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Cmd Markdown 公式指导手册
- 新增内容:戴帽符号
- 修补内容:如何输入一个交换图表 / 在字符间加入空格 Ver. 2020-10-03
本文为 MathJax 在 Cmd Markdown 环境下的常用语法指引。Cmd Markdown 编辑阅读器支持 编辑显示支持,例如:,访问 MathJax 以参考更多使用方法。
右键点击每一个公式,选择 [Show Math As] → [TeX Commands] 以查看该公式的命令详情。
一、公式使用参考
1.如何插入公式
的数学公式有两种:行中公式和独立公式。行中公式放在文中与其它文字混编,独立公式单独成行。
行中公式可以用如下方法表示:
: $ 数学公式 $
独立公式可以用如下方法表示:
: 数学公式
自动编号的公式可以用如下方法表示:
: 若需要手动编号,参见“大括号和行标的使用”。
: \begin{equation}
数学公式
\label{eq:当前公式名}
\end{equation}
自动编号后的公式可在全文任意处使用 \eqref{eq:公式名}
语句引用。
- 例子:
$ J_\alpha(x) = \sum_{m=0}^\infty \frac{(-1)^m}{m! \Gamma (m + \alpha + 1)} {\left({ \frac{x}{2} }\right)}^{2m + \alpha} \text {,行内公式示例} $
显示:$ J\alpha(x) = \sum{m=0}^\infty \frac{(-1)^m}{m! \Gamma (m + \alpha + 1)} {\left({ \frac{x}{2} }\right)}^{2m + \alpha} \text {,行内公式示例} $
例子:
$$ J_\alpha(x) = \sum_{m=0}^\infty \frac{(-1)^m}{m! \Gamma (m + \alpha + 1)} {\left({ \frac{x}{2} }\right)}^{2m + \alpha} \text {,独立公式示例} $$
显示: J\alpha(x) = \sum{m=0}^\infty \frac{(-1)^m}{m! \Gamma (m + \alpha + 1)} {\left({ \frac{x}{2} }\right)}^{2m + \alpha} \text {,独立公式示例}
例子:
$$ 在公式 \eqref{eq:sample} 中,我们看到了这个被自动编号的公式。$$
\begin{equation}
E=mc^2 \text{,自动编号公式示例}
\label{eq:sample}
\end{equation}
- 显示:
\begin{equation}
E=mc^2 \text{,自动编号公式示例}
\label{eq:sample}
\end{equation}
2.如何输入上下标
^
表示上标, _
表示下标。如果上下标的内容多于一个字符,需要用 {}
将这些内容括成一个整体。上下标可以嵌套,也可以同时使用。
- 例子:
$$ x^{y^z}=(1+{\rm e}^x)^{-2xy^w} $$
- 显示:$$ xz}=(1+{\rm e}{-2xy^w} $$
另外,如果要在左右两边都有上下标,可以使用 \sideset
命令;也可以简单地在符号前面多打一个上下标,此时会以行内公式渲染。
- 例子:
$$ \sideset{^1_2}{^3_4}\bigotimes \quad or \quad {^1_2}\bigotimes {^3_4} $$
- 显示:$$\sideset{3_4}\bigotimes \quad or \quad {^1_2}\bigotimes {^3_4} $$
3.如何输入括号和分隔符
()
、[]
和 |
表示符号本身,使用 \{\}
来表示 {}
。当要显示大号的括号或分隔符时,要用 \left
和 \right
命令。
一些特殊的括号:
输入 | 显示 | 输入 | 显示 |
---|---|---|---|
\langle | \rangle | ||
\lceil | \rceil | ||
\lfloor | \rfloor | ||
\lbrace | \rbrace | ||
\lvert | \rvert | ||
\lVert | \rVert |
@lymd 有时,我们需要在行内使用两个竖杠表示向量间的某种空间距离,可以这样写
\lVert \boldsymbol{X}_i - \boldsymbol{S}_j \rVert^2
→
- 例子:
$$ f(x,y,z) = 3y^2z \left( 3+\frac{7x+5}{1+y^2} \right) $$
- 显示:$$ f(x,y,z) = 3y^2z \left( 3+\frac{7x+5}{1+y^2} \right) $$
有时要用 \left.
或 \right.
进行匹配而不显示本身。
- 例子:
$$ \left. \frac{{\rm d}u}{{\rm d}x} \right| _{x=0} $$
- 显示:$$ \left. \frac{{\rm d}u}{{\rm d}x} \right| _{x=0} $$
4.如何输入分数
通常使用 \frac {分子} {分母}
来生成一个分数,分数可多层嵌套。如果分式较为复杂,亦可使用 分子 \over 分母
此时分数仅有一层。
- 例子:
$$ \frac{a-1}{b-1} \quad or \quad {a+1 \over b+1} $$
- 显示:$$ \frac{a-1}{b-1} \quad or \quad {a+1 \over b+1} $$
当分式 仅有两个字符时 可直接输入 \frac ab
来快速生成一个 。
- 例子:
$$ \frac 12,\frac 1a,\frac a2 \quad \mid \quad \text{2 letters only:} \quad \frac 12a \,, k\frac q{r^2} $$
- 显示:$$ \frac 12,\frac 1a,\frac a2 \quad \mid \quad \text{2 letters only:} \quad \frac 12a ,, k\frac q{r^2} $$
5.如何输入开方
使用 \sqrt [根指数,省略时为2] {被开方数}
命令输入开方。
- 例子:
$$ \sqrt{2} \quad or \quad \sqrt[n]{3} $$
- 显示:$$ \sqrt{2} \quad or \quad \sqrt[n]{3} $$
6.如何输入省略号
数学公式中常见的省略号有两种,\ldots
表示与 文本底线 对齐的省略号,\cdots
表示与 文本中线 对齐的省略号。
- 例子:
$$ f(x_1,x_2,\underbrace{\ldots}_{\rm ldots} ,x_n) = x_1^2 + x_2^2 + \underbrace{\cdots}_{\rm cdots} + x_n^2 $$
- 显示:$$ f(x1,x_2,\underbrace{\ldots}{\rm ldots} ,xn) = x_1^2 + x_2^2 + \underbrace{\cdots}{\rm cdots} + x_n^2 $$
7.如何输入向量
使用 \vec{向量}
来自动产生一个向量。也可以使用 \overrightarrow
等命令自定义字母上方的符号。
- 例子:
$$ \vec{a} \cdot \vec{b}=0 $$
显示: \vec{a} \cdot \vec{b}=0
例子:
$$ xy \text{ with arrows:} \quad \overleftarrow{xy} \; \mid \; \overleftrightarrow{xy} \; \mid \; \overrightarrow{xy} $$
- 显示:$$ xy \text{ with arrows:} \quad \overleftarrow{xy} ; \mid ; \overleftrightarrow{xy} ; \mid ; \overrightarrow{xy} $$
8.如何输入积分
使用 \int_积分下限^积分上限 {被积表达式}
来输入一个积分。
例子:
