KATEX_MATH_OP

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id: supported title: Supported Functions

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

  There is a similar Support Table, sorted alphabetically, that lists both supported and un-supported functions.

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}} \`{a} \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

Delimiters

(~) ( ) \lparen~\rparen \lparen~~~~\rparen ⌈~⌉ ⌈ ⌉ \lceil~\rceil \lceil~~~~~\rceil \uparrow \uparrow
[~] [ ] \lbrack~\rbrack \lbrack~~~~\rbrack ⌊~⌋ ⌊ ⌋ \lfloor~\rfloor \lfloor~~~~~\rfloor \downarrow \downarrow
\{ \} \{ \} \lbrace \rbrace \lbrace~~~~\rbrace ⎰⎱ ⎰⎱ \lmoustache \rmoustache \lmoustache~~~~\rmoustache \updownarrow \updownarrow
⟨~⟩ ⟨ ⟩ \langle~\rangle \langle~~~~\rangle ⟮~⟯ ⟮ ⟯ \lgroup~\rgroup \lgroup~~~~~\rgroup \Uparrow \Uparrow
\vert \vert \vert ┌ ┐ ┌ ┐ \ulcorner \urcorner \ulcorner~~~~\urcorner
\Vert | \Vert \Vert └ ┘ └ ┘ \llcorner \lrcorner \llcorner~~~~\lrcorner \Updownarrow \Updownarrow
\lvert~\rvert \lvert~~~~\rvert \lVert~\rVert \lVert~~~~~\rVert \left. \right. \backslash \backslash
\lang~\rang \lang~~~~\rang \lt~\gt \lt \gt ⟦~⟧ ⟦ ⟧ \llbracket~\rrbracket \llbracket~~~~\rrbracket \lBrace~\rBrace \lBrace \rBrace

  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

Environments

\begin{matrix} a & b \\ c & d \end{matrix} \begin{matrix} a & b \\ c & d``\end{matrix} \begin{array}{cc}a & b\\c & d\end{array} \begin{array}{cc} a & b \\ c & d``\end{array}
\begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} a & b \\ c & d``\end{pmatrix} \begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{bmatrix} a & b \\ c & d``\end{bmatrix}
\begin{vmatrix} a & b \\ c & d \end{vmatrix} \begin{vmatrix} a & b \\ c & d``\end{vmatrix} \begin{Vmatrix} a & b \\ c & d \end{Vmatrix} \begin{Vmatrix} a & b \\ c & d``\end{Vmatrix}
\begin{Bmatrix} a & b \\ c & d \end{Bmatrix} \begin{Bmatrix} a & b \\ c & d``\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} \begin{array}{c:c:c} a & b & c \\ \hline d & e & f \\ \hdashline g & h & i``\end{array}
\begin{equation}\begin{split}a &=b+c\\&=e+f\end{split}\end{equation}
\begin{equation}``\begin{split} a &=b+c\\ &=e+f``\end{split}``\end{equation}
\begin{equation*}\begin{split}a &=b+c\\&=e+f\end{split}\end{equation*}
\begin{equation*}``\begin{split} a &=b+c\\ &=e+f``\end{split}``\end{equation*}
\begin{align} a&=b+c \\ d+e&=f \end{align}
\begin{align} a&=b+c \\ d+e&=f``\end{align}
\begin{alignat}{2}10&x+&3&y=2\\3&x+&13&y=4\end{alignat}
\begin{align*} a&=b+c \\ d+e&=f \end{align*}
\begin{align*} a&=b+c \\ d+e&=f``\end{align*} \begin{aligned} a&=b+c \\ d+e&=f \end{aligned} \begin{aligned} a&=b+c \\ d+e&=f``\end{aligned}
\begin{alignedat}{2} 10&x+ &3&y = 2 \\ 3&x+&13&y = 4``\end{alignedat} \begin{alignedat}{2}10&x+&3&y=2\\3&x+&13&y=4\end{alignedat} \begin{alignedat}{2} 10&x+ &3&y = 2 \\ 3&x+&13&y = 4``\end{alignedat}
\begin{gather} a=b \\ e=b+c \end{gather}
\begin{gather} a=b \\ e=b+c``\end{gather} \begin{gathered} a=b \\ e=b+c \end{gathered} \begin{gathered} a=b \\ e=b+c``\end{gathered}
x = \begin{cases} a &\text{if } b \\ c &\text{if } d \end{cases} x = \begin{cases} a &\text{if } b \\ c &\text{if } d``\end{cases} \begin{rcases} a &\text{if } b \\ c &\text{if } d \end{rcases}⇒… \begin{rcases} a &\text{if } b \\ c &\text{if } d``\end{rcases}⇒…
\begin{smallmatrix} a & b \\ c & d \end{smallmatrix} \begin{smallmatrix} a & b \\ c & d``\end{smallmatrix}

