前言
最近开始使用起markdown来记学习笔记，因为经常有公式要写，就需要用到latex，到网上查来查去又不太方便，而且也很少能查到写的比较全的，就准备写下这篇文章。
插入数学公式
在markdown中插入数学公式的语法有两种：
- 行内公式
$数学公式$ - 行间公式
$$数学公式$$
如：
函数$ L(Y,f(X))=(Y-f(X))^2 $
函数
$$
L(Y,f(X))=(Y-f(X))^2
$$
函数$ L(Y,f(X))=(Y-f(X))^2 $
函数
\[L(Y,f(X))=(Y-f(X))^2
\]
\]
如果需要加编号，加上\tag{编号}即可，如：
$$
L(Y,f(X))=(Y-f(X))^2
\tag{1}
$$
\[L(Y,f(X))=(Y-f(X))^2
\tag{1}
\]
\tag{1}
\]
上下标
上标可由^表示，下标可由_表示，若上下标不止一个字符则需用花括号{}括起
如：
n_x n^x
\(n_x\) \(n^x\)
分数
分数输入格式为\frac{分子}{分母}
如：
$\frac{1}{N}$
\(\frac{1}{N}\)
括号
() [] 和|都表示自己，但是{}需加\
如：
$() [] | \{\}$
\(() [] | \{\}\)
上下划线
$$
\begin{array}
\overline{a+b} \\
\underline{a+b} \\
\overleftarrow{a+b} \\
\underleftarrow{a+b} \\
\underleftrightarrow{a+b} \\
\vec x = \vec{AB} \\
\overbrace {a+b}^\text{a,b} \\
a+\rlap{\overbrace{\phantom{b+c+d}}^m}b+\underbrace{c+d+e}_n+f
\end{array}
$$
\[\begin{array}
\overline{a+b} \\
\underline{a+b} \\
\overleftarrow{a+b} \\
\underleftarrow{a+b} \\
\underleftrightarrow{a+b} \\
\vec x = \vec{AB} \\
\overbrace {a+b}^\text{a,b} \\
a+\rlap{\overbrace{\phantom{b+c+d}}^m}b+\underbrace{c+d+e}_n+f
\end{array}
\]
\overline{a+b} \\
\underline{a+b} \\
\overleftarrow{a+b} \\
\underleftarrow{a+b} \\
\underleftrightarrow{a+b} \\
\vec x = \vec{AB} \\
\overbrace {a+b}^\text{a,b} \\
a+\rlap{\overbrace{\phantom{b+c+d}}^m}b+\underbrace{c+d+e}_n+f
\end{array}
\]
省略号
$$
\begin{eqnarray*} \\
\ldots \\
\cdots \\
\vdots \\
\ddots \\
\end{eqnarray*}
$$
\[\begin{eqnarray*} \\
\ldots \\
\cdots \\
\vdots \\
\ddots \\
\end{eqnarray*}
\]
\ldots \\
\cdots \\
\vdots \\
\ddots \\
\end{eqnarray*}
\]
线性方程组
使用case环境将多个公式组合
$$
L(Y,f(X))=
\begin{cases}
1,\quad &Y\neq f(X)\\
0,\quad &Y=f(X)
\end{cases}
$$
\[L(Y,f(X))=
\begin{cases}
1,\quad &Y\neq f(X)\\
0,\quad &Y=f(X)
\end{cases}
\]
\begin{cases}
1,\quad &Y\neq f(X)\\
0,\quad &Y=f(X)
\end{cases}
\]
另还有gathered环境
$$
\left. \begin{gathered}
S \subseteq T \\
S \supseteq T
\end{gathered} \right\}
\implies S = T
$$
\[\left. \begin{gathered}
A \subseteq B \\
A \supseteq B
\end{gathered} \right\}
\implies A = B
\]
A \subseteq B \\
A \supseteq B
\end{gathered} \right\}
\implies A = B
\]
数学模式重音符
$$
\hat{a} \check{a} \tilde{a} \acute{a}
\grave{a} \dot{a} \ddot{a} \breve{a}
\bar{a} \vec{a} \widehat{a} \widetilde{a}
$$
\[\hat{a} \check{a} \tilde{a} \acute{a}\\
\grave{a} \dot{a} \ddot{a} \breve{a}\\
\bar{a} \vec{a} \widehat{a} \widetilde{a}
\]
\grave{a} \dot{a} \ddot{a} \breve{a}\\
\bar{a} \vec{a} \widehat{a} \widetilde{a}
\]
矩阵
$$
X =
\left[
\begin{matrix}
