry("Junior Software Engineer", "Google", start_date: "Oct 2016", end_date: "Nov 2019", tasks: (
lorem(8),
lorem(12),
lorem(3)
),
location: "California, USA")
= Projects
*Project 1*. #lorem(40)
*Project 2*. #lorem(32)
*Project 3*. #lorem(40)
= Skills
// Ratings won't be displayed in this template.
#skill_entry("Technologies",
(
"Git",
"C++",
"Python",
"JavaScript",
"Vue.js",
"Docker",
"Kubernetes"
)
)
#skill_entry("Languages",
(
"English",
"German",
"Spanish",
"Japanese",
)
) |
https://github.com/JosephDavis/typst-starter | https://raw.githubusercontent.com/JosephDavis/typst-starter/main/readme.md | markdown | # Typst Starter
## Local Setup
### Rust and Typst Installation
1. [Install Rust](https://www.rust-lang.org/tools/install)
- `curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh`
- Downloads and runs the Rust installation script.
2. `cargo install --locked typst-cli`
- Installs the Typst command-line tool using Cargo (Rust's package manager).
3. `typst --version`
### `compile.sh`
This script automates the compilation of Typst documents within your project. It offers two modes of operation:
**Usage:**
1. **Compile All Documents:** This command will recursively search the `docs/` directory for all `.typ` files and compile them into corresponding PDFs in the `out/` directory. The output directory structure will mirror the `docs/` directory.
```bash
./compile.sh
```
2. **Compile a Single Document:** Provide the path to a specific `.typ` file you want to compile. The script will generate the PDF in the `out/` directory, maintaining the relative path.
```bash
./compile.sh <path/to/file.typ>
```
**Example:**
```bash
./compile.sh docs/papers/my_paper.typ
```
This would compile `my_paper.typ` and place the resulting PDF at `out/reports/my_paper.pdf`.
|
|
https://github.com/7sDream/fonts-and-layout-zhCN | https://raw.githubusercontent.com/7sDream/fonts-and-layout-zhCN/master/chapters/02-concepts/dimension/units-graph.typ | typst | Other | #import "/lib/draw.typ": *
#import "/template/theme.typ": theme
#import "/template/lang.typ": bengali
#let start = (0, 0)
#let end = (1000, 690)
#let graph = with-unit((ux, uy) => {
// mesh(start, end, (100, 100), stroke: 1 * ux + gray)
let char = bengali(
// TODO: Typst text stroke needs improvment
// stroke: (
// thickness: 10 * ux,
// join: "miter",
// miter-limit: 4,
// ),
// fill: white.transparentize(100%),
)[ব]
let subgraph = (dx, dy, scale) => {
txt(char, (dx, dy), size: 400 * ux * scale, anchor: "cb", dy: -5 * scale)
rect(
(-115 * scale + dx, 370 * scale + dy),
width: 230 * scale,
height: 490 * scale,
)
segment(
(-115 * scale + dx, 0 + dy),
(-115 * scale + dx + 230 * scale, 0 + dy),
)
arrow(
(80 * scale + dx, dy - 15 * scale),
(50 * scale + dx, dy - 15 * scale),
stroke: 2 * ux + theme.main,
head-scale: 2 * scale,
)
arrow-head(
(82 * scale + dx, dy - 15 * scale), 4 * scale,
)
arrow(
(-115 * scale + dx + 230 * scale + 20 * scale, 370 * scale + dy - 5),
(-115 * scale + dx + 230 * scale + 20 * scale, 370 * scale + dy - 490 * scale),
stroke: 2 * ux + theme.main,
head-scale: 5,
)
arrow-head(
(-115 * scale + dx + 230 * scale + 20 * scale, 370 * scale + dy), 10, theta: 90deg
)
}
subgraph(150, 175, 1)
subgraph(650, 175, 1.2)
txt([2048 个单位 = 10pt], (290, 560), anchor: "cb")
txt([157 个单位], (250, 140), anchor: "rt")
txt([0.766pt], (250, 100), anchor: "rt")
txt([2048 个单位 = 12pt], (800, 640), anchor: "cb")
txt([157 个单位], (760, 140), anchor: "rt")
txt([0.920pt], (760, 100), anchor: "rt")
})
#canvas(end, start: start, width: 80%, graph)
|
https://github.com/jgm/typst-hs | https://raw.githubusercontent.com/jgm/typst-hs/main/test/typ/compiler/import-03.typ | typst | Other | // A module import without items.
#import "module.typ"
#test(module.b, 1)
#test(module.item(1, 2), 3)
#test(module.push(2), 3)
|
https://github.com/typst-community/guidelines | https://raw.githubusercontent.com/typst-community/guidelines/main/src/chapters/style/delimiters.typ | typst | Creative Commons Attribution Share Alike 4.0 International | #import "/src/util.typ": *
#import mantys: *
= Delimiters
Opening delimiters to unfinished statements like `(...)`, `[...]`, etc. are placed on the same line as their preceding element, e.g. for loops, declarations, etc.
This is actually enforced by the compiler in most cases, as it uses line breaks to terminate most statements.
#do-dont[
```typst
// if it fits on one line avoid linebreaks
#let var = if { ... }
// if there's a little more we break K&R style
#let var = for x in xs [
...
]
// likewise, else must be on the same line as the if's closing brace
#if var {
// ...
} else {
// ...
}
```
][
```typst
// this doesn't parse
#let var =
{
}
// ask yourself not if you could, but if you should
#(
if true
{
}
else
{
}
)
```
]
|
https://github.com/Robotechnic/alchemist | https://raw.githubusercontent.com/Robotechnic/alchemist/master/src/links.typ | typst | MIT License | #import "@preview/cetz:0.2.2"
#import "drawer.typ"
#import "utils.typ"
/// Create a link function that is then used to draw a link between two points
///
///
/// - draw-function (function): The function that will be used to draw the link. It should takes three arguments: the length of the link, the context, and a dictionary of named arguments that can be used to configure the links
/// -> function
#let build-link(draw-function) = {
(..args) => {
if args.pos().len() != 0 {
panic("Links takes no positional arguments")
}
let args = args.named()
(
(
type: "link",
draw: (length, ctx, override: (:)) => {
let args = args
for (key, val) in override {
args.insert(key, val)
}
draw-function(length, ctx, args)
},
links: (:),
..args,
),
)
}
}
/// Draw a single line between two molecules
/// #example(```
/// #skeletize({
/// molecule("A")
/// single()
/// molecule("B")
/// })
///```)
/// It is possible to change the color and width of the line
/// with the `stroke` argument
/// #example(```
/// #skeletize({
/// molecule("A")
/// single(stroke: red + 5pt)
/// molecule("B")
/// })
///```)
#let single = build-link((length, _, args) => {
import cetz.draw: *
line((0, 0), (length, 0), stroke: args.at("stroke", default: black))
})
/// Draw a double line between two molecules
/// #example(```
/// #skeletize({
/// molecule("A")
/// double()
/// molecule("B")
/// })
///```)
/// It is possible to change the color and width of the line
/// with the `stroke` argument and the gap between the two lines
/// with the `gap` argument
/// #example(```
/// #skeletize({
/// molecule("A")
/// double(
/// stroke: orange + 2pt,
/// gap: .8em
/// )
/// molecule("B")
/// })
///```)
/// This link also supports an `offset` argument that can be set to `left`, `right` or `center`.
///It allows to make either the let side, right side or the center of the double line to be aligned with the link point.
