本文为Latex数学公式在 Markdown 环境下的语法指引

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本文为Latex数学公式在 Markdown 环境下的语法指引,以帮助每一个写文的人便利地把数学公式完整的编辑出来,并作出优美的排版。

1. Markdown中的Latex格式

LateX数学公式有两种:行中公式和独立公式(行间公式)。行中公式放在文中与其它文字混排,独立公式则单独成行。

1.1 行内公式

$E=mc^2$ E=mc2E=mc^2

1.2 独立公式

$$E=mc^2$$ E=mc2E=mc^2

2.Latex数学公式

2.1 函数、符号及特殊字符

  • 指数 $\exp_a b = a^b, \exp b = e^b, 10^m$ expab=ab,expb=eb,10m\exp_a b = a^b, \exp b = e^b, 10^m

  • 对数 \ln c, \lg d = \log e, \log_{10} f lnc,lgd=loge,log10f\ln c, \lg d = \log e, \log_{10} f

  • 三角函数 \sin a, \cos b, \tan c, \cot d, \sec e, \csc f sina,cosb,tanc,cotd,sece,cscf\sin a, \cos b, \tan c, \cot d, \sec e, \csc f\arcsin a, \arccos b, \arctan c arcsina,arccosb,arctanc\arcsin a, \arccos b, \arctan c\arccot d, \arcsec e, \arccsc f \arccotd,\arcsece,\arccscf\arccot d, \arcsec e, \arccsc f\sinh a, \cosh b, \tanh c, \coth d sinha,coshb,tanhc,cothd\sinh a, \cosh b, \tanh c, \coth d\operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n shk,chl,thm,cothn\operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q argsho,argchp,argthq\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q

  • 绝对值 \left\vert s \right\vert s\left\vert s \right\vert

  • 最大值,最小值 \min(x,y), \max(x,y$) min(x,y),max(x,y\min(x,y), \max(x,y)  

2.2 界限,极限

\min x, \max y, \inf s, \sup t minx,maxy,infs,supt\min x, \max y, \inf s, \sup t\lim u, \liminf v, \limsup w limu,lim infv,lim supw\lim u, \liminf v, \limsup w\lim_{x \to \infty} \frac{1}{n(n+1)} limx1n(n+1)\lim_{x \to \infty} \frac{1}{n(n+1)}\dim p, \deg q, \det m, \ker\phi dimp,degq,detm,kerϕ\dim p, \deg q, \det m, \ker\phi

2.3 投射

\Pr j, \hom l, \lVert z \rVert, \arg z Prj,homl,z,argz\Pr j, \hom l, \lVert z \rVert, \arg z

2.4 微积分和导数

dt, \mathrm{d}t, \partial t, \nabla\psi dt,dt,t,ψdt, \mathrm{d}t, \partial t, \nabla\psi

dy/dx, \mathrm{d}y/\mathrm{d}x, \frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x}, \frac{\partial^2}{\partial x_1\partial x_2}y dy/dx,dy/dx,dydx,dydx,2x1x2ydy/dx, \mathrm{d}y/\mathrm{d}x, \frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x}, \frac{\partial^2}{\partial x_1\partial x_2}y

\prime, \backprime, f^\prime, f', f'', f^{(3)}, \dot y, \ddot y ,,f,f,f,f(3),y˙,y¨\prime, \backprime, f^\prime, f', f'', f^{(3)}, \dot y, \ddot y

2.5 类字母符号及常数

\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar ,,,,ð,,\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar

\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS ,ı,ȷ,k,,,,,\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS

2.6 模运算

s_k \equiv 0 \pmod{m} sk0(modm)s_k \equiv 0 \pmod{m}

a \bmod b amodba \bmod b

\gcd(m, n), \operatorname{lcm}(m, n) gcd(m,n),lcm(m,n)\gcd(m, n), \operatorname{lcm}(m, n)

