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- Rouchdi Bahloul
- J. Symb. Comput.
- 2001

Let n, p be two strictly positive integers, and let f1(x), . . . , fp(x) ∈ K[x] := K[x1, . . . , xn] be p polynomials of n variables with coefficients in a fieldK of characteristic zero. Denote by An = K[x1, . . . , xn]〈∂x1 , . . . , ∂xn〉 the Weyl algebra with n variables and let s1, . . . , sp be new variables. Denote by L = K[x][f−1 1 , . . . , f−1 p ,… (More)

In 1987, C. Sabbah proved the existence of Bernstein-Sato polynomials associated with several analytic functions. The purpose of this article is to give a more elementary and constructive proof of the result of C. Sabbah based on the notion of the analytic Gröbner fan of a D-module. Introduction et énoncé des résultats principaux Fixons n > 1 et p > 1 deux… (More)

- Rouchdi Bahloul, Toshinori Oaku
- J. Symb. Comput.
- 2010

Let k be a field of characteristic 0. Given a polynomial mapping f = (f1, . . . , fp) from kn to kp, the local Bernstein–Sato ideal of f at a point a ∈ kn is defined as an ideal of the ring of polynomials in s = (s1, . . . , sp). We propose an algorithm for computing local Bernstein–Sato ideals by combining Gröbner bases in rings of differential operators… (More)

- ROUCHDI BAHLOUL
- 2003

Given p polynomials with coefficients in a commutative unitary integral ring C containing Q, we define the notion of a generic Bernstein-Sato polynomial on an irreducible affine scheme V ⊂ Spec(C). We prove the existence of such a non zero rational polynomial which covers and generalizes previous existing results by H. Biosca. When C is the ring of an… (More)

- ROUCHDI BAHLOUL
- 2003

The contribution of this paper lies in two aspects. The first one deals with a natural notion of generic Gröbner (or standard) bases on an irreducible affine scheme for an ideal depending on parameters. This takes place in rings of differential operators and concerns the algebraic and the formal case. Thus we obtain a generalization of some known results in… (More)

- ROUCHDI BAHLOUL
- 2004

Parametric Gröbner bases have been studied for more than 15 years and are now a further developed subject. Here we propose a general study of parametric standard bases, that is with local orders. We mainly focus on the commutative case but we also treat the case of differential operators rings. We will be concerned by two aspects: a theoretical aspect with… (More)

This note summarizes results concerning local Gröbner fans. Any Gröbner fan of an ideal in a power series ring, or in an analytic or formal differential operator ring, is found to be a polyhedral fan. We also compare the notions of global and local Gröbner fans, and discuss applications of our results. To cite this article: R. Bahloul, N. Takayama, C. R.… (More)

- ROUCHDI BAHLOUL
- 2004

In 1987, C. Sabbah proved the existence of Bernstein-Sato polynomials associated with several analytic functions. The purpose of this article is to give a more elementary and constructive proof of the result of C. Sabbah based on the notion of the analytic Gröbner fan of a D-module. This paper is a translation of [Bah]. Introduction and statement of the… (More)

- ROUCHDI BAHLOUL
- 2008

This is the first part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. The main result of this part is a constructibility result for the analytic Gröbner fan of a parametric ideal in the ring of analytic differential operators. In this part, the main tool is the notion of generic reduced… (More)

- ROUCHDI BAHLOUL
- 2003

The contribution of this paper lies in two aspects. The first one deals with a natural notion of generic Gröbner (or standard) bases on an irreducible affine scheme for an ideal depending on parameters. This takes place in rings of differential operators and concerns the algebraic and the formal case. This gives a generalization of some results of V.… (More)