LaTeX数学符号总结jupyter-notebook

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2024-12-28 约 2563 字预计阅读 6 分钟

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LaTeX数学符号总结（jupyter notebook）

1. LaTeX 数学公式基础知识

LaTeX的强大之处在于对数学符号和公式的排版，所以jupyter notebook采用LaTeX来进行数学符号和公式的显示排版。

首先，在jupyter notebook 里面，LaTeX数学公式用$$括起来。

数学模式和文本模式又很多的不同之处。例如在数学模式中：

空格和分行都会被忽略，所有的空格或是由数学表达式逻辑的衍生，或是由特殊命令如\，\quad或\qquad来得到。空格可以用 &emsp;或者  表示
不允许有空行，每个公式中只能有一个段落。
每个字符都将被看作是一个变量名并以此来排版。

2. 常用的排版命令

分式

命令 \frac{a}{b} 形式：

a b \frac{a}{b}

命令 \sum_{i=1}^n p_i 形式：

∑ i

1 n p i \sum_{i=1}^n p_i

∑

3. 常用的数学模式命令

1. 数学模式重音符

Symbol	Command	Symbol	Command	Symbol	Command
a ^ \hat{a} a ^	\hat{a}	a ˋ \grave{a} a ˋ	\grave{a}	a ˉ \bar{a} a ˉ	\bar{a}
a ˇ \check{a} a ˇ	\check{a}	a ˙ \dot{a} a ˙	\dot{a}	a ⃗ \vec{a} a	\vec{a}
a ~ \tilde{a} a ~	\tilde{a}	a ¨ \ddot{a} a ¨	\ddot{a}	A ^ \widehat{A} A	\widehat{A}
a ˊ \acute{a} a ˊ	\acute{a}	a ˘ \breve{a} a ˘	\breve{a}	A ~ \widetilde{A} A	\widetilde{A}

2. 小写希腊字母

Symbol	Command	Symbol	Command	Symbol	Command
α \alpha α	\alpha	θ \theta θ	\theta	o o o	o
β \beta β	\beta	ϑ \vartheta ϑ	\vartheta	π \pi π	\pi
γ \gamma γ	\gamma	ι \iota ι	\iota	ϖ \varpi ϖ	\varpi
δ \delta δ	\delta	κ \kappa κ	\kappa	ρ \rho ρ	\rho
ϵ \epsilon ϵ	\epsilon	λ \lambda λ	\lambda	ϱ \varrho ϱ	\varrho
ε \varepsilon ε	\varepsilon	μ \mu μ	\mu	σ \sigma σ	\sigma
ζ \zeta ζ	\zeta	ν \nu ν	\nu	ς \varsigma ς	\varsigma
η \eta η	\eta	ξ \xi ξ	\xi	τ \tau τ	\tau
υ \upsilon υ	\upsilon	ϕ \phi ϕ	\phi	φ \varphi φ	\varphi
χ \chi χ	\chi	ψ \psi ψ	\psi	ω \omega ω	\omega

3. 大写希腊字母

Symbol	Command	Symbol	Command	Symbol	Command
Γ \Gamma Γ	\Gamma	Λ \Lambda Λ	\Lambda	Σ \Sigma Σ	\Sigma
Δ \Delta Δ	\Delta	Ξ \Xi Ξ	\Xi	Υ \Upsilon Υ	\Upsilon
Θ \Theta Θ	\Theta	Π \Pi Π	\Pi	Φ \Phi Φ	\Phi
Ψ \Psi Ψ	\Psi	Ω \Omega Ω	\Omega

