
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 quasiisomorphic complexes without using CartanEilenberg
resolutionsq
'Vdres': compute quasiisomorphic complexes using CartanEilenberg
resolutions; the CE resolutions are computed via V__dhomogenization
and without using Schreyer's method
'Sres': compute quasiisomorphic complexes using CartanEilenberg
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 bfunction
'exactroots' computes the minimal and maximal integer root of the global
bfunction
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 (i1)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
==> [2]:
==> 1
==> [3]:
==> 0
==> [4]:
==> 1
==> [5]:
==> 1

