An algorithm for de Rham cohomology groups of the complement of an affine variety via D-module computation

AbstractWe give an algorithm to compute the following cohomology groups on U=Cn⧹V(f) for any non-zero polynomial f∈Q[x1,…,xn]:1. Hk(U,CU),CU is the constant sheaf on U with stalk C.2. Hk(U,V),V is a locally constant sheaf of rank 1 on U.We also give partial results on computation of cohomology groups on U for a locally constant sheaf of general rank and on computation of Hk(Cn⧹Z,C) where Z is a general algebraic set. Our algorithm is based on computations of Gröbner bases in the ring of differential operators with polynomial coefficients