Subresultants and generic monomial bases

CARLOS D'ANDREA; GABRIELA JERONIMO

JOURNAL OF SYMBOLIC COMPUTATION

Elsevier

Año: 2005 vol. 39 p. 259 - 277

0747-7171

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.