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## [0.13.23](https://github.com/KaTeX/KaTeX/compare/v0.13.22...v0.13.23) (2021-10-30) ### Bug Fixes * **fonts:** correct width of \cong glyph, fix \boldsymbol{\cong} ([#3206](https://github.com/KaTeX/KaTeX/issues/3206)) ([35db4ff](35db4ff403)), closes [#2199](https://github.com/KaTeX/KaTeX/issues/2199)
717 lines
44 KiB
Markdown
717 lines
44 KiB
Markdown
---
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id: supported
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title: Supported Functions
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---
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This is a list of TeX functions supported by KaTeX. It is sorted into logical groups.
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There is a similar [Support Table](support_table.md), sorted alphabetically, that lists both supported and un-supported functions.
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<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.13.23/dist/katex.min.css" integrity="sha384-z91AFMXXGZasvxZz5DtKJse3pKoTPU0QcNFj/B4gDFRmq6Q2bi1StsT7SOcIzLEN" crossorigin="anonymous">
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<style>
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p {overflow-wrap: break-word;}
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table tr,
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table td {
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vertical-align: middle;
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overflow-wrap: break-word;
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}
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</style>
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<div class="katex-hopscotch">
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## Accents
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|:----------------------------|:----------------------------------------------------|:------
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|$a'$ `a'` |$\tilde{a}$ `\tilde{a}`|$\mathring{g}$ `\mathring{g}`
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|$a''$ `a''`|$\widetilde{ac}$ `\widetilde{ac}` |$\overgroup{AB}$ `\overgroup{AB}`
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|$a^{\prime}$ `a^{\prime}` |$\utilde{AB}$ `\utilde{AB}` |$\undergroup{AB}$ `\undergroup{AB}`
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|$\acute{a}$ `\acute{a}`|$\vec{F}$ `\vec{F}` |$\Overrightarrow{AB}$ `\Overrightarrow{AB}`
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|$\bar{y}$ `\bar{y}` |$\overleftarrow{AB}$ `\overleftarrow{AB}`|$\overrightarrow{AB}$ `\overrightarrow{AB}`
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|$\breve{a}$ `\breve{a}`|$\underleftarrow{AB}$ `\underleftarrow{AB}` |$\underrightarrow{AB}$ `\underrightarrow{AB}`
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|$\check{a}$ `\check{a}`|$\overleftharpoon{ac}$ `\overleftharpoon{ac}` |$\overrightharpoon{ac}$ `\overrightharpoon{ac}`
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|$\dot{a}$ `\dot{a}` |$\overleftrightarrow{AB}$ `\overleftrightarrow{AB}` |$\overbrace{AB}$ `\overbrace{AB}`
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|$\ddot{a}$ `\ddot{a}` |$\underleftrightarrow{AB}$ `\underleftrightarrow{AB}`|$\underbrace{AB}$ `\underbrace{AB}`
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|$\grave{a}$ `\grave{a}`|$\overline{AB}$ `\overline{AB}` |$\overlinesegment{AB}$ `\overlinesegment{AB}`
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|$\hat{\theta}$ `\hat{\theta}`|$\underline{AB}$ `\underline{AB}` |$\underlinesegment{AB}$ `\underlinesegment{AB}`
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|$\widehat{ac}$ `\widehat{ac}`|$\widecheck{ac}$ `\widecheck{ac}` |$\underbar{X}$ `\underbar{X}`
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***Accent functions inside \\text{…}***
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|||||
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|:---------------------|:---------------------|:---------------------|:-----
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|$\text{\'{a}}$ `\'{a}`|$\text{\~{a}}$ `\~{a}`|$\text{\.{a}}$ `\.{a}`|$\text{\H{a}}$ `\H{a}`
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|$\text{\`{a}}$ <code>\\`{a}</code>|$\text{\={a}}$ `\={a}`|$\text{\"{a}}$ `\"{a}`|$\text{\v{a}}$ `\v{a}`
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|$\text{\^{a}}$ `\^{a}`|$\text{\u{a}}$ `\u{a}`|$\text{\r{a}}$ `\r{a}`|
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See also [letters and unicode](#letters-and-unicode).
