typora常用的数学公式编辑语法
目录
基本格式
上下标
\[A_1^2
\\
B_{12}
\\
2^{x^2+y}
\]
A_1^2
\\
B_{12}
\\
2^{x^2+y}
分数
\[\frac{x}{1+x^2}
\\
\frac{\frac{1}{2}+x}{y}
\\
\tfrac{a}{b}
\frac{a}{b}
\]
\frac{x}{1+x^2}
\\
\frac{\frac{1}{2}+x}{y}
\\
\tfrac{a}{b}
\frac{a}{b}
开根
\[\sqrt{x}
\sqrt[3]{x}
\]
\sqrt{x}
\sqrt[3]{x}
组合数
\[\binom{n}{k}
\tbinom{n}{k}
\]
\binom{n}{k}
\tbinom{n}{k}
导数
\[a'
a''
a^{\prime}
\]
偏微分
\[\partial \\
\nabla
\]
a'
a''
a^{\prime}
取模
\[x \pmod a
\\
2\mod{x}
\]
x \pmod a
\\
2\mod{x}
积分
\[\int_{1}^{2}
\intop_{2}^{1}
\oint
\smallint
\\
\iint
\oiint
\iiint
\oiiint
\]
\oiint和\oiiint在博客园中不能使用,对应的是带圆圈的二重和三重积分
\int_{1}^{2}
\intop_{2}^{1}
\oint
\smallint
\\
\iint
\oiint
\iiint
\oiiint
累加/累乘/极限
\[\sum_{i=1}^{k}
\displaystyle\sum_{i=1}^n
\textstyle\sum_{i=1}^n
\\
\prod_{i=1}^{k}
\displaystyle\prod_{i=1}^n
\textstyle\prod_{i=1}^n
\\
\lim_{k \to \infty}
\lim\limits_{k \to \infty}
\lim\nolimits_{k \to \infty}
\]
\sum_{i=1}^{k}
\displaystyle\sum_{i=1}^n
\textstyle\sum_{i=1}^n
\\
\prod_{i=1}^{k}
\displaystyle\prod_{i=1}^n
\textstyle\prod_{i=1}^n
\\
\lim_{k \to \infty}
\lim\limits_{k \to \infty}
\lim\nolimits_{k \to \infty}
修饰符号
简单的帽子
\[\hat{\theta}
\widehat{AB}
\\
\bar{y}
\overline{AB}
\\
\tilde{a}
\widetilde{ac}
\\
\bar{a}
\acute{a}
\check{a}
\grave{a}
\\
\dot{a}
\ddot{a}
\]
\hat{\theta}
\widehat{AB}
\\
\bar{y}
\overline{AB}
\\
\tilde{a}
\widetilde{ac}
\\
\bar{a}
\acute{a}
\check{a}
\grave{a}
\\
\dot{a}
\ddot{a}
帽子和袜子
\[\overleftarrow{AB}
\overrightarrow{AB}
\overleftrightarrow{AB}
\\
\underleftarrow{AB}
\underrightarrow{AB}
\underleftrightarrow{AB}
\\
\overbrace{AB}
\underbrace{AB}
\\
\overline{AB}
\underline{AB}
\]
\overleftarrow{AB}
\overrightarrow{AB}
\overleftrightarrow{AB}
\\
\underleftarrow{AB}
\underrightarrow{AB}
\underleftrightarrow{AB}
\\
\overbrace{AB}
\underbrace{AB}
\\
\overline{AB}
\underline{AB}
盖子和盒子
\[\overbrace{a+b+c}^{\text{note}}
\\
\underbrace{a+b+c}_{\text{note}}
\\
\boxed{\pi=3.14}
\]
\overbrace{a+b+c}^{\text{note}}
\\
\underbrace{a+b+c}_{\text{note}}
\\
\boxed{\pi=3.14}
各种括号
\[(
\big(
\Big(
\bigg(
\Bigg(
\]
(
\big(
\Big(
\bigg(
\Bigg(
\[[]
<>
|-2|
\{\}
\]
[]
<>
|-2|
\{\}
\[\lgroup x \rgroup
\lVert a \rVert
\lceil 2.6 \rceil
