LaTeX教程

· · 科技·工程

1 符号与字母

1.1 希腊字母

小写 LaTeX 大写 LaTeX
\alpha \alpha \Alpha \Alpha
\beta \beta \Beta \Beta
\gamma \gamma \Gamma \Gamma
\delta \delta \Delta \Delta
\epsilon \epsilon \Epsilon \Epsilon
\varepsilon \varepsilon ^ ^
\zeta \zeta \Zeta \Zeta
\eta \eta \Eta \Eta
\theta \theta \Theta \Theta
\vartheta \vartheta ^ ^
\iota \iota \Iota \Iota
\kappa \kappa \Kappa \Kappa
\lambda \lambda \Lambda \Lambda
\mu \mu \Mu \Mu
\nu \nu \Nu \Nu
\xi \xi \Xi \Xi
\pi \pi \Pi \Pi
\varpi \varpi ^ ^
\rho \rho \Rho \Rho
\varrho \varrho ^ ^
\sigma \sigma \Sigma \Sigma
\varsigma \varsigma ^ ^
\tau \tau \Tau \Tau
\upsilon \upsilon \Upsilon \Upsilon
\phi \phi \Phi \Phi
\varphi \varphi ^ ^
\chi \chi \Chi \Chi
\psi \psi \Psi \Psi
\omega \omega \Omega \Omega

1.2 希伯来字母

图标 LaTeX
\aleph \aleph
\beth \beth
\gimel \gimel
\daleth \daleth

1.3 二元运算符

图标 LaTeX 图标 LaTeX
+ + - -
\times \times \div \div
\pm \pm \mp \mp
\triangleleft \triangleleft \triangleright \triangleright
\cdot \cdot \setminus \setminus
\star \star \ast \ast
\cup \cup \cap \cap
\sqcup \sqcup \sqcap \sqcap
\vee \vee \wedge \wedge
\circ \circ \bullet \bullet
\oplus \oplus \ominus \ominus
\odot \odot \oslash \oslash
\otimes \otimes \bigcirc \bigcirc
\diamond \diamond \uplus \uplus
\bigtriangleup \bigtriangleup \bigtriangledown \bigtriangledown
\lhd \lhd \rhd \rhd
\unlhd \unlhd \unrhd \unrhd
\amalg \amalg \wr \wr
\dagger \dagger \ddagger \ddagger

1.4 二元关系符

图标 LaTeX 图标 LaTeX
= = \ne \ne
\equiv \equiv \not\equiv \not\equiv
\doteq \doteq \doteqdot \doteqdot
\overset{\underset{\mathrm{def}}{}}{=},\stackrel{\text{def}}{=},\xlongequal{\text{def}} \overset{\underset{\mathrm{def}}{}}{=},\stackrel{\text{def}}{=},\xlongequal{\text{def}} := :=
\sim \sim \nsim \nsim
\backsim \backsim \thicksim \thicksim
\simeq \simeq \eqsim \eqsim
\cong \cong \ncong \ncong
\approx \approx \approxeq \approxeq
\asymp \asymp \propto \propto
< < \nless \nless
\ll \ll \not\ll \not\ll
\lll \lll \not\lll \not\lll
\lessdot \lessdot > >
\ngtr \ngtr \gg \gg
\not\gg \not\gg \ggg \ggg
\not\ggg \not\ggg \gtrdot \gtrdot
\leq \leq \lneq \lneq
\leqq \leqq \nleq \nleq
\nleqq \nleqq \lneqq \lneqq
\geq \geq \gneq \gneq
\geqq \geqq \ngeq \ngeq
\ngeqq \ngeqq \gneqq \gneqq
\lessgtr \lessgtr \lesseqgtr \lesseqgtr
\lesseqqgtr \lesseqqgtr \gtrless \gtrless
\gtreqless \gtreqless \gtreqqless \gtreqqless
\leqslant \leqslant \nleqslant \nleqslant
\eqslantless \eqslantless \geqslant \geqslant
\ngeqslant \ngeqslant \eqslantgtr \eqslantgtr
\lesssim \lesssim \lnsim \lnsim
\lessapprox \lessapprox \lnapprox \lnapprox
\gtrsim \gtrsim \gnsim \gnsim
\gtrapprox \gtrapprox \gnapprox \gnapprox
\prec \prec \nprec \nprec
\preceq \preceq \npreceq \npreceq
\precneqq \precneqq \succ \succ
\nsucc \nsucc \succeq \succeq
\nsucceq \nsucceq \succneqq \succneqq
\preccurlyeq \preccurlyeq \curlyeqprec \curlyeqprec
\succcurlyeq \succcurlyeq \curlyeqsucc \curlyeqsucc
\precsim \precsim \precnsim \precnsim
\precapprox \precapprox \precnapprox \precnapprox
\succsim \succsim \succnsim \succnsim
\succapprox \succapprox \succnapprox \succnapprox