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## Delimiters
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|:-----------------------------------|:---------------------------------------|:----------|:-------------------------------------------------------|:-----
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|$(~)$ `( )` |$\lparen~\rparen$ `\lparen`<br>$~~~~$`\rparen`|$⌈~⌉$ `⌈ ⌉`|$\lceil~\rceil$ `\lceil`<br>$~~~~~$`\rceil` |$\uparrow$ `\uparrow`
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|$[~]$ `[ ]` |$\lbrack~\rbrack$ `\lbrack`<br>$~~~~$`\rbrack`|$⌊~⌋$ `⌊ ⌋`|$\lfloor~\rfloor$ `\lfloor`<br>$~~~~~$`\rfloor` |$\downarrow$ `\downarrow`
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|$\{ \}$ `\{ \}`|$\lbrace \rbrace$ `\lbrace`<br>$~~~~$`\rbrace`|$⎰⎱$ `⎰⎱` |$\lmoustache \rmoustache$ `\lmoustache`<br>$~~~~$`\rmoustache`|$\updownarrow$ `\updownarrow`
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|$⟨~⟩$ `⟨ ⟩` |$\langle~\rangle$ `\langle`<br>$~~~~$`\rangle`|$⟮~⟯$ `⟮ ⟯`|$\lgroup~\rgroup$ `\lgroup`<br>$~~~~~$`\rgroup` |$\Uparrow$ `\Uparrow`
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|$\vert$ <code>|</code> |$\vert$ `\vert` |$┌ ┐$ `┌ ┐`|$\ulcorner \urcorner$ `\ulcorner`<br>$~~~~$`\urcorner` |$\Downarrow$ `\Downarrow`
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|$\Vert$ <code>\|</code> |$\Vert$ `\Vert` |$└ ┘$ `└ ┘`|$\llcorner \lrcorner$ `\llcorner`<br>$~~~~$`\lrcorner` |$\Updownarrow$ `\Updownarrow`
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|$\lvert~\rvert$ `\lvert`<br>$~~~~$`\rvert`|$\lVert~\rVert$ `\lVert`<br>$~~~~~$`\rVert` |`\left.`| `\right.` |$\backslash$ `\backslash`
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|$\lang~\rang$ `\lang`<br>$~~~~$`\rang`|$\lt~\gt$ `\lt \gt`|$⟦~⟧$ `⟦ ⟧`|$\llbracket~\rrbracket$ `\llbracket`<br>$~~~~$`\rrbracket`|$\lBrace~\rBrace$ `\lBrace \rBrace`
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**Delimiter Sizing**
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$\left(\LARGE{AB}\right)$ `\left(\LARGE{AB}\right)`
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$( \big( \Big( \bigg( \Bigg($ `( \big( \Big( \bigg( \Bigg(`
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|:--------|:------|:--------|:-------|:------|
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|`\left` |`\big` |`\bigl` |`\bigm` |`\bigr`
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|`\middle`|`\Big` |`\Bigl` |`\Bigm` | `\Bigr`
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|`\right` |`\bigg`|`\biggl` |`\biggm`|`\biggr`
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| |`\Bigg`|`\Biggl` |`\Biggm`|`\Biggr`
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</div>
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## Environments
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<div class="katex-cards" id="environments">
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|||||
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|:---------------------|:---------------------|:---------------------|:--------
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|$\begin{matrix} a & b \\ c & d \end{matrix}$ | `\begin{matrix}`<br> `a & b \\`<br> `c & d`<br>`\end{matrix}` |$\begin{array}{cc}a & b\\c & d\end{array}$ | `\begin{array}{cc}`<br> `a & b \\`<br> `c & d`<br>`\end{array}`
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|$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ |`\begin{pmatrix}`<br> `a & b \\`<br> `c & d`<br>`\end{pmatrix}` |$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ | `\begin{bmatrix}`<br> `a & b \\`<br> `c & d`<br>`\end{bmatrix}`
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|$\begin{vmatrix} a & b \\ c & d \end{vmatrix}$ |`\begin{vmatrix}`<br> `a & b \\`<br> `c & d`<br>`\end{vmatrix}` |$\begin{Vmatrix} a & b \\ c & d \end{Vmatrix}$ |`\begin{Vmatrix}`<br> `a & b \\`<br> `c & d`<br>`\end{Vmatrix}`
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|$\begin{Bmatrix} a & b \\ c & d \end{Bmatrix}$ |`\begin{Bmatrix}`<br> `a & b \\`<br> `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> `\begin{array}{c:c:c}`<br> `a & b & c \\ \hline`<br> `d & e & f \\`<br> `\hdashline`<br> `g & h & i`<br>`\end{array}`
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|$x = \begin{cases} a &\text{if } b \\ c &\text{if } d \end{cases}$ |`x = \begin{cases}`<br> `a &\text{if } b \\`<br> `c &\text{if } d`<br>`\end{cases}`|$\begin{rcases} a &\text{if } b \\ c &\text{if } d \end{rcases}⇒…$ |`\begin{rcases}`<br> `a &\text{if } b \\`<br> `c &\text{if } d`<br>`\end{rcases}⇒…`|
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|$\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}$ | `\begin{smallmatrix}`<br> `a & b \\`<br> `c & d`<br>`\end{smallmatrix}` |$$\sum_{\begin{subarray}{l} i\in\Lambda\\ 0<j<n\end{subarray}}$$ | `\sum_{`<br>`\begin{subarray}{l}`<br> `i\in\Lambda\\`<br> `0<j<n`<br>`\end{subarray}}`|
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The auto-render extension will render the following environments even if they are not inside math delimiters such as `$$…$$`. They are display-mode only.
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<style>
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#env + table tr td:nth-child(1) { min-width: 11em }
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#env + table tr td:nth-child(3) { min-width: 13em }
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</style>
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<div id="env"></div>
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|||||
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|:---------------------|:---------------------|:---------------------|:--------
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|$$\begin{equation}\begin{split}a &=b+c\\&=e+f\end{split}\end{equation}$$ |`\begin{equation}`<br>`\begin{split}` `a &=b+c\\`<br> `&=e+f`<br>`\end{split}`<br>`\end{equation}` |$$\begin{align} a&=b+c \\ d+e&=f \end{align}$$ |`\begin{align}`<br> `a&=b+c \\`<br> `d+e&=f`<br>`\end{align}` |
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|$$\begin{gather} a=b \\ e=b+c \end{gather}$$ |`\begin{gather}`<br> `a=b \\ `<br> `e=b+c`<br>`\end{gather}`|$$\begin{alignat}{2}10&x+&3&y=2\\3&x+&13&y=4\end{alignat}$$ | `\begin{alignat}{2}`<br> `10&x+&3&y=2\\`<br> `3&x+&13&y=4`<br>`\end{alignat}`
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|$$\begin{CD}A @>a>> B \\@VbVV @AAcA\\C @= D\end{CD}$$ | `\begin{CD}`<br> `A @>a>> B \\`<br>`@VbVV @AAcA \\`<br> `C @= D`<br>`\end{CD}`
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#### Other KaTeX Environments
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| Environments | How they differ from those shown above |
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|:-----------------------------------------------|:------------------|
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| `darray`, `dcases`, `drcases` | … apply `displaystyle` |
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| `matrix*`, `pmatrix*`, `bmatrix*`<br>`Bmatrix*`, `vmatrix*`, `Vmatrix*` | … take an optional argument to set column<br>alignment, as in `\begin{matrix*}[r]`
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| `equation*`, `gather*`<br>`align*`, `alignat*` | … have no automatic numbering. |
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| `gathered`, `aligned`, `alignedat` | … do not need to be in display mode.<br> … have no automatic numbering.<br> … must be inside math delimiters in<br>order to be rendered by the auto-render<br>extension. |
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</div>
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Acceptable line separators include: `\\`, `\cr`, `\\[distance]`, and `\cr[distance]`. *Distance* can be written with any of the [KaTeX units](#units).
