A Math Symbol Stress Test

This is a deliberately broad test of the blog’s real Typst-to-HTML mathematics pipeline. Every specimen below is authored in this file, compiled by Typst, carried through the Rust generator as MathML, and finally rendered by the browser. Inline mathematics uses ordinary single delimiters, as in

𝑒^{𝑖 𝜋} + 1 = 0

, while the larger specimens use the convenient double-delimiter form.

The page is a rendering catalogue rather than a claim that every symbol belongs in one argument. The identity

𝛼 + 𝛽 = 𝛾

demonstrates that a note marker can be attached directly to native Typst mathematics.

Alphabets and letter styles§

Greek letters work by name, including variants and capital forms:

⊕

𝛼 𝛽 𝛾 𝛿 𝜀 𝜖 𝜁 𝜂 𝜃 𝜗 𝜄 𝜅 𝜆 𝜇 𝜈 𝜉 𝜊 𝜋 𝜛 𝜌 𝜚 𝜎 𝜍 𝜏 𝜐 𝜑 𝜙 𝜒 𝜓 𝜔

Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω

Typst also accepts literal Unicode mathematical characters, so the Hebrew cardinal symbols and a few historic letterforms can appear directly:

ℵ_{0} < ℵ_{1} \leq ℶ_{2} ℷ ℸ ℏ ℓ ℘

Several mathematical alphabets may be mixed without turning the expression into an image:

ℕ \subset ℤ \subset ℚ \subset ℝ \subset ℂ, ℱ︀, 𝔤, 𝘈, 𝚡

The familiar number-set shorthands are available too:

ℕ, ℤ, ℚ, ℝ,

and

ℂ

Arithmetic and large operators§

The basic and circled binary operations render together here:

𝑎 + 𝑏 - 𝑐 \pm 𝑑 \mp 𝑒 \times 𝑓 \cdot 𝑔 \div ℎ \circ 𝑘 * 𝑙 ⋆ 𝑚

𝐴 \cup 𝐵, 𝐴 \cap 𝐵, 𝑝 \land 𝑞, 𝑝 \lor 𝑞, 𝑥 \oplus 𝑦, 𝑢 \oplus 𝑣, 𝑢 \otimes 𝑣, 𝑢 ⊙ 𝑣

Large operators grow in display mathematics and carry limits in their conventional places:

\sum_{𝑘 = 1}^{𝑛} 𝑘 = \frac{𝑛 (𝑛 + 1)}{2}, \prod_{𝑝 \in 𝑃} 𝑝, ⋃_{𝑖 \in 𝐼} 𝐴_{𝑖}, ⋂_{𝑗 \in 𝐽} 𝐵_{𝑗}

A less common coproduct belongs to the same family:

\underset{𝜆 \in Λ}{∐} 𝑋_{𝜆}

Relations and order§

Equality, approximation, order, membership, and containment can all be chained:

𝑥 = 𝑦 \neq 𝑧, 𝑎 < 𝑏 \leq 𝑐 \neq 𝑑 \geq 𝑒 > 𝑓, 𝑢 \approx 𝑣 \equiv 𝑤, 𝑟 \propto 𝑠

𝑥 \in 𝐴, 𝑦 \notin 𝐵, \emptyset \subset 𝐶 \subseteq 𝐷, 𝐸 \supseteq 𝐹 \supset 𝐺

The same line can carry order-theoretic and geometric relations:

𝑎 ≺ 𝑏 ≼ 𝑐, 𝑑 ≽ 𝑒 ≻ 𝑓, 𝑚 ∣ 𝑛, 𝑚 ∤ 𝑟, 𝐿 ∥ 𝑀, 𝐿 ⟂ 𝑁

Arrows and mappings§

Short, long, single, and double arrows cover functions, implications, and equivalences:

𝐴 \to 𝐵, 𝐵 \leftarrow 𝐴, 𝐴 \leftrightarrow︎ 𝐵, 𝑃 \Rightarrow 𝑄, 𝑃 \Leftrightarrow 𝑄