1.5 几何符号

图标 LaTeX 图标 LaTeX
\parallel \parallel \nparallel \nparallel
\shortparallel \shortparallel \nshortparallel \nshortparallel
\perp \perp \angle \angle
\sphericalangle \sphericalangle \measuredangle \measuredangle
45^\circ 45^\circ \Box \Box
\blacksquare \blacksquare \diamond \diamond
\Diamond \Diamond \lozenge \lozenge
\blacklozenge \blacklozenge \bigstar \bigstar
\bigcirc \bigcirc \triangle \triangle
\bigtriangleup \bigtriangleup \bigtriangledown \bigtriangledown
\vartriangle \vartriangle \triangledown \triangledown
\blacktriangle \blacktriangle \blacktriangledown \blacktriangledown
\blacktriangleleft \blacktriangleleft \blacktriangleright \blacktriangleright

1.6 逻辑符号

图标 LaTeX 图标 LaTeX
\forall \forall \exists \exists
\nexists \nexists \therefore \therefore
\because \because \And \And
\lor \lor \vee \vee
\curlyvee \curlyvee \bigvee \bigvee
\land \land \wedge \wedge
\curlywedge \curlywedge \bigwedge \bigwedge
\bar{q} \bar{q} \bar{abc} \bar{abc}
\overline{q} \overline{q} \overline{abc} \overline{abc}
\lnot \lnot \neg \neg
\not\operatorname{R} \not\operatorname{R} \bot \bot
\top \top \vdash \vdash
\dashv \dashv \vDash \vDash
\Vdash \Vdash \models \models
\Vvdash \Vvdash \nvdash \nvdash
\nVdash \nVdash \nvDash \nvDash
\nVDash \nVDash \ulcorner \ulcorner
\urcorner \urcorner \llcorner \llcorner
\lrcorner \lrcorner

1.7 集合

图标 LaTeX 图标 LaTeX
\{\} \{\} \emptyset \emptyset
\varnothing \varnothing \in \in
\notin \notin \ni \ni
\cap \cap \Cap \Cap
\sqcap \sqcap \bigcap \bigcap
\cup \cup \Cup \Cup
\sqcup \sqcup \bigcup \bigcup
\bigsqcup \bigsqcup \uplus \uplus
\biguplus \biguplus \setminus \setminus
\smallsetminus \smallsetminus \times \times
\subset \subset \Subset \Subset
\sqsubset \sqsubset \supset \supset
\Supset \Supset \sqsupset \sqsupset
\subseteq \subseteq \nsubseteq \nsubseteq
\subsetneq \subsetneq \varsubsetneq \varsubsetneq
\sqsubseteq \sqsubseteq \supseteq \supseteq
\nsupseteq \nsupseteq \supsetneq \supsetneq
\varsupsetneq \varsupsetneq \sqsupseteq \sqsupseteq
\subseteqq \subseteqq \nsubseteqq \nsubseteqq
\subsetneqq \subsetneqq \varsubsetneqq \varsubsetneqq
\supseteqq \supseteqq \nsupseteqq \nsupseteqq
\supsetneqq \supsetneqq \varsupsetneqq \varsupsetneqq

1.8 箭头

图标 LaTeX 图标 LaTeX
\Rrightarrow \Rrightarrow \Lleftarrow \Lleftarrow
\Rightarrow \Rightarrow \nRightarrow \nRightarrow
\Longrightarrow \Longrightarrow \implies \implies
\Leftarrow \Leftarrow \nLeftarrow \nLeftarrow
\Longleftarrow \Longleftarrow \Leftrightarrow \Leftrightarrow
\nLeftrightarrow \nLeftrightarrow \Longleftrightarrow \Longleftrightarrow
\iff \iff \Uparrow \Uparrow
\Downarrow \Downarrow \Updownarrow \Updownarrow
\rightarrow \rightarrow \to \to
\nrightarrow \nrightarrow \longrightarrow \longrightarrow
\leftarrow \leftarrow \gets \gets
\nleftarrow \nleftarrow \longleftarrow \longleftarrow
\leftrightarrow \leftrightarrow \nleftrightarrow \nleftrightarrow
\longleftrightarrow \longleftrightarrow \uparrow \uparrow
\downarrow \downarrow \updownarrow \updownarrow
\nearrow \nearrow \swarrow \swarrow
\nwarrow \nwarrow \searrow \searrow
\mapsto \mapsto \longmapsto \longmapsto
\rightharpoonup \rightharpoonup \rightharpoondown \rightharpoondown
\leftharpoonup \leftharpoonup \leftharpoondown \leftharpoondown
\upharpoonleft \upharpoonleft \upharpoonright \upharpoonright
\downharpoonleft \downharpoonleft \downharpoonleft \downharpoonleft
\rightleftharpoons \rightleftharpoons \leftrightharpoons \leftrightharpoons
\curvearrowleft \curvearrowleft \circlearrowleft \circlearrowleft
\Lsh \Lsh \upuparrows \upuparrows
\rightrightarrows \rightrightarrows \rightleftarrows \rightleftarrows
\rightarrowtail \rightarrowtail \looparrowright \looparrowright
\curvearrowright \curvearrowright \circlearrowright \circlearrowright
\Rsh \Rsh \downdownarrows \downdownarrows
\leftleftarrows \leftleftarrows \leftrightarrows \leftrightarrows
\leftarrowtail \leftarrowtail \looparrowleft \looparrowleft
\hookrightarrow \hookrightarrow \hookleftarrow \hookleftarrow
\multimap \multimap \leftrightsquigarrow \leftrightsquigarrow
\rightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadrightarrow
\twoheadleftarrow \twoheadleftarrow

