[sintesoro]

Python is good, you could also consider Maxima.

A single example:

f(x):= x^2+3x+7;

Maxima provides: Symbolic computation, blas and laplack integration for numeric algebra, 500 pages manual in several languages, a complete library for statistics, differential equation, calculus, series. Graphics with matplotllib. Also maxima language is not much complicate that python:

for i in range(10):print ii versus for i:0 thru 9 do print ii;

[i2 for i in range(10)] versus makelist(i*2,i,0,9)

But Matlab libraries are greater than python and maxima.

[kwantam]

Maxima rocks for symbolic math. I prefer it to Mathematica, which is saying a lot. In contrast, octave always feels like "almost-Matlab" and I still prefer the latter.

Also see wxMaxima, which will (among many other things) produce LaTeX for you.

[nurbl]

If you haven't already, you might also want to check out Sage (http://www.sagemath.org/) It uses python to "glue" together other free math tools (e.g. Maxima) into a unified system with a nice interface.

[dagw]

Python has sage and sympy for doing symbolic math. Although admittedly they're quite primitive compared to maple and mathematica (haven't used Maxima, so I can't really compare)

[koenigdavidmj]

Sage actually includes Maxima, for ultimate convenience.