注：本人水平有限，如有谬误欢迎指出一 常用符号
\ = \ b a c k s l a s h × = \ t i m e s ⋅ = \ c d o t ⋯ = \ c d o t s ⋱ = \ d d o t s ⋮ = \ v d o t s ÷ = \ d i v ≡ = \ e q u i v ≈ = \ a p p r o x ≠ = \ n e ± = \ p m ∓ = \ m p ≯ = \ n o t > ≮ = \ n o t < ≥ = \ g e ≤ = \ l e ∗ = \ a s t ∪ = \ c u p ∩ = \ c a p ∈ = \ i n ∉ = \ n o t i n ⊂ = \ s u b s e t ⊃ = \ s u p s e t ⊆ = \ s u b s e t e q ⊇ = \ s u p s e t e q ∁ = \ c o m p l e m e n t ∵ = \ b e c a u s e ∴ = \ t h e r e f o r e △ = \ t r i a n g l e ⊥ = \ b o t ∠ = \ a n g l e → = \ t o ← = \ g e t s ⇔ = \ L e f t r i g h t a r r o w ⇒ = \ R i g h t a r r o w ⇐ = \ L e f t a r r o w ↙ = \ s w a r r o w ↗ = \ n e a r r o w ∞ = \ i n f t y ∀ = \ f o r a l l ¬ = \ n e g ∃ = \ e x i s t s ∼ = \ s i m \begin{equation*}
\begin{aligned}
\backslash&= \mathrm{\backslash backslash}\\
\times&=\mathrm{\backslash times}\\
\cdot&=\mathrm{\backslash cdot}\\
\cdots&=\mathrm{\backslash cdots}\\
\ddots&=\mathrm{\backslash ddots}\\
\vdots&=\mathrm{\backslash vdots}\\
\div&=\mathrm{\backslash div}\\
\equiv&=\mathrm{\backslash equiv}\\
\approx&=\mathrm{\backslash approx}\\
\ne&=\mathrm{\backslash ne}\\
\pm&=\mathrm{\backslash pm}\\
\mp&=\mathrm{\backslash mp}\\
\not>&=\mathrm{\backslash not>}\\
\not<&=\mathrm{\backslash not<}\\
\ge&=\mathrm{\backslash ge}\\
\le&=\mathrm{\backslash le}\\
\ast&=\mathrm{\backslash ast}\\
\cup&=\mathrm{\backslash cup}\\
\cap&=\mathrm{\backslash cap}\\
\in&=\mathrm{\backslash in}\\
\notin&=\mathrm{\backslash notin}\\
\subset&=\mathrm{\backslash subset}\\
\supset&=\mathrm{\backslash supset}\\
\subseteq&=\mathrm{\backslash subseteq}\\
\supseteq&=\mathrm{\backslash supseteq}\\
\complement&=\mathrm{\backslash complement}\\
\because&=\mathrm{\backslash because}\\
\therefore&=\mathrm{\backslash therefore}\\
\triangle&=\mathrm{\backslash triangle}\\
\bot&=\mathrm{\backslash bot}\\
\angle&=\mathrm{\backslash angle}\\
\to&=\mathrm{\backslash to}\\
\gets&=\mathrm{\backslash gets}\\
\Leftrightarrow&=\mathrm{\backslash Leftrightarrow}\\
\Rightarrow&=\mathrm{\backslash Rightarrow}\\
\Leftarrow&=\mathrm{\backslash Leftarrow}\\
\swarrow&=\mathrm{\backslash swarrow}\\
\nearrow&=\mathrm{\backslash nearrow}\\
\infty&=\mathrm{\backslash infty}\\
\forall&=\mathrm{\backslash forall}\\
\neg&=\mathrm{\backslash neg}\\
\exists&=\mathrm{\backslash exists}\\
\sim&=\mathrm{\backslash sim}\\
\end{aligned}
\end{equation*}