1.9 特殊

图标 LaTeX 图标 LaTeX
\infty \infty \aleph \aleph
\complement \complement \backepsilon \backepsilon
\eth \eth \Finv \Finv
\hbar \hbar \Im \Im
\imath \imath \jmath \jmath
\Bbbk \Bbbk \ell \ell
\mho \mho \wp \wp
\Re \Re \circledS \circledS
\amalg \amalg \% \%
\dagger \dagger \ddagger \ddagger
\ldots \ldots \cdots \cdots
\smile \smile \frown \frown
\wr \wr \triangleleft \triangleleft
\triangleright \triangleright \diamondsuit \diamondsuit
\heartsuit \heartsuit \clubsuit \clubsuit
\spadesuit \spadesuit \Game \Game
\flat \flat \natural \natural
\sharp \sharp \diagup \diagup
\diagdown \diagdown \centerdot \centerdot
\ltimes \ltimes \rtimes \rtimes
\leftthreetimes \leftthreetimes \rightthreetimes \rightthreetimes
\eqcirc \eqcirc \circeq \circeq
\triangleq \triangleq \bumpeq \bumpeq
\Bumpeq \Bumpeq \doteqdot \doteqdot
\risingdotseq \risingdotseq \fallingdotseq \fallingdotseq
\intercal \intercal \barwedge \barwedge
\veebar \veebar \doublebarwedge \doublebarwedge
\between \between \pitchfork \pitchfork
\vartriangleleft \vartriangleleft \ntriangleleft \ntriangleleft
\vartriangleright \vartriangleright \ntriangleright \ntriangleright
\trianglelefteq \trianglelefteq \ntrianglelefteq \ntrianglelefteq
\trianglerighteq \trianglerighteq \ntrianglerighteq \ntrianglerighteq

1.10 常用特殊符号

注： 这些符号在前文出现过，这里为了方便查找，整理到一起 字符 图标 LaTeX
# \# \#
% \% \%
^ ^\wedge ^\wedge
& \& \&
_ \_ \_
{ \{ \{
} \} \}
~ \sim \sim
\ \backslash \backslash

2 运算与函数

2.1 分数

类型 样式 LaTeX
分数 \frac{2}{4}x=0.5x \frac{2}{4}x=0.5x或{2 \over 4}x=0.5x
小型分数 \tfrac{2}{4}x = 0.5x \tfrac{2}{4}x = 0.5x
大型分数（不嵌套） \dfrac{2}{4} = 0.5 \dfrac{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

2.2 标准数值函数

样式 LaTeX
\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
\operatorname{arccot} d, \operatorname{arcsec} e, \operatorname{arccsc} f \operatorname{arccot} d, \operatorname{arcsec} e, \operatorname{arccsc} f
\sinh a, \cosh b, \tanh c, \coth d \sinh a, \cosh b, \tanh c, \coth d
\sh k, \ch l, \th m, \coth n \sh k, \ch l, \th m, \coth n
\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q \operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q
\operatorname{sgn}r, \left\vert s \right\vert \operatorname{sgn}r, \left\vert s \right\vert
\min(x,y), \max(x,y) \min(x,y), \max(x,y)

2.3 根式

样式 LaTeX
\surd \surd
\sqrt{\pi} \sqrt{\pi}
\sqrt[n]{\pi} \sqrt[n]{\pi}
\sqrt[3]{\frac{x^3+y^3}{2}} \sqrt[3]{\frac{x^3+y^3}{2}}

2.4 微分与导数

样式 LaTeX
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

2.5 同余与模算术

样式 LaTeX
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

2.6 极限

样式 LaTeX
\lim_{n \to \infty}x_n \lim_{n \to \infty}x_n
\textstyle \lim_{n \to \infty}x_n \textstyle \lim_{n \to \infty}x_n

2.7 界限与投影

样式 LaTeX
\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
\Pr j, \hom l, \lVert z \rVert, \arg z \Pr j, \hom l, \lVert z \rVert, \arg z