\mid, \nmid, \shortmid, \nshortmid ,,,\mid, \nmid, \shortmid, \nshortmid

2.7 根号

\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{\frac{x^3+y^3}{2}} ,2,n,x3+y323\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{\frac{x^3+y^3}{2}}

2.8 集合

\{ \}, \O \empty \emptyset, \varnothing {},\O,\{ \}, \O \empty \emptyset, \varnothing

\in, \notin \not\in, \ni, \not\ni ,∉,,∌\in, \notin \not\in, \ni, \not\ni

\cap, \Cap, \sqcap, \bigcap ,,,\cap, \Cap, \sqcap, \bigcap

\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus ,,,,,,\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus

\setminus, \smallsetminus, \times ,,×\setminus, \smallsetminus, \times

\subset, \Subset, \sqsubset ,,\subset, \Subset, \sqsubset

\supset, \Supset, \sqsupset ,,\supset, \Supset, \sqsupset

\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq ,,,,\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq

\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq ,,,,\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq

\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq ,,,\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq

\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq ,,,\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq

2.9 运算符

+, -, \pm, \mp, \dotplus +,,±,,+, -, \pm, \mp, \dotplus

\times, \div, \divideontimes, /, \backslash ×,÷,,/,\\times, \div, \divideontimes, /, \backslash

\cdot, * \ast, \star, \circ, \bullet ,,,,\cdot, * \ast, \star, \circ, \bullet

\boxplus, \boxminus, \boxtimes, \boxdot ,,,\boxplus, \boxminus, \boxtimes, \boxdot

\oplus, \ominus, \otimes, \oslash, \odot ,,,,\oplus, \ominus, \otimes, \oslash, \odot

\circleddash, \circledcirc, \circledast ,,\circleddash, \circledcirc, \circledast

\bigoplus, \bigotimes, \bigodot ,,\bigoplus, \bigotimes, \bigodot

2.10 关系符号

=, \ne, \neq, \equiv, \not\equiv =,,,,≢=, \ne, \neq, \equiv, \not\equiv \doteq, \doteqdot, ``\overset{\underset{\mathrm{def}}{}}{=},``:= ,,=def,:=\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=},:=

\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong ,,,,,,,,\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong

\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto ,,,,,\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto

<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot <,,,≪̸,,⋘̸,<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot

>, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot >,,,≫̸,,⋙̸,>, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot \le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq ,,,,,,,\le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq

\ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq ,,,,,,,\ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq

\lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless ,,,,,\lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless

\leqslant, \nleqslant, \eqslantless``\geqslant, \ngeqslant, \eqslantgtr ,,,,,\leqslant, \nleqslant, \eqslantless,\geqslant, \ngeqslant, \eqslantgtr

\lesssim, \lnsim, \lessapprox, \lnapprox``\gtrsim, \gnsim, \gtrapprox, \gnapprox ,,,,,,,\lesssim, \lnsim, \lessapprox, \lnapprox, \gtrsim, \gnsim, \gtrapprox, \gnapprox

\prec, \nprec, \preceq, \npreceq, \precneqq``\succ, \nsucc, \succeq, \nsucceq, \succneqq ,,,,,,,,,\prec, \nprec, \preceq, \npreceq, \precneqq,\succ, \nsucc, \succeq, \nsucceq, \succneqq

\preccurlyeq, \curlyeqprec``\succcurlyeq, \curlyeqsucc ,,,\preccurlyeq, \curlyeqprec,\succcurlyeq, \curlyeqsucc

\precsim, \precnsim, \precapprox, \precnappro``\succsim, \succnsim, \succapprox, \succnapprox ,,,\precnappro,,,,\precsim, \precnsim, \precapprox, \precnappro,\succsim, \succnsim, \succapprox, \succnapprox

2.11 几何符号

\parallel, \nparallel, \shortparallel, \nshortparallel ,,,\parallel, \nparallel, \shortparallel, \nshortparallel