x^{(1)} & x^{(2)} & \cdots & x^{(m)} \\
x^{(1)} & x^{(2)} & \cdots & x^{(m)} \\
x^{(1)} & x^{(2)} & \cdots & x^{(m)} \\
\end{matrix}
\right]
$$
\[X =
\left[
\begin{matrix}
x^{(1)} & x^{(2)} & \cdots & x^{(m)} \\
x^{(1)} & x^{(2)} & \cdots & x^{(m)} \\
x^{(1)} & x^{(2)} & \cdots & x^{(m)} \\
\end{matrix}
\right]
\]
\left[
\begin{matrix}
x^{(1)} & x^{(2)} & \cdots & x^{(m)} \\
x^{(1)} & x^{(2)} & \cdots & x^{(m)} \\
x^{(1)} & x^{(2)} & \cdots & x^{(m)} \\
\end{matrix}
\right]
\]
希腊字母
见下表
| 代码 | 大写 | 代码 | 小写 |
|---|---|---|---|
A |
A | \alpha |
α |
B |
B | \beta |
β |
\Gamma |
Γ | \gamma |
γ |
\Delta |
Δ | \delta |
δ |
E |
E | \epsilon |
ϵ |
Z |
Z | \zeta |
ζ |
H |
H | \eta |
η |
\Theta |
Θ | \theta |
θ |
I |
I | \iota |
ι |
K |
K | \kappa |
κ |
\Lambda |
Λ | \lambda |
λ |
M |
M | \mu |
μ |
N |
N | \nu |
ν |
\Xi |
Ξ | \xi |
ξ |
O |
O | \omicron |
ο |
\Pi |
Π | \pi |
π |
P |
P | \rho |
ρ |
\Sigma |
Σ | \sigma |
σ |
T |
T | \tau |
τ |
\Upsilon |
Υ | \upsilon |
υ |
\Phi |
Φ | \phi |
ϕ |
X |
X | \chi |
χ |
\Psi |
Ψ | \psi |
ψ |
\Omega |
Ω | \omega |
ω |
常用数学符号
包括积分符号、集合符号、累乘累加符号等
见下表：
| 转义符号 | 效果 |
|---|---|
\log_{x}y = \arccos z |
\(\log_{x}y = \arccos z\) |
\frac{a} {b} |
\(\frac{a} {b}\) |
_{a}^{b}\textrm{C} |
\(_{a}^{b}\textrm{C}\) |
\frac{\partial {z_x}}{\partial x} |
\(\frac{\partial {z_x}}{\partial x}\) |
\frac{\partial^2 {x}}{\partial x^2} |
\(\frac{\partial^2 {x}}{\partial x^2}\) |
\frac{\mathrm{d} y}{\mathrm{d} x} |
\(\frac{\mathrm{d} y}{\mathrm{d} x}\) |
\int x |
\(\int x\) |
\int_{a}^{b}x |
\(\int_{a}^{b}x\) |
\oint a |
\(\oint a\) |
\oint_{a}^{b}C |
\(\oint_{a}^{b}C\) |
\iint_{a}^{v}C |
\(\iint_{a}^{v}C\) |
\bigcap A |
\(\bigcap A\) |
\bigcap_{a}^{b}C |
\(\bigcap_{a}^{b}C\) |
\bigcup c |
\(\bigcup c\) |
\bigcup_{a}^{b}C |
\(\bigcup_{a}^{b}C\) |
\lim_{c}X |
\(\lim_{c}X\) |
\sum a |
\(\sum a\) |
\sum_{a}^{b}C |
\(\sum_{a}^{b}C\) |
\sqrt{X} |
\(\sqrt{X}\) |
\sqrt[a]{X} |
\(\sqrt[a]{X}\) |
\prod X |
\(\prod X\) |
\prod_{a}^{b} X |
\(\prod_{a}^{b} X\) |
\coprod X |
\(\coprod X\) |
\coprod_{a}^{b} X |
\(\coprod_{a}^{b} X\) |
\left [ a \right ] |
\(\left [ a \right ]\) |
\left ( a\right ) |
\(\left ( a\right )\) |
\left \{ a \right \} |
\(\left \{ a \right \}\) |
\left \langle a \right \rangle |
\(\left \langle a \right \rangle\) |
\left \lfloor a \right \rfloor |
\(\left \lfloor a \right \rfloor\) |
\left \lceil a \right \rceil |
\(\left \lceil a \right \rceil\) |
\supseteqq A |
\(\supseteqq A\) |
二元关系符
\[\begin{array}