2.8 积分

样式 LaTeX
\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx \int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx
\int_{1}^{3}\frac{e^3/x}{x^2}\, dx \int_{1}^{3}\frac{e^3/x}{x^2}\, dx
\textstyle \int\limits_{-N}^{N} e^x dx \textstyle \int\limits_{-N}^{N} e^x dx
\textstyle \int_{-N}^{N} e^x dx \textstyle \int_{-N}^{N} e^x dx
\iint\limits_D dx\,dy \iint\limits_D dx\,dy
\iiint\limits_E dx\,dy\,dz \iiint\limits_E dx\,dy\,dz
\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy \int_{(x,y)\in C} x^3\, dx + 4y^2\, dy
\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy \oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy

注意： 积分符号可以使用 \int_{}^{} 命令调用，如需双重积分符号只需将 int 替换成 iint 即可，以此类推，最高支持三重。曲线积分可使用 \oint 命令调用。

2.9 其他大型运算

类别 样式 LaTeX
求和 \sum_{a}^{b} \sum_{a}^{b}
求和 \textstyle \sum_{a}^{b} \textstyle \sum_{a}^{b}
连乘积 \prod_{a}^{b} \prod_{a}^{b}
连乘积 \textstyle \prod_{a}^{b} \textstyle \prod_{a}^{b}
余积 \coprod_{a}^{b} \coprod_{a}^{b}
余积 \textstyle \coprod_{a}^{b} \textstyle \coprod_{a}^{b}
并集 \bigcup_{a}^{b} \bigcup_{a}^{b}
并集 \textstyle \bigcup_{a}^{b} \textstyle \bigcup_{a}^{b}
交集 \bigcap_{a}^{b} \bigcap_{a}^{b}
交集 \textstyle \bigcap_{a}^{b} \textstyle \bigcap_{a}^{b}
析取 \bigvee_{a}^{b} \bigvee_{a}^{b}
析取 \textstyle \bigvee_{a}^{b} \textstyle \bigvee_{a}^{b}
合取 \bigwedge_{a}^{b} \bigwedge_{a}^{b}
合取 \textstyle \bigwedge_{a}^{b} \textstyle \bigwedge_{a}^{b}

3 上下标

类型 样式 LaTeX
上标 a^2, a^{x+3} a^2, a^{x+3}
下标 a_2 a_2
组合 10^{30} a^{2+2} 10^{30} a^{2+2}
组合 a_{i,j} b_{f'} a_{i,j} b_{f'}
上下标混合 x_2^3 x_2^3
上下标混合 {x_2}^3 {x_2}^3
上标的上标 10^{10^{8}} 10^{10^{8}}
混合标识 {}_ 1^2\Omega_3^4 {}_ 1^2\Omega_3^4
顶标底标 \overset{\alpha}{\omega} \overset{\alpha}{\omega}
顶标底标 \underset{\alpha}{\omega} \underset{\alpha}{\omega}
顶标底标 \overset{\alpha}{\underset{\gamma}{\omega}} \overset{\alpha}{\underset{\gamma}{\omega}}
顶标底标 \stackrel{\alpha}{\omega} \stackrel{\alpha}{\omega}
导数 x', y'', f', f' x', y'', f', f'
导数 x^\prime, y^{\prime\prime} x^\prime, y^{\prime\prime}
导数 \dot{x}, \ddot{x} \dot{x}, \ddot{x}
下划线、上划线与向量 \hat a \ \bar b \ \vec c \hat a \ \bar b \ \vec c
下划线、上划线与向量 \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f} \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}
下划线、上划线与向量 \overline{g h i} \ \underline{j k l} \overline{g h i} \ \underline{j k l}
弧度 \overset{\frown} {AB} \overset{\frown} {AB}
箭头 A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C
大括号 \overbrace{ 1+2+\cdots+100 }^{5050} \overbrace{ 1+2+\cdots+100 }^{5050}
底部大括号 \underbrace{ a+b+\cdots+z }_ {26} \underbrace{ a+b+\cdots+z }_ {26}
求和运算 \sum_{k=1}^N k^2 \sum_{k=1}^N k^2
文本模式下的求和运算 \textstyle \sum_{k=1}^N k^2 \textstyle \sum_{k=1}^N k^2
分式中的求和运算 \frac{\sum_{k=1}^N k^2}{a} \frac{\sum_{k=1}^N k^2}{a}
分式中的求和运算 \frac{\displaystyle \sum_{k=1}^N k^2}{a} \frac{\displaystyle \sum_{k=1}^N k^2}{a}
分式中的求和运算 \frac{\sum\limits^{^N}_ {k=1} k^2}{a} \frac{\sum\limits^{^N}_ {k=1} k^2}{a}
乘积运算 \prod_{i=1}^N x_i \prod_{i=1}^N x_i
乘积运算 \textstyle \prod_{i=1}^N x_i \textstyle \prod_{i=1}^N x_i
副乘运算 \coprod_{i=1}^N x_i \coprod_{i=1}^N x_i
副乘运算 \textstyle \coprod_{i=1}^N x_i \textstyle \coprod_{i=1}^N x_i
极限 \lim_{n \to \infty}x_n \lim_{n \to \infty}x_n
极限 \textstyle \lim_{n \to \infty}x_n \textstyle \lim_{n \to \infty}x_n
积分 \int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx \int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx
积分 \int_{1}^{3}\frac{e^3/x}{x^2}\, dx \int_{1}^{3}\frac{e^3/x}{x^2}\, dx
积分 \textstyle \int\limits_{-N}^{N} e^x dx \textstyle \int\limits_{-N}^{N} e^x dx
积分 \textstyle \int_{-N}^{N} e^x dx \textstyle \int_{-N}^{N} e^x dx
双重积分 \iint\limits_D dx\,dy \iint\limits_D dx\,dy
三重积分 \iiint\limits_E dx\,dy\,dz \iiint\limits_E dx\,dy\,dz
路径积分 \int_{(x,y)\in C} x^3\, dx + 4y^2\, dy \int_{(x,y)\in C} x^3\, dx + 4y^2\, dy
环路积分 \oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy \oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy
交集 \bigcap_{i=1}^n E_i \bigcap_{i=1}^n E_i
并集 \bigcup_{i=1}^n E_i \bigcup_{i=1}^n E_i

