---
title: 'KaTeX: Supported functions'
description: 'Supported functions within KaTeX syntaxes.'
---

# KaTeX: Supported function

::: tip note

This is an direct shameful copy of the documentation pulled from [KaTeX](https://raw.githubusercontent.com/Khan/KaTeX/master/docs/supported.md) documentation, **I do not own any of the content below on behalf of this part of the documentation**, the table might be outdated as versions migrates, please also refer to [KaTeX's official documentation](https://katex.org/docs/supported.html).

:::

This following is a list of TeX functions supported by KaTeX. It is sorted into logical groups.

There is a similar [Support Table](support-table.md) on the next page, sorted alphabetically in am more intuitive way with the lists both supported and un-supported functions, viewing both tables are suggested comprehensibly and interchangeably is highly suggested.

## 1: Accents

|                               |                                                       |                                                 |
| :---------------------------- | :---------------------------------------------------- | :---------------------------------------------- |
| $a'$ `a'`                     | $\tilde{a}$ `\tilde{a}`                               | $\mathring{g}$ `\mathring{g}`                   |
| $a''$ `a''`                   | $\widetilde{ac}$ `\widetilde{ac}`                     | $\overgroup{AB}$ `\overgroup{AB}`               |
| $a^{\prime}$ `a^{\prime}`     | $\utilde{AB}$ `\utilde{AB}`                           | $\undergroup{AB}$ `\undergroup{AB}`             |
| $\acute{a}$ `\acute{a}`       | $\vec{F}$ `\vec{F}`                                   | $\Overrightarrow{AB}$ `\Overrightarrow{AB}`     |
| $\bar{y}$ `\bar{y}`           | $\overleftarrow{AB}$ `\overleftarrow{AB}`             | $\overrightarrow{AB}$ `\overrightarrow{AB}`     |
| $\breve{a}$ `\breve{a}`       | $\underleftarrow{AB}$ `\underleftarrow{AB}`           | $\underrightarrow{AB}$ `\underrightarrow{AB}`   |
| $\check{a}$ `\check{a}`       | $\overleftharpoon{ac}$ `\overleftharpoon{ac}`         | $\overrightharpoon{ac}$ `\overrightharpoon{ac}` |
| $\dot{a}$ `\dot{a}`           | $\overleftrightarrow{AB}$ `\overleftrightarrow{AB}`   | $\overbrace{AB}$ `\overbrace{AB}`               |
| $\ddot{a}$ `\ddot{a}`         | $\underleftrightarrow{AB}$ `\underleftrightarrow{AB}` | $\underbrace{AB}$ `\underbrace{AB}`             |
| $\grave{a}$ `\grave{a}`       | $\overline{AB}$ `\overline{AB}`                       | $\overlinesegment{AB}$ `\overlinesegment{AB}`   |
| $\hat{\theta}$ `\hat{\theta}` | $\underline{AB}$ `\underline{AB}`                     | $\underlinesegment{AB}$ `\underlinesegment{AB}` |
| $\widehat{ac}$ `\widehat{ac}` | $\widecheck{ac}$ `\widecheck{ac}`                     |

**_Accent functions inside \\text{…}_**

|                                     |                        |                        |                        |
| :---------------------------------- | :--------------------- | :--------------------- | :--------------------- |
| $\text{\'{a}}$ `\'{a}`              | $\text{\~{a}}$ `\~{a}` | $\text{\.{a}}$ `\.{a}` | $\text{\H{a}}$ `\H{a}` |
| $\text{\`{a}}$ <code>\\\`{a}</code> | $\text{\={a}}$ `\={a}` | $\text{\"{a}}$ `\"{a}` | $\text{\v{a}}$ `\v{a}` |
| $\text{\^{a}}$ `\^{a}`              | $\text{\u{a}}$ `\u{a}` | $\text{\r{a}}$ `\r{a}` |

See also [letters](#_5-letters-and-unicode).

## 2: Delimiters

|                                            |                                                |             |                                                                |                               |
| :----------------------------------------- | :--------------------------------------------- | :---------- | :------------------------------------------------------------- | :---------------------------- |
| $(~)$ `( )`                                | $\lparen~\rparen$ `\lparen`<br>$~~~~$`\rparen` | $⌈~⌉$ `⌈ ⌉` | $\lceil~\rceil$ `\lceil`<br>$~~~~~$`\rceil`                    | $\uparrow$ `\uparrow`         |
| $[~]$ `[ ]`                                | $\lbrack~\rbrack$ `\lbrack`<br>$~~~~$`\rbrack` | $⌊~⌋$ `⌊ ⌋` | $\lfloor~\rfloor$ `\lfloor`<br>$~~~~~$`\rfloor`                | $\downarrow$ `\downarrow`     |
| $\{ \}$ `\{ \}`                            | $\lbrace \rbrace$ `\lbrace`<br>$~~~~$`\rbrace` | $⎰⎱$ `⎰⎱`   | $\lmoustache \rmoustache$ `\lmoustache`<br>$~~~~$`\rmoustache` | $\updownarrow$ `\updownarrow` |
| $⟨~⟩$ `⟨ ⟩`                                | $\langle~\rangle$ `\langle`<br>$~~~~$`\rangle` | $⟮~⟯$ `⟮ ⟯` | $\lgroup~\rgroup$ `\lgroup`<br>$~~~~~$`\rgroup`                | $\Uparrow$ `\Uparrow`         |
| $\vert$ <code>&#124;</code>                | $\vert$ `\vert`                                | $┌ ┐$ `┌ ┐` | $\ulcorner \urcorner$ `\ulcorner`<br>$~~~~$`\urcorner`         | $\Downarrow$ `\Downarrow`     |
| $\Vert$ <code>&#92;&#124;</code>           | $\Vert$ `\Vert`                                | $└ ┘$ `└ ┘` | $\llcorner \lrcorner$ `\llcorner`<br>$~~~~$`\lrcorner`         | $\Updownarrow$ `\Updownarrow` |
| $\lvert~\rvert$ `\lvert`<br>$~~~~$`\rvert` | $\lVert~\rVert$ `\lVert`<br>$~~~~~$`\rVert`    | `\left.`    | `\right.`                                                      | $\backslash$ `\backslash`     |
| $\lang~\rang$ `\lang`<br>$~~~~$`\rang`     | $\lt~\gt$ `\lt \gt`                            |

**Delimiter Sizing**

$\left(\LARGE{AB}\right)$ `\left(\LARGE{AB}\right)`

$( \big( \Big( \bigg( \Bigg($ `( \big( \Big( \bigg( \Bigg(`

|           |         |          |          |          |
| :-------- | :------ | :------- | :------- | :------- |
| `\left`   | `\big`  | `\bigl`  | `\bigm`  | `\bigr`  |
| `\middle` | `\Big`  | `\Bigl`  | `\Bigm`  | `\Bigr`  |
| `\right`  | `\bigg` | `\biggl` | `\biggm` | `\biggr` |
|           | `\Bigg` | `\Biggl` | `\Biggm` | `\Biggr` |