$$ \int_0^1 {x^2} \,{\rm d}x $$
显示: \int_0^1 {x^2} ,{\rm d}x
本例中 \,
和 {\rm d}
部分可省略,但加入能使式子更美观,详见“在字符间加入空格”及“如何进行字体转换”。
9.如何输入极限运算
使用 \lim_{变量 \to 表达式} 表达式
来输入一个极限。如有需求,可以更改 \to
符号至任意符号。
例子:
$$ \lim_{n \to \infty} \frac{1}{n(n+1)} \quad and \quad \lim_{x\leftarrow{示例}} \frac{1}{n(n+1)} $$
显示: \lim{n \to \infty} \frac{1}{n(n+1)} \quad and \quad \lim{x\leftarrow{示例}} \frac{1}{n(n+1)}
10.如何输入累加、累乘运算
使用 \sum_{下标表达式}^{上标表达式} {累加表达式}
来输入一个累加。与之类似,使用 \prod
\bigcup
\bigcap
来分别输入累乘、并集和交集,更多符号可参考“其它特殊字符”。
此类符号在行内显示时上下标表达式将会移至右上角和右下角,如 。
- 例子:
$$ \sum_{i=1}^n \frac{1}{i^2} \quad and \quad \prod_{i=1}^n \frac{1}{i^2} \quad and \quad \bigcup_{i=1}^{2} \Bbb{R} $$
- 显示:$$ \sum{i=1}^n \frac{1}{i^2} \quad and \quad \prod{i=1}^n \frac{1}{i^2} \quad and \quad \bigcup_{i=1}^{2} \Bbb{R} $$
11.如何输入希腊字母
输入 \小写希腊字母英文全称
和 \首字母大写希腊字母英文全称
来分别输入小写和大写希腊字母。
对于大写希腊字母与现有字母相同的,直接输入大写字母即可。
输入 | 显示 | 输入 | 显示 | 输入 | 显示 | 输入 | 显示 |
---|---|---|---|---|---|---|---|
\alpha | A | \beta | B | ||||
\gamma | \Gamma | \delta | \Delta | ||||
\epsilon | E | \zeta | Z | ||||
\eta | H | \theta | \Theta | ||||
\iota | I | \kappa | K | ||||
\lambda | \Lambda | \mu | M | ||||
\nu | N | \xi | \Xi | ||||
o | O | \pi | \Pi | ||||
\rho | P | \sigma | \Sigma | ||||
\tau | T | \upsilon | \Upsilon | ||||
\phi | \Phi | \chi | X | ||||
\psi | \Psi | \omega | \Omega |
部分字母有变量专用形式,以 \var-
开头。
小写形式 | 大写形式 | 变量形式 | 显示 |
---|---|---|---|
\epsilon | E | \varepsilon | |
\theta | \Theta | \vartheta | |
\rho | P | \varrho | |
\sigma | \Sigma | \varsigma | |
\phi | \Phi | \varphi |
12.如何输入其它特殊字符
完整的 可用符号列表可以在 这份文档 中查阅(极长,共 348 页),大部分常用符号可以参阅 这份精简版文档 查询。需要注意的是, 符号并不保证在 MathJax v2.2 中可用,即在 Cmd Markdown 编辑阅读器中可能并不支持所输入的特定命令。
若需要显示更大或更小的字符,在符号前插入
\large
或\small
命令。
MathJax 针对任意元素均提供从小至大\tiny
\Tiny
\scriptsize
\small
*默认值 \normalsize
\large
\Large
\LARGE
\huge
\Huge
共十种渲染大小,详见官方文档。
(1).关系运算符
输入 | 显示 | 输入 | 显示 | 输入 | 显示 | 输入 | 显示 |
---|---|---|---|---|---|---|---|
\pm | \times | \div | \mid | ||||
\nmid | \cdot | \circ | \ast | ||||
\bigodot | \bigotimes | \bigoplus | \leq | ||||
\geq | \neq | \approx | \equiv | ||||
\sum | \prod | \coprod | \backslash |
(2).集合运算符
输入 | 显示 | 输入 | 显示 | 输入 | 显示 |
---|---|---|---|---|---|
\emptyset | \in | \notin | |||
\subset | \supset | \subseteq | |||
\supseteq | \cap | \cup | |||
\vee | \wedge | \uplus | |||
\top | \bot | \complement |
(3).对数运算符
输入 | 显示 | 输入 | 显示 | 输入 | 显示 |
---|---|---|---|---|---|
\log | \lg | \ln |
(4).三角运算符
输入 | 显示 | 输入 | 显示 | 输入 | 显示 |
---|---|---|---|---|---|
\backsim | \cong | \angle A | |||
\sin | \cos | \tan | |||
\csc | \sec | \cot |
(5).微积分运算符
输入 | 显示 | 输入 | 显示 | 输入 | 显示 |
---|---|---|---|---|---|
\int | \iint | \iiint | |||
\partial | \oint | \prime | |||
\lim | \infty | \nabla |
(6).逻辑运算符
输入 | 显示 | 输入 | 显示 | 输入 | 显示 |
---|---|---|---|---|---|
\because | \therefore | \neg | |||
\forall | \exists | \not\subset | |||
\not< | \not> | \not= |
(7).戴帽符号
输入 | 显示 | 输入 | 显示 | 输入 | 显示 |
---|---|---|---|---|---|
\hat{xy} | \widehat{xyz} | \bar{y} | |||
\tilde{xy} | \widetilde{xyz} | \acute{y} | |||
\breve{y} | \check{y} | \grave{y} | |||
\dot{x} | \ddot{x} | \dddot{x} |
若需要在特定文字顶部\底部放置内容,可使用 \overset{顶部内容}{正常内容}
和 \underset{底部内容}{正常内容}
命令。
- 例子:
$$ \verb+\overset{above}{level}+ \qquad \overset{xx}{ABC} \;\; \mid \quad \overset{x^2}{\longmapsto}\ \, \mid \quad \overset{\bullet\circ\circ\bullet}{T} $$
- 显示:
- 例子:
$$ \verb+\underset{below}{level}+ \qquad \underset{xx}{ABC} \;\; \mid \quad \underset{x^2}{\longmapsto}\ \, \mid \quad \underset{\bullet\circ\circ\bullet}{T} $$
- 显示:
此命令可叠加嵌套使用,生成类似化学反应式的多重条件符号,
如 \overset{H_2}{\underset{1300℃}{\Longleftrightarrow}}
:
