Subresultants and Generic Monomial Bases

Details Subresultants and Generic Monomial Bases Subresultants and Generic Monomial Bases

2003-01-30

arxiv.org/abs/math/0301355v3

Journal of Symbolic Computation 39 (2005) 259-277

Mathematics

Algebraic Geometry

22 pages, uses elsart.cls. Revised version accepted for publication in the Journal of Symbolic Computation

Scientific paper

Given n polynomials in n variables of respective degrees d_1,...,d_n, and a set of monomials of cardinality d_1...d_n, we give an explicit subresultant-based polynomial expression in the coefficients of the input polynomials whose non-vanishing is a necessary and sufficient condition for this set of monomials to be a basis of the ring of polynomials in n variables modulo the ideal generated by the system of polynomials. This approach allows us to clarify the algorithms for the Bezout construction of the resultant.

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