TeX/LaTeX文本数学公式简易教程

乘简

Mathjax TeX/LaTeX简易教程

一、识别符（数学公式必须要夹在\(...\)与\[...\]之间）才能正确显示出来

1、行内公式，允许和文字混排版，以\(...\)夹住，可以手动加上\displaystyle。

例如：\(a^2+b^2=c^2\)，显示：\(a^2+b^2=c^2\)

2、行间公式，独占一行，以\[...\]夹住，自带\displaystyle效果，默认居中显示

例如：\[a^2+b^2=c^2\]，显示\[a^2+b^2=c^2\]

3、公式中输入的所有空格都不会显示，如想要显示空格，看下表

a\!b	a\,b	a~b	a\:b	a\ b	a\>b	a\;b	a\quad b	a\qquad b
\(a\!b\)	\(a\,b\)	\(a~b\)	\(a\:b\)	\(a\ b\)	\(a\>b\)	\(a\;b\)	\(a\quad b\)	\(a\qquad b\)
-3mu	3mu	4mu	4mu	4mu	4mu	5mu	18mu	36mu

4、公式中可以用两个反斜杠\\或\cr进行换行

例如：\[x+y=0\\y=0\]，显示\[x+y=0\\y=0\]

练习：\(a^2+b^2=c^2\)\[a^2+b^2=c^2\]

乘简

二、上下标，用^{}与_{}表示，如果后面只跟1位字符，则可以省略{}大括号

1、使用{}与不使用{}的区别

例如\(x_ij+y^{35}=0\)显示：\(x_ij+y^{35}=0\)，再如：\(f'\,f''\,f^\prime\)显示：\(f'\,f''\,f^\prime\)

2、结合上下标，也就是先下标后上标格式_{}^{}表示，可以和这些符号配合使用

\sum	\prod	\coprod	\lim	\int	\iint	\iiint	\iiiint	\oint	\bigcup	\bigcap
\(\sum\)	\(\prod\)	\(\coprod\)	\(\lim\)	\(\int\)	\(\iint\)	\(\iiint\)	\(\iiiint\)	\(\oint\)	\(\bigcup\)	\(\bigcap\)

例如：\(\lim_{n \to \infty}x_n\),显示\(\lim_{n \to \infty}x_n\)，\(\displaystyle\lim_{n \to \infty}x_n\)，显示\(\displaystyle\lim_{n \to \infty}x_n\)

\(\sum_{k=1}^N k^2\)，显示\(\sum_{k=1}^N k^2\)，\(\displaystyle\sum_{k=1}^N k^2\)，显示\(\displaystyle\sum_{k=1}^N k^2\)

3、前置上下标，有两种方法，用\sideset{}{}{}或\!都可以

3.1、用\sideset{}{}{}来设置，如\(\sideset{_1^2}{_3^4}X\)显示\(\sideset{_1^2}{_3^4}X\)

3.2、其实就是用\!把前面的上下标挨紧显示{}_1^2\!X_3^4显示\({}_1^2\!X_3^4\)

练习：\({x^5}^6 与 x^{5^6}\) 与 \(x_{i,j}\)

乘简

三、根式与分式

1、根式，使用\sqrt[]{}来表示。

例如：\(\sqrt 3\)显示：\(\sqrt 3\)，\(\sqrt[2]{32}\)显示：\(\sqrt[2]{32}\)

2、分式，直接用a/b即可，显示效果为\(a/b\)，如：\(e^{i\frac{\pi}{2}} \quad e^{\frac{i\pi}{2}} \quad e^{i\pi/2}\)，第三种字更大

3、使用\frac{a}{b}表示竖排行间分式，字号小一些，例如：\(\frac abc\)显示：\(\frac abc\)

4、小型分式，使用\tfrac{a}{b}，例如\(\tfrac abc\)显示\(\tfrac abc\)

5、大型分式（不嵌套），使用\dfrac{a}{b}，例如\(\dfrac abc\)显示\(\dfrac abc\)

6、大型分式（嵌套连分式），使用\cfrac{a}{b}，例如\(\cfrac abc\)显示\(\cfrac abc\)

7、使用{{}\over{}}来分隔一个组的前后两部分，例如\({a+1\over b+1}\)，显示\({a+1\over b+1}\)