%7D%20%24%24%20%E5%92%8C%20%60%5Coverset%7BSurface%2Fbulk%7D%7B%5Cunderset%7Bdiffusion%7D%7B%5Clongleftrightarrow%7D%7D%60%EF%BC%9A%0A%24%24%20%5Crm%7B2OH%5E%7B%5Cbullet%7D%7BO(STN)%7D%2B2O%5E%7B%5Ctimes%7D%7BO(YSZ)%7D%20%5C%3B%20%5Coverset%7BSurface%2Fbulk%7D%7B%5Cunderset%7Bdiffusion%7D%7B%5Clongleftrightarrow%7D%7D%20%5C%3B%5C%3B%202OH%5E%7B%5Cbullet%7D%7BO(YSZ)%7D%2B2O%5E%7B%5Ctimes%7D%7BO(STN)%7D%7D%20#card=math&code=%20%5Crm%7BSrO%2BV%5E%7B%27%27%7D%7BSr%7D%20%5Coverset%7BH_2%7D%7B%5Cunderset%7B1300%E2%84%83%7D%7B%5CLongleftrightarrow%7D%7D%20Sr%5E%7B%5Ctimes%7D%7BSr%7D%2B2e%5E%7B%27%7D%2B%5Cfrac%2012O2%28g%29%7D%20%24%24%20%E5%92%8C%20%60%5Coverset%7BSurface%2Fbulk%7D%7B%5Cunderset%7Bdiffusion%7D%7B%5Clongleftrightarrow%7D%7D%60%EF%BC%9A%0A%24%24%20%5Crm%7B2OH%5E%7B%5Cbullet%7D%7BO%28STN%29%7D%2B2O%5E%7B%5Ctimes%7D%7BO%28YSZ%29%7D%20%5C%3B%20%5Coverset%7BSurface%2Fbulk%7D%7B%5Cunderset%7Bdiffusion%7D%7B%5Clongleftrightarrow%7D%7D%20%5C%3B%5C%3B%202OH%5E%7B%5Cbullet%7D%7BO%28YSZ%29%7D%2B2O%5E%7B%5Ctimes%7D_%7BO%28STN%29%7D%7D%20)
一般建议在书写化学方程式时声明 \require{AMDcd}
语句,使用 MathJax 内置的交换图表功能,具体例子可参见下文。
(8).连线符号
其它可用的文字修饰符可参见官方文档 “Additional decorations”。
输入 | 显示 |
---|---|
\fbox{a+b+c+d} 高级框选需声明 enclose 标签 |
|
\overleftarrow{a+b+c+d} | |
\overrightarrow{a+b+c+d} | |
\overleftrightarrow{a+b+c+d} | |
\underleftarrow{a+b+c+d} | |
\underrightarrow{a+b+c+d} | |
\underleftrightarrow{a+b+c+d} | |
\overline{a+b+c+d} | |
\underline{a+b+c+d} | |
\overbrace{a+b+c+d}^{Sample} | |
\underbrace{a+b+c+d}_{Sample} | |
\overbrace{a+\underbrace{b+c}_{1.0}+d}^{2.0} | |
\underbrace{a\cdot a\cdots a}_{b\text{ times}} |
(9).箭头符号
推荐使用符号:
|输入|显示|输入|显示|输入|显示|
|:—:|:—:|:—:|:—:|:—:|:—:|
|\to||\mapsto||\underrightarrow{1℃/min} | |
|\implies||\iff||\impliedby||其它可用符号:
|输入|显示|输入|显示|
|:—:|:—:|:—:|:—:|
|\uparrow||\Uparrow||
|\downarrow||\Downarrow||
|\leftarrow||\Leftarrow||
|\rightarrow||\Rightarrow||
|\leftrightarrow||\Leftrightarrow||
|\longleftarrow||\Longleftarrow||
|\longrightarrow||\Longrightarrow||
|\longleftrightarrow||\Longleftrightarrow||
13.如何进行字体转换
若要对公式的某一部分字符进行字体转换,可以用 {\字体 {需转换的部分字符}}
命令,其中 \字体
部分可以参照下表选择合适的字体。一般情况下,公式默认为斜体字 。
示例中 全部大写 的字体仅大写可用。
输入 | 全字母可用 | 显示 | 输入 | 仅大写可用 | 显示 |
---|---|---|---|---|---|
\rm | 罗马体 | \mathcal | 花体(数学符号等) | ||
\it | 斜体 | \mathbb | 黑板粗体(定义域等) | ||
\bf | 粗体 | \mit | 数学斜体 | ||
\sf | 等线体 | \scr | 手写体 | ||
\tt | 打字机体 | ||||
\frak | 旧德式字体 |
@lymd
\boldsymbol{\alpha}
用来表示向量或者矩阵的加粗斜体,如向量 。
转换字体十分常用,例如在积分中:
- 例子:
\begin{array}{cc}
\mathrm{Bad} & \mathrm{Better} \\
\hline \\
\int_0^1 x^2 dx & \int_0^1 x^2 \,{\rm d}x
\end{array}
- 显示:
\begin{array}{cc}
\mathrm{Bad} & \mathrm{Better} \
\hline \
\int_0^1 x^2 dx & \int_0^1 x^2 ,{\rm d}x
\end{array}
注意比较两个式子间 与 的不同。
使用 \operatorname
命令也可以达到相同的效果,详见“定义新的运算符”。
14.如何高亮一行公式
使用 \bbox[底色, (可选)边距, (可选)边框 border: 框宽度 框类型 框颜色]
命令来高亮一行公式。
底色和框颜色支持详见“更改文字颜色”,边距及框宽度支持 绝对像素 px
或 相对大小 em
,框类型支持 实线 solid
或 虚线 dashed
。
- 例子:
$$
\bbox[yellow]{
e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n \qquad (1)
}
$$
- 显示:
%5En%20%5Cqquad%20(1)%0A%7D%0A#card=math&code=%5Cbbox%5Byellow%5D%7B%0A%20%20%20%20e%5Ex%3D%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5Cleft%28%201%2B%5Cfrac%7Bx%7D%7Bn%7D%20%5Cright%29%5En%20%5Cqquad%20%281%29%0A%7D%0A)
- 例子:
$$
\bbox[#9ff, 5px]{ % 此处向外添加 5 像素的边距
e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n \qquad (1)
}
$$
- 显示:
%5En%20%5Cqquad%20(1)%0A%7D%0A#card=math&code=%5Cbbox%5B%239ff%2C%205px%5D%7B%0A%20%20%20%20e%5Ex%3D%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5Cleft%28%201%2B%5Cfrac%7Bx%7D%7Bn%7D%20%5Cright%29%5En%20%5Cqquad%20%281%29%0A%7D%0A)
- 例子:
$$
% 此处使用 0.5 倍行高作为边距,附加 2 像素的实线边框(Ctrl+Alt+Y 可见)
\bbox[#2f3542, 0.5em, border:2px solid #f1f2f6]{
