函数、符号及特殊字符
声调 / 变音符号
\dot{a}, \ddot{a}, \acute{a}, \grave{a}
\({\displaystyle {\dot {a}},{\ddot {a}},{\acute {a}},{\grave {a}}}\)
\check{a}, \breve{a}, \tilde{a}, \bar{a}
\({\displaystyle {\check {a}},{\breve {a}},{\tilde {a}},{\bar {a}}}\)
\hat{a}, \widehat{a}, \vec{a}
\({\displaystyle {\hat {a}},{\widehat {a}},{\vec {a}}}\)
标准函数
指数
\exp_a b = a^b, \exp b = e^b, 10^m
\({\displaystyle \exp _{a}b=a^{b},\exp b=e^{b},10^{m}}\)
对数
\ln c, \lg d = \log e, \log_{10} f
\({\displaystyle \ln c,\lg d=\log e,\log _{10}f}\)
三角函数
\sin a, \cos b, \tan c, \cot d, \sec e, \csc f
\({\displaystyle \sin a,\cos b,\tan c,\cot d,\sec e,\csc f}\)
\arcsin a, \arccos b, \arctan c
\({\displaystyle \arcsin a,\arccos b,\arctan c}\)
\arccot d, \arcsec e, \arccsc f
\({\displaystyle \operatorname {arccot} d,\operatorname {arcsec} e,\operatorname {arccsc} f}\)
\sinh a, \cosh b, \tanh c, \coth d
\({\displaystyle \sinh a,\cosh b,\tanh c,\coth d}\)
\operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n
\({\displaystyle \operatorname {sh} k,\operatorname {ch} l,\operatorname {th} m,\operatorname {coth} n}\)
\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q
\({\displaystyle \operatorname {argsh} o,\operatorname {argch} p,\operatorname {argth} q}\)
符号函数，绝对值
\sgn r, \left\vert s \right\vert
\({\displaystyle \operatorname {sgn} r,\left\vert s\right\vert }\)
最大值，最小值
\min(x,y), \max(x,y)
\({\displaystyle \min(x,y),\max(x,y)}\)
界限，极限
\min x, \max y, \inf s, \sup t
\({\displaystyle \min x,\max y,\inf s,\sup t}\)
\lim u, \liminf v, \limsup w
\({\displaystyle \lim u,\liminf v,\limsup w}\)
\lim_{x \to \infty} \frac{1}{n(n+1)}
\({\displaystyle \lim_{x \to \infty} \frac{1}{n(n+1)}}\)
\dim p, \deg q, \det m, \ker\phi
\({\displaystyle \dim p,\deg q,\det m,\ker \phi}\)
投射
\Pr j, \hom l, \lVert z \rVert, \arg z
\({\displaystyle \Pr j,\hom l,\lVert z\rVert ,\arg z}\)
微分及导数
dt, \mathrm{d}t, \partial t, \nabla\psi
\({\displaystyle dt,\mathrm {d} t,\partial t,\nabla \psi }\)
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
\({\displaystyle dy/dx,\mathrm {d} y/\mathrm {d} x,{\frac {dy}{dx}},{\frac {\mathrm {d} y}{\mathrm {d} x}},{\frac {\partial ^{2}}{\partial x_{1}\partial x_{2}}}y}\)
\prime, \backprime, f^\prime, f', f'', f^{(3)}, \dot y, \ddot y
\({\displaystyle \prime ,\backprime ,f^{\prime},f',f'',f^{(3)}\!,{\dot {y}},{\ddot {y}}}\)
类字母符号及常数
\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar
\({\displaystyle \infty ,\aleph ,\complement ,\backepsilon ,\eth ,\Finv ,\hbar}\)
\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS
\({\displaystyle \Im ,\imath ,\jmath ,\Bbbk ,\ell ,\mho ,\wp ,\Re ,\circledS }\)
模运算
s_k \equiv 0 \pmod{m}
\({\displaystyle s_{k}\equiv 0{\pmod {m}}}\)
a \bmod b
\({\displaystyle a \bmod b}\)
\gcd(m, n), \operatorname{lcm}(m, n)
\({\displaystyle \gcd(m,n),\operatorname {lcm} (m,n)}\)
\mid, \nmid, \shortmid, \nshortmid
\({\displaystyle \mid ,\nmid ,\shortmid ,\nshortmid}\)
根号
\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{\frac{x^3+y^3}{2}}
