乘简 发表于 2020-7-25 21:05

TeX/LaTeX文本数学公式简易教程

<h1 align=center>Mathjax TeX/LaTeX简易教程</h1>
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<h2>一、识别符<font size=3>(数学公式必须要夹在<code><font color=red>\(</font>...<font color=red>\)</font>与<font color=red>\[</font>...<font color=red>\]</font></code>之间)才能正确显示出来</font></h2>
<h3>1、行内公式,允许和文字混排版,以<code><font color=red>\(</font>...<font color=red>\)</font></code>夹住,可以手动加上\displaystyle。</h3>
<p class=tp>例如:<code>\(a^2+b^2=c^2\)</code>,显示:\(a^2+b^2=c^2\)</p>
<br>
<h3>2、行间公式,独占一行,以<code><font color=red>\[</font>...<font color=red>\]</font></code>夹住,自带\displaystyle效果,默认居中显示</h3>
<p class=tp>例如:<code>\</code>,显示\</p>
<h3>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</h3>
<table class="t_table tb" style="width:80%">
<tr><td>a\!b</td><td>a\,b</td><td>a~b</td><td>a\:b</td><td>a\ b</td><td>a\>b</td><td>a\;b</td><td>a\quad b</td><td>a\qquad b</td></tr>
<tr><td>\(a\!b\)</td><td>\(a\,b\)</td><td>\(a~b\)</td><td>\(a\:b\)</td><td>\(a\ b\)</td><td>\(a\>b\)</td><td>\(a\;b\)</td><td>\(a\quad b\)</td><td>\(a\qquad b\)</td></tr>
<tr><td>-3mu</td><td>3mu</td><td>4mu</td><td>4mu</td><td>4mu</td><td>4mu</td><td>5mu</td><td>18mu</td><td>36mu</td></tr>
</table>
<br>
<h3>4、公式中可以用两个反斜杠\\或\cr进行换行</h3>
<p class=tp>例如:<code>\</code>,显示\</p>

<p class=lx>练习:<code>\(a^2+b^2=c^2\)\</code></p>
<div id=lx1></div>
<script>
lxs(1);
</script>

乘简 发表于 2020-7-25 21:07

<h2>二、上下标,用^{}与_{}表示,如果后面只跟1位字符,则可以省略<font color=red>{}</font>大括号</h2>
<h3>1、使用{}与不使用{}的区别</h3>
<p class=tp>例如<code>\(x_ij+y^{35}=0\)</code>显示:\(x_ij+y^{35}=0\),再如:<code>\(f'\,f''\,f^\prime\)</code>显示:\(f'\,f''\,f^\prime\)</p>
<br>
<h3>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</h3>
<table class="t_table tb" style="width:70%"><tr>
<td>\sum</td><td>\prod</td><td>\coprod</td><td>\lim</td><td>\int</td><td>\iint</td><td>\iiint</td><td>\iiiint</td><td>\oint</td><td>\bigcup</td><td>\bigcap</td>
</tr><tr>
<td>\(\sum\)</td><td>\(\prod\)</td><td>\(\coprod\)</td><td>\(\lim\)</td><td>\(\int\)</td><td>\(\iint\)</td><td>\(\iiint\)</td><td>\(\iiiint\)</td><td>\(\oint\)</td><td>\(\bigcup\)</td><td>\(\bigcap\)</td>
</tr></table>
<p class=tp>例如:<code>\(\lim_{n \to \infty}x_n\)</code>,显示\(\lim_{n \to \infty}x_n\),<code>\(\displaystyle\lim_{n \to \infty}x_n\)</code>,显示\(\displaystyle\lim_{n \to \infty}x_n\)</p>
<p class=tp><code>\(\sum_{k=1}^N k^2\)</code>,显示\(\sum_{k=1}^N k^2\)<code>,\(\displaystyle\sum_{k=1}^N k^2\)</code>,显示\(\displaystyle\sum_{k=1}^N k^2\)</p>

<h3>3、前置上下标,有两种方法,用\sideset{}{}{}或\!都可以</h3>
<h4>3.1、用\sideset{}{}{}来设置,如<code>\(\sideset{_1^2}{_3^4}X\)</code>显示\(\sideset{_1^2}{_3^4}X\)</h4>
<h4>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\({}_1^2\!X_3^4\)</h4>

<p class=lx>练习:<code>\({x^5}^6 与 x^{5^6}\) 与 \(x_{i,j}\)</code></p>
<div id=lx2></div>
<script>
lxs(2);
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乘简 发表于 2020-7-25 21:08

<h2>三、根式与分式</h2>
<h3>1、根式,使用\sqrt[]{}来表示。</h3>
<p class=tp>例如:<code>\(\sqrt 3\)</code>显示:\(\sqrt 3\),<code>\(\sqrt{32}\)</code>显示:\(\sqrt{32}\)</p>

<h3>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</h3>
<h3>3、使用\frac{a}{b}表示竖排行间分式,字号小一些,例如:<code>\(\frac abc\)</code>显示:\(\frac abc\)</h3>
<h3>4、小型分式,使用\tfrac{a}{b},例如<code>\(\tfrac abc\)</code>显示\(\tfrac abc\)</h3>
<h3>5、大型分式(不嵌套),使用\dfrac{a}{b},例如<code>\(\dfrac abc\)</code>显示\(\dfrac abc\)</h3>
<h3>6、大型分式(嵌套连分式),使用\cfrac{a}{b},例如<code>\(\cfrac abc\)</code>显示\(\cfrac abc\)</h3>
<h3>7、使用{{}\over{}}来分隔一个组的前后两部分,例如<code>\({a+1\over b+1}\)</code>,显示\({a+1\over b+1}\)</h3>

