Algorithms for residues and Łojasiewicz exponents
type: Item
instance of: scholarly article
title: Algorithms for residues and Łojasiewicz exponents
zbMATH Open document ID: 0974.13021
DOI: 10.1016/S0022-4049(99)00083-3
published in: Journal of Pure and Applied Algebra
publication date: 2001-12-06T00:00:00Z
review text: In this paper, the authors use some matrix techniques based on Bezoutian formulations to compute relations of algebraic dependence between \(n+1\) polynomials in \(n\) variables. They also compute bounds for the size of the involved matrices and for the height of their coefficients. Then, they apply these results to develop different algorithms: One for the computation of residues associated to polynomials, another one which decides whether a polynomial map \(f:\mathbb{C}\to\mathbb{C}\) is proper or not, another one to compute the Łojasiewicz exponent of a family of polynomials, and the last one to decide whether a polynomial map \(f:\mathbb{C}\to\mathbb{C}\) is invertible or not and, in case it is, to compute its inverse.
reviewed by: Juan Sabia
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13-04
Mathematics Subject Classification ID: 14E05
zbMATH DE Number: 1526261
zbMATH Keywords: computational aspects of commutative algebra
zbMATH Keywords: polynomial ideal
zbMATH Keywords: algebraic residue theory
zbMATH Keywords: Bezoutians
zbMATH Keywords: algebraic dependence between polynomials
zbMATH Keywords: Łojasiewicz exponent
zbMATH Keywords: polynomial map
author: Mohamed Elkadi
author: Bernard Mourrain
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1526261