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LaTeX

This cheat sheet summarizes a reference list of LaTeX commonly used display math notation and some application examples of KaTeX.

#Getting Started

#Introduction

LaTeX A TEX-based typesetting system suitable for producing scientific, mathematical, and physical documents of high print quality.

And KaTeX handles only a smaller subset of LaTeX's mathematical notation for display on the web

#Example

f(x)=fξ^e2πiξxdξ% \f is defined as #1f(#2) using the macro
f\relax(x) = \int_{-\infty}^\infty
    f\hat\xi\,e^{2 \pi i \xi x}
    \,d\xi

% \f is defined as #1f(#2) using the macro
f\relax(x) = \int_{-\infty}^\infty
    f\hat\xi\,e^{2 \pi i \xi x}
    \,d\xi

#Inline

Based on KaTeX in one line
Example: `KaTeX:\int_0^\infty x^2 dx`

Example based on KaTeX showing on one line: 0x2dx\int_0^\infty x^2 dx

#Supported Functions

#Accents

:- :- :-
aa' a' a~\tilde{a} \tilde{a} g˚\mathring{g} \mathring{g}
aa'' a'' ac~\widetilde{ac} \widetilde{ac} AB\overgroup{AB} \overgroup{AB}
aa^{\prime} a^{\prime} AB~\utilde{AB} \utilde{AB} AB\undergroup{AB} \undergroup{AB}
aˊ\acute{a} \acute{a} F\vec{F} \vec{F} AB\Overrightarrow{AB} \Overrightarrow{AB}
yˉ\bar{y} \bar{y} AB\overleftarrow{AB} \overleftarrow{AB} AB\overrightarrow{AB} \overrightarrow{AB}
a˘\breve{a} \breve{a} AB\underleftarrow{AB} \underleftarrow{AB} AB\underrightarrow{AB} \underrightarrow{AB}
aˇ\check{a} \check{a} ac\overleftharpoon{ac} \overleftharpoon{ac} ac\overrightharpoon{ac} \overrightharpoon{ac}
a˙\dot{a} \dot{a} AB\overleftrightarrow{AB} \overleftrightarrow{AB} AB\overbrace{AB} \overbrace{AB}
a¨\ddot{a} \ddot{a} AB\underleftrightarrow{AB} \underleftrightarrow{AB} AB\underbrace{AB} \underbrace{AB}
aˋ\grave{a} \grave{a} AB\overline{AB} \overline{AB} ABundefined\overlinesegment{AB} \overlinesegment{AB}
θ^\hat{\theta} \hat{\theta} AB\underline{AB} \underline{AB} ABundefined\underlinesegment{AB} \underlinesegment{AB}
ac^\widehat{ac} \widehat{ac} acˇ\widecheck{ac} \widecheck{ac} X\underbar{X} \underbar{X}

#Emphasis in \text

:- :- :-
aˊ\'{a} \'{a} a˜\~{a} \~{a}
a˙\.{a} \.{a} a˝\H{a} \H{a}
aˋ\\\`{a} \`{a} aˉ\={a} \={a}
a¨\"{a} \"{a} aˇ\v{a} \v{a}
aˆ\^{a} \^{a} a˘\u{a} \u{a}
a˚\r{a} \r{a}

#Delimiter Sizing

:- :-
(AB)\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

#Greek and Hebrew letters

preview method preview method preview method preview method preview method preview method
α\alpha \alpha κ\kappa \kappa ψ\psi \psi ϝ\digamma \digamma Δ\Delta \Delta Θ\Theta \Theta
β\beta \beta λ\lambda \lambda ρ\rho \rho ε\varepsilon \varepsilon Γ\Gamma \Gamma Υ\Upsilon \Upsilon
χ\chi \chi μ\mu \mu σ\sigma \sigma ϰ\varkappa \varkappa Λ\Lambda \Lambda Ξ\Xi \Xi
δ\delta \delta ν\nu \nu τ\tau \tau φ\varphi \varphi Ω\Omega \Omega
ϵ\epsilon \epsilon oo o θ\theta \theta ϖ\varpi \varpi Φ\Phi \Phi \aleph \aleph
η\eta \eta ω\omega \omega υ\upsilon \upsilon ϱ\varrho \varrho Π\Pi \Pi \beth \beth
γ\gamma \gamma ϕ\phi \phi ξ\xi \xi ς\varsigma \varsigma Ψ\Psi \Psi \daleth \daleth
ι\iota \iota π\pi \pi ζ\zeta \zeta ϑ\vartheta \vartheta Σ\Sigma \Sigma \gimel \gimel

