Data

Tools

Indexes

Applications

Experiments

Awesome

An open API service indexing awesome lists of open source software.

https://github.com/OrangeX4/typst-theorion

Out-of-the-box, customizable and multilingual theorem environment package for Typst.
https://github.com/OrangeX4/typst-theorion

colorful-box package theorem theorems typst typst-package

Last synced: over 1 year ago
JSON representation

Out-of-the-box, customizable and multilingual theorem environment package for Typst.

Awesome Lists containing this project

README 

          
# 🌌Theorion



[![Typst Universe](https://img.shields.io/badge/dynamic/xml?url=https%3A%2F%2Ftypst.app%2Funiverse%2Fpackage%2Ftheorion&query=%2Fhtml%2Fbody%2Fdiv%2Fmain%2Fdiv%5B2%5D%2Faside%2Fsection%5B2%5D%2Fdl%2Fdd%5B3%5D&logo=typst&label=universe&color=%2339cccc)](https://typst.app/universe/package/theorion)

![GitHub](https://img.shields.io/github/license/OrangeX4/typst-theorion)

![GitHub Repo stars](https://img.shields.io/github/stars/OrangeX4/typst-theorion)

![Cosmos badge](https://img.shields.io/badge/cosmos-4-aqua)



[Theorion](https://github.com/OrangeX4/typst-theorion) (The Orion) is an out-of-the-box, customizable and multilingual **theorem** environment package for [Typst](https://typst.app/docs/).



- **Out-of-the-box styles** 🎨

- **Built-in multilingual support** 🌐

- **Highly customizable** ⚙️:

  - Custom counters and numbering styles

  - Configurable inheritance levels

  - Custom theorem environments

  - Custom rendering functions

- **Rich theorem environments** 📚: theorem, definition, lemma, corollary, example, proof, and many more presets for note-taking

- **Theorem restatement** 🔄: `#theorion-restate(filter: it => it.outlined and it.identifier == "theorem")`

- **Additional features** 📑:

  - Theorem table of contents

  - Appendix numbering adjustments

  - Complete label and reference system

  - Optional outline and numbering display

  - [Touying](https://github.com/touying-typ/touying) animation support



## Quick Start



```typst

#import "@preview/theorion:0.3.2": *

#import cosmos.fancy: *

// #import cosmos.rainbow: *

// #import cosmos.clouds: *

#show: show-theorion



#theorem(title: "Euclid's Theorem")[

  There are infinitely many prime numbers.

] 



#theorem-box(title: "Theorem without numbering", outlined: false)[

  This theorem is not numbered.

]

```



## Customization



```typst

// 1. Change the counters and numbering:

#set-inherited-levels(1)

#set-zero-fill(true)

#set-leading-zero(true)

#set-theorion-numbering("1.1")



// 2. Other options:

#set-result("noanswer")

#set-qed-symbol[#math.qed]



// 3. Custom theorem environment for yourself

#let (theorem-counter, theorem-box, theorem, show-theorem) = make-frame(

  "theorem",

  "Theorem",  // supplement, string or dictionary like `(en: "Theorem")`, or `theorion-i18n-map.at("theorem")` for built-in i18n support

  counter: theorem-counter,  // inherit the old counter, `none` by default

  inherited-levels: 2,  // useful when you need a new counter

  inherited-from: heading,  // heading or just another counter

  render: (prefix: none, title: "", full-title: auto, body) => [#strong[#full-title.]#sym.space#emph(body)],

)

#show: show-theorem



// 4. Just use it.

#theorem(title: "Euclid's Theorem")[

  There are infinitely many prime numbers.

] 

#theorem-box(title: "Theorem without numbering", outlined: false)[

  This theorem is not numbered.

]



// 5. Example of appendix

#counter(heading).update(0)

#set heading(numbering: "A.1")

#set-theorion-numbering("A.1")



// 6. Table of contents

#outline(title: none, target: figure.where(kind: "theorem"))

```



## Restate Theorems



```typst

// 1. Restate all theorems

#theorion-restate(filter: it => it.outlined and it.identifier == "theorem", render: it => it.render)

// 2. Restate all theorems with custom render function

#theorion-restate(

  filter: it => it.outlined and it.identifier == "theorem",

  render: it => (prefix: none, title: "", full-title: auto, body) => block[#strong[#full-title.]#sym.space#emph(body)],

)

// 3. Restate a specific theorem

#theorion-restate(filter: it => it.label == )

```



## Example



[Source code](examples/example.typ)



