Extension dans un cadre algébrique d'une formule de Weil

Explicit representation of membership in polynomial ideals

“…In particular, if m ≥ n + 1 and Z is empty, then we get back the classical Macaulay theorem, [26], with an explicit formula representing the membership. Such a formula has also been obtained in [12] relying on [13].…”

About a Non-Standard Interpolation Problem

“…Cauchy-Weil's integral representation formula (originally introduced in [19]) plays a major role in this paper. Let us briefly recall it in the particular simple case where it happens to be the most useful (one refers for example to [2,8,13,10,18] for a more detailed as well as a presentation in its generality in the analytic or algebraic context). Let f 1 , ..., f n be n holomorphic functions in a bounded open set U ⊂ C n (possibly not connected) and continuous up to ∂U , with no common zero on ∂U , such that additionally there exists a matrix…”

Division-interpolation methods and Nullstellensätze

“…When expressed as (2.9), the Cauchy-Weil's formula has an algebraic counterpart. For a complete presentation of it, as well as for applications, we refer to [BoH2]. The algebraic version of the Cauchy-Weil formula is related to a generalization of the Transformation Law that was originally proposed by Kytmanov and later generalized to the algebraic setting [BY8,BY9,BoH1].…”