练习：\(x=a_0+\frac{1^2}{a_1+\frac{2^2}{a_2+\frac{3^2}{a_3+\frac{4^2}{a_4+...}}}}\)
与：\(x=a_0+\cfrac{1^2}{a_1+\cfrac{2^2}{a_2+\cfrac{3^2}{a_3+\cfrac{4^2}{a_4+...}}}}\)

乘简

四、上下符号，与上下标不同，符号出现在正上下方

1、上符号，用\overset{}{}，例如：\overset{\frown}{AB}，显示：\(\overset{\frown}{AB}\)，还有\(\overset\rightharpoonup{AB}\)等

2、下符号，用\underset{}{}表示

例如：\underset{|A|}{\underbrace{x+y}}，显示：\(\underset{|A|}{\underbrace{x+y}}\)

3、其它的上下符号

\underline{xy}	\dot x \ddot x	\dddot x \ddddot x	\bar a \overline{xy}	\acute{a} \grave{a}	\check{a} \breve{a}
\(\underline{xy}\)	\(\dot x\quad\ddot x\)	\(\dddot x\quad\ddddot x\)	\(\bar a\quad\overline{xy}\)	\(\acute{a}\quad\grave{a}\)	\(\check{a}\quad\breve{a}\)
\overleftarrow{xy}	\vec{xy} \overrightarrow{xy}	\hat x \widehat{xy}	\tilde{x} \widetilde{xy}	\overbrace{xy}	\underbrace{xy}
\(\overleftarrow{xy}\)	\(\vec{xy}\quad\overrightarrow {xy}\)	\(\hat x\quad\widehat{xy}\)	\(\tilde{x}\quad\widetilde{xy}\)	\(\overbrace{1+2+3}\)	\(\underbrace{1+2+3}\)

注意：\overbrace和\underbrace这两个后面使用上下标，会把文字加在正上方和正下方

例如：\(\overbrace{1+2+\cdots+100}^{5050}\) 与 \(\underbrace{x+y}_{|A|}\)显示为\(\underbrace{x+y}_{|A|}\)

练习：\(a + \rlap{\overbrace{\phantom{b+c+d}}^m} b+ \underbrace{c+d+e}_n + f\)

乘简

五、括号，()[]{}<>||等，前面加上\left与\right后可以自动调整高度

1、二项式，自动加上小括号，用\binom{}{}和{{}\choose{}}表示，小型二项式：\tbinom{}{}，大型二项式：\dbinom{}{}

例如：{n+1\choose 2k}显示为\({n+1\choose 2k}\)。\binom{n+1}{2k}=\tbinom{n+1}{2k}=\dbinom{n+1}{2k}，显示为\(\binom{n+1}{2k}=\tbinom{n+1}{2k}=\dbinom{n+1}{2k}\)

2、其它括号（定界符）

()	\lbrack 或 [ \rbrack 或 ]	\lbrace 或 \{ \rbrace 或 \}	\langle\rangle	\mid 或 |	\| \|	\lfloor\rfloor	\lceil\rceil
\(\left(~\right)\)	\(\left[~\right]\)	\(\left\{~\right\}\)	\(\left\langle~\right\rangle\)	\(\left|~\right|\)	\(\left\|~\right\|\)	\(\left\lfloor~\right\rfloor\)	\(\left\lceil~\right\rceil\)
\((\cfrac ab)\)	\([\cfrac{a}{b}]\)	\(\{\cfrac{a}{b}\}\)	\(\langle\cfrac{a}{b}\rangle\)	\(|\cfrac{a}{b}|\)	\(\|\cfrac{a}{b}\|\)	\(\lfloor\cfrac{a}{b}\rfloor\)	\(\lceil\cfrac{a}{b}\rceil\)
\left( \right)	\left[ \right]	\left\{ \right\}	\left\langle \right\rangle	\left| \right|	\left\| \right\|	\left\lfloor \right\rfloor	\left\lceil \right\rceil
\(\left(\cfrac ab\right)\)	\(\left[\cfrac{a}{b}\right]\)	\(\left\{\cfrac{a}{b}\right\}\)	\(\left\langle\cfrac{a}{b}\right\rangle\)	\(\left|\cfrac{a}{b}\right|\)	\(\left\|\cfrac{a}{b}\right\|\)	\(\left\lfloor\cfrac{a}{b}\right\rfloor\)	\(\left\lceil\cfrac{a}{b}\right\rceil\)

