机器学习数学公式符号大全（LaTex版）

公众号：尤而小屋
作者：Peter
编辑：Peter

大家好，我是Peter~

LaTeX是一种标记语言，主要用于创建高质量的学术文档，特别是数学、物理和计算机科学领域的文档。它基于TeX排版系统，由美国数学家Donald E. Knuth开发。在LaTeX中，你可以轻松地编写复杂的数学公式，并控制文档的布局和样式。

本文整理了丰富的数学公式编写过程中涉及到的的各种符号，建议收藏直接使用~

两种方式

在LaTeX中编辑数学公式的两种表现形式：

• 行内：使用一对$公式部分$即可，比如勾股定理的公式：$a^2 +b^2=c^2$
• 行外：使用两对$$公式部分$$，勾股定理$$a^2 +b^2=c^2$$会单独占据一行

常用希腊字母 Greek alphabet

希腊字母是希腊语所使用的字母，也广泛用于数学、物理、生物、化学、天文等学科。它是世界上最早拥有表示元音音位的字母的书写系统

序号小写LaTeX读音序号大写LaTeX读音

1	α	\alpha	/ˈælfə/	22	σ	\sigma	/ˈsɪɡmə/
2	β	\beta	/ˈbiːtə/, US: /ˈbeɪtə/	23	ς	\varsigma	/ˈsɪɡmə/
3	γ	\gamma	/ˈɡæmə/	24	τ	\tau	/taʊ, tɔː/
4	δ	\delta	/ˈdɛltə/	25	υ	\upsilon	/ˈʌpsɪlɒn/
5	ϵ	\epsilon	/ˈɛpsɪlɒn/	26	ϕ	\phi	/faɪ/
6	ε	\varepsilon	/ˈɛpsɪlɒn/	27	φ	\varphi	/faɪ/
7	ζ	\zeta	/ˈzeɪtə/	28	χ	\chi	/kaɪ/
8	η	\eta	/ˈeɪtə/	29	ψ	\psi	/psaɪ/
9	θ	\theta	/ˈθiːtə/	30	ω	\omega	/oʊˈmeɪɡə/
10	ϑ	\vartheta	/ˈθiːtə/	31	Γ	\Gamma	/ˈɡæmə/
11	ι	\iota	/aɪˈoʊtə/	32	Δ	\Delta	/ˈdɛltə/
12	κ	\kappa	/ˈkæpə/	33	Θ	\Theta	/ˈθiːtə/
13	λ	\lambda	/ˈlæmdə/	34	Λ	\Lambda	/ˈlæmdə/
14	μ	\mu	/mjuː/	35	Ξ	\Xi	/zaɪ, ksaɪ/
15	ν	\nu	/njuː/	36	Π	\Pi	/paɪ/
16	ξ	\xi	/zaɪ, ksaɪ/	37	Σ	\Sigma	/ˈsɪɡmə/
17	o	o	/ˈɒmɪkrɒn/	38	Υ	\Upsilon	/ˈʌpsɪlɒn/
18	π	\pi	/paɪ/	39	Φ	\Phi	/faɪ/
19	ϖ	\varpi	/paɪ/	40	Ψ	\Psi	/psaɪ/
20	ρ	\rho	/roʊ/	41	Ω	\Omega	/oʊˈmeɪɡə/
21	ϱ	\varrho	/roʊ/

常用希伯来字母Hebrew alphabet

序号图标LaTeX英文

1	ℵ	\aleph	aleph
2	ℶ	\beth	beth
3	ℷ	\gimel	gimel
4	ℸ	\daleth	daleth

在Typora中使用markdown编写LaTex符号的效果：

$\pi 、\zeta 、\pi 、\varrho 、\aleph$

源码为：

$\pi、\zeta、\pi、\varrho、\aleph$   # 一对$$

二元运算符 Binary operations

常用的二元运算符

序号图标LaTeX序号图标LaTeX

1	+	+	20	∙	\bullet
2	−	-	21	⊕	\oplus
3	×	\times	22	⊖	\ominus
4	$÷$	\div (在physics扩展开启状态下为)	23	⊙	\odot
5	±	\pm	24	⊘	\oslash
6	∓	\mp	25	⊗	\otimes
7	◃	\triangleleft	26	◯	\bigcirc
8	▹	\triangleright	27	⋄	\diamond
9	⋅	\cdot	28	⊎	\uplus
10	∖	\setminus	29	△	\bigtriangleup
11	⋆	\star	30	▽	\bigtriangledown
12	∗	\ast	31	⊲	\lhd
13	∪	\cup	32	⊳	\rhd
14	∩	\cap	33	⊴	\unlhd
15	⊔	\sqcup	34	⊵	\unrhd
16	⊓	\sqcap	35	⨿	\amalg
17	∨	\vee	36	≀	\wr
18	∧	\wedge	37	†	\dagger
19	∘	\circ	38	‡	\ddagger