4 矩阵与多行列式

类型 样式 LaTeX
二项式系数 \binom{n}{k} \binom{n}{k}
小型二项式系数 \tbinom{n}{k} \tbinom{n}{k}
大型二项式系数 \dbinom{n}{k} \dbinom{n}{k}
矩阵 \begin{matrix}x & y \\z & v\end{matrix} \begin{matrix}x & y \\z & v\end{matrix}
矩阵 \begin{vmatrix}x & y \\z & v \end{vmatrix} \begin{vmatrix}x & y \\z & v\end{vmatrix}
矩阵 \begin{Vmatrix}x & y \\z & v\end{Vmatrix} \begin{Vmatrix}x & y \\z & v\end{Vmatrix}
矩阵 \begin{bmatrix}0 & \cdots & 0 \\\vdots & \ddots & \vdots \\0 & \cdots & 0\end{bmatrix} \begin{bmatrix}0 & \cdots & 0 \\\vdots & \ddots & \vdots \\0 & \cdots & 0\end{bmatrix}
矩阵 \begin{Bmatrix}x & y \\z & v\end{Bmatrix} \begin{Bmatrix}x & y \\z & v\end{Bmatrix}
矩阵 \begin{pmatrix}x & y \\z & v\end{pmatrix} \begin{pmatrix}x & y \\z & v\end{pmatrix}
矩阵 \bigl( \begin{smallmatrix}a&b\\c&d\end{smallmatrix} \bigr) \bigl( \begin{smallmatrix}a&b\\c&d\end{smallmatrix} \bigr)
条件定义 f(n) =\begin{cases}n/2, & \text{if }n\text{ is even} \\3n+1, & \text{if }n\text{ is odd}\end{cases} f(n) =\begin{cases}n/2, & \text{if }n\text{ is even} \\3n+1, & \text{if }n\text{ is odd}\end{cases}
多行等式 \begin{array}{lcl}z & = & a \\f(x,y,z) & = & x + y + z\end{array} \begin{array}{lcl}z & = & a \\f(x,y,z) & = & x + y + z\end{array}
多行等式 \begin{array}{lcr}z & = & a \\f(x,y,z) & = & x + y + z\end{array} \begin{array}{lcr}z & = & a \\f(x,y,z) & = & x + y + z\end{array}
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}

