Latex Equations Cheatsheet¶
Functions, Symbols, and Characters¶
Accents and Diacritics¶
| Source | Rendering |
|---|---|
\dot{a}, \ddot{a}, \acute{a}, \grave{a} |
\(\dot{a}, \ddot{a}, \acute{a}, \grave{a}\) |
\check{a}, \breve{a}, \tilde{a}, \bar{a} |
\(\check{a}, \breve{a}, \tilde{a}, \bar{a}\) |
\hat{a}, \widehat{a}, \vec{a} |
\(\hat{a}, \widehat{a}, \vec{a}\) |
Standard Numerical Functions¶
| Source | Rendering |
|---|---|
\exp_a b = a^b, \exp b = e^b, 10^m |
\(\exp_a b = a^b, \exp b = e^b, 10^m\) |
\ln c, \lg d = \log e, \log_{10} f |
\(\ln c, \lg d = \log e, \log_{10} f\) |
\sin a, \cos b, \tan c, \cot d, \sec e, \csc f |
\(\sin a, \cos b, \tan c, \cot d, \sec e, \csc f\) |
\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}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n |
\(\operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n\) |
\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q |
\(\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q\) |
\sgn r, \left\vert s \right\vert |
\(sgn r, \left\vert s \right\vert\) |
\min(x,y), \max(x,y) |
\(\min(x,y), \max(x,y)\) |
Bounds¶
| Source | Rendering |
|---|---|
\min x, \max y, \inf s, \sup t |
\(\min x, \max y, \inf s, \sup t\) |
\lim u, \liminf v, \limsup w |
\(\lim u, \liminf v, \limsup w\) |
\dim p, \deg q, \det m, \ker\phi |
\(\dim p, \deg q, \det m, \ker\phi\) |
Projections¶
| Source | Rendering |
|---|---|
\Pr j, \hom l, \lVert z \rVert, \arg z |
\(\Pr j, \hom l, \lVert z \rVert, \arg z\) |
Differentials and Derivatives¶
| Source | Rendering |
|---|---|
| \(dt, \mathrm{d}t, \partial t, \nabla\psi\) | |
| \(dy/dx, \mathrm{d}y/\mathrm{d}x, \frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x}, \frac{\partial^2}{\partial x_1\partial x_2}y\) | |
| \(\prime, \backprime, f^\prime, f', f'', f^{(3)} \!, \dot y, \ddot y\) |
Letter-like Symbols or Constants¶
| Source | Rendering |
|---|---|
\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar |
\(\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar\) |
\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS, \S, \P, \AA |
\(\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS, \S, \P, \AA\) |
Modular Arithmetic¶
| Source | Rendering |
|---|---|
s_k \equiv 0 \pmod{m} |
\(s_k \equiv 0 \pmod{m}\) |
a \bmod b |
\(a \bmod b\) |
\gcd(m, n), \operatorname{lcm}(m, n) |
\(\gcd(m, n), \operatorname{lcm}(m, n)\) |
\mid, \nmid, \shortmid, \nshortmid |
\(\mid, \nmid, \shortmid, \nshortmid\) |
Radicals¶
| Source | Rendering |
|---|---|
\surd, \sqrt{2}, \sqrt[n]{2}, \sqrt[3]{\frac{x^3+y^3}{2}} |
\(\surd, \sqrt{2}, \sqrt[n]{2}, \sqrt[3]{\frac{x^3+y^3}{2}}\) |
Operators¶
| Source | Rendering |
|---|---|
+, -, \pm, \mp, \dotplus |
\(+, -, \pm, \mp, \dotplus\) |
\times, \div, \divideontimes, /, \backslash |
\(\times, \div, \divideontimes, /, \backslash\) |
\cdot, * \ast, \star, \circ, \bullet |
\(\cdot, * \ast, \star, \circ, \bullet\) |
\boxplus, \boxminus, \boxtimes, \boxdot |
\(\boxplus, \boxminus, \boxtimes, \boxdot\) |
\oplus, \ominus, \otimes, \oslash, \odot |
\(\oplus, \ominus, \otimes, \oslash, \odot\) |
\circleddash, \circledcirc, \circledast |
\(\circleddash, \circledcirc, \circledast\) |
\bigoplus, \bigotimes, \bigodot |
\(\bigoplus, \bigotimes, \bigodot\) |
Sets¶
| Source | Rendering |
|---|---|
\{ \}, \O \empty \emptyset, \varnothing |
\(\{ \}, \O \empty \emptyset, \varnothing\) |