\lfloor 1.2 \rfloor
\]
\lgroup x \rgroup
\lVert a \rVert
\lceil 2.6 \rceil
\lfloor 1.2 \rfloor
\[\ulcorner
\urcorner
\llcorner
\lrcorner
\]
\ulcorner
\urcorner
\llcorner
\lrcorner
希腊字母
算术运算符
\[+
-
\times
/
\div
\cdot
\#
\%
\]
+
-
\times
/
\div
\cdot
\#
\%
\[\cap
\cup
\land
\lor
\sqcup
\sqcap
\]
\cap
\cup
\land
\lor
\sqcup
\sqcap
\[\circ
\ast
\star
\otimes
\oplus
\odot
\]
\circ
\ast
\star
\otimes
\oplus
\odot
\[\pm
\mp
\dotplus
\divideontimes
\]
\pm
\mp
\dotplus
\divideontimes
比较运算符
\[=
= \not
\equiv
\approx
\approxeq
\cong
\sim
\]
=
= \not
\equiv
\approx
\approxeq
\cong
\sim
\[<
>
\le
\ge
\gg
\ll
\]
<
>
\le
\ge
\gg
\ll
\[\curlyeqprec
\curlyeqsucc
\prec
\succ
\preceq
\succeq
\]
\curlyeqprec
\curlyeqsucc
\prec
\succ
\preceq
\succeq
集合/逻辑相关
\[\in
\owns \not
\subset \not
\supset
\subseteq
\supseteq
\\
\cap
\cup
\land
\lor
\\
\neg
\emptyset
\varnothing
\\
\because
\forall
\exists
\therefore
\]
\in
\owns \not
\subset \not
\supset
\subseteq
\supseteq
\\
\cap
\cup
\land
\lor
\\
\neg
\emptyset
\varnothing
\\
\because
\forall
\exists
\therefore
各种箭头
细箭头
\[\gets
\leftarrow
\to
\rightarrow
\leftrightarrow
\\
\uparrow
\downarrow
\updownarrow
\]
\gets
\leftarrow
\to
\rightarrow
\leftrightarrow
\\
\uparrow
\downarrow
\updownarrow
粗箭头
\[\Leftarrow
\Rightarrow
\Leftrightarrow
\iff
\\
\Uparrow
\Downarrow
\Updownarrow
\]
\Leftarrow
\Rightarrow
\Leftrightarrow
\iff
\\
\Uparrow
\Downarrow
\Updownarrow
斜箭头
\[\nearrow
\searrow
\swarrow
\nwarrow
\]
\nearrow
\searrow
\swarrow
\nwarrow
半边箭头
\[\leftharpoonup
\leftharpoondown
\rightharpoonup
\rightharpoondown
\rightleftharpoons
\]
\leftharpoonup
\leftharpoondown
\rightharpoonup
\rightharpoondown
\rightleftharpoons
特殊箭头
\[\mapsto
\leadsto
\hookleftarrow
\hookrightarrow
\]
\mapsto
\leadsto
\hookleftarrow
\hookrightarrow
加长箭头
\[\longleftarrow
\longrightarrow
\longleftrightarrow
\Longleftarrow
\Longrightarrow
\Longleftrightarrow
\longmapsto
\]
\longleftarrow
\longrightarrow
\longleftrightarrow
\Longleftarrow
\Longrightarrow
\Longleftrightarrow
\longmapsto
带文本箭头
\[\xrightarrow{over}
\xrightarrow[over]{}
\xrightarrow[under]{over}
\\
\xleftarrow[]{over}
\xleftarrow[under]{}
\xleftarrow[under]{over}
\]
\xrightarrow{over}