## 3: Environments

|                                                  |                                                                                                     |                                                                                                                |                                                                                                                                                                                                                                         |
| :----------------------------------------------- | :-------------------------------------------------------------------------------------------------- | :------------------------------------------------------------------------------------------------------------- | :-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| $\begin{matrix} a & b \\ c & d \end{matrix}$     | `\begin{matrix}`<br>&nbsp;&nbsp;&nbsp;`a & b \\`<br>&nbsp;&nbsp;&nbsp;`c & d`<br>`\end{matrix}`     | $\begin{array}{cc}a & b\\c & d\end{array}$                                                                     | `\begin{array}{cc}`<br>&nbsp;&nbsp;&nbsp;`a & b \\`<br>&nbsp;&nbsp;&nbsp;`c & d`<br>`\end{array}`                                                                                                                                       |
| $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$   | `\begin{pmatrix}`<br>&nbsp;&nbsp;&nbsp;`a & b \\`<br>&nbsp;&nbsp;&nbsp;`c & d`<br>`\end{pmatrix}`   | $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$                                                                 | `\begin{bmatrix}`<br>&nbsp;&nbsp;&nbsp;`a & b \\`<br>&nbsp;&nbsp;&nbsp;`c & d`<br>`\end{bmatrix}`                                                                                                                                       |
| $\begin{vmatrix} a & b \\ c & d \end{vmatrix}$   | `\begin{vmatrix}`<br>&nbsp;&nbsp;&nbsp;`a & b \\`<br>&nbsp;&nbsp;&nbsp;`c & d`<br>`\end{vmatrix}`   | $\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}$                                                                 | `\begin{Vmatrix}`<br>&nbsp;&nbsp;&nbsp;`a & b \\`<br>&nbsp;&nbsp;&nbsp;`c & d`<br>`\end{Vmatrix}`                                                                                                                                       |
| $\begin{Bmatrix} a & b \\ c & d \end{Bmatrix}$   | `\begin{Bmatrix}`<br>&nbsp;&nbsp;&nbsp;`a & b \\`<br>&nbsp;&nbsp;&nbsp;`c & d`<br>`\end{Bmatrix}`   | $\def\arraystretch{1.5}\begin{array}{c:c:c} a & b & c \\ \hline d & e & f \\ \hdashline g & h & i \end{array}$ | `\def\arraystretch{1.5}`<br>&nbsp;&nbsp;&nbsp;`\begin{array}{c:c:c}`<br>&nbsp;&nbsp;&nbsp;`a & b & c \\ \hline`<br>&nbsp;&nbsp;&nbsp;`d & e & f \\`<br>&nbsp;&nbsp;&nbsp;`\hdashline`<br>&nbsp;&nbsp;&nbsp;`g & h & i`<br>`\end{array}` |
| $\begin{aligned} a&=b+c \\ d+e&=f \end{aligned}$ | `\begin{aligned}`<br>&nbsp;&nbsp;&nbsp;`a&=b+c \\`<br>&nbsp;&nbsp;&nbsp;`d+e&=f`<br>`\end{aligned}` | $\begin{alignedat}{2}10&x+&3&y=2\\3&x+&13&y=4\end{alignedat}$                                                  | `\begin{alignedat}{2}`<br>&nbsp;&nbsp;&nbsp;`10&x+ &3&y = 2 \\`<br>&nbsp;&nbsp;&nbsp;` 3&x+&13&y = 4`<br>`\end{alignedat}`                                                                                                              |
| $\begin{gathered} a=b \\ e=b+c \end{gathered}$   | `\begin{gathered}`<br>&nbsp;&nbsp;&nbsp;`a=b \\ `<br>&nbsp;&nbsp;&nbsp;`e=b+c`<br>`\end{gathered}`  | $x = \begin{cases} a &\text{if } b \\ c &\text{if } d \end{cases}$                                             | `x = \begin{cases}`<br>&nbsp;&nbsp;&nbsp;`a &\text{if } b  \\`<br>&nbsp;&nbsp;&nbsp;`c &\text{if } d`<br>`\end{cases}`                                                                                                                  |

KaTeX also supports `darray` and `dcases`.

Acceptable line separators include: `\\`, `\cr`, `\\[distance]`, and `\cr[distance]`. _Distance_ can be written with any of the [KaTeX units](#units).

The `{array}` environment supports `|` and `:` vertical separators.

The `{array}` environment does not yet support `\cline` or `\multicolumn`.

## 4: HTML

|                                     |                                     |
| :---------------------------------- | :---------------------------------- |
| $\href{https://katex.org/}{\KaTeX}$ | `\href{https://katex.org/}{\KaTeX}` |
| $\url{https://katex.org/}$          | `\url{https://katex.org/}`          |

## 5: Letters and Unicode

**Greek Letters**

Direct Input: $Α Β Γ Δ Ε Ζ Η Θ Ι \allowbreak Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω$
$\allowbreak α β γ δ ϵ ζ η θ ι κ λ μ ν ξ o π \allowbreak ρ σ τ υ ϕ χ ψ ω ε ϑ ϖ ϱ ς φ$

|                             |                         |                         |                             |
| --------------------------- | ----------------------- | ----------------------- | --------------------------- |
| $\Alpha$ `\Alpha`           | $\Beta$ `\Beta`         | $\Gamma$ `\Gamma`       | $\Delta$ `\Delta`           |
| $\Epsilon$ `\Epsilon`       | $\Zeta$ `\Zeta`         | $\Eta$ `\Eta`           | $\Theta$ `\Theta`           |
| $\Iota$ `\Iota`             | $\Kappa$ `\Kappa`       | $\Lambda$ `\Lambda`     | $\Mu$ `\Mu`                 |
| $\Nu$ `\Nu`                 | $\Xi$ `\Xi`             | $\Omicron$ `\Omicron`   | $\Pi$ `\Pi`                 |
| $\Sigma$ `\Sigma`           | $\Tau$ `\Tau`           | $\Upsilon$ `\Upsilon`   | $\Phi$ `\Phi`               |
| $\Chi$ `\Chi`               | $\Psi$ `\Psi`           | $\Omega$ `\Omega`       |
| $\varGamma$ `\varGamma`     | $\varDelta$ `\varDelta` | $\varTheta$ `\varTheta` | $\varLambda$ `\varLambda`   |
| $\varXi$ `\varXi`           | $\varPi$ `\varPi`       | $\varSigma$ `\varSigma` | $\varUpsilon$ `\varUpsilon` |
| $\varPhi$ `\varPhi`         | $\varPsi$ `\varPsi`     | $\varOmega$ `\varOmega` |                             |
| $\alpha$ `\alpha`           | $\beta$ `\beta`         | $\gamma$ `\gamma`       | $\delta$ `\delta`           |
| $\epsilon$ `\epsilon`       | $\zeta$ `\zeta`         | $\eta$ `\eta`           | $\theta$ `\theta`           |
| $\iota$ `\iota`             | $\kappa$ `\kappa`       | $\lambda$ `\lambda`     | $\mu$ `\mu`                 |
| $\nu$ `\nu`                 | $\xi$ `\xi`             | $\omicron$ `\omicron`   | $\pi$ `\pi`                 |
| $\rho$ `\rho`               | $\sigma$ `\sigma`       | $\tau$ `\tau`           | $\upsilon$ `\upsilon`       |
| $\phi$ `\phi`               | $\chi$ `\chi`           | $\psi$ `\psi`           | $\omega$ `\omega`           |
| $\varepsilon$ `\varepsilon` | $\varkappa$ `\varkappa` | $\vartheta$ `\vartheta` | $\thetasym$ `\thetasym`     |
| $\varpi$ `\varpi`           | $\varrho$ `\varrho`     | $\varsigma$ `\varsigma` | $\varphi$ `\varphi`         |

| $\digamma$ `\digamma`

**Other Letters**

|                       |                       |                       |                           |                           |
| :-------------------- | :-------------------- | :-------------------- | :------------------------ | :------------------------ |
| $\imath$ `\imath`     | $\nabla$ `\nabla`     | $\Im$ `\Im`           | $\Reals$ `\Reals`         | $\text{\OE}$ `\text{\OE}` |
| $\jmath$ `\jmath`     | $\partial$ `\partial` | $\image$ `\image`     | $\wp$ `\wp`               | $\text{\o}$ `\text{\o}`   |
| $\aleph$ `\aleph`     | $\Game$ `\Game`       | $\Bbbk$ `\Bbbk`       | $\weierp$ `\weierp`       | $\text{\O}$ `\text{\O}`   |
| $\alef$ `\alef`       | $\Finv$ `\Finv`       | $\N$ `\N`             | $\Z$ `\Z`                 | $\text{\ss}$ `\text{\ss}` |
| $\alefsym$ `\alefsym` | $\cnums$ `\cnums`     | $\natnums$ `\natnums` | $\text{\aa}$ `\text{\aa}` | $\text{\i}$ `\text{\i}`   |
| $\beth$ `\beth`       | $\Complex$ `\Complex` | $\R$ `\R`             | $\text{\AA}$ `\text{\AA}` | $\text{\j}$ `\text{\j}`   |
| $\gimel$ `\gimel`     | $\ell$ `\ell`         | $\Re$ `\Re`           | $\text{\ae}$ `\text{\ae}` |
| $\daleth$ `\daleth`   | $\hbar$ `\hbar`       | $\real$ `\real`       | $\text{\AE}$ `\text{\AE}` |
| $\eth$ `\eth`         | $\hslash$ `\hslash`   | $\reals$ `\reals`     | $\text{\oe}$ `\text{\oe}` |