\in, \notin \not\in, \ni, \not\ni |
\(\in, \notin \not\in, \ni, \not\ni\) |
\cap, \Cap, \sqcap, \bigcap |
\(\cap, \Cap, \sqcap, \bigcap\) |
\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus |
\(\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus\) |
\setminus, \smallsetminus, \times |
\(\setminus, \smallsetminus, \times\) |
\subset, \Subset, \sqsubset |
\(\subset, \Subset, \sqsubset\) |
\supset, \Supset, \sqsupset |
\(\supset, \Supset, \sqsupset\) |
\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq |
\(\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq\) |
\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq |
\(\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq\) |
\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq |
\(\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq\) |
\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq |
\(\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq\) |
Relations¶
| Source | Rendering |
|---|---|
=, \ne, \neq, \equiv, \not\equiv |
\(=, \ne, \neq, \equiv, \not\equiv\) |
\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, := |
\(\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, :=\) |
\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong |
\(\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong\) |
\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto |
\(\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto\) |
<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot |
\(<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot\) |
>, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot |
\(>, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot\) |
\le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq |
\(\le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq\) |
\ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq |
\(\ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq\) |
\lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless |
\(\lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless\) |
\leqslant, \nleqslant, \eqslantless |
\(\leqslant, \nleqslant, \eqslantless\) |
\geqslant, \ngeqslant, \eqslantgtr |
\(\geqslant, \ngeqslant, \eqslantgtr\) |
\lesssim, \lnsim, \lessapprox, \lnapprox |
\(\lesssim, \lnsim, \lessapprox, \lnapprox\) |
\gtrsim, \gnsim, \gtrapprox, \gnapprox |
\(\gtrsim, \gnsim, \gtrapprox, \gnapprox\) |
\prec, \nprec, \preceq, \npreceq, \precneqq |
\(\prec, \nprec, \preceq, \npreceq, \precneqq\) |
\succ, \nsucc, \succeq, \nsucceq, \succneqq |
\(\succ, \nsucc, \succeq, \nsucceq, \succneqq\) |
\preccurlyeq, \curlyeqprec |
\(\preccurlyeq, \curlyeqprec\) |
\succcurlyeq, \curlyeqsucc |
\(\succcurlyeq, \curlyeqsucc\) |
\precsim, \precnsim, \precapprox, \precnapprox |
\(\precsim, \precnsim, \precapprox, \precnapprox\) |
\succsim, \succnsim, \succapprox, \succnapprox |
\(\succsim, \succnsim, \succapprox, \succnapprox\) |
Geometric¶
| Source | Rendering |
|---|---|
\parallel, \nparallel, \shortparallel, \nshortparallel |
\(\parallel, \nparallel, \shortparallel, \nshortparallel\) |
\perp, \angle, \sphericalangle, \measuredangle, 45^\circ |
\(\perp, \angle, \sphericalangle, \measuredangle, 45^\circ\) |
\Box, \square, \blacksquare, \diamond, \Diamond, \lozenge, \blacklozenge, \bigstar |
\(\Box, \square, \blacksquare, \diamond, \Diamond, \lozenge, \blacklozenge, \bigstar\) |
