帮助:数学公式
本页面仅提供代码的简单参考，若想准确地使用LaTeX表达数学公式，请自行学习相关知识。
本页面仅提供代码的简单参考，若想准确地使用LaTeX表达数学公式，请自行学习相关知识。
PRTS通过使用LaTeX的变体和HTML标记的组合来渲染数学公式。
在页面中使用数学记号前，您应先确保页面中含有代码{{#Widget:Math}}
代码
首先，您应当在页面中输入代码{{#Widget:Math}}，否则数学记号将无法正常显示。
然后，您可以将数学记号放在合适的分隔符内，分隔符的选择取决于您排版的需要。
内联样式
当您要使用内联样式表现数学公式时，您可以选择使用 \( \) 来分隔数学记号与正文。
例如：
The well known Pythagorean theorem \(x^2 + y^2 = z^2\) was proved to be invalid for other exponents.
The well known Pythagorean theorem \(x^2 + y^2 = z^2\) was proved to be invalid for other exponents.
行内框样式
当您要使用行内框样式表现数学公式时，您可以选择使用 \[ \] 或 \begin{equation*} \end{equation*} 来分隔数学记号与正文。
例如：
The mass-energy equivalence is described by the famous equation
\[E=mc^2\]
discovered in 1905 by Albert Einstein. In natural units (\(c\) = 1), the formula expresses the identity
\begin{equation*} E=m \end{equation*}
The mass-energy equivalence is described by the famous equation
\[E=mc^2\]
discovered in 1905 by Albert Einstein.
In natural units (\(c\) = 1), the formula expresses the identity
\begin{equation*}
E=m
\end{equation*}
当您要表现的对象有编号时，则应该使用 \begin{equation} \end{equation} ，尽管 $$ $$ 也可实现同样的功能，但已不再推荐使用。
对齐样式
当您需要多个统一对齐的数学公式时，您应当使用 \begin{align} \end{align} ，若该公式过长，您可以配合使用 \begin{aligned} \end{aligned} 来分列表现公式的各个部分。
\begin{align} 2x+3 &= 7 & 2x+3-3 &= 7-3 \\ 2x &= 4 & \frac{2x}2 &= \frac42\\ x &= 2 \end{align}
\begin{align}
2x+3 &= 7 & 2x+3-3 &= 7-3 \\
2x &= 4 & \frac{2x}2 &= \frac42\\
x &= 2
\end{align}
函数、符号及特殊字符
声调/变音符号 | |
|---|---|
\dot{a}, \ddot{a}, \acute{a}, \grave{a}
|
\(\dot{a}, \ddot{a}, \acute{a}, \grave{a}\) |
\check{a}, \breve{a}, \tilde{a}, \bar{a}
|
\(\check{a}, \breve{a}, \tilde{a}, \bar{a}\) |
\hat{a}, \widehat{a}, \vec{a}
|
\(\hat{a}, \widehat{a}, \vec{a}\) |
标准函数 | |
\exp_a b = a^b, \exp b = e^b, 10^m
|
\(\exp_a b = a^b, \exp b = e^b, 10^m\) |
\ln c, \lg d = \log e, \log_{10} f
|
\(\ln c, \lg d = \log e, \log_{10} f\) |
\sin a, \cos b, \tan c, \cot d, \sec e, \csc f
|
\(\sin a, \cos b, \tan c, \cot d, \sec e, \csc f\) |
\arcsin a, \arccos b, \arctan c
|
\(\arcsin a, \arccos b, \arctan c\) |
\arccot d, \arcsec e, \arccsc f
|
\(\arccot d, \arcsec e, \arccsc f\) |
\sinh a, \cosh b, \tanh c, \coth d
|
\(\sinh a, \cosh b, \tanh c, \coth d\) |
\operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n
|
\(\operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n\) |
\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q
|
\(\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q\) |
\sgn r, \left\vert s \right\vert
|
\(\sgn r, \left\vert s \right\vert\) |
\min(x,y), \max(x,y)
|
\(\min(x,y), \max(x,y)\) |
界限 | |
\min x, \max y, \inf s, \sup t
|
\(\min x, \max y, \inf s, \sup t\) |
\lim u, \liminf v, \limsup w
|
\(\lim u, \liminf v, \limsup w\) |