<p class=lx>练习:<code>\(x=a_0+\frac{1^2}{a_1+\frac{2^2}{a_2+\frac{3^2}{a_3+\frac{4^2}{a_4+...}}}}\)<br>
与:\(x=a_0+\cfrac{1^2}{a_1+\cfrac{2^2}{a_2+\cfrac{3^2}{a_3+\cfrac{4^2}{a_4+...}}}}\)</code></p>
<div id=lx3></div>
<script>
lxs(3);
</script>

乘简 发表于 2020-7-25 21:08

<h2>四、上下符号,与上下标不同,符号出现在正上下方</h2>
<h3>1、上符号,用\overset{}{},例如:\overset{\frown}{AB},显示:\(\overset{\frown}{AB}\),还有\(\overset\rightharpoonup{AB}\)等</h3>
<h3>2、下符号,用\underset{}{}表示</h3>
<p class=tp>例如:\underset{|A|}{\underbrace{x+y}},显示:\(\underset{|A|}{\underbrace{x+y}}\)</p>
<h3>3、其它的上下符号</h3>
<table class="t_table tb">
<tr><td>\underline{xy}</td><td>\dot x<br>\ddot x</td><td>\dddot x<br>\ddddot x</td><td>\bar a<br>\overline{xy}</td><td>\acute{a}<br>\grave{a}</td><td>\check{a}<br>\breve{a}</td></tr>
<tr><td>\(\underline{xy}\)</td><td>\(\dot x\quad\ddot x\)</td><td>\(\dddot x\quad\ddddot x\)</td><td>\(\bar a\quad\overline{xy}\)</td><td>\(\acute{a}\quad\grave{a}\)</td><td>\(\check{a}\quad\breve{a}\)</td></tr>
<tr><td>\overleftarrow{xy}</td><td>\vec{xy}<br>\overrightarrow{xy}</td><td>\hat x<br>\widehat{xy}</td><td>\tilde{x}<br>\widetilde{xy}</td><td>\overbrace{xy}</td><td>\underbrace{xy}</td></tr>
<tr><td>\(\overleftarrow{xy}\)</td><td>\(\vec{xy}\quad\overrightarrow {xy}\)</td><td>\(\hat x\quad\widehat{xy}\)</td><td>\(\tilde{x}\quad\widetilde{xy}\)</td><td>\(\overbrace{1+2+3}\)</td><td>\(\underbrace{1+2+3}\)</td></tr>
</table>
<h3>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</h3>
<p class=tp>例如:\(\overbrace{1+2+\cdots+100}^{5050}\) 与 <code>\(\underbrace{x+y}_{|A|}\)</code>显示为\(\underbrace{x+y}_{|A|}\)</p>

<p class=lx>练习:<code>\(a + \rlap{\overbrace{\phantom{b+c+d}}^m} b+ \underbrace{c+d+e}_n + f\)</code></p>
<div id=lx4></div>
<script>
lxs(4);
</script>

乘简 发表于 2020-7-25 21:08

<h2>五、括号,()[]{}<>||等,前面加上\left与\right后可以自动调整高度</h2>
<h3>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{}{}</h3>
<p class=tp>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\(\binom{n+1}{2k}=\tbinom{n+1}{2k}=\dbinom{n+1}{2k}\)</p>
<h3>2、其它括号(定界符)</h3>
<table class="t_table tb">
<tr><td>()</td><td>\lbrack 或 [<br>\rbrack 或 ]</td><td>\lbrace 或 \{<br>\rbrace 或 \}</td><td>\langle\rangle</td><td>\mid 或 |</td><td>\| \|</td><td>\lfloor\rfloor</td><td>\lceil\rceil</td></tr>
<tr><td>\(\left(~\right)\)</td><td>\(\left[~\right]\)</td><td>\(\left\{~\right\}\)</td><td>\(\left\langle~\right\rangle\)</td><td>\(\left|~\right|\)</td><td>\(\left\|~\right\|\)</td><td>\(\left\lfloor~\right\rfloor\)</td><td>\(\left\lceil~\right\rceil\)</td></tr>
<tr><td>\((\cfrac ab)\)</td><td>\([\cfrac{a}{b}]\)</td><td>\(\{\cfrac{a}{b}\}\)</td><td>\(\langle\cfrac{a}{b}\rangle\)</td><td>\(|\cfrac{a}{b}|\)</td><td>\(\|\cfrac{a}{b}\|\)</td><td>\(\lfloor\cfrac{a}{b}\rfloor\)</td><td>\(\lceil\cfrac{a}{b}\rceil\)</td></tr>
<tr><td>\left(<br>\right)</td><td>\left[<br>\right]</td><td>\left\{<br>\right\}</td><td>\left\langle<br>\right\rangle</td><td>\left|<br>\right|</td><td>\left\|<br>\right\|</td><td>\left\lfloor<br>\right\rfloor</td><td>\left\lceil<br>\right\rceil</td></tr>
<tr><td>\(\left(\cfrac ab\right)\)</td><td>\(\left[\cfrac{a}{b}\right]\)</td><td>\(\left\{\cfrac{a}{b}\right\}\)</td><td>\(\left\langle\cfrac{a}{b}\right\rangle\)</td><td>\(\left|\cfrac{a}{b}\right|\)</td><td>\(\left\|\cfrac{a}{b}\right\|\)</td><td>\(\left\lfloor\cfrac{a}{b}\right\rfloor\)</td><td>\(\left\lceil\cfrac{a}{b}\right\rceil\)</td></tr>
</table>
<h3>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</h3>
<p class=tp>例如:<code>\(\Big[\sum_{k=0}^n e^{k^2}\Big]\)</code>显示为\(\Big[\sum_{k=0}^n e^{k^2}\Big]\)</p>

<p class=lx>练习:<code>\(x \in \left[\dfrac12,+\infty\right)\)<br>
与:\(\left\lbrace\sum_{i=0}^0 i^2 = \frac{(n^2+n)(2n+2)}{6}\right\rbrace\tag{1.2}\)</code></p>
<div id=lx5></div>
<script>
lxs(5);
</script>