\xrightarrow[over]{}
\xrightarrow[under]{over}
\xleftarrow[]{over}
\xleftarrow[under]{}
\xleftarrow[under]{over}
空格间距
\[A\!B
\\
AB
\\
A\thinspace B
\\
A\:B
\\
A\ B
\\
A \enspace B
\\
A\quad B
\\
A\qquad B
\]
A\!B
\\
AB
\\
A\thinspace B
\\
A\:B
\\
A\ B
\\
A \enspace B
\\
A\quad B
\\
A\qquad B
矩阵
\[A = \begin{matrix}
a & b\\
c & d
\end{matrix}
\]
A = \begin{matrix}
a & b\\
c & d
\end{matrix}
\[B = \begin{pmatrix}
a & b\\
c & d
\end{pmatrix}
\]
B = \begin{pmatrix}
a & b\\
c & d
\end{pmatrix}
\[C = \begin{vmatrix}
a & b\\
c & d
\end{vmatrix}
\]
C = \begin{vmatrix}
a & b\\
c & d
\end{vmatrix}
\[D = \begin{bmatrix}
a & b\\
c & d
\end{bmatrix}
\]
D = \begin{bmatrix}
a & b\\
c & d
\end{bmatrix}
\[E = \begin{Vmatrix}
a & b\\
c & d
\end{Vmatrix}
\]
E = \begin{Vmatrix}
a & b\\
c & d
\end{Vmatrix}
\[F = \begin{Bmatrix}
a & b\\
c & d
\end{Bmatrix}
\]
F = \begin{Bmatrix}
a & b\\
c & d
\end{Bmatrix}
\[[A\ b] =
\begin{bmatrix}
\begin{array}{c c c|c}
a_{11} & a_{12} & a_{13} & b_1\\
a_{21} & a_{22} & a_{23} & b_2\\
a_{31} & a_{32} & a_{33} & b_3\\
\end{array}
\end{bmatrix}
\]
[A\ b] =
\begin{bmatrix}
\begin{array}{c c c|c}
a_{11} & a_{12} & a_{13} & b_1\\
a_{21} & a_{22} & a_{23} & b_2\\
a_{31} & a_{32} & a_{33} & b_3\\
\end{array}
\end{bmatrix}
\[\begin{array}{c:c:c}
a & b & c \\
\hline
d & e & f \\
\hdashline
g & h & i
\end{array}
\]
\begin{array}{c:c:c}
a & b & c \\
\hline
d & e & f \\
\hdashline
g & h & i
\end{array}
\[L_{n\times n} = \begin{bmatrix}
a_{11} & a_{12} & \cdots & a_{1n} \\
a_{21} & a_{22} & \cdots & a_{2n} \\
\vdots & \vdots &\ddots & \vdots\\
a_{n1} & a_{n2} & \cdots & a_{nn} \\
\end{bmatrix}
\]
L_{n\times n} = \begin{bmatrix}
a_{11} & a_{12} & \cdots & a_{1n} \\
a_{21} & a_{22} & \cdots & a_{2n} \\
\vdots & \vdots &\ddots & \vdots\\
a_{n1} & a_{n2} & \cdots & a_{nn} \\
\end{bmatrix}
列式/方程组
\[\begin{aligned}
f(x) &= (x+1)^2\\
&= x^2 + 2x + 1
\end{aligned}
\]
\begin{aligned}
f(x) &= (x+1)^2\\
&= x^2 + 2x + 1
\end{aligned}
\[f(x) = \begin{cases}
a &\text{if b}\\
b &\text{if a}\\
\end{cases}
\]
f(x) = \begin{cases}
a &\text{if b}\\
b &\text{if a}\\
\end{cases}
\[\begin{cases}
\begin{aligned}
x + 2y &= 1\\
3x - y &= 5
\end{aligned}