\perp, \angle, \sphericalangle, \measuredangle, 45^\circ ,,,,45\perp, \angle, \sphericalangle, \measuredangle, 45^\circ

\Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar ,,,,,\Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar

\bigcirc, \triangle, \bigtriangleup, \bigtriangledown ,,,\bigcirc, \triangle, \bigtriangleup, \bigtriangledown

\vartriangle, \triangledown``\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright ,,,,,\vartriangle, \triangledown,\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright

2.12 逻辑符号

\forall, \exists, \nexists ,,\forall, \exists, \nexists \therefore, \because, \And ,,&\therefore, \because, \And

\or \lor \vee, \curlyvee, \bigvee \or,,\or \lor \vee, \curlyvee, \bigvee

\bar{q}, \bar{abc}, \overline{q}, \overline{abc},``\lnot \neg, \not\operatorname{R}, \bot, \top qˉ,abcˉ,q,abc,¬¬,̸R,,\bar{q}, \bar{abc}, \overline{q}, \overline{abc},\lnot \neg, \not\operatorname{R}, \bot, \top

\vdash \dashv, \vDash, \Vdash, \models ,,,\vdash \dashv, \vDash, \Vdash, \models

\Vvdash, \nvdash ,\nVdash ,\nvDash ,\nVDash ,,,,\Vvdash, \nvdash, \nVdash ,\nvDash ,\nVDash

\ulcorner \urcorner \llcorner \lrcorner \ulcorner \urcorner \llcorner \lrcorner

2.13 箭头

\Rrightarrow, \Lleftarrow ,\Rrightarrow, \Lleftarrow

\Rightarrow, \nRightarrow, \Longrightarrow \implies ,,    \Rightarrow, \nRightarrow, \Longrightarrow \implies

\Leftarrow, \nLeftarrow, \Longleftarrow ,,\Leftarrow, \nLeftarrow, \Longleftarrow

\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow \iff ,,    \Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow \iff

\Uparrow, \Downarrow, \Updownarrow ,,\Uparrow, \Downarrow, \Updownarrow

\rightarrow \to, \nrightarrow, \longrightarrow ,,\rightarrow \to, \nrightarrow, \longrightarrow

\leftarrow \gets, \nleftarrow, \longleftarrow ,,\leftarrow \gets, \nleftarrow, \longleftarrow

\leftrightarrow, \nleftrightarrow, \longleftrightarrow ,,\leftrightarrow, \nleftrightarrow, \longleftrightarrow

\uparrow, \downarrow, \updownarrow ,,\uparrow, \downarrow, \updownarrow \nearrow, \swarrow, \nwarrow, \searrow ,,,\nearrow, \swarrow, \nwarrow, \searrow \mapsto, \longmapsto ,\mapsto, \longmapsto

\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons ,,,,,,,,,\rightharpoonup ,\rightharpoondown ,\leftharpoonup ,\leftharpoondown ,\upharpoonleft,\upharpoonright, \downharpoonleft, \downharpoonright, \rightleftharpoons, \leftrightharpoons

\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright ,,,,,,\curvearrowleft, \circlearrowleft, \Lsh \upuparrows, \rightrightarrows, \rightleftarrows, \rightarrowtail, \looparrowright \curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft ,,,,,,,\curvearrowright, \circlearrowright, \Rsh, \downdownarrows, \leftleftarrows, \leftrightarrows, \leftarrowtail, \looparrowleft

\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow ,,,,,,\hookrightarrow, \hookleftarrow, \multimap, \leftrightsquigarrow, \rightsquigarrow, \twoheadrightarrow, \twoheadleftarrow

2.13 特殊符号

省略号:数学公式中常见的省略号有两种,\ldots 表示与文本底线对齐的省略号,\cdots 表示与文本中线对齐的省略号。

\amalg \% \dagger \ddagger \ldots \cdots ⨿%\amalg \% \dagger \ddagger \ldots \cdots

