1. What are the contributions mentioned in the paper "Comprehensive gröbner bases in a java computer algebra system" ?
The authors 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, the authors aim to provide and utilize all necessary algebraic structures occurring in the algorithm.. In the implementation of a condition the authors aim at the maximal semantic exploitation of the occurring algebraic structures: the set of equations 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, for example, square-free decomposition.. With their approach the authors can also make the transition of a comprehensive Gröbner system to a polynomial ring over a ( commutative, finite, von Neuman ) regular coefficient ring and test or compute Gröbner bases in such polynomial rings.
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2. What future works have the authors mentioned in the paper "Comprehensive gröbner bases in a java computer algebra system" ?
In the future the authors will finish the implementation of multivariate polynomial factorization and use it in the handling of the conditions.. Further the authors plan to implement comprehensive Gröbner bases for parametric solvable polynomial rings [ 13 ].
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