# (Older Version) MathML Browser Test (Presentation Markup)

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Formula Image of TeX rendering
(MiKTeX 2.9)
Image of MathML rendering
(Firefox 4.0 with STIX Fonts)
MathML rendering
(by this browser)
Axiom of
power set
$\forall A\exists P\forall B\phantom{\rule{thinmathspace}{0ex}}\left[B\in P⟺\forall C\phantom{\rule{thinmathspace}{0ex}}\left(C\in B⇒C\in A\right)\right]$
De Morgan's law
Formula
$x=\frac{-b±\sqrt{{b}^{2}-4ac}}{2a}$
Binomial
Coefficient
$C\left(n,k\right)={C}_{k}^{n}={}_{n}C_{k}=\left(\genfrac{}{}{0}{}{n}{k}\right)=\frac{n!}{k!\left(n-k\right)!}$
Sophomore's
dream
${\int }_{0}^{1}{x}^{x}dx=\sum _{n=1}^{\infty }{\left(-1\right)}^{n+1}{n}^{-n}$
Divergence $\nabla ·\stackrel{\to }{v}=\frac{\partial {v}_{x}}{\partial x}+\frac{\partial {v}_{y}}{\partial y}+\frac{\partial {v}_{z}}{\partial z}$
Complex
number
$c=\stackrel{\text{complex number}}{\overbrace{\underset{\text{real}}{\underbrace{\phantom{\rule{1.2em}{0ex}}a\phantom{\rule{1.2em}{0ex}}}}+\underset{\text{imaginary}}{\underbrace{\phantom{\rule{1em}{0ex}}bi\phantom{\rule{1em}{0ex}}}}}}$
Moore
determinant
$M=\left[\begin{array}{cccc}{\alpha }_{1}& {\alpha }_{1}^{q}& \dots & {\alpha }_{1}^{{q}^{n-1}}\\ {\alpha }_{2}& {\alpha }_{2}^{q}& \dots & {\alpha }_{2}^{{q}^{n-1}}\\ ⋮& ⋮& \ddots & ⋮\\ {\alpha }_{m}& {\alpha }_{m}^{q}& \dots & {\alpha }_{m}^{{q}^{n-1}}\end{array}\right]$
Sphere
volume
Spherical coordinates derivation of the volume of a sphere $\left(\frac{4}{3}\pi {R}^{3}\right)$ .
The formula $S$ for a sphere of radius $R$ in spherical coordinates is:
$S=\left\{0\le \varphi \le 2\pi ,0\le \theta \le \pi ,0\le \rho \le R\right\}$
$\begin{array}{rl}\text{Volume}& =\underset{S}{\iiint }{\rho }^{2}sin\theta d\rho d\theta d\varphi \\ & ={\int }_{0}^{2\pi }d\varphi {\int }_{0}^{\pi }sin\theta d\theta {\int }_{0}^{R}{\rho }^{2}d\rho \\ & =\phantom{\rule{mediummathspace}{0ex}}\varphi \phantom{\rule{verythinmathspace}{0ex}}{|}_{\phantom{\rule{verythinmathspace}{0ex}}0}^{\phantom{\rule{verythinmathspace}{0ex}}2\pi }\left(-\mathrm{cos}\theta \right)\phantom{\rule{verythinmathspace}{0ex}}{|}_{\phantom{\rule{verythinmathspace}{0ex}}0}^{\phantom{\rule{verythinmathspace}{0ex}}\pi }\phantom{\rule{veryverythickmathspace}{0ex}}\frac{1}{3}{\rho }^{3}\phantom{\rule{verythinmathspace}{0ex}}{|}_{\phantom{\rule{verythinmathspace}{0ex}}0}^{\phantom{\rule{verythinmathspace}{0ex}}R}\\ & =\phantom{\rule{mediummathspace}{0ex}}2\pi ×2×\frac{1}{3}{R}^{3}\\ & =\phantom{\rule{mediummathspace}{0ex}}\frac{4}{3}\pi {R}^{3}\end{array}$
Schwinger-Dyson
equation
$⟨\psi \phantom{\rule{thinmathspace}{0ex}}\left|\phantom{\rule{thinmathspace}{0ex}}𝒯\left\{\frac{\delta }{\delta \varphi }F\left[\varphi \right]\right\}\right|\phantom{\rule{thinmathspace}{0ex}}\psi ⟩=-i⟨\psi \phantom{\rule{thinmathspace}{0ex}}\left|\phantom{\rule{thinmathspace}{0ex}}𝒯\left\{F\left[\varphi \right]\frac{\delta }{\delta \varphi }S\left[\varphi \right]\right\}\right|\phantom{\rule{thinmathspace}{0ex}}\psi ⟩$
Differentiable
Manifold
(tangent vector)
${\gamma }_{1}\equiv {\gamma }_{2}⟺\left\{\begin{array}{l}{\gamma }_{1}\left(0\right)={\gamma }_{2}\left(0\right)=p\text{, and}\\ {\frac{d}{dt}\varphi \circ {\gamma }_{1}\left(t\right)\phantom{\rule{verythinmathspace}{0ex}}|}_{\phantom{\rule{verythinmathspace}{0ex}}t=0}={\frac{d}{dt}\varphi \circ {\gamma }_{2}\left(t\right)\phantom{\rule{verythinmathspace}{0ex}}|}_{\phantom{\rule{verythinmathspace}{0ex}}t=0}\end{array}\right\$
Cichoń's
Diagram
$\begin{array}{ccccccccccc}\multicolumn{2}{c}{}& cov\left(ℒ\right)& ⟶& non\left(𝒦\right)& ⟶& cof\left(𝒦\right)& ⟶& cof\left(ℒ\right)& ⟶& {2}^{{\aleph }_{0}}\\ \multicolumn{2}{c}{}& ↑& & ↑& & ↑& & ↑& \multicolumn{2}{c}{}\\ \multicolumn{4}{c}{}& 𝔟& ⟶& 𝔡& \multicolumn{5}{c}{}\\ \multicolumn{4}{c}{}& ↑& & ↑& \multicolumn{5}{c}{}\\ {\aleph }_{1}& ⟶& add\left(ℒ\right)& ⟶& add\left(𝒦\right)& ⟶& cov\left(𝒦\right)& ⟶& non\left(ℒ\right)& \multicolumn{2}{c}{}\end{array}$
multiscripts
&
greek alphabet