注意：普通括号也可以用\big \Big \bigg \Bigg放大显示，\(\{x|x\in\Bbb Z\}\)与\(\{x\mid x\in\Bbb Z\}\)的区别

例如：\(\Big[\sum_{k=0}^n e^{k^2}\Big]\)显示为\(\Big[\sum_{k=0}^n e^{k^2}\Big]\)

练习：\(x \in \left[\dfrac12,+\infty\right)\)
与：\(\left\lbrace\sum_{i=0}^0 i^2 = \frac{(n^2+n)(2n+2)}{6}\right\rbrace\tag{1.2}\)

乘简

六、多行公式，用\begin{xxx}...\end{xxx}夹住，可以用\hline画横线，最好不要省略\(...\)与\[...\]

1、对于超长的公式，手动换行并指定对齐，用\begin{split}...\end{split}夹住，用\\换行，用&对齐每行字符

\begin{split} (a+b)^2 &=(a+b)×(a+b)\\ &=a^2＋ab＋ab＋b^2\\ &=a^2＋2ab＋b^2 \end{split}

等于号对齐

\begin{split}(a+b)^2 &=(a+b)×(a+b)\\ &=a^2＋ab＋ab＋b^2\\ &=a^2＋2ab＋b^2\end{split}

2、方程组，用\cases{}或\begin{cases}...\end{cases}夹住的公式，前面自带等高的大括号{，用&符号对齐字符，\\换行

\begin{cases} 2x+y=8&(1)\\x+y=6&(2) \end{cases}

隔\quad对齐

\begin{cases}2x+y=8&(1)\\x+y=6&(2)\end{cases}

3、矩阵，用\begin{matrix}...\end{matrix}夹住的公式，以&分隔每项（居中对齐），以\\换行

\[ A = \left\langle \begin{smallmatrix} a_{11} & \dots & a_{1n} \\ & \ddots & \vdots \\ 0 && a_{mn} \end{smallmatrix}\right\rangle _{m×n } \]

小矩阵

\[ A = \left\langle \begin{smallmatrix}a_{11} & \dots & a_{1n} \\& \ddots & \vdots \\0 && a_{mn}\end{smallmatrix}\right\rangle _{m×n} \]

注意：矩阵外面其实是可以自动加不同的括号的，这样就可以省略\left与\right，比如

matrix	pmatrix	bmatrix	Bmatrix	vmatrix	Vmatrix
\[ \begin{matrix} aa & b\\ c & dd \end{matrix} \]	\[ \begin{pmatrix} aa & b\\ c & dd \end{pmatrix} \]	\[ \begin{bmatrix} aa & b\\ c & dd \end{bmatrix} \]	\[ \begin{Bmatrix} aa & b\\ c & dd \end{Bmatrix} \]	\[ \begin{vmatrix} aa & b\\ c & dd \end{vmatrix} \]	\[ \begin{Vmatrix} aa & b\\ c & dd \end{Vmatrix} \]

4、表格，用\begin{array}{lcr}...\end{array}夹住，lcr为左中右对齐，|竖线，\hline横线，&换列，\\换行

\begin{array}{|l|c|r|} \hline 左对齐(l) & 居中(c) & 右对齐(r)\\ \hline xy & xy & xy\\ \hline 123 & 123 & 123\\ \hline \end{array}	表格线全画上	\begin{array}{|l|c|r|} \hline 左对齐(l) & 居中(c) & 右对齐(r)\\ \hline xy & xy & xy\\ \hline 123 & 123 & 123\\ \hline \end{array}
\begin{array}{l|c|r} 左对齐(l) & 居中(c) & 右对齐(r)\\ \hline xy & xy & xy\\ \hline 123 & 123 & 123\\ \end{array}	去掉四周的线	\begin{array}{l|c|r} 左对齐(l) & 居中(c) & 右对齐(r)\\ \hline xy & xy & xy\\ \hline 123 & 123 & 123\\ \end{array}

注意：由于本论坛除了用\tag{}手动编号外，没有配置自动编号，一些的命令可以使用，但不会出现编号，如： equation、multline、align、gather等