#Other letters

:- :- :- :- :- :- :- :- :- :-
ı\imath \imath \nabla \nabla \Im \Im R\Reals \Reals Œ\text{\OE} \text{\OE}
ȷ\jmath \jmath \partial \partial \image \image \wp \wp ø\text{\o} \text{\o}
\aleph \aleph \Game \Game k\Bbbk \Bbbk \weierp \weierp Ø\text{\O} \text{\O}
\alef \alef \Finv \Finv N\N \N Z\Z \Z ß\text{\ss} \text{\ss}
\alefsym \alefsym C\cnums \cnums N\natnums \natnums a˚\text{\aa} \text{\aa} ı\text{\i} \text{\i}
\beth \beth C\Complex \Complex R\R \R A˚\text{\AA} \text{\AA} ȷ\text{\j} \text{\j}
\gimel \gimel \ell \ell \Re \Re æ\text{\ae} \text{\ae}
\daleth \daleth \hbar \hbar \real \real Æ\text{\AE} \text{\AE}
ð\eth \eth \hslash \hslash R\reals \reals œ\text{\oe} \text{\oe}

#Alphabets and Unicode

preview method preview method preview method preview method
A\Alpha \Alpha B\Beta \Beta Γ\Gamma \Gamma Δ\Delta \Delta
E\Epsilon \Epsilon Z\Zeta \Zeta H\Eta \Eta Θ\Theta \Theta
I\Iota \Iota K\Kappa \Kappa Λ\Lambda \Lambda M\Mu \Mu
N\Nu \Nu Ξ\Xi \Xi O\Omicron \Omicron Π\Pi \Pi
P\Rho \Rho Σ\Sigma \Sigma T\Tau \Tau Υ\Upsilon \Upsilon
Φ\Phi \Phi X\Chi \Chi Ψ\Psi \Psi Ω\Omega \Omega
Γ\varGamma \varGamma Δ\varDelta \varDelta Θ\varTheta \varTheta Λ\varLambda \varLambda
Ξ\varXi \varXi Π\varPi \varPi Σ\varSigma \varSigma Υ\varUpsilon \varUpsilon
Φ\varPhi \varPhi Ψ\varPsi \varPsi Ω\varOmega \varOmega
α\alpha \alpha β\beta \beta γ\gamma \gamma δ\delta \delta
ϵ\epsilon \epsilon ζ\zeta \zeta η\eta \eta θ\theta \theta
ι\iota \iota κ\kappa \kappa λ\lambda \lambda μ\mu \mu
ν\nu \nu ξ\xi \xi ο\omicron \omicron π\pi \pi
ρ\rho \rho σ\sigma \sigma τ\tau \tau υ\upsilon \upsilon
ϕ\phi \phi χ\chi \chi ψ\psi \psi ω\omega \omega
ε\varepsilon \varepsilon ϰ\varkappa \varkappa ϑ\vartheta \vartheta ϑ\thetasym \thetasym
ϖ\varpi \varpi ϱ\varrho \varrho ς\varsigma \varsigma φ\varphi \varphi
ϝ\digamma \digamma

#Annotation

:- :- :- :- :-
5\cancel{5} \cancel{5} a+b+cnote\overbrace{a+b+c}^{\text{note}} \overbrace{a+b+c}^{\text{note}}
5\bcancel{5} \bcancel{5} a+b+cnote\underbrace{a+b+c}_{\text{note}} \underbrace{a+b+c}_{\text{note}}
ABC\xcancel{ABC} \xcancel{ABC} \not = \not =
abc\sout{abc} \sout{abc} π=cd\boxed{\pi=\frac c d} \boxed{\pi=\frac c d}
$an\$a_{\angl n} MD syntax conflict $a_{\angl n} ana_\angln a_\angln
78\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}

#Vertical layout

:- :- :- :- :- :-
xnx_n x_n =!\stackrel{!}{=} \stackrel{!}{=} aba \atop b a \atop b
exe^x e^x =!\overset{!}{=} \overset{!}{=} abca\raisebox{0.25em}{$b$}c a\raisebox{0.25em}{$b$}c
uo_u^o _u^o =!\underset{!}{=} \underset{!}{=} a+(abc)a+\left(\vcenter{\hbox{$\frac{\frac a b}c$}}\right) a+\left(\vcenter{\hbox{$\frac{\frac a b}c$}}\right)
0<i<m0<j<n\sum_{\substack{0<i<m\\0<j<n}} \sum_{\substack{0<i<m\\0<j<n}}

