====== Math formulas ====== You can include math formulas inside your wiki pages, like this: <math block>a^2 + b^2 = c^2</math> <math block>f(x) = \int_{-\infty}^\infty \hat f(\xi)\,e^{2 \pi i \xi x} \,d\xi</math> or even inline (inside the body of your text, like so: We know <math>\frac {1}{0}</math> is indeterminant. ===== Syntax ===== The general syntax for including a math formula is: ''%%<math>%%//LaTex math formula//%%</math>%%'' for inline formulas, and: ''%%<math block>%%//LaTex math formula//%%</math>%%'' for block formulas. The syntax for math formulas inside the ''%%<math>%%...%%</math>%%'' tag is [[https://www.latex-project.org/|LaTeX]]. ===== Supported LaTeX commands ===== To render LaTeX math formulas, Polifonic uses the excellent [[http://khan.github.io/KaTeX/|KaTex]] library, so the LaTeX commands supported are those supported by KaTeX. The list of supported commands is available [[https://github.com/Khan/KaTeX/wiki/Function-Support-in-KaTeX|here]]. Please note that katex supports a smaller set of features than MathJax. Comparison between the 2 libraries can be found [[http://www.intmath.com/cg5/katex-mathjax-comparison.php|here]]. <alert warning>Please note that Polifonic is neither related to, nor endorsed by, KaTex, MathJax nor LaTex.</alert> ===== Examples ===== <col sm:6> %%<math block>c = \pm\sqrt{a^2 + b^2}</math>%% </col> <col sm:6> <math block>c = \pm\sqrt{a^2 + b^2}</math> </col> <col sm:6> %%<math block>\forall x \in X, \quad \exists y \leq \epsilon</math>%% </col> <col sm:6> <math block>\forall x \in X, \quad \exists y \leq \epsilon</math> </col> <col sm:6> %%<math block>\cos (2\theta) = \cos^2 \theta - \sin^2 \theta</math>%% </col> <col sm:6> <math block>\cos (2\theta) = \cos^2 \theta - \sin^2 \theta</math> </col> <col sm:6> %%<math block>\lim_{x \to \infty} \exp(-x) = 0</math>%% </col> <col sm:6> <math block>\lim_{x \to \infty} \exp(-x) = 0</math> </col> <col sm:6> %%<math block>\frac{3}{7}</math>%% </col> <col sm:6> <math block>\frac{3}{7}</math> </col> <col sm:6> %%Take <math>\frac{1}{2}</math> cup of sugar, ...%% %%<math block>3\times\frac{1}{2}=1\frac{1}{2}</math><math block>\frac{3}{7}</math>%% </col> <col sm:6> Take <math>\frac{1}{2}</math> cup of sugar, ... <math block>3\times\frac{1}{2}=1\frac{1}{2}</math> </col> <col sm:6> %%Take <math>{}^1/_2</math> cup of sugar, ...%% %%<math block>3\times{}^1/_2=1{}^1/_2</math>%% </col> <col sm:6> Take <math>{}^1/_2</math> cup of sugar, ... <math block>3\times{}^1/_2=1{}^1/_2</math> </col> <col sm:6> %%<math block> x = a_0 + \frac{1}{a_1 + \frac{1}{a_2 + \frac{1}{a_3 + \frac{1}{a_4} } } } </math>%% </col> <col sm:6> <math block> x = a_0 + \frac{1}{a_1 + \frac{1}{a_2 + \frac{1}{a_3 + \frac{1}{a_4} } } } </math> </col> ===== Other examples ===== The examples below are all taken from the [[http://www.intmath.com/cg5/katex-mathjax-comparison.php|Katex and MathJax comparison demo]] page. ==== Repeating fractions ==== <math block>\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\cdots} } } }</math> ==== Summation notation ==== <math block>\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)</math> ==== Sum of a series ==== <math block>\displaystyle\sum_{i=1}^{k+1}i</math> <math block>\displaystyle= \left(\sum_{i=1}^{k}i\right) +(k+1)</math> <math block>\displaystyle= \frac{k(k+1)}{2}+k+1</math> <math block>\displaystyle= \frac{k(k+1)+2(k+1)}{2}</math> <math block>\displaystyle= \frac{(k+1)(k+2)}{2}</math> ==== Product notation ==== <math block> \displaystyle 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \displaystyle \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \displaystyle\text{ for }\lvert q\rvert < 1. </math> ==== Inline math ==== And here is some in-line math: <math>k_{n+1} = n^2 + k_n^2 - k_{n-1}</math>, followed by some more text. ==== Greek letters ==== <math block>\Gamma\ \Delta\ \Theta\ \Lambda\ \Xi\ \Pi\ \Sigma\ \Upsilon\ \Phi\ \Psi\ \Omega</math> <math block>\alpha\ \beta\ \gamma\ \delta\ \epsilon\ \zeta\ \eta\ \theta\ \iota\ \kappa\ \lambda\ \mu\ \nu\ \xi \ \omicron\ \pi\ \rho\ \sigma\ \tau\ \upsilon\ \phi\ \chi\ \psi\ \omega\ \varepsilon\ \vartheta\ \varpi\ \varrho\ \varsigma\ \varphi</math> ==== Arrows ==== <math block>\gets\ \to\ \leftarrow\ \rightarrow\ \uparrow\ \Uparrow\ \downarrow\ \Downarrow\ \updownarrow\ \Updownarrow </math> <math block>\Leftarrow\ \Rightarrow\ \leftrightarrow\ \Leftrightarrow\ \mapsto\ \hookleftarrow</math> <math block>\leftharpoonup\ \leftharpoondown\ \rightleftharpoons\ \longleftarrow\ \Longleftarrow\ \longrightarrow</math> <math block>\Longrightarrow\ \longleftrightarrow\ \Longleftrightarrow\ \longmapsto\ \hookrightarrow\ \rightharpoonup</math> <math block>\rightharpoondown\ \leadsto\ \nearrow\ \searrow\ \swarrow\ \nwarrow</math> ==== Symbols ==== <math block>\surd\ \barwedge\ \veebar\ \odot\ \oplus\ \otimes\ \oslash\ \circledcirc\ \boxdot\ \bigtriangleup</math> <math block>\bigtriangledown\ \dagger\ \diamond\ \star\ \triangleleft\ \triangleright\ \angle\ \infty\ \prime\ \triangle</math> ==== Calculus ==== <math block>\int u \frac{dv}{dx}\,dx=uv-\int \frac{du}{dx}v\,dx</math> <math block>f(x) = \int_{-\infty}^\infty \hat f(\xi)\,e^{2 \pi i \xi x}</math> <math block>\oint \vec{F} \cdot d\vec{s}=0</math> ==== Lorenz equations ==== Alignment is not supported by KaTex. <math block>\dot{x} = \sigma(y-x)</math> <math block>\dot{y} = \rho x - y - xz</math> <math block>\dot{z} = -\beta z + xy</math> ==== Cross products ==== === Not working quite well in KaTex === <math block> \mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \end{vmatrix} </math> ==== Accents ==== <math block>\hat{x}\ \vec{x}\ \ddot{x} </math> === Not working in Katex ==== <math block>\overrightarrow{AB}</math> <math block>A\underset{0^{\circ}C }{\overset{100^{\circ}C}{\rightleftarrows}}B</math> ==== Stretchy brackets ==== <math block>\left(\frac{x^2}{y^3}\right)</math> ==== Evaluation at limits ==== <math block>\left.\frac{x^3}{3}\right|_0^1</math> ==== Case definitions ==== <math block>f(n) = \begin{cases} \frac{n}{2}, & \text{if } n\text{ is even} \\ 3n+1, & \text{if } n\text{ is odd} \end{cases}</math> ==== Maxwell's equations ==== <math block> \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} = \frac{4\pi}{c}\vec{\mathbf{j}}</math> <math block> \nabla \cdot \vec{\mathbf{E}} = 4 \pi \rho </math> <math block> \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} = \vec{\mathbf{0}} </math> <math block> \nabla \cdot \vec{\mathbf{B}} = 0 </math> ==== Statistics ==== Definition of combination: <math block>\frac{n!}{k!(n-k)!} = {^n}C_k</math> <math block>{n \choose k}</math> ==== Fractions on fractions ==== <math block>\frac{\frac{1}{x}+\frac{1}{y}}{y-z}</math> ==== n-th root ==== <math block>\sqrt[n]{1+x+x^2+x^3+\ldots}</math> ==== Matrices ==== <math block>\begin{pmatrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33} \end{pmatrix}</math> <math block> \begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix} </math> ==== Punctuation ==== <math block>f(x) = \sqrt{1+x} \quad (x \ge -1)</math> <math block>f(x) \sim x^2 \quad (x\to\infty)</math> <math block>f(x) = \sqrt{1+x}, \quad x \ge -1</math> <math block>f(x) \sim x^2, \quad x\to\infty</math> <math block></math> <math block></math> <math block></math>