next up previous
: debugMode : Macros in libraries :


[f v] deRham c
string f; string v;  f is a polynomial given by a string.
This function can be used by loading the experimental package cohom.sm1. 
The dimensions of the deRham cohomology groups H^i(C^n - V(f),C) i=0, i=1, ..
.., n are returned in c.
For example, if c=[1 4 6 4], then it means that dim H^0(C^3-V(f),C) = 1,
dim H^1(C^3-V(f),C) = 4, and so on.
For the algorithm, see "An algorithm for de Rham cohomology groups of the
complement of an affine variety via D-module computation", 
Journal of pure and applied algebra, 139 (1999), 201--233. math.AG/9801114
Example 0:  [(x (x-1) (x-2)) (x)] deRham 
Example 1: [(x y (x+y-1)(x-2)) (x,y)] deRham 
Example 2: [(x^3-y^2) (x,y)] deRham 
Example 3: [(x^3-y^2 z^2) (x,y,z)] deRham 
Example 4: [(x y z (x+y+z-1)) (x,y,z)] deRham

Nobuki Takayama 平成17年2月10日