Direct Input: $∂ ∇ ℑ Ⅎ ℵ ℶ ℷ ℸ ⅁ ℏ ð$
ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖÙÚÛÜÝÞßàáâãäåçèéêëìíîïðñòóôöùúûüýþÿ

**Unicode Mathematical Alphanumeric Symbols**

| Item        | Range                   | Item              | Range                |
| ----------- | ----------------------- | ----------------- | -------------------- |
| Bold        | $\text{𝐀-𝐙 𝐚-𝐳 𝟎-𝟗}$    | Double-struck     | $\text{𝔸-}ℤ\ 𝕜$      |
| Italic      | $\text{𝐴-𝑍 𝑎-𝑧}$        | Sans serif        | $\text{𝖠-𝖹 𝖺-𝗓 𝟢-𝟫}$ |
| Bold Italic | $\text{𝑨-𝒁 𝒂-𝒛}$        | Sans serif bold   | $\text{𝗔-𝗭 𝗮-𝘇 𝟬-𝟵}$ |
| Script      | $\text{𝒜-𝒵}$            | Sans serif italic | $\text{𝘈-𝘡 𝘢-𝘻}$     |
| Fractur     | $\text{𝔄-}ℨ\text{ 𝔞-𝔷}$ | Monospace         | $\text{𝙰-𝚉 𝚊-𝚣 𝟶-𝟿}$ |

**Unicode**

The letters listed above will render in any KaTeX rendering mode.

If the KaTeX rendering mode is set to `strict: false` or `strict:"warn"` (default), then KaTeX will accept all Unicode letters. The letters not listed above will be rendered from system fonts, not KaTeX-supplied fonts, so their typography may clash. They may also cause small vertical alignment issues. KaTeX has detailed metrics for glyphs in Latin, Greek, and Cyrillic, but other glyphs are treated as if they are each as tall as the letter M.

For Persian composite characters, a user-supplied [plug-in](https://github.com/HosseinAgha/persian-katex-plugin) is under development.

## 6: Layout

### 6.1: Annotation

|                                 |                                                                       |
| :------------------------------ | :-------------------------------------------------------------------- |
| $\cancel{5}$ `\cancel{5}`       | $\overbrace{a+b+c}^{\text{note}}$ `\overbrace{a+b+c}^{\text{note}}`   |
| $\bcancel{5}$ `\bcancel{5}`     | $\underbrace{a+b+c}_{\text{note}}$ `\underbrace{a+b+c}_{\text{note}}` |
| $\xcancel{ABC}$ `\xcancel{ABC}` | $\not =$ `\not =`                                                     |
| $\sout{abc}$ `\sout{abc}`       | $\boxed{\pi=\frac c d}$ `\boxed{\pi=\frac c d}`                       |

`\tag{hi} x+y^{2x}`
$$\tag{hi} x+y^{2x}$$

`\tag*{hi} x+y^{2x}`
$$\tag*{hi} x+y^{2x}$$

### 6.2: Line Breaks

KaTeX 0.10.0+ will insert automatic line breaks in inline math after relations or binary operators such as “=” or “+”. These can be suppressed by `\nobreak` or by placing math inside a pair of braces, as in `{F=ma}`. `\allowbreak` will allow automatic line breaks at locations other than relations or operators.

Hard line breaks are `\\` and `\newline`.

In display math, KaTeX does not insert automatic line breaks. It ignores display math hard line breaks when rendering option `strict: true`.

### 6.3: Vertical Layout

|                  |                                     |                                                   |
| :--------------- | :---------------------------------- | :------------------------------------------------ |
| $x_n$ `x_n`      | $\stackrel{!}{=}$ `\stackrel{!}{=}` | $a \atop b$ `a \atop b`                           |
| $e^x$ `e^x`      | $\overset{!}{=}$ `\overset{!}{=}`   | $a\raisebox{0.25em}{b}c$ `a\raisebox{0.25em}{b}c` |
| $\_u^o $ `_u^o ` | $\underset{!}{=}$ `\underset{!}{=}` |

The second argument of `\raisebox` can contain math if it is nested within `$…$` delimiters, as in `\raisebox{0.25em}{$\frac a b$}`

### 6.4: Overlap and Spacing

|                                         |                                                           |
| :-------------------------------------- | :-------------------------------------------------------- |
| ${=}\mathllap{/\,}$ `{=}\mathllap{/\,}` | $\left(x^{\smash{2}}\right)$ `\left(x^{\smash{2}}\right)` |
| $\mathrlap{\,/}{=}$ `\mathrlap{\,/}{=}` | $\sqrt{\smash[b]{y}}$ `\sqrt{\smash[b]{y}} `              |

$\displaystyle\sum_{\mathclap{1\le i\le j\le n}} x_{ij}$ `\sum_{\mathclap{1\le i\le j\le n}} x_{ij}`

KaTeX also supports `\llap`, `\rlap`, and `\clap`, but they will take only text, not math, as arguments.

**Spacing**

| Function        | Produces           | Function             | Produces                              |
| :-------------- | :----------------- | :------------------- | :------------------------------------ |
| `\,`            | ³∕₁₈ em space      | `\kern{distance}`    | space, width = _distance_             |
| `\thinspace`    | ³∕₁₈ em space      | `\mkern{distance}`   | space, width = _distance_             |
| `\:`            | ⁴∕₁₈ em space      | `\mskip{distance}`   | space, width = _distance_             |
| `\medspace`     | ⁴∕₁₈ em space      | `\hskip{distance}`   | space, width = _distance_             |
| `\;`            | ⁵∕₁₈ em space      | `\hspace{distance}`  | space, width = _distance_             |
| `\thickspace`   | ⁵∕₁₈ em space      | `\hspace*{distance}` | space, width = _distance_             |
| `\enspace`      | ½ em space         | `\phantom{content}`  | space the width and height of content |
| `\quad`         | 1 em space         | `\hphantom{content}` | space the width of content            |
| `\qquad`        | 2 em space         | `\vphantom{content}` | a strut the height of content         |
| `~`             | non-breaking space | `\!`                 | – ³∕₁₈ em space                       |
| `\<space>`      | space              | `\negthinspace`      | – ³∕₁₈ em space                       |
| `\nobreakspace` | non-breaking space | `\negmedspace`       | – ⁴∕₁₈ em space                       |
| `\space`        | space              | `\negthickspace`     | – ⁵∕₁₈ em space                       |

**Notes:**

`distance` will accept any of the [KaTeX units](#units).

`\kern`, `\mkern`, `\mskip`, and `\hspace` accept unbraced distances, as in: `\kern1em`.

`\mkern` and `\mskip` will not work in text mode and both will write a console warning for any unit except `mu`.