练习环节：

乘简

七、希腊字母与函数

1、希腊字母，首字母大写表示大写希腊字母，前加var表示斜体希腊字母，但不绝对

\alpha	\beta	\gamma \Gamma	\delta \Delta	\epsilon \varepsilon	\zeta	\eta	\theta \Theta	\iota	\kappa \varkappa
\(\alpha\)	\(\beta\)	\(\gamma\;\Gamma\)	\(\delta\;\Delta\)	\(\epsilon\;\varepsilon\)	\(\zeta\)	\(\eta\)	\(\theta\;\Theta\)	\(\iota\)	\(\kappa\;\varkappa\)
\lambda \Lambda	\mu	\nu	\xi \Xi	\omicron	\pi \Pi	\varpi	\rho \varrho	\sigma \Sigma	\tau
\(\lambda\;\Lambda\)	\(\mu\)	\(\nu\)	\(\xi\;\Xi\)	\(\omicron\)	\(\pi\;\Pi\)	\(\varpi\)	\(\rho\;\varrho\)	\(\sigma\;\Sigma\)	\(\tau\)
\upsilon \Upsilon	\phi \Phi	\varphi \varPhi	\chi	\psi \Psi	\omega \Omega	\digamma	\vartheta \varTheta	\varsigma \varSigma	\backepsilon
\(\upsilon\;\Upsilon\)	\(\phi\;\Phi\)	\(\varphi\;\varPhi\)	\(\chi\)	\(\psi\;\Psi\)	\(\omega\;\Omega\)	\(\digamma\)	\(\vartheta\;\varTheta\)	\(\varsigma\;\varSigma\)	\(\backepsilon\)

2、函数，是为了让字体显示正体字，因为默认情况下是斜体字，且自动留些间距

例如：\(sinx\)与\(\sin x\)的区别，显示\(sinx与\sin x\)，\pmod{m}与a\bmod b显示\(\pmod{m}与{a\bmod b}\)

