数学公式Lex

1. 声调/变音符号

\acute{a}, \grave{a}, \hat{a}, \tilde{a}, \breve{a}	\(\acute{a}, \grave{a}, \hat{a}, \tilde{a}, \breve{a}\)
\check{a}, \bar{a}, \ddot{a}, \dot{a}	\(\check{a}, \bar{a}, \ddot{a}, \dot{a}\)
\hat{a}, \widehat{a}, \vec{a}, \mathring{a}	\(\hat{a}, \widehat{a}, \vec{a}, \mathring{a}\)

2. 标准函数

\sin a, \cos b, \tan c	\(\sin a, \cos b, \tan c\)
\sec d, \csc e, \cot f	\(\sec d, \csc e, \cot f\)
\arcsin h, \arccos i, \arctan j	\(\arcsin h, \arccos i, \arctan j\)
\sinh k, \cosh l, \tanh m, \coth n	\(\sinh k, \cosh l, \tanh m, \coth n\)
\operatorname{sh}o\,\operatorname{ch}p\,\operatorname{th}q	\(\operatorname{sh}o\,\operatorname{ch}p\,\operatorname{th}q\)
\operatorname{arsinh}r\,\operatorname{arcosh}s\,\operatorname{artanh}t	\(\operatorname{arsinh}r\,\operatorname{arcosh}s\,\operatorname{artanh}t\)
\lim u, \limsup v, \liminf w, \min x, \max y	\(\lim u, \limsup v, \liminf w, \min x, \max y\)
\inf z, \sup a, \exp_a b, \ln c, \lg d, \log e, \log_{10} f, \ker g	\(\inf z, \sup a, \exp_a b, \ln c, \lg d, \log e, \log_{10} f, \ker g\)
\deg h, \gcd i, \Pr j, \det k, \hom l, \arg m, \dim n	\(\deg h, \gcd i, \Pr j, \det k, \hom l, \arg m, \dim n\)

3. 模代数

s_k \equiv 0 \pmod{m}	\(s_k \equiv 0 \pmod{m}\)
a\,\bmod\,b	\(a\,\bmod\,b\)

4. 微分

\nabla, \partial x, \mathrm{d}x, \dot x, \ddot y, \mathrm{d}y/\mathrm{d}x, \frac{\mathrm{d}y}{\mathrm{d}x}, \frac{\partial^2 y}{\partial x_1,\partial x_2}

\(\nabla, \partial x, \mathrm{d}x, \dot x, \ddot y, \mathrm{d}y/\mathrm{d}x, \frac{\mathrm{d}y}{\mathrm{d}x}, \frac{\partial^2 y}{\partial x_1,\partial x_2}\)

5. 集合

\forall, \exists, \emptyset	\(\forall, \exists, \emptyset\)
\in \ni \not \in \notin \subset \subseteq \supset \supseteq	\(\in \ni \not \in \notin \subset \subseteq \supset \supseteq\)
\cap \bigcap \cup \bigcup \biguplus \setminus	\(\cap \bigcap \cup \bigcup \biguplus \setminus\)
\sqsubseteq \sqsupseteq \sqcap \sqcup \bigsqcup	\(\sqsubseteq \sqsupseteq \sqcap \sqcup \bigsqcup\)

6. 运算符

+ \oplus \bigoplus \pm \mp -	\(+ \oplus \bigoplus \pm \mp -\)
\times \otimes \bigotimes \cdot \circ \bullet \bigodot	\(\times \otimes \bigotimes \cdot \circ \bullet \bigodot\)
\star * / \div \frac{1}{2}	\(\star * / \div \frac{1}{2}\)
\land \wedge \bigwedge \bar{q} \to p	\(\land \wedge \bigwedge \bar{q} \to p\)
\lor \vee \bigvee \lnot \neg q \And	\(\lor \vee \bigvee \lnot \neg q \And\)
\sqrt{x} \sqrt[n]{x}	\(\sqrt{x} \sqrt[n]{x}\)
=, \ne, \neq, \equiv, \not\equiv, \leq, \geq	\(=, \ne, \neq, \equiv, \not\equiv, \leq, \geq\)
\doteq, \overset{\underset{\mathrm{def}}{}}{=}, :=	\(\doteq, \overset{\underset{\mathrm{def}}{}}{=}, :=\)
\sim, \simeq, \cong, \approx, \asymp, \propto	\(\sim, \simeq, \cong, \approx, \asymp, \propto\)
\Rightarrow, \Longrightarrow, \rightarrow, \leftarrow, \Leftarrow, \Longleftarrow	\(\Rightarrow, \Longrightarrow, \rightarrow, \leftarrow, \Leftarrow, \Longleftarrow\)
\not \Rightarrow, \not \Longrightarrow, \not \rightarrow, \not \leftarrow, \not \Leftarrow, \not \Longleftarrow	\(\not \Rightarrow, \not \Longrightarrow, \not \rightarrow, \not \leftarrow, \not \Leftarrow, \not \Longleftarrow\)
\sqrt{2}, \sqrt[n]{n}, \sqrt[3]{\frac{x^3+y^3}{2}}	\(\sqrt{2}, \sqrt[n]{n}, \sqrt[3]{\frac{x^3+y^3}{2}}\)