## 7: Logic and Set Theory

|                       |                             |                                     |                             |
| :-------------------- | :-------------------------- | :---------------------------------- | :-------------------------- |
| $\forall$ `\forall`   | $\complement$ `\complement` | $\therefore$ `\therefore`           | $\emptyset$ `\emptyset`     |
| $\exists$ `\exists`   | $\subset$ `\subset`         | $\because$ `\because`               | $\empty$ `\empty`           |
| $\exist$ `\exist`     | $\supset$ `\supset`         | $\mapsto$ `\mapsto`                 | $\varnothing$ `\varnothing` |
| $\nexists$ `\nexists` | $\mid$ `\mid`               | $\to$ `\to`                         | $\implies$ `\implies`       |
| $\in$ `\in`           | $\land$ `\land`             | $\gets$ `\gets`                     | $\impliedby$ `\impliedby`   |
| $\isin$ `\isin`       | $\lor$ `\lor`               | $\leftrightarrow$ `\leftrightarrow` | $\iff$ `\iff`               |
| $\notin$ `\notin`     | $\ni$ `\ni`                 | $\notni$ `\notni`                   | $\neg$ `\neg` or `\lnot`    |

Direct Input: $∀ ∴ ∁ ∵ ∃ ∣ ∈ ∉ ∋ ⊂ ⊃ ∧ ∨ ↦ → ← ↔ ¬$ ℂ ℍ ℕ ℙ ℚ ℝ

## 8: Macros

|                                       |                                                  |
| :------------------------------------ | :----------------------------------------------- |
| $\def\foo{x^2} \foo + \foo$           | `\def\foo{x^2} \foo + \foo`                      |
| $\gdef\bar#1{#1^2} \bar{y} + \bar{y}$ | `\gdef\bar#1{#1^2} \bar{y} + \bar{y}`            |
|                                       | `\global\def\macroname#1#2…{definition}`         |
|                                       | `\newcommand\macroname[numargs]{definition}`     |
|                                       | `\renewcommand\macroname[numargs]{definition}`   |
|                                       | `\providecommand\macroname[numargs]{definition}` |

Macros can also be defined in the KaTeX rendering options.

Macros accept up to nine arguments: #1, #2, etc.

`\gdef` and `\global\def` macros will persist between math expressions.

Available functions include:

`\char` `\mathchoice` `\TextOrMath` `\@ifstar` `\@ifnextchar` `\@firstoftwo` `\@secondoftwo` `\relax`

@ is a valid character for commands, as if `\makeatletter` were in effect.

## 9: Operators

### 9.1: Big Operators

|                   |                         |                           |                         |
| ----------------- | ----------------------- | ------------------------- | ----------------------- |
| $\sum$ `\sum`     | $\prod$ `\prod`         | $\bigotimes$ `\bigotimes` | $\bigvee$ `\bigvee`     |
| $\int$ `\int`     | $\coprod$ `\coprod`     | $\bigoplus$ `\bigoplus`   | $\bigwedge$ `\bigwedge` |
| $\iint$ `\iint`   | $\intop$ `\intop`       | $\bigodot$ `\bigodot`     | $\bigcap$ `\bigcap`     |
| $\iiint$ `\iiint` | $\smallint$ `\smallint` | $\biguplus$ `\biguplus`   | $\bigcup$ `\bigcup`     |
| $\oint$ `\oint`   | $\oiint$ `\oiint`       | $\oiiint$ `\oiiint`       | $\bigsqcup$ `\bigsqcup` |

Direct Input: $∫ ∬ ∭ ∮ ∏ ∐ ∑ ⋀ ⋁ ⋂ ⋃ ⨀ ⨁ ⨂ ⨄ ⨆$

### 9.2: Binary Operators

|                         |                                     |                                     |                                       |
| ----------------------- | ----------------------------------- | ----------------------------------- | ------------------------------------- |
| $+$ `+`                 | $\cdot$ `\cdot`                     | $\gtrdot$ `\gtrdot`                 | $x \pmod a$ `x \pmod a`               |
| $-$ `-`                 | $\cdotp$ `\cdotp`                   | $\intercal$ `\intercal`             | $x \pod a$ `x \pod a`                 |
| $/$ `/`                 | $\centerdot$ `\centerdot`           | $\land$ `\land`                     | $\rhd$ `\rhd`                         |
| $*$ `*`                 | $\circ$ `\circ`                     | $\leftthreetimes$ `\leftthreetimes` | $\rightthreetimes$ `\rightthreetimes` |
| $\amalg$ `\amalg`       | $\circledast$ `\circledast`         | $\ldotp$ `\ldotp`                   | $\rtimes$ `\rtimes`                   |
| $\And$ `\And`           | $\circledcirc$ `\circledcirc`       | $\lor$ `\lor`                       | $\setminus$ `\setminus`               |
| $\ast$ `\ast`           | $\circleddash$ `\circleddash`       | $\lessdot$ `\lessdot`               | $\smallsetminus$ `\smallsetminus`     |
| $\barwedge$ `\barwedge` | $\Cup$ `\Cup`                       | $\lhd$ `\lhd`                       | $\sqcap$ `\sqcap`                     |
| $\bigcirc$ `\bigcirc`   | $\cup$ `\cup`                       | $\ltimes$ `\ltimes`                 | $\sqcup$ `\sqcup`                     |
| $\bmod$ `\bmod`         | $\curlyvee$ `\curlyvee`             | $x \mod a$ `x\mod a`                | $\times$ `\times`                     |
| $\boxdot$ `\boxdot`     | $\curlywedge$ `\curlywedge`         | $\mp$ `\mp`                         | $\unlhd$ `\unlhd`                     |
| $\boxminus$ `\boxminus` | $\div$ `\div`                       | $\odot$ `\odot`                     | $\unrhd$ `\unrhd`                     |
| $\boxplus$ `\boxplus`   | $\divideontimes$ `\divideontimes`   | $\ominus$ `\ominus`                 | $\uplus$ `\uplus`                     |
| $\boxtimes$ `\boxtimes` | $\dotplus$ `\dotplus`               | $\oplus$ `\oplus`                   | $\vee$ `\vee`                         |
| $\bullet$ `\bullet`     | $\doublebarwedge$ `\doublebarwedge` | $\otimes$ `\otimes`                 | $\veebar$ `\veebar`                   |
| $\Cap$ `\Cap`           | $\doublecap$ `\doublecap`           | $\oslash$ `\oslash`                 | $\wedge$ `\wedge`                     |
| $\cap$ `\cap`           | $\doublecup$ `\doublecup`           | $\pm$ `\pm` or `\plusmn`            | $\wr$ `\wr`                           |

Direct Input: $+ - / * ⋅ ± × ÷ ∓ ∔ ∧ ∨ ∩ ∪ ≀ ⊎ ⊓ ⊔ ⊕ ⊖ ⊗ ⊘ ⊙ ⊚ ⊛ ⊝$

### 9.3: Fractions and Binomials

|                             |                               |                                                             |
| :-------------------------- | :---------------------------- | :---------------------------------------------------------- |
| $\frac{a}{b}$ `\frac{a}{b}` | $\tfrac{a}{b}$ `\tfrac{a}{b}` | $\genfrac ( ] {2pt}{1}a{a+1}$ `\genfrac ( ] {2pt}{1}a{a+1}` |
| ${a \over b}$ `{a \over b}` | $\dfrac{a}{b}$ `\dfrac{a}{b}` | ${a \above{2pt} b+1}$ `{a \above{2pt} b+1}`                 |
| $a/b$ `a/b`                 |                               | $\cfrac{a}{1 + \cfrac{1}{b}}$ `\cfrac{a}{1 + \cfrac{1}{b}}` |

|                                 |                                 |                             |
| :------------------------------ | :------------------------------ | :-------------------------- |
| $\binom{n}{k}$ `\binom{n}{k}`   | $\dbinom{n}{k}$ `\dbinom{n}{k}` | ${n\brace k}$ `{n\brace k}` |
| ${n \choose k}$ `{n \choose k}` | $\tbinom{n}{k}$ `\tbinom{n}{k}` | ${n\brack k}$ `{n\brack k}` |