\bigcirc, \triangle, \bigtriangleup, \bigtriangledown |
\(\bigcirc, \triangle, \bigtriangleup, \bigtriangledown\) |
\vartriangle, \triangledown |
\(\vartriangle, \triangledown\) |
\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright |
\(\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright\) |
Logic¶
| Source | Rendering |
|---|---|
\forall, \exists, \nexists |
\(\forall, \exists, \nexists\) |
\therefore, \because, \And |
\(\therefore, \because, \And\) |
\lor \vee, \curlyvee, \bigvee don't use \or which is now deprecated |
|
| \(\lor, \vee, \curlyvee, \bigvee\) | |
\land \wedge, \curlywedge, \bigwedge don't use \and which is now deprecated |
\(\land, \wedge, \curlywedge, \bigwedge\) |
\bar{q}, \bar{abc}, \overline{q}, \overline{abc}, \lnot \neg, \not\operatorname{R}, \bot, \top |
\(\bar{q}, \bar{abc}, \overline{q}, \overline{abc}, \lnot \neg, \not\operatorname{R}, \bot, \top\) |
\vdash \dashv, \vDash, \Vdash, \models |
\(\vdash, \dashv, \vDash, \Vdash, \models\) |
\Vvdash \nvdash \nVdash \nvDash \nVDash |
\(\Vvdash, \nvdash, \nVdash, \nvDash, \nVDash\) |
\ulcorner \urcorner \llcorner \lrcorner |
\(\ulcorner \urcorner \llcorner \lrcorner\) |
Arrows¶
| Source | Rendering |
|---|---|
\Rrightarrow, \Lleftarrow |
\(\Rrightarrow, \Lleftarrow\) |
\Rightarrow, \nRightarrow, \Longrightarrow, \implies |
\(\Rightarrow, \nRightarrow, \Longrightarrow, \implies\) |
\Leftarrow, \nLeftarrow, \Longleftarrow |
\(\Leftarrow, \nLeftarrow, \Longleftarrow\) |
\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow, \iff |
\(\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow, \iff\) |
\Uparrow, \Downarrow, \Updownarrow |
\(\Uparrow, \Downarrow, \Updownarrow\) |
\rightarrow \to, \nrightarrow, \longrightarrow |
\(\rightarrow \to, \nrightarrow, \longrightarrow\) |
\leftarrow \gets, \nleftarrow, \longleftarrow |
\(\leftarrow \gets, \nleftarrow, \longleftarrow\) |
\leftrightarrow, \nleftrightarrow, \longleftrightarrow |
\(\leftrightarrow, \nleftrightarrow, \longleftrightarrow\) |
\uparrow, \downarrow, \updownarrow |
\(\uparrow, \downarrow, \updownarrow\) |
\nearrow, \swarrow, \nwarrow, \searrow |
\(\nearrow, \swarrow, \nwarrow, \searrow\) |
\mapsto, \longmapsto |
\(\mapsto, \longmapsto\) |
\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons |
\(\rightharpoonup, \rightharpoondown, \leftharpoonup, \leftharpoondown, \upharpoonleft, \upharpoonright, \downharpoonleft, \downharpoonright, \rightleftharpoons, \leftrightharpoons\) |
\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright |
\(\curvearrowleft, \circlearrowleft, \Lsh, \upuparrows, \rightrightarrows, \rightleftarrows, \rightarrowtail, \looparrowright\) |
\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft |
\(\curvearrowright, \circlearrowright, \Rsh, \downdownarrows, \leftleftarrows, \leftrightarrows, \leftarrowtail, \looparrowleft\) |
\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow |
\(\hookrightarrow, \hookleftarrow, \multimap, \leftrightsquigarrow, \rightsquigarrow, \twoheadrightarrow, \twoheadleftarrow\) |
Special¶
| Source | Rendering |
|---|---|
\amalg \P \S \% \dagger \ddagger \ldots \cdots |
\(\amalg \P \S \% \dagger \ddagger \ldots \cdots\) |
\smile \frown \wr \triangleleft \triangleright |
\(\smile \frown \wr \triangleleft \triangleright\) |
\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp |
\(\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp\) |
Unsorted (new stuff)¶
| Source | Rendering |
|---|---|
\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes |
\(\diagup, \diagdown, \centerdot, \ltimes, \rtimes, \leftthreetimes, \rightthreetimes\) |
\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq |
\(\eqcirc, \circeq, \triangleq, \bumpeq, \Bumpeq, \doteqdot, \risingdotseq, \fallingdotseq\) |
\intercal \barwedge \veebar \doublebarwedge \between \pitchfork |
\(\intercal, \barwedge, \veebar, \doublebarwedge, \between, \pitchfork\) |
\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright |
\(\vartriangleleft, \ntriangleleft, \vartriangleright, \ntriangleright\) |
\trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq |
\(\trianglelefteq, \ntrianglelefteq, \trianglerighteq, \ntrianglerighteq\) |
Expressions¶
| Source | Rendering |
|---|---|
a^2, a^{x+3} |
\(a^2, a^{x+3}\) |
a_2 |
\(a_2\) |
10^{30} a^{2+2} |
\(10^{30} a^{2+2}\) |
a_{i,j} b_{f'} |
\(a_{i,j} b_{f'}\) |
x_2^3 |
\(x_2^3\) |
{x_2}^3 |
\({x_2}^3\) |
10^{10^{8}} |
\(10^{10^{8}}\) |
\sideset{_1^2}{_3^4}\prod_a^b |
\(\sideset{_1^2}{_3^4}\prod_a^b\) |
{}_1^2\!\Omega_3^4 |
\({}_1^2\!\Omega_3^4\) |
\overset{\alpha}{\omega} |
\(\overset{\alpha}{\omega}\) |
\underset{\alpha}{\omega} |
\(\underset{\alpha}{\omega}\) |
\overset{\alpha}{\underset{\gamma}{\omega}} |
\(\overset{\alpha}{\underset{\gamma}{\omega}}\) |
\stackrel{\alpha}{\omega} |
\(\stackrel{\alpha}{\omega}\) |
x', y'', f', f'' |
\(x', y'', f', f''\) |
x^\prime, y^{\prime\prime} |
\(x^\prime, y^{\prime\prime}\) |
\dot{x}, \ddot{x} |
\(\dot{x}, \ddot{x}\) |
\hat a \bar b \vec c |
\(\hat a \bar b \vec c\) |
\overrightarrow{a b} \overleftarrow{c d} \widehat{d e f} |
\(\overrightarrow{a b} \overleftarrow{c d} \widehat{d e f}\) |
\overline{g h i} \underline{j k l} |
\(\overline{g h i} \ \underline{j k l}\) |
\overset{\frown} {AB} |
\(\overset{\frown} {AB}\) |
A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C |
\(A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C\) |
\overbrace{ 1+2+\cdots+100 }^{5050} |
\(\overbrace{ 1+2+\cdots+100 }^{5050}\) |
\underbrace{ a+b+\cdots+z }_{26} |
\(\underbrace{ a+b+\cdots+z }_{26}\) |
\sum_{k=1}^N k^2 |
\(\sum_{k=1}^N k^2\) |
\textstyle \sum_{k=1}^N k^2 |
\(\textstyle \sum_{k=1}^N k^2\) |
\frac{\sum_{k=1}^N k^2}{a} |
\(\frac{\sum_{k=1}^N k^2}{a}\) |
\frac{\displaystyle \sum_{k=1}^N k^2}{a} |
\(\frac{\displaystyle \sum_{k=1}^N k^2}{a}\) |
\frac{\sum\limits^{^N}_{k=1} k^2}{a} |
\(\frac{\sum\limits^{^N}_{k=1} k^2}{a}\) |
\prod_{i=1}^N x_i |
\(\prod_{i=1}^N x_i\) |
\textstyle \prod_{i=1}^N x_i |
\(\textstyle \prod_{i=1}^N x_i\) |
\coprod_{i=1}^N x_i |
\(\coprod_{i=1}^N x_i\) |
\textstyle \coprod_{i=1}^N x_i |
\(\textstyle \coprod_{i=1}^N x_i\) |
\lim_{n \to \infty}x_n |
\(\lim_{n \to \infty}x_n\) |
\textstyle \lim_{n \to \infty}x_n |
\(\textstyle \lim_{n \to \infty}x_n\) |
\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx |
\(\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx\) |
\int_{1}^{3}\frac{e^3/x}{x^2}\, dx |
\(\int_{1}^{3}\frac{e^3/x}{x^2}\, dx\) |
\textstyle \int\limits_{-N}^{N} e^x dx |
\(\textstyle \int\limits_{-N}^{N} e^x dx\) |
\textstyle \int_{-N}^{N} e^x dx |
\(\textstyle \int_{-N}^{N} e^x dx\) |
\iint\limits_D dx\,dy |
\(\iint\limits_D dx\,dy\) |
\iiint\limits_E dx\,dy\,dz |
\(\iiint\limits_E dx\,dy\,dz\) |