\smile \frown \wr \triangleleft \triangleright \smile \frown \wr \triangleleft \triangleright

\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp ,,,,,,,\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp

2.14 其他符号

\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes \diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes

\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq \eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq

\intercal \barwedge \veebar \doublebarwedge \between \pitchfork \intercal \barwedge \veebar \doublebarwedge \between \pitchfork

\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright \vartriangleleft \ntriangleleft \vartriangleright \ntriangleright \trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq \trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq

2.15 上标、下标及积分等

^表示上标, _ 表示下标。如果上下标的内容多于一个字符,需要用 {} 将这些内容括成一个整体。上下标可以嵌套,也可以同时使用。

  • 上标 a^2 a2a^2

  • 下标 a_2 a2a_2

  • 组合 a^{2+2} a2+2a^{2+2} a_{i,j} ai,ja_{i,j}

  • 结合上下标 x_2^3 x23x_2^3

  • 前置上下标 {}_1^2\!X_3^4 12 ⁣X34{}_1^2\!X_3^4

  • 导数(HTML) x' xx'

  • 导数(PNG) x^\prime xx^\prime

  • 导数(错误) x\prime xx\prime

  • 导数点 \dot{x} x˙\dot{x} \ddot{y} y¨\ddot{y}

  • 向量 \vec{c}(只有一个字母) c\vec{c} \overleftarrow{a b},\overrightarrow{c d} ab\overleftarrow{a b},cd\overrightarrow{c d} \overleftrightarrow{a b}``\widehat{e f g} ab\overleftrightarrow{a b}, efg^\widehat{e f g}

  • 上弧 (注: 正确应该用 \overarc,但在这里行不通。要用建议的语法作为解决办法。)(使用 \ overarc 时需要引入 {arcs} 包。) \overset{\frown} {AB} AB\overset{\frown} {AB}

  • 上下划线 \overline{h i j}, \underline{k l m} hij\overline{h i j}, klm\underline{k l m}

  • 上括号 \overbrace{1+2+\cdots+100} 1+2++100\overbrace{1+2+\cdots+100} \begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix} 50501+2++100\begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix}

  • 下括号 \underbrace{a+b+\cdots+z} a+b++z\underbrace{a+b+\cdots+z} \begin{matrix} \underbrace{ a+b+\cdots+z } \\ 26 \end{matrix} a+b++z26\begin{matrix} \underbrace{ a+b+\cdots+z } \\ 26 \end{matrix}

  • 求和(累加) \sum_{k=1}^N k^2 k=1Nk2\sum_{k=1}^N k^2 \begin{matrix} \sum_{k=1}^N k^2 \end{matrix} k=1Nk2\begin{matrix} \sum_{k=1}^N k^2 \end{matrix}

  • 求积(累乘) \prod_{i=1}^N x_i i=1Nxi\prod_{i=1}^N x_i \begin{matrix} \prod_{i=1}^N x_i \end{matrix} i=1Nxi\begin{matrix} \prod_{i=1}^N x_i \end{matrix}

  • 上积 \coprod_{i=1}^N x_i i=1Nxi\coprod_{i=1}^N x_i \begin{matrix} \coprod_{i=1}^N x_i \end{matrix} i=1Nxi\begin{matrix} \coprod_{i=1}^N x_i \end{matrix}

  • 极限 \lim_{n \to \infty}x_n limnxn\lim_{n \to \infty}x_n \begin{matrix} \lim_{n \to \infty}x_n \end{matrix} limnxn\begin{matrix} \lim_{n \to \infty}x_n \end{matrix}

  • 积分 \int_{-N}^{N} e^x\, {\rm d}x NNexdx\int_{-N}^{N} e^x\, {\rm d}x 本例中 \,{\rm d} 部分可省略,但建议加入,能使式子更美观。{\rm d}可以用\mathrm{d}等价替换。 \begin{matrix} \int_{-N}^{N} e^x\, \mathrm{d}x \end{matrix}(矩阵中积分符号变小) NNexdx\begin{matrix} \int_{-N}^{N} e^x\, \mathrm{d}x \end{matrix}

