Alec Smart wrote:
> I'm working with Python, currently... is there a specific programming
> language that is designed for math, or a package thats not as
> expensive as Mathematica? Pythons great for simple things, but not as
> optimized as I'd like it to be, and C is a pain in the butt for me.
You'll probably note, if you follow the discussions in this group,
that a large number of participants use the free PARI/GP package for
number theory calculations. Their speed and simplicity is often very
impressive. GP is a unique programming language that provides an
interface to the PARI C library of functions.
It is usually compiled with the very fast GMP multi-precision library
which makes most of its calculations with big numbers quite competitive
with the fastest mathematical packages out there. It has a wide variety
of algorithms already implemented efficiently, and should perform as
well or better as something that most programmers could implement in
about any language.
It's not designed to be as much of a general-purpose language as
Python, (Turing-completeness aside,) and you may find some things (e.g.
processing text) much more difficult to do in GP.
As an interesting data point, you might note that in the Project
Euler programming competition, there are a small number of users who
claim to use PARI/GP as their language of choice for solving the puzzle,
but their average number of puzzles solved is very high:
Alan Eliasen | "Furious activity is no substitute
| for understanding."
| --H.H. Williams