\({\displaystyle \surd ,{\sqrt {2}},{\sqrt[{n}]{}},{\sqrt[{3}]{\frac {x^{3}+y^{3}}{2}}}}\)
运算符
+, -, \pm, \mp, \dotplus
\({\displaystyle +,-,\pm ,\mp ,\dotplus}\)
\times, \div, \divideontimes, /, \backslash
\({\displaystyle \times ,\div ,\divideontimes ,/,\backslash}\)
\cdot, * \ast, \star, \circ, \bullet
\({\displaystyle \cdot ,*\ast ,\star ,\circ ,\bullet}\)
\boxplus, \boxminus, \boxtimes, \boxdot
\({\displaystyle \boxplus ,\boxminus ,\boxtimes ,\boxdot}\)
\oplus, \ominus, \otimes, \oslash, \odot
\({\displaystyle \oplus ,\ominus ,\otimes ,\oslash ,\odot}\)
\circleddash, \circledcirc, \circledast
\({\displaystyle \circleddash ,\circledcirc ,\circledast}\)
\bigoplus, \bigotimes, \bigodot
\({\displaystyle \bigoplus ,\bigotimes ,\bigodot}\)
集合
\{ \}, \O \empty \emptyset, \varnothing
\({\displaystyle \{\},\emptyset \emptyset \emptyset ,\varnothing }\)
\in, \notin \not\in, \ni, \not\ni
\({\displaystyle \in ,\notin \not \in ,\ni ,\not \ni}\)
\cap, \Cap, \sqcap, \bigcap
\({\displaystyle \cap ,\Cap ,\sqcap ,\bigcap}\)
\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus
\({\displaystyle \cup ,\Cup ,\sqcup ,\bigcup ,\bigsqcup ,\uplus ,\biguplus}\)
\setminus, \smallsetminus, \times
\({\displaystyle \setminus ,\smallsetminus ,\times}\)
\subset, \Subset, \sqsubset
\({\displaystyle \subset ,\Subset ,\sqsubset}\)
\supset, \Supset, \sqsupset
\({\displaystyle \supset ,\Supset ,\sqsupset}\)
\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq
\({\displaystyle \subseteq ,\nsubseteq ,\subsetneq ,\varsubsetneq ,\sqsubseteq}\)
\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq
\({\displaystyle \supseteq ,\nsupseteq ,\supsetneq ,\varsupsetneq ,\sqsupseteq}\)
\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq
\({\displaystyle \subseteqq ,\nsubseteqq ,\subsetneqq ,\varsubsetneqq}\)
\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq
\({\displaystyle \supseteqq ,\nsupseteqq ,\supsetneqq ,\varsupsetneqq}\)
关系符号
=, \ne, \neq, \equiv, \not\equiv
\({\displaystyle =,\neq ,\neq ,\equiv ,\not \equiv}\)
\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, :=
\({\displaystyle \doteq ,\doteqdot ,{\overset {\underset {\mathrm {def} }{}}{=}},:=}\)
\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong
\({\displaystyle \sim ,\nsim ,\backsim ,\thicksim ,\simeq ,\backsimeq ,\eqsim ,\cong ,\ncong}\)
\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto
\({\displaystyle \approx ,\thickapprox ,\approxeq ,\asymp ,\propto ,\varpropto}\)
<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot
\({\displaystyle <,\nless ,\ll ,\not \ll ,\lll ,\not \lll ,\lessdot}\)
>, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot
\({\displaystyle>,\ngtr ,\gg ,\not \gg ,\ggg ,\not \ggg ,\gtrdot }\)
\le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq
\({\displaystyle \leq ,\leq ,\lneq ,\leqq ,\nleq ,\nleqq ,\lneqq ,\lvertneqq}\)
\ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq
\({\displaystyle \geq ,\geq ,\gneq ,\geqq ,\ngeq ,\ngeqq ,\gneqq ,\gvertneqq}\)
\lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless
\({\displaystyle \lessgtr ,\lesseqgtr ,\lesseqqgtr ,\gtrless ,\gtreqless ,\gtreqqless}\)
\leqslant, \nleqslant, \eqslantless
\({\displaystyle \leqslant ,\nleqslant ,\eqslantless}\)
\geqslant, \ngeqslant, \eqslantgtr
\({\displaystyle \geqslant ,\ngeqslant ,\eqslantgtr}\)
\lesssim, \lnsim, \lessapprox, \lnapprox
\({\displaystyle \lesssim ,\lnsim ,\lessapprox ,\lnapprox}\)
\gtrsim, \gnsim, \gtrapprox, \gnapprox
\({\displaystyle \gtrsim ,\gnsim ,\gtrapprox ,\gnapprox}\)
\prec, \nprec, \preceq, \npreceq, \precneqq
\({\displaystyle \prec ,\nprec ,\preceq ,\npreceq ,\precneqq}\)
\succ, \nsucc, \succeq, \nsucceq, \succneqq
\({\displaystyle \succ ,\nsucc ,\succeq ,\nsucceq ,\succneqq}\)
\preccurlyeq, \curlyeqprec
\({\displaystyle \preccurlyeq ,\curlyeqprec}\)
\succcurlyeq, \curlyeqsucc
\({\displaystyle \succcurlyeq ,\curlyeqsucc}\)
\precsim, \precnsim, \precapprox, \precnapprox
\({\displaystyle \precsim ,\precnsim ,\precapprox ,\precnapprox}\)
\succsim, \succnsim, \succapprox, \succnapprox
\({\displaystyle \succsim ,\succnsim ,\succapprox ,\succnapprox}\)
几何符号
\parallel, \nparallel, \shortparallel, \nshortparallel
\({\displaystyle \parallel ,\nparallel ,\shortparallel ,\nshortparallel}\)
\perp, \angle, \sphericalangle, \measuredangle, 45^\circ
\({\displaystyle \perp ,\angle ,\sphericalangle ,\measuredangle ,45^{\circ}}\)
\Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar
\({\displaystyle \Box ,\blacksquare ,\diamond ,\Diamond \lozenge ,\blacklozenge ,\bigstar}\)
\bigcirc, \triangle, \bigtriangleup, \bigtriangledown
\({\displaystyle \bigcirc ,\triangle ,\bigtriangleup ,\bigtriangledown}\)
\vartriangle, \triangledown
\({\displaystyle \vartriangle ,\triangledown}\)
\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright
\({\displaystyle \blacktriangle ,\blacktriangledown ,\blacktriangleleft ,\blacktriangleright}\)
逻辑符号
\forall, \exists, \nexists
\({\displaystyle \forall ,\exists ,\nexists}\)
\therefore, \because, \And
\({\displaystyle \therefore ,\because ,\And}\)
\or \lor \vee, \curlyvee, \bigvee
\({\displaystyle \lor ,\lor ,\vee ,\curlyvee ,\bigvee}\)
\and \land \wedge, \curlywedge, \bigwedge
\({\displaystyle \land ,\land ,\wedge ,\curlywedge ,\bigwedge}\)
\bar{q}, \bar{abc}, \overline{q}, \overline{abc},
\lnot \neg, \not\operatorname{R}, \bot, \top
\({\displaystyle {\bar {q}},{\bar {abc}},{\overline {q}},{\overline {abc}},}\)
\({\displaystyle \lnot \neg ,\not \operatorname {R} ,\bot ,\top }\)
\vdash \dashv, \vDash, \Vdash, \models
\({\displaystyle \vdash ,\dashv ,\vDash ,\Vdash ,\models}\)
\Vvdash \nvdash \nVdash \nvDash \nVDash
\({\displaystyle \Vvdash ,\nvdash ,\nVdash ,\nvDash ,\nVDash}\)
\ulcorner \urcorner \llcorner \lrcorner
\({\displaystyle \ulcorner \urcorner \llcorner \lrcorner}\)
箭头
\Rrightarrow, \Lleftarrow
\({\displaystyle \Rrightarrow ,\Lleftarrow}\)
\Rightarrow, \nRightarrow, \Longrightarrow \implies
\({\displaystyle \Rightarrow ,\nRightarrow ,\Longrightarrow ,\implies}\)
\Leftarrow, \nLeftarrow, \Longleftarrow, \impliedby
