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目录
- 行间公式
- 各种数学符号和特性
- 算符名称
- \text 命令
- 积分与求和
- 插入表格
- 交换图
- 使用数学字体
- 参考文献
行间公式
- 简介
- 单个公式
- 不带对齐的换行公式
- 对齐的换行公式
- 不带对齐的公式组
- 带有多列对齐的公式组
- 对齐构建区块
- 调整标签的位置
- 垂直间距与多行公式的换行
- 中断行间公式
- 公式编号
- 编号秩序
- 编号公式的交叉引用
- 附属编号序列
- 编号风格
各种数学符号和特性
函数、符号及特殊字符
| 声调/变音符号 | |
|---|---|
| \dot{a}, \ddot{a}, \acute{a}, \grave{a} | ${\displaystyle {\dot {a}},{\ddot {a}},{\acute {a}},{\grave {a}}}$ |
| \check{a}, \breve{a}, \tilde{a}, \bar{a} | ${\displaystyle {\check {a}},{\breve {a}},{\tilde {a}},{\bar {a}}}$ |
| \hat{a}, \widehat{a}, \vec{a} | ${\displaystyle {\hat {a}},{\widehat {a}},{\vec {a}}}$ |
| 标准函数 | |
| \exp_a b = a^b, \exp b = e^b, 10^m | ${\displaystyle \exp _{a}b=a^{b},\exp b=e^{b},10^{m}}$ |
| \ln c, \lg d = \log e, \log_{10} f | ${\displaystyle \ln c,\lg d=\log e,\log _{10}f}$ |
| \sin a, \cos b, \tan c, \cot d, \sec e, \csc f | ${\displaystyle \sin a,\cos b,\tan c,\cot d,\sec e,\csc f}$ |
| \arcsin a, \arccos b, \arctan c | ${\displaystyle \arcsin a,\arccos b,\arctan c}$ |
| \arccot d, \arcsec e, \arccsc f | ${\displaystyle \operatorname {arccot} d,\operatorname {arcsec} e,\operatorname {arccsc} f}$ |
| \sinh a, \cosh b, \tanh c, \coth d | ${\displaystyle \sinh a,\cosh b,\tanh c,\coth d}$ |
| \operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n | ${\displaystyle \operatorname {sh} k,\operatorname {ch} l,\operatorname {th} m,\operatorname {coth} n}$ |
| \operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q | ${\displaystyle \operatorname {argsh} o,\operatorname {argch} p,\operatorname {argth} q}$ |
| \sgn r, \left\vert s \right\vert | ${\displaystyle \operatorname {sgn} r,\left\vert s\right\vert }$ |
| \min(x,y), \max(x,y) | ${\displaystyle \min(x,y),\max(x,y)}$ |
| 界限 | |
| \min x, \max y, \inf s, \sup t | ${\displaystyle \min x,\max y,\inf s,\sup t}$ |
| \lim u, \liminf v, \limsup w | ${\displaystyle \lim u,\liminf v,\limsup w}$ |
| \dim p, \deg q, \det m, \ker\phi | ${\displaystyle \dim p,\deg q,\det m,\ker \phi }$ |
| 投射 | |
| \Pr j, \hom l, \lVert z \rVert, \arg z | ${\displaystyle \Pr j,\hom l,\lVert z\rVert ,\arg z}$ |
| 微分及导数 | |
| dt, \mathrm{d}t, \partial t, \nabla\psi | ${\displaystyle dt,\mathrm {d} t,\partial t,\nabla \psi }$ |
| 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 | ${\displaystyle dy/dx,\mathrm {d} y/\mathrm {d} x,{\frac {dy}{dx}},{\frac {\mathrm {d} y}{\mathrm {d} x}},{\frac {\partial ^{2}}{\partial x_{1}\partial x_{2}}}y}$ |
| \prime, \backprime, f^\prime, f’, f’’, f^{(3)}, \dot y, \ddot y | ${\displaystyle \prime ,\backprime ,f^{\prime },f’,f’’,f^{(3)}!,{\dot {y}},{\ddot {y}}}$ |
| 类字母符号及常数 | |
| \infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar | ${\displaystyle \infty ,\aleph ,\complement ,\backepsilon ,\eth ,\Finv ,\hbar }$ |
| \Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS, \S, \P, \AA | ${\displaystyle \Im ,\imath ,\jmath ,\Bbbk ,\ell ,\mho ,\wp ,\Re ,\circledS ,\S ,\P ,\unicode{x212B} }$ |
| 模算数 | |
| s_k \equiv 0 \pmod{m} | ${\displaystyle s_{k}\equiv 0{\pmod {m}}}$ |
| a \bmod b | ${\displaystyle a{\bmod {b}}}$ |
| \gcd(m, n), \operatorname{lcm}(m, n) | ${\displaystyle \gcd(m,n),\operatorname {lcm} (m,n)}$ |
| \mid, \nmid, \shortmid, \nshortmid | ${\displaystyle \mid ,\nmid ,\shortmid ,\nshortmid }$ |
