4 papers
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…
An algorithm for de Rham cohomology groups of the complement of an affine variety via D-module computation
Toshinori Oaku, Nobuki Takayama
We give an algorithm to compute the following cohomology groups on $U = \C^n \setminus V(f)$ for any non-zero polynomial $f \in \Q[x_1, ..., x_n]$; 1. $H^k(U, \C_U)$, $\C_U$ is the…