Explicit factors of some iterated resultants and discriminants

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 [9] and McCallum [26, 27] whi...

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Laurent Busé, Bernard Mourrain
• Keywords: CORR 2006, Education, Generic Polynomials, Irreducible Factor, Polynomial