\ × ⋅ ⋯ ⋱ ⋮ ÷ ≡ ≈ = ± ∓ > < ≥ ≤ ∗ ∪ ∩ ∈ ∈ / ⊂ ⊃ ⊆ ⊇ ∁ ∵ ∴ △ ⊥ ∠ → ← ⇔ ⇒ ⇐ ↙ ↗ ∞ ∀ ¬ ∃ ∼ = \backslash = \times = \cdot = \cdots = \ddots = \vdots = \div = \equiv = \approx = \ne = \pm = \mp = \not > = \not < = \ge = \le = \ast = \cup = \cap = \in = \notin = \subset = \supset = \subseteq = \supseteq = \complement = \because = \therefore = \triangle = \bot = \angle = \to = \gets = \Leftrightarrow = \Rightarrow = \Leftarrow = \swarrow = \nearrow = \infty = \forall = \neg = \exists = \sim
二 常用希腊字母与字体
α = \ a l p h a β = \ b e t a γ = \ g a m m a Γ = \ G a m m a δ = \ d e l t a Δ = \ D e l t a ϵ = \ e p s i l o n ζ = \ z e t a θ = \ t h e t a Θ = \ T h e t a κ = \ k a p p a ε = \ v a r e p s i l o n η = \ e t a ι = \ i o t a μ = \ m u ν = \ n u ξ = \ x i Ξ = \ X i π = \ p i Π = \ P i ϖ = \ v a r p i ρ = \ r h o ϱ = \ v a r r h o ς = \ v a r s i g m a σ = \ s i g m a Σ = \ S i g m a τ = \ t a u υ = \ u p s i l o n Υ = \ U p s i l o n ϕ = \ p h i Φ = \ P h i φ = \ v a r p h i χ = \ c h i ψ = \ p s i Ψ = \ P s i λ = \ l a m b d a Λ = \ L a m b d a ω = \ o m e g a Ω = \ O m e g a ℧ = \ m h o ∂ = \ p a i t i a l ℵ = \ a l e p h ð = \ e t h ¶ = \ P § = \ S \begin{equation*}
\begin{aligned}
\alpha&=\mathrm{\backslash alpha}\\
\beta&=\mathrm{\backslash beta}\\
\gamma&=\mathrm{\backslash gamma}\\
\Gamma&=\mathrm{\backslash Gamma}\\
\delta&=\mathrm{\backslash delta}\\
\Delta&=\mathrm{\backslash Delta}\\
\epsilon&=\mathrm{\backslash epsilon}\\
\zeta&=\mathrm{\backslash zeta}\\
\theta&=\mathrm{\backslash theta}\\
\Theta&=\mathrm{\backslash Theta}\\
\kappa&=\mathrm{\backslash kappa}\\
\varepsilon&=\mathrm{\backslash varepsilon}\\
\eta&=\mathrm{\backslash eta}\\
\iota&=\mathrm{\backslash iota}\\
\mu&=\mathrm{\backslash mu}\\
\nu&=\mathrm{\backslash nu}\\
\xi&=\mathrm{\backslash xi}\\
\Xi&=\mathrm{\backslash Xi}\\
\pi&=\mathrm{\backslash pi}\\
\Pi&=\mathrm{\backslash Pi}\\
\varpi&=\mathrm{\backslash varpi}\\
\rho&=\mathrm{\backslash rho}\\
\varrho&=\mathrm{\backslash varrho}\\
\varsigma&=\mathrm{\backslash varsigma}\\
\sigma&=\mathrm{\backslash sigma}\\
\Sigma&=\mathrm{\backslash Sigma}\\
\tau&=\mathrm{\backslash tau}\\
\upsilon&=\mathrm{\backslash upsilon}\\
\Upsilon&=\mathrm{\backslash Upsilon}\\
\phi&=\mathrm{\backslash phi}\\
\Phi&=\mathrm{\backslash Phi}\\
\varphi&=\mathrm{\backslash varphi}\\
\chi&=\mathrm{\backslash chi}\\
\psi&=\mathrm{\backslash psi}\\
\Psi&=\mathrm{\backslash Psi}\\
\lambda&=\mathrm{\backslash lambda}\\
\Lambda&=\mathrm{\backslash Lambda}\\