$\underset{{}_{\varphi }{}^{\chi }𝔉_{\omega }^{\psi }}{\overset{{}_{\iota }{}^{\kappa }ℭ_{\mu }^{\lambda }}{{}_{{}_{\alpha }{}^{\beta }𝔄_{\delta }^{\gamma }}{}^{{}_{\epsilon }{}^{\zeta }𝔅_{\theta }^{\eta }}\prod _{{}_{\rho }{}^{\sigma }𝔈_{\upsilon }^{\tau }}^{{}_{\nu }{}^{\xi }𝔇_{\pi }^{ο}}}}$
nested roots $\frac{\sqrt{1+\sqrt[3]{2+\sqrt[5]{3+\sqrt[7]{4+\sqrt[11]{5+\sqrt[13]{6+\sqrt[17]{7+\sqrt[19]{A}}}}}}}}}{{e}^{\pi }}={x}^{‴}$
nested
matrices
$\left(\begin{array}{cc}\left(\begin{array}{cccc}{a}_{1}& {a}_{2}& {a}_{3}& {a}_{4}\\ {a}_{5}& {a}_{6}& {a}_{7}& {a}_{8}\end{array}\right)& \left(\begin{array}{c}{b}_{1}\\ {b}_{2}\\ \phantom{\rule{0ex}{1.4em}}{b}_{3}\\ {b}_{4}\end{array}\right)\\ \begin{array}{cc} 0 & \left(\begin{array}{cc}{c}_{1}& {c}_{2}\\ {c}_{3}& {c}_{4}\end{array}\right)\end{array}& \end{array}\right)$
font sizes $\text{scriptlevel :}-3,-2,-1,0,1$

## NOTES:

I hope this site can be used as a learning aid (tutorial by example) for mathematics in TeX/LaTeX and in coding MathML.
A small sample of many different types of mathematical expressions and equations is shown.
All the examples are complete with the source code available. (Just click on the equation/formula.)

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### Lessons Learned Working on MathML with STIX Fonts on Firefox:

When using an `mtable`, the table cell (`mtd`) default vertical padding produces excessive spacing. Setting the top and bottom padding to zero "`0`" fixes this.

When using the `mfenced` tag, the "fences" have no spacing around them.
When using the vertical bar "|" (`&vert;`) as a fence, adding a little spacing around it improves the readability of the result.

Firebug is an add-on to the Firefox browser. It is a great development tool that works well with MathML.