| 根号 | |
| \surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{\frac{x^3+y^3}{2}} | $\displaystyle \surd ,\sqrt {2},{\sqrt[{n}]{}},{\sqrt[{3}]{\frac {x^{3}+y^{3}}{2}}}$ |
| 运算符 | |
| +, -, \pm, \mp, \dotplus | ${\displaystyle +,-,\pm ,\mp ,\dotplus }$ |
| \times, \div, \divideontimes, /, \backslash | ${\displaystyle \times ,\div ,\divideontimes ,/,\backslash }$ |
| \cdot, * \ast, \star, \circ, \bullet | ${\displaystyle \cdot ,*\ast ,\star ,\circ ,\bullet }$ |
| \boxplus, \boxminus, \boxtimes, \boxdot | ${\displaystyle \boxplus ,\boxminus ,\boxtimes ,\boxdot }$ |
| \oplus, \ominus, \otimes, \oslash, \odot | ${\displaystyle \oplus ,\ominus ,\otimes ,\oslash ,\odot }$ |
| \circleddash, \circledcirc, \circledast | ${\displaystyle \circleddash ,\circledcirc ,\circledast }$ |
| \bigoplus, \bigotimes, \bigodot | ${\displaystyle \bigoplus ,\bigotimes ,\bigodot }$ |
| 集合 | |
| { }, \O \empty \emptyset, \varnothing | ${\displaystyle {},\emptyset \emptyset \emptyset ,\varnothing }$ |
| \in, \notin \not\in, \ni, \not\ni | ${\displaystyle \in ,\notin \not \in ,\ni ,\not \ni }$ |
| \cap, \Cap, \sqcap, \bigcap | ${\displaystyle \cap ,\Cap ,\sqcap ,\bigcap }$ |
| \cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus | ${\displaystyle \cup ,\Cup ,\sqcup ,\bigcup ,\bigsqcup ,\uplus ,\biguplus }$ |
| \setminus, \smallsetminus, \times | ${\displaystyle \setminus ,\smallsetminus ,\times }$ |
| \subset, \Subset, \sqsubset | ${\displaystyle \subset ,\Subset ,\sqsubset }$ |
| \supset, \Supset, \sqsupset | ${\displaystyle \supset ,\Supset ,\sqsupset }$ |
| \subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq | ${\displaystyle \subseteq ,\nsubseteq ,\subsetneq ,\varsubsetneq ,\sqsubseteq }$ |
| \supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq | ${\displaystyle \supseteq ,\nsupseteq ,\supsetneq ,\varsupsetneq ,\sqsupseteq }$ |
| \subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq | ${\displaystyle \subseteqq ,\nsubseteqq ,\subsetneqq ,\varsubsetneqq }$ |
| \supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq | ${\displaystyle \supseteqq ,\nsupseteqq ,\supsetneqq ,\varsupsetneqq }$ |
| 关系符号 | |
| =, \ne, \neq, \equiv, \not\equiv | ${\displaystyle =,\neq ,\neq ,\equiv ,\not \equiv }$ |
| \doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, := | ${\displaystyle \doteq ,\doteqdot ,{\overset {\underset {\mathrm {def} }{}}{=}},:=}$ |
| \sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong | ${\displaystyle \sim ,\nsim ,\backsim ,\thicksim ,\simeq ,\backsimeq ,\eqsim ,\cong ,\ncong }$ |
| \approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto | ${\displaystyle \approx ,\thickapprox ,\approxeq ,\asymp ,\propto ,\varpropto }$ |
| <, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot | ${\displaystyle <,\nless ,\ll ,\not \ll ,\lll ,\not \lll ,\lessdot }$ |
| >, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot | ${\displaystyle >,\ngtr ,\gg ,\not \gg ,\ggg ,\not \ggg ,\gtrdot }$ |
| \le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq | ${\displaystyle \leq ,\leq ,\lneq ,\leqq ,\nleq ,\nleqq ,\lneqq ,\lvertneqq }$ |
| \ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq | ${\displaystyle \geq ,\geq ,\gneq ,\geqq ,\ngeq ,\ngeqq ,\gneqq ,\gvertneqq }$ |
