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TitleStratification associated with local b-functions
Author(s) Kenta Nishiyama, Masayuki Noro
TypeArticle in Journal
AbstractThe local b -function b f , p ( s ) of an n -variate polynomial f ∈ C [ x ] ( x = ( x 1 , , x n ) ) at a point p ∈ C^n is constant on each stratum of a stratification of C n . We propose a new method for computing such a stratification and b f , p ( s ) on each stratum. In the existing method proposed in Oaku (1997b), a primary ideal decomposition of an ideal in C [ x , s ] is needed and our experiment shows that the primary decomposition can be a bottleneck for computing the stratification. In our new method, the computation can be done by just computing ideal quotients and examining inclusions of algebraic sets. The precise form of a stratum can be obtained by computing the decomposition of the radicals of the ideals in C [ x ] defining the stratum. We also introduce various techniques for improving the practical efficiency of the implementation and we show results of computations for some examples.
Keywordsb -function, Stratification, Weyl algebra, Gröbner basis, Differential operator, D -module
URL http://www.sciencedirect.com/science/article/pii/S0747717110000118
JournalJournal of Symbolic Computation
Pages462 - 480
Translation No
Refereed No