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TitleArtificial discontinuities of single-parametric Gröbner bases
Author(s) Jean-Charles Faugère, Ye Liang
TypeArticle in Journal
AbstractArtificial discontinuity is a kind of singularity at a parametric point in computing the Gröbner basis of a specialized parametric ideal w.r.t. a certain term order. When it occurs, though parameters change continuously at the point and the properties of the parametric ideal have no sudden changes, the Gröbner basis will still have a jump at the parametric point. This phenomenon can cause instabilities in computing approximate Gröbner bases. In this paper, we study artificial discontinuities in single-parametric case by proposing a solid theoretical foundation for them. We provide a criterion to recognize artificial discontinuities by comparing the zero point numbers of specialized parametric ideals. Moreover, we prove that for a single-parametric polynomial ideal with some restrictions, its artificially discontinuous specializations (ADS) can be locally repaired to continuous specializations (CS) by the TSV (Term Substitution with Variables) strategy.
KeywordsGröbner basis, Artificial discontinuity, Monomial basis, Local repair
URL http://www.sciencedirect.com/science/article/pii/S0747717110001999
JournalJournal of Symbolic Computation
Pages459 - 466
Translation No
Refereed No