\dim p, \deg q, \det m, \ker\phi
|
\(\dim p, \deg q, \det m, \ker\phi\) |
投射 | |
\Pr j, \hom l, \lVert z \rVert, \arg z
|
\(\Pr j, \hom l, \lVert z \rVert, \arg z\) |
微分及导数 | |
dt, \mathrm{d}t, \partial t, \nabla\psi
|
\(dt, \mathrm{d}t, \partial t, \nabla\psi\) |
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
|
\(dy/dx, \mathrm{d}y/\mathrm{d}x, \frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x}, \frac{\partial^2}{\partial x_1\partial x_2}y\) |
\prime, \backprime, f^\prime, f', f, f^{(3)}, \dot y, \ddot y
|
\(\prime, \backprime, f^\prime, f', f, f^{(3)} \!, \dot y, \ddot y\) |
类字母符号及常数 | |
\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar
|
\(\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar\) |
\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS, \S, \P, \AA
|
\(\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS, \S, \P, \AA\) |
模算数 | |
s_k \equiv 0 \pmod{m}
|
\(s_k \equiv 0 \pmod{m}\) |
a \bmod b
|
\(a \bmod b\) |
\gcd(m, n), \operatorname{lcm}(m, n)
|
\(\gcd(m, n), \operatorname{lcm}(m, n)\) |
\mid, \nmid, \shortmid, \nshortmid
|
\(\mid, \nmid, \shortmid, \nshortmid\) |
根号 | |
\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{\frac{x^3+y^3}{2}}
|
\(\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{\frac{x^3+y^3}{2}}\) |
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
|
\(\bigoplus, \bigotimes, \bigodot\) |
集合 | |
\{ \}, \O \empty \emptyset, \varnothing
|
\(\{ \}, \O \empty \emptyset, \varnothing\) |
\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
|
\(\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq\) |
关系符号 | |
=, \ne, \neq, \equiv, \not\equiv
|
\(=, \ne, \neq, \equiv, \not\equiv\) |
\doteq, \doteqdot, \overset{\underset{\mathrm{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
|
\(\leqslant, \nleqslant, \eqslantless\) |
\geqslant, \ngeqslant, \eqslantgtr
|
\(\geqslant, \ngeqslant, \eqslantgtr\) |
\lesssim, \lnsim, \lessapprox, \lnapprox
|
\(\lesssim, \lnsim, \lessapprox, \lnapprox\) |
\gtrsim, \gnsim, \gtrapprox, \gnapprox
|
\(\gtrsim, \gnsim, \gtrapprox, \gnapprox\) |
\prec, \nprec, \preceq, \npreceq, \precneqq
|
\(\prec, \nprec, \preceq, \npreceq, \precneqq\) |
\succ, \nsucc, \succeq, \nsucceq, \succneqq
|
\(\succ, \nsucc, \succeq, \nsucceq, \succneqq\) |
\preccurlyeq, \curlyeqprec
|
\(\preccurlyeq, \curlyeqprec\) |
\succcurlyeq, \curlyeqsucc
|
\(\succcurlyeq, \curlyeqsucc\) |
\precsim, \precnsim, \precapprox, \precnapprox
|
\(\precsim, \precnsim, \precapprox, \precnapprox\) |
\succsim, \succnsim, \succapprox, \succnapprox
|
\(\succsim, \succnsim, \succapprox, \succnapprox\) |
几何符号 | |
\parallel, \nparallel, \shortparallel, \nshortparallel
|
\(\parallel, \nparallel, \shortparallel, \nshortparallel\) |