  • 双重积分 \iint_{D}^{W} \, \mathrm{d}x\,\mathrm{d}y DWdxdy\iint_{D}^{W} \, \mathrm{d}x\,\mathrm{d}y

  • 三重积分 \iiint_{E}^{V} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z EVdxdydz\iiint_{E}^{V} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z

  • 闭合的曲线、曲面积分 \oint_{C} x^3\, \mathrm{d}x + 4y^2\, \mathrm{d}y Cx3dx+4y2dy\oint_{C} x^3\, \mathrm{d}x + 4y^2\, \mathrm{d}y

  • 交集 \bigcap_1^{n} p 1np\bigcap_1^{n} p

  • 并集 \bigcup_1^{k} p 1kp\bigcup_1^{k} p

2.16 分数

通常使用\frac {分子} {分母}命令产生一个分数,分数可嵌套。便捷情况可直接输入 \frac ab 来快速生成一个 ab\frac {a} {b} 。如果分式很复杂,亦可使用 分子 \over 分母 命令,此时分数仅有一层。 功能|语法|效果

  • 分数 \frac{2}{4}=0.5 24=0.5\frac{2}{4}=0.5
  • 小型分数 \tfrac{2}{4} = 0.5 24=0.5\tfrac{2}{4} = 0.5
  • 连分式(大型嵌套分式) \cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a 2c+2d+24=a\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a
  • 大型不嵌套分式 \dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a 24=0.52c+2d+24=a\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a

2.17 二项式系数

  • 二项式系数 \dbinom{n}{r}=\binom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r} (nr)=(nnr)=Cnr=Cnnr\dbinom{n}{r}=\binom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}
  • 小型二项式系数 \tbinom{n}{r}=\tbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r} (nr)=(nnr)=Cnr=Cnnr\tbinom{n}{r}=\tbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}
  • 大型二项式系数 \binom{n}{r}=\dbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r} (nr)=(nnr)=Cnr=Cnnr\binom{n}{r}=\dbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}

在以e为底的指数函数、极限和积分中尽量不要使用 \frac符号:它会使整段函数看起来很怪,而且可能产生歧义。也正是因此它在专业数学排版中几乎从不出现。 横着写这些分式,中间使用斜线间隔/ (用斜线代替分数线)。

示例:

\begin{array}{cc}
\mathrm{Bad} & \mathrm{Better} \\
\hline \\
e^{i\frac{\pi}2} \quad e^{\frac{i\pi}2}& e^{i\pi/2} \\
\int_{-\frac\pi2}^\frac\pi2 \sin x\,dx & \int_{-\pi/2}^{\pi/2}\sin x\,dx \\
\end{array}

显示: ::: hljs-center

BadBettereiπ2eiπ2eiπ/2π2π2sinxdxπ/2π/2sinxdx\begin{array}{cc} \mathrm{Bad} & \mathrm{Better} \\ \hline \\ e^{i\frac{\pi}2} \quad e^{\frac{i\pi}2}& e^{i\pi/2} \\ \int_{-\frac\pi2}^\frac\pi2 \sin x\,dx & \int_{-\pi/2}^{\pi/2}\sin x\,dx \\ \end{array}

:::

2.18 矩阵、条件表达式、方程组

语法:

\begin{类型}
公式内容
\end{类型}

类型可以是:矩阵 matrix pmatrix bmatrix Bmatrix vmatrix Vmatrix、条件表达式 cases、多行对齐方程式 aligned、数组 array