4. 二元关系符

Symbol	Command	Symbol	Command	Symbol	Command
> > >	>	< < <	<	= = =	=
≤ \leq ≤	\leq or \le	≥ \geq ≥	\geq or \ge	≡ \equiv ≡	\equiv
≪ \ll ≪	\ll	≫ \gg ≫	\gg	≐ \doteq ≐	\doteq
≺ \prec ≺	\prec	≻ \succ ≻	\succ	∼ \sim ∼	\sim
⪯ \preceq ⪯	\preceq	⪰ \succeq ⪰	\succeq	≃ \simeq ≃	\simeq
⊂ \subset ⊂	\subset	⊃ \supset ⊃	\supset	≈ \approx ≈	\approx
⊆ \subseteq ⊆	\subseteq	⊇ \supseteq ⊇	\supseteq	≅ \cong ≅	\cong
⊏ \sqsubset ⊏	\sqsubset	⊐ \sqsupset ⊐	\sqsupset	⋈ \Join ⋈	\Join
⊑ \sqsubseteq ⊑	\sqsubseteq	⊒ \sqsupseteq ⊒	\sqsupseteq	⋈ \bowtie ⋈	\bowtie
∈ \in ∈	\in	∋ \ni ∋	\ni or \owns	∝ \propto ∝	\propto
⊢ \vdash ⊢	\vdash	⊣ \dashv ⊣	\dashv	⊨ \models ⊨	\models
∣ \mid ∣	\mid	∥ \parallel ∥	\parallel	⊥ \perp ⊥	\perp
⌣ \smile ⌣	\smile	⌢ \frown ⌢	\frown	≍ \asymp ≍	\asymp
: : :	:	∉ \notin ∈ /	\notin	≠ \neq ̸ =	\neq or \ne

5. 二元运算符

Symbol	Command	Symbol	Command	Symbol	Command
+ + +	+	− - −	-
± \pm ±	\pm	∓ \mp ∓	\mp	◃ \triangleleft ◃	\triangleleft
⋅ \cdot ⋅	\cdot	÷ \div ÷	\div	▹ \triangleright ▹	\triangleright
× \times ×	\times	∖ \setminus ∖	\setminus	⋆ \star ⋆	\star
∪ \cup ∪	\cup	∩ \cap ∩	\cap	∗ \ast ∗	\ast
⊔ \sqcup ⊔	\sqcup	⊓ \sqcap ⊓	\sqcap	∘ \circ ∘	\circ
∨ \vee ∨	\vee or \lor	∧ \wedge ∧	\wedge or \land	∙ \bullet ∙	\bullet
⊕ \oplus ⊕	\oplus	⊖ \ominus ⊖	\ominus	⋄ \diamond ⋄	\diamond
⊙ \odot ⊙	\odot	⊘ \oslash ⊘	\oslash	⊎ \uplus ⊎	\uplus
⊗ \otimes ⊗	\otimes	◯ \bigcirc ◯	\bigcirc	⨿ \amalg ⨿	\amalg
△ \bigtriangleup △	\bigtriangleup	▽ \bigtriangledown ▽	\bigtriangledown	† \dagger †	\dagger
⊲ \lhd ⊲	\lhd	⊳ \rhd ⊳	\rhd	‡ \ddagger ‡	\ddagger
⊴ \unlhd ⊴	\unlhd	⊵ \unrhd ⊵	\unrhd	≀ \wr ≀	\wr

6. 大尺寸运算符

Symbol	Command	Symbol	Command	Symbol	Command
∑ \sum ∑	\sum	⋃ \bigcup ⋃	\bigcup	⋂ \bigcap ⋂	\bigcap
⋁ \bigvee ⋁	\bigvee	⨁ \bigoplus ⨁	\bigoplus	∏ \prod ∏	\prod
⋀ \bigwedge ⋀	\bigwedge	⨂ \bigotimes ⨂	\bigotimes	∐ \coprod ∐	\coprod
⨆ \bigsqcup ⨆	\bigsqcup	⨀ \bigodot ⨀	\bigodot	∫ \int ∫	\int
∮ \oint ∮	\oint	⨄ \biguplus ⨄	\biguplus