𝑥 ⟶ 𝑓 (𝑥), 𝐴 ↪︎ 𝐵, 𝐶 ↣ 𝐷, 𝐸 ⇝ 𝐹

Literal Unicode fills out some specialized directions and harpoons:

↑ ↓ ↗ ↘ ↙ ↖ \mapsto ⇀ ↽ ⇌ ⇋ ⟲ ⟳

Typst’s shorthand sequences compile to their mathematical arrows rather than to punctuation:

𝑥 \to 𝑦 𝑥 ⟶ 𝑦 𝑥 \mapsto 𝑦 𝑥 ↠ 𝑦 𝐴 \leftarrow 𝐵 𝐴 \leftrightarrow 𝐵 𝑃 \Rightarrow 𝑄 𝑃 ⟹ 𝑄 𝑃 \Leftrightarrow 𝑄

Delimiters and grouping§

Parentheses, brackets, braces, bars, floors, ceilings, and norms adapt to their contents:

\frac{1 + 𝑥^{2}}{1 - 𝑥^{2}}, [\sum_{𝑘 = 0}^{𝑛} 𝑎_{𝑘}], {𝑥 \in ℝ | 𝑥^{2} < 2}

| \frac{𝑎 + 𝑏}{𝑐} |, ‖ (\begin{matrix} 𝑥 \\ 𝑦 \\ 𝑧 \end{matrix}) ‖, ⌊ 𝛼 ⌋, ⌈ 𝛽 ⌉, ⌊ 𝛾 ⌉

Angle brackets and mismatched delimiters are useful in inner products and half-open intervals:

⟨ 𝑢, 𝑣 ⟩ = \sum_{𝑖} 𝑢_{𝑖} \bar{𝑣_{𝑖}}, [0, 1), (𝑎, 𝑏]

Accents, primes, and scripts§

Common accents may sit over single letters or longer expressions:

\hat{𝑥} \tilde{𝑦} \bar{𝑧} \dot{𝑞} \ddot{𝑟} \vec{𝑣} \overset{⃡}{𝐴 𝐵} \hat{𝑢 + 𝑣} \bar{𝑥 + 𝑦}

The generic accent function and grouped-prime function cover marks that need explicit arguments:

\overset{́}{𝑥} \overset{̆}{𝑦} \bar{𝑧} 𝑓^{⁗} (𝑥)

Subscripts, superscripts, primes, and combined attachments stay attached to their bases:

𝑥_{𝑖}^{2} + 𝑥_{𝑖, 𝑗}^{𝑛 + 1}, 𝑓^{'} (𝑥), 𝑔^{″} (𝑥), 𝑎_{0}, 𝑎_{1}, \dots, 𝑎_{𝑛}

Limits and annotated braces provide another kind of attachment:

lim_{𝑛 \to \infty} {(1 + \frac{1}{𝑛})}^{𝑛} = 𝑒, \underset{𝑛 terms}{\underset{⏟}{𝑎 + \dots + 𝑎}}, \overset{sample sum}{\overset{⏞}{𝑥_{1} + \dots + 𝑥_{𝑘}}}

Brackets, parentheses, and shell decorations exercise the rest of Typst’s under/over family:

\underset{below}{\underset{⎵}{𝑎 + 𝑏}} \overset{above}{\overset{⎴}{𝑎 + 𝑏}} \underset{below}{\underset{⏝}{𝑐 + 𝑑}} \overset{above}{\overset{⏜}{𝑐 + 𝑑}}

\underset{below}{\underset{⏡}{𝑥 + 𝑦}} \overset{above}{\overset{⏠}{𝑥 + 𝑦}}

Corner attachments, forced script placement, and stretched relations expose lower-level math layout:

