Solutions of systems of algebraic equations and linear maps on residue class rings
type: Item
instance of: scholarly article
title: Solutions of systems of algebraic equations and linear maps on residue class rings
zbMATH Open document ID: 0757.13013
DOI: 10.1016/0747-7171(92)90014-U
author: Kazuhiro Yokoyama
author: Masayuki Noro
author: Taku Takeshima
published in: Journal of Symbolic Computation
publication date: 1993-01-17T00:00:00Z
review text: The authors present new mathematical results and several new algorithms for solving a system of algebraic equations algebraically. They translate some theoretical arguments for the problem into their counterparts in the theory of linear maps, then they give a new description for the \(U\)- resultant and forms of solutions of systems straighforwardly. New algorithms proposed in the paper apply algorithms of linear algebra to avoid repeated computations of Gröbner bases under lexicographic order, and they require computations of a Gröbner basis, under arbitrary order, only once in principle. The new algorithms improve the efficiency of computation. Among others, the paper contains sections of a new presentation of the theory of solutions of systems and construction of the solutions in simple form. Comparison with other algorithms is given at the end of the paper.
reviewed by: Yueh-er Kuo
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 12E12
zbMATH DE Number: 97806
zbMATH Keywords: resultant
zbMATH Keywords: algorithms for solving a system of algebraic equations
zbMATH Keywords: Gröbner basis
zbMATH Keywords: efficiency
MaRDI profile type: Publication
cites work: Q3806684
cites work: Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems
cites work: Q3714165
cites work: Q3798767
cites work: Gröbner bases and primary decomposition of polynomial ideals
cites work: Q4143433
cites work: Solving systems of algebraic equations by a general elimination method
cites work: On radical zero-dimensional ideals
cites work: Résolution des systèmes d'équations algébriques
cites work: Q3325833
cites work: Solving zero-dimensional algebraic systems
cites work: Constructions in Algebra
cites work: Über B. Buchbergers Verfahren, Systeme algebraischer Gleichungen zu lösen
cites work: Q4477898
cites work: Q3997667
cites work: Computing primitive elements of extension fields
cites work: Q5732721
cites work: Interpolating polynomials from their values
full work available at URL: 0747-7171(92)90014-u
OpenAlex ID: W2066753705
description: scientific article; zbMATH DE number 97806