二元关系符 Binary relations

常见的二元关系符：

序号图标LaTeX序号图标LaTeX

1	=	=	49	⪈	\gneq
2	≠	\ne	50	≧	\geqq
3	≠	\neq	51	≱	\ngeq
4	≡	\equiv	52	≱	\ngeqq
5	≢	\not\equiv	53	≩	\gneqq
6	≐	\doteq	54	≩	\gvertneqq
7	≑	\doteqdot	55	≶	\lessgtr
8	=dff\stackrel{\mathrm{dff}}{=}=dff	\stackrel{\mathrm{dff}}{=}	56	⋚	\lesseqgtr
9	:=	:=	57	⪋	\lesseqqgtr
10	∼	\sim	58	≷	\gtrless
11	≁	\nsim	59	⋛	\gtreqless
12	∽	\backsim	60	⪌	\gtreqqless
13	∼	\thicksim	61	⩽	\leqslant
14	≃	\simeq	62	⪇	\nleqslant
15	⋍	\backsimeq	63	⪕	\eqslantless
16	≂	\eqsim	64	⩾	\geqslant
17	≅	\cong	65	⪈	\ngeqslant
18	≇	\ncong	66	⪖	\eqslantgtr
19	≈	\approx	67	≲	\lesssim
20	≈	\thickapprox	68	⋦	\lnsim
21	≊	\approxeq	69	⪅	\lessapprox
22	≍	\asymp	70	⪉	\lnapprox
23	∝	\propto	71	≳	\gtrsim
24	∝	\varpropto	72	⋧	\gnsim
25	<< /td>	<	73	⪆	\gtrapprox
26	≮	\nless	74	⪊	\gnapprox
27	≪	\ll	75	≺	\prec
28	≪̸	\not\ll	76	⊀	\nprec
29	⋘	\lll	77	⪯	\preceq
30	⋘̸	\not\lll	78	⋠	\npreceq
31	⋖	\lessdot	79	⪵	\precneqq
32	80			≻	\succ
33	≯	\ngtr	81	⊁	\nsucc
34	≫	\gg	82	⪰	\succeq
35	≫̸	\not\gg	83	⋡	\nsucceq
36	⋙	\ggg	84	⪶	\succneqq
37	⋙̸	\not\ggg	85	≼	\preccurlyeq
38	⋗	\gtrdot	86	⋞	\curlyeqprec
39	≤	\le	87	≽	\succcurlyeq
40	≤	\leq	88	⋟	\curlyeqsucc
41	⪇	\lneq	89	≾	\precsim
42	≦	\leqq	90	⋨	\precnsim
43	≰	\nleq	91	⪷	\precapprox
44	≰	\nleqq	92	⪹	\precnapprox
45	≨	\lneqq	93	≿	\succsim
46	≨	\lvertneqq	94	⋩	\succnsim
47	≥	\ge	95	⪸	\succapprox
48	≥	\geq	96	⪺	\succnapprox

几何关系符号Geometric symbols

常见的几何关系符号：

序号图标LaTeX序号图标LaTeX

1	∥	\parallel	14	◊	\lozenge
2	∦	\nparallel	15	⧫	\blacklozenge
3	∥	\shortparallel	16	★	\bigstar
4	∦	\nshortparallel	17	◯	\bigcirc
5	⊥	\perp	18	△	\triangle
6	∠	\angle	19	△	\bigtriangleup
7	∢	\sphericalangle	20	▽	\bigtriangledown
8	∡	\measuredangle	21	△	\vartriangle
9	45∘	45^\circ	22	▽	\triangledown
10	◻	\Box	23	▴	\blacktriangle
11	◼	\blacksquare	24	▾	\blacktriangledown
12	⋄	\diamond	25	◂	\blacktriangleleft
13	◊	\Diamond \lozenge	26	▸	\blacktriangleright

逻辑符号 Logic symbols

常用的逻辑关系运算符：

序号图标LaTeX序号图标LaTeX

1	∀	\forall	20	¬	\neg
2	∃	\exists	21	R̸	\not\operatorname{R}
3	∄	\nexists	22	⊥	\bot
4	∴	\therefore	23	⊤	\top
5	∵	\because	24	⊢	\vdash
6	&	\And	25	⊣	\dashv
7	∨	\lor	26	⊨	\vDash
8	∨	\vee	27	⊩	\Vdash
9	⋎	\curlyvee	28	⊨	\models
10	⋁	\bigvee	29	⊪	\Vvdash
11	∧	\land	30	⊬	\nvdash
12	∧	\wedge	31	⊮	\nVdash
13	⋏	\curlywedge	32	⊭	\nvDash
14	⋀	\bigwedge	33	⊯	\nVDash
15	q¯	\bar{q}	34	⌜	\ulcorner
16	abc¯	\bar{abc}	35	⌝	\urcorner
17	q―	\overline{q}	36	⌞	\llcorner
18	abc―	\overline{abc}	37	⌟	\lrcorner
19	¬	\lnot