#Overlap and Spacing

:- :- :- :-
=/{=}\mathllap{/\,} {=}\mathllap{/,} (x2)\left(x^{\smash{2}}\right) \left(x^{\smash{2}}\right)
/=\mathrlap{\,/}{=} \mathrlap{,/}{=} y\sqrt{\smash[b]{y}} \sqrt{\smash[b]{y}}

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

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

#LaTeX\LaTeX math constructs

预览 方法 预览 方法 预览 方法
abcxyz\frac{abc}{xyz} \frac{abc}{xyz} abc\overline{abc} \overline{abc} abc\overrightarrow{abc} \overrightarrow{abc}
ff' f' abc\underline{abc} \underline{abc} abc\overleftarrow{abc} \overleftarrow{abc}
abc\sqrt{abc} \sqrt{abc} abc^\widehat{abc} \widehat{abc} abc\overbrace{abc} \overbrace{abc}
abcn\sqrt[n]{abc} \sqrt[n]{abc} abc~\widetilde{abc} \widetilde{abc} abc\underbrace{abc} \underbrace{abc}

#Delimiters

preview method preview method preview method preview method preview method
()() () ()\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 ┌ ┐ ┌ ┐ \ulcorner \urcorner \ulcorner \urcorner \Downarrow \Downarrow
\| (MD syntax conflict) \| \Vert \Vert └ ┘ └ ┘ \llcorner \lrcorner \llcorner \lrcorner \Updownarrow \Updownarrow
∣ ∣ \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

The pair of expressions \left s1s_1 and \right s2s_2 can be used to match the height of the separators s1s_1 and s2s_2 to the height of their content, e.g. :

:- :- :- :- :- :- :- :- :- :- :-
\left\| exprexpr \right\| \left\{ exprexpr \right\} \left\Vert exprexpr \right.

#Variable Size Symbols

preview method preview method preview method preview method preview method
\sum \sum \int \int \biguplus \biguplus \bigoplus \bigoplus \bigvee \bigvee
\prod \prod \oint \oint \bigcap \bigcap \bigotimes \bigotimes \bigwedge \bigwedge
\coprod \coprod \iint \iint \bigcup \bigcup \bigodot \bigodot \bigodot \bigodot

#standard function name

preview method preview method preview method preview method
arccos\arccos \arccos arcsin\arcsin \arcsin arcsin\arcsin \arcsin arg\arg \arg
cos\cos \cos cosh\cosh \cosh cot\cot \cot coth\coth \coth
csc\csc \csc deg\deg \deg det\det \det dim\dim \dim
exp\exp \exp gcd\gcd \gcd hom\hom \hom inf\inf \inf
ker\ker \ker lg\lg \lg lim\lim \lim lim inf\liminf \liminf
lim sup\limsup \limsup ln\ln \ln log\log \log max\max \max
min\min \min Pr\Pr \Pr sec\sec \sec sin\sin \sin
sinh\sinh \sinh sup\sup \sup tan\tan \tan tanh\tanh \tanh

#Function names should be in roman font, not italics, for example:

:- :- :- :-
Correct: \tan(at-n\pi) \rightarrow tan(atnπ)\tan(at-n\pi)
Incorrect: tan(at-n\pi) katex:\rightarrow tan(atnπ)tan(at-n\pi)

#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 ¬\lnot \neg or \lnot

:- :- :- :-
{x    x<12}\Set{ x \| x<\frac 1 2 } \Set{ x | x<\frac 1 2 } {xx<5}\set{x\|x<5} \set{x|x<5}

#special symbols

:- :- :- :- :- :-
ϕ\bra{\phi} \bra{\phi} ψ\ket{\psi} \ket{\psi} ϕψ\braket{\phi\|\psi} \braket{\phi\|\psi}
ϕ\Bra{\phi} \Bra{\phi} ψ\Ket{\psi} \Ket{\psi} ϕ|2t2|ψ\Braket{ ϕ \| \frac{∂^2}{∂ t^2} \| ψ } \Braket{ ϕ \| \frac{∂^2}{∂ t^2} \| ψ }

