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Subresultants and generic monomial bases. (English) Zbl 1120.13031

Summary: Given \(n\) polynomials in \(n\) variables of respective degrees \(d_{1},\ldots ,d_{n}\), and a set of monomials of cardinality \(d_{1}\cdots d_{n}\), 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 Bézout construction of the resultant.

MSC:

13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
68W30 Symbolic computation and algebraic computation
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References:

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