\color{#f1f2f6}{e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n \qquad (1)}
}
$$
- 显示:
%5En%20%5Cqquad%20(1)%7D%0A%7D%0A#card=math&code=%5Cbbox%5B%232f3542%2C%200.5em%2C%20border%3A2px%20solid%20%23f1f2f6%5D%7B%0A%20%20%20%20%5Ccolor%7B%23f1f2f6%7D%7Be%5Ex%3D%5Clim_%7Bn%5Cto%5Cinfty%7D%20%5Cleft%28%201%2B%5Cfrac%7Bx%7D%7Bn%7D%20%5Cright%29%5En%20%5Cqquad%20%281%29%7D%0A%7D%0A)
15.大括号和行标的使用
在 \left
和 \right
之后加上要使用的括号来创建自动匹配高度的圆括号 (
)
,方括号 [
]
和花括号 \{
\}
。
在每个公式末尾前使用 \tag {行标}
来实现行标。
- 例子:
$$
f\left(
\left[
\frac{
1+\left\{x,y\right\}
}{
\left(
\frac xy + \frac yx
\right)
(u+1)
}+a
\right]^{3/2}
\right)
\tag {行标}
$$
- 显示:
%0A%20%20%20%20%20%20%20(u%2B1)%0A%20%20%20%20%20%7D%2Ba%0A%20%20%20%5Cright%5D%5E%7B3%2F2%7D%0A%5Cright)%0A%5Ctag%20%7B%E8%A1%8C%E6%A0%87%7D%0A#card=math&code=f%5Cleft%28%0A%20%20%20%5Cleft%5B%20%0A%20%20%20%20%20%5Cfrac%7B%0A%20%20%20%20%20%20%201%2B%5Cleft%5C%7Bx%2Cy%5Cright%5C%7D%0A%20%20%20%20%20%7D%7B%0A%20%20%20%20%20%20%20%5Cleft%28%0A%20%20%20%20%20%20%20%20%20%20%5Cfrac%20xy%20%2B%20%5Cfrac%20yx%0A%20%20%20%20%20%20%20%5Cright%29%0A%20%20%20%20%20%20%20%28u%2B1%29%0A%20%20%20%20%20%7D%2Ba%0A%20%20%20%5Cright%5D%5E%7B3%2F2%7D%0A%5Cright%29%0A%5Ctag%20%7B%E8%A1%8C%E6%A0%87%7D%0A)
如果你需要在不同的行显示对应括号,可以在每一行对应处使用 \left.
或 \right.
来放一个“不存在的括号”。
- 例子:
$$
\begin{align*}
a=&\left(1+2+3+ \cdots \right. \\
&\cdots+\left. \infty-2+\infty-1+\infty\right)
\end{align*}
$$
- 显示:
%0A%5Cend%7Balign*%7D%0A#card=math&code=%5Cbegin%7Balign%2A%7D%0A%20%20%20%20a%3D%26%5Cleft%281%2B2%2B3%2B%20%5Ccdots%20%5Cright.%20%5C%5C%0A%20%20%20%20%20%20%26%5Ccdots%2B%5Cleft.%20%5Cinfty-2%2B%5Cinfty-1%2B%5Cinfty%5Cright%29%0A%5Cend%7Balign%2A%7D%0A)
如果你需要将大括号里面显示的分隔符也变大,可以使用 \middle
命令,此处分别使用单竖线 |
和双竖线 \\|
。
- 例子:
$$
\left\langle
q \; \middle|
\frac{\frac xy}{\frac uv}
\middle\| p
\right\rangle
$$
- 显示:
16.其它命令
(1).定义新的运算符 \operatorname
当需要使用的运算符不在 MathJax 的内置库中时,程序可能会报错或产生错误的渲染结果。此时可以使用 \operatorname
命令定义一个新的运算符号。
- 反例:
\begin{array}{c|c}
\mathrm{Error} & \text{Wrong rendering} \\
\hline \\
\arsinh(x) & arsinh(x) \\
\Res_{z=1} & Res_{z=1}{\frac{1}{z^2-z}=1} \\
\end{array}
- 显示:
\begin{array}{c|c}
\mathrm{Error} & \text{Wrong rendering} \
\hline \
\arsinh(x) & arsinh(x) \
\Res{z=1} & Res{z=1}{\frac{1}{z^2-z}=1} \
\end{array}
使用 \operatorname{运算符}{式子}
来生成一个普通运算,或使用 \operatorname*{运算符}_{下标}^{上标}{式子}
来生成一个含上下标的自定义运算。
- 例子:
\begin{array}{c|c}
\text{Normal Operator} & \text{Operator with label above and below} \\
\hline \\
\scriptsize\text{\operatorname{arsinh}{x}} & \scriptsize\text{\operatorname*{Res}_{z=1}{\frac{1}{z^2-z}=1}} \\
\operatorname{arsinh}{x} & \operatorname*{Res}_{z=1}{\frac{1}{z^2-z}=1} \\
\end{array}
- 显示:
\begin{array}{c|c}
\text{Normal Operator} & \text{Operator with label above and below} \
\scriptsize\text{\operatorname{arsinh}{x}} & \scriptsize\text{\operatorname{Res}_{z=1}{\frac{1}{z^2-z}=1}} [2ex]
\hline \
\operatorname{arsinh}{x} & \operatorname{Res}_{z=1}{\frac{1}{z^2-z}=1}
\end{array}
(2).添加注释文字 \text
在 \text {文字}
中仍可以使用 $公式$
插入其它公式。
- 例子:
$$ f(n)= \begin{cases} n/2, & \text {if $n$ is even} \\ 3n+1, & \text{if $n$ is odd} \end{cases} $$
- 显示:
%3D%20%5Cbegin%7Bcases%7D%20n%2F2%2C%20%26%20%5Ctext%20%7Bif%20%24n%24%20is%20even%7D%20%5C%5C%203n%2B1%2C%20%26%20%5Ctext%7Bif%20%24n%24%20is%20odd%7D%20%5Cend%7Bcases%7D%20%0A#card=math&code=f%28n%29%3D%20%5Cbegin%7Bcases%7D%20n%2F2%2C%20%26%20%5Ctext%20%7Bif%20%24n%24%20is%20even%7D%20%5C%5C%203n%2B1%2C%20%26%20%5Ctext%7Bif%20%24n%24%20is%20odd%7D%20%5Cend%7Bcases%7D%20%0A)
(3).在字符间加入空格
有四种宽度的空格可以使用: \,
、\;
、\quad
和 \qquad
,灵活使用 \text{n个空格}
也可以在任意位置实现空格。
同时存在一种负空格 \!
用来减小字符间距,一般在物理单位中使用。
反复使用 \!