#Operator

#Mathematical operator

:- :- :- :- :- :- :- :-
arcsin\arcsin \arcsin cosec\cosec \cosec deg\deg \deg sec\sec \sec
arccos\arccos \arccos cosh\cosh \cosh dim\dim \dim sin\sin \sin
arctan\arctan \arctan cot\cot \cot exp\exp \exp sinh\sinh \sinh
arctg\arctg \arctg cotg\cotg \cotg hom\hom \hom sh\sh \sh
arcctg\arcctg \arcctg coth\coth \coth ker\ker \ker tan\tan \tan
arg\arg \arg csc\csc \csc lg\lg \lg tanh\tanh \tanh
ch\ch \ch ctg\ctg \ctg ln\ln \ln tg\tg \tg
cos\cos \cos cth\cth \cth log\log \log th\th \th
f\operatorname{f} \operatorname{f}
arg max\argmax \argmax inj lim\injlim \injlim min\min \min lim\varinjlim \varinjlim
arg min\argmin \argmin lim\lim \lim plim\plim \plim lim\varliminf \varliminf
det\det \det lim inf\liminf \liminf Pr\Pr \Pr lim\varlimsup \varlimsup
gcd\gcd \gcd lim sup\limsup \limsup proj lim\projlim \projlim lim\varprojlim \varprojlim
inf\inf \inf max\max \max sup\sup \sup f\operatorname*{f} \operatorname*{f}
f\operatornamewithlimits{f} \operatornamewithlimits{f}

#Big operator

:- :- :- :- :- :- :- :-
\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

#Fractions and binomials

:- :- :- :-
ab\frac{a}{b} \frac{a}{b} ab\tfrac{a}{b} \tfrac{a}{b}
ab{a \over b} {a \over b} ab\dfrac{a}{b} \dfrac{a}{b}
(aa+1]\genfrac ( ] {2pt}{1}a{a+1} \genfrac ( ] {2pt}{1}a{a+1} ab+1{a \above{2pt} b+1} {a \above{2pt} b+1}
a/ba/b a/b a1+1b\cfrac{a}{1 + \cfrac{1}{b}} \cfrac{a}{1 + \cfrac{1}{b}}
:- :- :- :-
(nk)\binom{n}{k} \binom{n}{k} (nk)\dbinom{n}{k} \dbinom{n}{k}
{nk}{n\brace k} {n\brace k} (nk){n \choose k} {n \choose k}
(nk)\tbinom{n}{k} \tbinom{n}{k} [nk]{n\brack k} {n\brack k}

#\sqrt

:- :- :- :-
x\sqrt{x} \sqrt{x} x3\sqrt[3]{x} \sqrt[3]{x}

#Binary operator

:- :- :- :- :- :- :- :-
++ + \cdot \cdot \gtrdot \gtrdot x(moda)x \pmod a x \pmod a
- - \cdotp \cdotp \intercal \intercal x(a)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
mod\bmod \bmod \curlyvee \curlyvee xmodax\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 ±\plusmn \plusmn
\wr \wr` |

#Relation

#Relation

:- :- :- :- :- :- :- :-
== = \doteqdot \doteqdot \lessapprox \lessapprox \smile \smile
<< < \eqcirc \eqcirc \lesseqgtr \lesseqgtr \sqsubset \sqsubset
>> > \eqcolon \eqcolon or \minuscolon \lesseqqgtr \lesseqqgtr \sqsubseteq \sqsubseteq
:: : \Eqcolon \Eqcolon or \minuscoloncolon \lessgtr \lessgtr \sqsupset \sqsupset
\approx \approx \eqqcolon \eqqcolon or \equalscolon \lesssim \lesssim \sqsupseteq \sqsupseteq
:\approxcolon \approxcolon =\Eqqcolon \Eqqcolon or \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 \coloncolonapprox \gggtr \gggtr \precapprox \precapprox \thickapprox \thickapprox
:\coloneq \coloneq or \colonminus >\gt \gt \preccurlyeq \preccurlyeq \thicksim \thicksim
\Coloneq \Coloneq or \coloncolonminus \gtrapprox \gtrapprox \preceq \preceq \trianglelefteq \trianglelefteq
\coloneqq \coloneqq or \colonequals \gtreqless \gtreqless \precsim \precsim \triangleq \triangleq
=\Coloneqq \Coloneqq or \coloncolonequals \gtreqqless \gtreqqless \propto \propto \trianglerighteq \trianglerighteq
:\colonsim \colonsim \gtrless \gtrless \risingdotseq \risingdotseq \varpropto \varpropto
\Colonsim \Colonsim or \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 \ratio
\dashv \dashv \le \le \simcoloncolon \simcoloncolon \vdash \vdash
\dblcolon \dblcolon or \coloncolon \leq \leq \simeq \simeq \vDash \vDash
\doteq \doteq \leqq \leqq \smallfrown \smallfrown \Vdash \Vdash
\Doteq \Doteq \leqslant \leqslant \smallsmile \smallsmile \Vvdash \Vvdash