& < &\texttt{"<"} & > &\texttt{">"} &= &\texttt{"="}\\
\leq &\texttt{"\leq or \le"} & \geq &\texttt{"\geq or \ge"} &\equiv &\texttt{"\equiv"}\\
\ll &\texttt{"\ll"} & \gg &\texttt{"\gg"} &\doteq &\texttt{"\doteq"}\\
\prec &\texttt{"\prec"} & \succ &\texttt{"\succ"} &\sim &\texttt{"\sim"}\\
\preceq &\texttt{"\preceq"} & \succeq &\texttt{"\succeq"} &\simeq &\texttt{"\simeq"}\\
\subset &\texttt{"\subset"} & \supset &\texttt{"\supset"} &\approx &\texttt{"\approx"}\\
\subseteq &\texttt{"\subseteq"} & \supseteq &\texttt{"\supseteq"} &\approxeq &\texttt{"\approxeq"}\\
\sqsubset &\texttt{"\sqsubset"} & \sqsupset&\texttt{"\sqsupset"} &\Join &\texttt{"\Join"}\\
\sqsubseteq &\texttt{"\sqsubseteq"} & \sqsupseteq&\texttt{"\sqsupseteq"} &\bowtie &\texttt{"\bowtie"}\\
\in &\texttt{"\in"} & \ni &\texttt{"\ni or \owns"} &\propto &\texttt{"\propto"}\\
\vdash &\texttt{"\vdash"} & \dashv &\texttt{"\dashv"} &\models &\texttt{"\models"}\\
\mid &\texttt{"\mid"} & \parallel &\texttt{"\parallel"} &\perp &\texttt{"\perp"}\\
\smile &\texttt{"\smile"} & \frown &\texttt{"\frown"} &\asymp &\texttt{"\asymp"}\\
: &\texttt{":"} & \notin &\texttt{"\notin"} &\neq &\texttt{"\neq or \ne"}\\
\end{array}
\]
& < &\texttt{"<"} & > &\texttt{">"} &= &\texttt{"="}\\
\leq &\texttt{"\leq or \le"} & \geq &\texttt{"\geq or \ge"} &\equiv &\texttt{"\equiv"}\\
\ll &\texttt{"\ll"} & \gg &\texttt{"\gg"} &\doteq &\texttt{"\doteq"}\\
\prec &\texttt{"\prec"} & \succ &\texttt{"\succ"} &\sim &\texttt{"\sim"}\\
\preceq &\texttt{"\preceq"} & \succeq &\texttt{"\succeq"} &\simeq &\texttt{"\simeq"}\\
\subset &\texttt{"\subset"} & \supset &\texttt{"\supset"} &\approx &\texttt{"\approx"}\\
\subseteq &\texttt{"\subseteq"} & \supseteq &\texttt{"\supseteq"} &\approxeq &\texttt{"\approxeq"}\\
\sqsubset &\texttt{"\sqsubset"} & \sqsupset&\texttt{"\sqsupset"} &\Join &\texttt{"\Join"}\\
\sqsubseteq &\texttt{"\sqsubseteq"} & \sqsupseteq&\texttt{"\sqsupseteq"} &\bowtie &\texttt{"\bowtie"}\\
\in &\texttt{"\in"} & \ni &\texttt{"\ni or \owns"} &\propto &\texttt{"\propto"}\\
\vdash &\texttt{"\vdash"} & \dashv &\texttt{"\dashv"} &\models &\texttt{"\models"}\\
\mid &\texttt{"\mid"} & \parallel &\texttt{"\parallel"} &\perp &\texttt{"\perp"}\\
\smile &\texttt{"\smile"} & \frown &\texttt{"\frown"} &\asymp &\texttt{"\asymp"}\\
: &\texttt{":"} & \notin &\texttt{"\notin"} &\neq &\texttt{"\neq or \ne"}\\
\end{array}
\]
三角函数与逻辑数学字符
| 数学字符 | 输入 | 数学字符 | 输入 |
|---|---|---|---|
| ± | \pm | × | \times |
| ÷ | \div | | | \mid |