\iiiint\limits_F dx\,dy\,dz\,dt |
\(\iiiint\limits_F dx\,dy\,dz\,dt\) |
\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy |
\(\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy\) |
\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy |
\(\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy\) |
\bigcap_{i=1}^n E_i |
\(\bigcap_{i=1}^n E_i\) |
\bigcup_{i=1}^n E_i |
\(\bigcup_{i=1}^n E_i\) |
Display Attribute¶
Fractions, Matrices, Multilines¶
| Source | Rendering |
|---|---|
\frac{2}{4}=0.5 or {2 \over 4}=0.5 |
\(\frac{2}{4}=0.5\) |
\tfrac{2}{4} = 0.5 |
\(\tfrac{2}{4} = 0.5\) |
\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a |
\(\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a\) |
\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a |
\(\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a\) |
\cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2} |
\(\cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2}\) |
\binom{n}{k} |
\(\binom{n}{k}\) |
\tbinom{n}{k} |
\(\tbinom{n}{k}\) |
\dbinom{n}{k} |
\(\dbinom{n}{k}\) |
\begin{matrix} x & y \\ z & v \end{matrix} |
\(\begin{matrix} x & y \\ z & v \end{matrix}\) |
\begin{vmatrix} x & y \\ z & v \end{vmatrix} |
\(\begin{vmatrix} x & y \\ z & v \end{vmatrix}\) |
\begin{Vmatrix} x & y \\ z & v \end{Vmatrix} |
\(\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}\) |
\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix} |
\(\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}\) |
\begin{Bmatrix} x & y \\ z & v \end{Bmatrix} |
\(\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}\) |
\begin{pmatrix} x & y \\ z & v \end{pmatrix} |
\(\begin{pmatrix} x & y \\ z & v \end{pmatrix}\) |
\bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr) |
\(\bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr)\) |
f(n) = \begin{cases} n/2, & \text{if }n\text{ is even} \\ 3n+1, & \text{if }n\text{ is odd} \end{cases} |
\(f(n) = \begin{cases} n/2, & \text{if }n\text{ is even} \\ 3n+1, & \text{if }n\text{ is odd} \end{cases}\) |
\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases} |
\(\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}\) |
\begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align} |
\(\begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align}\) |
\begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \\ \end{alignat} |
\(\begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \\ \end{alignat}\) |
\begin{align} f(a,b) & = (a+b)^2 && = (a+b)(a+b) \\ & = a^2+ab+ba+b^2 && = a^2+2ab+b^2 \\ \end{align} |
\(\begin{align} f(a,b) & = (a+b)^2 && = (a+b)(a+b) \\ & = a^2+ab+ba+b^2 && = a^2+2ab+b^2 \\ \end{align}\) |
\begin{alignat}{3} f(a,b) & = (a+b)^2 && = (a+b)(a+b) \\ & = a^2+ab+ba+b^2 && = a^2+2ab+b^2 \\ \end{alignat} |
\(\begin{alignat}{3} f(a,b) & = (a+b)^2 && = (a+b)(a+b) \\ & = a^2+ab+ba+b^2 && = a^2+2ab+b^2 \\ \end{alignat}\) |
\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array} |
\(\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}\) |
\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array} |
\(\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}\) |
\begin{alignat}{4} F:\; && C(X) && \;\to\; & C(X) \\ && g && \;\mapsto\; & g^2 \end{alignat} |
\(\begin{alignat}{4} F:\; && C(X) && \;\to\; & C(X) \\ && g && \;\mapsto\; & g^2 \end{alignat}\) |