/// #example(```
/// #skeletize({
/// molecule("A")
/// double(offset: "right")
/// molecule("B")
/// double(offset: "left")
/// molecule("C")
/// double(offset: "center")
/// molecule("D")
/// })
///```)
#let double = build-link((length, ctx, args) => {
import cetz.draw: *
let gap = utils.convert-length(ctx, args.at("gap", default: .25em)) / 2
let offset = args.at("offset", default: "center")
let coeff = args.at("offset-coeff", default: 0.85)
if coeff < 0 or coeff > 1 {
panic("Invalid offset-coeff value: must be between 0 and 1")
}
if offset == "right" {
translate((0, -gap))
} else if offset == "left" {
translate((0, gap))
} else if offset == "center" { } else {
panic("Invalid offset value: must be \"left\", \"right\" or \"center\"")
}
translate((0, -gap))
line(
..if offset == "right" {
let x = length * (1 - coeff) / 2
((x, 0), (x + length * coeff, 0))
} else {
((0, 0), (length, 0))
},
stroke: args.at("stroke", default: black),
)
translate((0, 2 * gap))
line(
..if offset == "left" {
let x = length * (1 - coeff) / 2
((x, 0), (x + length * coeff, 0))
} else {
((0, 0), (length, 0))
},
stroke: args.at("stroke", default: black),
)
})
/// Draw a triple line between two molecules
/// #example(```
/// #skeletize({
/// molecule("A")
/// triple()
/// molecule("B")
/// })
///```)
/// It is possible to change the color and width of the line
/// with the `stroke` argument and the gap between the three lines
/// with the `gap` argument
/// #example(```
/// #skeletize({
/// molecule("A")
/// triple(
/// stroke: blue + .5pt,
/// gap: .15em
/// )
/// molecule("B")
/// })
///```)
#let triple = build-link((length, ctx, args) => {
import cetz.draw: *
let gap = utils.convert-length(ctx, args.at("gap", default: .25em))
line((0, 0), (length, 0), stroke: args.at("stroke", default: black))
translate((0, -gap))
line((0, 0), (length, 0), stroke: args.at("stroke", default: black))
translate((0, 2 * gap))
line((0, 0), (length, 0), stroke: args.at("stroke", default: black))
})
/// Draw a filled cram between two molecules with the arrow pointing to the right
/// #example(```
/// #skeletize({
/// molecule("A")
/// cram-filled-right()
/// molecule("B")
/// })
///```)
/// It is possible to change the stroke and fill color of the arrow
/// with the `stroke` and `fill` arguments. You can also change the base length of the arrow with the `base-length` argument
/// #example(```
/// #skeletize({
/// molecule("A")
/// cram-filled-right(
/// stroke: red + 2pt,
/// fill: green,
/// base-length: 2em
/// )
/// molecule("B")
/// })
///```)
#let cram-filled-right = build-link((length, ctx, args) => drawer.cram(
(0, 0),
(length, 0),
ctx,
args,
))
/// Draw a filled cram between two molecules with the arrow pointing to the left
/// #example(```
/// #skeletize({
/// molecule("A")
/// cram-filled-left()
/// molecule("B")
/// })
///```)
/// It is possible to change the stroke and fill color of the arrow
/// with the `stroke` and `fill` arguments. You can also change the base length of the arrow with the `base-length` argument
/// #example(```
/// #skeletize({
/// molecule("A")
/// cram-filled-left(
/// stroke: red + 2pt,
/// fill: green,
/// base-length: 2em
/// )
/// molecule("B")
/// })
///```)
#let cram-filled-left = build-link((length, ctx, args) => drawer.cram(
(length, 0),
(0, 0),
ctx,
args,
))
/// Draw a hollow cram between two molecules with the arrow pointing to the right
/// It is a shorthand for `cram-filled-right(fill: none)`
#let cram-hollow-right = build-link((length, ctx, args) => {
args.fill = none
args.stroke = args.at("stroke", default: black)
drawer.cram((0, 0), (length, 0), ctx, args)
})
/// Draw a hollow cram between two molecules with the arrow pointing to the left
/// It is a shorthand for `cram-filled-left(fill: none)`
#let cram-hollow-left = build-link((length, ctx, args) => {
args.fill = none
args.stroke = args.at("stroke", default: black)
drawer.cram((length, 0), (0, 0), ctx, args)
})
/// Draw a dashed cram between two molecules with the arrow pointing to the right
/// #example(```
/// #skeletize({
/// molecule("A")
/// cram-dashed-right()
/// molecule("B")
/// })
///```)
/// It is possible to change the stroke of the lines in the arrow
/// with the `stroke` argument. You can also change the base length of the arrow with the `base-length` argument and distance between the dashes with the `dash-gap` argument
/// #example(```
/// #skeletize({
/// molecule("A")
/// cram-dashed-right(
/// stroke: red + 2pt,
/// base-length: 2em,
/// dash-gap: .5em
/// )
/// molecule("B")
/// })
///```)
#let cram-dashed-right = build-link((length, ctx, args) => drawer.dashed-cram(
(0, 0),
(length, 0),
length,
ctx,
args,
))
/// Draw a dashed cram between two molecules with the arrow pointing to the left
/// #example(```
/// #skeletize({
/// molecule("A")
/// cram-dashed-left()
/// molecule("B")
/// })
///```)
/// It is possible to change the stroke of the lines in the arrow
/// with the `stroke` argument. You can also change the base length of the arrow with the `base-length` argument and distance between the dashes with the `dash-gap` argument
/// #example(```
/// #skeletize({
/// molecule("A")
/// cram-dashed-left(
/// stroke: red + 2pt,
/// base-length: 2em,
/// dash-gap: .5em
/// )
/// molecule("B")
/// })
///```)
#let cram-dashed-left = build-link((length, ctx, args) => drawer.dashed-cram(
(length, 0),
(0, 0),
length,
ctx,
args,
)) |
https://github.com/UriMtzF/uaemex-typst-template | https://raw.githubusercontent.com/UriMtzF/uaemex-typst-template/main/template.typ | typst | Apache License 2.0 | #let getDate(date) = {
if date.month < 1 or date.month > 12 {
panic("Fecha no valida")
}
let monthTxt = ("enero", "febrero", "marzo", "abril", "mayo", "junio", "julio", "agosto", "septiembre", "octubre", "noviembre", "diciembre")
return str(date.day) + " de " + monthTxt.at(date.month - 1) + " de " + str(date.year)
}
#let project(subject:"", title: "", authors: (), date: (), isIndexed: bool ,body) = {
set document(author: authors, title: title)
set page(
paper: "us-letter",
numbering: none,
number-align: center,
margin: (x: 2cm, y: 2cm)
)
set text(font: "New Computer Modern", lang: "es")
align(center)[
// You can change the header of the cover page by your own image, recommended sizes
// width: 1800px; height: 320px
#block((image("encabezado.jpg", width: 100%)))
// The faculty name can be changed
#block(text(weight: 700, 1.8em, "Facultad de ingeniería"))
#v(15%, weak: true)
#block(text(weight: 500, 2em, subject))
#v(15%, weak: true)
#block(text(weight: 300, 2em, style: "italic", title))
#align(bottom)[
#if authors.len() == 1{
text(weight: 300, 1.5em, "Alumno:")
}else if authors.len() > 2 {
text(weight: 300, 1.5em, "Alumnos:")
}
#for author in authors [
#block(text(weight: 300, 1.5em, author))
]
#v(10%, weak: true)
#block(text(weight: 300, 1.3em, getDate(date)))
]
]
set page(numbering: "1")
if isIndexed == true {
outline(depth: 3, indent: true)
pagebreak()
}
body
}
|
https://github.com/herbhuang/utdallas-thesis-template-typst | https://raw.githubusercontent.com/herbhuang/utdallas-thesis-template-typst/main/content/requirements_analysis.typ | typst | MIT License | #import "/utils/todo.typ": TODO
= Requirements Analysis
#TODO[
This chapter follows the Requirements Analysis Document Template in @bruegge2004object. Important: Make sure that the whole chapter is independent of the chosen technology and development platform. The idea is that you illustrate concepts, taxonomies and relationships of the application domain independent of the solution domain! Cite @bruegge2004object several times in this chapter.
]
== Overview
#TODO[
Provide a short overview about the purpose, scope, objectives and success criteria of the system that you like to develop.
]
== Current System
#TODO[
This section is only required if the proposed system (i.e. the system that you develop in the thesis) should replace an existing system.
]
== Proposed System
#TODO[
If you leave out the section “Current system”, you can rename this section into “Requirements”.
]
=== Functional Requirements
#TODO[
List and describe all functional requirements of your system. Also mention requirements that you were not able to realize. The short title should be in the form “verb objective”
- FR1 Short Title: Short Description.
- FR2 Short Title: Short Description.
- FR3 Short Title: Short Description.
]
=== Nonfunctional Requirements
#TODO[
List and describe all nonfunctional requirements of your system. Also mention requirements that you were not able to realize. Categorize them using the FURPS+ model described in @bruegge2004object without the category functionality that was already covered with the functional requirements.
- NFR1 Category: Short Description.
- NFR2 Category: Short Description.
- NFR3 Category: Short Description.
]
== System Models
#TODO[
This section includes important system models for the requirements analysis.
]
=== Scenarios
#TODO[
If you do not distinguish between visionary and demo scenarios, you can remove the two subsubsections below and list all scenarios here.
*Visionary Scenarios*
Describe 1-2 visionary scenario here, i.e. a scenario that would perfectly solve your problem, even if it might not be realizable. Use free text description.
*Demo Scenarios*
Describe 1-2 demo scenario here, i.e. a scenario that you can implement and demonstrate until the end of your thesis. Use free text description.
]
=== Use Case Model
#TODO[
This subsection should contain a UML Use Case Diagram including roles and their use cases. You can use colors to indicate priorities. Think about splitting the diagram into multiple ones if you have more than 10 use cases. *Important:* Make sure to describe the most important use cases using the use case table template (./tex/use-case-table.tex). Also describe the rationale of the use case model, i.e. why you modeled it like you show it in the diagram.
]
=== Analysis Object Model
#TODO[
This subsection should contain a UML Class Diagram showing the most important objects, attributes, methods and relations of your application domain including taxonomies using specification inheritance (see @bruegge2004object). Do not insert objects, attributes or methods of the solution domain. *Important:* Make sure to describe the analysis object model thoroughly in the text so that readers are able to understand the diagram. Also write about the rationale how and why you modeled the concepts like this.
]
=== Dynamic Model
#TODO[
This subsection should contain dynamic UML diagrams. These can be a UML state diagrams, UML communication diagrams or UML activity diagrams.*Important:* Make sure to describe the diagram and its rationale in the text. *Do not use UML sequence diagrams.*
]
=== User Interface
#TODO[
Show mockups of the user interface of the software you develop and their connections / transitions. You can also create a storyboard. *Important:* Describe the mockups and their rationale in the text.
