Best polynomial approximation equal ripple error

Mathematica does have an implementation of the Parks-McClellan algorithm (Remez exchange applied to digital filter design) so somewhere in there is a Remez implementation.

I've been studying Chebfun lately, a Matlab library implementing these approximation techniques. It's written by some of the leading researchers in the field, and their documentation is so well done that it reads like a graduate textbook on the subject:

http://www.chebfun.org/docs/guide/

In particular chapter 4 is relevant.