集合Sets

集合相关的符号：空集、并集、子集、包含与被包含、存在于等各种符号

序号图标LaTeX序号图标LaTeX

1	{}	{}	23	⊏	\sqsubset
2	∅	\emptyset	24	⊃	\supset
3	∅	\varnothing	25	⋑	\Supset
4	∈	\in	26	⊐	\sqsupset
5	∉	\notin	27	⊆	\subseteq
6	∋	\ni	28	⊈	\nsubseteq
7	∩	\cap	29	⊊	\subsetneq
8	⋒	\Cap	30	⊊	\varsubsetneq
9	⊓	\sqcap	31	⊑	\sqsubseteq
10	⋂	\bigcap	32	⊇	\supseteq
11	∪	\cup	33	⊉	\nsupseteq
12	⋓	\Cup	34	⊋	\supsetneq
13	⊔	\sqcup	35	⊋	\varsupsetneq
14	⋃	\bigcup	36	⊒	\sqsupseteq
15	⨆	\bigsqcup	37	⫅	\subseteqq
16	⊎	\uplus	38	⊈	\nsubseteqq
17	⨄	\biguplus	39	⫋	\subsetneqq
18	∖	\setminus	40	⫋	\varsubsetneqq
19	∖	\smallsetminus	41	⫆	\supseteqq
20	×	\times	42	⊉	\nsupseteqq
21	⊂	\subset	43	⫌	\supsetneqq
22	⋐	\Subset	44	⫌	\varsupsetneqq

箭头Arrows

和箭头相关的各种符号：

序号图标LaTeX序号图标LaTeX

1	⇛	\Rrightarrow	36	⟼	\longmapsto
2	⇚	\Lleftarrow	37	⇀	\rightharpoonup
3	⇒	\Rightarrow	38	⇁	\rightharpoondown
4	⇏	\nRightarrow	39	↼	\leftharpoonup
5	⟹	\Longrightarrow	40	↽	\leftharpoondown
6	⟹	\implies	41	↿	\upharpoonleft
7	⇐	\Leftarrow	42	↾	\upharpoonright
8	⇍	\nLeftarrow	43	⇃	\downharpoonleft
9	⟸	\Longleftarrow	44	⇂	\downharpoonright
10	⇔	\Leftrightarrow	45	⇌	\rightleftharpoons
11	⇎	\nLeftrightarrow	46	⇋	\leftrightharpoons
12	⟺	\Longleftrightarrow	47	↶	\curvearrowleft
13	⟺	\iff	48	↺	\circlearrowleft
14	⇑	\Uparrow	49	↰	\Lsh
15	⇓	\Downarrow	50	⇈	\upuparrows
16	⇕	\Updownarrow	51	⇉	\rightrightarrows
17	→	\rightarrow	52	⇄	\rightleftarrows
18	→	\to	53	↣	\rightarrowtail
19	↛	\nrightarrow	54	↬	\looparrowright
20	⟶	\longrightarrow	55	↷	\curvearrowright
21	←	\leftarrow	56	↻	\circlearrowright
22	←	\gets	57	↱	\Rsh
23	↚	\nleftarrow	58	⇊	\downdownarrows
24	⟵	\longleftarrow	59	⇇	\leftleftarrows
25	↔	\leftrightarrow	60	⇆	\leftrightarrows
26	↮	\nleftrightarrow	61	↢	\leftarrowtail
27	⟷	\longleftrightarrow	62	↫	\looparrowleft
28	↑	\uparrow	63	↪	\hookrightarrow
29	↓	\downarrow	64	↩	\hookleftarrow
30	↕	\updownarrow	65	⊸	\multimap
31	↗	\nearrow	66	↭	\leftrightsquigarrow
32	↙	\swarrow	67	⇝	\rightsquigarrow
33	↖	\nwarrow	68	↠	\twoheadrightarrow
34	↘	\searrow	69	↞	\twoheadleftarrow
35	↦	\mapsto

特殊关系符号

其他少见的特殊符号：

序号图标LaTeX序号图标LaTeX

1	∞	\infty	33	♭	\flat
2	ℵ	\aleph	34	♮	\natural
3	∁	\complement	35	♯	\sharp
4	∍	\backepsilon	36	╱	\diagup
5	ð	\eth	37	╲	\diagdown
6	Ⅎ	\Finv	38	⋅	\centerdot
7	ℏ	\hbar	39	⋉	\ltimes
8	Im	\Im	40	⋊	\rtimes
9	ı	\imath	41	⋋	\leftthreetimes
10	ȷ	\jmath	42	⋌	\rightthreetimes
11	𝕜k	\Bbbk	43	≖	\eqcirc
12	ℓ	\ell	44	≗	\circeq
13	℧	\mho	45	≜	\triangleq
14	℘	\wp	46	≏	\bumpeq
15	Re	\Re	47	≎	\Bumpeq
16	Ⓢ	\circledS	48	≑	\doteqdot
17	⨿	\amalg	49	≓	\risingdotseq
18	%	%	50	≒	\fallingdotseq
19	†	\dagger	51	⊺	\intercal
20	‡	\ddagger	52	⊼	\barwedge
21	…	\ldots	53	⊻	\veebar
22	⋯	\cdots	54	⩞	\doublebarwedge
23	$⌣$	\smile	55	≬	\between
24	$⌢$	\frown	56	⋔	\pitchfork
25	≀	\wr	57	⊲	\vartriangleleft
26	◃	\triangleleft	58	⋪	\ntriangleleft
27	▹	\triangleright	59	⊳	\vartriangleright
28	♢	\diamondsuit	60	⋫	\ntriangleright
29	♡	\heartsuit	61	⊴	\trianglelefteq
30	♣	\clubsuit	62	⋬	\ntrianglelefteq
31	♠	\spadesuit	63	⊵	\trianglerighteq
32	⅁	\Game	64	⋭	\ntrianglerighteq