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The `{array}` environment supports `|` and `:` vertical separators.
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The `{array}` environment does not yet support `\cline` or `\multicolumn`.
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`\tag` can not yet be applied to individual environment rows.
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<div class="katex-hopscotch">
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## HTML
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The following "raw HTML" features are potentially dangerous for untrusted
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inputs, so they are disabled by default, and attempting to use them produces
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the command names in red (which you can configure via the `errorColor`
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[option](options.md)). To fully trust your LaTeX input, you need to pass
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an option of `trust: true`; you can also enable just some of the commands
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or for just some URLs via the `trust` [option](options.md).
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|||
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|:----------------|:-------------------|
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| $\href{https://katex.org/}{\KaTeX}$ | `\href{https://katex.org/}{\KaTeX}` |
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| $\url{https://katex.org/}$ | `\url{https://katex.org/}` |
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| $\includegraphics[height=0.8em, totalheight=0.9em, width=0.9em, alt=KA logo]{https://katex.org/img/khan-academy.png}$ | `\includegraphics[height=0.8em, totalheight=0.9em, width=0.9em, alt=KA logo]{https://katex.org/img/khan-academy.png}` |
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| $\htmlId{bar}{x}$ <code>…<span id="bar" class="enclosing">…x…</span>…</code> | `\htmlId{bar}{x}` |
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| $\htmlClass{foo}{x}$ <code>…<span class="enclosing foo">…x…</span>…</code> | `\htmlClass{foo}{x}` |
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| $\htmlStyle{color: red;}{x}$ <code>…<span style="color: red;" class="enclosing">…x…</span>…</code> | `\htmlStyle{color: red;}{x}` |
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| $\htmlData{foo=a, bar=b}{x}$ <code>…<span data-foo="a" data-bar="b" class="enclosing">…x…</span>…</code> | `\htmlData{foo=a, bar=b}{x}` |
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`\includegraphics` supports `height`, `width`, `totalheight`, and `alt` in its first argument. `height` is required.
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HTML extension (`\html`-prefixed) commands are non-standard, so loosening `strict` option for `htmlExtension` is required.
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## Letters and Unicode
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**Greek Letters**
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Direct Input: $Α Β Γ Δ Ε Ζ Η Θ Ι \allowbreak Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω$
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$\allowbreak α β γ δ ϵ ζ η θ ι κ λ μ ν ξ o π \allowbreak ρ σ τ υ ϕ χ ψ ω ε ϑ ϖ ϱ ς φ ϝ$
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|---------------|-------------|-------------|---------------|
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| $\Alpha$ `\Alpha` | $\Beta$ `\Beta` | $\Gamma$ `\Gamma`| $\Delta$ `\Delta`
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| $\Epsilon$ `\Epsilon` | $\Zeta$ `\Zeta` | $\Eta$ `\Eta` | $\Theta$ `\Theta`
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| $\Iota$ `\Iota` | $\Kappa$ `\Kappa` | $\Lambda$ `\Lambda` | $\Mu$ `\Mu`
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| $\Nu$ `\Nu` | $\Xi$ `\Xi` | $\Omicron$ `\Omicron` | $\Pi$ `\Pi`
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| $\Rho$ `\Rho` | $\Sigma$ `\Sigma` | $\Tau$ `\Tau` | $\Upsilon$ `\Upsilon`
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| $\Phi$ `\Phi` | $\Chi$ `\Chi` | $\Psi$ `\Psi` | $\Omega$ `\Omega`
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| $\varGamma$ `\varGamma`| $\varDelta$ `\varDelta` | $\varTheta$ `\varTheta` | $\varLambda$ `\varLambda` |
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| $\varXi$ `\varXi`| $\varPi$ `\varPi` | $\varSigma$ `\varSigma` | $\varUpsilon$ `\varUpsilon` |
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| $\varPhi$ `\varPhi` | $\varPsi$ `\varPsi`| $\varOmega$ `\varOmega` ||
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| $\alpha$ `\alpha`| $\beta$ `\beta` | $\gamma$ `\gamma` | $\delta$ `\delta`|
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| $\epsilon$ `\epsilon` | $\zeta$ `\zeta` | $\eta$ `\eta`| $\theta$ `\theta`|
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| $\iota$ `\iota` | $\kappa$ `\kappa` | $\lambda$ `\lambda`| $\mu$ `\mu`|
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| $\nu$ `\nu`| $\xi$ `\xi` | $\omicron$ `\omicron` | $\pi$ `\pi`|
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| $\rho$ `\rho` | $\sigma$ `\sigma` | $\tau$ `\tau`| $\upsilon$ `\upsilon` |
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| $\phi$ `\phi` | $\chi$ `\chi`| $\psi$ `\psi`| $\omega$ `\omega`|
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| $\varepsilon$ `\varepsilon` | $\varkappa$ `\varkappa` | $\vartheta$ `\vartheta` | $\thetasym$ `\thetasym`
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| $\varpi$ `\varpi`| $\varrho$ `\varrho` | $\varsigma$ `\varsigma` | $\varphi$ `\varphi`
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| $\digamma $ `\digamma`
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**Other Letters**
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|:----------|:----------|:----------|:----------|:----------|
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|$\imath$ `\imath`|$\nabla$ `\nabla`|$\Im$ `\Im`|$\Reals$ `\Reals`|$\text{\OE}$ `\text{\OE}`
