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Comprehensive Gröbner Bases in a Java Computer Algebra System

In: Computer Mathematics

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  • Heinz Kredel

    (University of Mannheim, IT-Center)

Abstract

We present an implementation of the algorithms for computing comprehensive Gröbner bases in a Java computer algebra system (JAS). Contrary to approaches to implement comprehensive Gröbner 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 Gröbner 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 Gröbner system to a polynomial ring over a regular coefficient ring and test or compute Gröbner bases.

Suggested Citation

  • Heinz Kredel, 2014. "Comprehensive Gröbner Bases in a Java Computer Algebra System," Springer Books, in: Ruyong Feng & Wen-shin Lee & Yosuke Sato (ed.), Computer Mathematics, edition 127, pages 93-108, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-43799-5_9
    DOI: 10.1007/978-3-662-43799-5_9
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