下面介绍和数学运算相关的符号：

分数Fractions

编号类型样式LaTeX

1	分数 Fractions	24x=0.5xor24x=0.5x\frac{2}{4}x=0.5x or {2 \over 4}x=0.5x42​x=0.5xor42​x=0.5x	\frac{2}{4}x=0.5x or {2 \over 4}x=0.5x
2	小型分数 Small fractions (force \textstyle)	24x=0.5x\tfrac{2}{4}x = 0.5x42​x=0.5x	\tfrac{2}{4}x = 0.5x
3	大型分数（不嵌套） Large (normal) fractions (force \displaystyle)	24=0.52c+2d+24=a\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a42​=0.5c+d+42​2​2​=a	\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a
4	大型分数（嵌套） Large (nested) fractions	2c+2d+24=a\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = ac+d+42​2​2​=a	\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a
5	约分线的使用 Cancellations in fractions	x1+yy=x2\cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2}1+y​y​​x​=2x​	\cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2}

标准数值函数 Standard numerical functions

编号样式LaTeX

1	exp⁡ab=ab,exp⁡b=eb,10m\exp_a b = a^b, \exp b = e^b, 10^mexpa​b=ab,expb=eb,10m	\exp_a b = a^b, \exp b = e^b, 10^m
2	ln⁡c,lg⁡d=log⁡e,log⁡10f\ln c, \lg d = \log e, \log_{10} flnc,lgd=loge,log10​f	\ln c, \lg d = \log e, \log_{10} f
3	$\sin a,\cos b,\tan c,\cot d,\sec e,\csc f$	\sin a, \cos b, \tan c, \cot d, \sec e, \csc f
4	$\arcsin a,\arccos b,\arctan c$	\arcsin a, \arccos b, \arctan c
5	$\mathrm{arccot}d,\mathrm{arcsec}e,\mathrm{arccsc}f$	\operatorname{arccot} d, \operatorname{arcsec} e, \operatorname{arccsc} f
6	$\sinh a,\cosh b,\tanh c,\coth d$	\sinh a, \cosh b, \tanh c, \coth d
7	$\mathrm{sh}k,\mathrm{ch}l,\mathrm{th}m,\coth n$	\operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n
8	$\mathrm{argsh}o,\mathrm{argch}p,\mathrm{argth}q$	\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q
9	$\mathrm{sgn}r,\left|s\right|$	\operatorname{sgn}r, \left\vert s \right\vert
10	$\min (x,y),\max (x,y)$	\min(x,y), \max(x,y)

根式符号 Radicals

编号样式LaTeX

1	4\sqrt 44​	\sqrt 4
2	$\surd$	\surd
3	π\sqrt{\pi}π​	\sqrt{\pi}
4	πn\sqrt[n]{\pi}nπ​	\sqrt[n]{\pi}
5	x3+y323\sqrt[3]{\frac{x^3+y^3}{2}}32x3+y3​​	\sqrt[3]{\frac{x^3+y^3}{2}}

微分和导数 Differentials and derivatives

编号样式LaTeX

1	dt,dt,∂t,∇ψ	dt, \mathrm{d}t, \partial t, \nabla\psi
2	dy/dx,dy/dx,dydx,dydx,∂2∂x1∂x2ydy/dx, \mathrm{d}y/\mathrm{d}x, \frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x}, \frac{\partial^2}{\partial x_1\partial x_2}ydy/dx,dy/dx,dxdy​,dxdy​,∂x1​∂x2​∂2​y	dy/dx, \mathrm{d}y/\mathrm{d}x, \frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x}, \frac{\partial^2}{\partial x_1\partial x_2}y
3	′,‵,f′,f′,f′′,f(3),y˙,y¨\prime, \backprime, f^\prime, f', f'', f^{(3)}, \dot y, \ddot y′,‵,f′,f′,f′′,f(3),y˙​,y¨​	\prime, \backprime, f^\prime, f', f'', f^{(3)}, \dot y, \ddot y

同余与模算术 Modular arithmetic

编号样式LaTeX

1	sk≡0(modm)s_k \equiv 0 \pmod{m}sk​≡0(modm)	s_k \equiv 0 \pmod{m}
2	$a\mathrm{mod}b$	a \bmod b
3	$\gcd (m,n),\mathrm{lcm}(m,n)$	\gcd(m, n), \operatorname{lcm}(m, n)
4	$\mid ,\nmid ,\mid ,$	\mid, \nmid, \shortmid, \nshortmid

极限 Limits

编号样式LaTeX

1	lim⁡n→∞xn\lim_{n \to \infty}x_nlimn→∞​xn​	\lim_{n \to \infty}x_n
2	lim⁡n→∞xn\textstyle \lim_{n \to \infty}x_nlimn→∞​xn​	\textstyle \lim_{n \to \infty}x_n

界限与投影 Bounds and Projections

编号样式LaTeX

1	$\min x,\max y,\inf s,\sup t$	\min x, \max y, \inf s, \sup t
2	$\lim u,\mathrm{liminf}v,\mathrm{limsup}w$	\lim u, \liminf v, \limsup w
3	$\dim p,\mathrm{deg}q,\det m,\ker \varphi$	\dim p, \deg q, \det m, \ker\phi
4	$\mathrm{Pr}j,\mathrm{hom}l,\Vert z\Vert ,\arg z$	\Pr j, \hom l, \lVert z \rVert, \arg z

