Paper Info
Title
Explicit factors of some iterated resultants and discriminants
Abstract
In this paper, the result of applying iterative univariate resultant constructions to multivariate polynomials is analyzed. We consider the input polynomials as generic polynomials of a given degree and exhibit explicit decompositions into irreducible factors of several constructions involving two times iterated univariate resultants and discriminants over the integer universal ring of coefficients of the entry polynomials. Cases involving from two to four generic polynomials and resultants or discriminants in one of their variables are treated. The decompositions into irreducible factors we get are obtained by exploiting fundamental properties of the univariate resultants and discriminants and induction on the degree of the polynomials. As a consequence, each irreducible factor can be separately and explicitly computed in terms of a certain multivariate resultant. With this approach, we also obtain as direct corollaries some results conjectured by Collins ( 1975) and McCallum ( 1999, 2001 preprint) which correspond to the case of polynomials whose coefficients are themselves generic polynomials in other variables. Finally, a geometric interpretation of the algebraic factorization of the iterated discriminant of a single polynomial is detailled.
Year
DOI
Venue
2009
10.1090/S0025-5718-08-02111-X
MATHEMATICS OF COMPUTATION
Keywords
DocType
Volume
algebraic geometry,symbolic computation
Journal
78
Issue
ISSN
Citations 
265
0025-5718
9
PageRank 
References 
Authors
0.82
2
2
Name
Order
Citations
PageRank
Laurent Busé113114.74
Bernard Mourrain21074113.70