7. 箭头

Symbol	Command	Symbol	Command	Symbol	Command
← \gets ←	\leftarrow or \gets	⟵ \longleftarrow ⟵	\longleftarrow	↑ \uparrow ↑	\uparrow
→ \to →	\rightarrow or \to	⟶ \longrightarrow ⟶	\longrightarrow	↓ \downarrow ↓	\downarrow
↔ \leftrightarrow ↔	\leftrightarrow	⟷ \longleftrightarrow ⟷	\longleftrightarrow	↕ \updownarrow ↕	\updownarrow
⇐ \Leftarrow ⇐	\Leftarrow	⟸ \Longleftarrow ⟸	\Longleftarrow	⇑ \Uparrow ⇑	\Uparrow
⇒ \Rightarrow ⇒	\Rightarrow	⟹ \Longrightarrow ⟹	\Longrightarrow	⇓ \Downarrow ⇓	\Downarrow
⇔ \Leftrightarrow ⇔	\Leftrightarrow	⟺ \Longleftrightarrow ⟺	\Longleftrightarrow	⇕ \Updownarrow ⇕	\Updownarrow
↦ \mapsto ↦	\mapsto	⟼ \longmapsto ⟼	\longmapsto	↗ \nearrow ↗	\nearrow
↩ \hookleftarrow ↩	\hookleftarrow	↪ \hookrightarrow ↪	\hookrightarrow	↘ \searrow ↘	\searrow
↼ \leftharpoonup ↼	\leftharpoonup	⇀ \rightharpoonup ⇀	\rightharpoonup	↙ \swarrow ↙	\swarrow
↽ \leftharpoondown ↽	\leftharpoondown	⇁ \rightharpoondown ⇁	\rightharpoondown	↖ \nwarrow ↖	\nwarrow
⇌ \rightleftharpoons ⇌	\rightleftharpoons	⟺   \iff ⟺	\iff	⇝ \leadsto ⇝	\leadsto

8. 定界符

Symbol	Command	Symbol	Command	Symbol	Command
( ( (	(	) ) )	)	↑ \uparrow ↑	\uparrow
[ [ [	[ or \lbrack	] ] ]	] or \rbrack	↓ \downarrow ↓	\downarrow
{ { {	{ or \lbrace	} } }	} or \rbrace	↕ \updownarrow ↕	\updownarrow
⟨ \langle ⟨	\langle	⟩ \rangle ⟩	\rangle	⇑ \Uparrow ⇑	\Uparrow
$	$	\vert	∥ \| ∥		or \Vert
⌊ \lfloor ⌊	\lfloor	⌋ \rfloor ⌋	\rfloor	⇕ \Updownarrow ⇕	\Updownarrow
⌈ \lceil ⌈	\lceil	⌉ \rceil ⌉	\rceil	/ / /	/
\ \backslash \	\backslash

9. 大尺寸定界符

Symbol	Command	Symbol	Command	Symbol	Command
⟮ \lgroup ⟮	\lgroup	⟯ \rgroup ⟯	\rgroup	⎰ \lmoustache ⎰	\lmoustache
⎱ \rmoustache ⎱	\rmoustache	KaTeX parse error: Expected ‘EOF’, got ‘\arrowvert’ at position 1: \̲a̲r̲r̲o̲w̲v̲e̲r̲t̲	\arrowvert	KaTeX parse error: Expected ‘EOF’, got ‘\Arrowvert’ at position 1: \̲A̲r̲r̲o̲w̲v̲e̲r̲t̲	\Arrowvert
KaTeX parse error: Expected ‘EOF’, got ‘\bracevert’ at position 1: \̲b̲r̲a̲c̲e̲v̲e̲r̲t̲	\bracevert

10. 其他符号

Symbol	Command	Symbol	Command	Symbol	Command
… \dots …	\dots	⋯ \cdots ⋯	\cdots	⋮ \vdots ⋮	\vdots
⋱ \ddots ⋱	\ddots	ℏ \hbar ℏ	\hbar	ı \imath ı	\imath
ȷ \jmath ȷ	\jmath	ℓ \ell ℓ	\ell	ℜ \Re ℜ	\Re
ℑ \Im ℑ	\Im	ℵ \aleph ℵ	\aleph	℘ \wp ℘	\wp
∀ \forall ∀	\forall	∃ \exists ∃	\exists	℧ \mho ℧	\mho
∂ \partial ∂	\partial	′ ' ′	’	′ \prime ′	\prime
∅ \emptyset ∅	\emptyset	∞ \infty ∞	\infty	∇ \nabla ∇	\nabla
△ \triangle △	\triangle	□ \Box □	\Box	◊ \Diamond ◊	\Diamond
⊥ \bot ⊥	\bot	⊤ \top ⊤	\top	∠ \angle ∠	\angle
√ \surd √	\surd	♢ \diamondsuit ♢	\diamondsuit	♡ \heartsuit ♡	\heartsuit
♣ \clubsuit ♣	\clubsuit	♠ \spadesuit ♠	\spadesuit	¬ \neg ¬	\neg or \lnot
♭ \flat ♭	\flat	♮ \natural ♮	\natural	♯ \sharp ♯	\sharp