| ∤∤ | \nmid | ⋅ | \cdot |
| ∘ | \circ | ∗ | \ast |
| ⨀ | \bigodot | ⨂ | \bigotimes |
| ⨁ | \bigoplus | ∅ | \emptyset |
| ⋁ | \bigvee | ⋀ | \bigwedge |
| ⨄ | \biguplus | ⨆ | \bigsqcup |
| ∠ | \angle | 30^∘ | 30 ^ \circ |
| sin | \sin | cos | \cos |
| tan | \tan | cot | \cot |
| ′ | \prime | ∭ | \iiint |
| ⨌ | \iiiint | ∞ | \infty |
| ∇ | \nabla | ∵ | \because |
| ∴ | \therefore | ∀ | \forall |
| ∃ | \exists | ≯ | \not> |
| ⊄ | \not\subset | sec | \sec |
| ↑ | \uparrow | ↓ | \downarrow |
| ⇑ | \Uparrow | ⇓ | \Downarrow |
| → | \rightarrow | ← | \leftarrow |
| ⇒ | \Rightarrow | ⇐ | \Leftarrow |
| ⟶ | \longrightarrow | ⟵ | \longleftarrow |
| ⟹ | \Longrightarrow | ⟸ | \Longleftarrow |
| \quad (空格) | # | # | |
| ⊥ | \bot |
数学字体
字体表
\[\begin{array}
\texttt{"normal"} &\texttt{} & ABCDEFGHIJKLMNOPQRSTUVWXYZ\\
\texttt{"blackboard"} &\texttt{\mathbb} &\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\texttt{"boldface"} &\texttt{\mathbf} &\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\texttt{"typewriter"} &\texttt{\mathtt} &\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\texttt{"roman"} &\texttt{\mathrm} &\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\texttt{"sans-serif"} &\texttt{\mathsf} &\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\texttt{"calligraphic"}&\texttt{\mathcal} &\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\texttt{"script"} &\texttt{\mathscr} &\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\texttt{"fraktur"} &\texttt{\mathfrak}&\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\end{array}
\]
\texttt{"normal"} &\texttt{} & ABCDEFGHIJKLMNOPQRSTUVWXYZ\\
\texttt{"blackboard"} &\texttt{\mathbb} &\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\texttt{"boldface"} &\texttt{\mathbf} &\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\texttt{"typewriter"} &\texttt{\mathtt} &\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\texttt{"roman"} &\texttt{\mathrm} &\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\texttt{"sans-serif"} &\texttt{\mathsf} &\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\texttt{"calligraphic"}&\texttt{\mathcal} &\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\texttt{"script"} &\texttt{\mathscr} &\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\texttt{"fraktur"} &\texttt{\mathfrak}&\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\
\end{array}
\]
色彩表
\[\begin{array}
\hline
\verb+\color{black}{黑色}+ & \color{black}{黑色} \\
