Computational Analysis of Hypergeometric Differential Equations

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We have obtained the following results1. We constructed vol(A)-linearly independent convergent series solutions for A-hypergeometric differential-difference equations.2. We prove that any local Grober fan is a polyhedral fan. As an application of this fact, we give an algorithm of computing local BS polynomials, that of computing local tropical varieties, and discuss a relation of slopes and local Grobner fan.3. We gave a tangent cone algorithm to study D-modules locally.We have more results. As to these, refer to Japanese version of this research report and papers.