#Negative relationship

:- :- :- :- :- :- :- :-
\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

\not = \not =

#Arrow

:- :- :- :- :- :-
\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

#可扩展箭头

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

#Symbols and Punctuation

#Symbols and Punctuation

:- :- :- :- :- :-
% comment % comment \dots \dots KaTeX\KaTeX \KaTeX
%\% \% \cdots \cdots LaTeX\LaTeX \LaTeX
#\# \# \ddots \ddots TeX\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} 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
a\text{\textcircled a} \text{\textcircled a} \maltese \maltese \minuso \minuso

#Environments

#Environments 1

abcd\begin{matrix}
   a & b \\
   c & d
\end{matrix}
\begin{matrix}
   a & b \\
   c & d
\end{matrix}

#Environments 2

abcd\begin{array}{cc}
   a & b \\
   c & d
\end{array}
\begin{array}{cc}
   a & b \\
   c & d
\end{array}

#Environments 3

(abcd)\begin{pmatrix}
   a & b \\
   c & d
\end{pmatrix}
\begin{pmatrix}
   a & b \\
   c & d
\end{pmatrix}

#Environments 4

[abcd]\begin{bmatrix}
   a & b \\
   c & d
\end{bmatrix}
\begin{bmatrix}
   a & b \\
   c & d
\end{bmatrix}

#Environments 5

abcd\begin{vmatrix}
   a & b \\
   c & d
\end{vmatrix}
\begin{vmatrix}
   a & b \\
   c & d
\end{vmatrix}

#Environments 6

abcd\begin{Vmatrix}
   a & b \\
   c & d
\end{Vmatrix}
\begin{Vmatrix}
   a & b \\
   c & d
\end{Vmatrix}

#Environments 7

{abcd}\begin{Bmatrix}
   a & b \\
   c & d
\end{Bmatrix}
\begin{Bmatrix}
   a & b \\
   c & d
\end{Bmatrix}

#Environments 8

abcdefghi\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}

#Environments 9

x={aif bcif dx = \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}

#Environments 10

aif bcif d}\begin{rcases}
   a &\text{if } b \\
   c &\text{if } d
\end{rcases}⇒…
\begin{rcases}
   a &\text{if } b \\
   c &\text{if } d
\end{rcases}⇒…

#Environments 11

abcd\begin{smallmatrix}
   a & b \\
   c & d
\end{smallmatrix}
\begin{smallmatrix}
   a & b \\
   c & d
\end{smallmatrix}

#Environments 12

iΛ0<j<n\sum_{
\begin{subarray}{l}
   i\in\Lambda\\
   0<j<n
\end{subarray}}
\sum_{
\begin{subarray}{l}
   i\in\Lambda\\
   0<j<n
\end{subarray}}

#Environments 13

\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}

#Environments 14

\begin{align}
   a&=b+c \\
   d+e&=f
\end{align}
\begin{align}
   a&=b+c \\
   d+e&=f
\end{align}

#Environments 15

\begin{gather}
   a=b \\
   e=b+c
\end{gather}
\begin{gather}
   a=b \\
   e=b+c
\end{gather}

#Environments 16

\begin{alignat}{2}
   10&x+&3&y=2\\
   3&x+&13&y=4
\end{alignat}
\begin{alignat}{2}
   10&x+&3&y=2\\
   3&x+&13&y=4
\end{alignat}

#Environments 17

\begin{CD}
   A @>a>> B \\
@VbVV @AAcA \\
   C @= D
\end{CD}
\begin{CD}
   A @>a>> B \\
@VbVV @AAcA \\
   C @= D
\end{CD}

#Style, Color, Size and Font

#Color

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

#Font

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

#Style

:- :- :- :-
i=1n\displaystyle\sum_{i=1}^n \displaystyle\sum_{i=1}^n i=1n\textstyle\sum_{i=1}^n \textstyle\sum_{i=1}^n
x\scriptstyle x \scriptstyle x x\scriptscriptstyle x \scriptscriptstyle x
limx\lim\limits_x \lim\limits_x limx\lim\nolimits_x \lim\nolimits_x
x^2\verb!x^2! \verb!x^2!

#Also See