編輯你的數學公式——markdown中latex的使用
前言
最近開始使用起markdown來記學習筆記，因為經常有公式要寫，就需要用到latex，到網上查來查去又不太方便，而且也很少能查到寫的比較全的，就準備寫下這篇文章。
插入數學公式
在markdown中插入數學公式的語法有兩種：
$數學公式$ $$數學公式$$
如：
函式$ L(Y,f(X))=(Y-f(X))^2 $ 函式 $$ L(Y,f(X))=(Y-f(X))^2 $$
函式$ L(Y,f(X))=(Y-f(X))^2 $
函式
\[ L(Y,f(X))=(Y-f(X))^2 \]
如果需要加編號，加上\tag{編號}即可，如：
$$
L(Y,f(X))=(Y-f(X))^2
\tag{1}
$$
\[ L(Y,f(X))=(Y-f(X))^2 \tag{1} \]
上下標
上標可由^
表示，下標可由_
表示，若上下標不止一個字元則需用花括號{}括起
如：
n_x n^x
\(n_x\) \(n^x\)
分數
分數輸入格式為\frac{分子}{分母}
如：
$\frac{1}{N}$
\(\frac{1}{N}\)
括號
()
[]
和|
都表示自己，但是{}
需加\
如：
$() [] | \{\}$
\(() [] | \{\}\)
上下劃線
$$
\begin{array}
\overline{a+b} \\
\underline{a+b} \\
\overleftarrow{a+b} \\
\underleftarrow{a+b} \\
\underleftrightarrow{a+b} \\
\vec x = \vec{AB} \\
\overbrace {a+b}^\text{a,b} \\
a+\rlap{\overbrace{\phantom{b+c+d}}^m}b+\underbrace{c+d+e}_n+f
\end{array}
$$
\[ \begin{array} \overline{a+b} \\ \underline{a+b} \\ \overleftarrow{a+b} \\ \underleftarrow{a+b} \\ \underleftrightarrow{a+b} \\ \vec x = \vec{AB} \\ \overbrace {a+b}^\text{a,b} \\ a+\rlap{\overbrace{\phantom{b+c+d}}^m}b+\underbrace{c+d+e}_n+f \end{array} \]
省略號
$$
\begin{eqnarray*} \\
\ldots \\
\cdots \\
\vdots \\
\ddots \\
\end{eqnarray*}
$$
\[ \begin{eqnarray*} \\ \ldots \\ \cdots \\ \vdots \\ \ddots \\ \end{eqnarray*} \]
線性方程組
使用case
環境將多個公式組合
$$
L(Y,f(X))=
\begin{cases}
1,\quad &Y\neq f(X)\\
0,\quad &Y=f(X)
\end{cases}
$$
\[ L(Y,f(X))= \begin{cases} 1,\quad &Y\neq f(X)\\ 0,\quad &Y=f(X) \end{cases} \]
另還有gathered
環境
$$
\left. \begin{gathered}
S \subseteq T \\
S \supseteq T
\end{gathered} \right\}
\implies S = T
$$
\[ \left. \begin{gathered} A \subseteq B \\ A \supseteq B \end{gathered} \right\} \implies A = B \]
數學模式重音符
$$
\hat{a} \check{a} \tilde{a} \acute{a}
\grave{a} \dot{a} \ddot{a} \breve{a}
\bar{a} \vec{a} \widehat{a} \widetilde{a}
$$
\[ \hat{a} \check{a} \tilde{a} \acute{a}\\ \grave{a} \dot{a} \ddot{a} \breve{a}\\ \bar{a} \vec{a} \widehat{a} \widetilde{a} \]
矩陣
$$
X =
\left[
\begin{matrix}
x^{(1)} & x^{(2)} & \cdots & x^{(m)} \\
x^{(1)} & x^{(2)} & \cdots & x^{(m)} \\
x^{(1)} & x^{(2)} & \cdots & x^{(m)} \\
\end{matrix}
\right]
$$
\[ X = \left[ \begin{matrix} x^{(1)} & x^{(2)} & \cdots & x^{(m)} \\ x^{(1)} & x^{(2)} & \cdots & x^{(m)} \\ x^{(1)} & x^{(2)} & \cdots & x^{(m)} \\ \end{matrix} \right] \]
希臘字母
見下表
| 程式碼 | 大寫 | 程式碼 | 小寫 |
|---|---|---|---|
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 |
常用數學符號
包括積分符號、集合符號、累乘累加符號等
見下表：
| 轉義符號 | 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
|
\(\supseteqq A\) |
二元關係符
\[ \begin{array} & <&\texttt{"<"}& >&\texttt{">"} &=&\texttt{"="}\\ \leq&\texttt{"\leq or \le"}& \geq&\texttt{"\geq or \ge"} &\equiv&\texttt{"\equiv"}\\ \ll&\texttt{"\ll"}& \gg&\texttt{"\gg"} &\doteq&\texttt{"\doteq"}\\ \prec&\texttt{"\prec"}& \succ&\texttt{"\succ"} &\sim&\texttt{"\sim"}\\ \preceq&\texttt{"\preceq"}& \succeq&\texttt{"\succeq"} &\simeq&\texttt{"\simeq"}\\ \subset&\texttt{"\subset"}& \supset&\texttt{"\supset"} &\approx&\texttt{"\approx"}\\ \subseteq&\texttt{"\subseteq"}& \supseteq&\texttt{"\supseteq"} &\approxeq&\texttt{"\approxeq"}\\ \sqsubset&\texttt{"\sqsubset"}& \sqsupset&\texttt{"\sqsupset"} &\Join&\texttt{"\Join"}\\ \sqsubseteq&\texttt{"\sqsubseteq"}& \sqsupseteq&\texttt{"\sqsupseteq"} &\bowtie&\texttt{"\bowtie"}\\ \in&\texttt{"\in"}& \ni&\texttt{"\ni or \owns"} &\propto&\texttt{"\propto"}\\ \vdash&\texttt{"\vdash"}& \dashv&\texttt{"\dashv"} &\models&\texttt{"\models"}\\ \mid&\texttt{"\mid"}& \parallel&\texttt{"\parallel"} &\perp&\texttt{"\perp"}\\ \smile&\texttt{"\smile"}& \frown&\texttt{"\frown"} &\asymp&\texttt{"\asymp"}\\ :&\texttt{":"}& \notin&\texttt{"\notin"} &\neq&\texttt{"\neq or \ne"}\\ \end{array} \]
三角函式與邏輯數學字元
| 數學字元 | 輸入 | 數學字元 | 輸入 |
|---|---|---|---|
| ± | \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 |
數學字型
字體表
\[ \begin{array} \texttt{"normal"}&\texttt{}& ABCDEFGHIJKLMNOPQRSTUVWXYZ\\ \texttt{"blackboard"}&\texttt{\mathbb}&\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \texttt{"boldface"}&\texttt{\mathbf}&\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \texttt{"typewriter"}&\texttt{\mathtt}&\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \texttt{"roman"}&\texttt{\mathrm}&\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \texttt{"sans-serif"}&\texttt{\mathsf}&\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \texttt{"calligraphic"}&\texttt{\mathcal} &\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \texttt{"script"}&\texttt{\mathscr} &\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \texttt{"fraktur"}&\texttt{\mathfrak}&\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\\ \end{array} \]
色彩表
\[ \begin{array} \hline \verb+\color{black}{黑色}+& \color{black}{黑色}\\ \verb+\color{darkgray}{深灰}+ & \color{darkgray}{深灰}\\ \verb+\color{gray}{灰色}+& \color{gray}{灰色}\\ \verb+\color{silver}{銀色}+& \color{silver}{銀色}\\ \verb+\color{lightgray}{淺灰}+&\color{lightgray}{淺灰}\\ \verb+\color{white}{白色}+& \color{white}{白色}\\ \hline \verb+\color{brown}{棕色}+& \color{brown}{棕色}\\ \verb+\color{maroon}{栗色}+& \color{maroon}{栗色}\\ \verb+\color{red}{紅色}+& \color{red}{紅色}\\ \verb+\color{fuchsia}{桃紅}+& \color{fuchsia}{桃紅} \\ \verb+\color{magenta}{品紅}+& \color{magenta}{品紅} \\ \verb+\color{pink}{粉紅}+& \color{pink}{粉紅}\\ \verb+\color{orange}{橙色}+& \color{orange}{橙色}\\ \verb+\color{yellow}{黃色}+& \color{yellow}{黃色}\\ \verb+\color{lime}{青檸}+& \color{lime}{青檸}\\ \verb+\color{olive}{橄欖}+& \color{olive}{橄欖}\\ \verb+\color{green}{綠色}+& \color{green}{綠色}\\ \verb+\color{aqua}{水綠}+& \color{aqua}{水綠}\\ \verb+\color{cyan}{青色}+& \color{cyan}{青色}\\ \verb+\color{teal}{靛青}+& \color{teal}{靛青}\\ \verb+\color{blue}{藍色}+& \color{blue}{藍色}\\ \verb+\color{navy}{海藍}+& \color{navy}{海藍}\\ \verb+\color{violet}{羅蘭}+& \color{purple}{羅蘭}\\ \verb+\color{purple}{紫色}+& \color{purple}{紫色}\\ \hline \end{array}參考 \]
參考：
https://www.cnblogs.com/nowgood/p/Latexstart.html
http://jzqt.github.io/2015/06/30/Markdown%E4%B8%AD%E5%86%99%E6%95%B0%E5%AD%A6%E5%85%AC%E5%BC%8F/