Isolated points, duality and residues

[摘要] In this paper, we are interested in the use of duality in effective computations on polynomials. We represent the elements of the dual of the algebra R of polynomials over the field K as formal series is an element of K[[partial derivative]] in differential operators. We use the correspondence between ideals of R and vector spaces of K[[partial derivative]], stable by derivation and closed for the (partial derivative)-adic topology, in order to construct the local inverse system of an isolated point, We propose an algorithm, which computes the orthogonal D of the primary component of this isolated point, by integration of polynomials in the dual space K[partial derivative], with good complexity bounds, Then we apply this algorithm to the computation of local residues, the analysis of real branches of a locally complete intersection curve, the computation of resultants of homogeneous polynomials. (C) 1997 Elsevier Science B.V.

[发布日期] 1997-05-01

[效力级别]  Proceedings Paper