Fast reduction of bivariate polynomials with respect to sufficiently regular Gröbner bases
Résumé
Let G be the reduced Gröbner basis of a zero-dimensional ideal I ⊆ K[X, Y] of bivariate polynomials over an effective field K. Modulo suitable regularity assumptions on G and suitable precomputations as a function of G, we prove the existence of a quasi-optimal algorithm for the reduction of polynomials in K[X, Y] with respect to G. Applications include fast algorithms for multiplication in the quotient algebra A = K[X, Y]/I and for conversions due to changes of the term ordering.
Origine : Fichiers produits par l'(les) auteur(s)
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