在公式内容中:在每一行中插入 & 来指定需要对齐的内容,在每行结尾处使用 \ 换行。

  • 无框矩阵 在开头使用 begin{matrix},在结尾使用 end{matrix},在中间插入矩阵元素,每个元素之间插入 & ,并在每行结尾处使用 \\
\begin{matrix}
x & y \\
z & v
\end{matrix}

hljs-center

xyzv\begin{matrix} x & y \\ z & v \end{matrix}

  • 有框矩阵 在开头将 matrix 替换为 pmatrix bmatrix Bmatrix vmatrix Vmatrix
\begin{vmatrix}
x & y \\
z & v
\end{vmatrix}

xyzv\begin{vmatrix} x & y \\ z & v \end{vmatrix}

\begin{Vmatrix}
x & y \\
z & v
\end{Vmatrix}

xyzv\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}

使用 \cdots , \cdots, \ddots ,\cdots , \vdots, \cdots 来输入省略符号。

\begin{bmatrix}
0      & \cdots & 0      \\
\vdots & \ddots & \vdots \\
0      & \cdots & 0
\end{bmatrix}

[0000]\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}

\begin{Bmatrix}
x & y \\
z & v
\end{Bmatrix}

{xyzv}\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}

\begin{pmatrix}
x & y \\
z & v
\end{pmatrix}

(xyzv)\begin{pmatrix} x & y \\ z & v \end{pmatrix}

2.19 条件表达式

f(n) =
\begin{cases} 
n/2,  & \text{if }n\text{ is even} \\
3n+1, & \text{if }n\text{ is odd}
\end{cases}

f(n)={n/2,if n is even3n+1,if n is oddf(n) = \begin{cases} n/2, & \text{if }n\text{ is even} \\ 3n+1, & \text{if }n\text{ is odd} \end{cases}

2.20 多行等式、同余式

人们经常想要一列整齐且居中的方程式序列。使用 \begin{aligned}…\end{aligned}

\begin{aligned}
f(x) & = (m+n)^2 \\
     & = m^2+2mn+n^2 \\
\end{aligned}

f(x)=(m+n)2=m2+2mn+n2\begin{aligned} f(x) & = (m+n)^2 \\ & = m^2+2mn+n^2 \\ \end{aligned}

\begin{alignedat}{3}
f(x) & = (m-n)^2 \\
f(x) & = (-m+n)^2 \\
     & = m^2-2mn+n^2 \\
\end{alignedat}

f(x)=(mn)2f(x)=(m+n)2=m22mn+n2\begin{alignedat}{3} f(x) & = (m-n)^2 \\ f(x) & = (-m+n)^2 \\ & = m^2-2mn+n^2 \\ \end{alignedat}

2.21 方程组

\begin{cases}
3x + 5y +  z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}

{3x+5y+z7x2y+4z6x+3y+2z\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}

\left\{\begin{aligned}
3x + 5y +  z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{aligned}\right.

{3x+5y+z7x2y+4z6x+3y+2z\left\{\begin{aligned} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{aligned}\right.

2.22 数组与表格

通常,一个格式化后的表格比单纯的文字或排版后的文字更具有可读性。数组和表格均以 \begin{array} 开头,并在其后定义列数及每一列的文本对齐属性,c l r 分别代表居中、左对齐及右对齐。若需要插入垂直分割线,在定义式中插入 | ,若要插入水平分割线,在下一行输入前插入 \hline 。与矩阵相似,每行元素间均须要插入& ,每行元素以 \\ 结尾,最后以 \end{array} 结束数组。 示例1:

\begin{array}{c|lcr}
n & \text{左对齐} & \text{居中对齐} & \text{右对齐} \\
\hline
1 & 0.24 & 1 & 125 \\
2 & -1 & 189 & -8 \\
3 & -20 & 2000 & 1+10i
\end{array}

显示: n左对齐居中对齐右对齐10.24112521189832020001+10i\begin{array}{c|lcr} n & \text{左对齐} & \text{居中对齐} & \text{右对齐} \\ \hline 1 & 0.24 & 1 & 125 \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \end{array}