\({\displaystyle \Leftarrow ,\nLeftarrow ,\Longleftarrow, \impliedby}\)
\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow \iff
\({\displaystyle \Leftrightarrow ,\nLeftrightarrow ,\Longleftrightarrow \iff}\)
\Uparrow, \Downarrow, \Updownarrow
\({\displaystyle \Uparrow ,\Downarrow ,\Updownarrow}\)
\rightarrow \to, \nrightarrow, \longrightarrow
\({\displaystyle \rightarrow \to ,\nrightarrow ,\longrightarrow}\)
\leftarrow \gets, \nleftarrow, \longleftarrow
\({\displaystyle \leftarrow \gets ,\nleftarrow ,\longleftarrow}\)
\leftrightarrow, \nleftrightarrow, \longleftrightarrow
\({\displaystyle \leftrightarrow ,\nleftrightarrow ,\longleftrightarrow}\)
\uparrow, \downarrow, \updownarrow
\({\displaystyle \uparrow ,\downarrow ,\updownarrow}\)
\nearrow, \swarrow, \nwarrow, \searrow
\({\displaystyle \nearrow ,\swarrow ,\nwarrow ,\searrow}\)
\mapsto, \longmapsto
\({\displaystyle \mapsto ,\longmapsto}\)
\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons
\({\displaystyle \rightharpoonup ,\rightharpoondown ,\leftharpoonup ,\leftharpoondown ,\upharpoonleft ,\upharpoonright ,\downharpoonleft ,\downharpoonright ,\rightleftharpoons ,\leftrightharpoons}\)
\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright
\({\displaystyle \curvearrowleft ,\circlearrowleft ,\Lsh ,\upuparrows ,\rightrightarrows ,\rightleftarrows ,\rightarrowtail ,\looparrowright}\)
\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft
\({\displaystyle \curvearrowright ,\circlearrowright ,\Rsh ,\downdownarrows ,\leftleftarrows ,\leftrightarrows ,\leftarrowtail ,\looparrowleft}\)
\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow
\({\displaystyle \hookrightarrow ,\hookleftarrow ,\multimap ,\leftrightsquigarrow ,\rightsquigarrow ,\twoheadrightarrow ,\twoheadleftarrow}\)
特殊符号
省略号：数学公式中常见的省略号有两种，\ldots 表示与文本底线对齐的省略号，\cdots 表示与文本中线对齐的省略号。
\amalg \% \dagger \ddagger \ldots \cdots
\({\displaystyle \amalg \%\dagger \ddagger \ldots \cdots}\)
\smile \frown \wr \triangleleft \triangleright
\({\displaystyle \smile \frown \wr \triangleleft \triangleright}\)
\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp
\({\displaystyle \diamondsuit ,\heartsuit ,\clubsuit ,\spadesuit ,\Game ,\flat ,\natural ,\sharp}\)
未分类
\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes
\({\displaystyle \diagup ,\diagdown ,\centerdot ,\ltimes ,\rtimes ,\leftthreetimes ,\rightthreetimes}\)
\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq
\({\displaystyle \eqcirc ,\circeq ,\triangleq ,\bumpeq ,\Bumpeq ,\doteqdot ,\risingdotseq ,\fallingdotseq}\)
\intercal \barwedge \veebar \doublebarwedge \between \pitchfork
\({\displaystyle \intercal ,\barwedge ,\veebar ,\doublebarwedge ,\between ,\pitchfork}\)
\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright
\({\displaystyle \vartriangleleft ,\ntriangleleft ,\vartriangleright ,\ntriangleright}\)
\trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq
\({\displaystyle \trianglelefteq ,\ntrianglelefteq ,\trianglerighteq ,\ntrianglerighteq}\)
关于这些符号的更多语义，参阅 TeX Cookbook 的简述。