乘简 发表于 2020-7-25 21:09

<h2>六、多行公式,用<code>\begin{xxx}...\end{xxx}</code>夹住,可以用\hline画横线,最好不要省略<code>\(...\)与\[...\]</code></h2>
<h3>1、对于超长的公式,手动换行并指定对齐,用<code>\begin{split}...\end{split}</code>夹住,用<font color=red>\\</font>换行,用<font color=red>&</font>对齐每行字符</h3>
<table class="t_table tb" style="width:95%"><tr><td><code>\begin{split}<br>
(a+b)^2 &=(a+b)×(a+b)\\<br> &=a^2+ab+ab+b^2\\<br> &=a^2+2ab+b^2<br>
\end{split}</code></td><td>等于号对齐</td>
<td>\begin{split}(a+b)^2 &=(a+b)×(a+b)\\ &=a^2+ab+ab+b^2\\ &=a^2+2ab+b^2\end{split}</td></tr></table>

<h3>2、方程组,用<code>\cases{}或\begin{cases}...\end{cases}</code>夹住的公式,前面自带等高的大括号{,用<font color=red>&</font>符号对齐字符,<font color=red>\\</font>换行</h3>
<table class="t_table tb" style="width:95%">
<tr><td><code>\begin{cases}<br>2x+y=8<font color=red>&</font>(1)<font color=red>\\</font>x+y=6<font color=red>&</font>(2)<br>\end{cases}</code></td><td>隔\quad对齐</td><td>\begin{cases}2x+y=8&(1)\\x+y=6&(2)\end{cases}</td></tr>
</table>

<h3>3、矩阵,用<code>\begin{matrix}...\end{matrix}</code>夹住的公式,以<font color=red>&</font>分隔每项(居中对齐),以<font color=red>\\</font>换行</h3>
<table class="t_table tb" style="width:95%"><tr><td><code>\[ A = \left\langle \begin{smallmatrix}<br>
a_{11} & \dots & a_{1n} \\<br>
& \ddots & \vdots \\<br>
0 && a_{mn}<br>
\end{smallmatrix}\right\rangle _{m×n }\]</code></td>
<td>小矩阵</td>
<td>\[ A = \left\langle \begin{smallmatrix}a_{11} & \dots & a_{1n} \\& \ddots & \vdots \\0 && a_{mn}\end{smallmatrix}\right\rangle _{m×n} \]</td></tr></table>
<h4>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</h4>
<table class="t_table tb" style="width:95%">
<tr><td>matrix</td><td>pmatrix</td><td>bmatrix</td><td>Bmatrix</td><td>vmatrix</td><td>Vmatrix</td></tr>
<tr><td>\[ \begin{matrix}<br>aa &amp; b\\<br>c &amp; dd<br>\end{matrix} \]</td>
<td>\[ \begin{pmatrix}<br>aa &amp; b\\<br>c &amp; dd<br>\end{pmatrix} \]</td>
<td>\[ \begin{bmatrix}<br>aa &amp; b\\<br>c &amp; dd<br>\end{bmatrix} \]</td>
<td>\[ \begin{Bmatrix}<br>aa &amp; b\\<br>c &amp; dd<br>\end{Bmatrix} \]</td>
<td>\[ \begin{vmatrix}<br>aa &amp; b\\<br>c &amp; dd<br>\end{vmatrix} \]</td>
<td>\[ \begin{Vmatrix}<br>aa &amp; b\\<br>c &amp; dd<br>\end{Vmatrix} \]</td></tr></table>

<h3>4、表格,用<code>\begin{array}{lcr}...\end{array}</code>夹住,lcr为左中右对齐,|竖线,\hline横线,&换列,\\换行</h3>
<table class="t_table tb" style="width:95%"><tr><td><code>\begin{array}{|l|c|r|}<br>
\hline 左对齐(l)& 居中(c) & 右对齐(r)\\<br>
\hline xy & xy & xy\\<br>
\hline 123 & 123 & 123\\<br>
\hline \end{array}</code></td>
<td>表格线全画上</td>
<td>\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}</td></tr>

<tr><td><code>\begin{array}{l|c|r}<br>
左对齐(l)& 居中(c) & 右对齐(r)\\<br>
\hline xy & xy & xy\\<br>
\hline 123 & 123 & 123\\<br>
\end{array}</code></td>
<td>去掉四周的线</td>
<td>\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}</td></tr></table>