\omega&=\mathrm{\backslash omega}\\
\Omega&=\mathrm{\backslash Omega}\\
\mho&=\mathrm{\backslash mho}\\
\partial&=\mathrm{\backslash paitial}\\
\aleph&=\mathrm{\backslash aleph}\\
\eth&=\mathrm{\backslash eth}\\
\P&=\mathrm{\backslash P}\\
\S&=\mathrm{\backslash S}\\
\end{aligned}
\end{equation*}
α β γ Γ δ Δ ϵ ζ θ Θ κ ε η ι μ ν ξ Ξ π Π ϖ ρ ϱ ς σ Σ τ υ Υ ϕ Φ φ χ ψ Ψ λ Λ ω Ω ℧ ∂ ℵ ð ¶ § = \alpha = \beta = \gamma = \Gamma = \delta = \Delta = \epsilon = \zeta = \theta = \Theta = \kappa = \varepsilon = \eta = \iota = \mu = \nu = \xi = \Xi = \pi = \Pi = \varpi = \rho = \varrho = \varsigma = \sigma = \Sigma = \tau = \upsilon = \Upsilon = \phi = \Phi = \varphi = \chi = \psi = \Psi = \lambda = \Lambda = \omega = \Omega = \mho = \paitial = \aleph = \eth = \P = \S
2 字体
原版字体 : A a B b C c 原版字体:AaBbCc
原版字体 : A a B b C c
A a B b C c : \ m a t h r m { A a B b C c } ( 罗马体 ) A a B b C c : \ m a t h c a l { A a B b C c } ( 手写体 ) A a B b C c : \ m a t h f r a k { A a B b C c } ( 德文尖角体 ) A a B b C c : \ m a t h r m { A a B b C c } ( 黑板报粗体 ) A a B b C c : \ m a t h s c r { A a B b C c } ( 手写体 ) A a B b C c : \ m a t h c a l { A a B b C c } ( 花体 ) \begin{equation*}
\begin{aligned}
\mathrm{AaBbCc}&:\mathrm{\backslash mathrm\{AaBbCc\}}(罗马体)\\
\mathcal{AaBbCc}&:\mathrm{\backslash mathcal\{AaBbCc\}}(手写体)\\
\mathfrak{AaBbCc}&:\mathrm{\backslash mathfrak\{AaBbCc\}}(德文尖角体)\\
\mathbb{AaBbCc}&:\mathrm{\backslash mathrm\{AaBbCc\}}(黑板报粗体)\\
\mathscr{AaBbCc}&:\mathrm{\backslash mathscr\{AaBbCc\}}(手写体)\\
\mathcal{AaBbCc}&:\mathrm{\backslash mathcal\{AaBbCc\}}(花体)\\
\end{aligned}
\end{equation*}
AaBbCc A a B b C c AaBbCc A a B b C c A a B b C c A a B b C c : \mathrm { AaBbCc } ( 罗马体 ) : \mathcal { AaBbCc } ( 手写体 ) : \mathfrak { AaBbCc } ( 德文尖角体 ) : \mathrm { AaBbCc } ( 黑板报粗体 ) : \mathscr { AaBbCc } ( 手写体 ) : \mathcal { AaBbCc } ( 花体 )
对于一些特殊字体的特殊字符，有快捷方式，如：
R = \ R ℜ = \ R e Z = \ Z N = \ N k = \ B b b k \begin{equation*}
\begin{aligned}
\R&=\mathrm{\backslash R}\\
\Re&=\mathrm{\backslash Re}\\
\Z&=\mathrm{\backslash Z}\\
\N&=\mathrm{\backslash N}\\
\Bbbk&=\mathrm{\backslash Bbbk}\\
\end{aligned}
\end{equation*}
R ℜ Z N k = \R = \Re = \Z = \N = \Bbbk
三 函数 log , sin , sup \log,\sin,\sup log , sin , sup
\cos (2 x) = 2 \cos^2 (x)-1 = 1 -2 \sin^2 (x) = \cos^2 {x} - \sin^2 {x}
之输出为：
cos ( 2 x ) = 2 cos 2 ( x ) − 1 = 1 − 2 sin 2 ( x ) = cos 2 x − sin 2 x \cos(2x) = 2\cos^2(x)-1 = 1-2\sin^2(x) = \cos^2{x} - \sin^2{x}