示例2:

\begin{array}{lcl}
z        & = & a \\
f(x,y,z) & = & x + y + z 
\end{array}

显示: z=af(x,y,z)=x+y+z\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}

示例3:

\begin{array}{lcr}
z        & = & a \\
f(x,y,z) & = & x + y + z    
\end{array}

显示: z=af(x,y,z)=x+y+z\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}

示例4:

\begin{array}{ccc}
a & b & S \\
\hline
0&0&1\\
0&1&1\\
1&0&1\\
1&1&0\\
\end{array}

显示: abS001011101110\begin{array}{ccc} a & b & S \\ \hline 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0\\ \end{array}

2.23 嵌套数组或表格

多个数组/表格可 互相嵌套 并组成一组数组/一组表格。 使用嵌套前必须声明 $$ 符号。 示例:

% outer vertical array of arrays 外层垂直表格
\begin{array}{c}
    % inner horizontal array of arrays 内层水平表格
    \begin{array}{cc}
        % inner array of minimum values 内层"最小值"数组
        \begin{array}{c|cccc}
        \text{min} & 0 & 1 & 2 & 3\\
        \hline
        0 & 0 & 0 & 0 & 0\\
        1 & 0 & 1 & 1 & 1\\
        2 & 0 & 1 & 2 & 2\\
        3 & 0 & 1 & 2 & 3
        \end{array}
    &
        % inner array of maximum values 内层"最大值"数组
        \begin{array}{c|cccc}
        \text{max}&0&1&2&3\\
        \hline
        0 & 0 & 1 & 2 & 3\\
        1 & 1 & 1 & 2 & 3\\
        2 & 2 & 2 & 2 & 3\\
        3 & 3 & 3 & 3 & 3
        \end{array}
    \end{array}
    % 内层第一行表格组结束
    \\
    % inner array of delta values 内层第二行Delta值数组
        \begin{array}{c|cccc}
        \Delta&0&1&2&3\\
        \hline
        0 & 0 & 1 & 2 & 3\\
        1 & 1 & 0 & 1 & 2\\
        2 & 2 & 1 & 0 & 1\\
        3 & 3 & 2 & 1 & 0
        \end{array}
        % 内层第二行表格组结束
\end{array}

显示: min012300000101112012230123max012300123111232222333333Δ012300123110122210133210% outer vertical array of arrays 外层垂直表格 \begin{array}{c} % inner horizontal array of arrays 内层水平表格 \begin{array}{cc} % inner array of minimum values 内层"最小值"数组 \begin{array}{c|cccc} \text{min} & 0 & 1 & 2 & 3\\ \hline 0 & 0 & 0 & 0 & 0\\ 1 & 0 & 1 & 1 & 1\\ 2 & 0 & 1 & 2 & 2\\ 3 & 0 & 1 & 2 & 3 \end{array} & % inner array of maximum values 内层"最大值"数组 \begin{array}{c|cccc} \text{max}&0&1&2&3\\ \hline 0 & 0 & 1 & 2 & 3\\ 1 & 1 & 1 & 2 & 3\\ 2 & 2 & 2 & 2 & 3\\ 3 & 3 & 3 & 3 & 3 \end{array} \end{array} % 内层第一行表格组结束 \\ % inner array of delta values 内层第二行Delta值数组 \begin{array}{c|cccc} \Delta&0&1&2&3\\ \hline 0 & 0 & 1 & 2 & 3\\ 1 & 1 & 0 & 1 & 2\\ 2 & 2 & 1 & 0 & 1\\ 3 & 3 & 2 & 1 & 0 \end{array} % 内层第二行表格组结束 \end{array}

2.24 用数组实现带分割符号的矩阵

示例:

\left[
    \begin{array}{cc|c}
      1&2&3\\
      4&5&6
    \end{array}
\right]

显示:

[123456]\left[ \begin{array}{cc|c} 1&2&3\\ 4&5&6 \end{array} \right]