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|$\jmath$ `\jmath`|$\partial$ `\partial`|$\image$ `\image`|$\wp$ `\wp`|$\text{\o}$ `\text{\o}`
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|$\aleph$ `\aleph`|$\Game$ `\Game`|$\Bbbk$ `\Bbbk`|$\weierp$ `\weierp`|$\text{\O}$ `\text{\O}`
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|$\alef$ `\alef`|$\Finv$ `\Finv`|$\N$ `\N`|$\Z$ `\Z`|$\text{\ss}$ `\text{\ss}`
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|$\alefsym$ `\alefsym`|$\cnums$ `\cnums`|$\natnums$ `\natnums`|$\text{\aa}$ `\text{\aa}`|$\text{\i}$ `\text{\i}`
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|$\beth$ `\beth`|$\Complex$ `\Complex`|$\R$ `\R`|$\text{\AA}$ `\text{\AA}`|$\text{\j}$ `\text{\j}`
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|$\gimel$ `\gimel`|$\ell$ `\ell`|$\Re$ `\Re`|$\text{\ae}$ `\text{\ae}`
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|$\daleth$ `\daleth`|$\hbar$ `\hbar`|$\real$ `\real`|$\text{\AE}$ `\text{\AE}`
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|$\eth$ `\eth`|$\hslash$ `\hslash`|$\reals$ `\reals`|$\text{\oe}$ `\text{\oe}`
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Direct Input: $∂ ∇ ℑ Ⅎ ℵ ℶ ℷ ℸ ⅁ ℏ ð − ∗$
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ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖÙÚÛÜÝÞßàáâãäåçèéêëìíîïðñòóôöùúûüýþÿ
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</div>
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<div class="katex-cards" id="math-alpha">
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**Unicode Mathematical Alphanumeric Symbols**
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| Item | Range | Item | Range |
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|-------------|---------------------|-------------------|---------------|
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| Bold | $\text{𝐀-𝐙 𝐚-𝐳 𝟎-𝟗}$ | Double-struck | $\text{𝔸-}ℤ\ 𝕜$
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| Italic | $\text{𝐴-𝑍 𝑎-𝑧}$ | Sans serif | $\text{𝖠-𝖹 𝖺-𝗓 𝟢-𝟫}$
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| Bold Italic | $\text{𝑨-𝒁 𝒂-𝒛}$ | Sans serif bold | $\text{𝗔-𝗭 𝗮-𝘇 𝟬-𝟵}$
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| Script | $\text{𝒜-𝒵}$ | Sans serif italic | $\text{𝘈-𝘡 𝘢-𝘻}$
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| Fractur | $\text{𝔄-}ℨ\text{ 𝔞-𝔷}$| Monospace | $\text{𝙰-𝚉 𝚊-𝚣 𝟶-𝟿}$
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</div>
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<div class="katex-hopscotch">
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**Unicode**
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The letters listed above will render properly in any KaTeX rendering mode.
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In addition, Armenian, Brahmic, Georgian, Chinese, Japanese, and Korean glyphs are always accepted in text mode. However, these glyphs will be rendered from system fonts (not KaTeX-supplied fonts) so their typography may clash.
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You can provide rules for CSS classes `.latin_fallback`, `.cyrillic_fallback`, `.brahmic_fallback`, `.georgian_fallback`, `.cjk_fallback`, and `.hangul_fallback` to provide fallback fonts for these languages.
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Use of these glyphs may cause small vertical alignment issues: KaTeX has detailed metrics for listed symbols and most Latin, Greek, and Cyrillic letters, but other accepted glyphs are treated as if they are each as tall as the letter M in the current KaTeX font.
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If the KaTeX rendering mode is set to `strict: false` or `strict: "warn"` (default), then KaTeX will accept all Unicode letters in both text and math mode.
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All unrecognized characters will be treated as if they appeared in text mode, and are subject to the same issues of using system fonts and possibly using incorrect vertical alignment.
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For Persian composite characters, a user-supplied [plug-in](https://github.com/HosseinAgha/persian-katex-plugin) is under development.
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Any character can be written with the `\char` function and the Unicode code in hex. For example `\char"263a` will render as $\char"263a$.
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## Layout
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### Annotation
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|||
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|:------------------------------|:-----
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|$\cancel{5}$ `\cancel{5}`|$\overbrace{a+b+c}^{\text{note}}$ `\overbrace{a+b+c}^{\text{note}}`
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|$\bcancel{5}$ `\bcancel{5}` |$\underbrace{a+b+c}_{\text{note}}$ `\underbrace{a+b+c}_{\text{note}}`
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|$\xcancel{ABC}$ `\xcancel{ABC}`|$\not =$ `\not =`
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|$\sout{abc}$ `\sout{abc}`|$\boxed{\pi=\frac c d}$ `\boxed{\pi=\frac c d}`
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|$a_{\angl n}$ `$a_{\angl n}`|$a_\angln$ `a_\angln`
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|$\phase{-78^\circ}$`\phase{-78^\circ}` |
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`\tag{hi} x+y^{2x}`
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$$\tag{hi} x+y^{2x}$$
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`\tag*{hi} x+y^{2x}`
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$$\tag*{hi} x+y^{2x}$$
|
||
|
||
### 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`.
|
||
|
||
### 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{!}{=}` | $a+\left(\vcenter{\frac{\frac a b}c}\right)$ `a+\left(\vcenter{\hbox{$\frac{\frac a b}c$}}\right)`
|
||
||| $$\sum_{\substack{0<i<m\\0<j<n}}$$ `\sum_{\substack{0<i<m\\0<j<n}}`
|
||
|
||
`\raisebox` and `\hbox` put their argument into text mode. To raise math, nest `$…$` delimiters inside the argument as shown above.