### 9.4: Math Operators

|                     |                 |                                       |                     |
| ------------------- | --------------- | ------------------------------------- | ------------------- |
| $\arcsin$ `\arcsin` | $\cotg$ `\cotg` | $\ln$ `\ln`                           | $\det$ `\det`       |
| $\arccos$ `\arccos` | $\coth$ `\coth` | $\log$ `\log`                         | $\gcd$ `\gcd`       |
| $\arctan$ `\arctan` | $\csc$ `\csc`   | $\sec$ `\sec`                         | $\inf$ `\inf`       |
| $\arctg$ `\arctg`   | $\ctg$ `\ctg`   | $\sin$ `\sin`                         | $\lim$ `\lim`       |
| $\arcctg$ `\arcctg` | $\cth$ `\cth`   | $\sinh$ `\sinh`                       | $\liminf$ `\liminf` |
| $\arg$ `\arg`       | $\deg$ `\deg`   | $\sh$ `\sh`                           | $\limsup$ `\limsup` |
| $\ch$ `\ch`         | $\dim$ `\dim`   | $\tan$ `\tan`                         | $\max$ `\max`       |
| $\cos$ `\cos`       | $\exp$ `\exp`   | $\tanh$ `\tanh`                       | $\min$ `\min`       |
| $\cosec$ `\cosec`   | $\hom$ `\hom`   | $\tg$ `\tg`                           | $\Pr$ `\Pr`         |
| $\cosh$ `\cosh`     | $\ker$ `\ker`   | $\th$ `\th`                           | $\sup$ `\sup`       |
| $\cot$ `\cot`       | $\lg$ `\lg`     | $\operatorname{f}$ `\operatorname{f}` |

Functions on the right column of this table can take `\limits`.

### 9.5: `\sqrt`

$\sqrt{x}$ `\sqrt{x}`

$\sqrt[3]{x}$ `\sqrt[3]{x}`

## 10: Relations

$\stackrel{!}{=}$ `\stackrel{!}{=}`

|                               |                                   |                                   |                                         |
| :---------------------------- | :-------------------------------- | :-------------------------------- | :-------------------------------------- |
| $=$ `=`                       | $\eqcirc$ `\eqcirc`               | $\lesseqgtr$ `\lesseqgtr`         | $\sqsupset$ `\sqsupset`                 |
| $<$ `<`                       | $\eqcolon$ `\eqcolon`             | $\lesseqqgtr$ `\lesseqqgtr`       | $\sqsupseteq$ `\sqsupseteq`             |
| $>$ `>`                       | $\Eqcolon$ `\Eqcolon`             | $\lessgtr$ `\lessgtr`             | $\Subset$ `\Subset`                     |
| $:$ `:`                       | $\eqqcolon$ `\eqqcolon`           | $\lesssim$ `\lesssim`             | $\subset$ `\subset` or `\sub`           |
| $\approx$ `\approx`           | $\Eqqcolon$ `\Eqqcolon`           | $\ll$ `\ll`                       | $\subseteq$ `\subseteq` or `\sube`      |
| $\approxeq$ `\approxeq`       | $\eqsim$ `\eqsim`                 | $\lll$ `\lll`                     | $\subseteqq$ `\subseteqq`               |
| $\asymp$ `\asymp`             | $\eqslantgtr$ `\eqslantgtr`       | $\llless$ `\llless`               | $\succ$ `\succ`                         |
| $\backepsilon$ `\backepsilon` | $\eqslantless$ `\eqslantless`     | $\lt$ `\lt`                       | $\succapprox$ `\succapprox`             |
| $\backsim$ `\backsim`         | $\equiv$ `\equiv`                 | $\mid$ `\mid`                     | $\succcurlyeq$ `\succcurlyeq`           |
| $\backsimeq$ `\backsimeq`     | $\fallingdotseq$ `\fallingdotseq` | $\models$ `\models`               | $\succeq$ `\succeq`                     |
| $\between$ `\between`         | $\frown$ `\frown`                 | $\multimap$ `\multimap`           | $\succsim$ `\succsim`                   |
| $\bowtie$ `\bowtie`           | $\ge$ `\ge`                       | $\owns$ `\owns`                   | $\Supset$ `\Supset`                     |
| $\bumpeq$ `\bumpeq`           | $\geq$ `\geq`                     | $\parallel$ `\parallel`           | $\supset$ `\supset`                     |
| $\Bumpeq$ `\Bumpeq`           | $\geqq$ `\geqq`                   | $\perp$ `\perp`                   | $\supseteq$ `\supseteq` or `\supe`      |
| $\circeq$ `\circeq`           | $\geqslant$ `\geqslant`           | $\pitchfork$ `\pitchfork`         | $\supseteqq$ `\supseteqq`               |
| $\colonapprox$ `\colonapprox` | $\gg$ `\gg`                       | $\prec$ `\prec`                   | $\thickapprox$ `\thickapprox`           |
| $\Colonapprox$ `\Colonapprox` | $\ggg$ `\ggg`                     | $\precapprox$ `\precapprox`       | $\thicksim$ `\thicksim`                 |
| $\coloneq$ `\coloneq`         | $\gggtr$ `\gggtr`                 | $\preccurlyeq$ `\preccurlyeq`     | $\trianglelefteq$ `\trianglelefteq`     |
| $\Coloneq$ `\Coloneq`         | $\gt$ `\gt`                       | $\preceq$ `\preceq`               | $\triangleq$ `\triangleq`               |
| $\coloneqq$ `\coloneqq`       | $\gtrapprox$ `\gtrapprox`         | $\precsim$ `\precsim`             | $\trianglerighteq$ `\trianglerighteq`   |
| $\Coloneqq$ `\Coloneqq`       | $\gtreqless$ `\gtreqless`         | $\propto$ `\propto`               | $\varpropto$ `\varpropto`               |
| $\colonsim$ `\colonsim`       | $\gtreqqless$ `\gtreqqless`       | $\risingdotseq$ `\risingdotseq`   | $\vartriangle$ `\vartriangle`           |
| $\Colonsim$ `\Colonsim`       | $\gtrless$ `\gtrless`             | $\shortmid$ `\shortmid`           | $\vartriangleleft$ `\vartriangleleft`   |
| $\cong$ `\cong`               | $\gtrsim$ `\gtrsim`               | $\shortparallel$ `\shortparallel` | $\vartriangleright$ `\vartriangleright` |
| $\curlyeqprec$ `\curlyeqprec` | $\in$ `\in` or `\isin`            | $\sim$ `\sim`                     | $\vcentcolon$ `\vcentcolon`             |
| $\curlyeqsucc$ `\curlyeqsucc` | $\Join$ `\Join`                   | $\simeq$ `\simeq`                 | $\vdash$ `\vdash`                       |
| $\dashv$ `\dashv`             | $\le$ `\le`                       | $\smallfrown$ `\smallfrown`       | $\vDash$ `\vDash`                       |
| $\dblcolon$ `\dblcolon`       | $\leq$ `\leq`                     | $\smallsmile$ `\smallsmile`       | $\Vdash$ `\Vdash`                       |
| $\doteq$ `\doteq`             | $\leqq$ `\leqq`                   | $\smile$ `\smile`                 | $\Vvdash$ `\Vvdash`                     |
| $\Doteq$ `\Doteq`             | $\leqslant$ `\leqslant`           | $\sqsubset$ `\sqsubset`           |
| $\doteqdot$ `\doteqdot`       | $\lessapprox$ `\lessapprox`       | $\sqsubseteq$ `\sqsubseteq`       |