11. 非数学符号

Symbol	Command
KaTeX parse error: Expected ‘EOF’, got ‘\S’ at position 1: \̲S̲	\S

12. AMS定界符

Symbol	Command	Symbol	Command	Symbol	Command
┌ \ulcorner ┌	\ulcorner	┐ \urcorner ┐	\urcorner	└ \llcorner └	\llcorner
┘ \lrcorner ┘	\lrcorner	∣ \lvert ∣	\lvert	∣ \rvert ∣	\rvert
∥ \lVert ∥	\lVert	∥ \rVert ∥	\rVert

13. AMS希腊和希伯来字母

Symbol	Command	Symbol	Command	Symbol	Command
ϝ \digamma ϝ	\digamma	ϰ \varkappa ϰ	\varkappa	ℶ \beth ℶ	\beth
ℸ \daleth ℸ	\daleth	ℷ \gimel ℷ	\gimel

14. AMS二元关系符

Symbol	Command	Symbol	Command	Symbol	Command
⋖ \lessdot ⋖	\lessdot	⋗ \gtrdot ⋗	\gtrdot	≑ \doteqdot ≑	\doteqdot or \Doteq
⩽ \leqslant ⩽	\leqslant	⩾ \geqslant ⩾	\geqslant	≓ \risingdotseq ≓	\risingdotseq
⪕ \eqslantless ⪕	\eqslantless	⪖ \eqslantgtr ⪖	\eqslantgtr	≒ \fallingdotseq ≒	\fallingdotseq
≦ \leqq ≦	\leqq	≧ \geqq ≧	\geqq	≖ \eqcirc ≖	\eqcirc
⋘ \lll ⋘	\lll or \llless	⋙ \ggg ⋙	\ggg or \gggtr	≗ \circeq ≗	\circeq
≲ \lesssim ≲	\lesssim	≳ \gtrsim ≳	\gtrsim	≜ \triangleq ≜	\triangleq
⪅ \lessapprox ⪅	\lessapprox	⪆ \gtrapprox ⪆	\gtrapprox	≏ \bumpeq ≏	\bumpeq
≶ \lessgtr ≶	\lessgtr	≷ \gtrless ≷	\gtrless	≎ \Bumpeq ≎	\Bumpeq
⋚ \lesseqgtr ⋚	\lesseqgtr	⋛ \gtreqless ⋛	\gtreqless	∼ \thicksim ∼	\thicksim
⪋ \lesseqqgtr ⪋	\lesseqqgtr	⪌ \gtreqqless ⪌	\gtreqqless	≈ \thickapprox ≈	\thickapprox
≼ \preccurlyeq ≼	\preccurlyeq	≽ \succcurlyeq ≽	\succcurlyeq	≊ \approxeq ≊	\approxeq
⋞ \curlyeqprec ⋞	\curlyeqprec	⋟ \curlyeqsucc ⋟	\curlyeqsucc	∽ \backsim ∽	\backsim
≾ \precsim ≾	\precsim	≿ \succsim ≿	\succsim	⋍ \backsimeq ⋍	\backsimeq
⪷ \precapprox ⪷	\precapprox	⪸ \succapprox ⪸	\succapprox	⊨ \vDash ⊨	\vDash
⫅ \subseteqq ⫅	\subseteqq	⫆ \supseteqq ⫆	\supseteqq	⊩ \Vdash ⊩	\Vdash
⋐ \Subset ⋐	\Subset	⋑ \Supset ⋑	\Supset	⊪ \Vvdash ⊪	\Vvdash
⊏ \sqsubset ⊏	\sqsubset	⊐ \sqsupset ⊐	\sqsupset	∍ \backepsilon ∍	\backepsilon
∴ \therefore ∴	\therefore	∵ \because ∵	\because	∝ \varpropto ∝	\varpropto
ϝ \digamma ϝ	\digamma	ϰ \varkappa ϰ	\varkappa	ℶ \beth ℶ	\beth
ϝ \digamma ϝ	\digamma	ϰ \varkappa ϰ	\varkappa	ℶ \beth ℶ	\beth

