Algorithms forb-Functions, Restrictions, and Algebraic Local Cohomology Groups ofD-Modules

Restriction of hypergeometric 𝒟-modules with respect to coordinate subspaces

“…2.2.4]). There is an algorithm due to Oaku-Takayama (see [Oak97,OT01]) for the effective computation of the restriction of holonomic D-modules to linear subspaces by means of Gröbner basis calculations in the Weyl algebra. This algorithm is employed in the proof of the explicit restriction formulas in [CJT03,Thm.…”

A Quick Introduction to Gröbner Bases

“…A dramatic breakthrough was done by Oaku [16,17], where, based on Buchberger algorithm, new and effective algorithms on D-modules were created. Since regular triangulations originated in the study of hypergeometric equations, the algebraic development of toric ideals naturally had the great influence on the study of hypergeometric equations.…”

Algebraic Algorithms for D-Modules and Numerical Analysis

“…An algorithm of finding generators of J from those of I is given in [11]. By an elimination, we can find a system of equations for u(…”