Theorion (The Orion) is an out-of-the-box, customizable and multilingual theorem environment package for Typst.
- 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 animation support
Just import and use theorion.
#import "@preview/theorion:0.3.3": *
#import cosmos.fancy: *
// #import cosmos.rainbow: *
// #import cosmos.clouds: *
#show: show-theorion
#theorem(title: "Euclid's Theorem")[
There are infinitely many prime numbers.
] <thm:euclid>
#theorem-box(title: "Theorem without numbering", outlined: false)[
This theorem is not numbered.
]
// 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.
] <thm:euclid>
#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"))// 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 == <thm:euclid>)
#import "@preview/theorion:0.3.3": *
#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.
// ] <thm:euclid>
// #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.
] <def:prime>
#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.
] <thm:euclid>
#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.
] <cor:infinite-prime>
#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.
] <thm: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:
$x^2 + y^2 = z^2$
] <thm:pythagoras>
#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.
] <cor:pythagoras>
#lemma[
Given two line segments of lengths $a$ and $b$, there exists a real number $r$
such that $b = r a$.
] <lem:proportion>
== 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.
] <def:ring>
#proposition[
Every field is a ring, but not every ring is a field. This concept builds upon @def:ring.
] <prop:ring-field>
#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.
] <thm:max-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
] <axiom:group>
#postulate(title: "Fundamental Theorem of Algebra")[
Every non-zero polynomial with complex coefficients has a complex root.
] <post:fta>
#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 == <thm:euclid>)#import "@preview/theorion:0.3.3": *
#import cosmos.simple: *
#show: show-theorion
#import "@preview/theorion:0.3.3": *
#import cosmos.rainbow: *
#show: show-theorion/// Custom color
#let theorem = theorem.with(fill: blue.darken(10%))
#let theorem-box = theorem-box.with(fill: blue.darken(10%))
#import "@preview/theorion:0.3.3": *
#import cosmos.clouds: *
#show: show-theorion/// Custom color
#let theorem = theorem.with(fill: blue.lighten(85%))
#let theorem-box = theorem-box.with(fill: blue.lighten(85%))
/// Custom block style
#let theorem = theorem.with(radius: 0pt)
#let theorem-box = theorem-box.with(radius: 0pt)
#import "@preview/theorion:0.3.3": *
#import cosmos.fancy: *
#show: show-theorion/// Custom color
#set-primary-border-color(red)
#set-primary-body-color(red.lighten(95%))
#set-primary-symbol[#sym.suit.diamond.filled]
Welcome to open a pull request and contribute your beautiful cosmos to Theorion!
- Thanks Johann Birnick for rich-counters
- Thanks Satvik Saha for ctheorems
- Thanks s15n for typst-thmbox
- Thanks 0x6b for octique
- Thanks Pablo González Calderón for showybox
