7 citations · 11 across the 2 of their papers we have counts for
7 papers · 1 filter
Local Gröbner fan: polyhedral and computational approach
Rouchdi Bahloul, Nobuki Takayama
The goal of this paper is to show that the local Gröbner fan is a polyhedral fan for ideals in the ring of power series and the homogenized ring of analytic differential operators.…
An Algorithm of Constructing Cohomological Series Solutions of Holonomic Systems
Nobuki Takayama
We present an algorithm to construct a basis of k-th extension group of a D-module M in ring of the formal power series Ext_D^k(M,O).
Slopes of a Hypergeometric System Associated to a Monomial Curve
F. J. Castro-Jimenez, N. Takayama
We compute, by D-module restrictions, the slopes of irregular hypergeometric systems associated to a monomial curve.
Polynomial and rational solutions of holonomic systems
T. Oaku, N. Takayama, H. Tsai
The aim of this paper is to give two new algorithms, which are elimination free, to find polynomial and rational solutions for a given holonomic system associated to a set of linea…
A Localization Algorithm for -modules
Toshinori Oaku, Nobuki Takayama, Uli Walther
We present a method to compute the holonomic extension of a -module from a Zariski open set in affine space to the whole space. A particular application is the localization of c…
Algorithms for D-modules --- restriction, tensor product, localization, and local cohomology groups
Toshinori Oaku, Nobuki Takayama
We describe algorithms for computing various functors for algebraic D-modules, i.e. systems of linear partial differential equations with polynomial coefficients. We will give algo…