|
||
|
||
`\vcenter` can be written without an `\hbox` if the `strict` rendering option is *false*. In that case, omit the nested `$…$` delimiters.
|
||
|
||
### 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.
|
||
|
||
</div>
|
||
<div class="katex-cards" id="spacing-tbl">
|
||
|
||
**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*
|
||
| `\:` | ⁴∕₁₈ em space | `\hskip{distance}` | space, width = *distance*
|
||
| `\medspace` | ⁴∕₁₈ em space | `\hspace{distance}` | space, width = *distance*
|
||
| `\;` | ⁵∕₁₈ em space | `\hspace*{distance}` | space, width = *distance*
|
||
| `\thickspace` | ⁵∕₁₈ em space | `\phantom{content}` | space the width and height of content
|
||
| `\enspace` | ½ em space | `\hphantom{content}` | space the width of content
|
||
| `\quad` | 1 em space | `\vphantom{content}` | a strut the height of content
|
||
| `\qquad` | 2 em space | `\!` | – ³∕₁₈ em space
|
||
| `~` | non-breaking space | `\negthinspace` | – ³∕₁₈ em space
|
||
| `\<space>` | space | `\negmedspace` | – ⁴∕₁₈ em space
|
||
| `\nobreakspace` | non-breaking space | `\negthickspace` | – ⁵∕₁₈ em space
|
||
| `\space` | space | `\mathstrut` | `\vphantom{(}`
|
||
|
||
</div>
|
||
|
||
**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`.
|
||
|
||
<div class="katex-hopscotch">
|
||
|
||
## 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
|
||
|
||
## 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}`
|
||
| | `\edef\macroname#1#2…{definition to be expanded}`
|
||
| | `\xdef\macroname#1#2…{definition to be expanded}`
|
||
| | `\let\foo=\bar`
|
||
| | `\futurelet\foo\bar x`
|
||
| | `\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](options.md).
|
||
|
||
Macros accept up to nine arguments: #1, #2, etc.
|
||
|
||
</div>
|
||
|
||
<div id="gdef">
|
||
|
||
Macros defined by `\gdef`, `\xdef`, `\global\def`, `\global\edef`, `\global\let`, and `\global\futurelet` will persist between math expressions. (Exception: macro persistence may be disabled. There are legitimate security reasons for that.)
|
||
|
||
KaTeX has no `\par`, so all macros are long by default and `\long` will be ignored.
|
||
|
||
Available functions include:
|
||
|
||
`\char` `\mathchoice` `\TextOrMath` `\@ifstar` `\@ifnextchar` `\@firstoftwo` `\@secondoftwo` `\relax` `\expandafter` `\noexpand`
|
||
|
||
@ is a valid character for commands, as if `\makeatletter` were in effect.
|
||
|
||
## Operators
|
||
|
||
### 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: $∫ ∬ ∭ ∮ ∏ ∐ ∑ ⋀ ⋁ ⋂ ⋃ ⨀ ⨁ ⨂ ⨄ ⨆$ ∯ ∰
|
||
|
||
### 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: $+ - / * ⋅ ± × ÷ ∓ ∔ ∧ ∨ ∩ ∪ ≀ ⊎ ⊓ ⊔ ⊕ ⊖ ⊗ ⊘ ⊙ ⊚ ⊛ ⊝ ◯$
|
||
|
||
### 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}`
|
||
|
||
### Math Operators
|
||
|
||
|||||
|
||
|:--------------------|:--------------------|:----------------|:--------------|
|
||
| $\arcsin$ `\arcsin` | $\cosec$ `\cosec` | $\deg$ `\deg` | $\sec$ `\sec` |
|
||
| $\arccos$ `\arccos` | $\cosh$ `\cosh` | $\dim$ `\dim` | $\sin$ `\sin` |
|
||
| $\arctan$ `\arctan` | $\cot$ `\cot` | $\exp$ `\exp` | $\sinh$ `\sinh` |
|
||
| $\arctg$ `\arctg` | $\cotg$ `\cotg` | $\hom$ `\hom` | $\sh$ `\sh` |
|
||
| $\arcctg$ `\arcctg` | $\coth$ `\coth` | $\ker$ `\ker` | $\tan$ `\tan` |
|
||
| $\arg$ `\arg` | $\csc$ `\csc` | $\lg$ `\lg` | $\tanh$ `\tanh` |
|
||
| $\ch$ `\ch` | $\ctg$ `\ctg` | $\ln$ `\ln` | $\tg$ `\tg` |
|
||
| $\cos$ `\cos` | $\cth$ `\cth` | $\log$ `\log` | $\th$ `\th` |
|
||
| $\operatorname{f}$ `\operatorname{f}` | |||
|
||
| $\argmax$ `\argmax` | $\injlim$ `\injlim` | $\min$ `\min` | $\varinjlim$ `\varinjlim` |
|
||
| $\argmin$ `\argmin` | $\lim$ `\lim` | $\plim$ `\plim` | $\varliminf$ `\varliminf` |
|
||
| $\det$ `\det` | $\liminf$ `\liminf` | $\Pr$ `\Pr` | $\varlimsup$ `\varlimsup` |
|
||
| $\gcd$ `\gcd` | $\limsup$ `\limsup` | $\projlim$ `\projlim` | $\varprojlim$ `\varprojlim` |
|
||
| $\inf$ `\inf` | $\max$ `\max` | $\sup$ `\sup` ||
|
||
| $\operatorname*{f}$ `\operatorname*{f}` | $\operatornamewithlimits{f}$ `\operatornamewithlimits{f}` |||
|
||
|
||
Functions in the bottom six rows of this table can take `\limits`.