\perp, \angle, \sphericalangle, \measuredangle, 45^\circ
|
\(\perp, \angle, \sphericalangle, \measuredangle, 45^\circ\) |
\Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar
|
\(\Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar\) |
\bigcirc, \triangle, \bigtriangleup, \bigtriangledown
|
\(\bigcirc, \triangle, \bigtriangleup, \bigtriangledown\) |
\vartriangle, \triangledown
|
\(\vartriangle, \triangledown\) |
\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright
|
\(\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright\) |
逻辑符号 | |
\forall, \exists, \nexists
|
\(\forall, \exists, \nexists\) |
\therefore, \because, \And
|
\(\therefore, \because, \And\) |
\or \lor \vee, \curlyvee, \bigvee
|
\(\or, \lor, \vee, \curlyvee, \bigvee\) |
\and \land \wedge, \curlywedge, \bigwedge
|
\(\and, \land, \wedge, \curlywedge, \bigwedge\) |
\bar{q}, \bar{abc}, \overline{q}, \overline{abc},
|
\(\bar{q}, \bar{abc}, \overline{q}, \overline{abc},\) \(\lnot \neg, \not\operatorname{R}, \bot, \top\) |
\vdash \dashv, \vDash, \Vdash, \models
|
\(\vdash, \dashv, \vDash, \Vdash, \models\) |
\Vvdash \nvdash \nVdash \nvDash \nVDash
|
\(\Vvdash, \nvdash, \nVdash, \nvDash, \nVDash\) |
\ulcorner \urcorner \llcorner \lrcorner
|
\(\ulcorner \urcorner \llcorner \lrcorner\) |
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
|
\(\hookrightarrow, \hookleftarrow, \multimap, \leftrightsquigarrow, \rightsquigarrow, \twoheadrightarrow, \twoheadleftarrow\) |
特殊符号 | |
\amalg \P \S \% \dagger \ddagger \ldots \cdots
|
\(\amalg \P \S \% \dagger \ddagger \ldots \cdots\) |
\smile \frown \wr \triangleleft \triangleright
|
\(\smile \frown \wr \triangleleft \triangleright\) |
\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp
|
\(\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp\) |
未排序 | |
\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
|
\(\trianglelefteq, \ntrianglelefteq, \trianglerighteq, \ntrianglerighteq\) |
关于这些符号的更多语义，参阅TeX Cookbook的简述。
上标、下标及积分等
| 功能 | 语法 | 效果 |
|---|---|---|
| 上标 | a^2 |
\( a^2\) |
| 下标 | a_2 |
\( a_2\) |
| 组合 | a^{2+2} |
\( a^{2+2}\) |
a_{i,j} |
\( a_{i,j}\) | |
| 结合上下标 | x_2^3 |
\( x_2^3\) |
| 前置上下标 | {}_1^2\!X_3^4 |
\( {}_1^2\!X_3^4\) |
| 导数 （HTML） |
x' |
\( x'\) |
| 导数 （PNG） |
x^\prime |
\( x^\prime\) |
| 导数 （错误） |
x\prime |
\( x\prime\) |
| 导数点 | \dot{x}
|
\( \dot{x}\) |
\ddot{y}
|
\( \ddot{y}\) | |
| 向量 | \vec{c}
|
\( \vec{c}\) |
\overleftarrow{a b}
|
\( \overleftarrow{a b}\) | |
\overrightarrow{c d}
|
\( \overrightarrow{c d}\) | |
\overleftrightarrow{a b}
|
\( \overleftrightarrow{a b}\) | |
\widehat{e f g}
|
\( \widehat{e f g}\) | |
| 上弧 （註: 正確應該用 \overarc，但在這裡行不通。要用建議的語法作為解決辦法。）（使用\overarc時需要引入{arcs}套件。） |