<h3>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</h3>

<p class=lx>练习环节:</p>
<div id=lx6></div>
<script>
lxs(6);
</script>

乘简 发表于 2020-7-25 21:09

<h2>七、希腊字母与函数</h2>
<h3>1、希腊字母,首字母大写表示大写希腊字母,前加<font color=red>var</font>表示斜体希腊字母,但不绝对</h3>
<table class="tb">
<tr><td>\alpha</td><td>\beta</td><td>\gamma<br>\Gamma</td><td>\delta<br>\Delta</td><td>\epsilon<br>\varepsilon</td><td>\zeta</td><td>\eta</td><td>\theta<br>\Theta</td><td>\iota</td><td>\kappa<br>\varkappa</td></tr>
<tr><td>\(\alpha\)</td><td>\(\beta\)</td><td>\(\gamma\;\Gamma\)</td><td>\(\delta\;\Delta\)</td><td>\(\epsilon\;\varepsilon\)</td><td>\(\zeta\)</td><td>\(\eta\)</td><td>\(\theta\;\Theta\)</td><td>\(\iota\)</td><td>\(\kappa\;\varkappa\)</td></tr>
<tr><td>\lambda<br>\Lambda</td><td>\mu</td><td>\nu</td><td>\xi<br>\Xi</td><td>\omicron</td><td>\pi<br>\Pi</td><td>\varpi</td><td>\rho<br>\varrho</td><td>\sigma<br>\Sigma</td><td>\tau</td></tr>
<tr><td>\(\lambda\;\Lambda\)</td><td>\(\mu\)</td><td>\(\nu\)</td><td>\(\xi\;\Xi\)</td><td>\(\omicron\)</td><td>\(\pi\;\Pi\)</td><td>\(\varpi\)</td><td>\(\rho\;\varrho\)</td><td>\(\sigma\;\Sigma\)</td><td>\(\tau\)</td></tr>
<tr><td>\upsilon<br>\Upsilon</td><td>\phi&nbsp;\Phi</td><td>\varphi<br>\varPhi</td><td>\chi</td><td>\psi<br>\Psi</td><td>\omega<br>\Omega</td><td>\digamma</td><td>\vartheta<br>\varTheta</td><td>\varsigma<br>\varSigma</td><td>\backepsilon</td></tr>
<tr><td>\(\upsilon\;\Upsilon\)</td><td>\(\phi\;\Phi\)</td><td>\(\varphi\;\varPhi\)</td><td>\(\chi\)</td><td>\(\psi\;\Psi\)</td><td>\(\omega\;\Omega\)</td><td>\(\digamma\)</td><td>\(\vartheta\;\varTheta\)</td><td>\(\varsigma\;\varSigma\)</td><td>\(\backepsilon\)</td></tr>
</table>
<br>
<h3>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</h3>
<p class=tp>例如:<code>\(sinx\)与\(\sin x\)</code>的区别,显示\(sinx与\sin x\),<code>\pmod{m}与a\bmod b</code>显示\(\pmod{m}与{a\bmod b}\)</p>
<table class="t_table tb" style="width:85%">
<tr><td>\(\sin\)</td><td>\(\cos\)</td><td>\(\tan\)</td><td>\(\sec\)</td><td>\(\csc\)</td><td>\(\cot\)</td><td>\(\exp\)</td><td>\(\log\)</td><td>\(\ln\)</td><td>\(\lg\)</td><td>mod</td></tr>
<tr><td>\(\sinh\)</td><td>\(\cosh\)</td><td>\(\tanh\)</td><td>\(\coth\)</td><td>\(\det\)</td><td>\(\dim\)</td><td>\(\ker\)</td><td>\(\deg\)</td><td>\(\arg\)</td><td>\(\gcd\)</td><td>\(\hom\)</td></tr>
<tr><td>\(\arcsin\)</td><td>\(\arccos\)</td><td>\(\arctan\)</td><td>\(\min\)</td><td>\(\max\)</td><td>\(\inf\)</td><td>\(\sup\)</td><td>\(\liminf\)</td><td>\(\limsup\)</td><td>\(\lim\)</td><td>\(\Pr\)</td></tr>
</table>

<p class=lx>练习环节:</p>
<div id=lx7></div>
<script>
lxs(7);
</script>

乘简 发表于 2020-7-25 21:09

<h2>八、符号大全</h2>
<h3>1、箭头</h3>
<table class="t_table tb">
<tr><td>\to<br>\rightarrow</td><td>\gets<br>\leftarrow</td><td>\leftrightarrow</td><td>\nearrow</td><td>\searrow</td></tr>
<tr><td>\(\to\;\rightarrow\)</td><td>\(\gets\;\leftarrow\)</td><td>\(\leftrightarrow\)</td><td>\(\nearrow\)</td><td>\(\searrow\)</td></tr>

<tr><td>\downarrow</td><td>\uparrow</td><td>\updownarrow</td><td>\swarrow</td><td>\nwarrow</td></tr>
<tr><td>\(\downarrow\)</td><td>\(\uparrow\)</td><td>\(\updownarrow\)</td><td>\(\swarrow\)</td><td>\(\nwarrow\)</td></tr>

<tr><td>\Leftarrow</td><td>\Rightarrow</td><td>\Leftrightarrow</td><td>\rightharpoonup</td><td>\rightharpoondown</td></tr>
<tr><td>\(\Leftarrow\)</td><td>\(\Rightarrow\)</td><td>\(\Leftrightarrow\)</td><td>\(\rightharpoonup\)</td><td>\(\rightharpoondown\)</td></tr>

<tr><td>\impliedby<br>\Longleftarrow</td><td>\implies<br>\Longrightarrow</td><td>\iff<br>\Longleftrightarrow</td><td>\leftharpoonup</td><td>\leftharpoondown</td></tr>
<tr><td>\(\impliedby\;\Longleftarrow\)</td><td>\(\implies\;\Longrightarrow\)</td><td>\(\iff\;\Longleftrightarrow\)</td><td>\(\leftharpoonup\)</td><td>\(\leftharpoondown\)</td></tr>

<tr><td>\longleftarrow</td><td>\longrightarrow</td><td>\longleftrightarrow</td><td>\upharpoonleft</td><td>\upharpoonright<br>\restriction</td></tr>
<tr><td>\(\longleftarrow\)</td><td>\(\longrightarrow\)</td><td>\(\longleftrightarrow\)</td><td>\(\upharpoonleft\)</td><td>\(\upharpoonright\;\restriction\)</td></tr>

<tr><td>\Uparrow</td><td>\Downarrow</td><td>\Updownarrow</td><td>\rightleftharpoons<br>\leftrightharpoons</td><td>\downharpoonright<br>\downharpoonleft</td></tr>
<tr><td>\(\Uparrow\)</td><td>\(\Downarrow\)</td><td>\(\Updownarrow\)</td><td>\(\rightleftharpoons\;\leftrightharpoons\)</td><td>\(\downharpoonright\;\downharpoonleft\)</td></tr>

<tr><td>\nleftarrow</td><td>\nleftrightarrow</td><td>\nrightarrow</td><td>\rightleftarrows<br>\leftrightarrows</td><td>\hookleftarrow<br>\hookrightarrow</td></tr>
<tr><td>\(\nleftarrow\)</td><td>\(\nleftrightarrow\)</td><td>\(\nrightarrow\)</td><td>\(\rightleftarrows\;\leftrightarrows\)</td><td>\(\hookleftarrow\;\hookrightarrow\)</td></tr>

