In addition to Octave, PARI/GP and Singular should be mentioned, especially for number theory and algebraic computations: http://pari.math.u-bordeaux.fr/ http:

In addition to Octave, PARI/GP and Singular should be mentioned, especially for number theory and algebraic computations: http://pari.math.u-bordeaux.fr/ http://pari.math.u-bordeaux.fr/ http://www.singular.uni-kl.de/ http://www.singular.uni-kl.de/