Comprehensive Gröbner Bases in a Java Computer Algebra System

We present an implementation of the algorithms for computing comprehensive Grobner bases in a Java computer algebra system (JAS). Contrary to approaches to implement comprehensive Grobner bases with minimal requirements to the computer algebra system, we aim to provide all necessary algebraic structures occurring in the algorithm. In the implementation of a condition we aim at the maximal semantic exploitation of the occurring algebraic structures: the set of equations that equal zero are implemented as an ideal (with Grobner base computation) and the set of inequalities are implemented as a multiplicative set which is simplified to polynomials of minimal degrees using squarefree or irreducible decomposition. The performance of our implementation is compared on well-known examples. With our approach we can also make the transition of a comprehensive Grobner system to a polynomial ring over a regular coefficient ring and test or compute Grobner bases.