![example](examples/example.png)



```typst

#import "@preview/theorion:0.3.2": *

#import cosmos.fancy: *

// #import cosmos.rainbow: *

// #import cosmos.clouds: *

#show: show-theorion



#set page(height: auto)

#set heading(numbering: "1.1")

#set text(lang: "en")



/// 1. Change the counters and numbering:

// #set-inherited-levels(1)

// #set-zero-fill(true)

// #set-leading-zero(true)

// #set-theorion-numbering("1.1")



/// 2. Other options:

// #set-result("noanswer")

// #set-qed-symbol[#math.qed]



/// 3. Custom theorem environment for yourself

// #let (theorem-counter, theorem-box, theorem, show-theorem) = make-frame(

//   "theorem",

//   "Theorem",  // supplement, string or dictionary like `(en: "Theorem")`, or `theorion-i18n-map.at("theorem")` for built-in i18n support

//   counter: theorem-counter,  // inherit the counter, `none` by default

//   inherited-levels: 2,  // useful when you need a new counter

//   inherited-from: heading,  // heading or another counter

//   render: (prefix: none, title: "", full-title: auto, body) => [#strong[#full-title.]#sym.space#emph(body)],

// )

// #show: show-theorem



/// 4. Just use it.

// #theorem(title: "Euclid's Theorem")[

//   There are infinitely many prime numbers.

// ] 

// #theorem-box(title: "Theorem without numbering", outlined: false)[

//   This theorem is not numbered.

// ]



/// 5. Example of appendix

// #counter(heading).update(0)

// #set heading(numbering: "A.1")

// #set-theorion-numbering("A.1")



/// 6. Table of contents

// #outline(title: none, target: figure.where(kind: "theorem"))



= Theorion Environments



== Table of Theorems



#outline(title: none, target: figure.where(kind: "theorem"))



== Basic Theorem Environments



Let's start with the most fundamental definition.



#definition[

  A natural number is called a #highlight[_prime number_] if it is greater than 1

  and cannot be written as the product of two smaller natural numbers.

] 



#example[

  The numbers $2$, $3$, and $17$ are prime. As proven in @cor:infinite-prime,

  this list is far from complete! See @thm:euclid for the full proof.

]



#theorem(title: "Euclid's Theorem")[

  There are infinitely many prime numbers.

] 



#proof[

  By contradiction: Suppose $p_1, p_2, dots, p_n$ is a finite enumeration of all primes.

  Let $P = p_1 p_2 dots p_n$. Since $P + 1$ is not in our list,

  it cannot be prime. Thus, some prime $p_j$ divides $P + 1$.

  Since $p_j$ also divides $P$, it must divide their difference $(P + 1) - P = 1$,

  a contradiction.

]



#corollary[

  There is no largest prime number.

] 



#lemma[

  There are infinitely many composite numbers.

]



== Functions and Continuity



#theorem(title: "Continuity Theorem")[

  If a function $f$ is differentiable at every point, then $f$ is continuous.

] 



#tip-box[

  @thm:continuous tells us that differentiability implies continuity,

  but not vice versa. For example, $f(x) = |x|$ is continuous but not differentiable at $x = 0$.

  For a deeper understanding of continuous functions, see @thm:max-value in the appendix.

]



== Geometric Theorems



#theorem(title: "Pythagorean Theorem")[

  In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides:

  $x^2 + y^2 = z^2$

] 



#important-box[

  @thm:pythagoras is one of the most fundamental and important theorems in plane geometry,

  bridging geometry and algebra.

]



#corollary[

  There exists no right triangle with sides measuring 3cm, 4cm, and 6cm.

  This directly follows from @thm:pythagoras.

] 



#lemma[

  Given two line segments of lengths $a$ and $b$, there exists a real number $r$

  such that $b = r a$.

] 



== Algebraic Structures



#definition(title: "Ring")[

  Let $R$ be a non-empty set with two binary operations $+$ and $dot$, satisfying:

  1. $(R, +)$ is an abelian group

  2. $(R, dot)$ is a semigroup

  3. The distributive laws hold

  Then $(R, +, dot)$ is called a ring.

] 



#proposition[

  Every field is a ring, but not every ring is a field. This concept builds upon @def:ring.

] 



#example[

  Consider @def:ring. The ring of integers $ZZ$ is not a field, as no elements except $plus.minus 1$

  have multiplicative inverses.

]



/// Appendix

#counter(heading).update(0)

#set heading(numbering: "A.1")

#set-theorion-numbering("A.1")



= Theorion Appendices



== Advanced Analysis



#theorem(title: "Maximum Value Theorem")[

  A continuous function on a closed interval must attain both a maximum and a minimum value.

] 



#warning-box[

  Both conditions of this theorem are essential:

  - The function must be continuous

  - The domain must be a closed interval

]



== Advanced Algebra Supplements



#axiom(title: "Group Axioms")[

  A group $(G, \cdot)$ must satisfy:

  1. Closure

  2. Associativity

  3. Identity element exists

  4. Inverse elements exist

] 



#postulate(title: "Fundamental Theorem of Algebra")[

  Every non-zero polynomial with complex coefficients has a complex root.

] 



#remark[

  This theorem is also known as Gauss's theorem, as it was first rigorously proved by Gauss.

]



== Common Problems and Solutions



#problem[

  Prove: For any integer $n > 1$, there exists a sequence of $n$ consecutive composite numbers.

]



#solution[

  Consider the sequence: $n! + 2, n! + 3, ..., n! + n$



  For any $2 <= k <= n$, $n! + k$ is divisible by $k$ because:

  $n! + k = k(n! / k + 1)$



  Thus, this forms a sequence of $n-1$ consecutive composite numbers.

]



#exercise[

  1. Prove: The twin prime conjecture remains unproven.

  2. Try to explain why this problem is so difficult.

]



#conclusion[

  Number theory contains many unsolved problems that appear deceptively simple

  yet are profoundly complex.

]



== Important Notes



#note-box[

  Remember that mathematical proofs should be both rigorous and clear.

  Clarity without rigor is insufficient, and rigor without clarity is ineffective.

]



#caution-box[

  When dealing with infinite series, always verify convergence before discussing other properties.

]



#quote-box[

  Mathematics is the queen of sciences, and number theory is the queen of mathematics.

  — Gauss

]



#emph-box[

  Chapter Summary:

  - We introduced basic number theory concepts

  - Proved several important theorems

  - Demonstrated different types of mathematical environments

]



== Restated Theorems



// 1. Restate all theorems

#theorion-restate(filter: it => it.outlined and it.identifier == "theorem", render: it => it.render)

// 2. Restate all theorems with custom render function

// #theorion-restate(

//   filter: it => it.outlined and it.identifier == "theorem",

//   render: it => (prefix: none, title: "", full-title: auto, body) => block[#strong[#full-title.]#sym.space#emph(body)],

// )

// 3. Restate a specific theorem

// #theorion-restate(filter: it => it.label == )