Direct Input: $= < > : ∈ ∋ ∝ ∼ ∽ ≂ ≃ ≅ ≈ ≊ ≍ ≎ ≏ ≐ ≑ ≒ ≓ ≖ ≗ ≜ ≡ ≤ ≥ ≦ ≧ ≫ ≬ ≳ ≷ ≺ ≻ ≼ ≽ ≾ ≿ ⊂ ⊃ ⊆ ⊇ ⊏ ⊐ ⊑ ⊒ ⊢ ⊣ ⊩ ⊪ ⊸ ⋈ ⋍ ⋐ ⋑ ⋔ ⋙ ⋛ ⋞ ⋟ ⌢ ⌣ ⩾ ⪆ ⪌ ⪕ ⪖ ⪯ ⪰ ⪷ ⪸ ⫅ ⫆ ≲ ⩽ ⪅ ≶ ⋚ ⪋ ⟂ ⊨$ `≔ ≕ ⩴`

### 10.1: Negated Relations

$\not =$ `\not =`

|                           |                                     |                                         |                                   |
| ------------------------- | ----------------------------------- | --------------------------------------- | --------------------------------- |
| $\gnapprox$ `\gnapprox`   | $\ngeqslant$ `\ngeqslant`           | $\nsubseteq$ `\nsubseteq`               | $\precneqq$ `\precneqq`           |
| $\gneq$ `\gneq`           | $\ngtr$ `\ngtr`                     | $\nsubseteqq$ `\nsubseteqq`             | $\precnsim$ `\precnsim`           |
| $\gneqq$ `\gneqq`         | $\nleq$ `\nleq`                     | $\nsucc$ `\nsucc`                       | $\subsetneq$ `\subsetneq`         |
| $\gnsim$ `\gnsim`         | $\nleqq$ `\nleqq`                   | $\nsucceq$ `\nsucceq`                   | $\subsetneqq$ `\subsetneqq`       |
| $\gvertneqq$ `\gvertneqq` | $\nleqslant$ `\nleqslant`           | $\nsupseteq$ `\nsupseteq`               | $\succnapprox$ `\succnapprox`     |
| $\lnapprox$ `\lnapprox`   | $\nless$ `\nless`                   | $\nsupseteqq$ `\nsupseteqq`             | $\succneqq$ `\succneqq`           |
| $\lneq$ `\lneq`           | $\nmid$ `\nmid`                     | $\ntriangleleft$ `\ntriangleleft`       | $\succnsim$ `\succnsim`           |
| $\lneqq$ `\lneqq`         | $\notin$ `\notin`                   | $\ntrianglelefteq$ `\ntrianglelefteq`   | $\supsetneq$ `\supsetneq`         |
| $\lnsim$ `\lnsim`         | $\notni$ `\notni`                   | $\ntriangleright$ `\ntriangleright`     | $\supsetneqq$ `\supsetneqq`       |
| $\lvertneqq$ `\lvertneqq` | $\nparallel$ `\nparallel`           | $\ntrianglerighteq$ `\ntrianglerighteq` | $\varsubsetneq$ `\varsubsetneq`   |
| $\ncong$ `\ncong`         | $\nprec$ `\nprec`                   | $\nvdash$ `\nvdash`                     | $\varsubsetneqq$ `\varsubsetneqq` |
| $\ne$ `\ne`               | $\npreceq$ `\npreceq`               | $\nvDash$ `\nvDash`                     | $\varsupsetneq$ `\varsupsetneq`   |
| $\neq$ `\neq`             | $\nshortmid$ `\nshortmid`           | $\nVDash$ `\nVDash`                     | $\varsupsetneqq$ `\varsupsetneqq` |
| $\ngeq$ `\ngeq`           | $\nshortparallel$ `\nshortparallel` | $\nVdash$ `\nVdash`                     |
| $\ngeqq$ `\ngeqq`         | $\nsim$ `\nsim`                     | $\precnapprox$ `\precnapprox`           |

Direct Input:

$$
∉ ∌ ∤ ∦ ≁ ≆ ≠ ≨ ≩ ≮ ≯ ≰ ≱ ⊀ ⊁ ⊈ ⊉ ⊊ ⊋ ⊬ ⊭ ⊮ ⊯ ⋠ ⋡ ⋦ ⋧ ⋨ ⋩ ⋬ ⋭ ⪇ ⪈ ⪉ ⪊ ⪵ ⪶ ⪹ ⪺ ⫋ ⫌
$$

### 10.2: Arrows

|                                         |                                               |                                           |
| :-------------------------------------- | :-------------------------------------------- | :---------------------------------------- |
| $\circlearrowleft$ `\circlearrowleft`   | $\leftharpoonup$ `\leftharpoonup`             | $\rArr$ `\rArr`                           |
| $\circlearrowright$ `\circlearrowright` | $\leftleftarrows$ `\leftleftarrows`           | $\rarr$ `\rarr`                           |
| $\curvearrowleft$ `\curvearrowleft`     | $\leftrightarrow$ `\leftrightarrow`           | $\restriction$ `\restriction`             |
| $\curvearrowright$ `\curvearrowright`   | $\Leftrightarrow$ `\Leftrightarrow`           | $\rightarrow$ `\rightarrow`               |
| $\Darr$ `\Darr`                         | $\leftrightarrows$ `\leftrightarrows`         | $\Rightarrow$ `\Rightarrow`               |
| $\dArr$ `\dArr`                         | $\leftrightharpoons$ `\leftrightharpoons`     | $\rightarrowtail$ `\rightarrowtail`       |
| $\darr$ `\darr`                         | $\leftrightsquigarrow$ `\leftrightsquigarrow` | $\rightharpoondown$ `\rightharpoondown`   |
| $\dashleftarrow$ `\dashleftarrow`       | $\Lleftarrow$ `\Lleftarrow`                   | $\rightharpoonup$ `\rightharpoonup`       |
| $\dashrightarrow$ `\dashrightarrow`     | $\longleftarrow$ `\longleftarrow`             | $\rightleftarrows$ `\rightleftarrows`     |
| $\downarrow$ `\downarrow`               | $\Longleftarrow$ `\Longleftarrow`             | $\rightleftharpoons$ `\rightleftharpoons` |
| $\Downarrow$ `\Downarrow`               | $\longleftrightarrow$ `\longleftrightarrow`   | $\rightrightarrows$ `\rightrightarrows`   |
| $\downdownarrows$ `\downdownarrows`     | $\Longleftrightarrow$ `\Longleftrightarrow`   | $\rightsquigarrow$ `\rightsquigarrow`     |
| $\downharpoonleft$ `\downharpoonleft`   | $\longmapsto$ `\longmapsto`                   | $\Rrightarrow$ `\Rrightarrow`             |
| $\downharpoonright$ `\downharpoonright` | $\longrightarrow$ `\longrightarrow`           | $\Rsh$ `\Rsh`                             |
| $\gets$ `\gets`                         | $\Longrightarrow$ `\Longrightarrow`           | $\searrow$ `\searrow`                     |
| $\Harr$ `\Harr`                         | $\looparrowleft$ `\looparrowleft`             | $\swarrow$ `\swarrow`                     |
| $\hArr$ `\hArr`                         | $\looparrowright$ `\looparrowright`           | $\to$ `\to`                               |
| $\harr$ `\harr`                         | $\Lrarr$ `\Lrarr`                             | $\twoheadleftarrow$ `\twoheadleftarrow`   |
| $\hookleftarrow$ `\hookleftarrow`       | $\lrArr$ `\lrArr`                             | $\twoheadrightarrow$ `\twoheadrightarrow` |
| $\hookrightarrow$ `\hookrightarrow`     | $\lrarr$ `\lrarr`                             | $\Uarr$ `\Uarr`                           |
| $\iff$ `\iff`                           | $\Lsh$ `\Lsh`                                 | $\uArr$ `\uArr`                           |
| $\impliedby$ `\impliedby`               | $\mapsto$ `\mapsto`                           | $\uarr$ `\uarr`                           |
| $\implies$ `\implies`                   | $\nearrow$ `\nearrow`                         | $\uparrow$ `\uparrow`                     |
| $\Larr$ `\Larr`                         | $\nleftarrow$ `\nleftarrow`                   | $\Uparrow$ `\Uparrow`                     |
| $\lArr$ `\lArr`                         | $\nLeftarrow$ `\nLeftarrow`                   | $\updownarrow$ `\updownarrow`             |
| $\larr$ `\larr`                         | $\nleftrightarrow$ `\nleftrightarrow`         | $\Updownarrow$ `\Updownarrow`             |
| $\leadsto$ `\leadsto`                   | $\nLeftrightarrow$ `\nLeftrightarrow`         | $\upharpoonleft$ `\upharpoonleft`         |
| $\leftarrow$ `\leftarrow`               | $\nrightarrow$ `\nrightarrow`                 | $\upharpoonright$ `\upharpoonright`       |
| $\Leftarrow$ `\Leftarrow`               | $\nRightarrow$ `\nRightarrow`                 | $\upuparrows$ `\upuparrows`               |
| $\leftarrowtail$ `\leftarrowtail`       | $\nwarrow$ `\nwarrow`                         |
| $\leftharpoondown$ `\leftharpoondown`   | $\Rarr$ `\Rarr`                               |

