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→Math code Display
==Math code Display==
==Math code Display==
The Math library installed in this wiki provides support for Mathematics Notation.
The Math library installed in this wiki provides support for Mathematics Notation.
== Functions, symbols, special characters ==
<!-- Eight symbols per line seems to be optimal -->
{| class="wikitable"
|-
!colspan="2"|
=== Accents/diacritics ===
|-
| <source lang="text" enclose="none">\dot{a}, \ddot{a}, \acute{a}, \grave{a} </source>
| <math>\dot{a}, \ddot{a}, \acute{a}, \grave{a} \!</math>
|-
| <source lang="text" enclose="none">\check{a}, \breve{a}, \tilde{a}, \bar{a} </source>
| <math>\check{a}, \breve{a}, \tilde{a}, \bar{a} \!</math>
|-
| <source lang="text" enclose="none">\hat{a}, \widehat{a}, \vec{a} </source>
| <math>\hat{a}, \widehat{a}, \vec{a} \!</math>
|-
!colspan="2"|
=== Standard numerical functions ===
|-
| <source lang="latex" enclose="none">\exp_a b = a^b, \exp b = e^b, 10^m </source>
| <math>\exp_a b = a^b, \exp b = e^b, 10^m \!</math>
|-
| <source lang="latex" enclose="none">\ln c, \lg d = \log e, \log_{10} f </source>
| <math>\ln c, \lg d = \log e, \log_{10} f \!</math>
|-
| <source lang="latex" enclose="none">\sin a, \cos b, \tan c, \cot d, \sec e, \csc f</source>
| <math>\sin a, \cos b, \tan c, \cot d, \sec e, \csc f\!</math>
|-
| <source lang="latex" enclose="none">\arcsin h, \arccos i, \arctan j </source>
| <math>\arcsin h, \arccos i, \arctan j \!</math>
|-
| <source lang="latex" enclose="none">\sinh k, \cosh l, \tanh m, \coth n </source>
| <math>\sinh k, \cosh l, \tanh m, \coth n \!</math>
|-
| <source lang="text" enclose="none">\operatorname{sh}\,k, \operatorname{ch}\,l, \operatorname{th}\,m, \operatorname{coth}\,n </source>
| <math>\operatorname{sh}\,k, \operatorname{ch}\,l, \operatorname{th}\,m, \operatorname{coth}\,n \!</math>
|-
| <source lang="text" enclose="none">\operatorname{argsh}\,o, \operatorname{argch}\,p, \operatorname{argth}\,q </source>
| <math>\operatorname{argsh}\,o, \operatorname{argch}\,p, \operatorname{argth}\,q \!</math>
|-
| <source lang="latex" enclose="none">\sgn r, \left\vert s \right\vert </source>
| <math>\sgn r, \left\vert s \right\vert \!</math>
|-
| <source lang="latex" enclose="none">\min(x,y), \max(x,y) </source>
| <math>\min(x,y), \max(x,y) \!</math>
|-
!colspan="2"|
=== Bounds ===
|-
| <source lang="latex" enclose="none">\min x, \max y, \inf s, \sup t </source>
| <math>\min x, \max y, \inf s, \sup t \!</math>
|-
| <source lang="latex" enclose="none">\lim u, \liminf v, \limsup w </source>
| <math>\lim u, \liminf v, \limsup w \!</math>
|-
| <source lang="latex" enclose="none">\dim p, \deg q, \det m, \ker\phi </source>
| <math>\dim p, \deg q, \det m, \ker\phi \!</math>
|-
!colspan="2"|
=== Projections ===
|-
| <source lang="latex" enclose="none">\Pr j, \hom l, \lVert z \rVert, \arg z </source>
| <math>\Pr j, \hom l, \lVert z \rVert, \arg z \!</math>
|-
!colspan="2"|
=== Differentials and derivatives ===
|-
| <source lang="latex" enclose="none">dt, \operatorname{d}\!t, \partial t, \nabla\psi</source>
| <math>dt, \operatorname{d}\!t, \partial t, \nabla\psi\!</math>
|-
| <source lang="text" enclose="none">dy/dx, \operatorname{d}\!y/\operatorname{d}\!x, {dy \over dx}, {\operatorname{d}\!y\over\operatorname{d}\!x}, {\partial^2\over\partial x_1\partial x_2}y </source>
| <math>dy/dx, \operatorname{d}\!y/\operatorname{d}\!x, {dy \over dx}, {\operatorname{d}\!y\over\operatorname{d}\!x}, {\partial^2\over\partial x_1\partial x_2}y \!</math>
|-
| <source lang="latex" enclose="none">\prime, \backprime, f^\prime, f', f'', f^{(3)}, \dot y, \ddot y </source>
| <math>\prime, \backprime, f^\prime, f', f'', f^{(3)} \!, \dot y, \ddot y</math>
|-
!colspan="2"|
=== Letter-like symbols or constants ===
|-
| <source lang="latex" enclose="none">\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar </source>
| <math>\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar \!</math>
|-
| <source lang="latex" enclose="none">\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS </source>
| <math>\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS \!</math>
|-
!colspan="2"|
=== Modular arithmetic ===
|-
| <source lang="latex" enclose="none">s_k \equiv 0 \pmod{m} </source>
| <math>s_k \equiv 0 \pmod{m} \!</math>
|-
| <source lang="latex" enclose="none">a\,\bmod\,b </source>