积分 Integral

编号样式LaTeX

1	∫13e3/xx2 dx\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx1∫3​x2e3/x​dx	\int\limits_{1}^{3}\frac{e^3/x}{x^2}, dx
2	∫13e3/xx2 dx\int_{1}^{3}\frac{e^3/x}{x^2}\, dx∫13​x2e3/x​dx	\int_{1}^{3}\frac{e^3/x}{x^2}, dx
3	∫−NNexdx\textstyle \int\limits_{-N}^{N} e^x dx−N∫N​exdx	\textstyle \int\limits_{-N}^{N} e^x dx
4	∫−NNexdx\textstyle \int_{-N}^{N} e^x dx∫−NN​exdx	\textstyle \int_{-N}^{N} e^x dx
5	∬Ddx dy\iint\limits_D dx\,dyD∬​dxdy	\iint\limits_D dx,dy
6	∭Edx dy dz\iiint\limits_E dx\,dy\,dzE∭​dxdydz	\iiint\limits_E dx,dy,dz
7	\iiiint\limits_F dx\,dy\,dz\,dt	\iiiint\limits_F dx,dy,dz,dt
8	∫(x,y)∈Cx3 dx+4y2 dy\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy∫(x,y)∈C​x3dx+4y2dy	\int_{(x,y)\in C} x^3, dx + 4y^2, dy
9	∮(x,y)∈Cx3 dx+4y2 dy\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy∮(x,y)∈C​x3dx+4y2dy	\oint_{(x,y)\in C} x^3, dx + 4y^2, dy
10	\unicode8751\unicodex222FC\unicode{8751} \unicode{x222F}_C\unicode8751\unicodex222FC​	\unicode{8751} \unicode{x222F}_C
11	\unicode8752\unicodex2230C\unicode{8752} \unicode{x2230}_C\unicode8752\unicodex2230C​	\unicode{8752} \unicode{x2230}_C
12	\unicode8753\unicodex2231c\unicode{8753} \unicode{x2231}_c \unicode8753\unicodex2231c​	\unicode{8753} \unicode{x2231}_c
13	\unicode8754\unicodex2232c\unicode{8754} \unicode{x2232}_c \unicode8754\unicodex2232c​	\unicode{8754} \unicode{x2232}_c
14	\unicode8755\unicodex2233c\unicode{8755} \unicode{x2233}_c\unicode8755\unicodex2233c​	\unicode{8755} \unicode{x2233}_c

最后3组图标的区别在于箭头的方向：

其他运算符号operators

编号类别样式LaTeX

1	求和 Summation	∑ab\sum_{a}^{b}∑ab​	\sum_{a}^{b}
2	求和 Summation	∑ab\textstyle \sum_{a}^{b}∑ab​	\textstyle \sum_{a}^{b}
3	连乘积 Product	∏ab\prod_{a}^{b}∏ab​	\prod_{a}^{b}
4	连乘积 Product	∏ab\textstyle \prod_{a}^{b}∏ab​	\textstyle \prod_{a}^{b}
5	余积 Coproduct	∐ab\coprod_{a}^{b}∐ab​	\coprod_{a}^{b}
6	余积 Coproduct	∐ab\textstyle \coprod_{a}^{b}∐ab​	\textstyle \coprod_{a}^{b}
7	并集 Union	⋃ab\bigcup_{a}^{b}⋃ab​	\bigcup_{a}^{b}
8	并集 Union	⋃ab\textstyle \bigcup_{a}^{b}⋃ab​	\textstyle \bigcup_{a}^{b}
9	交集 Intersection	⋂ab\bigcap_{a}^{b}⋂ab​	\bigcap_{a}^{b}
10	交集 Intersection	⋂ab\textstyle \bigcap_{a}^{b}⋂ab​	\textstyle \bigcap_{a}^{b}
11	析取 Disjunction	⋁ab\bigvee_{a}^{b}⋁ab​	\bigvee_{a}^{b}
12	析取 Disjunction	⋁ab\textstyle \bigvee_{a}^{b}⋁ab​	\textstyle \bigvee_{a}^{b}
13	合取 Conjunction	⋀ab\bigwedge_{a}^{b}⋀ab​	\bigwedge_{a}^{b}
14	合取 Conjunction	⋀ab\textstyle \bigwedge_{a}^{b}⋀ab​	\textstyle \bigwedge_{a}^{b}