| \lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless | ${\displaystyle \lessgtr ,\lesseqgtr ,\lesseqqgtr ,\gtrless ,\gtreqless ,\gtreqqless }$ |
| \leqslant, \nleqslant, \eqslantless | ${\displaystyle \leqslant ,\nleqslant ,\eqslantless }$ |
| \geqslant, \ngeqslant, \eqslantgtr | ${\displaystyle \geqslant ,\ngeqslant ,\eqslantgtr }$ |
| \lesssim, \lnsim, \lessapprox, \lnapprox | ${\displaystyle \lesssim ,\lnsim ,\lessapprox ,\lnapprox }$ |
| \gtrsim, \gnsim, \gtrapprox, \gnapprox | ${\displaystyle \gtrsim ,\gnsim ,\gtrapprox ,\gnapprox }$ |
| \prec, \nprec, \preceq, \npreceq, \precneqq | ${\displaystyle \prec ,\nprec ,\preceq ,\npreceq ,\precneqq }$ |
| \succ, \nsucc, \succeq, \nsucceq, \succneqq | ${\displaystyle \succ ,\nsucc ,\succeq ,\nsucceq ,\succneqq }$ |
| \preccurlyeq, \curlyeqprec | ${\displaystyle \preccurlyeq ,\curlyeqprec }$ |
| \succcurlyeq, \curlyeqsucc | ${\displaystyle \succcurlyeq ,\curlyeqsucc }$ |
| \precsim, \precnsim, \precapprox, \precnapprox | ${\displaystyle \precsim ,\precnsim ,\precapprox ,\precnapprox }$ |
| \succsim, \succnsim, \succapprox, \succnapprox | ${\displaystyle \succsim ,\succnsim ,\succapprox ,\succnapprox }$ |
| 几何符号 | |
| \parallel, \nparallel, \shortparallel, \nshortparallel | ${\displaystyle \parallel ,\nparallel ,\shortparallel ,\nshortparallel }$ |
| \perp, \angle, \sphericalangle, \measuredangle, 45^\circ | ${\displaystyle \perp ,\angle ,\sphericalangle ,\measuredangle ,45^{\circ }}$ |
| \Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar | ${\displaystyle \Box ,\blacksquare ,\diamond ,\Diamond \lozenge ,\blacklozenge ,\bigstar }$ |
| \bigcirc, \triangle, \bigtriangleup, \bigtriangledown | ${\displaystyle \bigcirc ,\triangle ,\bigtriangleup ,\bigtriangledown }$ |
| \vartriangle, \triangledown | ${\displaystyle \vartriangle ,\triangledown }$ |
| \blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright | ${\displaystyle \blacktriangle ,\blacktriangledown ,\blacktriangleleft ,\blacktriangleright }$ |
| 逻辑符号 | |
| \forall, \exists, \nexists | ${\displaystyle \forall ,\exists ,\nexists }$ |
| \therefore, \because, \And | ${\displaystyle \therefore ,\because ,\And }$ |
| \or \lor \vee, \curlyvee, \bigvee | ${\displaystyle \lor ,\lor ,\vee ,\curlyvee ,\bigvee }$ |
| \and \land \wedge, \curlywedge, \bigwedge | ${\displaystyle \land ,\land ,\wedge ,\curlywedge ,\bigwedge }$ |
| \bar{q}, \bar{abc}, \overline{q}, \overline{abc}, | ${\displaystyle {\bar {q}},{\bar {abc}},{\overline {q}},{\overline {abc}},}$ |
| \lnot \neg, \not\operatorname{R}, \bot, \top | ${\displaystyle \lnot \neg ,\not \operatorname {R} ,\bot ,\top }$ |
| \vdash \dashv, \vDash, \Vdash, \models | ${\displaystyle \vdash ,\dashv ,\vDash ,\Vdash ,\models }$ |
| \Vvdash \nvdash \nVdash \nvDash \nVDash | ${\displaystyle \Vvdash ,\nvdash ,\nVdash ,\nvDash ,\nVDash }$ |
| \ulcorner \urcorner \llcorner \lrcorner | ${\displaystyle \ulcorner \urcorner \llcorner \lrcorner }$ |
| 箭头 | |
| \Rrightarrow, \Lleftarrow | ! ${\displaystyle \Rrightarrow ,\Lleftarrow }$ |
| \Rightarrow, \nRightarrow, \Longrightarrow \implies | ${\displaystyle \Rightarrow ,\nRightarrow ,\Longrightarrow ,\implies }$ |
| \Leftarrow, \nLeftarrow, \Longleftarrow | ${\displaystyle \Leftarrow ,\nLeftarrow ,\Longleftarrow }$ |