命令能够实现不同元素的叠加渲染,如 和 $ }!!!!!\div $
- 例子:
\begin{array}{c|c}
\text{Spaces} & \text{Negative Space in Units} \\
\hline \\
\overbrace{a \! b}^{\text{\!}} \mid \underbrace{ab}_{\rm{default}} \mid \overbrace{a \, b}^{\text{\,}} \mid \underbrace{a \; b}_{\text{\;}} \mid \overbrace{a \quad b}^{\text{\quad}} \mid \underbrace{a \qquad b}_{\text{\qquad}} & \mathrm{N}\!\cdot\!\mathrm{m} \mid \mathrm{s}\!\cdot\!\mathrm{A} \mid \mathrm{kg}\!\cdot\!\mathrm{m}^2 \\
\end{array}
- 显示:
\begin{array}{c|c}
\text{Spaces} & \text{Negative Space in Units} \
\hline \
\overbrace{a ! b}^{\text{!}} \mid \underbrace{ab}{\rm{default}} \mid \overbrace{a , b}^{\text{,}} \mid \underbrace{a ; b}{\text{;}} \mid \overbrace{a \quad b}^{\text{\quad}} \mid \underbrace{a \qquad b}_{\text{\qquad}} & \mathrm{N}!\cdot!\mathrm{m} \mid \mathrm{s}!\cdot!\mathrm{A} \mid \mathrm{kg}!\cdot!\mathrm{m}^2 \
\end{array}
一些常见的公式单位可表达如下:
- 例子:
$$ \mu_0=4\pi\times10^{-7} \ \left.\mathrm{\mathrm{T}\!\cdot\!\mathrm{m}}\middle/\mathrm{A}\right. $$
$$ 180^\circ=\pi \ \mathrm{rad} $$
$$ \mathrm{N_A} = 6.022\times10^{23} \ \mathrm{mol}^{-1} $$
- 显示:
(4).更改文字颜色 \color
使用 \color{颜色}{文字}
来更改特定的文字颜色。
更改文字颜色需要浏览器支持 ,如果浏览器不知道你所需的颜色,那么文字将被渲染为黑色。对于较旧的浏览器(HTML4 & CSS2),以下颜色是被支持的:
输入 | 显示 | 输入 | 显示 |
---|---|---|---|
black | grey | ||
silver | white | ||
maroon | red | ||
yellow | lime | ||
olive | green | ||
teal | auqa | ||
blue | navy | ||
purple | fuchsia |
对于较新的浏览器(HTML5 & CSS3),HEX 颜色将被支持:
输入 \color {#rgb} {text}
来自定义更多的颜色,其中 #rgb
或 #rrggbb
的 r
g
b
可输入 0-9
和 a-f
来表示红色、绿色和蓝色的纯度(饱和度)。
- 例子:
\begin{array}{|rrrrrrrr|}\hline
\verb+#000+ & \color{#000}{text} & & &
\verb+#00F+ & \color{#00F}{text} & & \\
& & \verb+#0F0+ & \color{#0F0}{text} &
& & \verb+#0FF+ & \color{#0FF}{text} \\
\verb+#F00+ & \color{#F00}{text} & & &
\verb+#F0F+ & \color{#F0F}{text} & & \\
& & \verb+#FF0+ & \color{#FF0}{text} &
& & \verb+#FFF+ & \color{#FFF}{text} \\
\hline\end{array}
显示:
\begin{array}{|rrrrrrrr|}\hline
\verb+#000+ & \color{#000}{text} & & &
\verb+#00F+ & \color{#00F}{text} & & \
& & \verb+#0F0+ & \color{#0F0}{text} &
& & \verb+#0FF+ & \color{#0FF}{text} \
\verb+#F00+ & \color{#F00}{text} & & &
\verb+#F0F+ & \color{#F0F}{text} & & \
& & \verb+#FF0+ & \color{#FF0}{text} &
& & \verb+#FFF+ & \color{#FFF}{text} \
\hline\end{array}例子:
\begin{array}{|rrrrrrrr|}\hline
\verb+#000+ & \color{#000}{text} & \verb+#005+ & \color{#005}{text} & \verb+#00A+ & \color{#00A}{text} & \verb+#00F+ & \color{#00F}{text} \\
\verb+#500+ & \color{#500}{text} & \verb+#505+ & \color{#505}{text} & \verb+#50A+ & \color{#50A}{text} & \verb+#50F+ & \color{#50F}{text} \\
\verb+#A00+ & \color{#A00}{text} & \verb+#A05+ & \color{#A05}{text} & \verb+#A0A+ & \color{#A0A}{text} & \verb+#A0F+ & \color{#A0F}{text} \\
\verb+#F00+ & \color{#F00}{text} & \verb+#F05+ & \color{#F05}{text} & \verb+#F0A+ & \color{#F0A}{text} & \verb+#F0F+ & \color{#F0F}{text} \\
\hline
\verb+#080+ & \color{#080}{text} & \verb+#085+ & \color{#085}{text} & \verb+#08A+ & \color{#08A}{text} & \verb+#08F+ & \color{#08F}{text} \\
\verb+#580+ & \color{#580}{text} & \verb+#585+ & \color{#585}{text} & \verb+#58A+ & \color{#58A}{text} & \verb+#58F+ & \color{#58F}{text} \\
\verb+#A80+ & \color{#A80}{text} & \verb+#A85+ & \color{#A85}{text} & \verb+#A8A+ & \color{#A8A}{text} & \verb+#A8F+ & \color{#A8F}{text} \\
\verb+#F80+ & \color{#F80}{text} & \verb+#F85+ & \color{#F85}{text} & \verb+#F8A+ & \color{#F8A}{text} & \verb+#F8F+ & \color{#F8F}{text} \\
\hline
\verb+#0F0+ & \color{#0F0}{text} & \verb+#0F5+ & \color{#0F5}{text} & \verb+#0FA+ & \color{#0FA}{text} & \verb+#0FF+ & \color{#0FF}{text} \\
\verb+#5F0+ & \color{#5F0}{text} & \verb+#5F5+ & \color{#5F5}{text} & \verb+#5FA+ & \color{#5FA}{text} & \verb+#5FF+ & \color{#5FF}{text} \\
\verb+#AF0+ & \color{#AF0}{text} & \verb+#AF5+ & \color{#AF5}{text} & \verb+#AFA+ & \color{#AFA}{text} & \verb+#AFF+ & \color{#AFF}{text} \\