上下标Sub & Super

编号类型样式代码

1	上标 Superscript	a2,ax+3a^2, a^{x+3}a2,ax+3	a^2, a^{x+3}
2	下标 Subscript	a2a_2a2​	a_2
3	组合1 Grouping	1030a2+210^{30} a^{2+2}1030a2+2	10^{30} a^{2+2}
4	组合2 Grouping	ai,jbf′a_{i,j} b_{f'}ai,j​bf′​	a_{i,j} b_{f'}
5	上下标混合1 Combining sub & super	x23x_2^3x23​	x_2^3
6	上下标混合2 Combining sub & super	x23{x_2}^3x2​3	{x_2}^3
7	上标的上标 Super super	1010810^{10^{8}}10108	10^{10^{8}}
8	混合标识1 Preceding and/or additional sub & super	\sideset1234Xab\sideset{_1^2}{_3^4}X_a^b\sideset12​34​Xab​	\sideset{_1^2}{_3^4}X_a^b
9	混合标识2 Preceding and/or additional sub & super	12!Ω34{}_1^2!\Omega_3^412​!Ω34​	{}_1^2!\Omega_3^4
10	顶标底标1 Stacking	ωα\overset{\alpha}{\omega}ωα	\overset{\alpha}{\omega}
11	顶标底标2 Stacking	ωα\underset{\alpha}{\omega}αω​	\underset{\alpha}{\omega}
12	顶标底标3 Stacking	ωγα\overset{\alpha}{\underset{\gamma}{\omega}}γω​α​	\overset{\alpha}{\underset{\gamma}{\omega}}
13	顶标底标4 Stacking	ωα\stackrel{\alpha}{\omega}ωα	\stackrel{\alpha}{\omega}
14	导数1 Derivatives	x′,y′′,f′,f′′x', y'', f', f''x′,y′′,f′,f′′	x', y'', f', f''
15	导数2 Derivatives	x′,y′′x^\prime, y^{\prime\prime}x′,y′′	x^\prime, y^{\prime\prime}
16	导数 Derivative dots	x˙,x¨\dot{x}, \ddot{x}x˙,x¨	\dot{x}, \ddot{x}
17	下划线、上划线与向量1 Underlines, overlines, vectors	a^ bˉ c⃗\hat a \ \bar b \ \vec ca^ bˉ c	\hat a \ \bar b \ \vec c
18	下划线、上划线与向量2 Underlines, overlines, vectors	ab→ cd← def^\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}ab cd def​	\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}
19	下划线、上划线与向量3 Underlines, overlines, vectors	ghi‾ jkl‾\overline{g h i} \ \underline{j k l}ghi​ jkl​	\overline{g h i} \ \underline{j k l}
20	弧度 Arc (workaround)	AB⌢\overset{\frown} {AB}AB⌢	\overset{\frown} {AB}
21	箭头 Arrows	A←n+μ−1B→Tn±i−1CA \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} CAn+μ−1​Bn±i−1T​C	A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C
22	大括号 Overbraces	1+2+⋯+100⏞5050\overbrace{ 1+2+\cdots+100 }^{5050}1+2+⋯+100​5050​	\overbrace{ 1+2+\cdots+100 }^{5050}
23	底部大括号 Underbraces	a+b+⋯+z⏟26\underbrace{ a+b+\cdots+z }_{26}26a+b+⋯+z​​	\underbrace{ a+b+\cdots+z }_{26}
24	求和运算 Sum	∑k=1Nk2\sum_{k=1}^N k^2∑k=1N​k2	\sum_{k=1}^N k^2
25	文本模式下的求和运算 Sum (force \textstyle)	∑k=1Nk2\textstyle \sum_{k=1}^N k^2∑k=1N​k2	\textstyle \sum_{k=1}^N k^2
26	分式中的求和运算1 Sum in a fraction (default \textstyle)	∑k=1Nk2a\frac{\sum_{k=1}^N k^2}{a}a∑k=1N​k2​	\frac{\sum_{k=1}^N k^2}{a}
27	分式中的求和运算2 Sum in a fraction (force \displaystyle)	∑k=1Nk2a\frac{\displaystyle \sum_{k=1}^N k^2}{a}ak=1∑N​k2​	\frac{\displaystyle \sum_{k=1}^N k^2}{a}
28	分式中的求和运算3 Sum in a fraction (alternative limits style)	∑Nk=1k2a\frac{\sum\limits{N}_{k=1} k^2}{a}a∑Nk=1​k2​	\frac{\sum\limits{N}_{k=1} k^2}{a}
29	乘积运算 Product	∏i=1Nxi\prod_{i=1}^N x_i∏i=1N​xi​	\prod_{i=1}^N x_i
30	乘积运算 Product (force \textstyle)	∏i=1Nxi\textstyle \prod_{i=1}^N x_i∏i=1N​xi​	\textstyle \prod_{i=1}^N x_i
31	副乘运算 Coproduct	∐i=1Nxi\coprod_{i=1}^N x_i∐i=1N​xi​	\coprod_{i=1}^N x_i
32	副乘运算 Coproduct (force \textstyle)	∐i=1Nxi\textstyle \coprod_{i=1}^N x_i∐i=1N​xi​	\textstyle \coprod_{i=1}^N x_i
33	极限 Limit	lim⁡n→∞xn\lim_{n \to \infty}x_nlimn→∞​xn​	\lim_{n \to \infty}x_n
34	极限 Limit (force \textstyle)	lim⁡n→∞xn\textstyle \lim_{n \to \infty}x_nlimn→∞​xn​	\textstyle \lim_{n \to \infty}x_n
35	积分 Integral	∫13e3/xx2 dx\int\limits_{1}{3}\frac{e3/x}{x^2}\, dx1∫​3x2e3/x​dx	\int\limits_{1}{3}\frac{e3/x}{x^2}, dx
36	积分 Integral (alternative limits style)	∫13e3/xx2 dx\int_{1}{3}\frac{e3/x}{x^2}\, dx∫1​3x2e3/x​dx	\int_{1}{3}\frac{e3/x}{x^2}, dx
37	积分 Integral (force \textstyle)	∫−NNexdx\textstyle \int\limits_{-N}^{N} e^x dx−N∫N​exdx	\textstyle \int\limits_{-N}^{N} e^x dx
38	积分 Integral (force \textstyle, alternative limits style)	∫−NNexdx\textstyle \int_{-N}^{N} e^x dx∫−NN​exdx	\textstyle \int_{-N}^{N} e^x dx
39	双重积分 Double integral	∬Ddx dy\iint\limits_D dx\,dyD∬​dxdy	\iint\limits_D dx,dy
40	三重积分 Triple integral	∭Edx dy dz\iiint\limits_E dx\,dy\,dzE∭​dxdydz	\iiint\limits_E dx,dy,dz
41	四重积分 Quadruple integral	\iiiint\limits_F dx\,dy\,dz\,dt	\iiiint\limits_F dx,dy,dz,dt
42	路径积分 Line or path integral	∫(x,y)∈Cx3 dx+4y2 dy\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy∫(x,y)∈C​x3dx+4y2dy	\int_{(x,y)\in C} x^3, dx + 4y^2, dy
43	环路积分 Closed line or path integral	∮(x,y)∈Cx3 dx+4y2 dy\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy∮(x,y)∈C​x3dx+4y2dy	\oint_{(x,y)\in C} x^3, dx + 4y^2, dy
44	交集 Intersections	⋂i=1nEi\bigcap_{i=1}^n E_i⋂i=1n​Ei​	\bigcap_{i=1}^n E_i
45	并集 Unions	⋃i=1nEi\bigcup_{i=1}^n E_i⋃i=1n​Ei​	\bigcup_{i=1}^n E_i