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

练习环节：

乘简

八、符号大全

1、箭头

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

2、其它符号，一些符号如\#,\&,\_,\%,\{,\}等，前面必须要加\

\Cup \Cap	\subset \supset	\succneqq \precneqq	\subsetneqq \supsetneqq	\varsupsetneqq \varsubsetneqq	\nsupseteqq \nsubseteqq	\subseteq \supseteq	\ni \not\ni	\in \notin
\(\Cup\;\Cap\)	\(\subset\;\supset\)	\(\succneqq\;\precneqq\)	\(\subsetneqq\;\supsetneqq\)	\(\varsupsetneqq\;\varsubsetneqq\)	\(\nsupseteqq\;\nsubseteqq\)	\(\subseteq\;\supseteq\)	\(\ni\;\not\ni\)	\(\in\;\notin\)
\nprec \nsucc	\Subset \Supset	\succnsim \precnsim	\supseteqq \subseteqq	\supsetneq \varsupsetneq	\nsupseteq \nsubseteq	\succsim \precsim	\succ \succeq	\lt \gt
\(\nprec\;\nsucc\)	\(\Subset\;\Supset\)	\(\succnsim\;\precnsim\)	\(\supseteqq\;\subseteqq\)	\(\supsetneq\;\varsupsetneq\)	\(\nsupseteq\;\nsubseteq\)	\(\succsim\;\precsim\)	\(\succ\;\succeq\)	\(\lt\;\gt\)
\leqq \geqq	\cap \bigcap	\lnapprox \gnapprox	\succnapprox \precnapprox	\subsetneq \varsubsetneq	\doublecap \doublecup	\lessgtr \gtrless	\prec \preceq	\ge \le
\(\leqq\;\geqq\)	\(\cap\;\bigcap\)	\(\lnapprox\;\gnapprox\)	\(\succnapprox\;\precnapprox\)	\(\subsetneq\;\varsubsetneq\)	\(\doublecap\;\doublecup\)	\(\lessgtr\;\gtrless\)	\(\prec\;\preceq\)	\(\ge\;\le\)
\lnot \net	\cup \bigcup	\uplus \biguplus	\succcurlyeq \preccurlyeq	\risingdotseq \fallingdotseq	\curlyeqprec \curlyeqsucc	\lessdot \gtrdot	\not\lt \ngtr	\ll \gg
\(\lnot\;\neg\)	\(\cup\;\bigcup\)	\(\uplus\;\biguplus\)	\(\succcurlyeq\;\preccurlyeq\)	\(\risingdotseq\;\fallingdotseq\)	\(\curlyeqprec\;\curlyeqsucc\)	\(\lessdot\;\gtrdot\)	\( \not\lt\;\ngtr\)	\(\ll\;\gg\)
\lneq \gneq	\equiv \eqcirc	\approx \approxeq	\succapprox \precapprox	\doublebarwedge	\curlyvee \curlywedge	\lesssim \gtrsim	\lll \ggg	\lnsim \gnsim
\(\lneq\;\gneq\)	\(\equiv\;\eqcirc\)	\(\approx\;\approxeq\)	\(\succapprox\;\precapprox\)	\(\doublebarwedge\)	\(\curlyvee\;\curlywedge\)	\(\lesssim\;\gtrsim\)	\(\lll\;\ggg\)	\(\lnsim\;\gnsim\)
\nleq \ngeq	\doteq \Doteq	\sim \backsim	\eqslantgtr \eqslantless	\vartriangle \bigtriangleup	\gtreqqless \lesseqqgtr	\leqslant \geqslant	\gneqq \lneqq	\ncong \cong
\(\nleq\;\ngeq\)	\(\doteq\;\Doteq\)	\(\sim\;\backsim\)	\(\eqslantgtr\;\eqslantless\)	\(\vartriangle\;\bigtriangleup\)	\(\gtreqqless\;\lesseqqgtr\)	\(\leqslant\;\geqslant\)	\(\gneqq\;\lneqq\)	\(\ncong\;\cong\)
\ne \neq	\Vvdash \Vdash	\lesseqgtr \gtreqless	\lessapprox \gtrapprox	\ntrianglerighteq \ntrianglelefteq	\ngeqslant \nleqslant	\simeq \backsimeq	\nleqq \ngeqq	\nsim \eqsim
\(\ne\;\neq\)	\(\Vvdash\;\Vdash\)	\(\lesseqgtr\;\gtreqless\)	\(\lessapprox\;\gtrapprox\)	\(\ntrianglerighteq\;\ntrianglelefteq\)	\(\ngeqslant\;\nleqslant\)	\(\simeq\;\backsimeq\)	\(\nleqq\;\ngeqq\)	\(\nsim\;\eqsim\)
\dashv \vdash	\nVDash \nVdash	\vDash \models	\sqsubset \sqsubseteq	\ntriangleright \ntriangleleft	\sqsupset \sqsupseteq	\sqcup \bigsqcup	\nvDash \nvdash	\bot \perp
\(\dashv\;\vdash\)	\(\nVDash\;\nVdash\)	\(\vDash\;\models\)	\(\sqsubset\;\sqsubseteq\)	\(\ntriangleright\;\ntriangleleft\)	\(\sqsupset\;\sqsupseteq\)	\(\sqcup\;\bigsqcup\)	\(\nvDash\;\nvdash\)	\(\bot\perp\)
\lor \vee	\exists \nexists	\land \wedge	\circeq \triangleq	\triangledown \bigtriangledown	\veebar \barwedge	\sqcap	\partial	\eth