<tr><td>\nLeftarrow</td><td>\nLeftrightarrow</td><td>\nRightarrow</td><td>\rightrightarrows<br>\leftleftarrows</td><td>\rightarrowtail<br>\leftarrowtail</td></tr>
<tr><td>\(\nLeftarrow\)</td><td>\(\nLeftrightarrow\)</td><td>\(\nRightarrow\)</td><td>\(\rightrightarrows\;\leftleftarrows\)</td><td>\(\rightarrowtail\;\leftarrowtail\)</td></tr>

<tr><td>\mapsto<br>\longmapsto</td><td>\leadsto<br>\leftrightsquigarrow</td><td>\dashrightarrow<br>\dashleftarrow</td><td>\curvearrowright<br>\curvearrowleft</td><td>\Rsh \Lsh</td></tr>
<tr><td>\(\mapsto\;\longmapsto\)</td><td>\(\leadsto\;\leftrightsquigarrow\)</td><td>\(\dashrightarrow\;\dashleftarrow\)</td><td>\(\curvearrowright\;\curvearrowleft\)</td><td>\(\Rsh\;\Lsh\)</td></tr>

<tr><td>\circlearrowleft<br>\circlearrowright</td><td>\twoheadrightarrow<br>\twoheadleftarrow</td><td>\Lleftarrow<br>\Rrightarrow</td><td>\upuparrows<br>\downdownarrows</td><td>\looparrowleft<br>\looparrowright</td></tr>
<tr><td>\(\circlearrowleft\;\circlearrowright\)</td><td>\(\twoheadrightarrow\;\twoheadleftarrow\)</td><td>\(\Lleftarrow\;\Rrightarrow\)</td><td>\(\upuparrows\;\downdownarrows\)</td><td>\(\looparrowleft\;\looparrowright\)</td></tr>
</table>

<h3>2、其它符号,一些符号如\#,\&,\_,\%,\{,\}等,前面必须要加\</h3>
<table class="tb">
<tr><td>\Cup<br>\Cap</td><td>\subset<br>\supset</td><td>\succneqq<br>\precneqq</td><td>\subsetneqq<br>\supsetneqq</td><td>\varsupsetneqq<br>\varsubsetneqq</td><td>\nsupseteqq<br>\nsubseteqq</td><td>\subseteq<br>\supseteq</td><td>\ni<br>\not\ni</td><td>\in<br>\notin</td></tr>
<tr><td>\(\Cup\;\Cap\)</td><td>\(\subset\;\supset\)</td><td>\(\succneqq\;\precneqq\)</td><td>\(\subsetneqq\;\supsetneqq\)</td><td>\(\varsupsetneqq\;\varsubsetneqq\)</td><td>\(\nsupseteqq\;\nsubseteqq\)</td><td>\(\subseteq\;\supseteq\)</td><td>\(\ni\;\not\ni\)</td><td>\(\in\;\notin\)</td></tr>

<tr><td>\nprec<br>\nsucc</td><td>\Subset<br>\Supset</td><td>\succnsim<br>\precnsim</td><td>\supseteqq<br>\subseteqq</td><td>\supsetneq<br>\varsupsetneq</td><td>\nsupseteq<br>\nsubseteq</td><td>\succsim<br>\precsim</td><td>\succ<br>\succeq</td><td>\lt<br>\gt</td></tr>
<tr><td>\(\nprec\;\nsucc\)</td><td>\(\Subset\;\Supset\)</td><td>\(\succnsim\;\precnsim\)</td><td>\(\supseteqq\;\subseteqq\)</td><td>\(\supsetneq\;\varsupsetneq\)</td><td>\(\nsupseteq\;\nsubseteq\)</td><td>\(\succsim\;\precsim\)</td><td>\(\succ\;\succeq\)</td><td>\(\lt\;\gt\)</td></tr>

<tr><td>\leqq<br>\geqq</td><td>\cap<br>\bigcap</td><td>\lnapprox<br>\gnapprox</td><td>\succnapprox<br>\precnapprox</td><td>\subsetneq<br>\varsubsetneq</td><td>\doublecap<br>\doublecup</td><td>\lessgtr<br>\gtrless</td><td>\prec<br>\preceq</td><td>\ge<br>\le</td></tr>
<tr><td>\(\leqq\;\geqq\)</td><td>\(\cap\;\bigcap\)</td><td>\(\lnapprox\;\gnapprox\)</td><td>\(\succnapprox\;\precnapprox\)</td><td>\(\subsetneq\;\varsubsetneq\)</td><td>\(\doublecap\;\doublecup\)</td><td>\(\lessgtr\;\gtrless\)</td><td>\(\prec\;\preceq\)</td><td>\(\ge\;\le\)</td></tr>

<tr><td>\lnot<br>\net</td><td>\cup<br>\bigcup</td><td>\uplus<br>\biguplus</td><td>\succcurlyeq<br>\preccurlyeq</td><td>\risingdotseq<br>\fallingdotseq</td><td>\curlyeqprec<br>\curlyeqsucc</td><td>\lessdot<br>\gtrdot</td><td>\not\lt<br>\ngtr</td><td>\ll<br>\gg</td></tr>
<tr><td>\(\lnot\;\neg\)</td><td>\(\cup\;\bigcup\)</td><td>\(\uplus\;\biguplus\)</td><td>\(\succcurlyeq\;\preccurlyeq\)</td><td>\(\risingdotseq\;\fallingdotseq\)</td><td>\(\curlyeqprec\;\curlyeqsucc\)</td><td>\(\lessdot\;\gtrdot\)</td><td>\( \not\lt\;\ngtr\)</td><td>\(\ll\;\gg\)</td></tr>