| \Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow \iff | ${\displaystyle \Leftrightarrow ,\nLeftrightarrow ,\Longleftrightarrow \iff }$ |
| \Uparrow, \Downarrow, \Updownarrow | ${\displaystyle \Uparrow ,\Downarrow ,\Updownarrow }$ |
| \rightarrow \to, \nrightarrow, \longrightarrow | ${\displaystyle \rightarrow \to ,\nrightarrow ,\longrightarrow }$ |
| \leftarrow \gets, \nleftarrow, \longleftarrow | ${\displaystyle \leftarrow \gets ,\nleftarrow ,\longleftarrow }$ |
| \leftrightarrow, \nleftrightarrow, \longleftrightarrow | ${\displaystyle \leftrightarrow ,\nleftrightarrow ,\longleftrightarrow }$ |
| \uparrow, \downarrow, \updownarrow | ${\displaystyle \uparrow ,\downarrow ,\updownarrow }$ |
| \nearrow, \swarrow, \nwarrow, \searrow | ${\displaystyle \nearrow ,\swarrow ,\nwarrow ,\searrow }$ |
| \mapsto, \longmapsto | ${\displaystyle \mapsto ,\longmapsto }$ |
| \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons | ${\displaystyle \rightharpoonup ,\rightharpoondown ,\leftharpoonup ,\leftharpoondown ,\upharpoonleft ,\upharpoonright ,\downharpoonleft ,\downharpoonright ,\rightleftharpoons ,\leftrightharpoons }$ |
| \curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright | ${\displaystyle \curvearrowleft ,\circlearrowleft ,\Lsh ,\upuparrows ,\rightrightarrows ,\rightleftarrows ,\rightarrowtail ,\looparrowright }$ |
| \curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft | ${\displaystyle \curvearrowright ,\circlearrowright ,\Rsh ,\downdownarrows ,\leftleftarrows ,\leftrightarrows ,\leftarrowtail ,\looparrowleft }$ |
| \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow | ${\displaystyle \hookrightarrow ,\hookleftarrow ,\multimap ,\leftrightsquigarrow ,\rightsquigarrow ,\twoheadrightarrow ,\twoheadleftarrow }$ |
| 特殊符号 | |
| \amalg \P \S % \dagger \ddagger \ldots \cdots | ! ${\displaystyle \amalg \P \S %\dagger \ddagger \ldots \cdots }$ |
| \smile \frown \wr \triangleleft \triangleright | ${\displaystyle \smile \frown \wr \triangleleft \triangleright }$ |
| \diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp | ${\displaystyle \diamondsuit ,\heartsuit ,\clubsuit ,\spadesuit ,\Game ,\flat ,\natural ,\sharp }$ |
| 未排序 | |
| \diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes | ${\displaystyle \diagup ,\diagdown ,\centerdot ,\ltimes ,\rtimes ,\leftthreetimes ,\rightthreetimes }$ |
| \eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq | ${\displaystyle \eqcirc ,\circeq ,\triangleq ,\bumpeq ,\Bumpeq ,\doteqdot ,\risingdotseq ,\fallingdotseq }$ |
| \intercal \barwedge \veebar \doublebarwedge \between \pitchfork | ${\displaystyle \intercal ,\barwedge ,\veebar ,\doublebarwedge ,\between ,\pitchfork }$ |
| \vartriangleleft \ntriangleleft \vartriangleright \ntriangleright | ${\displaystyle \vartriangleleft ,\ntriangleleft ,\vartriangleright ,\ntriangleright }$ |
| \trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq | ${\displaystyle \trianglelefteq ,\ntrianglelefteq ,\trianglerighteq ,\ntrianglerighteq }$ |
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 |
$\displaystyle a^{2}$ |
| 下标 | a_2 |
$\displaystyle a_{2}$ |
| 组合 | a^{2+2} |
$\displaystyle a^{2+2}$ |
a_{i,j} |
$\displaystyle a_{i,j}$ | |
| 结合上下标 | x_2^3 |
$\displaystyle x_{2}^{3}$ |
| 前置上下标 | {}_1^2 \! X_3^4 |
$\displaystyle {}_1^2 X_3^4$ |
| 导数(HTML) | x' |