cos ( 2 x ) = 2 cos 2 ( x ) − 1 = 1 − 2 sin 2 ( x ) = cos 2 x − sin 2 x
对于一些特殊的函数，有特殊的输出方法：
12 \equiv 2 \pmod 5 ,12 \bmod 5 = 2
之输出为：
12 ≡ 2 ( m o d 5 ) , 12 m o d 5 = 2 12\equiv 2 \pmod 5,12\bmod 5 = 2
12 ≡ 2 ( mod 5 ) , 12 mod 5 = 2
可认为\pmod自带括号而\bmod没有
\mathrm{Im}(a+bi)=3
之输出为：
I m ( a + b i ) = 3 \mathrm{Im}(a+bi)=3
Im ( a + bi ) = 3
2 如要上标，我们使用符号"^",如要添加下标，则使用符号"_"，特别的，如果上、下标的内容多余一个字符，必须用{}将其扩起来，如代码：
f_1 (x) = kx + b,\sum_{i = 1 }^{\infty}\cfrac{1 }{i^2 } = \cfrac{\pi^2 }{6 }
的输出为
f 1 ( x ) = k x + b , ∑ i = 1 ∞ 1 i 2 = π 2 6 f_1(x)=kx+b,\sum_{i=1}^{\infty}\cfrac{1}{i^2}=\cfrac{\pi^2}{6}
f 1 ( x ) = k x + b , i = 1 ∑ ∞ i 2 1 = 6 π 2
大型运算符的输出都是如此，使用大型运算符名^{上标}_{下标}的形式输出，顺序可反。这里给出三组输出样例：
\sum_{cyc}x^2 y = x^2 y + y^2 z + z^2 x
输出：
∑ c y c x 2 y = x 2 y + y 2 z + z 2 x \sum_{cyc}x^2y=x^2y+y^2z+z^2x
cyc ∑ x 2 y = x 2 y + y 2 z + z 2 x
G_{n} = \sqrt[n]{\prod_{i = 1 }^{n} x_{i}}
输出：
G n = ∏ i = 1 n x i n G_{n}=\sqrt[n]{\prod_{i=1}^{n}x_{i}}
G n = n i = 1 ∏ n x i
\bigcup_{a}^{b},\bigcap_{a}^{b},\bigvee_{a}^{b} ,\bigwedge_{a}^{b}
输出：
⋃ a b , ⋂ a b , ⋁ a b , ⋀ a b \bigcup_{a}^{b},\bigcap_{a}^{b},\bigvee_{a}^{b} ,\bigwedge_{a}^{b}
a ⋃ b , a ⋂ b , a ⋁ b , a ⋀ b
lim , max \lim,\max lim , max
\lim_{x \to \infty} \cfrac{1 }{x} = 0
输出：
lim x → ∞ 1 x = 0 \lim_{x\to\infty}\cfrac{1}{x}=0
x → ∞ lim x 1 = 0
3 在括号前添加\left,\right创建可以自动匹配高度的括号，特别的，如要输出"{}",需要加反斜杠取消转义，如代码：
\cfrac{1 }{3 }\left\{\cfrac{1 }{(0.2 )^2 }\div\left[\cfrac{5 }{2 }-\left (-1 +\cfrac{9 }{4 }\right)\right]\right\}+1
的输出为
1 3 { 1 ( 0.2 ) 2 ÷ [ 5 2 − ( − 1 + 9 4 ) ] } + 1 \cfrac{1}{3}\left\{\cfrac{1}{(0.2)^2}\div\left[\cfrac{5}{2}-\left(-1+\cfrac{9}{4}\right)\right]\right\}+1
3 1 { ( 0.2 ) 2 1 ÷ [ 2 5 − ( − 1 + 4 9 ) ] } + 1
下面是一些特殊的括号：
括号名
代码
输出
尖括号
\langle x \rangle
⟨ x ⟩ \langle x\rangle ⟨ x ⟩
向上取整
\lceil x \rceil
⌈ x ⌉ \lceil x\rceil ⌈ x ⌉
向下取整
\lfloor x \rfloor
⌊ x ⌋ \lfloor x\rfloor ⌊ x ⌋
4 如果要输出分式，可以使用函数\frac{分子表达式}{分母表达式}。需要注意的时，如果\frac{分子表达式}{分母表达式}在行内样式被使用(即被一个美元符号括起来)，会变得小小的，像1 2 \frac{1}{2} 2 1 1 2 \cfrac{1}{2} 2 1 \frac{分子表达式}{分母表达式}变为\cfrac{分子表达式}{分母表达式}或在整个表达式前添加\displaystyle转换样式
\cfrac xy
的输出为：
x y \cfrac xy
y x
相反的，如果分式很复杂，可使用\quad{分子 \over 分母}，如：
\quad{x^2 + 2 x + 1 \over x^2 - 2 x + 1 }
的输出为：
x 2 + 2 x + 1 x 2 − 2 x + 1 \quad{x^2+2x+1 \over x^2-2x+1}
x 2 − 2 x + 1 x 2 + 2 x + 1
5 如果要输出根式，需使用函数\sqrt[指数]{被开方数}，其中若不写[指数]，则默认输出被开方数 \sqrt{被开方数} 被开方数
\sqrt{3 - \sqrt{5 }} = \cfrac{\sqrt{10 } - \sqrt{2 }}{2 }，\sqrt[4 ]{y} = y^{0.25 }