5 括号

常用的括号符号例如 ( )[ ]{ }…… 这些也可以直接使用：

2(x+y)=z
2(x+y)=z

但如果是在较大的表达式中这些符号就显得不合适了：

( \frac{1}{\frac{3}{4}} )^n
( \frac{1}{2+\frac{3}{1+\frac{1}{3}}} )^n

正确用法应配合 \left 和 \right 命令使用。

\left ( \frac{1}{2+\frac{3}{1+\frac{1}{3}}} \right )^n
具体可参考下表： |类型|样式|LaTeX| |-|-|-| |圆括号、小括号|$\left ( \frac{a}{b} \right )$|`\left ( \frac{a}{b} \right )`| |方括号、中括号|$\left [ \frac{a}{b} \right ] \quad,\left \lbrack \frac{a}{b} \right \rbrack$|`\left [ \frac{a}{b} \right ] \quad,\left \lbrack \frac{a}{b} \right \rbrack`| |花括号、大括号|$\left \lbrace \frac{a}{b} \right \rbrace$|`\left \lbrace \frac{a}{b} \right \rbrace`| |角括号|$\left \langle \frac{a}{b} \right \rangle$|`\left \langle \frac{a}{b} \right \rangle`| |单竖线和双竖线|$\left \| \frac{a}{b} \right \vert \quad, \left \Vert \frac{c}{d} \right \Vert$|`\left \| \frac{a}{b} \right \vert \quad ,\left \Vert \frac{c}{d} \right \Vert`| |取整函数与取顶函数|$\left \lfloor \frac{a}{b} \right \rfloor \quad,\left \lceil \frac{c}{d} \right \rceil$|`\left \lfloor \frac{a}{b} \right \rfloor \quad,\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 \quad,\left \Uparrow \frac{a}{b} \right \Downarrow \quad,\left \updownarrow \frac{a}{b} \right \Updownarrow$|`\left \uparrow \frac{a}{b} \right \downarrow \quad,\left \Uparrow \frac{a}{b} \right \Downarrow \quad,\left \updownarrow \frac{a}{b} \right \Updownarrow`| |混合括号|$\left [ 0,1 \right ),\left \langle \psi \right \|$|`[ 0,1 \right ),\left \langle \psi \right \|`| |如果您不希望某一侧括号显示，可以使用 `\left.` 和 `\right.`（带有英文句号）|$\left . \frac{A}{B} \right \rbrace \to X$|`\left . \frac{A}{B} \right \rbrace \to X`| |括号的大小|$ ( \bigl( \Bigl( \biggl( \Biggl( \dots \Biggr] \biggr] \Bigr] \bigr] ]$|` ( \bigl( \Bigl( \biggl( \Biggl( \dots \Biggr] \biggr] \Bigr] \bigr] ]`| |括号的大小|$\lbrace \bigl\lbrace \Bigl\lbrace \biggl\lbrace \Biggl\lbrace \dots\Biggr\rangle \biggr\rangle \Bigr\rangle \bigr\rangle \rangle$|`\lbrace \bigl\lbrace \Bigl\lbrace \biggl\lbrace \Biggl\lbrace \dots\Biggr\rangle \biggr\rangle \Bigr\rangle \bigr\rangle \rangle`| |括号的大小|$\| \big\| \Big\| \bigg\| \Bigg\| \dots \Bigg \| \bigg \| \Big \| \big \|$|` \| \big \| \Big \| \bigg \| \Bigg \| \dots \Bigg \| \bigg \| \Big \| \big \|`| |括号的大小|$\lfloor \bigl\lfloor \Bigl\lfloor \biggl\lfloor \Biggl\lfloor \dots\Biggr\rceil \biggr\rceil \Bigr\rceil \bigr\rceil \rceil$|`\lfloor \bigl\lfloor \Bigl\lfloor \biggl\lfloor \Biggl\lfloor \dots\Biggr\rceil \biggr\rceil \Bigr\rceil \bigr\rceil \rceil`| |括号的大小|$\uparrow \big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots\Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow \Downarrow$|`\uparrow \big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots\Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow \Downarrow`| |括号的大小|$ \updownarrow \big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots\Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow \Updownarrow$|` \updownarrow \big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots\Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow \Updownarrow`| |括号的大小|$/ \big/ \Big/ \bigg/ \Bigg/ \dots\Bigg\backslash \bigg\backslash \Big\backslash \big\backslash \backslash$|`/ \big/ \Big/ \bigg/ \Bigg/ \dots\Bigg\backslash \bigg\backslash \Big\backslash \big\backslash \backslash`| # 6 空格 |样式|LaTeX|说明| |-|-|-| |$a \hspace{1cm} b$|`a \hspace{1cm} b`|自主控制大小| |$a \qquad b$|`a \qquad b`|双空格| |$a \quad b$|`a \quad b`|单空格| |$a\ b$|`a\ b`|字符空格| |$a\text{ } b$|`a \text{ } b`|文本模式中的字符空格| |$a\;b$|`a\;b`|大空格| |$a\,b$|`a\,b`|小空格| |$ab$|`ab`|极小空格(用于乘因子)| |$a b$|`a b`|极小空格(用于区分其它语法)| |$\mathit{ab}$|`\mathit{ab}`|没有空格(用于多字母变量)| |$a\!b$|`a\!b`|反向空格| |$a \hspace{-.4cm} b$|`a \hspace{-.4cm} b`|反向空格（自主控制大小）| # 7 颜色 ## 7.1 字体颜色 在公式中可以使用 `\color{options}{math}` 来调用颜色命令，第一个参数为颜色，第二个参数为公式或文本内容。例如: ```latex {\color{Blue}x^2}+{\color{Orange}2x}-{\color{LimeGreen}1} ``` ${\color{Blue}x^2}+{\color{Orange}2x}-{\color{LimeGreen}1} 
x_{1,2}=\frac{{\color{Blue}-b}\pm\sqrt{\color{Red}b^2-4ac}}{\color{Green}2a }
**注意：** 使用 `\color` 命令时，请将需要设置颜色的部分用 `{ }` 整体扩住，以表明 `\color` 函数作用范围。 ## 7.2 背景颜色 在文本环境中可以使用 `\colorbox{options}{text}` 来调用背景颜色命令，第一个参数为颜色，第二个参数为文本内容。例如： ```latex \colorbox{yellow}{Thistext} ``` $\colorbox{yellow}{Thistext}