] |
https://github.com/7sDream/fonts-and-layout-zhCN | https://raw.githubusercontent.com/7sDream/fonts-and-layout-zhCN/master/chapters/08-adv-features/random.typ | typst | Other | #import "/template/template.typ": web-page-template
#import "/template/components.typ": note
#import "/lib/glossary.typ": tr
#show: web-page-template
// ## Randomization
== 随机性
|
https://github.com/LucaCiucci/tesi-triennale | https://raw.githubusercontent.com/LucaCiucci/tesi-triennale/main/slide.typ | typst | Creative Commons Zero v1.0 Universal |
#let title = [Monopoli Magnetici]
#let page_scale = 35pt
//#let __slide-final-only = state("slide-final-only", false)
#let slide-final-only = if sys.inputs.keys().contains("compact-slides") {
lower(sys.inputs.compact-slides) == "true"
} else {
false
}
#let slide-final-result = if sys.inputs.keys().contains("final") {
lower(sys.inputs.final) == "true"
} else {
false
}
#let sub-slide-index = state("sub-slide-index", 0)
#let config-slides(
//final-only: none,
) = {
//if final-only != none {
// __slide-final-only.update(final-only)
//}
}
#let data-laurea = datetime(
year: 2024,
month: 7,
day: 17,
);
#let data-laurea-d = data-laurea.display("[year]/[month]/[day]")
#let logo_path = "img/logo/cherubino_white144.gif"
#let logo_path_2 = "img/logo/cherubino_pant541_144.gif"
#let theme_blue = rgb("#0F406B")
#let theme_blue_light = rgb("#4A7EBB")
#let pause = metadata((
lc-type: "pause",
))
#let raw-slide = (
counter-name: "slide",
counter-increment: true,
counter-display: "1",
section: (),
new-section: true,
side-content: [],
sub-step: 0,
sub-steps: 0,
body,
) => page(
width: 16 * page_scale,
height: 9 * page_scale,
margin: 0pt,
flipped: false,
{
let header_height = 17pt
let header_stroke_width = 2pt
let logo_with = 50pt
if counter-increment {
counter(counter-name).step()
}
let n_pages = context counter("slide").final().at(0)
let slide_number_display = counter(counter-name).display(counter-display)
if section.len() > 0 {
let section_heading = heading(section.last(), supplement: [section], level: section.len())
if (new-section) {
place(center + top, hide(section_heading))
}
}
place(top + left, rect(stroke: none, fill: white, width: 100%, height: 100%))
place(
top + right,
box(
radius: ( bottom: 50%, ),
stroke: theme_blue_light + header_stroke_width * 2,
inset: 2pt,
hide(image(logo_path, width: logo_with)),
),
)
place(
top,
rect(
fill: theme_blue,
stroke: ( bottom: theme_blue_light + header_stroke_width, ),
width: 100%,
height: header_height,
align(horizon, [
#set text(white, 10pt)
#title #section.map(s => [ $->$ #s ]).join()
#place(
right + horizon,
dx: -logo_with - 5pt,
text(size: 8pt)[Università di Pisa - Dipartimento di Fisica],
)
])
),
)
place(
top + right,
box(
fill: theme_blue,
radius: ( bottom: 50%, ),
inset: 2pt,
image(logo_path, width: logo_with),
),
)
place(
bottom,
rect(
fill: theme_blue,
stroke: ( top: theme_blue_light + header_stroke_width, ),
width: 100%,
height: header_height,
align(horizon, [
#set text(white, 10pt)
<NAME> - Appello Laurea Triennale #data-laurea-d
#place(
right + horizon,
[
#box(
width: 4em,
//stroke: red,
if sub-steps <= 5 {
align(
left,
" " + range(sub-steps)
.map(s => if s <= sub-step { sym.circle.filled } else { sym.circle.stroked })
.join(),
)
} else {
align(
left,
rect(
width: 100%,
height: 0.75em,
stroke: white,
radius: 50%,
inset: if sub-step == sub-steps - 1 { 0pt } else { 2pt },
rect(
width: (sub-step + 1) * 100% / sub-steps,
height: 100%,
radius: 50%,
fill: white,
stroke: none,
),
)
)
},
)
#box(
//width: 3.5em,
[#slide_number_display / #n_pages],
)
#h(1.0em)
#box(link("https://creativecommons.org/publicdomain/zero/1.0/", stack(dir: ltr, image("img/CC/cc.svg", height: 1em), image("img/CC/zero.svg", height: 1em))))
#h(0.5em)
#box(link("https://github.com/LucaCiucci/tesi-triennale", image("img/github/github-mark-white.svg", height: 1em)))
],
)
])
),
)
place(
right + top,
dx: -2pt,
dy: logo_with + 5pt,
rect(
width: logo_with * 1.5,
stroke: none,
inset: 0pt,
)[
#show outline.entry: it => {
text(
size: 6pt,
link(
it.element.location(),
if section.len() > 0 and it.element.body == section.last() {
text(blue, sym.circle.filled + h(0.5em) + it.body)
} else {
context if counter(page).at(it.element.location()).at(0) < counter(page).get().first() { sym.circle.filled } else { sym.circle.stroked } + h(0.5em) + it.body
},
)
)
}
#align(
left,
[
#outline(
depth: 5,
indent: 5pt,
fill: [],
title: [],
target: heading.where(supplement: [section])
)
#side-content
],
)
]
)
rect(
//stroke: red,
stroke: none,
//fill: red,
width: 100%,
height: 100%,
inset: (
top: header_height + header_stroke_width + 5pt,
bottom: header_height + header_stroke_width,
left: 15pt,
right: logo_with * 1.5 + header_stroke_width * 2 + 1em,
),
{
show link: link => text(link, rgb("#0000CD").darken(50%))
show ref: ref => text(ref, rgb("#0000CD").darken(50%))
body
},
)
}
)
#let current-step() = [#sub-slide-index.get()]
#let steps = (
switch: false,
skip: 0,
..pieces
) => {
locate(loc => {
let step = sub-slide-index.at(loc)
if switch {
pieces
.pos()
.enumerate()
.map(it => if it.at(0) + skip == step or (step > it.at(0) and it.at(0) + 1 == pieces.pos().len() + skip) { it.at(1) } else { [] })
.join()
} else {
pieces
.pos()
.enumerate()
.map(it => if it.at(0) + skip <= step { it.at(1) } else { hide(it.at(1)) })
.join()
}
})
}
#let slide(
section: (),
steps: (),
body,
) = {
if steps == () {
return raw-slide(
section: section,
body,
)
}
if type(steps) == "integer" {
steps = range(steps)
}
if slide-final-only {
let step = steps.last()
raw-slide(
section: section,
counter-increment: true,
new-section: true,
[#sub-slide-index.update(steps.len())] + body,
)
} else {
for (index, step) in steps.enumerate() {
raw-slide(
section: section,
counter-increment: step == steps.first(),
new-section: step == steps.last(),
sub-step: index,
sub-steps: steps.len(),
[#sub-slide-index.update(index)] + body,
)
}
}
}
#let non-slide(
color: gray,
header: [HEADER],
body
) = if not slide-final-result {
page(
width: 16 * page_scale,
height: 9 * page_scale,
margin: 1cm,
flipped: false,
header: [
#rect(
width: 100%,
stroke: color + 2pt,
radius: 2pt,
fill: color.lighten(80%),
align(center)[
#text(black, header)
]
)
],
{
set heading(numbering: "1.")