\end{cases}
\]
\begin{cases}
\begin{aligned}
x + 2y &= 1\\
3x - y &= 5
\end{aligned}
\end{cases}
字体操作
修改字体
修改大小
\[d
\Huge AB
d
\\
d
\normalsize AB
\]
\Huge AB
d
\\
d
\normalsize AB
修改字体的操作影响效果到行末。
\[AB
\Huge AB
\huge AB
\\
AB
\LARGE AB
\Large AB
\large AB
\\
AB
\small AB
\tiny AB
\]
AB
\Huge AB
\huge AB
\\
AB
\LARGE AB
\Large AB
\large AB
\\
AB
\small AB
\tiny AB
修改颜色
\[\textcolor{blue}{F=ma}
\\
\textcolor{#00ff00}{F=ma}
\\
\textcolor{#ff0000}{F=ma}
\\
\color{blue} one\ line
\\
nothing
\]
博客园的MD不能使用,给大伙一张在typora中的演示图康康
\textcolor{blue}{F=ma}
\\
\textcolor{#00ff00}{F=ma}
\\
\textcolor{#ff0000}{F=ma}
\\
\color{blue} one\ line
\\
nothing
\[\colorbox{#00ff00}{F=ma}
\\
\colorbox{aqua}{A}
\\
\fcolorbox{red}{aqua}{A}
\]
博客园的MD同样不能使用
\colorbox{#00ff00}{F=ma}
\\
\colorbox{aqua}{A}
\\
\fcolorbox{red}{aqua}{A}
划掉
\[\cancel{5}
\bcancel{5}
\xcancel{ABC}
\not =
\]
博客园的MD同样不能使用
\cancel{5}
\bcancel{5}
\xcancel{ABC}
\not =
常见图形
\[\Box
\square
\blacksquare
\triangle
\triangledown
\blacktriangle
\diamond
\Diamond
\star
\bigstar
\circ
\bullet
\bigcirc
\bigodot
\]
\Box
\square
\blacksquare
\triangle
\triangledown
\blacktriangle
\diamond
\Diamond
\star
\bigstar
\circ
\bullet
\bigcirc
\bigodot
\[\diamondsuit
\clubsuit
\heartsuit
\spadesuit
\]
\diamondsuit
\clubsuit
\heartsuit
\spadesuit
\[\angle
\measuredangle
\top
\bot
\infty
\]
\angle
\measuredangle
\top
\bot
\infty
\[\checkmark
\dagger
\ddagger
\yen
\$
\]
\checkmark
\dagger
\ddagger
\yen
\$
声明宏
对于一些复杂但只是有少许不同的表达式,可以声明一个函数来调用,提高原码的可读性,减少出错。
基本的语法为
\def\macroname#1#2{
your command
}
宏允许带任意数量的参数(也可以不带参),必须是#1,#2,……
这样的命名格式,同时注意再定义宏的时候注意让#1
与\
中间隔一个空格,否则会解析成#。再调用的时候格式为\macroname{x}{y}{z}
,可以参考一下的例子:
\[\def\Normal#1#2#3{
\frac{1}{\sqrt{2\pi}\ #3}\exp{[-\frac{(#1 - #2)^2}{2\ #3^2}]}
}
f(x)=\Normal{x}{u_1}{\sigma_1}\\
f(y)=\Normal{y}{u_2}{\sigma_2}\\
\]
\def\Normal#1#2#3{
\frac{1}{\sqrt{2\pi}\ #3}\exp{[-\frac{(#1 - #2)^2}{2\ #3^2}]}
}
f(x)=\Normal{x}{u_1}{\sigma_1}\\
f(y)=\Normal{y}{u_2}{\sigma_2}\\
\[\def\EXP{
e^x = 1 + x + \frac{1}{2!}x^2 + \frac{1}{3!}x^3 + \cdots
}
\EXP
\]
\def\EXP{
e^x = 1 + x + \frac{1}{2!}x^2 + \frac{1}{3!}x^3 + \cdots
}
\EXP
参考资料
以上代码都可以在typora
中运行,给出的图片链接语法是Ketax
,可能有少数的不适用,但基本可以。