\verb+#FF0+ & \color{#FF0}{text} & \verb+#FF5+ & \color{#FF5}{text} & \verb+#FFA+ & \color{#FFA}{text} & \verb+#FFF+ & \color{#FFF}{text} \\
\hline\end{array}
- 显示:
\begin{array}{|rrrrrrrr|}\hline
\verb+#000+ & \color{#000}{text} & \verb+#005+ & \color{#005}{text} & \verb+#00A+ & \color{#00A}{text} & \verb+#00F+ & \color{#00F}{text} \
\verb+#500+ & \color{#500}{text} & \verb+#505+ & \color{#505}{text} & \verb+#50A+ & \color{#50A}{text} & \verb+#50F+ & \color{#50F}{text} \
\verb+#A00+ & \color{#A00}{text} & \verb+#A05+ & \color{#A05}{text} & \verb+#A0A+ & \color{#A0A}{text} & \verb+#A0F+ & \color{#A0F}{text} \
\verb+#F00+ & \color{#F00}{text} & \verb+#F05+ & \color{#F05}{text} & \verb+#F0A+ & \color{#F0A}{text} & \verb+#F0F+ & \color{#F0F}{text} \
\hline
\verb+#080+ & \color{#080}{text} & \verb+#085+ & \color{#085}{text} & \verb+#08A+ & \color{#08A}{text} & \verb+#08F+ & \color{#08F}{text} \
\verb+#580+ & \color{#580}{text} & \verb+#585+ & \color{#585}{text} & \verb+#58A+ & \color{#58A}{text} & \verb+#58F+ & \color{#58F}{text} \
\verb+#A80+ & \color{#A80}{text} & \verb+#A85+ & \color{#A85}{text} & \verb+#A8A+ & \color{#A8A}{text} & \verb+#A8F+ & \color{#A8F}{text} \
\verb+#F80+ & \color{#F80}{text} & \verb+#F85+ & \color{#F85}{text} & \verb+#F8A+ & \color{#F8A}{text} & \verb+#F8F+ & \color{#F8F}{text} \
\hline
\verb+#0F0+ & \color{#0F0}{text} & \verb+#0F5+ & \color{#0F5}{text} & \verb+#0FA+ & \color{#0FA}{text} & \verb+#0FF+ & \color{#0FF}{text} \
\verb+#5F0+ & \color{#5F0}{text} & \verb+#5F5+ & \color{#5F5}{text} & \verb+#5FA+ & \color{#5FA}{text} & \verb+#5FF+ & \color{#5FF}{text} \
\verb+#AF0+ & \color{#AF0}{text} & \verb+#AF5+ & \color{#AF5}{text} & \verb+#AFA+ & \color{#AFA}{text} & \verb+#AFF+ & \color{#AFF}{text} \
\verb+#FF0+ & \color{#FF0}{text} & \verb+#FF5+ & \color{#FF5}{text} & \verb+#FFA+ & \color{#FFA}{text} & \verb+#FFF+ & \color{#FFF}{text} \
\hline\end{array}
(5).添加删除线
使用删除线功能必须声明 $$
符号。
在公式内使用 \require{cancel}
来允许片段删除线的显示。
声明片段删除线后,使用 \cancel{字符}
、\bcancel{字符}
、\xcancel{字符}
和 \cancelto{字符}
来实现各种片段删除线效果。
- 例子:
$$
\require{cancel}
\begin{array}{rl}
\verb|y+\cancel{x}| & y+\cancel{x} \\
\verb|\cancel{y+x}| & \cancel{y+x} \\
\verb|y+\bcancel{x}| & y+\bcancel{x} \\
\verb|y+\xcancel{x}| & y+\xcancel{x} \\
\verb|y+\cancelto{0}{x}| & y+\cancelto{0}{x} \\
\verb+\frac{1\cancel9}{\cancel95} = \frac15+& \frac{1\cancel9}{\cancel95} = \frac15 \\
\end{array}
$$
- 显示:
使用 \require{enclose}
来允许整段删除线的显示。
声明整段删除线后,使用 \enclose{删除线效果}{字符}
来实现各种整段删除线效果。
其中,删除线效果有 horizontalstrike
、verticalstrike
、updiagonalstrike
和 downdiagonalstrike
,可叠加使用。
- 例子:
$$
\require{enclose}
\begin{array}{rl}
\verb|\enclose{horizontalstrike}{x+y}| & \enclose{horizontalstrike}{x+y} \\
\verb|\enclose{verticalstrike}{\frac xy}| & \enclose{verticalstrike}{\frac xy} \\
\verb|\enclose{updiagonalstrike}{x+y}| & \enclose{updiagonalstrike}{x+y} \\
\verb|\enclose{downdiagonalstrike}{x+y}| & \enclose{downdiagonalstrike}{x+y} \\
\verb|\enclose{horizontalstrike,updiagonalstrike}{x+y}| & \enclose{horizontalstrike,updiagonalstrike}{x+y} \\
\end{array}
$$
- 显示:
此外, \enclose
命令还可以产生包围的边框和圆等,参见 MathML Menclose Documentation 以查看更多效果。
- 例子:
| 分别使用
circle
和roundedbox
包围的公式 | | :—-: |
$$
\require{enclose}
\begin{array}{c}
\enclose{circle}{f(\top),\, f^2(\top),\, f^3(\top) \,\cdots\, f^n(\top)} \\
\enclose{roundedbox}{f(\bot),\, f^2(\bot),\, f^3(\bot) \,\cdots\, f^n(\bot)} \\
\end{array}
$$
使用 box 框住所有公式 |
---|
$$
\require{enclose}
\enclose{box}{
\begin{array}{c}
f(\top),\, f^2(\top),\, f^3(\top) \,\cdots\, f^n(\top) \\
f(\bot),\, f^2(\bot),\, f^3(\bot) \,\cdots\, f^n(\bot) \\
\end{array}
}
$$
- 显示:
| 分别使用
circle
和roundedbox
包围的公式 | 使用box
框住所有公式 | | :—-: | :—-: | | $$ | |
\require{enclose}
\begin{array}{c}
\enclose{circle}{f(\top),, f^2(\top),, f^3(\top) ,\cdots, f^n(\top)} \
\enclose{roundedbox}{f(\bot),, f^2(\bot),, f^3(\bot) ,\cdots, f^n(\bot)} \
\end{array}
\require{enclose}
\enclose{box}{
\begin{array}{c}