{}_{3}^{1}Π_{4}^{2}_{𝛽}^{𝛼}, \sum_{1}^{𝑛}, 𝐴_{1}^{𝑛}, 𝐻 \overset{def}{=} 𝑈 + 𝑉

Fractions, roots, and continued structure§

Slash fractions, explicit fractions, binomial coefficients, and roots all preserve their nested structure:

\frac{1}{2} + \frac{𝑎 + 𝑏}{𝑐 + 𝑑}, (\binom{𝑛}{𝑘}) = \frac{𝑛!}{𝑘! (𝑛 - 𝑘)!}, \sqrt{2}, \sqrt[3]{𝑥}, \sqrt[𝑛]{1 + 𝑥}

Nested notation remains readable when several levels are combined:

𝑥 = 1 + \frac{1}{2 + \frac{1}{3 + \frac{1}{4 + \dots}}}, \sqrt{1 + \sqrt{1 + \sqrt{1 + \dots}}}

The same fraction may be forced through display, inline, script, and scriptscript sizes:

\frac{𝑥 + 1}{𝑥 - 1} \frac{𝑥 + 1}{𝑥 - 1} \frac{𝑥 + 1}{𝑥 - 1} \frac{𝑥 + 1}{𝑥 - 1}

A genuinely wide equation§

A display can deliberately use the same right-hand gutter as a wide image. For

𝑎 𝑥^{3} + 𝑏 𝑥^{2} + 𝑐 𝑥 + 𝑑 = 0

with

𝑎 \neq 0

, all three roots may be written in one uninterrupted line:

𝑥_{𝑘} = - \frac{1}{3 𝑎} (𝑏 + {\frac{- 1 + 𝑖 \sqrt{3}}{2}}^{𝑘} \sqrt[3]{\frac{2 𝑏^{3} - 9 𝑎 𝑏 𝑐 + 27 𝑎^{2} 𝑑 + \sqrt{{(2 𝑏^{3} - 9 𝑎 𝑏 𝑐 + 27 𝑎^{2} 𝑑)}^{2} - 4 {(𝑏^{2} - 3 𝑎 𝑐)}^{3}}}{2}} + \frac{𝑏^{2} - 3 𝑎 𝑐}{{\frac{- 1 + 𝑖 \sqrt{3}}{2}}^{𝑘} \sqrt[3]{\frac{2 𝑏^{3} - 9 𝑎 𝑏 𝑐 + 27 𝑎^{2} 𝑑 + \sqrt{{(2 𝑏^{3} - 9 𝑎 𝑏 𝑐 + 27 𝑎^{2} 𝑑)}^{2} - 4 {(𝑏^{2} - 3 𝑎 𝑐)}^{3}}}{2}}}), 𝑘 \in {0, 1, 2}

The repeated radical is written twice on purpose: there is no discriminant or cube-root abbreviation hiding any of the expression. Choose the sign of the square root so the repeated cube-root argument is nonzero; if the displayed plus sign makes it zero, replace both occurrences with a minus sign. Any of the three resulting cube roots may be used—it only permutes the values of

𝑘

. When

𝑏^{2} - 3 𝑎 𝑐 = 0

and

2 𝑏^{3} - 9 𝑎 𝑏 𝑐 + 27 𝑎^{2} 𝑑 = 0

, all three roots equal

- \frac{𝑏}{3 𝑎}

Calculus and analysis§

Ordinary, partial, directional, and vector derivatives can share a display:

d \frac{𝑓}{d 𝑥}, \frac{d^{𝑛} 𝑓}{d 𝑥^{𝑛}}, 𝜕 \frac{𝑓}{𝜕 𝑥}, \frac{𝜕^{2} 𝑓}{𝜕 𝑥 𝜕 𝑦}, 𝐷_{𝑣} 𝑓, \nabla 𝑓

Single, multiple, contour, and surface-style integrals are supported:

\int_{0}^{1} 𝑥^{2} d 𝑥 = \frac{1}{3}, \iint_{Ω} 𝑓 d 𝐴, ∭_{𝑉} 𝜌 d 𝑉, \oint_{𝛾} 𝐹 \cdot d 𝑟, ∯_{𝑆} 𝐹 \cdot 𝑛 d 𝑆

The equivalent named integral variants pass through the same route:

\iint_{𝐷} 𝑓 d 𝐴 ∭_{𝑉} 𝜌 d 𝑉 \oint_{𝛾} 𝐹 \cdot d 𝑟 ∯_{𝑆} 𝐹 \cdot 𝑛 d 𝑆

The classical vector-calculus operators are ordinary mathematical input as well:

\nabla \cdot 𝐹 = 0, \nabla \times 𝐹 = 𝐺, Δ 𝑢 = 𝜕_{𝑡} 𝑢, □ 𝜑 = 0

Named functions use upright operator typography:

{sin}^{2} 𝜃 + {cos}^{2} 𝜃 = 1, exp (log 𝑥) = 𝑥, det (𝐴 - 𝜆 𝐼) = 0, gcd (𝑚, 𝑛), min_{𝑥} 𝑓 (𝑥), sup_{𝑥 \in 𝑋} 𝑓 (𝑥)

Custom names use the same operator spacing:

Spec 𝑅 rank 𝐴 Hom (𝑉, 𝑊) Aut (𝐺)

Sets and logic§

Set-builder notation, powersets, complements, and symmetric differences can be expressed compactly:

𝐴 = {𝑥 \in ℝ | 𝑥 \geq 0}, 𝒫︀ (𝑋) = {𝐴 | 𝐴 \subseteq 𝑋}, 𝐴 ∖ 𝐵, 𝐴 △ 𝐵

Quantifiers and connectives make a useful logic stress test:

\forall 𝑥 \in 𝑋, \exists 𝑦 \in 𝑌 : 𝑃 (𝑥, 𝑦), \neg 𝑝 \lor 𝑞, 𝑝 \Rightarrow 𝑞, 𝑝 \Leftrightarrow 𝑞

A custom relation can retain relation spacing without becoming an image:

𝑥 ♥︎ 𝑦 𝑦 ♥︎ 𝑧

Literal turnstiles and semantic consequence symbols are supported alongside the usual therefore signs:

Γ ⊢ 𝜑, Γ ⊨ 𝜓, ⊤ ⊥, ∴ 𝑃, ∵ 𝑄, ∎

Matrices, vectors, and piecewise definitions§

Matrices may use different delimiters and may contain full expressions:

𝐴 = (\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}), 𝐵 = [\begin{matrix} 𝑎_{11} & \dots & 𝑎_{1 𝑛} \\ ⋮ & ⋱ & ⋮ \\ 𝑎_{𝑚 1} & \dots & 𝑎_{𝑚 𝑛} \end{matrix}]

Column vectors, determinants, and bar-delimited arrays use the same underlying layout machinery:

𝑣 = (\begin{matrix} 𝑥 \\ 𝑦 \\ 𝑧 \end{matrix}), det (\begin{matrix} 𝑎 & 𝑏 \\ 𝑐 & 𝑑 \end{matrix}) = 𝑎 𝑑 - 𝑏 𝑐, | \begin{matrix} 1 & 0 & 2 \\ 0 & 1 & 3 \end{matrix} |

A piecewise definition aligns conditions independently from their values:

𝑓 (𝑥) ≔ {\begin{cases} 𝑥^{2} & if 𝑥 \geq 0 \\ - 𝑥 & if 𝑥 < 0 \end{cases}

Long derivations can align at relation signs across several rows:

\begin{aligned} 𝑆_{𝑛} & = \sum_{𝑘 = 1}^{𝑛} 𝑘 \\ = \frac{𝑛 (𝑛 + 1)}{2} \\ = (\binom{𝑛 + 1}{2}) \end{aligned}

Typst code may calculate and spread data directly into mathematical structures:

(\begin{matrix} 1 \\ 4 \\ 9 \\ 16 \end{matrix}) (\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix})