\overset{\frown} {AB}
|
\( \overset{\frown} {AB}\) |
| 上划线 | \overline{h i j}
|
\( \overline{h i j}\) |
| 下划线 | \underline{k l m}
|
\( \underline{k l m}\) |
| 上括号 | \overbrace{1+2+\cdots+100}
|
\( \overbrace{1+2+\cdots+100}\) |
\begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix}
|
\( \begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix}\) | |
| 下括号 | \underbrace{a+b+\cdots+z}
|
\( \underbrace{a+b+\cdots+z}\) |
\begin{matrix} \underbrace{ a+b+\cdots+z } \\ 26 \end{matrix}
|
\( \begin{matrix} \underbrace{ a+b+\cdots+z } \\ 26 \end{matrix}\) | |
| 求和 | \sum_{k=1}^N k^2 |
\( \sum_{k=1}^N k^2\) |
\begin{matrix} \sum_{k=1}^N k^2 \end{matrix} |
\( \begin{matrix} \sum_{k=1}^N k^2 \end{matrix}\) | |
| 求积 | \prod_{i=1}^N x_i |
\( \prod_{i=1}^N x_i\) |
\begin{matrix} \prod_{i=1}^N x_i \end{matrix} |
\( \begin{matrix} \prod_{i=1}^N x_i \end{matrix}\) | |
| 上积 | \coprod_{i=1}^N x_i |
\( \coprod_{i=1}^N x_i\) |
\begin{matrix} \coprod_{i=1}^N x_i \end{matrix} |
\( \begin{matrix} \coprod_{i=1}^N x_i \end{matrix}\) | |
| 极限 | \lim_{n \to \infty}x_n |
\( \lim_{n \to \infty}x_n\) |
\begin{matrix} \lim_{n \to \infty}x_n \end{matrix} |
\( \begin{matrix} \lim_{n \to \infty}x_n \end{matrix}\) | |
| 积分 | \int_{-N}^{N} e^x\, \mathrm{d}x |
\( \int_{-N}^{N} e^x\, \mathrm{d}x\) |
\begin{matrix} \int_{-N}^{N} e^x\, \mathrm{d}x \end{matrix} |
\( \begin{matrix} \int_{-N}^{N} e^x\, \mathrm{d}x \end{matrix}\) | |
| 双重积分 | \iint_{D}^{W} \, \mathrm{d}x\,\mathrm{d}y |
\( \iint_{D}^{W} \, \mathrm{d}x\,\mathrm{d}y\) |
| 三重积分 | \iiint_{E}^{V} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z |
\( \iiint_{E}^{V} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z\) |
| 四重积分 | \iiiint_{F}^{U} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z\,\mathrm{d}t |
\( \iiiint_{F}^{U} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z\,\mathrm{d}t\) |
| 闭合的路径积分、曲面积分 | \oint_{C} x^3\, \mathrm{d}x + 4y^2\, \mathrm{d}y |
\( \oint_{C} x^3\, \mathrm{d}x + 4y^2\, \mathrm{d}y\) |
| 交集 | \bigcap_1^{n} p |
\( \bigcap_1^{n} p\) |
| 并集 | \bigcup_1^{k} p |
\( \bigcup_1^{k} p\) |
分数、矩阵和多行列式
| 功能 | 语法 | 效果 |
|---|---|---|
| 分数 | \frac{2}{4}=0.5 |
\(\frac{2}{4}=0.5\) |
| 小型分数 | \tfrac{2}{4} = 0.5
|
\(\tfrac{2}{4} = 0.5\) |
| 大型分数（嵌套） | \cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a
|
\(\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a\) |
| 大型分数（不嵌套） | \dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a
|
\(\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a\) |
| 二项式系数 | \dbinom{n}{r}=\binom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}
|
\(\dbinom{n}{r}=\binom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}\) |
n \choose n-r, n^2 \choose r_1, a-b \choose c+d, {n \choose 0}+{n \choose 1}
