Multipolynomial resultant algorithms
type: Item
instance of: scholarly article
title: Multipolynomial resultant algorithms
zbMATH Open document ID: 0778.13023
author: Dinesh Manocha
author: John Canny
published in: Journal of Symbolic Computation
publication date: 1993-08-25T00:00:00Z
review text: The paper describes informally algorithms for computing determinants of matrices with polynomial entries from \(Z(x)=Z(x_ 1,\ldots,x_ n)\). In contrast to methods applied in most computer algebra systems the determinants are computed indirectly by a homomorphism/reconstruction method: map the matrix from \(Z(x)\) to \(Z\) by substituting sets of numbers for \((x_ 1,\dots,x_ n)\), compute for each a numerical determinant in \(Z\) and construct the determinant in \(Z(x)\) by interpolation. Several aspects for the interpolation are discussed: A Vandermonde type equation system (using sets \((p_ 1^ k,\dots,p_ n^ k)\) with primes \(p_ i)\), sparse interpolation, probabilistic interpolation and modular evaluation/Chinese remainder reconstruction. The use of the determinant computation for resultants of multivariate polynomial sets is presented in examples: Implication of rational parametric surfaces, real solutions of polynomial equation systems. The theory of multipolynomial resultants and algorithms for their construction are not covered in this article.
reviewed by: H.Melenk
Mathematics Subject Classification ID: 13P99
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 65F30
zbMATH DE Number: 370646
zbMATH Keywords: algorithms for computing determinants of matrices
zbMATH Keywords: interpolation
zbMATH Keywords: resultants of multivariate polynomial
MaRDI profile type: Publication
OpenAlex ID: W2084860168
Wikidata QID: Q57425908
DOI: 10.1006/JSCO.1993.1009
description: scientific article; zbMATH DE number 370646