# 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!

### Codecogs images render mathematics

Filed under: LaTeX — Kevin @ 3:46 pm

So I was a little upset at how poorly Blogger.com handled math, so I did a little searching. I found a website called codecogs.com which has a LaTeX image generator. One can just direct an img tag to that website and get images such as this one:




It seems that in-line variables, such as a variable called , look fine as well.

This code is open-source, so it would be very helpful if Blogger.com would install it so that it can be used without relying on CodeCogs’ website to be up. With my luck, I’ll start using this as my sole method of rendering math and they’ll go out of business…