|
\(n \choose n-r\) \(n^2 \choose r_1\) \(a-b \choose c+d\) \({n \choose 0}+{n \choose 1}\) | |
| 小型二项式系数 | \tbinom{n}{r}=\tbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}
|
\(\tbinom{n}{r}=\tbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}\) |
| 大型二项式系数 | \binom{n}{r}=\dbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}
|
\(\binom{n}{r}=\dbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}\) |
| 矩阵 | \begin{smallmatrix}
a&b\\ c&d
\end{smallmatrix}
|
\begin{smallmatrix} a&b\\ c&d \end{smallmatrix} |
| 多行等式、同餘式 | \begin{align}
f(x) & = (m+n)^2 \\
& = m^2+2mn+n^2 \\
\end{align}
|
\begin{align} f(x) & = (m+n)^2 \\ & = m^2+2mn+n^2 \\ \end{align} |
\begin{alignat}{3}
f(x) & = (m-n)^2 \\
f(x) & = (-m+n)^2 \\
& = m^2-2mn+n^2 \\
\end{alignat}
|
\begin{alignat}{3} f(x) & = (m-n)^2 \\ f(x) & = (-m+n)^2 \\ & = m^2-2mn+n^2 \\ \end{alignat} | |
| 长公式换行 |
\(f(x) \,\!\)
\(= \sum_{n=0}^\infty a_n x^n \)
\(= a_0+a_1x+a_2x^2+\cdots\)
|
\(f(x) \,\!\)\(= \sum_{n=0}^\infty a_n x^n \)\(= a_0 +a_1x+a_2x^2+\cdots\) |
| 方程组 | \begin{cases}
3x + 5y + z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}
|
\(\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}\) |
| 数组 | \begin{array}{|c|c||c|} a & b & S \\
\hline
0&0&1\\
0&1&1\\
1&0&1\\
1&1&0\\
\end{array}
|
\begin{array}{|c|c||c|} a & b & S \\ \hline 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0\\ \end{array} |
字体
| 希腊字母 | |
|---|---|
\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta
|
\(\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta\) |
\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi
|
\(\Iota \Kappa \Lambda \Mu \Nu \Omicron \Xi \Pi\) |
\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega
|
\(\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega\) |
\alpha \beta \gamma \delta \epsilon \zeta \eta \theta
|
\(\alpha \beta \gamma \delta \epsilon \zeta \eta \theta\) |
\iota \kappa \lambda \mu \nu \omicron \xi \pi
|
\(\iota \kappa \lambda \mu \nu \omicron \xi \pi\) |
\rho \sigma \tau \upsilon \phi \chi \psi \omega
|
\(\rho \sigma \tau \upsilon \phi \chi \psi \omega\) |
\varepsilon \digamma \varkappa \varpi
|
\(\varepsilon \digamma \varkappa \varpi\) |
\varrho \varsigma \vartheta \varphi
|
\(\varrho \varsigma \vartheta \varphi\) |
| 希伯来符号 | |
\aleph \beth \gimel \daleth
|
\(\aleph \beth \gimel \daleth\) |
| 黑板报粗体 | |
\mathbb{ABCDEFGHI}
|
\(\mathbb{ABCDEFGHI}\) |
\mathbb{JKLMNOPQR}
|
\(\mathbb{JKLMNOPQR}\) |
\mathbb{STUVWXYZ}
|
\(\mathbb{STUVWXYZ}\) |
| 粗体 | |
\mathbf{ABCDEFGHI}
|
\(\mathbf{ABCDEFGHI}\) |
\mathbf{JKLMNOPQR}
|
\(\mathbf{JKLMNOPQR}\) |
\mathbf{STUVWXYZ}
|
\(\mathbf{STUVWXYZ}\) |
\mathbf{abcdefghijklm}
|
\(\mathbf{abcdefghijklm}\) |