7.3 默认支持颜色

{\color{Orange}Orange}\; {\color{Salmon}Salmon}$\ ${\color{Fuchsia}Fuchsia}\; {\color{OrangeRed}OrangeRed}\; {\color{SeaGreen}SeaGreen}\; {\color{Goldenrod}Goldenrod}$\ ${\color{Orchid}Orchid}\;{\color{Blue}Blue}\;{\color{Gray}Gray}\;{\color{SkyBlue}SkyBlue}$\ ${\color{Green}Green}\; {\color{SpringGreen}SpringGreen}\;{\color{BlueViolet}BlueViolet}\;{\color{GreenYellow}GreenYellow}$\ ${\color{Tan}Tan}\;{\color{Plum}Plum}\;{\color{Brown}Brown}\;{\color{Lavender}Lavender}$\

{\color{Thistle}Thistle}\;{\color{LimeGreen}LimeGreen}\; {\color{Purple}Purple}\; {\color{Turquoise}Turquoise}$\

{\color{Violet}Violet}\;{\color{Red}Red}$\ ${\color{maroon}Maroon}\; {\color{White}White}\;{\color{Black}Black}\;{\color{CornflowerBlue}CornflowerBlue}$←这里有个 White.\ ${\color{Cyan}Cyan}\;{\color{MidnightBlue}MidnightBlue}\; {\color{Yellow}Yellow}\;{\color{RoyalBlue}RoyalBlue}$\ ${\color{YellowGreen}YellowGreen}\;{\color{DarkOrchid}DarkOrchid}

8 字体字号

8.1 字体

样式 LaTeX
希腊字母 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 \Pi \Iota \Kappa \Lambda \Mu \Nu \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 \xi \omicron \pi \iota \kappa \lambda \mu \nu \xi \omicron \pi
\rho \sigma \tau \upsilon \phi \chi \psi \omega \rho \sigma \tau \upsilon \phi \chi \psi \omega
\varGamma \varDelta \varTheta \varLambda \varXi \varPi \varSigma \varPhi \varUpsilon \varOmega \varGamma \varDelta \varTheta \varLambda \varXi \varPi \varSigma \varPhi \varUpsilon \varOmega
\varepsilon \digamma \varkappa \varpi \varrho \varsigma \vartheta \varphi \varepsilon \digamma \varkappa \varpi \varrho \varsigma \vartheta \varphi
希伯来字母 希伯来字母
\aleph \beth \gimel \daleth \aleph \beth \gimel \daleth
黑板报体 黑板报体
\mathbb{ABCDEFGHI} \mathbb{ABCDEFGHI}
\mathbb{JKLMNOPQR} \mathbb{JKLMNOPQR}
\mathbb{STUVWXYZ} \mathbb{STUVWXYZ}
粗体 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 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} \boldsymbol{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi}
\boldsymbol{\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega} \boldsymbol{\Rho \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 \omicron \pi} \boldsymbol{\iota \kappa \lambda \mu \nu \xi \omicron \pi}
\boldsymbol{\rho \sigma \tau \upsilon \phi \chi \psi \omega} \boldsymbol{\rho \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 斜体
\mathit{0123456789} \mathit{0123456789}
罗马体 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 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}
手写体/花体 手写体/花体
\mathcal{ABCDEFGHI} \mathcal{ABCDEFGHI}
\mathcal{JKLMNOPQR} \mathcal{JKLMNOPQR}
\mathcal{STUVWXYZ} \mathcal{STUVWXYZ}
德文尖角体 德文尖角体
\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 小型手写体
{\scriptstyle\text{abcdefghijklm}} {\scriptstyle\text{abcdefghijklm}}

8.2 字号

样式 LaTeX
{\tiny abc巨小tiny} {\tiny abc巨小tiny}
{\scriptsize abc超小scriptsize} {\scriptsize abc超小scriptsize}
{\small abc小small} {\small abc小small}
{\normalsize abc正常normal} {\normalsize abc正常normal}
{\large abc大large} {\large abc大large}
{\Large abc超大Large} {\Large abc超大Large}
{\LARGE abc特大LARGE} {\LARGE abc特大LARGE}
{\huge abc巨大huge} {\huge abc巨大huge}
{\Huge abc巨无霸Huge} {\Huge abc巨无霸Huge}

9 LaTeX 环境

环境通常是对代码段的整体描述，用于表达此段代码的角色，如，是矩阵？单行公式？多行公式？还是对齐公式等（只有矩阵和数组），不同的环境起到的作用不同。以 \begin{名字} 开始，\end{名字} 结束。如最常用的矩阵命令，也是环境的一种，用法如下：

\begin{bmatrix}
          1 & 0 \\
          0 & 1
          \end{bmatrix}
\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}

具体矩阵用法可参考章节 1.4，下面给出几种其它常用环境的具体用法：

9.1 array 环境

\begin{array}{} 是数组环境，需手动输入对齐参数：

\begin{array}{|c|l|r|}
          a & b & S \\
          \hline
          0 & 0 & 1 \\
          0 & 1 & 1 \\
          1 & 0 & 1 \\
          1 & 1 & 0 \\
          \end{array}
a & b & S \\ \hline 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{array}