| <math>a\,\bmod\,b \!</math>
|-
| <source lang="latex" enclose="none">\gcd(m, n), \operatorname{lcm}(m, n)</source>
| <math>\gcd(m, n), \operatorname{lcm}(m, n)</math>
|-
| <source lang="latex" enclose="none">\mid, \nmid, \shortmid, \nshortmid </source>
| <math>\mid, \nmid, \shortmid, \nshortmid \!</math>
|-
!colspan="2"|
=== Radicals ===
|-
| <source lang="text" enclose="none">\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{x^3+y^3 \over 2} </source>
| <math>\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{x^3+y^3 \over 2} \!</math>
|-
!colspan="2"|
=== Operators ===
|-
| <source lang="latex" enclose="none">+, -, \pm, \mp, \dotplus </source>
| <math>+, -, \pm, \mp, \dotplus \!</math>
|-
| <source lang="latex" enclose="none">\times, \div, \divideontimes, /, \backslash </source>
| <math>\times, \div, \divideontimes, /, \backslash \!</math>
|-
| <source lang="latex" enclose="none">\cdot, * \ast, \star, \circ, \bullet </source>
| <math>\cdot, * \ast, \star, \circ, \bullet \!</math>
|-
| <source lang="latex" enclose="none">\boxplus, \boxminus, \boxtimes, \boxdot </source>
| <math>\boxplus, \boxminus, \boxtimes, \boxdot \!</math>
|-
| <source lang="latex" enclose="none">\oplus, \ominus, \otimes, \oslash, \odot</source>
| <math>\oplus, \ominus, \otimes, \oslash, \odot\!</math>
|-
| <source lang="latex" enclose="none">\circleddash, \circledcirc, \circledast </source>
| <math>\circleddash, \circledcirc, \circledast \!</math>
|-
| <source lang="latex" enclose="none">\bigoplus, \bigotimes, \bigodot </source>
| <math>\bigoplus, \bigotimes, \bigodot \!</math>
|-
!colspan="2"|
=== Sets ===
|-
| <source lang="text" enclose="none">\{ \}, \O \empty \emptyset, \varnothing </source>
| <math>\{ \}, \O \empty \emptyset, \varnothing \!</math>
|-
| <source lang="latex" enclose="none">\in, \notin \not\in, \ni, \not\ni </source>
| <math>\in, \notin \not\in, \ni, \not\ni \!</math>
|-
| <source lang="latex" enclose="none">\cap, \Cap, \sqcap, \bigcap </source>
| <math>\cap, \Cap, \sqcap, \bigcap \!</math>
|-
| <source lang="latex" enclose="none">\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus </source>
| <math>\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus \!</math>
|-
| <source lang="latex" enclose="none">\setminus, \smallsetminus, \times </source>
| <math>\setminus, \smallsetminus, \times \!</math>
|-
| <source lang="latex" enclose="none">\subset, \Subset, \sqsubset </source>
| <math>\subset, \Subset, \sqsubset \!</math>
|-
| <source lang="latex" enclose="none">\supset, \Supset, \sqsupset </source>
| <math>\supset, \Supset, \sqsupset \!</math>
|-
| <source lang="latex" enclose="none">\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq </source>
| <math>\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq \!</math>
|-
| <source lang="latex" enclose="none">\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq </source>
| <math>\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq \!</math>
|-
| <source lang="latex" enclose="none">\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq </source>
| <math>\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq \!</math>
|-
| <source lang="latex" enclose="none">\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq </source>
| <math>\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq \!</math>
|-
!colspan="2"|
=== Relations ===
|-
| <source lang="latex" enclose="none">=, \ne, \neq, \equiv, \not\equiv </source>
| <math>=, \ne, \neq, \equiv, \not\equiv \!</math>
|-
| <source lang="latex" enclose="none">\doteq, \doteqdot,</source> <source lang="text" enclose="none">\overset{\underset{\mathrm{def}}{}}{=},</source> <source lang="latex" enclose="none">:=</source>
| <math>\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, := \!</math>
|-
| <source lang="latex" enclose="none">\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong </source>
| <math>\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong \!</math>
|-
| <source lang="latex" enclose="none">\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto </source>
| <math>\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto \!</math>
|-
| <source lang="latex" enclose="none"><, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot </source>
| <math><, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot \!</math>