$\displaystyle x’$ |
| 导数(PNG) | x^\prime |
$\displaystyle x^{\prime }$ |
| 导数(错误) | x\prime |
$\displaystyle x\prime $ |
| 导数点 | \dot{x} |
$\displaystyle \dot {x}$ |
\ddot{y} |
$\displaystyle \ddot {y}$ | |
| 向量 | \vec{c} |
$\displaystyle \vec {c}$ |
\overleftarrow{a b} |
$\displaystyle \overleftarrow {ab}$ | |
\overrightarrow{c d} |
$\displaystyle \overrightarrow {cd}$ | |
\overleftrightarrow{a b} |
$\displaystyle \overleftrightarrow {ab}$ | |
\widehat{e f g} |
$\displaystyle \widehat {efg}$ | |
| 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} |
$\displaystyle \overset {\frown }{AB}$ |
| 上划线 | \overline{h i j} |
$\displaystyle \overline {hij}$ |
| 下划线 | \underline{k l m} |
$\displaystyle \underline {klm}$ |
| 上括号 | \overbrace{1+2+\cdots+100} |
$\displaystyle \overbrace {1+2+\cdots +100}$ |
\begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix} |
$\displaystyle \begin{matrix}5050 \\ \overbrace{1+2+\cdots +100} \end{matrix}$ | |
| 下括号 | \underbrace{a+b+\cdots+z} |
$\displaystyle \underbrace {a+b+\cdots +z}$ |
\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 |
$\displaystyle \sum _{k=1}^{N}k^{2}$ |
\begin{matrix} \sum_{k=1}^N k^2 \end{matrix} |
$\displaystyle \begin{matrix}\sum _{k=1}^{N}k^{2}\end{matrix}$ | |
| 求积 | \prod_{i=1}^N x_i |
$\displaystyle \prod_{i=1}^N x_i$ |
\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 |
$\displaystyle \coprod_{i=1}^N x_i$ |
\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 |
$\displaystyle \lim_{n \to \infty}x_n$ |
\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 |
$\displaystyle \int _{-N}^{N}e^{x},\mathrm {d} x$ |
\begin{matrix} \int_{-N}^{N} e^x\, \mathrm{d}x \end{matrix} |
$\displaystyle \begin{matrix}\int _{-N}^{N}e^{x},\mathrm {d} x\end{matrix}$ | |
| 双重积分 | \iint_{D}^{W} \, \mathrm{d}x\,\mathrm{d}y |
${\displaystyle \iint _{D}^{W},\mathrm {d} x,\mathrm {d} y}$ |
| 三重积分 | \iiint_{E}^{V} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z |
${\displaystyle \iiint _{E}^{V},\mathrm {d} x,\mathrm {d} y,\mathrm {d} z}$ |
| 四重积分 | \iiiint_{F}^{U} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z\,\mathrm{d}t |
${\displaystyle \iiiint _{F}^{U},\mathrm {d} x,\mathrm {d} y,\mathrm {d} z,\mathrm {d} t}$ |
| 闭合的曲线、曲面积分 | \oint_{C} x^3\, \mathrm{d}x + 4y^2\, \mathrm{d}y |
${\displaystyle \oint _{C}x^{3},\mathrm {d} x+4y^{2},\mathrm {d} y}$ |
| 交集 | \bigcap_1^{n} p |
${\displaystyle \bigcap _{1}^{n}p}$ |
| 并集 | \bigcup_1^{k} p |
${\displaystyle \bigcup _{1}^{k}p}$ |
分数、矩阵和多行列式
| 功能 | 语法 | 效果 |
|---|---|---|
| 分数 | \frac{2}{4}=0.5 | ${\displaystyle {\frac {2}{4}}=0.5}$ |
| 小型分数 | \tfrac{2}{4} = 0.5 | ${\displaystyle {\tfrac {2}{4}}=0.5}$ |
| 大型分数(嵌套) | \cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a | ${\displaystyle {\cfrac {2}{c+{\cfrac {2}{d+{\cfrac {2}{4}}}}}}=a}$ |
| 大型分数(不嵌套) | \dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a | ${\displaystyle {\dfrac {2}{4}}=0.5\qquad {\dfrac {2}{c+{\dfrac {2}{d+{\dfrac {2}{4}}}}}}=a}$ |
| 二项式系数 | \dbinom{n}{r}=\binom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r} |
$\displaystyle\dbinom{n}{r}=\binom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}$ |
| 小型二项式系数 | \tbinom{n}{r}=\tbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r} |
$\displaystyle \tbinom{n}{r}=\tbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}$ |