对齐参数使用 c l r 分别表示居中、居左和居右，如需竖线边框可直接在对齐参数区域输入 | 即可，如需横线边框可使用 \hline 命令。

9.2 matrix 及其衍生环境

9.2.1 matrix

\begin{matrix} 是矩阵环境：

\begin{matrix}
          0 & 0 & 1 \\
          0 & 1 & 1 \\
          1 & 0 & 1 \\
          1 & 1 & 0 \\
          \end{matrix}
0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{matrix}

9.2.2 bmatrix

\begin{bmatrix} 是周围带中括号的矩阵环境：

\begin{bmatrix}
          0 & 0 & 1 \\
          0 & 1 & 1 \\
          1 & 0 & 1 \\
          1 & 1 & 0 \\
          \end{bmatrix}
0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{bmatrix}

9.2.3 Bmatrix

\begin{Bmatrix} 是周围带大括号的矩阵环境：

\begin{Bmatrix}
          0 & 0 & 1 \\
          0 & 1 & 1 \\
          1 & 0 & 1 \\
          1 & 1 & 0 \\
          \end{Bmatrix}
0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{Bmatrix}

9.2.3 vmatrix

\begin{vmatrix} 是周围带单竖线的矩阵环境：

\begin{vmatrix}
          0 & 0 & 1 \\
          0 & 1 & 1 \\
          1 & 0 & 1 \\
          1 & 1 & 0 \\
          \end{vmatrix}
0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{vmatrix}

9.2.4 Vmatrix

\begin{Vmatrix} 是周围带双竖线的矩阵环境：

\begin{Vmatrix}
          0 & 0 & 1 \\
          0 & 1 & 1 \\
          1 & 0 & 1 \\
          1 & 1 & 0 \\
          \end{Vmatrix}
0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{Vmatrix}

9.2.5 pmatrix

\begin{pmatrix} 是周围带小括号的矩阵环境：

\begin{pmatrix}
          0 & 0 & 1 \\
          0 & 1 & 1 \\
          1 & 0 & 1 \\
          1 & 1 & 0 \\
          \end{pmatrix}
0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{pmatrix}

9.2.6 smallmatrix

\begin{smallmatrix} 是小型矩阵环境：

\begin{smallmatrix}
          0 & 0 & 1 \\
          0 & 1 & 1 \\
          1 & 0 & 1 \\
          1 & 1 & 0 \\
          \end{smallmartix}
0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{smallmatrix}$\ 若想要周围带括号，可以在左边右边加上括号，可见第 4 章 ```latex \bigl( \begin{smallmatrix} 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{smallmatrix} \bigr) ```

\left( \begin{smallmatrix} 0 & 0 & 1 \ 0 & 1 & 1 \ 1 & 0 & 1 \ 1 & 1 & 0 \ \end{smallmatrix} \right)$

9.3 cases 环境

\begin{cases} 是方程组/分段函数环境：

\begin{cases}
          3x + 5y + z = 2 \\
          7x - 2y + 4z = 3 \\
          -6x + 3y + 2z = 4 \\
          \end{cases}
\begin{cases} 3x + 5y + z = 2 \\ 7x - 2y + 4z = 3 \\ -6x + 3y + 2z = 4 \\ \end{cases} 
f(x) =
\begin{cases}
x^2, & \text{if } x \text{ is even} \\
x+1, & \text{if } x \text{ is odd}
\end{cases}
f(x) = \begin{cases} x^2, & \text{if } x \text{ is even} \\ x+1, & \text{if } x \text{ is odd} \end{cases}

9.4 equation 环境

\begin{equation} 环境是带编号公式的基础环境：

\begin{equation}
E = mc^2
\end{equation}
\\
\begin{equation}
a^2 + b^2 = c^2
\end{equation}
\begin{equation} E = mc^2 \end{equation} \\ \begin{equation} a^2 + b^2 = c^2 \end{equation}

可搭配 aligned 使用：

\begin{equation}
\begin{aligned}
f(x) &= (x+a)(x+b) \\
     &= x^2 + (a+b)x + ab
\end{aligned}
\end{equation}
\begin{equation} \begin{aligned} f(x) &= (x+a)(x+b) \\ &= x^2 + (a+b)x + ab \end{aligned} \end{equation}

可以使用 equation* 环境隐藏编号

\begin{equation*}
E = mc^2
\end{equation*}
\\
\begin{equation}
a^2 + b^2 = c^2
\end{equation}
\begin{equation*} E = mc^2 \end{equation*} \\ \begin{equation} a^2 + b^2 = c^2 \end{equation}

9.5 CD 环境

\begin{CD} 是交换图环境：

\begin{CD}
A @>{f}>> B \\
@V{g}VV @AA{h}A \\
C @>{k}>> D
\end{CD}
\begin{CD} A @>{f}>> B \\ @V{g}VV @AA{h}A \\ C @>{k}>> D \end{CD}