Direct Input: $← ↑ → ↓ ↔ ↕ ↖ ↗ ↘ ↙ ↚ ↛ ↞ ↠ ↢ ↣ ↦ ↩ ↪ ↫ ↬ ↭ ↮ ↰ ↱↶ ↷ ↺ ↻ ↼ ↽ ↾ ↾ ↿ ⇀ ⇁ ⇂ ⇃ ⇄ ⇆ ⇇ ⇈ ⇉ ⇊ ⇋ ⇌⇍ ⇎ ⇏ ⇐ ⇑ ⇒ ⇓ ⇔ ⇕ ⇚ ⇛ ⇝ ⇠ ⇢ ⟵ ⟶ ⟷ ⟸ ⟹ ⟺ ⟼$ ↽

**Extensible Arrows**

|                                                       |                                                         |
| :---------------------------------------------------- | :------------------------------------------------------ |
| $\xleftarrow{abc}$ `\xleftarrow{abc}`                 | $\xrightarrow[under]{over}$ `\xrightarrow[under]{over}` |
| $\xLeftarrow{abc}$ `\xLeftarrow{abc}`                 | $\xRightarrow{abc}$ `\xRightarrow{abc}`                 |
| $\xleftrightarrow{abc}$ `\xleftrightarrow{abc}`       | $\xLeftrightarrow{abc}$ `\xLeftrightarrow{abc}`         |
| $\xhookleftarrow{abc}$ `\xhookleftarrow{abc}`         | $\xhookrightarrow{abc}$ `\xhookrightarrow{abc}`         |
| $\xtwoheadleftarrow{abc}$ `\xtwoheadleftarrow{abc}`   | $\xtwoheadrightarrow{abc}$ `\xtwoheadrightarrow{abc}`   |
| $\xleftharpoonup{abc}$ `\xleftharpoonup{abc}`         | $\xrightharpoonup{abc}$ `\xrightharpoonup{abc}`         |
| $\xleftharpoondown{abc}$ `\xleftharpoondown{abc}`     | $\xrightharpoondown{abc}$ `\xrightharpoondown{abc}`     |
| $\xleftrightharpoons{abc}$ `\xleftrightharpoons{abc}` | $\xrightleftharpoons{abc}$ `\xrightleftharpoons{abc}`   |
| $\xtofrom{abc}$ `\xtofrom{abc}`                       | $\xmapsto{abc}$ `\xmapsto{abc}`                         |

|$\xlongequal{abc}$ `\xlongequal{abc}`

Extensible arrows all can take an optional argument in the same manner, as `\xrightarrow[under]{over}`.

## 11: Style, Color, Size, and Font

**Class Assignment**

-   `\mathbin` `\mathclose` `\mathinner` `\mathop`

-   `\mathopen` `\mathord` `\mathpunct` `\mathrel`

**Color**

$\color{blue} F=ma$ `\color{blue} F=ma`

Note that KaTeX `\color` acts like a switch. This aligns with LaTeX and differs from MathJax.
Other KaTeX color functions expect the content to be a function argument:

-   $\textcolor{blue}{F=ma}$ `\textcolor{blue}{F=ma}`
-   $\textcolor{#228B22}{F=ma}$ `\textcolor{#228B22}{F=ma}`
-   $\colorbox{aqua}{A}$ `\colorbox{aqua}{A}`
-   $\fcolorbox{red}{aqua}{A}$ `\fcolorbox{red}{aqua}{A}`

For color definition, KaTeX color functions will accept the standard HTML [predefined color names](https://developer.mozilla.org/en-US/docs/Web/CSS/color_value#Color_keywords). They will also accept an RGB argument in CSS hexa­decimal style. The "#" is optional before a six-digit specification.

**Font**

|                                       |                                     |                                   |
| :------------------------------------ | :---------------------------------- | :-------------------------------- |
| $\mathrm{Ab0}$ `\mathrm{Ab0}`         | $\mathbf{Ab0}$ `\mathbf{Ab0}`       | $\mathit{Ab}$ `\mathit{Ab}`       |
| $\mathnormal{Ab0}$ `\mathnormal{Ab0}` | $\textbf{Ab0}$ `\textbf{Ab0}`       | $\textit{Ab}$ `\textit{Ab}`       |
| $\textrm{Ab0}$ `\textrm{Ab0}`         | $\bf Ab0$ `\bf Ab0`                 | $\it Ab$ `\it Ab`                 |
| $\rm Ab0$ `\rm Ab0`                   | $\bold{Ab0}$ `\bold{Ab0}`           | $\Bbb{AB}$ `\Bbb{AB}`             |
| $\textnormal{Ab0}$ `\textnormal{Ab0}` | $\boldsymbol{Ab}$ `\boldsymbol{Ab}` | $\mathbb{AB}$ `\mathbb{AB}`       |
| $\text{Ab0}$ `\text{Ab0}`             | $\bm{Ab}$ `\bm{Ab}`                 | $\frak{Ab0}$ `\frak{Ab0}`         |
| $\mathsf{Ab0}$ `\mathsf{Ab0}`         | $\mathtt{Ab0}$ `\mathtt{Ab0}`       | $\mathfrak{Ab0}$ `\mathfrak{Ab0}` |
| $\textsf{Ab0}$ `\textsf{Ab0}`         | $\texttt{Ab0}$ `\texttt{Ab0}`       | $\mathcal{AB0}$ `\mathcal{AB0}`   |
| $\sf Ab0$ `\sf Ab0`                   | $\tt Ab0$ `\tt Ab0`                 | $\mathscr{AB}$ `\mathscr{AB}`     |

One can stack font family, font weight, and font shape by using the `\textXX` versions of the font functions. So `\textsf{\textbf{H}}` will produce $\textsf{\textbf{H}}$. The other versions do not stack, e.g., `\mathsf{\mathbf{H}}` will produce $\mathsf{\mathbf{H}}$.

In cases where KaTeX fonts do not have a bold glyph, `\pmb` can simulate one. For example, `\pmb{\mu}` renders as : $\pmb{\mu}$

**Size**

|                         |                                       |
| :---------------------- | :------------------------------------ |
| $\Huge AB$ `\Huge AB`   | $\normalsize AB$ `\normalsize AB`     |
| $\huge AB$ `\huge AB`   | $\small AB$ `\small AB`               |
| $\LARGE AB$ `\LARGE AB` | $\footnotesize AB$ `\footnotesize AB` |
| $\Large AB$ `\Large AB` | $\scriptsize AB$ `\scriptsize AB`     |
| $\large AB$ `\large AB` | $\tiny AB$ `\tiny AB`                 |

**Style**

|     |
| :-- |

|$\displaystyle\sum_{i=1}^n$ `\displaystyle\sum_{i=1}^n`
|$\textstyle\sum_{i=1}^n$ `\textstyle\sum_{i=1}^n`
|$\scriptstyle x$ `\scriptstyle x` &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(The size of a first sub/superscript)
|$\scriptscriptstyle x$ `\scriptscriptstyle x` (The size of subsequent sub/superscripts)
|$\lim\limits_x$ `\lim\limits_x`
|$\lim\nolimits_x$ `\lim\nolimits_x`
|$\verb!x^2!$ `\verb!x^2!`

`\text{…}` will accept nested `$…$` fragments and render them in math mode.

