On Factorizing the Symbolic U-resultant — Application of the ddet operator

This paper presents a new, practical, efficient algorithm for factorizing the U-resultant of a system of algebraic equations with finitely many solutions. Given a matrix whose determinant is the U-resultant, our algorithm obtains the true linear factors with exact multiplicities, directly from the m...

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Bibliographic Details
Published inJournal of symbolic computation Vol. 15; no. 2; pp. 123 - 142
Main Authors Murao, Hirokazu, Kobayashi, Hidetsune, Fujise, Tetsuro
Format Journal Article
LanguageEnglish
Published Orlando, FL Elsevier Ltd 01.02.1993
London Academic Press
Subjects
Exact sciences and technology
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis. Scientific computation
Sciences and techniques of general use
Algebraic equation
Equation system solving
Gröbner basis
Symbolic computation
Factorization
Determinant
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Summary:This paper presents a new, practical, efficient algorithm for factorizing the U-resultant of a system of algebraic equations with finitely many solutions. Given a matrix whose determinant is the U-resultant, our algorithm obtains the true linear factors with exact multiplicities, directly from the matrix without expanding the multivariate determinant. The main focuses are laid upon the use of a new operator, which enables us to treat only matrices of univariate polynomial elements, and also upon the exact treatment of multiplicities, which is made possible by the symbolic representation of solutions in simple algebraic extensions of Q. The algorithm is probabilistic in the sense that there exists no deterministic method to give an appropriate parameterization. The efficiency of our algorithm will be demonstrated with some empirical problems.
ISSN:0747-7171
1095-855X
DOI:10.1006/jsco.1993.1010