| 大型二项式系数 | \binom{n}{r}=\dbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r} |
$\displaystyle\binom{n}{r}=\dbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}$ |
| 矩阵 | \begin{matrix} |
$\displaystyle \begin{matrix} x & y \\ z & v \end{matrix}$ |
\begin{vmatrix} |
$\displaystyle \begin{vmatrix} x & y \\ z & v \end{vmatrix}$ |
|
\begin{Vmatrix} |
$\displaystyle \begin{Vmatrix} x & y \\ z & v \end{Vmatrix}$ |
|
\begin{bmatrix} |
$\displaystyle \begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}$ |
|
\begin{Bmatrix} |
$\displaystyle \begin{Bmatrix} x & y \\ z & v \end{Bmatrix}$ |
|
\begin{pmatrix} |
$\displaystyle \begin{pmatrix} x & y \\ z & v \end{pmatrix}$ |
|
\bigl( \begin{smallmatrix} |
$\displaystyle \bigl( \begin{smallmatrix} a&b\ c&d \end{smallmatrix} \bigr)$ |
|
| 条件定义 | f(n) = |
$\displaystyle f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases}$ |
| 多行等式、同余式 | \begin{align} |
$\displaystyle \begin{align} f(x)&=(m+n)^{2}\\ &=m^{2}+2mn+n^{2}\\ \end{align}$ |
\begin{align} |
$\displaystyle \begin{align} 3^{6n+3}+4^{6n+3} &\equiv (3^{3})^{2n+1}+ (4^{3})^{2n+1}\\ &\equiv 27^{2n+1}+64^{2n+1}\\ &\equiv 27^{2n+1}+ (-27)^{2n+1}\\ &\equiv 27^{2n+1}-27^{2n+1}\\ &\equiv 0{\pmod {91}}\\ \end{align}$ |
|
\begin{alignedat}{3} |
$\displaystyle \begin{alignedat}{3} f(x)&=(m-n)^{2}\\ f(x)&=(-m+n)^{2}\\ &=m^{2}-2mn+n^{2}\\ \end{alignedat}$ |
|
| 多行等式(左对齐) | \begin{array}{lcl} |
$\displaystyle \begin{array}{lcl} z &=&a\\ f(x,y,z)&=&x+y+z \end{array}$ |
| 多行等式(右对齐) | \begin{array}{lcr} |
$\displaystyle \begin{array}{lcr} z &=&a\\ f(x,y,z)&=&x+y+z \end{array}$ |
| 长公式换行 | |
$\displaystyle f(x) , = \sum_{n=0}^\infty a_n x^n \\ = a_0+a_1x+a_2x^2+\cdots$ |
| 方程组 | \begin{cases} |
$\displaystyle \begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}$ |
| 数组 | \begin{array}{| c | c | | c|} a & b & S \\ |
$\begin{array}{| c | c | | c|} a & b & S \\ \hline 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0\\ \end{array}$ |
字体
| 希腊字母 | |
|---|---|
| \Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta | ${\displaystyle \mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }$ |
| \Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi | ${\displaystyle \mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \mathrm {O} \Xi \Pi }$ |
| \Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega | ${\displaystyle \mathrm {P} \Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }$ |
| \alpha \beta \gamma \delta \epsilon \zeta \eta \theta | ${\displaystyle \alpha \beta \gamma \delta \epsilon \zeta \eta \theta }$ |
| \iota \kappa \lambda \mu \nu \omicron \xi \pi | ${\displaystyle \iota \kappa \lambda \mu \nu \mathrm {o} \xi \pi }$ |
| \rho \sigma \tau \upsilon \phi \chi \psi \omega | ${\displaystyle \rho \sigma \tau \upsilon \phi \chi \psi \omega }$ |
| \varepsilon \digamma \varkappa \varpi | ${\displaystyle \varepsilon \digamma \varkappa \varpi }$ |
| \varrho \varsigma \vartheta \varphi | ${\displaystyle \varrho \varsigma \vartheta \varphi }$ |
| 希伯来符号 | |
| \aleph \beth \gimel \daleth | ${\displaystyle \aleph \beth \gimel \daleth }$ |
| 黑板报粗体 | |
| \mathbb{ABCDEFGHI} | ${\displaystyle \mathbb {ABCDEFGHI} }$ |
| \mathbb{JKLMNOPQR} | ${\displaystyle \mathbb {JKLMNOPQR} }$ |