的输出为：
3 − 5 = 10 − 2 2 ， y 4 = y 0.25 \sqrt{3-\sqrt{5}}=\cfrac{\sqrt{10}-\sqrt{2}}{2}，\sqrt[4]{y}=y^{0.25}
3 − 5 = 2 10 − 2 ， 4 y = y 0.25
6 积分的输出如大型运算符一致，使用int_{积分下限}^{积分上限}被积表达式的形式输出，如：
\int_{a}^{b} f (x)\mathrm{d}x = F (b) - F (a)
输出：
∫ a b f ( x ) d x = F ( b ) − F ( a ) \int_{a}^{b}f(x)\mathrm{d}x=F(b)-F(a)
∫ a b f ( x ) d x = F ( b ) − F ( a )
多重积分的符号的输出就比较有意思，几重积分就加几个"i"，如\iint输出∬ \displaystyle\iint ∬ \iiint输出∭ \displaystyle \iiint ∭ \int前加上一个"o",如\oint输出∮ \displaystyle \oint ∮ \oiint输出∯ \displaystyle\oiint ∬ ∫ \int ∫ ∫ \displaystyle \int ∫ \displaystyle
7 矩阵的输出较为复杂，下面是一个三行三列的矩阵的模板：
A=\begin{bmatrix}
a & b & c\\
d & e & f\\
g & h & i
\end{bmatrix}
输出：
A = [ a b c d e f g h i ] A=\begin{bmatrix}
a & b & c\\
d & e & f\\
g & h & i
\end{bmatrix}
A = a d g b e h c f i
在上面的例子中，我们使用了\begin{矩阵样式}...\end{矩阵样式}的格式，矩阵的内容填在\begin{}和\end{}之间即可。矩阵的行与行之间用\\分隔(在一些环境内，\\表示换行，这将在之后被提到)，列与列之间使用&分隔。
A = \begin{vmatrix}
a & b & c\\
d & e & f\\
g & h & i
\end{vmatrix},
B = \begin{pmatrix}
a & b & c\\
d & e & f\\
g & h & i
\end{pmatrix},
C = \begin{Vmatrix}
a & b & c\\
d & e & f\\
g & h & i
\end{Vmatrix},
D = \begin{matrix}
a & b & c\\
d & e & f\\
g & h & i
\end{matrix}
输出：
A = ∣ a b c d e f g h i ∣ , B = ( a b c d e f g h i ) , C = ∥ a b c d e f g h i ∥ , D = a b c d e f g h i A=\begin{vmatrix}
a & b & c\\
d & e & f\\
g & h & i
\end{vmatrix},
B=\begin{pmatrix}
a & b & c\\
d & e & f\\
g & h & i
\end{pmatrix},
C = \begin{Vmatrix}
a & b & c\\
d & e & f\\
g & h & i
\end{Vmatrix},
D = \begin{matrix}
a & b & c\\
d & e & f\\
g & h & i
\end{matrix}
A = a d g b e h c f i , B = a d g b e h c f i , C = a d g b e h c f i , D = a d g b e h c f i
矩阵中，如果需要省略元素，可以使用\cdots⋯ \cdots ⋯ \ddots⋱ \ddots ⋱ \vdots⋮ \vdots ⋮
E = \begin{bmatrix}
a & \cdots & c\\
\vdots & \ddots & \vdots\\
g & \cdots & i
\end{bmatrix}
输出：
E = [ a ⋯ c ⋮ ⋱ ⋮ g ⋯ i ] E = \begin{bmatrix}
a & \cdots & c\\
\vdots & \ddots & \vdots\\
g & \cdots & i
\end{bmatrix}
E = a ⋮ g ⋯ ⋱ ⋯ c ⋮ i
如果需要在矩阵中插入横线、竖线，可以考虑如下例子：
F = \begin{bmatrix}
\begin{array}{c | c | c}
a & b & c\\
\hline
d & e & f\\
\hline
g & h & i
\end{array}
\end{bmatrix}
输出：
F = [ a b c d e f g h i ] F = \begin{bmatrix}
\begin{array}{c | c | c}
a & b & c\\
\hline
d & e & f\\
\hline
g & h & i
\end{array}
\end{bmatrix}
F = a d g b e h c f i
在上面的例子中，第二行的右半部分表示的是这个矩阵的对齐方式，c表示居中对齐，r表示右对齐，l表示左对齐，|表示在两列之间添加分隔”|“。同时\hline表示在两行之间插入分隔”——“
未完待续
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