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An analysis of inhomogeneous signature-based Gröbner basis computations

Christian Eder 1
1 PolSys - Polynomial Systems
Inria Paris-Rocquencourt, LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : 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.
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https://hal.inria.fr/hal-00930286
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Submitted on : Tuesday, January 14, 2014 - 3:37:52 PM
Last modification on : Friday, January 8, 2021 - 5:42:02 PM

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Christian Eder. An analysis of inhomogeneous signature-based Gröbner basis computations. Journal of Symbolic Computation, Elsevier, 2013, 59, pp.21--35. ⟨10.1016/j.jsc.2013.08.001⟩. ⟨hal-00930286⟩

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