Ideal basis and primary decompositions: case of two variables
type: Item
instance of: scholarly article
title: Ideal basis and primary decompositions: case of two variables
zbMATH Open document ID: 0616.68036
DOI: 10.1016/S0747-7171(85)80035-3
author: D. Lazard
published in: Journal of Symbolic Computation
publication date: 1985-01-01T00:00:00Z
review text: Gröbner bases provide a universal technique for computer-algebraic treatment of algebraic and geometric problems. However, the question of structural complexity of Gröbner bases and that of the computational complexity of the relevant algorithms remain as yet practically open. The present paper contains a complete and constructive description of Gröbner bases for the class of two-variable polynomials over a field and that of univariate polynomials over a Euclidean ring. This description gives rise to a simple algorithm for computing primary decompositions. A natural factorization is also found for the resultant of two univariate polynomials.
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 68Q25
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 3999283
zbMATH Keywords: Gröbner bases
zbMATH Keywords: structural complexity
zbMATH Keywords: computational complexity
zbMATH Keywords: two- variable polynomials over a field
zbMATH Keywords: univariate polynomials over a Euclidean ring
zbMATH Keywords: algorithm for computing primary decompositions
zbMATH Keywords: factorization
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3999283