set math.equation(numbering: "(1)")
body
}
)
} else {}
#let note(body) = non-slide(
color: green,
header: [#emoji.book.open *Note* #emoji.book.open],
body
)
#let script(body) = non-slide(
color: blue,
header: [#emoji.scroll *Script* #emoji.scroll],
text(size: 1.25em, body)
)
#let abstract(body) = non-slide(
color: purple,
header: [#emoji.page *Long Abstract* #emoji.page],
{
import "@preview/wordometer:0.1.2"
let n-chars = wordometer.extract-text(body).trim().len()
let expected = 3000
let tolerance = 300
body
place(bottom + right)[
Lunghezza: #if calc.abs(n-chars - expected) < tolerance { text(green)[#n-chars] } else { text(red)[#n-chars] } / #expected #sym.plus.minus #tolerance caratteri
]
}
)
#let cols(..columns) = {
// take positional list:
let columns = columns.pos();
let n = columns.len();
let columns = columns.map(it => box(
//fill: red,
//stroke: red,
width: 100% / n,
height: 100%,
it
))
stack(
dir: ltr,
spacing: 5pt,
..columns
)
} |
https://github.com/sitandr/typst-examples-book | https://raw.githubusercontent.com/sitandr/typst-examples-book/main/src/basics/scripting/index.md | markdown | MIT License | # Scripting
**Typst** has a complete interpreted language inside. One of key aspects of working with your document in a nicer way
|
https://github.com/crd2333/crd2333.github.io | https://raw.githubusercontent.com/crd2333/crd2333.github.io/main/src/docs/Math/数据建模与分析.typ | typst | #import "/src/components/TypstTemplate/lib.typ": *
#show: project.with(
title: "数据建模与分析笔记",
lang: "zh",
)
= 机器学习简介
- 没记
= 感知机
- 没记
= k-近邻算法
- 没记
= 朴素贝叶斯分类器
- 没记
= 决策树
- 没记
= Logistic回归和最大熵模型
- 关于特征函数与期望
特征函数$f(x, y)$关于经验分布 $hat(P)(X, Y)$ 的期望值:$ E_(hat(P)) (f) = sum_(x, y)hat(P) (x,y)f(x,y) $
关于联合分布 $P(X,Y)$ 的期望值：$ E_(P) (f) = sum_(x, y)P (x,y)f(x,y) = sum_(x,y)P(x)P(y|x)f(x,y) $
用 $hat(P)(x)$ 代替（or 估计）未知的 $P(x)$，就得到书上的公式。
- 关于条件熵
定义在条件概率分布 $P(Y|X)$ 上的条件熵： $ underbrace(H(P(Y|X)), H(P)) = -sum_(x,y)hat(P)(x)P(y|x) log P(y|x) $
疑惑这里跟以往的 $H(P)=-sum P(x) log P(x)$ 不一样。
注意条件熵的定义是，在一个变量$X$的条件下（变量$X$的每个值都会取），另一个变量$Y$熵对$X$的期望，即：$ H(Y|X)=sum_(x,y) p(x) H(Y|X=x) $用经验分布 $hat(P)(x)$ 估计 $P(x)$，就得到书上的公式。
- 最大熵模型的距离，讲的是更复杂的条件熵，距离用的是简单的熵。
- 最大熵模型把内部极小化问题做好了，实际运用时考虑外部极大化问题。
- 对偶函数的极大化等价于最大熵模型的极大似然估计：
- 这里对数似然函数少个无关紧要的常数项乘积
- 拟牛顿法看懵了
- P43 最后又用了个近似？
- 改进的迭代尺度法，通过对 $A(delta|w)$ 的进一步放缩，把 $f_i(x,y)$ 从 exp 中独立出来，方便后面求导
= 支持向量机SVM
- PPT 51 页缺少了由两个不等式约束导出的两个对偶互补条件
$
alpha_i (1-xi_i - y_i (w dot x_i+b)) = 0\
-mu_i xi_i = 0
$
$alpha_j$ 为 0 时，无法求出 $b$；$alpha_j$ 为 $C$ 时，推出 $mu_j = 0$，导致无法确定 $xi_j$ 为 $0$，因而也无法求出 $b$。
= EM 算法
- #link("https://blog.csdn.net/weixin_41566471/article/details/106219019")[三硬币模型的推导（有点小错）]
= 聚类方法
- 欧式距离和夹角余弦的推广 $d_(i j)=(sum_(k=1)^m |x_(k i)-x_(k j)|^2)^(1/2) "or" (sum_(k=1)^m x_(k i) x_(k j)) / (norm(x_i) norm(x_j))$
- $=> d_(i j)=((x_i-x_j)^T M (x_i-x_j))^(1/2) "or" d_(i j)=x_i^T M x_j$，令 $M=L^T L$
- 这个 $M$ 是需要学习出来的，相当与是对所有数据先进行一个线性变换，再计算欧式距离或夹角余弦并聚类
- 这样，两个数据之间的距离考虑到了整个数据集性质，效果会更好，这就是“度量学习”。
- 关于机器学习中的协方差矩阵和数学中的协方差矩阵，#link("https://zhuanlan.zhihu.com/p/422028586")[对机器学习中的协方差矩阵还是傻傻的搞不清楚？这次我终于捋明白了！]
$ "聚类"=cases(
"层次聚类"=cases(
"聚合聚类",
"分裂聚类"
)
) $
= 谱聚类
- 应该算是拓展？书上没有
- 拉普拉斯矩阵一定有一个 0 特征值，对应的特征向量是全 1 向量，
- 它的重数就是图的连通分量数，但在实际情况中，可能会小于（因为图的联通分量之间可能还有*很弱的链接*），为此采用前 k 个最小特征值
- 本质上就是从原始空间转到与谱定理相关的特征空间，在特征空间中进行聚类
- 而归一化的目的就是让这个特征空间的效果更好。理论上是否有解释？还是就是工程经验？
- P42 页怎么理解，$H$ 就是我们要学习的特征空间（之前表述为 $U$），设其中一个向量为 $u_i$，$u_i^T L u_i=lambda_i u_i^T u_i=lambda_i norm(u_i)$，如果让 $u_i$ 归一化，那么就等于 $lambda_i$，求 $"trace"$ 的最小也就是取最小的 $k$ 个特征值
|
|
https://github.com/curvenote/pubmatter | https://raw.githubusercontent.com/curvenote/pubmatter/main/docs.typ | typst | MIT License | #import "@preview/tidy:0.2.0"
#import "./pubmatter.typ"
#let example = (it) => {
box(fill: luma(95%), inset: (x: 10pt), width: 100%, it)
}
#let fm = pubmatter.load((
title: "pubmatter",
subtitle: "A typst library for parsing, normalizing and showing publication frontmatter",
authors: (
(
name: "<NAME>",
email: "<EMAIL>",
orcid: "0000-0002-7859-8394",
github: "rowanc1",
affiliations: ("Curvenote Inc.", "Executable Books"),
),
),
open-access: true,
license: "CC-BY-4.0",
venue: "Typst Package",
date: "2024/01/26",
abstract: [
Utilities for loading and working with authors, affiliations, abstracts, keywords and other frontmatter information common in scientific publications.
Our goal is to introduce standardized ways of working with this content to expose metadata to scientific publishers who are interested in using typst in a standardized way. The specification for this pubmatter is based on MyST Markdown and Quarto, and can load their YAML files directly.
],
keywords: ("typst package", "open-science", "standards")
))
#show raw.where(lang: "example"): (it) => {
set text(font: "Noto Sans", size: 9pt)
box(inset: (left: 10pt, y: 5pt), stroke: (left: blue + 2pt))[
#raw(lang: "typst", it.text.replace(regex("pubmatter."), ""))
#box(fill: luma(95%), inset: (x: 10pt, y: 5pt), width: 100%, eval("[" + it.text + "]", scope: (
pubmatter: pubmatter,
fm: fm,
authors: fm.authors,
affiliations: fm.affiliations,
)
))
]
}
#let theme = (color: red.darken(20%), font: "Noto Sans")
#state("THEME").update(theme)
#set page(header: pubmatter.show-page-header(theme: theme, fm), footer: pubmatter.show-page-footer(fm))
#show link: it => [#text(fill: blue)[#it]]
#pubmatter.show-title-block(fm)
#state("THEME").update((color: purple.darken(20%), font: "Noto Sans"))
#pubmatter.show-abstract-block(fm)
#set text(font: "Noto Serif", size: 9pt)
== Loading Frontmatter
The frontmatter can contain all information for an article, including title, authors, affiliations, abstracts and keywords. These are then normalized into a standardized format that can be used with a number of `show` functions like `show-authors`. For example, we might have a YAML file that looks like this:
```yaml
author: <NAME>
date: 2024/01/26
```
You can load that file with `yaml`, and pass it to the `load` function:
```typst
#let fm = pubmatter.load(yaml("pubmatter.yml"))
```
This will give you a normalized data-structure that can be used with the `show` functions for showing various parts of a document.
You can also use a `dictionary` directly:
```example
#let fm = pubmatter.load((
author: (
(
name: "<NAME>",
email: "<EMAIL>",
orcid: "0000-0002-7859-8394",
affiliations: "Curvenote Inc.",
),
),
date: datetime(year: 2024, month: 01, day: 26),
doi: "10.1190/tle35080703.1",
))
#pubmatter.show-author-block(fm)
```
#pagebreak()
= Theming
The theme including color and font choice can be set using the `THEME` state.
For example, this document has the following theme set:
```typst
#let theme = (color: red.darken(20%), font: "Noto Sans")
#state("THEME").update(theme)
#set page(header: pubmatter.show-page-header(theme: theme, fm), footer: pubmatter.show-page-footer(fm))
```
Note that for the `header` the theme must be passed in directly. This will hopefully become easier in the future, however, there is a current bug that removes the page header/footer if you set this above the `set page`. See #link("https://github.com/typst/typst/issues/2987")[\#2987].
The `font` option only corresponds to the frontmatter content (abstracts, title, header/footer etc.) allowing the body of your document to have a different font choice.
#pagebreak()
= Normalized Frontmatter Object
The frontmatter object has the following normalized structure:
```yaml
title: content
subtitle: content
short-title: string # alias: running-title, running-head
# Authors Array
# simple string provided for author is turned into ((name: string),)
authors: # alias: author
- name: string
url: string # alias: website, homepage
email: string
phone: string
fax: string
orcid: string # alias: ORCID
note: string
corresponding: boolean # default: `true` when email set
equal-contributor: boolean # alias: equalContributor, equal_contributor
deceased: boolean
roles: string[] # must be a contributor role
affiliations: # alias: affiliation
- id: string
index: number
# Affiliations Array
affiliations: # alias: affiliation
- string # simple string is turned into (name: string)
- id: string
index: number
name: string
institution: string # use either name or institution
# Other publication metadata
open-access: boolean
license: # Can be set with a SPDX ID for creative commons
id: string
url: string
name: string
doi: string # must be only the ID, not the full URL
date: datetime # validates from 'YYYY-MM-DD' if a string
citation: content
# Abstracts Array
# content is turned into ((title: "Abstract", content: string),)
abstracts: # alias: abstract
- title: content
content: content
```
#pagebreak()
Note that you will usually write the affiliations directly in line, in the following example, we can see that the output is a normalized affiliation object that is linked by the `id` of the affiliation (just the name if it is a string!).