|-
| <source lang="latex" enclose="none">>, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot </source>
| <math>>, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot \!</math>
|-
| <source lang="latex" enclose="none">\le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq </source>
| <math>\le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq \!</math>
|-
| <source lang="latex" enclose="none">\ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq </source>
| <math>\ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq \!</math>
|-
| <source lang="latex" enclose="none">\lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless </source>
| <math>\lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless \!</math>
|-
| <source lang="latex" enclose="none">\leqslant, \nleqslant, \eqslantless </source>
| <math>\leqslant, \nleqslant, \eqslantless \!</math>
|-
| <source lang="latex" enclose="none">\geqslant, \ngeqslant, \eqslantgtr </source>
| <math>\geqslant, \ngeqslant, \eqslantgtr \!</math>
|-
| <source lang="latex" enclose="none">\lesssim, \lnsim, \lessapprox, \lnapprox </source>
| <math>\lesssim, \lnsim, \lessapprox, \lnapprox \!</math>
|-
| <source lang="latex" enclose="none">\gtrsim, \gnsim, \gtrapprox, \gnapprox </source>
| <math>\gtrsim, \gnsim, \gtrapprox, \gnapprox \,</math>
|-
| <source lang="latex" enclose="none">\prec, \nprec, \preceq, \npreceq, \precneqq </source>
| <math>\prec, \nprec, \preceq, \npreceq, \precneqq \!</math>
|-
| <source lang="latex" enclose="none">\succ, \nsucc, \succeq, \nsucceq, \succneqq </source>
| <math>\succ, \nsucc, \succeq, \nsucceq, \succneqq \!</math>
|-
| <source lang="latex" enclose="none">\preccurlyeq, \curlyeqprec </source>
| <math>\preccurlyeq, \curlyeqprec \,</math>
|-
| <source lang="latex" enclose="none">\succcurlyeq, \curlyeqsucc </source>
| <math>\succcurlyeq, \curlyeqsucc \,</math>
|-
| <source lang="latex" enclose="none">\precsim, \precnsim, \precapprox, \precnapprox </source>
| <math>\precsim, \precnsim, \precapprox, \precnapprox \,</math>
|-
| <source lang="latex" enclose="none">\succsim, \succnsim, \succapprox, \succnapprox </source>
| <math>\succsim, \succnsim, \succapprox, \succnapprox \,</math>
|-
!colspan="2"|
=== Geometric ===
|-
| <source lang="latex" enclose="none">\parallel, \nparallel, \shortparallel, \nshortparallel </source>
| <math>\parallel, \nparallel, \shortparallel, \nshortparallel \!</math>
|-
| <source lang="latex" enclose="none">\perp, \angle, \sphericalangle, \measuredangle, 45^\circ </source>
| <math>\perp, \angle, \sphericalangle, \measuredangle, 45^\circ \!</math>
|-
| <source lang="latex" enclose="none">\Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar </source>
| <math>\Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar \!</math>
|-
| <source lang="latex" enclose="none">\bigcirc, \triangle \bigtriangleup, \bigtriangledown </source>
| <math>\bigcirc, \triangle \bigtriangleup, \bigtriangledown \!</math>
|-
| <source lang="latex" enclose="none">\vartriangle, \triangledown </source>
| <math>\vartriangle, \triangledown\!</math>
|-
| <source lang="latex" enclose="none">\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright </source>
| <math>\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright \!</math>
|-
!colspan="2"|
=== Logic ===
|-
| <source lang="latex" enclose="none">\forall, \exists, \nexists </source>
| <math>\forall, \exists, \nexists \!</math>
|-
| <source lang="latex" enclose="none">\therefore, \because, \And </source>
| <math>\therefore, \because, \And \!</math>
|-
| <source lang="latex" enclose="none">\or \lor \vee, \curlyvee, \bigvee </source>
| <math>\or \lor \vee, \curlyvee, \bigvee \!</math>
|-
| <source lang="latex" enclose="none">\and \land \wedge, \curlywedge, \bigwedge </source>
| <math>\and \land \wedge, \curlywedge, \bigwedge \!</math>
|-
| <source lang="text" enclose="none">\bar{q}, \bar{abc}, \overline{q}, \overline{abc}, </source><br />
<source lang="latex" enclose="none">\lnot \neg, \not\operatorname{R}, \bot, \top</source>
| <math>\bar{q}, \bar{abc}, \overline{q}, \overline{abc}, \!</math><br />
<math>\lnot \neg, \not\operatorname{R}, \bot, \top \!</math>
|-
| <source lang="latex" enclose="none">\vdash \dashv, \vDash, \Vdash, \models </source>
| <math>\vdash \dashv, \vDash, \Vdash, \models \!</math>
|-
