Details:
Title  An algorithm for de Rham cohomology groups of the complement of an affine variety via Dmodule computation  Author(s)  Toshinori Oaku, Nobuki Takayama  Type  Article in Journal  Abstract  We give an algorithm to compute the following cohomology groups on U=C^n45 degree ruleV(f) for any nonzero polynomial fset membership, variantQ[x1, ... ,xn]:
1. H^k(U,CU), CU is the constant sheaf on U with stalk C.
2. Image 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 H^k(C^n45 degree rule 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.  Length  33  Copyright  Elsevier Science B.V. 
File 
 URL 
dx.doi.org/10.1016/S00224049(99)000122 
Language  English  Journal  Journal of Pure and Applied Algebra  Volume  139  Number  13  Pages  201233  Year  1999  Month  June  Translation 
No  Refereed 
No 
