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TitleLocal Bernstein–Sato ideals: Algorithm and examples
Author(s) Rouchdi Bahloul, Toshinori Oaku
TypeArticle in Journal
AbstractLet k be a field of characteristic 0. Given a polynomial mapping f = (f_1, … ,f_p) from k^n to k^p , the local Bernstein–Sato ideal of f at a point a ∈ k^n is defined as an ideal of the ring of polynomials in s = (s_1, … ,s_p) . We propose an algorithm for computing local Bernstein–Sato ideals by combining Gröbner bases in rings of differential operators with primary decomposition in a polynomial ring. It also enables us to compute a constructible stratification of k n such that the local Bernstein–Sato ideal is constant along each stratum. We also present examples, some of which have non-principal Bernstein–Sato ideals, computed with our algorithm by using the computer algebra system Risa/Asir.
KeywordsBernstein–Sato ideal, D -module, Gröbner base, Primary decomposition
URL http://www.sciencedirect.com/science/article/pii/S0747717109001230
JournalJournal of Symbolic Computation
Pages46 - 59
Translation No
Refereed No