| \mathbb{STUVWXYZ} | ${\displaystyle \mathbb {STUVWXYZ} }$ |
| 粗体 | |
| \mathbf{ABCDEFGHI} | ${\displaystyle \mathbf {ABCDEFGHI} }$ |
| \mathbf{JKLMNOPQR} | ${\displaystyle \mathbf {JKLMNOPQR} }$ |
| \mathbf{STUVWXYZ} | ${\displaystyle \mathbf {STUVWXYZ} }$ |
| \mathbf{abcdefghijklm} | ${\displaystyle \mathbf {abcdefghijklm} }$ |
| \mathbf{nopqrstuvwxyz} | ${\displaystyle \mathbf {nopqrstuvwxyz} }$ |
| \mathbf{0123456789} | ${\displaystyle \mathbf {0123456789} }$ |
| 粗体希腊字母 | |
| \boldsymbol{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta} | ${\displaystyle {\boldsymbol {\mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }}}$ |
| \boldsymbol{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho} | ${\displaystyle {\boldsymbol {\mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \Pi \mathrm {P} }}}$ |
| \boldsymbol{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega} | ${\displaystyle {\boldsymbol {\Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }}}$ |
| \boldsymbol{\alpha\beta\gamma\delta\epsilon\zeta\eta\theta} | ${\displaystyle {\boldsymbol {\alpha \beta \gamma \delta \epsilon \zeta \eta \theta }}}$ |
| \boldsymbol{\iota\kappa\lambda\mu\nu\xi\pi\rho} | ${\displaystyle {\boldsymbol {\iota \kappa \lambda \mu \nu \xi \pi \rho }}}$ |
| \boldsymbol{\sigma\tau\upsilon\phi\chi\psi\omega} | ${\displaystyle {\boldsymbol {\sigma \tau \upsilon \phi \chi \psi \omega }}}$ |
| \boldsymbol{\varepsilon\digamma\varkappa\varpi} | ${\displaystyle {\boldsymbol {\varepsilon \digamma \varkappa \varpi }}}$ |
| \boldsymbol{\varrho\varsigma\vartheta\varphi} | ${\displaystyle {\boldsymbol {\varrho \varsigma \vartheta \varphi }}}$ |
| 斜体(拉丁字母默认) | |
| \mathit{0123456789} | ${\displaystyle {\mathit {0123456789}}}$ |
| 斜体希腊字母(小写字母默认) | |
| \mathit{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta} | ${\displaystyle {\mathit {\mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }}}$ |
| \mathit{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho} | ${\displaystyle {\mathit {\mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \Pi \mathrm {P} }}}$ |
| \mathit{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega} | ${\displaystyle {\mathit {\Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }}}$ |
| 罗马体 | |
| \mathrm{ABCDEFGHI} | ${\displaystyle \mathrm {ABCDEFGHI} }$ |
| \mathrm{JKLMNOPQR} | ${\displaystyle \mathrm {JKLMNOPQR} }$ |
| \mathrm{STUVWXYZ} | ${\displaystyle \mathrm {STUVWXYZ} }$ |
| \mathrm{abcdefghijklm} | ${\displaystyle \mathrm {abcdefghijklm} }$ |
| \mathrm{nopqrstuvwxyz} | ${\displaystyle \mathrm {nopqrstuvwxyz} }$ |
| \mathrm{0123456789} | ${\displaystyle \mathrm {0123456789} }$ |
| 无衬线体 | |
| \mathsf{ABCDEFGHI} | ${\displaystyle {\mathsf {ABCDEFGHI}}}$ |
| \mathsf{JKLMNOPQR} | ${\displaystyle {\mathsf {JKLMNOPQR}}}$ |
| \mathsf{STUVWXYZ} | ${\displaystyle {\mathsf {STUVWXYZ}}}$ |
| \mathsf{abcdefghijklm} | ${\displaystyle {\mathsf {abcdefghijklm}}}$ |
| \mathsf{nopqrstuvwxyz} | ${\displaystyle {\mathsf {nopqrstuvwxyz}}}$ |
| \mathsf{0123456789} | ${\displaystyle {\mathsf {0123456789}}}$ |
| 无衬线体希腊字母(仅大写) | |
| \mathsf{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta} | ${\displaystyle {\mathsf {\mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }}}$ |