f(\top),, f^2(\top),, f^3(\top) ,\cdots, f^n(\top) \
f(\bot),, f^2(\bot),, f^3(\bot) ,\cdots, f^n(\bot) \
\end{array}
}
%E2%80%9D%E3%80%82%0A%0A%23%E4%BA%8C%E3%80%81%E7%9F%A9%E9%98%B5%E4%BD%BF%E7%94%A8%E5%8F%82%E8%80%83%0A%0A%23%231%EF%BC%8E%E5%A6%82%E4%BD%95%E8%BE%93%E5%85%A5%E6%97%A0%E6%A1%86%E7%9F%A9%E9%98%B5%0A%0A%E5%9C%A8%E5%BC%80%E5%A4%B4%E4%BD%BF%E7%94%A8%20%60%5Cbegin%7Bmatrix%7D%60%EF%BC%8C%E5%9C%A8%E7%BB%93%E5%B0%BE%E4%BD%BF%E7%94%A8%20%60%5Cend%7Bmatrix%7D%60%EF%BC%8C%E5%9C%A8%E4%B8%AD%E9%97%B4%E6%8F%92%E5%85%A5%E7%9F%A9%E9%98%B5%E5%85%83%E7%B4%A0%EF%BC%8C%E6%AF%8F%E4%B8%AA%E5%85%83%E7%B4%A0%E4%B9%8B%E9%97%B4%E6%8F%92%E5%85%A5%20%60%26%60%20%EF%BC%8C%E5%B9%B6%E5%9C%A8%E6%AF%8F%E8%A1%8C%E7%BB%93%E5%B0%BE%E5%A4%84%E4%BD%BF%E7%94%A8%20%60%5C%5C%60%20%E3%80%82%0A%E4%BD%BF%E7%94%A8%E7%9F%A9%E9%98%B5%E6%97%B6%E5%BF%85%E9%A1%BB%E5%A3%B0%E6%98%8E%20%60%24%60%20%E6%88%96%20%60%24%24%60%20%E7%AC%A6%E5%8F%B7%E3%80%82%0A%0A-%20%E4%BE%8B%E5%AD%90%EF%BC%9A%0A%60%60%60%0A#card=math&code=%7C%0A%0A%E6%AD%A4%E4%BE%8B%E8%AF%AD%E6%B3%95%E5%8F%AF%E5%8F%82%E8%A7%81%E2%80%9C%5B%E5%A6%82%E4%BD%95%E8%BE%93%E5%85%A5%E4%B8%80%E4%B8%AA%E6%95%B0%E7%BB%84%E6%88%96%E8%A1%A8%E6%A0%BC%5D%28%23%E4%BA%94%E6%95%B0%E7%BB%84%E4%B8%8E%E8%A1%A8%E6%A0%BC%E4%BD%BF%E7%94%A8%E5%8F%82%E8%80%83%29%E2%80%9D%E3%80%82%0A%0A%23%E4%BA%8C%E3%80%81%E7%9F%A9%E9%98%B5%E4%BD%BF%E7%94%A8%E5%8F%82%E8%80%83%0A%0A%23%231%EF%BC%8E%E5%A6%82%E4%BD%95%E8%BE%93%E5%85%A5%E6%97%A0%E6%A1%86%E7%9F%A9%E9%98%B5%0A%0A%E5%9C%A8%E5%BC%80%E5%A4%B4%E4%BD%BF%E7%94%A8%20%60%5Cbegin%7Bmatrix%7D%60%EF%BC%8C%E5%9C%A8%E7%BB%93%E5%B0%BE%E4%BD%BF%E7%94%A8%20%60%5Cend%7Bmatrix%7D%60%EF%BC%8C%E5%9C%A8%E4%B8%AD%E9%97%B4%E6%8F%92%E5%85%A5%E7%9F%A9%E9%98%B5%E5%85%83%E7%B4%A0%EF%BC%8C%E6%AF%8F%E4%B8%AA%E5%85%83%E7%B4%A0%E4%B9%8B%E9%97%B4%E6%8F%92%E5%85%A5%20%60%26%60%20%EF%BC%8C%E5%B9%B6%E5%9C%A8%E6%AF%8F%E8%A1%8C%E7%BB%93%E5%B0%BE%E5%A4%84%E4%BD%BF%E7%94%A8%20%60%5C%5C%60%20%E3%80%82%0A%E4%BD%BF%E7%94%A8%E7%9F%A9%E9%98%B5%E6%97%B6%E5%BF%85%E9%A1%BB%E5%A3%B0%E6%98%8E%20%60%24%60%20%E6%88%96%20%60%24%24%60%20%E7%AC%A6%E5%8F%B7%E3%80%82%0A%0A-%20%E4%BE%8B%E5%AD%90%EF%BC%9A%0A%60%60%60%0A)
\begin{matrix}
1 & x & x^2 \
1 & y & y^2 \
1 & z & z^2 \
\end{matrix}
\begin{matrix}
1 & x & x^2 \
1 & y & y^2 \
1 & z & z^2 \
\end{matrix}
\begin{pmatrix}
1 & a_1 & a_1^2 & \cdots & a_1^n \
1 & a_2 & a_2^2 & \cdots & a_2^n \
\vdots & \vdots & \vdots & \ddots & \vdots \
1 & a_m & a_m^2 & \cdots & a_m^n \
\end{pmatrix}
\begin{pmatrix}
1 & a_1 & a_1^2 & \cdots & a_1^n \
1 & a_2 & a_2^2 & \cdots & a_2^n \
\vdots & \vdots & \vdots & \ddots & \vdots \
1 & a_m & a_m^2 & \cdots & a_m^n \
\end{pmatrix}
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f(n) =
\begin{cases}
n/2, & \text{if $n$ is even} \\
3n+1, & \text{if $n$ is odd} \\
\end{cases}
f(n) =
\begin{cases}
n/2, & \text{if $n$ is even} \\
3n+1, & \text{if $n$ is odd} \\
\end{cases}
%60%0A%0A%23%232%EF%BC%8E%E5%A6%82%E4%BD%95%E8%BE%93%E5%85%A5%E4%B8%80%E4%B8%AA%E5%B7%A6%E4%BE%A7%E5%AF%B9%E9%BD%90%E7%9A%84%E6%9D%A1%E4%BB%B6%E8%A1%A8%E8%BE%BE%E5%BC%8F%0A%0A%E8%8B%A5%E6%83%B3%E8%AE%A9%E6%96%87%E5%AD%97%E5%9C%A8%E5%B7%A6%E4%BE%A7%E5%AF%B9%E9%BD%90%E6%98%BE%E7%A4%BA%EF%BC%8C%E5%88%99%E6%9C%89%E5%A6%82%E4%B8%8B%E6%96%B9%E5%BC%8F%EF%BC%9A%0A%0A-%20%E4%BE%8B%E5%AD%90%EF%BC%9A%0A%60%60%60%0A#card=math&code=%0A%3E%20%2A%2A%40Sherlockk%2A%2A%20%E7%94%A8%20markdown%2Bmath%20%E7%BC%96%E8%BE%91%E6%97%B6%20%60%5Ctext%60%20%E5%86%85%E9%9C%80%E7%94%A8%20%60%5C%28equation%5C%29%60%0A%0A%23%232%EF%BC%8E%E5%A6%82%E4%BD%95%E8%BE%93%E5%85%A5%E4%B8%80%E4%B8%AA%E5%B7%A6%E4%BE%A7%E5%AF%B9%E9%BD%90%E7%9A%84%E6%9D%A1%E4%BB%B6%E8%A1%A8%E8%BE%BE%E5%BC%8F%0A%0A%E8%8B%A5%E6%83%B3%E8%AE%A9%E6%96%87%E5%AD%97%E5%9C%A8%2A%2A%E5%B7%A6%E4%BE%A7%E5%AF%B9%E9%BD%90%E6%98%BE%E7%A4%BA%2A%2A%EF%BC%8C%E5%88%99%E6%9C%89%E5%A6%82%E4%B8%8B%E6%96%B9%E5%BC%8F%EF%BC%9A%0A%0A-%20%E4%BE%8B%E5%AD%90%EF%BC%9A%0A%60%60%60%0A)
\left.
