Various MathML Tests

Overview of Presentation MathML elements

• Testing tensor indices <mmultiscripts>: ${}_k{}^{3}R_i^1{}_j{}^2$ ; This with <none/>, ${}_{i}A_q^p$
• A bit of calculus: ${\int }_a^{b}f\left(x\right)\mathrm{dx}\frac{\partial }{\partial x}F(x,y)+\frac{\partial }{\partial y}F(x,y)$
• Here is the alphabet with invisible portions wrapped by <mphantom> in between: $abc\phantom{defghij}klmno\phantom{pqrs}tuvwxyz$.
• Testing MathML <msub>: $a_b$; $a_i$; $A_{I_k}$
• Testing MathML <msup>: $d^b{2}^{a_x}{2^2}^x{\left(\frac{1}{2}\right)}^{y^{a_x}}$.
• Testing MathML <munder>, <mover>, and <munderover>: $\underset{\mathrm{un}}{\mathrm{abcd}}\stackrel{\mathrm{ov}}{\mathrm{abcd}}\underset{\mathrm{under}}{\overset{\mathrm{over}}{\mathrm{abcd}}}$.
• Testing MathML <msubsup>: $a_p^q{a}_{b+c}^x$.
• Testing MathML <mrow>: $d^{\left(\frac{a}{b}\right)}$
• $x^2+4*x+\frac{p}{q}=0$, with this <mfrac> hanging here $\frac{d*T^{\left(\frac{i+j}{n}\right)}+p_y*q}{p^x*b_x+\frac{a+c}{d}}$ in the middle of a lot of running text to try to explain what this means to those who care to read.
• Testing MathML <merror>, <mtext>: $\text{This is a text in mtext}\text{This is a text in merror}$
• Testing <maction>: Click to toggle between expressions, and watch the status line onmouseover/onmouseout:

  $$\mathrm{statusline\#First\; Expression}\text{First Expression}\mathrm{statusline\#Second\; Expression}\text{Second Expression}\mathrm{statusline\#And\; so\; on...}\text{And so on..}$$

  Click the expression below to see several definitions of pi:
  $$\pi =3.14159265358\mathbf{...}\pi =2iLog\frac{1-i}{1+i}\pi =2\phantom{.}\frac{2}{\sqrt{2}}\phantom{.}\frac{2}{\sqrt{2+\sqrt{2}}}\phantom{.}\frac{2}{\sqrt{2+\sqrt{2+\sqrt{2}}}}\mathbf{...}\frac{\pi }{4}=\frac{1}{2+\frac{1^2}{2+\frac{3^2}{2+\frac{5^2}{2+\frac{7^2}{2+\mathbf{...}}}}}}$$

Thomson scattering theory

$$\begin{array}{ccc}\frac{d^{2}P}{d{\Omega }_s\hspace{0.17em}d{\omega }_s}\hfill & =\hfill & r_e^2{\int }_V<S_i>d^3\mathbf{r}\int {|\widehat{\mathbf{e}}.\overleftrightarrow{\Pi }.\widehat{\mathbf{e}}|}^2{\kappa }^{2}f\hspace{0.17em}\delta (\mathbf{k}.\mathbf{v}-\omega )d^3\mathbf{v}\hfill \\ & =\hfill & r_e^2{\int }_V<S_i>d^3\mathbf{r}\int {|1-\frac{(1-\widehat{\mathbf{s}}.\widehat{\mathbf{ı}})}{(1-{\beta }_i)(1-{\beta }_s)}{\beta }_e^2|}^2{\left|\frac{1-{\beta }_i}{1-{\beta }_s}\right|}^2\hfill \\ & & \times (1-{\beta }^2)\hspace{0.17em}f\hspace{0.17em}\delta (\mathbf{k}.\mathbf{v}-\omega )d^3\mathbf{v}\hfill \end{array}$$

Maxwell's Equations

${\displaystyle \{\begin{array}{rcl}\nabla \times \overrightarrow{\mathbf{B}}-\frac{1}{c}\frac{\partial \overrightarrow{\mathbf{E}}}{\partial t}& =& \frac{4\pi }{c}\overrightarrow{\mathbf{j}}\\ \nabla ċ\overrightarrow{\mathbf{E}}& =& 4\pi \rho \\ \nabla \times \overrightarrow{\mathbf{E}}+\frac{1}{c}\frac{\partial \overrightarrow{\mathbf{B}}}{\partial t}& =& \overrightarrow{0}\\ \nabla ċ\overrightarrow{\mathbf{B}}& =& 0\end{array}}$

Einstein's field equations

${\displaystyle {\mathrm{R}}_{\mu \nu }-\frac{1}{2}{g}_{\mu \nu }\mathrm{R}=\frac{8\pi \mathrm{G}}{c^4}{\mathrm{T}}_{\mu \nu }}$