# Unused Cycles

## May 24, 2008

### LaTeX Tests

Filed under: LaTeX — Tags: , — Kevin @ 5:11 pm

So I just imported my (few) files from Blogger.com because I was unhappy with how it handled math equations. I did some research and found out that WordPress handles them natively with $\LaTeX$, so I was quick to switch since I’ll probably be using mathematics quite a bit.

For example, did you know that if, for a function $f$ of one variable,

$|f(x)-f(y)| \le (x-y)^2$

implies that $f$ is actually a constant function?

The geodesic equation that test particles follow in a given metric is

$\displaystyle\frac{du^\alpha}{d\tau}=\Gamma^\alpha_{\beta\gamma}u^\beta u^\gamma$,

where the Christoffel symbols $\Gamma^\alpha_{\beta\gamma}$ are given by

$\displaystyle\Gamma^\alpha_{\beta\gamma}=\frac{1}{2} g^{\alpha\epsilon}\left(\frac{\partial g_{\alpha\epsilon}}{\partial x^\beta}+\frac{\partial g_{\beta\epsilon}}{\partial x^\alpha}-\frac{\partial g_{\alpha\beta}}{\partial x^\epsilon}\right).$

There are a few things missing such as equation arrays, but I’ve been able to figure out how to emulate such things using arrays. For example, in a commutative ring $R$ with elements $a$ and $b$,

$\begin{array}{rcl}\displaystyle(a+b)^2&\displaystyle=&\displaystyle a^2+ab+ba+b^2\vspace{0.3 cm}\\&\displaystyle=&\displaystyle a^2+2ab+b^2.\end{array}$

Overall, some things are a bit annoying, but it’s definitely workable!