\(\lor\;\vee\)	\(\exists\;\nexists\)	\(\land\;\wedge\)	\(\circeq\;\triangleq\)	\(\triangledown\;\bigtriangledown\)	\(\veebar\;\barwedge\)	\(\sqcap\)	\(\partial\)	\(\eth\)
\nabla	\forall	\top \intercal	\bigvee \bigwedge	\trianglelefteq \trianglerighteq	\emptyset \varnothing	\ominus \oslash	\star \bigstar	\ddots
\(\nabla\)	\(\forall\)	\(\top\;\intercal\)	\(\bigvee\;\bigwedge\)	\(\trianglelefteq\;\trianglerighteq\)	\(\emptyset\;\varnothing\)	\(\ominus\;\oslash\)	\(\star\;\bigstar\)	\(\ddots\)
\unlhd \unrhd	\angle	\ulcorner \urcorner	\Diamond \diamondsuit	\triangleleft \triangleright	\lvertneqq \gvertneqq	\triangle	\Box \square	\rhd \lhd
\(\unlhd\;\unrhd\)	\(\angle\)	\(\ulcorner\;\urcorner\)	\(\Diamond\;\diamondsuit\)	\(\triangleleft\;\triangleright\)	\(\lvertneqq\;\gvertneqq\)	\(\triangle\)	\(\Box\;\square\)	\(\rhd\;\lhd\)
\cdot \ldotp	\infty \propto	\llcorner \lrcorner	\boxtimes \boxplus	\sphericalangle \measuredangle	\lmoustache \rmoustache	\lgroup \rgroup	\rtimes \ltimes	\aleph
\(\cdot\;\ldotp\)	\(\infty\;\propto\)	\(\llcorner\;\lrcorner\)	\(\boxtimes\;\boxplus\)	\(\sphericalangle\;\measuredangle\)	\(\lmoustache\;\rmoustache\)	\(\lgroup\;\rgroup\)	\(\rtimes\ltimes\)	\(\aleph\)
\S	\circ \bigcirc	\dagger \ddagger	\backslash \setminus	\leftthreetimes \rightthreetimes	\smallsmile \smallfrown	\diagup \diagdown	\smile \frown	\wr
\(\S\)	\(\circ\;\bigcirc\)	\(\dagger\;\ddagger\)	\(\backslash\;\setminus\)	\(\leftthreetimes\;\rightthreetimes\)	\(\smallsmile\;\smallfrown\)	\(\diagup\;\diagdown\)	\(\smile\;\frown\)	\(\wr\)
\pm \mp	\Join \bowtie	\bumpeq \Bumpeq	\circledcirc \circleddash	\blacktriangle \blacktriangledown	\otimes \bigotimes	\sharp \natural	\vdots	\Game
\(\pm\;\mp\)	\(\Join\;\bowtie\)	\(\bumpeq\;\Bumpeq\)	\(\circledcirc\;\circleddash\)	\(\blacktriangle\;\blacktriangledown\)	\(\otimes\;\bigotimes\)	\(\sharp\;\natural\)	\(\vdots\)	\(\Game\)
\times	\div	\circledR \circledS	\because \therefore	\blacktriangleleft \blacktriangleright	\oplus \bigoplus	\odot \bigodot	\boxdot	\gimel \beth
\(\times\)	\(\div\)	\(\circledR\;\circledS\)	\(\because\;\therefore\)	\(\blacktriangleleft\;\blacktriangleright\)	\(\oplus\;\bigoplus\)	\(\odot\;\bigodot\)	\(\boxdot\)	\(\gimel\;\beth\)
\flat	\Finv	\asymp \between	\clubsuit \spadesuit	\circledast \divideontimes	\parallel \nparallel	\diamond \lozenge	\amalg \coprod	\nmid
\(\flat\)	\(\Finv\)	\(\asymp\;\between\)	\(\clubsuit\;\spadesuit\)	\(\circledast\;\divideontimes\)	\(\parallel\;\nparallel\)	\(\diamond\;\lozenge\)	\(\amalg\;\coprod\)	\(\nmid\)
\yen	\ldots \cdots	\bullet \centerdot	\surd \checkmark	\blacksquare \blacklozenge	\pitchfork	\multimap	\daleth	\ell \iota
\(\yen\)	\(\ldots\;\cdots\)	\(\bullet\;\centerdot\)	\(\surd \checkmark\)	\(\blacksquare\;\blacklozenge\)	\(\pitchfork\)	\(\multimap\)	\(\daleth\)	\(\ell\;\iota\)
\dots	\hbar \hslash	\dotplus	\nshortmid \shortmid	\shortparallel \nshortparallel	f' \backprime	\intop \smallint	\jmath	\Im \imath
\(\dots\)	\(\hbar\;\hslash\)	\(\dotplus\)	\(\nshortmid\;\shortmid\)	\(\shortparallel\;\nshortparallel\)	\(f'\;\backprime\)	\(\intop\;\smallint\)	\(\jmath\)	\(\Im\;\imath\)
\Re	\maltese	\boxminus	\complement	\smallsetminus	\heartsuit	\idotsint	\wp	\mho
\(\Re\)	\(\maltese\)	\(\boxminus\)	\(\complement\)	\(\smallsetminus\)	\(\heartsuit\)	\(\idotsint\)	\(\wp\)	\(\mho\)