其中 cc|c 代表在一个三列矩阵中的第二和第三列之间插入分割线。

2.25 括号

()[]| 表示符号本身,使用 \{\} 来表示 {}

  • 短括号 \frac{1}{2} 12\frac{1}{2}
  • 长括号 \left(\frac{1}{2} \right) (12)\left(\frac{1}{2} \right)

使用 \left\right 来创建自动匹配高度的 (圆括号),[方括号] 和 {花括号}

  • 圆括号,小括号 \left( \frac{a}{b} \right) (ab)\left( \frac{a}{b} \right)

  • 方括号,中括号 \left[ \frac{a}{b} \right] [ab]\left[ \frac{a}{b} \right]

  • 花括号,大括号 \left{ \frac{a}{b} \right}

\left{ \frac{a}{b} \right}

  • 角括号 \left \langle \frac{a}{b} \right \rangle ab\left \langle \frac{a}{b} \right \rangle
  • 单竖线,绝对值 \left| \frac{a}{b} \right| ab\left| \frac{a}{b} \right|
  • 双竖线,范 \left \| \frac{a}{b} \right \| ab\left \| \frac{a}{b} \right \|
  • 取整函数 \left \lfloor \frac{a}{b} \right \rfloor ab\left \lfloor \frac{a}{b} \right \rfloor
  • 取顶函数 \left \lceil \frac{c}{d} \right \rceil cd\left \lceil \frac{c}{d} \right \rceil
  • 斜线与反斜线 \left / \frac{a}{b} \right \backslash /ab\\left / \frac{a}{b} \right \backslash
  • 上下箭头 \left / \frac{a}{b} \right \backslash /ab\\left / \frac{a}{b} \right \backslash
  • 混合括号 \left[ 0,1 \right) [0,1)\left[ 0,1 \right)
  • 单左括号 \left \{\frac{a}{b} \right. {ab\left \{\frac{a}{b} \right.
  • 单右括号 \left. \frac{a}{b} \right \} ab}\left. \frac{a}{b} \right \}

可以使用 \big, \Big, \bigg, \Bigg 控制括号的大小,比如代码 \Bigg ( \bigg [ \Big \{ \big \langle \left | \| \frac{a}{b} \| \right | \big \rangle \Big \} \bigg ] \Bigg ) 显示︰ ([{ab}])\Bigg ( \bigg [ \Big \{ \big \langle \left | \| \frac{a}{b} \| \right | \big \rangle \Big \} \bigg ] \Bigg )

2.28 颜色

使用 \color{颜色}{文字} 来更改特定的文字颜色。 更改文字颜色 需要浏览器支持 ,如果浏览器不知道你所需的颜色,那么文字将被渲染为黑色。

\begin{array}{|rrrrrrrr|}\hline
\verb+#000+ & \color{#000}{text} & & &
\verb+#00F+ & \color{#00F}{text} & & \\
& & \verb+#0F0+ & \color{#0F0}{text} &
& & \verb+#0FF+ & \color{#0FF}{text}\\
\verb+#F00+ & \color{#F00}{text} & & &
\verb+#F0F+ & \color{#F0F}{text} & & \\
& & \verb+#FF0+ & \color{#FF0}{text} &
& & \verb+#FFF+ & \color{#FFF}{text}\\
\hline
\end{array}

#000text#00Ftext#0F0text#0FFtext#F00text#F0Ftext#FF0text#FFFtext\begin{array}{|rrrrrrrr|}\hline \verb+#000+ & \color{#000}{text} & & & \verb+#00F+ & \color{#00F}{text} & & \\ & & \verb+#0F0+ & \color{#0F0}{text} & & & \verb+#0FF+ & \color{#0FF}{text}\\ \verb+#F00+ & \color{#F00}{text} & & & \verb+#F0F+ & \color{#F0F}{text} & & \\ & & \verb+#FF0+ & \color{#FF0}{text} & & & \verb+#FFF+ & \color{#FFF}{text}\\ \hline \end{array}