## 12: Symbols and Punctuation

|                                                         |                                               |                                                 |
| :------------------------------------------------------ | :-------------------------------------------- | :---------------------------------------------- |
| `% comment`                                             | $\dots$ `\dots`                               | $\KaTeX$ `\KaTeX`                               |
| $\%$ `\%`                                               | $\cdots$ `\cdots`                             | $\LaTeX$ `\LaTeX`                               |
| $\#$ `\#`                                               | $\ddots$ `\ddots`                             | $\TeX$ `\TeX`                                   |
| $\&$ `\&`                                               | $\ldots$ `\ldots`                             | $\nabla$ `\nabla`                               |
| $\_$ `\_`                                               | $\vdots$ `\vdots`                             | $\infty$ `\infty`                               |
| $\text{\textunderscore}$ `\text{\textunderscore}`       | $\dotsb$ `\dotsb`                             | $\infin$ `\infin`                               |
| $\text{--}$ `\text{--}`                                 | $\dotsc$ `\dotsc`                             | $\checkmark$ `\checkmark`                       |
| $\text{\textendash}$ `\text{\textendash}`               | $\dotsi$ `\dotsi`                             | $\dag$ `\dag`                                   |
| $\text{---}$ `\text{---}`                               | $\dotsm$ `\dotsm`                             | $\dagger$ `\dagger`                             |
| $\text{\textemdash}$ `\text{\textemdash}`               | $\dotso$ `\dotso`                             | $\text{\textdagger}$ `\text{\textdagger}`       |
| $\text{\textasciitilde}$ `\text{\textasciitilde}`       | $\sdot$ `\sdot`                               | $\ddag$ `\ddag`                                 |
| $`$ <code>`</code>                                      | $\mathellipsis$ `\mathellipsis`               | $\ddagger$ `\ddagger`                           |
| $\text{\textquoteleft}$ `text{\textquoteleft}`          | $\text{\textellipsis}$ `\text{\textellipsis}` | $\text{\textdaggerdbl}$ `\text{\textdaggerdbl}` |
| $\lq$ `\lq`                                             | $\Box$ `\Box`                                 | $\Dagger$ `\Dagger`                             |
| $\text{\textquoteright}$ `\text{\textquoteright}`       | $\square$ `\square`                           | $\angle$ `\angle`                               |
| $\rq$ `\rq`                                             | $\blacksquare$ `\blacksquare`                 | $\measuredangle$ `\measuredangle`               |
| $\text{\textquotedblleft}$ `\text{\textquotedblleft}`   | $\triangle$ `\triangle`                       | $\sphericalangle$ `\sphericalangle`             |
| $"$ `"`                                                 | $\triangledown$ `\triangledown`               | $\top$ `\top`                                   |
| $\text{\textquotedblright}$ `\text{\textquotedblright}` | $\triangleleft$ `\triangleleft`               | $\bot$ `\bot`                                   |
| $\colon$ `\colon`                                       | $\triangleright$ `\triangleright`             | $\$$ `\$`                                       |
| $\backprime$ `\backprime`                               | $\bigtriangledown$ `\bigtriangledown`         | $\text{\textdollar}$ `\text{\textdollar}`       |
| $\prime$ `\prime`                                       | $\bigtriangleup$ `\bigtriangleup`             | $\pounds$ `\pounds`                             |
| $\text{\textless}$ `\text{\textless}`                   | $\blacktriangle$ `\blacktriangle`             | $\mathsterling$ `\mathsterling`                 |
| $\text{\textgreater}$ `\text{\textgreater}`             | $\blacktriangledown$ `\blacktriangledown`     | $\text{\textsterling}$ `\text{\textsterling}`   |
| $\text{\textbar}$ `\text{\textbar}`                     | $\blacktriangleleft$ `\blacktriangleleft`     | $\yen$ `\yen`                                   |
| $\text{\textbardbl}$ `\text{\textbardbl}`               | $\blacktriangleright$ `\blacktriangleright`   | $\surd$ `\surd`                                 |
| $\text{\textbraceleft}$ `\text{\textbraceleft}`         | $\diamond$ `\diamond`                         | $\degree$ `\degree`                             |
| $\text{\textbraceright}$ `\text{\textbraceright}`       | $\Diamond$ `\Diamond`                         | $\text{\textdegree}$ `\text{\textdegree}`       |
| $\text{\P}$ `\text{\P}`                                 | $\lozenge$ `\lozenge`                         | $\mho$ `\mho`                                   |
| $\text{\S}$ `\text{\S}`                                 | $\blacklozenge$ `\blacklozenge`               | $\diagdown$ `\diagdown`                         |
| $\text{\sect}$ `\text{\sect}`                           | $\star$ `\star`                               | $\diagup$ `\diagup`                             |
| $\copyright$ `\copyright`                               | $\bigstar$ `\bigstar`                         | $\flat$ `\flat`                                 |
| $\circledR$ `\circledR`                                 | $\clubsuit$ `\clubsuit`                       | $\natural$ `\natural`                           |
| $\text{\textregistered}$ `\text{\textregistered}`       | $\clubs$ `\clubs`                             | $\sharp$ `\sharp`                               |
| $\circledS$ `\circledS`                                 | $\diamondsuit$ `\diamondsuit`                 | $\heartsuit$ `\heartsuit`                       |
| $\text{\textcircled a}$ `\text{\textcircled a}`         | $\diamonds$ `\diamonds`                       | $\hearts$ `\hearts`                             |
| $\maltese$ `\maltese`                                   | $\spadesuit$ `\spadesuit`                     | $\spades$ `\spades`                             |

Direct Input: $£ ¥ ∇ ∞ · ∠ ∡ ∢ ♠ ♡ ♢ ♣ ♭ ♮ ♯ ✓ …  ⋮  ⋯  ⋱  !$ ‼

## 13: Units

In KaTeX, units are proportioned as they are in TeX. KaTeX units are different than CSS units.

| KaTeX Unit | Value                | KaTeX Unit | Value               |
| :--------- | :------------------- | :--------- | :------------------ |
| em         | CSS em               | bp         | 1/72​ inch × F × G  |
| ex         | CSS ex               | pc         | 12 KaTeX pt         |
| mu         | 1/18 CSS em          | dd         | 1238/1157​ KaTeX pt |
| pt         | 1/72.27 inch × F × G | cc         | 14856/1157 KaTeX pt |
| mm         | 1 mm × F × G         | nd         | 685/642 KaTeX pt    |
| cm         | 1 cm × F × G         | nc         | 1370/107​ KaTeX pt  |
| in         | 1 inch × F × G       | sp         | 1/65536 KaTeX pt    |

where:

-   F = (font size of surrounding HTML text)/(10 pt)

-   G = 1.21 by default, because KaTeX font-size is normally 1.21 × the surrounding font size. This value can be overridden by the CSS of an HTML page.

The effect of style and size:

|   Unit   |      textstyle      |             scriptscript              |           huge           |
| :------: | :-----------------: | :-----------------------------------: | :----------------------: |
| em or ex |  $\rule{1em}{1em}$  |  $\scriptscriptstyle\rule{1em}{1em}$  |  $\huge\rule{1em}{1em}$  |
|    mu    | $\rule{18mu}{18mu}$ | $\scriptscriptstyle\rule{18mu}{18mu}$ | $\huge\rule{18mu}{18mu}$ |
|  others  | $\rule{10pt}{10pt}$ | $\scriptscriptstyle\rule{10pt}{10pt}$ | $\huge\rule{10pt}{10pt}$ |