\mathbf{nopqrstuvwxyz}
|
\(\mathbf{nopqrstuvwxyz}\) |
\mathbf{0123456789}
|
\(\mathbf{0123456789}\) |
| 粗体希腊字母 | |
\boldsymbol{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta}
|
\(\boldsymbol{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta}\) |
\boldsymbol{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho}
|
\(\boldsymbol{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho}\) |
\boldsymbol{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega}
|
\(\boldsymbol{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega}\) |
\boldsymbol{\alpha\beta\gamma\delta\epsilon\zeta\eta\theta}
|
\(\boldsymbol{\alpha\beta\gamma\delta\epsilon\zeta\eta\theta}\) |
\boldsymbol{\iota\kappa\lambda\mu\nu\xi\pi\rho}
|
\(\boldsymbol{\iota\kappa\lambda\mu\nu\xi\pi\rho}\) |
\boldsymbol{\sigma\tau\upsilon\phi\chi\psi\omega}
|
\(\boldsymbol{\sigma\tau\upsilon\phi\chi\psi\omega}\) |
\boldsymbol{\varepsilon\digamma\varkappa\varpi}
|
\(\boldsymbol{\varepsilon\digamma\varkappa\varpi}\) |
\boldsymbol{\varrho\varsigma\vartheta\varphi}
|
\(\boldsymbol{\varrho\varsigma\vartheta\varphi}\) |
| 斜体（拉丁字母默认） | |
\mathit{0123456789}
|
\(\mathit{0123456789}\) |
| 斜体希腊字母（小写字母默认） | |
\mathit{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta}
|
\(\mathit{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta}\) |
\mathit{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho}
|
\(\mathit{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho}\) |
\mathit{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega}
|
\(\mathit{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega}\) |
| 罗马体 | |
\mathrm{ABCDEFGHI}
|
\(\mathrm{ABCDEFGHI}\) |
\mathrm{JKLMNOPQR}
|
\(\mathrm{JKLMNOPQR}\) |
\mathrm{STUVWXYZ}
|
\(\mathrm{STUVWXYZ}\) |
\mathrm{abcdefghijklm}
|
\(\mathrm{abcdefghijklm}\) |
\mathrm{nopqrstuvwxyz}
|
\(\mathrm{nopqrstuvwxyz}\) |
\mathrm{0123456789}
|
\(\mathrm{0123456789}\) |
| 无衬线体 | |
\mathsf{ABCDEFGHI}
|
\(\mathsf{ABCDEFGHI}\) |
\mathsf{JKLMNOPQR}
|
\(\mathsf{JKLMNOPQR}\) |
\mathsf{STUVWXYZ}
|
\(\mathsf{STUVWXYZ}\) |
\mathsf{abcdefghijklm}
|
\(\mathsf{abcdefghijklm}\) |
\mathsf{nopqrstuvwxyz}
|
\(\mathsf{nopqrstuvwxyz}\) |
\mathsf{0123456789}
|
\(\mathsf{0123456789}\) |
| 无衬线体希腊字母（仅大写） | |
\mathsf{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}
|
\(\mathsf{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}\) |
\mathsf{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho}
|
\(\mathsf{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho}\) |
\mathsf{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}
|
\(\mathsf{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}\) |
| 手写体/花体 | |
\mathcal{ABCDEFGHI}
|
\(\mathcal{ABCDEFGHI}\) |
