User:Afwings/sandbox

Just testing math on the sandbox here. Here's a couple of equations using "normal" Wikipedia math notation $$u=\phi \cdot \exp \left\{ \tfrac{1}{2}\sigma \left( x+y \right) \right\}$$ and $$x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$$, and one more $$\sqrt{2}$$. Here are the same equations using MathJax LaTeX \(u = \phi \cdot \exp \left\{ {{\textstyle{1 \over 2}}\sigma \left( {x + y} \right)} \right\}\) and \[x = \frac{ {2a} }\] Now MathJax MathML. Well that's not working anymore. This is from MathType: $$r=\sqrt{{{x}^{2}}+{{y}^{2}}}$$. Something more complex: $$\text{Bond Value}=\text{C}\left[ \frac{1-\frac{1}}{\text{r}} \right]+\frac{\text{FV}}$$. Now for a long equation: $$\begin{align} & {{E}_{t}}\left[ {{D}_{u}} \right] \\ & ={{D}_{t}}\exp \left( {{{{\tau }'}}_{c}}r\Delta {{u}_{t}} \right)-\int_{t}^{u}{\left( {{E}_{t}}\left[ {{c}_{v}} \right]-{{\tau }_{c}}{{E}_{t}}\left[ {{e}_{v}} \right]-{{E}_{t}}\left[ {{\delta }_{v}} \right] \right)\exp \left( {{{{\tau }'}}_{c}}r\Delta {{u}_{v}} \right)dv} \\ & ={{D}_{t}}\exp \left( {{{{\tau }'}}_{c}}r\Delta {{u}_{t}} \right)-\left( {{c}_{t}}-{{\tau }_{c}}{{e}_{t}} \right)\int_{t}^{u}{\exp \left( \int_{t}^{v}{{{g}_{s}}ds} \right)\exp \left( {{{{\tau }'}}_{c}}r\Delta {{u}_{v}} \right)dv}+\int_{t}^{u}{{{E}_{t}}\left[ {{\delta }_{v}} \right]\exp \left( {{{{\tau }'}}_{c}}r\Delta {{u}_{v}} \right)dv} \end{align}$$