A p-adic approach to the computation of Gröbner bases
type: Item
instance of: scholarly article
title: A p-adic approach to the computation of Gröbner bases
zbMATH Open document ID: 0669.13009
DOI: 10.1016/S0747-7171(88)80049-X
author: Franz Winkler
published in: Journal of Symbolic Computation
publication date: 1988-01-01T00:00:00Z
review text: To deal with the problem of coefficient growth in the computation of Gröbner bases of polynomial ideals over the rational number field \({\mathbb{Q}}\) the paper presents a lifting algorithm that computes a p-adic approximation to the normalized reduced Gröbner basis for the ideal generated by a finite set of polynomials F in \({\mathbb{Q}}[x_ 1,...,x_ v]\). For the lucky prime p for F (it is shown that almost all primes are lucky) a normalized reduced Gröbner basis for F modulo p is computed and then lifted to the desired result.
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 13-04
zbMATH DE Number: 4095636
zbMATH Keywords: coefficient growth
zbMATH Keywords: computation of Gröbner bases of polynomial ideals
zbMATH Keywords: p-adic approximation
describes a project that uses: Algorithm 628
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4095636