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Haskell's overloaded numerical classes can be (ab)used to do some symbolic maths. This is in no way a new discovery, but I thought I'd write a few lines about it anyway since I've been playing with it the last few days. First we need a data type to repres

DoCon is a program for symbolic computation in mathematics - package of modules DoCon joins the categorial approach to the mathematical computation expressed via the Haskell type classes, and explicit processing of the domain description terms. It implements recently a good piece of commutative algebra: linear algebra, polynomial gcd, factorization, Groebner bases, and other functions. They are programmed under the very generic assumptions , like "over any Euclidean ring", over any GCD-ring, any field, and so on. DoCon also supports the constructions on domains: Fraction, Polynomial, Residue ring, and others. That is certain set of operations on a constructed domain is built automatically.

Eureqa is a software tool for detecting equations and hidden mathematical relationships in your data. Its primary goal is to identify the simplest mathematical formulas which could describe the underlying mechanisms that produced the data. Eureqa is free to download and use

NuSMV is a symbolic model checker NuSMV is a reimplementation and extension of SMV, the first model checker based on BDDs. NuSMV has been designed to be an open architecture for model checking, which can be reliably used for the verification of industrial designs, as a core for custom verification tools, as a testbed for formal verification techniques, and applied to other research areas. NuSMV2, combines BDD-based model checking component that exploits the CUDD library developed by Fabio Somenzi at Colorado University and SAT-based model checking component that includes an RBC-based Bounded Model Checker, connected to the SIM SAT library developed by the University of Genova.