矩阵与多行列式 Matrices & Multilines

编号类型样式LaTeX

1	二项式系数 Binomial coefficients	(nk)\binom{n}{k}(kn​)	\binom{n}{k}
2	小型二项式系数 Small binomial coefficients (force \textstyle)	(nk)\tbinom{n}{k}(kn​)	\tbinom{n}{k}
3	大型二项式系数 Large (normal) binomial coefficients (force \displaystyle)	(nk)\dbinom{n}{k}(kn​)	\dbinom{n}{k}
4	矩阵1 Matrices	xyzv\begin{matrix} x & y \\ z & v \end{matrix}xz​yv​	\begin{matrix} x & y \ z & v \end{matrix}
5	矩阵2 Matrices	∣xyzv∣\begin{vmatrix} x & y \\ z & v \end{vmatrix}∣∣​xz​yv​∣∣​	\begin{vmatrix} x & y \ z & v \end{vmatrix}
6	矩阵3 Matrices	∥xyzv∥\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}∥∥​xz​yv​∥∥​	\begin{Vmatrix} x & y \ z & v \end{Vmatrix}
7	矩阵4 Matrices	[0⋯0⋮⋱⋮0⋯0]\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}⎣⎡​0⋮0​⋯⋱⋯​0⋮0​⎦⎤​	\begin{bmatrix} 0 & \cdots & 0 \ \vdots & \ddots & \vdots \ 0 & \cdots & 0 \end{bmatrix}
8	矩阵5 Matrices	{xyzv}\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}{xz​yv​}	\begin{Bmatrix} x & y \ z & v \end{Bmatrix}
9	矩阵6 Matrices	(xyzv)\begin{pmatrix} x & y \\ z & v \end{pmatrix}(xz​yv​)	\begin{pmatrix} x & y \ z & v \end{pmatrix}
10	矩阵7 Matrices	(abcd)\bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr)(ac​bd​)	\bigl( \begin{smallmatrix} a&b\ c&d \end{smallmatrix} \bigr)
11	条件定义 Case distinctions	f(n)={n/2,if n is even3n+1,if n is oddf(n) = \begin{cases} n/2, & \text{if }n\text{ is even} \\ 3n+1, & \text{if }n\text{ is odd} \end{cases}f(n)={n/2,3n+1,​if n is evenif n is odd​	f(n) = \begin{cases} n/2, & \text{if }n\text{ is even} \ 3n+1, & \text{if }n\text{ is odd} \end{cases}
12	多行等式1 Multiline equations	\begin{align} f(x) & = (a+b)^2\\ & = a^2+2ab+b^2 \end{align}	\begin{align} f(x) & = (a+b)^2\ & = a^2+2ab+b^2 \end{align}
13	多行等式2 Multiline equations	\begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \end{alignat}	\begin{alignat}{2} f(x) & = (a-b)^2 \ & = a^2-2ab+b^2 \end{alignat}
14	多行等式3 Multiline equations	z=af(x,y,z)=x+y+z\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}zf(x,y,z)​==​ax+y+z​	\begin{array}{lcl} z & = & a \ f(x,y,z) & = & x + y + z \end{array}
15	多行等式4 Multiline equations	z=af(x,y,z)=x+y+z\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}zf(x,y,z)​==​ax+y+z​	$\begin{array}{lcr} z & = & a \ f(x,y,z) & = & x + y + z \end{array}
16	方程组 Simultaneous equations	{3x+5y+z7x−2y+4z−6x+3y+2z\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}⎩⎨⎧​3x+5y+z7x−2y+4z−6x+3y+2z​	\begin{cases} 3x + 5y + z \ 7x - 2y + 4z \ -6x + 3y + 2z \end{cases}
17	数组 Arrays	$\begin{array}{	c	c	c	} a & b & S \ \hline 0 & 0 & 1 \ 0 & 1 & 1 \ 1 & 0 & 1 \ 1 & 1 & 0 \end{array}$	\begin{array}{ | c | c | c | } a & b & S \ \hline 0 & 0 & 1 \ 0 & 1 & 1 \ 1 & 0 & 1 \ 1 & 1 & 0 \end{array}