|
||
|
||
### \sqrt
|
||
|
||
$\sqrt{x}$ `\sqrt{x}`
|
||
|
||
$\sqrt[3]{x}$ `\sqrt[3]{x}`
|
||
|
||
## Relations
|
||
|
||
$\stackrel{!}{=}$ `\stackrel{!}{=}`
|
||
|
||
|||||
|
||
|:--------|:------------------------|:----------------------------|:------------------|
|
||
| $=$ `=` | $\doteqdot$ `\doteqdot` | $\lessapprox$ `\lessapprox` | $\smile$ `\smile` |
|
||
| $<$ `<` | $\eqcirc$ `\eqcirc` | $\lesseqgtr$ `\lesseqgtr` | $\sqsubset$ `\sqsubset` |
|
||
| $>$ `>` | $\eqcolon$ `\eqcolon` or<br> `\minuscolon` | $\lesseqqgtr$ `\lesseqqgtr` | $\sqsubseteq$ `\sqsubseteq` |
|
||
| $:$ `:` | $\Eqcolon$ `\Eqcolon` or<br> `\minuscoloncolon` | $\lessgtr$ `\lessgtr` | $\sqsupset$ `\sqsupset` |
|
||
| $\approx$ `\approx` | $\eqqcolon$ `\eqqcolon` or<br> `\equalscolon` | $\lesssim$ `\lesssim` | $\sqsupseteq$ `\sqsupseteq` |
|
||
| $\approxcolon$ `\approxcolon` | $\Eqqcolon$ `\Eqqcolon` or<br> `\equalscoloncolon` | $\ll$ `\ll` | $\Subset$ `\Subset` |
|
||
| $\approxcoloncolon$ `\approxcoloncolon` | $\eqsim$ `\eqsim` | $\lll$ `\lll` | $\subset$ `\subset` or `\sub` |
|
||
| $\approxeq$ `\approxeq` | $\eqslantgtr$ `\eqslantgtr` | $\llless$ `\llless` | $\subseteq$ `\subseteq` or `\sube` |
|
||
| $\asymp$ `\asymp` | $\eqslantless$ `\eqslantless` | $\lt$ `\lt` | $\subseteqq$ `\subseteqq` |
|
||
| $\backepsilon$ `\backepsilon` | $\equiv$ `\equiv` | $\mid$ `\mid` | $\succ$ `\succ` |
|
||
| $\backsim$ `\backsim` | $\fallingdotseq$ `\fallingdotseq` | $\models$ `\models` | $\succapprox$ `\succapprox` |
|
||
| $\backsimeq$ `\backsimeq` | $\frown$ `\frown` | $\multimap$ `\multimap` | $\succcurlyeq$ `\succcurlyeq` |
|
||
| $\between$ `\between` | $\ge$ `\ge` | $\origof$ `\origof` | $\succeq$ `\succeq` |
|
||
| $\bowtie$ `\bowtie` | $\geq$ `\geq` | $\owns$ `\owns` | $\succsim$ `\succsim` |
|
||
| $\bumpeq$ `\bumpeq` | $\geqq$ `\geqq` | $\parallel$ `\parallel` | $\Supset$ `\Supset` |
|
||
| $\Bumpeq$ `\Bumpeq` | $\geqslant$ `\geqslant` | $\perp$ `\perp` | $\supset$ `\supset` |
|
||
| $\circeq$ `\circeq` | $\gg$ `\gg` | $\pitchfork$ `\pitchfork` | $\supseteq$ `\supseteq` or `\supe` |
|
||
| $\colonapprox$ `\colonapprox` | $\ggg$ `\ggg` | $\prec$ `\prec` | $\supseteqq$ `\supseteqq` |
|
||
| $\Colonapprox$ `\Colonapprox` or<br> `\coloncolonapprox` | $\gggtr$ `\gggtr` | $\precapprox$ `\precapprox` | $\thickapprox$ `\thickapprox` |
|
||
| $\coloneq$ `\coloneq` or<br> `\colonminus` | $\gt$ `\gt` | $\preccurlyeq$ `\preccurlyeq` | $\thicksim$ `\thicksim` |
|
||
| $\Coloneq$ `\Coloneq` or<br> `\coloncolonminus` | $\gtrapprox$ `\gtrapprox` | $\preceq$ `\preceq` | $\trianglelefteq$ `\trianglelefteq` |
|
||
| $\coloneqq$ `\coloneqq` or<br> `\colonequals` | $\gtreqless$ `\gtreqless` | $\precsim$ `\precsim` | $\triangleq$ `\triangleq` |
|
||
| $\Coloneqq$ `\Coloneqq` or<br> `\coloncolonequals` | $\gtreqqless$ `\gtreqqless` | $\propto$ `\propto` | $\trianglerighteq$ `\trianglerighteq` |
|
||
| $\colonsim$ `\colonsim` | $\gtrless$ `\gtrless` | $\risingdotseq$ `\risingdotseq` | $\varpropto$ `\varpropto` |
|
||
| $\Colonsim$ `\Colonsim` or<br> `\coloncolonsim` | $\gtrsim$ `\gtrsim` | $\shortmid$ `\shortmid` | $\vartriangle$ `\vartriangle` |
|
||
| $\cong$ `\cong` | $\imageof$ `\imageof` | $\shortparallel$ `\shortparallel` | $\vartriangleleft$ `\vartriangleleft` |
|
||
| $\curlyeqprec$ `\curlyeqprec` | $\in$ `\in` or `\isin` | $\sim$ `\sim` | $\vartriangleright$ `\vartriangleright` |
|
||