<tr><td>\lneq<br>\gneq</td><td>\equiv<br>\eqcirc</td><td>\approx<br>\approxeq</td><td>\succapprox<br>\precapprox</td><td><font size=2>\doublebarwedge</font></td><td>\curlyvee<br>\curlywedge</td><td>\lesssim<br>\gtrsim</td><td>\lll<br>\ggg</td><td>\lnsim<br>\gnsim</td></tr>
<tr><td>\(\lneq\;\gneq\)</td><td>\(\equiv\;\eqcirc\)</td><td>\(\approx\;\approxeq\)</td><td>\(\succapprox\;\precapprox\)</td><td>\(\doublebarwedge\)</td><td>\(\curlyvee\;\curlywedge\)</td><td>\(\lesssim\;\gtrsim\)</td><td>\(\lll\;\ggg\)</td><td>\(\lnsim\;\gnsim\)</td></tr>

<tr><td>\nleq<br>\ngeq</td><td>\doteq<br>\Doteq</td><td>\sim<br>\backsim</td><td>\eqslantgtr<br>\eqslantless</td><td>\vartriangle<br>\bigtriangleup</td><td>\gtreqqless<br>\lesseqqgtr</td><td>\leqslant<br>\geqslant</td><td>\gneqq<br>\lneqq</td><td>\ncong<br>\cong</td></tr>
<tr><td>\(\nleq\;\ngeq\)</td><td>\(\doteq\;\Doteq\)</td><td>\(\sim\;\backsim\)</td><td>\(\eqslantgtr\;\eqslantless\)</td><td>\(\vartriangle\;\bigtriangleup\)</td><td>\(\gtreqqless\;\lesseqqgtr\)</td><td>\(\leqslant\;\geqslant\)</td><td>\(\gneqq\;\lneqq\)</td><td>\(\ncong\;\cong\)</td></tr>

<tr><td>\ne<br>\neq</td><td>\Vvdash<br>\Vdash</td><td>\lesseqgtr<br>\gtreqless</td><td>\lessapprox<br>\gtrapprox</td><td><font size=2>\ntrianglerighteq</font><br>\ntrianglelefteq</td><td>\ngeqslant<br>\nleqslant</td><td>\simeq<br>\backsimeq</td><td>\nleqq<br>\ngeqq</td><td>\nsim<br>\eqsim</td></tr>
<tr><td>\(\ne\;\neq\)</td><td>\(\Vvdash\;\Vdash\)</td><td>\(\lesseqgtr\;\gtreqless\)</td><td>\(\lessapprox\;\gtrapprox\)</td><td>\(\ntrianglerighteq\;\ntrianglelefteq\)</td><td>\(\ngeqslant\;\nleqslant\)</td><td>\(\simeq\;\backsimeq\)</td><td>\(\nleqq\;\ngeqq\)</td><td>\(\nsim\;\eqsim\)</td></tr>

<tr><td>\dashv<br>\vdash</td><td>\nVDash<br>\nVdash</td><td>\vDash<br>\models</td><td>\sqsubset<br>\sqsubseteq</td><td>\ntriangleright<br>\ntriangleleft</td><td>\sqsupset<br>\sqsupseteq</td><td>\sqcup<br>\bigsqcup</td><td>\nvDash<br>\nvdash</td><td>\bot<br>\perp</td></tr>
<tr><td>\(\dashv\;\vdash\)</td><td>\(\nVDash\;\nVdash\)</td><td>\(\vDash\;\models\)</td><td>\(\sqsubset\;\sqsubseteq\)</td><td>\(\ntriangleright\;\ntriangleleft\)</td><td>\(\sqsupset\;\sqsupseteq\)</td><td>\(\sqcup\;\bigsqcup\)</td><td>\(\nvDash\;\nvdash\)</td><td>\(\bot\perp\)</td></tr>

<tr><td>\lor<br>\vee</td><td>\exists<br>\nexists</td><td>\land<br>\wedge</td><td>\circeq<br>\triangleq</td><td>\triangledown<br><font size=2>\bigtriangledown</font></td><td>\veebar<br>\barwedge</td><td>\sqcap</td><td>\partial</td><td>\eth</td></tr>
<tr><td>\(\lor\;\vee\)</td><td>\(\exists\;\nexists\)</td><td>\(\land\;\wedge\)</td><td>\(\circeq\;\triangleq\)</td><td>\(\triangledown\;\bigtriangledown\)</td><td>\(\veebar\;\barwedge\)</td><td>\(\sqcap\)</td><td>\(\partial\)</td><td>\(\eth\)</td></tr>

<tr><td>\nabla</td><td>\forall</td><td>\top<br>\intercal</td><td>\bigvee<br>\bigwedge</td><td>\trianglelefteq<br>\trianglerighteq</td><td>\emptyset<br>\varnothing</td><td>\ominus<br>\oslash</td><td>\star<br>\bigstar</td><td>\ddots</td></tr>
<tr><td>\(\nabla\)</td><td>\(\forall\)</td><td>\(\top\;\intercal\)</td><td>\(\bigvee\;\bigwedge\)</td><td>\(\trianglelefteq\;\trianglerighteq\)</td><td>\(\emptyset\;\varnothing\)</td><td>\(\ominus\;\oslash\)</td><td>\(\star\;\bigstar\)</td><td>\(\ddots\)</td></tr>

<tr><td>\unlhd<br>\unrhd</td><td>\angle</td><td>\ulcorner<br>\urcorner</td><td>\Diamond<br>\diamondsuit</td><td>\triangleleft<br>\triangleright</td><td>\lvertneqq<br>\gvertneqq</td><td>\triangle</td><td>\Box<br>\square</td><td>\rhd<br>\lhd</td></tr>
<tr><td>\(\unlhd\;\unrhd\)</td><td>\(\angle\)</td><td>\(\ulcorner\;\urcorner\)</td><td>\(\Diamond\;\diamondsuit\)</td><td>\(\triangleleft\;\triangleright\)</td><td>\(\lvertneqq\;\gvertneqq\)</td><td>\(\triangle\)</td><td>\(\Box\;\square\)</td><td>\(\rhd\;\lhd\)</td></tr>