| <source lang="latex" enclose="none">\Vvdash \nvdash \nVdash \nvDash \nVDash </source>
| <math>\Vvdash \nvdash \nVdash \nvDash \nVDash \!</math>
|-
| <source lang="latex" enclose="none">\ulcorner \urcorner \llcorner \lrcorner </source>
| <math>\ulcorner \urcorner \llcorner \lrcorner \,</math>
|-
!colspan="2"|
=== Arrows ===
|-
| <source lang="latex" enclose="none">\Rrightarrow, \Lleftarrow </source>
| <math>\Rrightarrow, \Lleftarrow \!</math>
|-
| <source lang="latex" enclose="none">\Rightarrow, \nRightarrow, \Longrightarrow \implies </source>
| <math>\Rightarrow, \nRightarrow, \Longrightarrow \implies\!</math>
|-
| <source lang="latex" enclose="none">\Leftarrow, \nLeftarrow, \Longleftarrow </source>
| <math>\Leftarrow, \nLeftarrow, \Longleftarrow \!</math>
|-
| <source lang="latex" enclose="none">\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow \iff </source>
| <math>\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow \iff \!</math>
|-
| <source lang="latex" enclose="none">\Uparrow, \Downarrow, \Updownarrow </source>
| <math>\Uparrow, \Downarrow, \Updownarrow \!</math>
|-
| <source lang="latex" enclose="none">\rightarrow \to, \nrightarrow, \longrightarrow </source>
| <math>\rightarrow \to, \nrightarrow, \longrightarrow\!</math>
|-
| <source lang="latex" enclose="none">\leftarrow \gets, \nleftarrow, \longleftarrow </source>
| <math>\leftarrow \gets, \nleftarrow, \longleftarrow\!</math>
|-
| <source lang="latex" enclose="none">\leftrightarrow, \nleftrightarrow, \longleftrightarrow </source>
| <math>\leftrightarrow, \nleftrightarrow, \longleftrightarrow \!</math>
|-
| <source lang="latex" enclose="none">\uparrow, \downarrow, \updownarrow </source>
| <math>\uparrow, \downarrow, \updownarrow \!</math>
|-
| <source lang="latex" enclose="none">\nearrow, \swarrow, \nwarrow, \searrow </source>
| <math>\nearrow, \swarrow, \nwarrow, \searrow \!</math>
|-
| <source lang="latex" enclose="none">\mapsto, \longmapsto </source>
| <math>\mapsto, \longmapsto \!</math>
|-
| <source lang="latex" enclose="none">\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons</source>
| <math>\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons \,\!</math>
|-
| <source lang="latex" enclose="none">\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright</source>
| <math>\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright \,\!</math>
|-
| <source lang="latex" enclose="none">\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft</source>
| <math>\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft \,\!</math>
|-
| <source lang="latex" enclose="none">\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow </source>
| <math>\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow \!</math>
|-
!colspan="2"|
=== Special ===
|-
| <source lang="latex" enclose="none">\amalg \P \S \% \dagger \ddagger \ldots \cdots </source>
| <math>\amalg \P \S \% \dagger \ddagger \ldots \cdots \!</math>
|-
| <source lang="latex" enclose="none">\smile \frown \wr \triangleleft \triangleright</source>
| <math>\smile \frown \wr \triangleleft \triangleright\!</math>
|-
| <source lang="latex" enclose="none">\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp </source>
| <math>\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp \!</math>
|-
!colspan="2"|
=== Unsorted (new stuff) ===
|-
| <source lang="latex" enclose="none">\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes </source>
| <math>\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes \!</math>
|-
| <source lang="latex" enclose="none">\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq </source>
| <math>\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq \!</math>
|-
| <source lang="latex" enclose="none">\intercal \barwedge \veebar \doublebarwedge \between \pitchfork </source>
| <math>\intercal \barwedge \veebar \doublebarwedge \between \pitchfork \!</math>
|-
| <source lang="latex" enclose="none">\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright </source>
| <math>\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright \!</math>
|-
| <source lang="latex" enclose="none">\trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq </source>
| <math>\trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq \!</math>
|}
For a little more semantics on these symbols, see the brief [http://www.math.upenn.edu/tex-stuff/cookbook.pdf TeX Cookbook].