  KaTeX also supports darray, dcases, and drcases, which apply displaystyle.

  And KaTeX supports matrix*, pmatrix*, bmatrix*, Bmatrix*, vmatrix*, and Vmatrix*, which take an optional argument to set column alignment, as in \begin{matrix}[1], \begin{matrix}[c], or \begin{matrix}[r].

  Acceptable line separators include: \\, \cr, \\[distance], and \cr[distance]. Distance can be written with any of the KaTeX units.

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

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

HTML

  The following "raw HTML" features are potentially dangerous for untrusted
inputs, so they are disabled by default, and attempting to use them produces
the command names in red (which you can configure via the errorColor
option). To fully trust your LaTeX input, you need to pass
an option of trust: true; you can also enable just some of the commands
or for just some URLs via the trust option.

\href{https://katex.org/}{\KaTeX} \href{https://katex.org/}{\KaTeX}
\url{https://katex.org/} \url{https://katex.org/}
\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}
\htmlId{bar}{x}…x… \htmlId{bar}{x}
\htmlClass{foo}{x}…x… \htmlClass{foo}{x}
\htmlStyle{color: red;}{x}…x… \htmlStyle{color: red;}{x}
\htmlData{foo=a, bar=b}{x}…x… \htmlData{foo=a, bar=b}{x}

  \includegraphics supports height, width, totalheight, and alt in its first argument. height is required.

  HTML extension (\html-prefixed) commands are non-standard, so loosening strict option for htmlExtension is required.

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 ϝ

\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
\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 properly in any KaTeX rendering mode.

  In addition, 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.
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.
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.

  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.
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.

  For Persian composite characters, a user-supplied plug-in is under development.

Layout

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}
a_{\angl n} $a_{\angl n} a_\angln a_\angln
\phase{-78^\circ}\phase{-78^\circ}

  \tag{hi} x+y^{2x}

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

  \tag*{hi} x+y^{2x}

\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{!}{=} $$\sum_{\substack{0

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

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
\: 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 \negmedspace – ⁴∕₁₈ em space
\nobreakspace non-breaking space \negthickspace – ⁵∕₁₈ em space
\space space \mathstrut \vphantom{(}

  Notes:

  distance will accept any of the KaTeX 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.

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.

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

  \gdef, \xdef, \global\def, \global\edef, \global\let, and \global\futurelet will persist between math expressions.

  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}

  Functions in the bottom five rows of this table can take \limits.

\sqrt

  \sqrt{x} \sqrt{x}

  \sqrt[3]{x} \sqrt[3]{x}

Relations

  \stackrel{!}{=} \stackrel{!}{=}

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

\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}

\textcolor{#228B22}{F=ma} \textcolor{#228B22}{F=ma}

\colorbox{aqua}{F=ma} \colorbox{aqua}{$F=ma$}

\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. 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
` ` \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} \star \star \diagup \diagup
\text{\S} \text{\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.

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}

标题:KATEX_MATH_OP
作者:fe
地址:https://blog.eiyouhe.com/articles/2020/10/20/1603189006997.html