Yacas[1] looks to me an obvious candidate for the mathematics
task. However I've not actually used it, nor am I a mathematician, so
objections/support for adding it would be appreciated.

Chris


[1] http://packages.debian.org/unstable/math/yacas 
Computer Algebra System
 Yacas is a small and highly flexible computer algebra language.
 The syntax is very close to Mathematica. The distribution contains a
 small library of mathematical functions, but its real strength is in
 the language in which you can easily write your own symbolic
 manipulation algorithms. It supports arbitrary precision arithmetic.


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