# Singular          #### D.15.11.1 deRhamCohomology

Procedure from library `deRham.lib` (see deRham_lib).

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

Example:
 ```LIB "deRham.lib"; ring r = 0,(x,y,z),dp; list L=(xy,xz); deRhamCohomology(L); ==> : ==> 1 ==> : ==> 1 ==> : ==> 0 ==> : ==> 1 ==> : ==> 1 ```

### Misc 