User-defined Typst functions and explicit spacing remain available inside formulas:

𝑥^{2} + 𝑥^{2} = 𝑥^{2}, 𝑎 𝑏 𝑐 𝑑 𝑒 𝑓

Geometry§

Angles, triangles, circles, parallel lines, congruence, and degrees render as mathematical symbols rather than prose approximations:

∠ 𝐴 𝐵 𝐶 = 60 °, △ 𝐴 𝐵 𝐶 ≅ △ 𝐷 𝐸 𝐹, 𝐴 𝐵 ∥ 𝐶 𝐷, 𝐴 𝐵 ⟂ 𝐵 𝐶

⊙ 𝑂, ⌒ 𝐴 𝐵, ∡ 𝐴 𝑂 𝐵 = 𝜃, ℓ_{1} \cap ℓ_{2} = {𝑃}

Coordinates, distances, and the dot and cross products cover the analytic side of geometry:

𝑑 (𝑃, 𝑄) = \sqrt{{(𝑥_{2} - 𝑥_{1})}^{2} + {(𝑦_{2} - 𝑦_{1})}^{2}}, 𝑢 \cdot 𝑣 = ‖ 𝑢 ‖ ‖ 𝑣 ‖ cos 𝜃, 𝑢 \times 𝑣

Probability and statistics§

Probability, expectation, conditional notation, and independence can be combined without special image assets:

ℙ (𝐴 \cup 𝐵) = ℙ (𝐴) + ℙ (𝐵) - ℙ (𝐴 \cap 𝐵), ℙ (𝐴 | 𝐵) = \frac{ℙ (𝐴 \cap 𝐵)}{ℙ (𝐵)}

𝔼 [𝑋] = \int_{- \infty}^{\infty} 𝑥 𝑓_{𝑋} (𝑥) d 𝑥, Var (𝑋) = 𝔼 [{(𝑋 - 𝜇)}^{2}], Cov (𝑋, 𝑌) = 𝜌 𝜎_{𝑋} 𝜎_{𝑌}

Finite samples bring in estimators, averages, and asymptotic convergence:

{\bar{𝑋}}_{𝑛} = \frac{1}{𝑛} \sum_{𝑖 = 1}^{𝑛} 𝑋_{𝑖}, 𝑠^{2} = \frac{1}{𝑛 - 1} \sum_{𝑖 = 1}^{𝑛} {(𝑋_{𝑖} - \bar{𝑋})}^{2}, \sqrt{𝑛} ({\bar{𝑋}}_{𝑛} - 𝜇) \Rightarrow 𝒩︀ (0, 𝜎^{2})

Unusual and miscellaneous symbols§

The final tray mixes symbols from algebra, physics, astronomy, music, card suits, and proof notation. Literal Unicode is useful when a descriptive Typst name would be harder to remember:

\infty 𝜕 \nabla ℏ ℧ ℜ ℑ ℵ ℶ ℷ ℸ ⊥ ⊤ ⊢ ⊨

♠ ♣ ♥ ♦ ♭ ♮ ♯ ♩ ♪ ♫ ♬ ♂ ♀ ☿ ♃ ♄

□ ■ △ ▲ ◇ ◆ ○ ● ⋆ † ‡ § ¶ ※ ∎

Finally, the horizontal, vertical, and diagonal ellipses remain distinct:

\dots \dots ⋮ ⋱ ⋰

Current HTML boundary§

This catalogue only labels a feature as supported when it survives semantic HTML export. In the pinned Typst version, cancel, overline, and underline are accepted for paged output but their decorations are omitted from MathML; this site’s Rust build therefore rejects their warnings instead of quietly publishing the wrong result. Equation numbering and explicit alternative descriptions are also not yet carried into Typst’s HTML output, so they are not presented here as working web features.

If every row above remains legible and structurally aligned, the complete route from Typst source through Rust to browser MathML is doing its job.