[2020-01-14]Groebner Bases: Universality, Parametricity and Canonicity

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Title: Groebner Bases: Universality, Parametricity and Canonicity
Speaker: Prof. Deepak Kapur,University of New Mexico
Time: 10:00 a.m. 2020-01-14(Tuesday)
Venue: Lecture room (334),  Building 5, SKLCS, Institute of Software, CAS
Abstract: The talk will integrate the concepts of a universal Groebner basis which serves as a Groebner basis for all admissible term orderings, with parametric (more popularly called comprehensive) Groebner basis which serves as a Groebner basis for all possible specializations of parameters. Three different but related approaches will be presented. First one extends Kapur's algorithm for computing a parametric Groebner basis in which along with branching based on making the head coefficient nonzero or not, branching on ordering constraints is also done in order first to choose a term that could serve as the head term. The second one is based on the Kapur, Sun and Wang's algorithm for computing comprehensive Groebner basis and system but uses a reduced universal Groebner basis to generate a universal parametric Groebner basis. The third one starts with a reduced Groebner basis using one arbitrary ordering and then generate a universal comprehensive Groebner basis by incrementally changing the orderings along with partitioning specializations. The result of these algorithm is a mega Groebner basis that works for every admissible ordering as well as for any specialization of parameters.
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