```



## All Cosmos



### 📄Simple



```typst

#import "@preview/theorion:0.3.2": *

#import cosmos.simple: *

#show: show-theorion

```



[Customize from source code](cosmos/simple.typ)



![image](https://github.com/user-attachments/assets/f1876cfb-1bc9-4edb-a19a-a1922a8babc0)



### 🌈Rainbow



```typst

#import "@preview/theorion:0.3.2": *

#import cosmos.rainbow: *

#show: show-theorion

```



[Customize from source code](cosmos/rainbow.typ)



```typst

/// Custom color

#let (theorem-counter, theorem-box, theorem, show-theorem) = make-frame(

  "theorem",

  theorion-i18n-map.at("theorem"),

  counter: theorem-counter,

  render: render-fn.with(fill: blue.darken(10%)),

)

#show: show-theorem

```



![image](https://github.com/user-attachments/assets/5e6e29f9-c493-4e21-b14a-347f3ca83b99)



### ☁️Clouds



```typst

#import "@preview/theorion:0.3.2": *

#import cosmos.clouds: *

#show: show-theorion

```



[Customize from source code](cosmos/clouds.typ)



```typst

/// Custom color

#let (theorem-counter, theorem-box, theorem, show-theorem) = make-frame(

  "theorem",

  theorion-i18n-map.at("theorem"),

  counter: theorem-counter,

  render: render-fn.with(fill: blue.lighten(85%)),

)

#show: show-theorem

```



![image](https://github.com/user-attachments/assets/1f0f280b-94f5-43b7-b685-d2998d867b58)



### ✨Fancy



```typst

#import "@preview/theorion:0.3.2": *

#import cosmos.fancy: *

#show: show-theorion

```



[Customize from source code](cosmos/fancy.typ)



```typst

/// Custom color

#set-primary-border-color(red)

#set-primary-body-color(red.lighten(95%))

#set-primary-symbol[#sym.suit.diamond.filled]

```



![image](https://github.com/user-attachments/assets/a8938339-9510-4371-ae23-7f73a828c17d)



### Contributing your cosmos



Welcome to [open a pull request](htps://github.com/OrangeX4/typst-theorion/pulls) and contribute your beautiful cosmos to Theorion!



## Acknowledgements



- Thanks [Johann Birnick](https://github.com/jbirnick) for [rich-counters](https://github.com/jbirnick/typst-rich-counters)

- Thanks [Satvik Saha](https://github.com/sahasatvik) for [ctheorems](https://github.com/sahasatvik/typst-theorems)

- Thanks [s15n](https://github.com/s15n) for [typst-thmbox](https://github.com/s15n/typst-thmbox)

- Thanks [0x6b](https://github.com/0x6b) for [octique](https://github.com/0x6b/typst-octique)

- Thanks [Pablo González Calderón](https://github.com/Pablo-Gonzalez-Calderon) for [showybox](https://github.com/Pablo-Gonzalez-Calderon/showybox-package)