15. AMS箭头

Symbol	Command	Symbol	Command	Symbol	Command
⇠ \dashleftarrow ⇠	\dashleftarrow	⇢ \dashrightarrow ⇢	\dashrightarrow	⊸ \multimap ⊸	\multimap
⇇ \leftleftarrows ⇇	\leftleftarrows	⇉ \rightrightarrows ⇉	\rightrightarrows	⇈ \upuparrows ⇈	\upuparrows
⇆ \leftrightarrows ⇆	\leftrightarrows	⇄ \rightleftarrows ⇄	\rightleftarrows	⇊ \downdownarrows ⇊	\downdownarrows
⇚ \Lleftarrow ⇚	\Lleftarrow	⇛ \Rrightarrow ⇛	\Rrightarrow	↿ \upharpoonleft ↿	\upharpoonleft
↞ \twoheadleftarrow ↞	\twoheadleftarrow	↠ \twoheadrightarrow ↠	\twoheadrightarrow	↾ \upharpoonright ↾	\upharpoonright
↢ \leftarrowtail ↢	\leftarrowtail	↣ \rightarrowtail ↣	\rightarrowtail	⇃ \downharpoonleft ⇃	\downharpoonleft
⇋ \leftrightharpoons ⇋	\leftrightharpoons	⇌ \rightleftharpoons ⇌	\rightleftharpoons	⇂ \downharpoonright ⇂	\downharpoonright
↰ \Lsh ↰	\Lsh	↱ \Rsh ↱	\Rsh	⇝ \rightsquigarrow ⇝	\rightsquigarrow
↫ \looparrowleft ↫	\looparrowleft	↬ \looparrowright ↬	\looparrowright	↭ \leftrightsquigarrow ↭	\leftrightsquigarrow
↶ \curvearrowleft ↶	\curvearrowleft	↷ \curvearrowright ↷	\curvearrowright	↺ \circlearrowleft ↺	\circlearrowleft
↻ \circlearrowright ↻	\circlearrowright

16. AMS二元否定关系符和箭头

Symbol	Command	Symbol	Command	Symbol	Command
≮ \nless ≮	\nless	≯ \ngtr ≯	\ngtr	 \varsubsetneqq 	\varsubsetneqq
⪇ \lneq ⪇	\lneq	⪈ \gneq ⪈	\gneq	 \varsupsetneqq 	\varsupsetneqq
≰ \nleq ≰	\nleq	≱ \ngeq ≱	\ngeq	 \nsubseteqq 	\nsubseteqq
 \nleqslant 	\nleqslant	 \ngeqslant 	\ngeqslant	 \nsupseteqq 	\nsupseteqq
≨ \lneqq ≨	\lneqq	≩ \gneqq ≩	\gneqq	∤ \nmid ∤	\nmid
 \lvertneqq 	\lvertneqq	 \gvertneqq 	\gvertneqq	∦ \nparallel ∦	\nparallel
 \nleqq 	\nleqq	 \ngeqq 	\ngeqq	 \nshortmid 	\nshortmid
⋦ \lnsim ⋦	\lnsim	⋧ \gnsim ⋧	\gnsim	 \nshortparallel 	\nshortparallel
⪉ \lnapprox ⪉	\lnapprox	⪊ \gnapprox ⪊	\gnapprox	≁ \nsim ≁	\nsim
⊀ \nprec ⊀	\nprec	⊁ \nsucc ⊁	\nsucc	≆ \ncong ≆	\ncong
⋠ \npreceq ⋠	\npreceq	⋡ \nsucceq ⋡	\nsucceq	⊬ \nvdash ⊬	\nvdash
⪵ \precneqq ⪵	\precneqq	⪶ \succneqq ⪶	\succneqq	⊭ \nvDash ⊭	\nvDash
⋨ \precnsim ⋨	\precnsim	⋩ \succnsim ⋩	\succnsim	⊮ \nVdash ⊮	\nVdash
⪹ \precnapprox ⪹	\precnapprox	⪺ \succnapprox ⪺	\succnapprox	⊯ \nVDash ⊯	\nVDash
⊊ \subsetneq ⊊	\subsetneq	⊋ \supsetneq ⊋	\supsetneq	⋪ \ntriangleleft ⋪	\ntriangleleft
 \varsubsetneq 	\varsubsetneq	 \varsupsetneq 	\varsupsetneq	⋫ \ntriangleright ⋫	\ntriangleright
⊈ \nsubseteq ⊈	\nsubseteq	⊉ \nsupseteq ⊉	\nsupseteq	⋬ \ntrianglelefteq ⋬	\ntrianglelefteq
⫋ \subsetneqq ⫋	\subsetneqq	⫌ \supsetneqq ⫌	\supsetneqq	⋭ \ntrianglerighteq ⋭	\ntrianglerighteq
↚ \nleftarrow ↚	\nleftarrow	↛ \nrightarrow ↛	\nrightarrow	↮ \nleftrightarrow ↮	\nleftrightarrow
⇍ \nLeftarrow ⇍	\nLeftarrow	⇏ \nRightarrow ⇏	\nRightarrow	⇎ \nLeftrightarrow ⇎	\nLeftrightarrow

