2012/03/28 by Christian Eder, Eder, Christian
Computer Science · Mathematics · #13P10 #Coding theory and cryptography #Commutative Algebra (math.AC) #Cryptography and Residue Arithmetic #F.2.1 #FOS: Mathematics #I.1.2 #Polynomial and algebraic computation #acm:13P10 #math.AC #msc:13P10
paper · pdf · doi:10.48550/arxiv.1203.6186
18 pages, 1 figure, 1 table
openalex publication_date 2012/03/28 · arxiv created 2013/04/16 · arxiv updated 2013/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we give an insight into the behaviour 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.