7. 上标、下标

上标	a^2	\(a^2\)
下标	a_2	\(a_2\)
组合	a^{2+2}, a_{i,j}	\(a^{2+2}, a_{i,j}\)
结合上下标	x_2^3, {}_1^2\!X_3^4	\(x_2^3, {}_1^2\!X_3^4\)
导数	x', x^\prime, \dot{x}, \ddot{x}	\(x', x^\prime, \dot{x}, \ddot{x}\)
积分	\int_{-N}^{N} e^x\, \mathrm{d}x	\(\int_{-N}^{N} e^x\, \mathrm{d}x\)
向量	\vec{c}, \overleftarrow{a b}, \overrightarrow{c d}, \widehat{e f g}, \overset{\frown} {AB}	\(\vec{c}, \overleftarrow{a b}, \overrightarrow{c d}, \widehat{e f g}, \overset{\frown} {AB}\)
上下划线	\overline{h i j}, \underline{k l m}, \overbrace{1+2+\cdots+100} \underbrace{1+2+\cdots + 100}	\(\overline{h i j}, \underline{k l m}, \overbrace{1+2+\cdots+100}, \underbrace{1+2+\cdots + 100}\)
上下括号	\(\begin{matrix} \underbrace{a + b + \cdots + z} \\ 26 \end{matrix}\), \(\underset{\mathcal{N}(x)}{\underbrace{(\alpha_0 x^n + \cdots + \alpha_n)}}\)	\(\begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix}\)

8. 求和、求积、积分

求和求积	\sum_{k=1}^N k^2, \prod_{k=1}^N k^2, \coprod_{i=1}^N x_i, \bigcap_1^n p, \bigcup_1^m p	\(\sum_{k=1}^N k^2, \prod_{k=1}^N k^2, \coprod_{i=1}^N x_i, \bigcap_1^n p, \bigcup_1^m p, \underset{i = 1}{\overset{n-1}{\Sigma}}i^2\)
极限	\lim_{n \to +\infty} \frac{1}{n}	\(\lim_{n \to +\infty} \frac{1}{n}\)
积分	\int_{-N}^N e^x dx, \iint_{D}^{W} xy \mathrm{d}x\mathrm{d}y, \oint_{C} x^2\mathrm{d}x + y^2\mathrm{d}y	\(\int_{-N}^N e^x dx, \iint_{D}^{W} xy \mathrm{d}x\mathrm{d}y, \oint_{C} x^2\mathrm{d}x + y^2\mathrm{d}y\)

9. 字母

小写希腊字母	\alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta \iota, \kappa, \lambda, \mu, \nu, \omicron, \xi, \pi \sigma, \tau, \upsilon, \phi, \chi, \psi, \omega \varepsilon, \varpi, \varrho, \varsigma, \vartheta, \varphi	\(\alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta\) \(\iota, \kappa, \lambda, \mu, \nu, \omicron, \xi, \pi\) \(\sigma, \tau, \upsilon, \phi, \chi, \psi, \omega\) \(\varepsilon, \varpi, \varrho, \varsigma, \vartheta, \varphi\)
花体字	\mathcal{A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z}	\(\mathcal{A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z}\)
空心粗体	\mathbb{A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z}	\(\mathbb{A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z}\)

10. 括号

圆括号，小括号	\(\left(\cfrac{a}{b}\right)\)	方括号，中括号	\(\left[\cfrac{a}{b}\right]\)	花括号，大括号	\(\left\{\cfrac{a}{b}\right\}\)	尖括号，角括号	\(\left\langle \cfrac{a}{b} \right\rangle\)
绝对值	\(\left|\cfrac{a}{b}\right|\)	范式	\(\left\|\cfrac{a}{b}\right\|\)	向下取整	\(\left \lfloor \cfrac{a}{b} \right \rfloor\)	向上取整	\(\left \lceil \cfrac{a}{b} \right \rceil\)

11. 分式

\(f_2(x) = \cfrac{\cfrac{x}{\sqrt{1+nx^2}}}{1 + \cfrac{nx^2}{1 + nx^2}}\), \(f_2(x) = \frac{\frac{x}{\sqrt{1+nx^2}}}{1 + \frac{nx^2}{1 + nx^2}}\)