17. AMS二元运算符

Symbol	Command	Symbol	Command	Symbol	Command
∔ \dotplus ∔	\dotplus	⋅ \centerdot ⋅	\centerdot	⊺ \intercal ⊺	\intercal
⋉ \ltimes ⋉	\ltimes	⋊ \rtimes ⋊	\rtimes	⋇ \divideontimes ⋇	\divideontimes
⋓ \Cup ⋓	\Cup or \doublecup	⋒ \Cap ⋒	\Cap or \doublecap	∖ \smallsetminus ∖	\smallsetminus
⊻ \veebar ⊻	\veebar	⊼ \barwedge ⊼	\barwedge	⩞ \doublebarwedge ⩞	\doublebarwedge
⊞ \boxplus ⊞	\boxplus	⊟ \boxminus ⊟	\boxminus	⊝ \circleddash ⊝	\circleddash
⊠ \boxtimes ⊠	\boxtimes	⊡ \boxdot ⊡	\boxdot	⊚ \circledcirc ⊚	\circledcirc
⋋ \leftthreetimes ⋋	\leftthreetimes	⋌ \rightthreetimes ⋌	\rightthreetimes	⊛ \circledast ⊛	\circledast
⋎ \curlyvee ⋎	\curlyvee	⋏ \curlywedge ⋏	\curlywedge

18. AMS其它符号

Symbol	Command	Symbol	Command	Symbol	Command
ℏ \hbar ℏ	\hbar	ℏ \hslash ℏ	\hslash	k \Bbbk k	\Bbbk
□ \square □	\square	■ \blacksquare ■	\blacksquare	Ⓢ \circledS Ⓢ	\circledS
△ \vartriangle △	\vartriangle	▲ \blacktriangle ▲	\blacktriangle	∁ \complement ∁	\complement
▽ \triangledown ▽	\triangledown	▼ \blacktriangledown ▼	\blacktriangledown	⅁ \Game ⅁	\Game
◊ \lozenge ◊	\lozenge	⧫ \blacklozenge ⧫	\blacklozenge	★ \bigstar ★	\bigstar
∠ \angle ∠	\angle	∡ \measuredangle ∡	\measuredangle	∢ \sphericalangle ∢	\sphericalangle
╱ \diagup ╱	\diagup	╲ \diagdown ╲	\diagdown	‵ \backprime ‵	\backprime
∄ \nexists ∄	\nexists	Ⅎ \Finv Ⅎ	\Finv	∅ \varnothing ∅	\varnothing
ð \eth ð	\eth	℧ \mho ℧	\mho