<tr><td>\cdot<br>\ldotp</td><td>\infty<br>\propto</td><td>\llcorner<br>\lrcorner</td><td>\boxtimes<br>\boxplus</td><td>\sphericalangle<br>\measuredangle</td><td>\lmoustache<br>\rmoustache</td><td>\lgroup<br>\rgroup</td><td>\rtimes<br>\ltimes</td><td>\aleph</td></tr>
<tr><td>\(\cdot\;\ldotp\)</td><td>\(\infty\;\propto\)</td><td>\(\llcorner\;\lrcorner\)</td><td>\(\boxtimes\;\boxplus\)</td><td>\(\sphericalangle\;\measuredangle\)</td><td>\(\lmoustache\;\rmoustache\)</td><td>\(\lgroup\;\rgroup\)</td><td>\(\rtimes\ltimes\)</td><td>\(\aleph\)</td></tr>

<tr><td>\S</td><td>\circ<br>\bigcirc</td><td>\dagger<br>\ddagger</td><td>\backslash<br>\setminus</td><td>\leftthreetimes<br>\rightthreetimes</td><td>\smallsmile<br>\smallfrown</td><td>\diagup<br>\diagdown</td><td>\smile<br>\frown</td><td>\wr</td></tr>
<tr><td>\(\S\)</td><td>\(\circ\;\bigcirc\)</td><td>\(\dagger\;\ddagger\)</td><td>\(\backslash\;\setminus\)</td><td>\(\leftthreetimes\;\rightthreetimes\)</td><td>\(\smallsmile\;\smallfrown\)</td><td>\(\diagup\;\diagdown\)</td><td>\(\smile\;\frown\)</td><td>\(\wr\)</td></tr>

<tr><td>\pm<br>\mp</td><td>\Join<br>\bowtie</td><td>\bumpeq<br>\Bumpeq</td><td>\circledcirc<br>\circleddash</td><td>\blacktriangle<br><font size=2>\blacktriangledown</font></td><td>\otimes<br>\bigotimes</td><td>\sharp<br>\natural</td><td>\vdots</td><td>\Game</td></tr>
<tr><td>\(\pm\;\mp\)</td><td>\(\Join\;\bowtie\)</td><td>\(\bumpeq\;\Bumpeq\)</td><td>\(\circledcirc\;\circleddash\)</td><td>\(\blacktriangle\;\blacktriangledown\)</td><td>\(\otimes\;\bigotimes\)</td><td>\(\sharp\;\natural\)</td><td>\(\vdots\)</td><td>\(\Game\)</td></tr>

<tr><td>\times</td><td>\div</td><td>\circledR<br>\circledS</td><td>\because<br>\therefore</td><td><font size=2>\blacktriangleleft<br>\blacktriangleright<font></td><td>\oplus<br>\bigoplus</td><td>\odot<br>\bigodot</td><td>\boxdot</td><td>\gimel<br>\beth</td></tr>
<tr><td>\(\times\)</td><td>\(\div\)</td><td>\(\circledR\;\circledS\)</td><td>\(\because\;\therefore\)</td><td>\(\blacktriangleleft\;\blacktriangleright\)</td><td>\(\oplus\;\bigoplus\)</td><td>\(\odot\;\bigodot\)</td><td>\(\boxdot\)</td><td>\(\gimel\;\beth\)</td></tr>

<tr><td>\flat</td><td>\Finv</td><td>\asymp<br>\between</td><td>\clubsuit<br>\spadesuit</td><td>\circledast<br>\divideontimes</td><td>\parallel<br>\nparallel</td><td>\diamond<br>\lozenge</td><td>\amalg<br>\coprod</td><td>\nmid</td></tr>
<tr><td>\(\flat\)</td><td>\(\Finv\)</td><td>\(\asymp\;\between\)</td><td>\(\clubsuit\;\spadesuit\)</td><td>\(\circledast\;\divideontimes\)</td><td>\(\parallel\;\nparallel\)</td><td>\(\diamond\;\lozenge\)</td><td>\(\amalg\;\coprod\)</td><td>\(\nmid\)</td></tr>

<tr><td>\yen</td><td>\ldots<br>\cdots</td><td>\bullet<br>\centerdot</td><td>\surd<br>\checkmark</td><td>\blacksquare</br>\blacklozenge</td><td>\pitchfork</td><td>\multimap</td><td>\daleth</td><td>\ell<br>\iota</td></tr>
<tr><td>\(\yen\)</td><td>\(\ldots\;\cdots\)</td><td>\(\bullet\;\centerdot\)</td><td>\(\surd<br>\checkmark\)</td><td>\(\blacksquare\;\blacklozenge\)</td><td>\(\pitchfork\)</td><td>\(\multimap\)</td><td>\(\daleth\)</td><td>\(\ell\;\iota\)</td></tr>

<tr><td>\dots</td><td>\hbar<br>\hslash</td><td>\dotplus</td><td>\nshortmid<br>\shortmid</td><td>\shortparallel<br>\nshortparallel</td><td>f'<br>\backprime</td><td>\intop<br>\smallint</td><td>\jmath</td><td>\Im<br>\imath</td></tr>
<tr><td>\(\dots\)</td><td>\(\hbar\;\hslash\)</td><td>\(\dotplus\)</td><td>\(\nshortmid\;\shortmid\)</td><td>\(\shortparallel\;\nshortparallel\)</td><td>\(f'\;\backprime\)</td><td>\(\intop\;\smallint\)</td><td>\(\jmath\)</td><td>\(\Im\;\imath\)</td></tr>