\begin{alignat}{4} F:\; && C(X) && \;\to\; && C(X) \\ && g && \;\mapsto\; && g^2 \end{alignat} |
\(\begin{alignat}{4} F:\; && C(X) && \;\to\; && C(X) \\ && g && \;\mapsto\; && g^2 \end{alignat}\) |
\begin{array}{|c|c|c|} a & b & S \\ \hline 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{array} |
\(\begin{array}{\|c\|c\|c\|} a & b & S \\ \hline 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{array}\) |
Parenthesizing Big Expressions, Brackets, Bars¶
| Source | Rendering |
|---|---|
\left ( \frac{a}{b} \right ) |
\(\left ( \frac{a}{b} \right )\) |
\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack |
\(\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack\) |
\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace |
\(\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace\) |
\left \langle \frac{a}{b} \right \rangle |
\(\left \langle \frac{a}{b} \right \rangle\) |
\left | \frac{a}{b} \right \vert \quad \left \Vert \frac{c}{d} \right \| |
$\left |
\left \lfloor \frac{a}{b} \right \rfloor \quad \left \lceil \frac{c}{d} \right \rceil |
\(\left \lfloor \frac{a}{b} \right \rfloor \quad \left \lceil \frac{c}{d} \right \rceil\) |
\left / \frac{a}{b} \right \backslash |
\(\left / \frac{a}{b} \right \backslash\) |
\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow |
\(\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow\) |
\left [ 0,1 \right ) \left \langle \psi \right | |
\(\left [ 0,1 \right )\) |
\left . \frac{A}{B} \right \} \to X |
\(\left . \frac{A}{B} \right \} \to X\) |
( \bigl( \Bigl( \biggl( \Biggl( \dots \Biggr] \biggr] \Bigr] \bigr] ] |
\(( \bigl( \Bigl( \biggl( \Biggl( \dots \Biggr] \biggr] \Bigr] \bigr] ]\) |
\{ \bigl\{ \Bigl\{ \biggl\{ \Biggl\{ \dots \Biggr\rangle \biggr\rangle \Bigr\rangle \bigr\rangle \rangle |
\(\{ \bigl\{ \Bigl\{ \biggl\{ \Biggl\{ \dots \Biggr\rangle \biggr\rangle \Bigr\rangle \bigr\rangle \rangle\) |
\| \big\| \Big\| \bigg\| \Bigg\| \dots \Bigg\| \bigg\| \Big\| \big\| \| |
\(\| \big\| \Big\| \bigg\| \Bigg\| \dots \Bigg\| \bigg\| \Big\| \big\| \|\) |
\lfloor \bigl\lfloor \Bigl\lfloor \biggl\lfloor \Biggl\lfloor \dots \Biggr\rceil \biggr\rceil \Bigr\rceil \bigr\rceil \ceil |
\(\lfloor \bigl\lfloor \Bigl\lfloor \biggl\lfloor \Biggl\lfloor \dots \Biggr\rceil \biggr\rceil \Bigr\rceil \bigr\rceil \rceil\) |
\uparrow \big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow \Downarrow |
\(\uparrow \big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow \Downarrow\) |
\updownarrow \big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow \Updownarrow |
\(\updownarrow \big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow \Updownarrow\) |
/ \big/ \Big/ \bigg/ \Bigg/ \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash \backslash |
\(/ \big/ \Big/ \bigg/ \Bigg/ \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash \backslash\) |
Alphabets and Typefaces¶
Greek Alphabet¶
| Source | Rendering |
|---|---|
\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta |
\(\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta\) |
\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi |
\(\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi\) |
\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega |
\(\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega\) |
\alpha \beta \gamma \delta \epsilon \zeta \eta \theta |