| $\curlyeqsucc$ `\curlyeqsucc` | $\Join$ `\Join` | $\simcolon$ `\simcolon` | $\vcentcolon$ `\vcentcolon` or<br> `\ratio` |
|
||
| $\dashv$ `\dashv` | $\le$ `\le` | $\simcoloncolon$ `\simcoloncolon` | $\vdash$ `\vdash` |
|
||
| $\dblcolon$ `\dblcolon` or<br> `\coloncolon` | $\leq$ `\leq` | $\simeq$ `\simeq` | $\vDash$ `\vDash` |
|
||
| $\doteq$ `\doteq` | $\leqq$ `\leqq` | $\smallfrown$ `\smallfrown` | $\Vdash$ `\Vdash` |
|
||
| $\Doteq$ `\Doteq` | $\leqslant$ `\leqslant` | $\smallsmile$ `\smallsmile` | $\Vvdash$ `\Vvdash` |
|
||
|
||
Direct Input: $= < > : ∈ ∋ ∝ ∼ ∽ ≂ ≃ ≅ ≈ ≊ ≍ ≎ ≏ ≐ ≑ ≒ ≓ ≖ ≗ ≜ ≡ ≤ ≥ ≦ ≧ ≫ ≬ ≳ ≷ ≺ ≻ ≼ ≽ ≾ ≿ ⊂ ⊃ ⊆ ⊇ ⊏ ⊐ ⊑ ⊒ ⊢ ⊣ ⊩ ⊪ ⊸ ⋈ ⋍ ⋐ ⋑ ⋔ ⋙ ⋛ ⋞ ⋟ ⌢ ⌣ ⩾ ⪆ ⪌ ⪕ ⪖ ⪯ ⪰ ⪷ ⪸ ⫅ ⫆ ≲ ⩽ ⪅ ≶ ⋚ ⪋ ⟂ ⊨ ⊶ ⊷$ `≔ ≕ ⩴`
|
||
|
||
### 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: $∉ ∌ ∤ ∦ ≁ ≆ ≠ ≨ ≩ ≮ ≯ ≰ ≱ ⊀ ⊁ ⊈ ⊉ ⊊ ⊋ ⊬ ⊭ ⊮ ⊯ ⋠ ⋡ ⋦ ⋧ ⋨ ⋩ ⋬ ⋭ ⪇ ⪈ ⪉ ⪊ ⪵ ⪶ ⪹ ⪺ ⫋ ⫌$
|
||
|
||
### 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<br>as `\xrightarrow[under]{over}`.
|
||
|
||
## Special Notation
|
||
|
||
**Bra-ket Notation**
|
||
|
||
||||
|
||
|:----------|:----------|:----------|
|
||
|$\bra{\phi}$ `\bra{\phi}` |$\ket{\psi}$ `\ket{\psi}` |$\braket{\phi\vert\psi}$ `\braket{\phi\vert\psi}` |
|
||
|$\Bra{\phi}$ `\Bra{\phi}` |$\Ket{\psi}$ `\Ket{\psi}` ||
|
||
|
||
## Style, Color, Size, and Font
|
||
|
||
**Class Assignment**
|
||
|
||
`\mathbin` `\mathclose` `\mathinner` `\mathop`<br>
|
||
`\mathopen` `\mathord` `\mathpunct` `\mathrel`
|
||
|
||
**Color**
|
||
|
||
$\color{blue} F=ma$ `\color{blue} F=ma`
|
||
|
||
Note that `\color` acts like a switch. Other color functions expect the content to be a function argument:
|
||
|
||
$\textcolor{blue}{F=ma}$ `\textcolor{blue}{F=ma}`<br>
|
||
$\textcolor{#228B22}{F=ma}$ `\textcolor{#228B22}{F=ma}`<br>
|
||
$\colorbox{aqua}{$F=ma$}$ `\colorbox{aqua}{$F=ma$}`<br>
|
||
$\fcolorbox{red}{aqua}{$F=ma$}$ `\fcolorbox{red}{aqua}{$F=ma$}`
|
||
|
||
Note that, as in LaTeX, `\colorbox` & `\fcolorbox` renders its third argument as text, so you may want to switch back to math mode with `$` as in the examples above.
|
||
|
||
For color definition, KaTeX color functions will accept the standard HTML [predefined color names](https://developer.mozilla.org/en-US/docs/Web/CSS/color_value#Color_keywords). They will also accept an RGB argument in CSS hexadecimal style. The "#" is optional before a six-digit specification.
|
||
|
||
**Font**
|
||
|
||
||||
|
||
|:------------------------------|:------------------------------|:-----
|
||
|$\mathrm{Ab0}$ `\mathrm{Ab0}` |$\mathbf{Ab0}$ `\mathbf{Ab0}` |$\mathit{Ab0}$ `\mathit{Ab0}`
|
||
|$\mathnormal{Ab0}$ `\mathnormal{Ab0}`|$\textbf{Ab0}$ `\textbf{Ab0}` |$\textit{Ab0}$ `\textit{Ab0}`
|
||
|$\textrm{Ab0}$ `\textrm{Ab0}` |$\bf Ab0$ `\bf Ab0` |$\it Ab0$ `\it Ab0`
|
||
|$\rm Ab0$ `\rm Ab0` |$\bold{Ab0}$ `\bold{Ab0}` |$\textup{Ab0}$ `\textup{Ab0}`
|
||
|$\textnormal{Ab0}$ `\textnormal{Ab0}`|$\boldsymbol{Ab0}$ `\boldsymbol{Ab}`|$\Bbb{AB}$ `\Bbb{AB}`
|
||
|$\text{Ab0}$ `\text{Ab0}` |$\bm{Ab0}$ `\bm{Ab0}` |$\mathbb{AB}$ `\mathbb{AB}`
|
||
|$\mathsf{Ab0}$ `\mathsf{Ab0}` |$\textmd{Ab0}$ `\textmd{Ab0}` |$\frak{Ab0}$ `\frak{Ab0}`
|
||
|$\textsf{Ab0}$ `\textsf{Ab0}` |$\mathtt{Ab0}$ `\mathtt{Ab0}` |$\mathfrak{Ab0}$ `\mathfrak{Ab0}`
|
||
|$\sf Ab0$ `\sf Ab0` |$\texttt{Ab0}$ `\texttt{Ab0}` |$\mathcal{AB0}$ `\mathcal{AB0}`
|
||
| |$\tt Ab0$ `\tt Ab0` |$\cal AB0$ `\cal 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` (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.