<tr><td>\Re</td><td>\maltese</td><td>\boxminus</td><td>\complement</td><td>\smallsetminus</td><td>\heartsuit</td><td>\idotsint</td><td>\wp</td><td>\mho</td></tr>
<tr><td>\(\Re\)</td><td>\(\maltese\)</td><td>\(\boxminus\)</td><td>\(\complement\)</td><td>\(\smallsetminus\)</td><td>\(\heartsuit\)</td><td>\(\idotsint\)</td><td>\(\wp\)</td><td>\(\mho\)</td></tr>
</table>   
   
<p class=lx>练习环节:</p>
<div id=lx8></div>
<script>
lxs(8);
</script>

乘简 发表于 2020-7-25 21:09

<h2>九、字体与颜色</h2>
<h3>1、字体</h3>
<table class="t_table tb" style="width:80%">
<tr><td>默认</td><td>\mathsf{}</td><td>\mathbf{}</td><td>\mathtt{}</td><td>\mathbb{}</td><td>\mathit{}</td></tr>
<tr><td>\[{ABCabc123}\]</td><td>\[\mathsf{ABCabc123}\]</td><td>\[\mathbf{ABCabc123}\]</td><td>\[\mathtt{ABCabc123}\]</td><td>\[\mathbb{ABCabc123}\]</td><td>\[\mathit{ABCabc123}\]</td></tr>
<tr><td>\mathrm{}</td><td>\mathcal{}</td><td>\mathscr{}</td><td>\mathfrak{}</td><td>\boldsymbol{}</td><td></td></tr>
<tr><td>\[\mathrm{ABCabc123}\]</td><td>\[\mathcal{ABCabc123}\]</td><td>\[\mathscr{ABCabc123}\]</td><td>\[\mathfrak{ABCabc123}\]</td><td>\[\boldsymbol{ABCabc123}\]</td><td></td></tr>
</table>
<h3>2、字号,从小到大</h3>
<table class="t_table tb">
<tr><td>\tiny</td><td>\Tiny</td><td>\small</td><td>默认</td><td>\large</td><td>\Large</td><td>\LARGE</td><td>\huge</td><td>\Huge</td></tr>
<tr><td>\(\tiny{Aa12}\)</td><td>\(\Tiny{Aa12}\)</td><td>\(\small{Aa12}\)</td><td>\(Aa12\)</td><td>\(\large{Aa12}\)</td><td>\(\Large{Aa12}\)</td><td>\(\LARGE{Aa12}\)</td><td>\(\huge{Aa12}\)</td><td>\(\Huge{Aa12}\)</td></tr>
</table>
<br>
<h3>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</h3>
<p class=tp>例如:<code>\(\color{red}{www}.\color{#168}{mathchina}.com\)</code>显示:\(\color{red}{www}.\color{#168}{mathchina}.com\)</p>
<table class="t_table tb">
<tr><td>\(\rm\color{black}{black}\)</td><td>\(\rm\color{red}{red}\)</td><td>\(\rm\color{green}{green}\)</td><td>\(\rm\color{blue}{blue}\)</td><td>\(\rm\color{maroon}{maroon}\)</td>
    <td>\(\rm\color{yellow}{yellow}\)</td><td>\(\rm\color{lime}{lime}\)</td><td>\(\rm\color{olive}{olive}\)</td><td>\(\rm\color{teal}{teal}\)</td><td>\(\rm\color{aqua}{aqua}\)</td>
        <td>\(\rm\color{navy}{navy}\)</td><td>\(\rm\color{purple}{purple}\)</td><td>\(\rm\color{fuchsia}{fuchsia}\)</td></tr>
</table>
<br>
<h3>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</h3>
<p class=tp>例如:<code>\(\style{background-color:aqua}{c=2\pi r}\)</code>显示为\(\style{background-color:aqua}{c=2\pi r}\),当然\style{}{}可以设置任何的css样式</p>

<p class=lx>练习环节:</p>
<div id=lx9></div>
<script>
lxs(9);
</script>

乘简 发表于 2020-7-25 21:09

<h2>十、其它公式</h2>
<h3>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</h3>
<p class=tp>例如:<code>\(x+\boxed{y^2}=0\)与\(x+\fbox{y^2}=0\)</code>显示为\(x+\boxed{y^2}=0\)与\(x+\fbox{y^2}=0\)</p>
<br>
<h3>2、垂直居中显示\vcenter{}</h3>
<p class=tp>例如:<code>\(y_2\)</code>显示为\(y_2\),而用\vcenter{y}_2后,显示为\(\vcenter{y}_2\)</p>
<br>
<h3>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</h3>
<h4>px:屏幕像素点,如1920*1080分辩率表示横坐标有1920px,纵坐标有1080px
<br>pt:磅,也就是1/72英寸
<br>以96dpi来计算,1em=12pt=16px=18mu</h4>
<br>
<h3>4、水平移动XX单位,负值为左移,正值为右移\kern{}{}</h3>
<p class=tp>例如:<code>\(I\kern{-3pt}R\)</code>,显示为\(I\kern{-3pt}R\),<code>\(I\kern{1em}R\)</code>显示为\(I\kern{1em}R\)</p>
<br>
<h3>5、上下升降XX单位,\raise{}{}上移,\lower{}{}下移,负号正好相反</h3>
<p class=tp>例如:<code>\(a\raise{5pt}{bc}d\)</code>,显示为\(a\raise{5pt}{bc}d\),<code>\(a\lower{5pt}{bc}d\)</code>显示为\(a\lower{5pt}{bc}d\)</p>
<br>
<h3>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?
<p class=tp>例如:<code>\(\unicode{x2153}\)</code>,显示为\(\unicode{x2153}\)</p>
<br>
<h3>7、当公式中出现与论坛主贴标签[b]冲突时怎么办?</h3>
<p class=tp>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[],<code>\(\lbrack b\rbrack\)</code>显示为\(\lbrack b\rbrack\)</p>

<p class=lx>练习:<code>\(\kern3mu\raise1mu{.}\kern3mu\raise6mu{.}\kern3mu\raise12mu{.}\)</code></p>
<div id=lx10></div>
<script>
lxs(10);
</script>
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