\(\alpha \beta \gamma \delta \epsilon \zeta \eta \theta\) |
\iota \kappa \lambda \mu \nu \xi \omicron \pi |
\(\iota \kappa \lambda \mu \nu \xi \omicron \pi\) |
\rho \sigma \tau \upsilon \phi \chi \psi \omega |
\(\rho \sigma \tau \upsilon \phi \chi \psi \omega\) |
\varGamma \varDelta \varTheta \varLambda \varXi \varPi \varSigma \varPhi \varUpsilon \varOmega |
\(\varGamma \varDelta \varTheta \varLambda \varXi \varPi \varSigma \varPhi \varUpsilon \varOmega\) |
\varepsilon \digamma \varkappa \varpi \varrho \varsigma \vartheta \varphi |
\(\varepsilon \digamma \varkappa \varpi \varrho \varsigma \vartheta \varphi\) |
Hebrew Symbols¶
| Source | Rendering |
|---|---|
\aleph \beth \gimel \daleth |
\(\aleph \beth \gimel \daleth\) |
Blackboard Bold/Scripts¶
| Source | Rendering |
|---|---|
\mathbb{ABCDEFGHI} |
\(\mathbb{ABCDEFGHI}\) |
\mathbb{JKLMNOPQR} |
\(\mathbb{JKLMNOPQR}\) |
\mathbb{STUVWXYZ} |
\(\mathbb{STUVWXYZ}\) |
Boldface¶
| Source | Rendering |
|---|---|
\mathbf{ABCDEFGHI} |
\(\mathbf{ABCDEFGHI}\) |
\mathbf{JKLMNOPQR} |
\(\mathbf{JKLMNOPQR}\) |
\mathbf{STUVWXYZ} |
\(\mathbf{STUVWXYZ}\) |
\mathbf{abcdefghijklm} |
\(\mathbf{abcdefghijklm}\) |
\mathbf{nopqrstuvwxyz} |
\(\mathbf{nopqrstuvwxyz}\) |
\mathbf{0123456789} |
\(\mathbf{0123456789}\) |
Boldface (Greek)¶
| Source | Rendering |
|---|---|
\boldsymbol{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta} |
\(\boldsymbol{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}\) |
\boldsymbol{\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi} |
\(\boldsymbol{\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi}\) |
\boldsymbol{\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega} |
\(\boldsymbol{\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}\) |
\boldsymbol{\alpha \beta \gamma \delta \epsilon \zeta \eta \theta} |
\(\boldsymbol{\alpha \beta \gamma \delta \epsilon \zeta \eta \theta}\) |
\boldsymbol{\iota \kappa \lambda \mu \nu \xi \omicron \pi} |
\(\boldsymbol{\iota \kappa \lambda \mu \nu \xi \omicron \pi}\) |
\boldsymbol{\rho \sigma \tau \upsilon \phi \chi \psi \omega} |
\(\boldsymbol{\rho \sigma \tau \upsilon \phi \chi \psi \omega}\) |
\boldsymbol{\varepsilon\digamma\varkappa\varpi} |
\(\boldsymbol{\varepsilon\digamma\varkappa\varpi}\) |
\boldsymbol{\varrho\varsigma\vartheta\varphi} |
\(\boldsymbol{\varrho\varsigma\vartheta\varphi}\) |
Italics (default for Latin alphabet)¶
| Source | Rendering |
|---|---|
\mathit{0123456789} |
\(\mathit{0123456789}\) |
Greek Italics (default for lowercase Greek)¶
| Source | Rendering |
|---|---|
\mathit{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta} |
\(\mathit{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}\) |
\mathit{\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi} |
\(\mathit{\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi}\) |
\mathit{\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega} |
\(\mathit{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega}\) |
Greek Uppercase Boldface Italics¶
| Source | Rendering |
|---|---|
\boldsymbol{\varGamma \varDelta \varTheta \varLambda} |
\(\boldsymbol{\varGamma \varDelta \varTheta \varLambda}\) |
\boldsymbol{\varXi \varPi \varSigma \varUpsilon \varOmega} |
\(\boldsymbol{\varXi \varPi \varSigma \varUpsilon \varOmega}\) |
Roman Typeface¶
| Source | Rendering |
|---|---|
\mathrm{ABCDEFGHI} |
\(\mathrm{ABCDEFGHI}\) |
\mathrm{JKLMNOPQR} |