```example
#let fm = pubmatter.load((
authors: (
(
name: "<NAME>",
affiliations: "Curvenote Inc.",
),
(
name: "<NAME>",
affiliations: ("Executable Books", "Curvenote Inc."),
),
),
))
#raw(lang:"yaml", yaml.encode(fm))
```
#pagebreak()
= API Documentation
#let docs = tidy.parse-module(
read("./pubmatter.typ"),
name: "pubmatter",
)
#let validate-docs = tidy.parse-module(
read("./validate-frontmatter.typ"),
name: "validate-frontmatter",
)
#tidy.show-module(docs)
#tidy.show-module(validate-docs)
|
https://github.com/miestrode/sourcerer | https://raw.githubusercontent.com/miestrode/sourcerer/main/src/lib.typ | typst | MIT License | #let code(
line-spacing: 5pt,
line-offset: 5pt,
numbering: true,
inset: 5pt,
radius: 3pt,
number-align: left,
stroke: 1pt + luma(180),
fill: luma(250),
text-style: (),
width: 100%,
lines: auto,
lang: none,
lang-box: (
gutter: 5pt,
radius: 3pt,
outset: 1.75pt,
fill: rgb("#ffbfbf"),
stroke: 1pt + rgb("#ff8a8a")
),
source
) = {
show raw.line: set text(..text-style)
show raw: set text(..text-style)
set par(justify: false, leading: line-spacing)
let label-regex = regex("<((\w|_|-)+)>[ \t\r\f]*(\n|$)")
let labels = source
.text
.split("\n")
.map(line => {
let match = line.match(label-regex)
if match != none {
match.captures.at(0)
} else {
none
}
})
// We need to have different lines use different tables to allow for the text after the lang-box to go in its horizontal space.
// This means we need to calculate a size for the number column. This requires AOT knowledge of the maximum number horizontal space.
let number-style(number) = text(
fill: stroke.paint,
size: 1.25em,
raw(str(number))
)
let unlabelled-source = source.text.replace(
label-regex,
"\n"
)
show raw.where(block: true): it => style(styles => {
let lines = lines
if lines == auto {
lines = (auto, auto)
}
if lines.at(0) == auto {
lines.at(0) = 1
}
if lines.at(1) == auto {
lines.at(1) = it.lines.len()
}
lines = (lines.at(0) - 1, lines.at(1))
let maximum-number-length = measure(number-style(lines.at(1)), styles).width
block(
inset: inset,
radius: radius,
stroke: stroke,
fill: fill,
width: width,
{
stack(
dir: ttb,
spacing: line-spacing,
..it
.lines
.slice(..lines)
.map(line => table(
stroke: none,
inset: 0pt,
columns: (maximum-number-length, 1fr, auto),
column-gutter: (line-offset, if line.number - 1 == lines.at(0) { lang-box.gutter } else { 0pt }),
align: (number-align, left, top + right),
if numbering {
text(
fill: stroke.paint,
size: 1.25em,
raw(str(line.number))
)
},
{
let line-label = labels.at(line.number - 1)
if line-label != none {
show figure: it => it.body
counter(figure.where(kind: "sourcerer")).update(line.number - 1)
[
#figure(supplement: "Line", kind: "sourcerer", outlined: false, line)
#label(line-label)
]
} else {
line
}
},
if line.number - 1 == lines.at(0) and lang != none {
rect(
fill: lang-box.fill,
stroke: lang-box.stroke,
inset: 0pt,
outset: lang-box.outset,
radius: radius,
text(size: 1.25em, raw(lang))
)
}
))
.flatten()
)
}
)
})
raw(block: true, lang: source.lang, unlabelled-source)
}
|
https://github.com/hanxuanliang/opentyp | https://raw.githubusercontent.com/hanxuanliang/opentyp/main/typ/risinglight/sql.typ | typst | MIT License | #import "../cv.typ": *
#show: cv.with(
author: "SQL执行全流程"
)
RisingLight中 SELECT 语句的执行过程可以分解为以下几个步骤:
+ 解析：使用SQL解析器将输入的SQL字符串(例如: #codeText("SELECT a，sum(b) FROM t GROUP BY a"))解析成抽象语法树(AST)。此步骤在 src/sql_parser 目录中
+ 绑定：绑定程序分析AST以绑定必要信息，例如每个变量所属的表、它们的类型和相应列。此步骤可在src/binder目录中看到
+ 逻辑规划：然后将绑定语句映射到逻辑计划中，这是查询如何处理的基本草图。该逻辑计划包括：Projection、Aggregation、TableScan、Filter和Join等运算符。此步骤可在src/logical_planner目录中找到
+ 优化和物理规划：优化器通过选择每个逻辑运算符的最佳执行者，并应用在一些诸如：filter join、filter scan、constant folding等优化来将逻辑计划转换为物理计划
== egg::EGraph
#codeInline("egg::EGraph")\(来自egg库)是一种维护等价类并提供高效搜索和操作表达式框架的 `e-graph` 数据结构。它在 `Builder` 结构体的上下文中使用，负责为给定的查询计划构建执行器。
在该项目中egg::EGraph被用于存储Expr(表示查询计划的一部分)以及相关联的 `TypeSchemaAnalysis` 数据。
#codeText("TypeSchemaAnalysis") 反过来又持有目录引用，并用于类型检查和确定表达式输出模式。
Builder 使用 egg::EGraph 在执行器构建过程中执行各种操作，例如提取给定节点的 RecExpr、解析列索引、获取计划节点的输出类型以及从 e-graph 中包含的 RecExpr 构建查询最终执行器。e-graph 帮助管理查询计划，在执行器构建过程中提供对表达式及其相应元信息高效访问\ |
https://github.com/MLAkainu/Network-Comuter-Report | https://raw.githubusercontent.com/MLAkainu/Network-Comuter-Report/main/contents/index.typ | typst | Apache License 2.0 | #include "01_task/index.typ"
#include "02_yeu_cau/index.typ"
#include "03_protocol/index.typ"
#include "04_socket/index.typ"
#include "05_demo/index.typ"
#include "06_errorhandle/index.typ" |
https://github.com/CaldeCrack/Typst-Templates | https://raw.githubusercontent.com/CaldeCrack/Typst-Templates/main/modules/auto_table.typ | typst | /*
width: width of the table
height: height of the table
position: alignment of the table
values: values to display in the table
*/
#let auto_table(width, height, position, cell_position, inset: 5pt, values) = {
let col_number = values.at(0).len()
let row_number = values.len()
let hor_percentage = if width != auto {width / col_number} else {auto}
let ver_percentage = if height != auto {height / row_number} else {auto}
align(position)[
#table(
columns: (for i in range(col_number) {(hor_percentage, )}),
rows: (for i in range(row_number) {(ver_percentage, )}),
align: cell_position,
inset: inset,
..for i in range(values.len()) {
values.at(i).map(n => if type(n) == int or type(n) == float {str(n)} else {n})
}
)
]
}
|
|
https://github.com/Nrosa01/TFG-2023-2024-UCM | https://raw.githubusercontent.com/Nrosa01/TFG-2023-2024-UCM/main/Memoria%20Typst/capitulos/3.5.ProgramaciónParalelaCPU.typ | typst | #import "@preview/subpar:0.1.0"
Para poder ejecutar los programas se requiere de una estructura que pueda procesar un conjunto de instrucciones dados, esta estructura es la Unidad Central de Procesamiento (CPU, por sus siglas en inglés). La CPU es el componente principal de un ordenador y otros dispositivos programables, que interpreta y ejecuta instrucciones contenidas en los programas informáticos. La CPU lleva a cabo la mayoría de los cálculos que permiten a un sistema operativo y sus aplicaciones funcionar. La CPU no es una pieza única, sino que está compuesta por una series núcleos que a su vez están compuestos por otras partes @ComputerOrganizationPatterson. Cada CPU es distinta pero todas presentan al menos los siguientes componentes en la estructura de su núcleo: la Unidad de Control (UC), la Unidad Aritmético Lógica (ALU), varios registros, la Unidad de Punto Flotante (FPU), una memoria de muy rápido acceso llamada caché y un conjunto de buses que conectan estos componentes.
La UC supervisa y coordina las operaciones de la CPU. Controla la secuencia de ejecución de las instrucciones y dirige el flujo de datos entre la CPU y otras partes del sistema. La ALU realiza operaciones aritméticas y lógicas en los datos, como sumas, restas, multiplicaciones, divisiones y operaciones booleanas con la restricción de estar limitada a números enteros. Los registros son pequeñas áreas de almacenamiento de alta velocidad que se utilizan para almacenar datos temporales y direcciones de memoria, estos forman parte del ensamblado principal de la CPU, suelen estar muy cerca de las ALUs. La FPU es una unidad especializada que realiza operaciones en números de punto flotante, como sumas, restas, multiplicaciones y divisiones, suele ser una subparte de la ALU. La caché es una memoria de muy rápido acceso que almacena copias de datos, tienen más almacenamiento que los registros pero son más lentas en comparación y suelen estar un poco más alejadas de las ALUs respecto a los registros. Los buses son caminos de comunicación que permiten que los datos se muevan entre los componentes de la CPU y otros dispositivos del sistema. A continuación se muestra un diagrama generalizado de la estructura de un núcleo de CPU. Cabe destacar que existen distintos tipos de arquitecturas y la siguiente ilustración no pretende represeentar un tipo de CPU en específico sino el concepto general de CPU.