|
||
|
||
## 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`
|
||
|$\text{\textasciicircum}$ `\text{\textasciicircum}`|$\mathellipsis$ `\mathellipsis`|$\ddagger$ `\ddagger`
|
||
|$`$ <code>`</code>|$\text{\textellipsis}$ `\text{\textellipsis}`|$\text{\textdaggerdbl}$ `\text{\textdaggerdbl}`
|
||
|$\text{\textquoteleft}$ `text{\textquoteleft}`|$\Box$ `\Box`|$\Dagger$ `\Dagger`
|
||
|$\lq$ `\lq`|$\square$ `\square`|$\angle$ `\angle`
|
||
|$\text{\textquoteright}$ `\text{\textquoteright}`|$\blacksquare$ `\blacksquare`|$\measuredangle$ `\measuredangle`
|
||
|$\rq$ `\rq`|$\triangle$ `\triangle`|$\sphericalangle$ `\sphericalangle`
|
||
|$\text{\textquotedblleft}$ `\text{\textquotedblleft}`|$\triangledown$ `\triangledown`|$\top$ `\top`
|
||
|$"$ `"`|$\triangleleft$ `\triangleleft`|$\bot$ `\bot`
|
||
|$\text{\textquotedblright}$ `\text{\textquotedblright}`|$\triangleright$ `\triangleright`|$\$$ `\$`
|
||
|$\colon$ `\colon`|$\bigtriangledown$ `\bigtriangledown`|$\text{\textdollar}$ `\text{\textdollar}`
|
||
|$\backprime$ `\backprime`|$\bigtriangleup$ `\bigtriangleup`|$\pounds$ `\pounds`
|
||
|$\prime$ `\prime`|$\blacktriangle$ `\blacktriangle`|$\mathsterling$ `\mathsterling`
|
||
|$\text{\textless}$ `\text{\textless}`|$\blacktriangledown$ `\blacktriangledown`|$\text{\textsterling}$ `\text{\textsterling}`
|
||
|$\text{\textgreater}$ `\text{\textgreater}`|$\blacktriangleleft$ `\blacktriangleleft`|$\yen$ `\yen`
|
||
|$\text{\textbar}$ `\text{\textbar}`|$\blacktriangleright$ `\blacktriangleright`|$\surd$ `\surd`
|
||
|$\text{\textbardbl}$ `\text{\textbardbl}`|$\diamond$ `\diamond`|$\degree$ `\degree`
|
||
|$\text{\textbraceleft}$ `\text{\textbraceleft}`|$\Diamond$ `\Diamond`|$\text{\textdegree}$ `\text{\textdegree}`
|
||
|$\text{\textbraceright}$ `\text{\textbraceright}`|$\lozenge$ `\lozenge`|$\mho$ `\mho`
|
||
|$\text{\textbackslash}$ `\text{\textbackslash}`|$\blacklozenge$ `\blacklozenge`|$\diagdown$ `\diagdown`
|
||
|$\text{\P}$ `\text{\P}` or `\P`|$\star$ `\star`|$\diagup$ `\diagup`
|
||
|$\text{\S}$ `\text{\S}` or `\S`|$\bigstar$ `\bigstar`|$\flat$ `\flat`
|
||
|$\text{\sect}$ `\text{\sect}`|$\clubsuit$ `\clubsuit`|$\natural$ `\natural`
|
||
|$\copyright$ `\copyright`|$\clubs$ `\clubs`|$\sharp$ `\sharp`
|
||
|$\circledR$ `\circledR`|$\diamondsuit$ `\diamondsuit`|$\heartsuit$ `\heartsuit`
|
||
|$\text{\textregistered}$ `\text{\textregistered}`|$\diamonds$ `\diamonds`|$\hearts$ `\hearts`
|
||
|$\circledS$ `\circledS`|$\spadesuit$ `\spadesuit`|$\spades$ `\spades`
|
||
|$\text{\textcircled a}$ `\text{\textcircled a}`|$\maltese$ `\maltese`|$\minuso$ `\minuso`|
|
||
|
||
Direct Input: § ¶ $ £ ¥ ∇ ∞ · ∠ ∡ ∢ ♠ ♡ ♢ ♣ ♭ ♮ ♯ ✓ … ⋮ ⋯ ⋱ !$ ‼ ⦵
|
||
|
||
## Units
|
||
|
||
In KaTeX, units are proportioned as they are in TeX.<br>
|
||
KaTeX units are different than CSS units.
|
||
|
||
</div>
|
||
<div class="katex-cards" id="unit-tbl">
|
||
|
||
| 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 |
|
||
|
||
</div>
|
||
|
||
where:
|
||
|
||
<div style="margin-left: 1.5em;">
|
||
|
||
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](font.md#font-size-and-lengths) by the CSS of an HTML page.
|
||
|
||
</div>
|
||
|
||
The effect of style and size:
|
||
|
||
<div class="katex-cards" id="unit-blocks">
|
||
|
||
| 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 |$\rule{10pt}{10pt}$|$\scriptscriptstyle\rule{10pt}{10pt}$|$\huge\rule{10pt}{10pt}$
|
||
|
||
</div>
|