\begin{array}{l}
\text{if $n$ is even:} & n/2 \\
\text{if $n$ is odd:} & 3n+1 \\
\end{array}
\right\}
=f(n)
\left.
\begin{array}{l}
\text{if $n$ is even:} & n/2 \\
\text{if $n$ is odd:} & 3n+1 \\
\end{array}
\right\}
=f(n)
f(n) =
\begin{cases}
\frac{n}{2}, & \text{if is even} \
3n+1, & \text{if is odd} \
\end{cases}
f(n) =
\begin{cases}
\frac{n}{2}, & \text{if is even} [2ex]
3n+1, & \text{if is odd} \
\end{cases}
f(n) =
\begin{cases}
\frac{n}{2}, & \text{if is even} \
3n+1, & \text{if is odd} \
\end{cases}
f(n) =
\begin{cases}
\frac{n}{2}, & \text{if is even} [2ex]
3n+1, & \text{if is odd} \
\end{cases}
\begin{array}{c} % 总表格
\begin{array}{cc} % 第一行内分成两列
\begin{array}{c|cccc} % 第一列”最小值”数组
\text{min} & 0 & 1 & 2 & 3 \
\hline
0 & 0 & 0 & 0 & 0 \
1 & 0 & 1 & 1 & 1 \
2 & 0 & 1 & 2 & 2 \
3 & 0 & 1 & 2 & 3 \
\end{array}
&
\begin{array}{c|cccc} % 第二列”最大值”数组
\text{max} & 0 & 1 & 2 & 3 \
\hline
0 & 0 & 1 & 2 & 3 \
1 & 1 & 1 & 2 & 3 \
2 & 2 & 2 & 2 & 3 \
3 & 3 & 3 & 3 & 3 \
\end{array}
\end{array} % 第一行表格组结束
\
\begin{array}{c|cccc} % 第二行 Delta 值数组
\Delta & 0 & 1 & 2 & 3 \
\hline
0 & 0 & 1 & 2 & 3 \
1 & 1 & 0 & 1 & 2 \
2 & 2 & 1 & 0 & 1 \
3 & 3 & 2 & 1 & 0 \
\end{array} % 第二行表格结束
\end{array} % 总表格结束
\begin{array}{c} % 总表格
\begin{array}{cc} % 第一行内分成两列
\begin{array}{c|cccc} % 第一列”最小值”数组
\text{min} & 0 & 1 & 2 & 3 \
\hline
0 & 0 & 0 & 0 & 0 \
1 & 0 & 1 & 1 & 1 \
2 & 0 & 1 & 2 & 2 \
3 & 0 & 1 & 2 & 3 \
\end{array}
&
\begin{array}{c|cccc} % 第二列”最大值”数组
\text{max} & 0 & 1 & 2 & 3 \
\hline
0 & 0 & 1 & 2 & 3 \
1 & 1 & 1 & 2 & 3 \
2 & 2 & 2 & 2 & 3 \
3 & 3 & 3 & 3 & 3 \
\end{array}
\end{array} % 第一行表格组结束
\
\begin{array}{c|cccc} % 第二行 Delta 值数组
\Delta & 0 & 1 & 2 & 3 \
\hline
0 & 0 & 1 & 2 & 3 \
1 & 1 & 0 & 1 & 2 \
2 & 2 & 1 & 0 & 1 \
3 & 3 & 2 & 1 & 0 \
\end{array} % 第二行表格结束
\end{array} % 总表格结束
\left{
\begin{array}{c}
a_1x+b_1y+c_1z=d_1 \
a_2x+b_2y+c_2z=d_2 \
a_3x+b_3y+c_3z=d_3 \
\end{array}
\right.
\left{
\begin{array}{c}
a_1x+b_1y+c_1z=d_1 \
a_2x+b_2y+c_2z=d_2 \
a_3x+b_3y+c_3z=d_3 \
\end{array}
\right.
x = a_0 + \cfrac{1^2}{a_1 +
\cfrac{2^2}{a_2 +
\cfrac{3^2}{a_3 +
\cfrac{4^4}{a_4 +
\cdots
}
}
}
}
x = a_0 + \cfrac{1^2}{a_1 +
\cfrac{2^2}{a_2 +
\cfrac{3^2}{a_3 +
\cfrac{4^4}{a_4 +
\cdots
}
}
}
}
x = a_0 + \frac{1^2}{a_1 +
\frac{2^2}{a_2 +
\frac{3^2}{a_3 +
\frac{4^4}{a_4 +
\cdots
}
}
}
}
x = a_0 + \frac{1^2}{a_1 +
\frac{2^2}{a_2 +
\frac{3^2}{a_3 +
\frac{4^4}{a_4 +
\cdots
}
}
}
}
x = a_0 + \frac{1^2}{a_1 +}
\frac{2^2}{a_2 +}
\frac{3^2}{a_3 +}
\frac{4^4}{a_4 +}
\cdots
x = a_0 + \frac{1^2}{a_1 +}
\frac{2^2}{a_2 +}
\frac{3^2}{a_3 +}
\frac{4^4}{a_4 +}
\cdots
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\require{AMScd}
\begin{CD}
A @>a>> B \
@V b V V# @VV c V \
C @>>d> D \
\end{CD}
\require{AMScd}
\begin{CD}
A @>a>> B \
@V b V V# @VV c V \
C @>>d> D \
\end{CD}
\require{AMDcd}
\begin{CD}
A @>>> B @>{\text{very long label}}>> C \
@. @AAA @| \
D @= E @<<< F \
\end{CD}
\require{AMDcd}
\begin{CD}
A @>>> B @>{\text{very long label}}>> C \
@. @AAA @| \
D @= E @<<< F \
\end{CD}
\require{AMDcd}
\begin{CD}
\rm{RCOHR^{‘}SO_3Na} @>{\large\text{Hydrolysis, , Dil.HCl}}>> \rm{(RCOR^{‘})+NaCl+SO_2+ H_2O}
\end{CD}
\require{AMDcd}
\begin{CD}
\rm{RCOHR^{‘}SO_3Na} @>{\large\text{Hydrolysis, , Dil.HCl}}>> \rm{(RCOR^{‘})+NaCl+SO_2+ H_2O}
\end{CD}
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\require{AMSmath}
\begin{array}{cc}
\mathrm{Bad} & \mathrm{Better} \
\hline \
\int\intS f(x),dy,dx & \iint{\boldsymbol{S}} f(x),{\rm d}y,{\rm d}x \
\int\int\intV f(x),dz,dy,dx & \iiint{\boldsymbol{V}} f(x),{\rm d}z,{\rm d}y,{\rm d}x [3ex]
\hline \
\text{多重积分示例} & \idotsint_{\boldsymbol{D}} f(x_1,x_2,,\cdots, ,x_n),{\rm d}x_1\cdots{\rm d}x_n
\end{array}
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