\(\mathrm{JKLMNOPQR}\) |
\mathrm{STUVWXYZ} |
\(\mathrm{STUVWXYZ}\) |
\mathrm{abcdefghijklm} |
\(\mathrm{abcdefghijklm}\) |
\mathrm{nopqrstuvwxyz} |
\(\mathrm{nopqrstuvwxyz}\) |
\mathrm{0123456789} |
\(\mathrm{0123456789}\) |
Sans Serif¶
| Source | Rendering |
|---|---|
\mathsf{ABCDEFGHI} |
\(\mathsf{ABCDEFGHI}\) |
\mathsf{JKLMNOPQR} |
\(\mathsf{JKLMNOPQR}\) |
\mathsf{STUVWXYZ} |
\(\mathsf{STUVWXYZ}\) |
\mathsf{abcdefghijklm} |
\(\mathsf{abcdefghijklm}\) |
\mathsf{nopqrstuvwxyz} |
\(\mathsf{nopqrstuvwxyz}\) |
\mathsf{0123456789} |
\(\mathsf{0123456789}\) |
Sans Serif Greek (capital only)¶
| Source | Rendering |
|---|---|
\mathsf{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta} |
\(\mathsf{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}\) |
\mathsf{\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi} |
\(\mathsf{\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi}\) |
\mathsf{\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega} |
\(\mathsf{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}\) |
Calligraphy/Script¶
| Source | Rendering |
|---|---|
\mathcal{ABCDEFGHI} |
\(\mathcal{ABCDEFGHI}\) |
\mathcal{JKLMNOPQR} |
\(\mathcal{JKLMNOPQR}\) |
\mathcal{STUVWXYZ} |
\(\mathcal{STUVWXYZ}\) |
\mathcal{abcdefghi} |
\(\mathcal{abcdefghi}\) |
\mathcal{jklmnopqr} |
\(\mathcal{jklmnopqr}\) |
\mathcal{stuvwxyz} |
\(\mathcal{stuvwxyz}\) |
Fraktur Typeface¶
| Source | Rendering |
|---|---|
\mathfrak{ABCDEFGHI} |
\(\mathfrak{ABCDEFGHI}\) |
\mathfrak{JKLMNOPQR} |
\(\mathfrak{JKLMNOPQR}\) |
\mathfrak{STUVWXYZ} |
\(\mathfrak{STUVWXYZ}\) |
\mathfrak{abcdefghijklm} |
\(\mathfrak{abcdefghijklm}\) |
\mathfrak{nopqrstuvwxyz} |
\(\mathfrak{nopqrstuvwxyz}\) |
\mathfrak{0123456789} |
\(\mathfrak{0123456789}\) |
Small Scriptstyle Text¶
| Source | Rendering |
|---|---|
{\scriptstyle\text{abcdefghijklm}} |
\({\scriptstyle\text{abcdefghijklm}}\) |
Mixed Text Faces¶
| Source | Rendering |
|---|---|
x y z |
\(x y z\) |
\text{x y z} |
\(\text{x y z}\) |
\text{if} n \text{is even} |
\(\text{if} n \text{is even}\) |
\text{if }n\text{ is even} |
\(\text{if }n\text{ is even}\) |
\text{if}~n\ \text{is even} |
\(\text{if}~n\ \text{is even}\) |
Color¶
Equations can use color with the \color command. For example:
-{\color{Blue}x^2}+{\color{Orange}2x}-{\color{LimeGreen}1}
\[
{\color{Blue}x^2}+{\color{Orange}2x}-{\color{LimeGreen}1}
\]
x_{1,2}=\frac{{\color{Blue}-b}\pm\sqrt{\color{Red}b^2-4ac}}{\color{Green}2a }
\[
x_{1,2}=\frac{{\color{Blue}-b}\pm\sqrt{\color{Red}b^2-4ac}}{\color{Green}2a}
\]
There are several alternate notations styles
{\color{Blue}x^2}+{\color{Orange}2x}-{\color{LimeGreen}1}works with both texvc and MathJax
\[
{\color{Blue}x^2}+{\color{Orange}2x}-{\color{LimeGreen}1}
\]
\color{Blue}x^2\color{Black}+\color{Orange}2x\color{Black}-\color{LimeGreen}1works with both texvc and MathJax
\[
\color{Blue}x^2\color{Black}+\color{Orange}2x\color{Black}-\color{LimeGreen}1
\]
\color{Blue}{x^2}+\color{Orange}{2x}-\color{LimeGreen}{1}only works with MathJax
\[
\color{Blue}{x^2}+\color{Orange}{2x}-\color{LimeGreen}{1}
\]
Formatting Issures¶
Spacing¶
| Source | Rendering |
|---|---|
a \qquad b |
\(a \qquad b\) |
a \quad b |
\(a \quad b\) |
a\ b |
\(a\ b\) |
a \text{ } b |
\(a \text{ } b\) |
a\;b |
\(a\;b\) |
a\,b |
\(a\,b\) |
ab |
\(ab\) |
a b |
\(a b\) |
\mathit{ab} |
\(\mathit{ab}\) |
a\!b |
\(a\!b\) |