#v(5pt)
#figure(image("../images/CPUDiagram.png", width: 50%), gap: 10pt, caption: [
Generalización de la estructura de un núcleo de CPU
])
#v(5pt)
Un núcleo de CPU es una unidad de procesamiento que puede ejecutar instrucciones de programa usando los componentes mencionados. En los sistemas modernos, una CPU puede tener múltiples núcleos, lo que permite que se ejecuten múltiples instrucciones simultáneamente.
Los hilos, o threads @ComputerOrganizationPatterson, son una forma de dividir un programa en dos o más tareas paralelas. Cada hilo en un programa ejecuta su propio flujo de control. En un sistema con un solo núcleo,, donde el sistema operativo alterna rápidamente entre ejecutar hilos de diferentes programas.
Es posible aprovechar aún más el rendimiento mediante una tecnología llamada Hyperthreading. Esta, es una tecnología desarrollada por Intel que permite a un solo núcleo de CPU simular dos núcleos lógicos. Como se ha visto, un núcleo tiene distintos componentes, simular dos núcleos lógicos permite usar más de un componente al mismo tiempo. Por ejemplo, si una parte del programa está haciendo una operación con números enteros (usando la ALU), es posible que otra parte de este use la FPU simultáneamente para hacer operaciones con números de punto flotante. De esta forma se aprovechan mejor los recursos de la CPU y se obtiene más rendimiento.
Cada hilo posee su propia región de memoria en el stack, o pila. La pila es una estructura de datos que sigue el principio de "último en entrar, primero en salir" (LIFO, por sus siglas en inglés). Se utiliza para almacenar variables locales y para rastrear el progreso en la ejecución del hilo, como las llamadas a funciones. No obstante, todos los hilos en un proceso comparten el mismo espacio de memoria del heap. El heap es una región de memoria utilizada para el almacenamiento dinámico de datos, es decir, para variables globales y datos asignados dinámicamente durante la ejecución del programa.
La programación paralela es una técnica que se utiliza para mejorar el rendimiento de los programas al permitir que se ejecuten múltiples tareas simultáneamente. Esta técnica se refiere a la capacidad de un programa para ejecutar tareas de manera simultánea en diferentes núcleos o procesadores.
No obstante, la programación paralela presenta desafíos únicos. Entre estos se incluyen problemas de sincronización, donde diferentes hilos intentan acceder o modificar los mismos datos al mismo tiempo. También se pueden presentar problemas de bloqueo o 'deadlocks', donde dos o más hilos se bloquean mutuamente al esperar que el otro libere un recurso.
Sin embargo, dichos problemas tienen soluciones y permiten lograr un incremento de velocidad considerable. Esto será relevante para el siguiente apartado, donde se explicarán las distintas implementeciones de simuladore de arena realizadas en CPU. Posteriormente, se compararán con las implementaciones realizadas en GPU en términos de rendimiento y usabilidad. |
|
https://github.com/Arrata-TTRPG/Arrata-TTRPG | https://raw.githubusercontent.com/Arrata-TTRPG/Arrata-TTRPG/main/src/template.typ | typst | Other | #set heading(numbering: "1.1.1")
// The project function defines how your document looks.
// It takes your content and some metadata and formats it.
// Go ahead and customize it to your liking!
#let project(title: "", authors: (), logo: none, version: "", body) = {
// Set the document's basic properties.
set document(author: authors, title: title)
set page(
paper: "a6",
width: 115mm,
fill: black,
number-align: center,
)
// Save heading and body font families in variables.
let body-font = "Fira Sans"
let heading-font = "Fira Mono"
// Set body font family.
set text(
size: 10pt,
font: "Fira Sans",
fill: white,
)
// Set paragraph spacing.
show par: set block(above: 1.2em, below: 1.2em)
show heading: set text(font: heading-font)
set heading(numbering: "1.1.1.")
// Set run-in subheadings, starting at level 3.
show heading: it => {
if it.level > 3 {
parbreak()
text(10pt, style: "italic", weight: "regular", it.body + ".")
} else {
it
}
}
set par(
justify: true,
leading: 0.52em,
)
// Title page.
// The page can contain a logo if you pass one with `logo: "logo.png"`.
v(0.6fr)
if logo != none {
align(center, image(logo, width: 90%))
}
v(9.6fr)
text(font: heading-font, 2em, weight: 700, title)
// Author information.
pad(
top: 0.7em,
grid(
columns: (1fr,) * calc.min(3, authors.len()),
gutter: 1em,
..authors.map(author => align(center, strong(author))),
),
)
v(1.2fr)
align(center, strong(version))
align(center, strong(datetime.today().display()))
v(2.4fr)
pagebreak()
// Table of contents.
outline(depth: 3, indent: true)
pagebreak()
// Main body.
set par(justify: true)
show link: underline
body
} |
https://github.com/lxl66566/my-college-files | https://raw.githubusercontent.com/lxl66566/my-college-files/main/信息科学与工程学院/嵌入式系统/实验/报告/7/7.typ | typst | The Unlicense | #import "../../../../template.typ": *
#show: project.with(
title: "实验报告 7",
authors: (
"absolutex",
)
)
= 综合实验
== 实验目的
根据此前实验所学到的知识，综合运用开发板上的各模块，实现一个相对复
杂的嵌入式系统，实现数据传输，（传感器）数据输入，数据展示的功能。
本小组选择挑战使用一个之前实验未使用过的模块 —— USB 模块来完成综合实验。主要内容是实现一个小游戏：接球游戏。
游戏内容：小球从 LCD 屏幕的最上方的随机位置落下。同一时间，屏幕上只会有一个小球下落。玩家需要按下按键控制板子位置，尝试接住小球。成功接球则加分，失败则减分。
== 实验原理
开发板与 USB 键盘建立连接，将键盘按键信息通过 IIC 协议写入 24C02 芯片。在程序主循环中，开发板将不断从 24C02 读取数据，并以此操作游戏元素（板子）。当球落到预定结束位置时，判断此时是否接球成功，并对分数进行更新。
其中游戏逻辑部分负责 LCD 显示屏的控制和游戏运行事件监测，而 USB HID 设备运行库负责初始化 USB HOST，并不断轮询。当检测到 USB 键盘的插入后，监听按键按下，并传递到其他组件上。
== 代码修改与说明
由于原USB 鼠标键盘(Host)实验代码没有添加 24CXX 模块，因此需要自行添加。以下是 `main.c` 文件的内容：
#include_code("嵌入式系统/实验/代码/12.main.c")
#linebreak()
程序删除了前面的 USB 连接状态信息显示代码，避免了显示的信息影响游戏观感，并添加了 24CXX 模块的初始化代码。
程序在全局空间中定义了两个结构：`circle` 和 `rect`，并带有一点 “面向对象” 的思想，为这两个结构定义了一些函数，作为复杂操作的抽象。
然后程序使用 `const u16` 定义了一大堆常量，这些常量主要用于界面设计，例如总游戏区域的坐标（`areax`, `areay`），小球下落柱状区域间隔（`edge`），小球半径（`rr`），矩形区域高度（`rect_area_height`）与间隔（`rect_area_gap`），还有信息显示区域的坐标（`string_pos_y`）。这些常量之间相互耦合，使后续对坐标的处理大大简化。
最后，程序定义了一些映射函数，例如键盘代码映射到柱状区域，柱状区域映射到绝对坐标等，我们可以很方便地使用映射函数进行数据的计算处理。
程序对游戏逻辑的处理主要发生在 main 函数主循环中。
主循环每次都会读取24C02芯片存储的键盘按键数据，转换为索引值（`index`），并将其与矩形的当前位置做比较。如果位置发生了偏移，则移动矩形到新的位置。与历史位置进行比较，差分更新，有利于减少矩形绘制的次数，提高游戏的流畅度。
`flag` 指示当前场上是否存在小球。如果不存在，则重新生成小球，并且在每一帧过后，移动小球到更下方的新位置，实现小球下落的功能。
最后程序判断小球是否下落到了指定位置。如果下落到预计位置，则执行分数更新程序，程序判断板子是否接到了小球，更新分数，并将新的分数显示在 LCD 屏上。
下面是 `usbh_usr.c` 的部分代码。原先的代码比较复杂，涉及了字符缓存和区域显示功能，但是本次实验用不到这些功能，因此删除了那些代码，然后手动添加写入 24C02 芯片的程序。
#include_code("嵌入式系统/实验/代码/12.usbh_usr.c")
== 实验结果
等待程序初始化完成后，小球从屏幕上方以恒定速度落下。按动键盘的 `A` `S` `Num4` `Num5` 键，可以控制板子的位置。当小球落到最下方时，若板子接住小球，分数加一。若未接住，分数减一。下面是游戏运行的截图展示。