\mathcal{JKLMNOPQR}
|
\(\mathcal{JKLMNOPQR}\) |
\mathcal{STUVWXYZ}
|
\(\mathcal{STUVWXYZ}\) |
| Fraktur体 | |
\mathfrak{ABCDEFGHI}
|
\(\mathfrak{ABCDEFGHI}\) |
\mathfrak{JKLMNOPQR}
|
\(\mathfrak{JKLMNOPQR}\) |
\mathfrak{STUVWXYZ}
|
\(\mathfrak{STUVWXYZ}\) |
\mathfrak{abcdefghijklm}
|
\(\mathfrak{abcdefghijklm}\) |
\mathfrak{nopqrstuvwxyz}
|
\(\mathfrak{nopqrstuvwxyz}\) |
\mathfrak{0123456789}
|
\(\mathfrak{0123456789}\) |
| 小型手写体 | |
{\scriptstyle\text{abcdefghijklm}}
|
\({\scriptstyle\text{abcdefghijklm}}\) |
混合字体
| 特征 | 语法 | 渲染效果 |
|---|---|---|
| 斜体字符（忽略空格） | x y z
|
\(x y z\) |
| 非斜体字符 | \text{x y z}
|
\(\text{x y z}\) |
| 混合斜体（差） | \text{if} n \text{is even}
|
\(\text{if} n \text{is even}\) |
| 混合斜体（好） | \text{if }n\text{ is even}
|
\(\text{if }n\text{ is even}\) |
| 混合斜体（ 替代品：~ 或者"\ "强制空格） | \text{if}~n\ \text{is even}
|
\(\text{if}~n\ \text{is even}\) |
括号
| 功能 | 语法 | 显示 |
|---|---|---|
| 短括号 | ( \frac{1}{2} ) | \(( \frac{1}{2} )\) |
| 长括号 | \left( \frac{1}{2} \right) | \(\left ( \frac{1}{2} \right )\) |
您可以使用 \left 和 \right 来显示不同的括号：
| 功能 | 语法 | 显示 |
|---|---|---|
| 圆括号，小括号 | \left( \frac{a}{b} \right) | \(\left( \frac{a}{b} \right)\) |
| 方括号，中括号 | \left[ \frac{a}{b} \right] | \(\left[ \frac{a}{b} \right]\) |
| 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 | \(\left\langle \frac{a}{b} \right \rangle\) |
| 取整函数 | \left \lfloor \frac{a}{b} \right \rfloor | \(\left \lfloor \frac{a}{b} \right \rfloor\) |
| 取顶函数 | \left \lceil \frac{c}{d} \right \rceil | \(\left \lceil \frac{c}{d} \right \rceil\) |
| 斜线与反斜线 | \left / \frac{a}{b} \right \backslash | \(\left / \frac{a}{b} \right \backslash \) |
| 上下箭头 | \left \uparrow \frac{a}{b} \right \downarrow | \(\left \uparrow \frac{a}{b} \right \downarrow \) |
| \left \Uparrow \frac{a}{b} \right \Downarrow | \(\left \Uparrow \frac{a}{b} \right \Downarrow \) | |
| \left \updownarrow \frac{a}{b} \right \Updownarrow | \(\left \updownarrow \frac{a}{b} \right \Updownarrow\) | |
| 单左括号 | \left \{ \frac{a}{b} \right . | \(\left \{ \frac{a}{b} \right .\) |
| 单右括号 | \left . \frac{a}{b} \right \} | \(\left . \frac{a}{b} \right \}\) |
备注：
- 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︰
- \(\Bigg ( \bigg [ \Big \{ \big \langle \left | \| \frac{a}{b} \| \right | \big \rangle \Big \} \bigg ] \Bigg )\)
空格
| 功能 | 语法 | 显示 | 宽度 |
|---|---|---|---|
| 2个quad空格 | \alpha\qquad\beta
|
\(\alpha\qquad\beta\) | \(2m\ \) |
| quad空格 | \alpha\quad\beta
|
\(\alpha\quad\beta\) | \(m\ \) |
| 大空格 | \alpha\ \beta
|
\(\alpha\ \beta\) | \(\frac{m}{3}\) |
| 中等空格 | \alpha\;\beta
|
\(\alpha\;\beta\) | \(\frac{2m}{7}\) |
| 小空格 | \alpha\,\beta
|
\(\alpha\,\beta\) | \(\frac{m}{6}\) |
| 紧贴 | \alpha\!\beta
|
\(\alpha\!\beta\) | \(-\frac{m}{6}\) |