Unlike the areas mentioned above this is one area where it is most likely that one will be unable to find public domain software since by definition it is not something that a lot of people use--hence the lack of motivation for user groups to develop it. At the same time there are very few commercial packages too.

Examples from the author's own area of specialisation are GPari and KANT which are packages for computations in Number Theory; JACAL for computations in Algebra and Macaulay for computations in Algebraic Geometry. All these are in the public domain. A commercially available package that has a number of nice features is Mathematica. However, many of its ``features'' are of little or no use to mathematicians. On the other hand the specialised packages like GPari and Macaulay are written by mathematicians and have only essential features.

Kapil Hari Paranjape 2002-11-22