#figure(
image("result.jpg", width:40%),
caption: [游戏画面],
)
== 心得体会
=== 困难
这一次实验花了整整四节课，难度确实还是比较高的。
首先实验的主要部分是USB键盘通信，这个在之前的实验中没有做过，并且建立外设通信本身也是一个非常复杂的过程。不过好在原先的代码已经比较成熟，不需要手动改太多东西就能直接投入使用。
其次就是要考虑游戏程序架构。如果将不同元素的动作都做成单独的函数，并且在其中加上延迟效果，则会阻塞其他元素的运动。这一个问题也在之前的实验中多次出现，有了处理经验。因此。本次实验将所有元素都放入主循环，由主循环调函数，统一调度这些元素的运动。
然后一个比较现实的问题就是，USB按键按下以后通过回调函数（`USR_KEYBRD_ProcessData`）对按键进行处理。这个回调函数类似于 EXTI 外部中断，需要考虑如何把获取到的按键传给主程序，在主循环中进行处理。然后想到了之前做过的 IIC 实验，干脆就使用 24C02 传递按键。
最后也是最大的困难就是如何编写一个游戏的完整逻辑。由于我的C语言使用不够熟练。C语言又是比较底层的语言，没有办法提供太高层的抽象，因此也走了不少弯路。但是我还是尽可能地将不同功能的代码抽象成了函数，结构和全局常量，方便主循环进行后续调用。
=== 遇到的问题
实验中也遇到了不少的问题。
首先是引入其他库。这个操作本应是嵌入式开发的基础，但是之前的实验都不需要自己手动添加，因此并没有实际经验。在上网搜索以后学会了引入库的方法。
1. 将库所在的文件夹复制到项目中的相同结构下。（例如将 `24CXX` 放到 `HARDWARE`下）
2. 在 Keil 中，右击放入的目录（`HARDWARE`），选择 _Add Existing Files to Group..._，选中库内的 `*.c` 文件。
3. 点开工具栏 `Options for Target`，选择 `C/C++`，在 `Include Paths` 中仿照例子添加库的路径。
然后第一天在改完代码以后，发现每一个文件都能过编译，但是在链接的时候会报错：`Library reports error: __use_no_semihosting was requested, but _ttywrch was referenced`。网上也搜不到解决方法，于是只能慢慢排查。最后发现是调用了`malloc`的缘故。然后明白了，嵌入式系统与一般操作系统的系统库不同，在这个项目中应该要调用`mymalloc`而不是`malloc`。
第二天实验中，进行到了插入键盘测试的环节，结果程序一直无法从键盘上读数据。我同样检查了好几遍代码还是没有找到原因，因此只能像上一次那样二分代码排查。最后发现居然是在主循环中使用`delay_ms`引起的问题。这个应该涉及到了USB 协议的底层问题，可能是由于这一个`delay`语句把键盘的轮询给阻塞了。这也不是我能解决的，因此我把`delay`去掉，改成使用程序本身执行的时间作为延迟。这也最终导致了一个很有意思的现象，就是在最终测试时，键盘如果按的越快，程序没有办法在正常的时间内处理完这些事件，就会导致刷新率变低，小球下落变慢，降低了游戏难度。
最后这个程序其实还有一个bug没有解决，就是当分数从 10 以上降低到 10 以下时，分数会从 $+-1$ 的变化幅度变为 $+-10$，并且超出了显示范围。我认为应该是 `sprintf` 函数的具体实现的问题。
=== 可能的改进
我认为在游戏的趣味性和难度方面可以加以改进。
一方面，可以增添更多的游戏元素，例如添加游戏音乐，打击音效，击打特效，背景图等。这些是能够用STM32F429开发板实现的，例如音乐播放实验，图像显示实验中都有相应的例子。
另一方面，游戏的难度也能够继续增加。游戏中同一时间只有一个球并不是一个硬性规定。屏幕上完全可以出现多个球。接球的板子只有一个，这意味着两球不能同时落下，必需有依次的顺序关系，这可以用链表/队列实现。 |
https://github.com/Myriad-Dreamin/typst.ts | https://raw.githubusercontent.com/Myriad-Dreamin/typst.ts/main/README.md | markdown | Apache License 2.0 | # typst.ts
[Markdown](https://github.com/Myriad-Dreamin/typst.ts/blob/main/README.md) | [typst](./docs/cookery/introduction.typ) |
[Online SVG](https://myriad-dreamin.github.io/typst.ts/cookery/) |
[Online Canvas](https://myriad-dreamin.github.io/typst.ts/)
<p align="center">
<a href="https://github.com/Myriad-Dreamin/typst.ts/actions/workflows/ci.yaml">
<img alt="typst_ts::ci" src="https://github.com/Myriad-Dreamin/typst.ts/actions/workflows/ci.yaml/badge.svg"/>
</a>
<a href="https://github.com/Myriad-Dreamin/typst.ts/blob/main/LICENSE">
<img alt="Apache-2 License" src="https://img.shields.io/badge/license-Apache%202-brightgreen"/>
</a>
</p>
`typst.ts` is a project dedicated to bring the power of
[typst](https://github.com/typst/typst) to the world of JavaScript. In short, it
provides an `typst::World` implementation and several exporters to help compile
and render your Typst document typically inside _Browser Environment_. In the scope of server-side rendering
collaborated by
$\textcolor{#3c9123}{\textsf{server}}$ and $\textcolor{#0074d9}{\textsf{browser}}$, there would be a data flow like this:
<p align="center">
<picture>
<source media="(prefers-color-scheme: dark)" srcset="https://github.com/Myriad-Dreamin/typst.ts/blob/main/github-pages/docs/data-flow-standalone.dark.artifact.svg">
<img width="100%" alt="Data Flow" src="https://github.com/Myriad-Dreamin/typst.ts/blob/main/github-pages/docs/data-flow-standalone.artifact.svg"/>
</picture>
</p>
Specifically, it first typically presents a typst document in three forms:
- [Form1](https://myriad-dreamin.github.io/typst.ts/cookery/guide/compiler/ts-cli.html): Render to SVG and then embed it as a high-quality vectored image directly.
- [Form2](https://myriad-dreamin.github.io/typst.ts/cookery/guide/compiler/ts-cli.html): Preprocessed to a Vector Format artifact.
- [Form3](https://myriad-dreamin.github.io/typst.ts/cookery/guide/compiler/serverless.html): Manipulate a canvas element directly.
The _Form2: Vector Format_ is developed specially for typst documents, and it has several fancy features:
<p align="center">
<picture>
<source media="(prefers-color-scheme: dark)" srcset="https://github.com/Myriad-Dreamin/typst.ts/blob/main/github-pages/docs/ir-features.dark.artifact.svg">
<img width="100%" alt="Data Flow" src="https://github.com/Myriad-Dreamin/typst.ts/blob/main/github-pages/docs/ir-features.artifact.svg"/>
</picture>
</p>
So with _Form2_, you can continue rendering the document in different ways:
##### Static but <ins>responsive</ins> rendering
Example Application: [single-file](https://github.com/Myriad-Dreamin/typst.ts/blob/main/packages/typst.ts/index.html), [typst-book](https://github.com/Myriad-Dreamin/typst-book) and [hexo-renderer-typst](https://github.com/Myriad-Dreamin/typst.ts/tree/main/projects/hexo-renderer-typst)
A compressed artifact containing data for different theme and screen settings. The bundle size of artifacts is optimized for typst documents.
##### <ins>Incremental</ins> server-side rendering
Example Application: [typst-preview](https://github.com/Enter-tainer/typst-preview-vscode)
Build a server for compilation with [Compiler Service](https://myriad-dreamin.github.io/typst.ts/cookery/guide/compiler/service.html), streaming the artifact, and render it incrementally.
##### <ins>Serverless</ins> client-side rendering
Example Application: [single-file](https://github.com/Myriad-Dreamin/typst.ts/blob/main/github-pages/preview.html)
Run the entire typst directly in browser, like [typst.app](https://typst.app).
### Application
- [A Website built with Typst.ts](https://myriad-dreamin.github.io/typst.ts/)
- [Instant VSCode Preview Plugin](https://github.com/Enter-tainer/typst-preview-vscode)
- [typst-book - A simple tool for creating modern online books in pure typst.](https://github.com/Myriad-Dreamin/typst-book)
- [Renderer Plugin for Hexo, a Blog-aware Static Site Generator](https://www.npmjs.com/package/hexo-renderer-typst)
- Renderer/Component Library for [JavaScript](https://www.npmjs.com/package/@myriaddreamin/typst.ts), [React](https://www.npmjs.com/package/@myriaddreamin/typst.react), and [Angular](https://www.npmjs.com/package/@myriaddreamin/typst.angular)
### Installation (CLI)
Install latest CLI of typst.ts via cargo:
```shell
cargo install --locked --git https://github.com/Myriad-Dreamin/typst.ts typst-ts-cli
```
Or Download the latest release from [GitHub Releases](https://github.com/Myriad-Dreamin/typst.ts/releases).
### Installation (Packages)
The JavaScript packages are published on [npm](https://www.npmjs.com/).
