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TitleAn analysis of inhomogeneous signature-based Gröbner basis computations
Author(s) Christian Eder
TypeArticle in Journal
AbstractAbstract In this paper we give an insight into the behavior of signature-based Gröbner basis algorithms, like F5, G2V or SB, for inhomogeneous input. On the one hand, it seems that the restriction to sig-safe reductions puts a penalty on the performance. The lost connection between polynomial degree and signature degree can disallow lots of reductions and can lead to an overhead in the computations. On the other hand, the way critical pairs are sorted and corresponding s-polynomials are handled in signature-based algorithms is a very efficient one, strongly connected to sorting w.r.t. the well-known sugar degree of polynomials.
KeywordsGröbner bases, Sugar degree, Signature-based algorithms, F5, G2V, GVW, GVWHS
URL http://www.sciencedirect.com/science/article/pii/S0747717113001089
JournalJournal of Symbolic Computation
Pages21 - 35
Translation No
Refereed No