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4.13.1 Introduction to Groebner Bases in CoCoA
The heart of the CoCoA system is a implementation of Buchberger's algorithm for computing Groebner bases for ideals and modules over polynomial rings with coefficients in a field. CoCoA's Groebner basis engine can be used to compute Groebner bases, syzygies, free resolutions, Hilbert functions and Poincare series, and to eliminate variables and find minimal sets of generators. Considerable control over the computations is provided through CoCoA's The Interactive Groebner Framework.

Groebner bases can be calculated over Q, but large calculations depending on Groebner bases will take much less time over finite fields. A common tactic is to work mod large primes to get an idea of behavior expected over Q.

It would eventually be nice to have descriptions within this online help system of the specific algorithms used by CoCoA. For now, see Pointers to the Literature for references.