Polynomial and rational solutions of holonomic systems

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 linear differential operators in the Weyl algebra D = k where k is a subfield of the complex numbers.Comment: 20 page

Algebraic computation of some intersection D-modules

Let $X$ be a complex analytic manifold, $D\subset X$ a locally quasi-homogeneous free divisor, $E$ an integrable logarithmic connection with respect to $D$ and $L$ the local system of the horizontal sections of $E$ on $X-D$. In this paper we give an algebraic description in terms of $E$ of the regular holonomic D-module whose de Rham complex is the intersection complex associated with $L$. As an application, we perform some effective computations in the case of quasi-homogeneous plane curves.Comment: 18 page

On Computing Groebner Basis in the Rings of Differential Operators

Insa and Pauer presented a basic theory of Groebner basis for differential operators with coefficients in a commutative ring in 1998, and a criterion was proposed to determine if a set of differential operators is a Groebner basis. In this paper, we will give a new criterion such that Insa and Pauer's criterion could be concluded as a special case and one could compute the Groebner basis more efficiently by this new criterion