Singular Manual: deRhamCohomology

| #### D.5.3.1 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 successive 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 integer 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
    ==> [2]:
    ==>    1
    ==> [3]:
    ==>    0
    ==> [4]:
    ==>    1
    ==> [5]:
    ==>    1

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