练习环节：

乘简

九、字体与颜色

1、字体

默认	\mathsf{}	\mathbf{}	\mathtt{}	\mathbb{}	\mathit{}
\[{ABCabc123}\]	\[\mathsf{ABCabc123}\]	\[\mathbf{ABCabc123}\]	\[\mathtt{ABCabc123}\]	\[\mathbb{ABCabc123}\]	\[\mathit{ABCabc123}\]
\mathrm{}	\mathcal{}	\mathscr{}	\mathfrak{}	\boldsymbol{}
\[\mathrm{ABCabc123}\]	\[\mathcal{ABCabc123}\]	\[\mathscr{ABCabc123}\]	\[\mathfrak{ABCabc123}\]	\[\boldsymbol{ABCabc123}\]

2、字号，从小到大

\tiny	\Tiny	\small	默认	\large	\Large	\LARGE	\huge	\Huge
\(\tiny{Aa12}\)	\(\Tiny{Aa12}\)	\(\small{Aa12}\)	\(Aa12\)	\(\large{Aa12}\)	\(\Large{Aa12}\)	\(\LARGE{Aa12}\)	\(\huge{Aa12}\)	\(\Huge{Aa12}\)

3、前景颜色，用\color{}{}表示，前面那个大括号中填写颜色名称或颜色值#RGB表示

例如：\(\color{red}{www}.\color{#168}{mathchina}.com\)显示：\(\color{red}{www}.\color{#168}{mathchina}.com\)

\(\rm\color{black}{black}\)

\(\rm\color{red}{red}\)

\(\rm\color{green}{green}\)

\(\rm\color{blue}{blue}\)

\(\rm\color{maroon}{maroon}\)

\(\rm\color{yellow}{yellow}\)

\(\rm\color{lime}{lime}\)

\(\rm\color{olive}{olive}\)

\(\rm\color{teal}{teal}\)

\(\rm\color{aqua}{aqua}\)

\(\rm\color{navy}{navy}\)

\(\rm\color{purple}{purple}\)

\(\rm\color{fuchsia}{fuchsia}\)

4、背景颜色，可以用\style{background-color:red}{}来设置公式区的背景颜色，颜色可以是代码或#RGB值

例如：\(\style{background-color:aqua}{c=2\pi r}\)显示为\(\style{background-color:aqua}{c=2\pi r}\)，当然\style{}{}可以设置任何的css样式

练习环节：

乘简

十、其它公式

1、加框，可以用\boxed或\fbox，二者的区别是\fbox中文本原样显示，而\boxed中则以公式显示

例如：\(x+\boxed{y^2}=0\)与\(x+\fbox{y^2}=0\)显示为\(x+\boxed{y^2}=0\)与\(x+\fbox{y^2}=0\)

2、垂直居中显示\vcenter{}

例如：\(y_2\)显示为\(y_2\)，而用\vcenter{y}_2后，显示为\(\vcenter{y}_2\)

3、单位，也就是指定一些字符上下左右微调，单位有pt,em,mu,px等

px：屏幕像素点，如1920*1080分辩率表示横坐标有1920px，纵坐标有1080px
pt：磅，也就是1/72英寸
以96dpi来计算，1em=12pt=16px=18mu

4、水平移动XX单位，负值为左移，正值为右移\kern{}{}

例如：\(I\kern{-3pt}R\)，显示为\(I\kern{-3pt}R\)，\(I\kern{1em}R\)显示为\(I\kern{1em}R\)

5、上下升降XX单位，\raise{}{}上移，\lower{}{}下移，负号正好相反

例如：\(a\raise{5pt}{bc}d\)，显示为\(a\raise{5pt}{bc}d\)，\(a\lower{5pt}{bc}d\)显示为\(a\lower{5pt}{bc}d\)

6、本教程中没有包函的字符，但在符号库中有，如何打入数学公式呢？

例如：\(\unicode{x2153}\)，显示为\(\unicode{x2153}\)

7、当公式中出现与论坛主贴标签[b]冲突时怎么办？

例如：论坛用来设置粗体字，此时公式中只能用\lbrack与\rbrack来代替[],\(\lbrack b\rbrack\)显示为\(\lbrack b\rbrack\)

练习：\(\kern3mu\raise1mu{.}\kern3mu\raise6mu{.}\kern3mu\raise12mu{.}\)