- Core (Wrapper) Library: [@myriaddreamin/typst.ts][npm::typst.ts]
- React Library: [@myriaddreamin/typst.react][npm::typst.react]
- Angular Library: [@myriaddreamin/typst.angular][npm::typst.angular]
- (Internal) Web compiler WASM module:
[@myriaddreamin/typst-ts-web-compiler](https://www.npmjs.com/package/@myriaddreamin/typst-ts-web-compiler)
- (Internal) Renderer WASM module:
[@myriaddreamin/typst-ts-renderer](https://www.npmjs.com/package/@myriaddreamin/typst-ts-renderer)
The rust crates are not published on [crates.io](https://crates.io/) yet, since
it has the git dependency on [typst](https://github.com/typst/typst).
- Compiler Library: [reflexo-typst](./crates/reflexo-typst/)
- CLI as a Library: [typst-ts-cli](./cli/)
### Installation (All-in-one Bundle)
Download the latest bundle file from [GitHub Releases](https://github.com/Myriad-Dreamin/typst.ts/releases).
### Documentation
See [Documentation](https://myriad-dreamin.github.io/typst.ts/cookery).
### Templates
Please check [Templates](./templates) and usage in [Get Started](https://myriad-dreamin.github.io/typst.ts/cookery/get-started.html).
### Minimal Example
Note: In default, `all-in-one.bundle.js` will download the font assets from
GitHub in browser, so you need to connect to the Internet.
Download `all-in-one.bundle.js` from [GitHub Releases](https://github.com/Myriad-Dreamin/typst.ts/releases) and start a local server with following
content of `index.html`:
```html
<!doctype html>
<html lang="en">
<head>
<meta charset="UTF-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<title>Svg Document</title>
<script type="module" src="http://localhost:12345/all-in-one.bundle.js" id="typst"></script>
</head>
<body>
<textarea id="input" style="width: 100%"></textarea>
<div id="content"></div>
<script>
const input = document.getElementById('input');
input.value = 'Hello, Typst!';
document.getElementById('typst').addEventListener('load', function () {
const compile = function (mainContent) {
$typst.svg({ mainContent }).then(svg => {
console.log(`rendered! SvgElement { len: ${svg.length} }`);
// append svg text
document.getElementById('content').innerHTML = svg;
});
};
input.oninput = () => compile(input.value);
compile(input.value);
});
</script>
</body>
</html>
```
And you will see the result.
You can also load the all-in-one bundle file and wasm modules from [jsdelivr](https://www.jsdelivr.com/):
```html
<!doctype html>
<html lang="en">
<head>
<meta charset="UTF-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<title>Svg Document</title>
<script
type="module"
src="https://cdn.jsdelivr.net/npm/@myriaddreamin/typst.ts/dist/esm/contrib/all-in-one-lite.bundle.js"
id="typst"
></script>
</head>
<body>
<textarea id="input" style="width: 100%"></textarea>
<div id="content"></div>
<script>
const input = document.getElementById('input');
input.value = 'Hello, Typst!';
document.getElementById('typst').addEventListener('load', function () {
$typst.setCompilerInitOptions({
getModule: () =>
'https://cdn.jsdelivr.net/npm/@myriaddreamin/typst-ts-web-compiler/pkg/typst_ts_web_compiler_bg.wasm',
});
$typst.setRendererInitOptions({
getModule: () =>
'https://cdn.jsdelivr.net/npm/@myriaddreamin/typst-ts-renderer/pkg/typst_ts_renderer_bg.wasm',
});
const compile = function (mainContent) {
$typst.svg({ mainContent }).then(svg => {
console.log(`rendered! SvgElement { len: ${svg.length} }`);
// append svg text
document.getElementById('content').innerHTML = svg;
});
};
input.oninput = () => compile(input.value);
compile(input.value);
});
</script>
</body>
</html>
```
### Develop projects along with a local built typst.ts
You can put your owned projects under the `projects` folder, and that yarn workspace will
automatically identify your project. We recommend you to use [git](https://git-scm.com/), [Yarn](https://yarnpkg.com/), and
[turbo](https://turbo.build/) to manage your projects.
##### Example: link a project by git submodule
To develop core external projects, e.g. `typst-preview`, you could initialize them
by command:
```shell
git submodule update --init --checkout projects/typst-preview
```
##### Example: build and run
Ensured that you have [built typst.ts from
source](#build-from-source-and-check), you can build and run the project by
(typst-preview as an example):
```shell
# install dependencies for project
yarn install --pure-lockfile
# build typst-preview and its dependencies
turbo build --filter=typst-preview
@myriaddreamin/typst-ts-renderer:build: cache hit, replaying logs bc0a0b151bd8eb6d
@myriaddreamin/typst.ts:build: cache hit, replaying logs 729cb43a3242b80
typst-preview-frontend:build: cache miss, executing 5ae30471e8957877
typst-preview-frontend:build: ...
typst-preview-frontend:build: ✓ built in 1.25s
typst-preview-frontend:build: Done in 4.57s.
typst-preview:build: cache miss, executing a1bd8ca8233f8a0c
typst-preview:build: ...
typst-preview:build: ✓ built in 1.01s
typst-preview:build: Done in 3.73s.
```
The project (typst-preview as an example) will cache and use the local built packages.
### Build from source and check
Note: you could build from source with/without wasm-pack.
Note: see [Troubleshooting WASM Build](docs/troubleshooting-wasm-build.md) for (especially) **Arch Linux** users.
Note: Since we use turborepo for `>=v0.4.0` development, if you are the earlier developer of `typst.ts`, please clean up all of your node_modules and dist folders before running the commands.
```shell
# Install and build the renderer
$ yarn install && yarn build:pkg
# Build the example artifacts
$ yarn corpus
# Run development server
$ yarn dev
```
And open `http://127.0.0.1:20810` in your browser.
You can also run `yarn run build:core` instead of `yarn run build:pkg` to build
core library (`@myriaddreamin/typst.ts`) and avoid building the WASM modules from source.
<!-- ### Example: generate documentation site for packages developers.
- Link [typst-doc](https://github.com/Mc-Zen/typst-doc) by `typst-ts-cli package link --manifest ./typst.toml`.
- Generate documentation by `typst-ts-cli package doc --manifest ./contrib/templates/typst-ts-templates/typst.toml`. -->
##### Hot Reload
To develop typst.ts with its Wasm renderer, you can run the following command:
```bash
cargo run --bin typst-ts-dev-server -- watch renderer
# or run with yarn script
yarn watch:renderer
```
And open your browser to `http://localhost:20810/`.
### Concept: Precompiler
The precompiler is capable of producing artifact outputs from a Typst project. Thet artifact outputs can be easily distributed to remote endpoints.
Install latest precompiler via cargo:
```shell
cargo install --locked --git https://github.com/Myriad-Dreamin/typst.ts typst-ts-cli
```
Or Download the latest release from [GitHub Releases](https://github.com/Myriad-Dreamin/typst.ts/releases).
### Concept: Renderer
The renderer accepts an input in artifact format and renders the document as HTML elements.
Import `typst.ts` in your project:
- Using [@myriaddreamin/typst.ts][npm::typst.ts]
```typescript
import { $typst } from '@myriaddreamin/typst.ts/dist/esm/contrib/snippet.mjs';
const mainContent = 'Hello, typst!';
console.log(await $typst.svg({ mainContent }));
```
Specify correct path to the wasm modules if it complains.
```typescript
$typst.setCompilerInitOptions({ getModule: ... });
$typst.setRendererInitOptions({ getModule: ... });
```
The path option is likely required in browser but not in node.js.
Further reading: [Get Started with Typst.ts](https://myriad-dreamin.github.io/typst.ts/cookery/get-started.html)
- Using [@myriaddreamin/typst.react][npm::typst.react]
```typescript
import { TypstDocument } from '@myriaddreamin/typst.react';
export const App = (artifact: Uint8Array) => {
return (
<div>
<h1>Demo: Embed Your Typst Document in React</h1>
<TypstDocument fill="#343541" artifact={artifact} />
</div>
);
};
```
- Using [@myriaddreamin/typst.angular][npm::typst.angular]
In the module file of your awesome component.
```typescript
/// component.module.ts
import { TypstDocumentModule } from '@myriaddreamin/typst.angular';
```
Using directive `typst-document` in your template file.
```html
<typst-document fill="#343541" artifact="{{ artifact }}"></typst-document>
```
- Using [@myriaddreamin/typst.vue3][npm::typst.vue3]
```vue
<template>
<Typst v-bind:content="sourceCode" />
</template>
```
- Using typst math equations in Markdown with [@myriaddreamin/rehype-typst][npm::rehype-typst]
Inline style math equations:
```html
<p><code class="language-math">C_L</code> like the following equation.</p>
```
Block style math equations:
```html
<pre><code class="language-math">
L = 1/2 rho v^2 S C_L
</code></pre>
```
[npm::typst.ts]: https://www.npmjs.com/package/@myriaddreamin/typst.ts
[npm::typst.react]: https://www.npmjs.com/package/@myriaddreamin/typst.react
[npm::typst.angular]: https://www.npmjs.com/package/@myriaddreamin/typst.angular
[npm::typst.vue3]: ./packages/typst.vue3/README.md
[npm::rehype-typst]: https://www.npmjs.com/package/@myriaddreamin/rehype-typst
|
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