Singular

D.15.7.1 deRhamCohomology

Usage:

deRhamCohomology(L[,choices]); L a list consisting of polynomials, choices optional list consisting of one up to three strings
The optional strings may be one of the strings
-'noCE': compute quasi-isomorphic complexes without using Cartan-Eilenberg resolutionsq
-'Vdres': compute quasi-isomorphic complexes using Cartan-Eilenberg resolutions; the CE resolutions are computed via V__d-homogenization and without using Schreyer's method
-'Sres': compute quasi-isomorphic complexes using Cartan-Eilenberg resolutions in the homogenized Weyl algebra via Schreyer's method
one of the strings
-'iterativeloc': compute localizations by factorizing the polynomials and sucessive localization of the factors
-'no iterativeloc': compute localizations by directly localizing the product
and one of the strings
-'onlybounds': computes bounds for the minimal and maximal interger roots of the global b-function
-'exactroots' computes the minimal and maximal integer root of the global b-function
The default is 'noCE', 'iterativeloc' and 'onlybounds'.

Assume:

-The basering must be a polynomial ring over the field of rational numbers

Return:

list, where the ith entry is the (i-1)st de Rham cohomology group of the complement of the complex affine variety given by the polynomials in L

LIB "deRham.lib";
ring r = 0,(x,y,z),dp;
list L=(xy,xz);
deRhamCohomology(L);
==> [1]:
==>    1
==> [2]:
==>    1
==> [3]:
==>    0
==> [4]:
==>    1
==> [5]:
==>    1