括号Brackets

编号类型样式LaTeX

1	圆括号、小括号 Parentheses	(ab)\left ( \frac{a}{b} \right )(ba​)	\left ( \frac{a}{b} \right )
2	方括号、中括号 Brackets	[ab][ab]\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack[ba​][ba​]	\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack
3	花括号、大括号 Braces	{ab}{ab}\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace{ba​}{ba​}	\left { \frac{a}{b} \right } \quad \left \lbrace \frac{a}{b} \right \rbrace
4	角括号 Angle brackets	⟨ab⟩\left \langle \frac{a}{b} \right \rangle⟨ba​⟩	\left \langle \frac{a}{b} \right \rangle
5	单竖线和双竖线 Bars and double bars	$	\frac{a}{b}			\frac{c}{d}		$	|\frac{a}{b}| ||\frac{c}{d}||
6	取整函数与取顶函数 Floor and ceiling functions:	⌊ab⌋⌈cd⌉\left \lfloor \frac{a}{b} \right \rfloor \quad \left \lceil \frac{c}{d} \right \rceil⌊ba​⌋⌈dc​⌉	\left \lfloor \frac{a}{b} \right \rfloor \quad \left \lceil \frac{c}{d} \right \rceil
7	斜线与反斜线 Slashes and backslashes	/ab\\left / \frac{a}{b} \right \backslash/ba​\	\left / \frac{a}{b} \right \backslash
8	上下箭头 Up, down, and up-down arrows	↑ab↓⇑ab⇓↕ab⇕\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow⏐↑​ba​↓⏐​‖⇑​ba​⇓‖​↓↑​ba​⇓⇑​	\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow
9	混合括号 Delimiters can be mixed,as long as \left and \right match	$\left [0,1 \right ) \left \langle \psi \right	$	\left [ 0,1 \right ) \left \langle \psi \right |
10	单侧括号，使用\left. 和 \right.（带有英文句号）	AB}→X\left. \frac{A}{B} \right \} \to XBA​}→X	\left. \frac{A}{B} \right } \to X
11	括号的大小1	$((\left(\right((\dots ]\left]\right]]]$	( \bigl( \Bigl( \biggl( \Biggl( \dots \Biggr] \biggr] \Bigr] \bigr] ]
12	括号的大小2	$\lfloor \lfloor \lfloor \lfloor \lfloor \cdots <br/>\rceil \rceil \rceil \rceil \rceil$	\lfloor \bigl\lfloor \Bigl\lfloor \biggl\lfloor \Biggl\lfloor \dots \Biggr\rceil \biggr\rceil \Bigr\rceil \bigr\rceil \rceil
13	括号的大小3	$\uparrow \uparrow \uparrow \uparrow \uparrow \cdots <br/>\Downarrow \Downarrow \Downarrow \Downarrow \Downarrow$	\uparrow \big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow \Downarrow
14	括号的大小4	$\updownarrow \updownarrow \updownarrow \updownarrow \updownarrow \cdots <br/>\Updownarrow \Updownarrow \Updownarrow \Updownarrow \Updownarrow$	\updownarrow \big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow \Updownarrow
15	括号的大小5	$/////\cdots <br/>\backslash \backslash \backslash \backslash \backslash$	/ \big/ \Big/ \bigg/ \Bigg/ \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash \backslash

注意：在使用大括号的时候需要添加转义字符\{\}

空格与换行

关于空格的使用可以参考下表。

编号样式LaTeX中文说明英文说明

1	$ab$	a \qquad b	双空格
2	$ab$	a \quad b	单空格
3	$ab$	a\ b	字符空格
4	$ab$	a \text{ } b	文本模式中的字符空格
5	$ab$	a;b	大空格
6	$ab$	a,b	小空格
7	$ab$	ab	极小空格(用于乘因子)
8	$ab$	a b	极小空格(用于区分其它语法)
9	$ab$	\mathit{ab}	没有空格(用于多字母变量)
10	$ab$	a\!b	负空格

关于换行，使用一对\\进行强制换行，看一个案例：

f(x,y)=a2+b2+2ab=(a+b)2f(x,y) = a^2+b^2+2ab \\ =(a+b)^2f(x,y)=a2+b2+2ab=(a+b)2

实际源码为：

$$f(x,y) = a^2+b^2+2ab \\ =(a+b)^2$$