\verb+\color{darkgray}{深灰}+ & \color{darkgray}{深灰}\\
\verb+\color{gray}{灰色}+ & \color{gray}{灰色} \\
\verb+\color{silver}{银色}+ & \color{silver}{银色} \\
\verb+\color{lightgray}{浅灰}+&\color{lightgray}{浅灰}\\
\verb+\color{white}{白色}+ & \color{white}{白色} \\
\hline
\verb+\color{brown}{棕色}+ & \color{brown}{棕色} \\
\verb+\color{maroon}{栗色}+ & \color{maroon}{栗色} \\
\verb+\color{red}{红色}+ & \color{red}{红色} \\
\verb+\color{fuchsia}{桃红}+ & \color{fuchsia}{桃红} \\
\verb+\color{magenta}{品红}+ & \color{magenta}{品红} \\
\verb+\color{pink}{粉红}+ & \color{pink}{粉红} \\
\verb+\color{orange}{橙色}+ & \color{orange}{橙色} \\
\verb+\color{yellow}{黄色}+ & \color{yellow}{黄色} \\
\verb+\color{lime}{青柠}+ & \color{lime}{青柠} \\
\verb+\color{olive}{橄榄}+ & \color{olive}{橄榄} \\
\verb+\color{green}{绿色}+ & \color{green}{绿色} \\
\verb+\color{aqua}{水绿}+ & \color{aqua}{水绿} \\
\verb+\color{cyan}{青色}+ & \color{cyan}{青色} \\
\verb+\color{teal}{靛青}+ & \color{teal}{靛青} \\
\verb+\color{blue}{蓝色}+ & \color{blue}{蓝色} \\
\verb+\color{navy}{海蓝}+ & \color{navy}{海蓝} \\
\verb+\color{violet}{罗兰}+ & \color{purple}{罗兰} \\
\verb+\color{purple}{紫色}+ & \color{purple}{紫色} \\
\hline
\end{array}参考
\]
\hline
\verb+\color{black}{黑色}+ & \color{black}{黑色} \\
\verb+\color{darkgray}{深灰}+ & \color{darkgray}{深灰}\\
\verb+\color{gray}{灰色}+ & \color{gray}{灰色} \\
\verb+\color{silver}{银色}+ & \color{silver}{银色} \\
\verb+\color{lightgray}{浅灰}+&\color{lightgray}{浅灰}\\
\verb+\color{white}{白色}+ & \color{white}{白色} \\
\hline
\verb+\color{brown}{棕色}+ & \color{brown}{棕色} \\
\verb+\color{maroon}{栗色}+ & \color{maroon}{栗色} \\
\verb+\color{red}{红色}+ & \color{red}{红色} \\
\verb+\color{fuchsia}{桃红}+ & \color{fuchsia}{桃红} \\
\verb+\color{magenta}{品红}+ & \color{magenta}{品红} \\
\verb+\color{pink}{粉红}+ & \color{pink}{粉红} \\
\verb+\color{orange}{橙色}+ & \color{orange}{橙色} \\
\verb+\color{yellow}{黄色}+ & \color{yellow}{黄色} \\
\verb+\color{lime}{青柠}+ & \color{lime}{青柠} \\
\verb+\color{olive}{橄榄}+ & \color{olive}{橄榄} \\
\verb+\color{green}{绿色}+ & \color{green}{绿色} \\
\verb+\color{aqua}{水绿}+ & \color{aqua}{水绿} \\
\verb+\color{cyan}{青色}+ & \color{cyan}{青色} \\
\verb+\color{teal}{靛青}+ & \color{teal}{靛青} \\
\verb+\color{blue}{蓝色}+ & \color{blue}{蓝色} \\
\verb+\color{navy}{海蓝}+ & \color{navy}{海蓝} \\
\verb+\color{violet}{罗兰}+ & \color{purple}{罗兰} \\
\verb+\color{purple}{紫色}+ & \color{purple}{紫色} \\
\hline
\end{array}参考
\]
参考：
https://www.cnblogs.com/nowgood/p/Latexstart.html
http://jzqt.github.io/2015/06/30/Markdown中写数学公式/