| \mathsf{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho} | ${\displaystyle {\mathsf {\mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \Pi \mathrm {P} }}}$ |
| \mathsf{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega} | ${\displaystyle {\mathsf {\Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }}}$ |
| 手写体/花体 | |
| \mathcal{ABCDEFGHI} | ${\displaystyle {\mathcal {ABCDEFGHI}}}$ |
| \mathcal{JKLMNOPQR} | ${\displaystyle {\mathcal {JKLMNOPQR}}}$ |
| \mathcal{STUVWXYZ} | ${\displaystyle {\mathcal {STUVWXYZ}}}$ |
| Fraktur体 | |
| \mathfrak{ABCDEFGHI} | ${\displaystyle {\mathfrak {ABCDEFGHI}}}$ |
| \mathfrak{JKLMNOPQR} | ${\displaystyle {\mathfrak {JKLMNOPQR}}}$ |
| \mathfrak{STUVWXYZ} | ${\displaystyle {\mathfrak {STUVWXYZ}}}$ |
| \mathfrak{abcdefghijklm} | ${\displaystyle {\mathfrak {abcdefghijklm}}}$ |
| \mathfrak{nopqrstuvwxyz} | ${\displaystyle {\mathfrak {nopqrstuvwxyz}}}$ |
| \mathfrak{0123456789} | ${\displaystyle {\mathfrak {0123456789}}}$ |
| 小型手写体 | |
| {\scriptstyle\text{abcdefghijklm}} | ${\displaystyle {\scriptstyle {\text{abcdefghijklm}}}}$ |
混合字体
| 特征 | 语法 | $渲染效果$ |
|---|---|---|
| 斜体字符(忽略空格) | x y z | ${\displaystyle xyz}$ |
| 非斜体字符 | \text{x y z} | ${\displaystyle {\text{x y z}}}$ |
| 混合斜体(差) | \text{if} n \text{is even} | ${\displaystyle {\text{if}}n{\text{is even}}}$ |
| 混合斜体(好) | \text{if }n\text{ is even} | ${\displaystyle {\text{if }}n{\text{ is even}}}$ |
| 混合斜体( 替代品:~ 或者”\ “强制空格) | \text{if}~n\ \text{is even} | ${\displaystyle {\text{if}}~n\ {\text{is even}}}$ |
括号
| 功能 | 语法 | 显示 |
|---|---|---|
| 短括号 | ( \frac{1}{2} ) | ${\displaystyle ({\frac {1}{2}})}$ |
| 长括号 | \left( \frac{1}{2} \right) | ${\displaystyle \left({\frac {1}{2}}\right)}$ |
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**)** | |
| 方括号,中括号 | \left**[** \frac{a}{b} \right**]** | |
| 花括号,大括号 | \left{ \frac{a}{b} \right} | |
| 角括号 | \left \langle \frac{a}{b} \right \rangle | |
| 单竖线,绝对值 | \left**|** \frac{a}{b} \right**|** |
|
| 双竖线,范 | \left | \frac{a}{b} \right | |
|
| 取整函数 | \left \lfloor \frac{a}{b} \right \rfloor | |
| 取顶函数 | \left \lceil \frac{c}{d} \right \rceil | |
| 斜线与反斜线 | \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 \updownarrow \frac{a}{b} \right \Updownarrow | ||
| 混合括号 | \left [ 0,1 \right ) \left \langle \psi \right | |
|
| 单左括号 | \left { \frac{a}{b} \right . | |
| 单右括号 | \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︰
空格
TEX能够自动处理大多数的空格,但是有时候需要自己来控制。
| 功能 | 语法 | 显示 | 宽度 |
|---|---|---|---|
| 2个quad空格 | \alpha\qquad\beta |
||
| quad空格 | \alpha\quad\beta |
||
| 大空格 | \alpha\ \beta |
||
| 中等空格 | \alpha\;\beta |
||
| 小空格 | \alpha\,\beta |
||
| 没有空格 | \alpha\beta |
||
| 紧贴 | \alpha\!\beta |
颜色
语法
- 字体颜色︰
{\color{色调}表达式} 背景颜色︰[c]~ 这个命令已经失效{\pagecolor{色调}表达式}
支持色调表
| ${\displaystyle \color {White}{\text{White}}}$ | |||
*注︰输入时第一个字母必需以大写输入,如\color{OliveGreen}。
例子
小型数学公式
10 的 $\displaystyle f(x)=5+{\frac {1}{5}}$ 是 2。
- 🙁并不好看。
10 的 $\displaystyle {\begin{smallmatrix}f(x)=5+{\frac {1}{5}}\end{smallmatrix}}$ 是 2。
- 😁好看些了。
可以使用
1 | \begin{smallmatrix}...\end{smallmatrix} |
或直接使用模板。
1 | {{Smallmath|f= f(x)=5+\frac{1}{5} }} |
算符名称
\text 命令
积分与求和
插入表格
如果需要插入复杂表格(批量导入网页上的表格)
markdown 插入表格不支持合并单元格
当需要导入的表格太大时markdown手动输入工作量大不太友好,而利用 html 或者 excel 复制表格后粘贴至markdown 编辑器可以省去繁杂的编辑。这里做了一个实例来演示这个方法 –>markdown 插入复杂表格