The function reduces the Cech complex skeleton produced by populateCechComplexCC leaving the pieces of the characteristic cycles of the chains that together constitute the characteristic cycles of the local cohomology modules.
i1 : W = QQ[x_1..x_6, a_1..a_6];
i2 : I = minors(2, matrix{{x_1, x_2, x_3}, {x_4, 0, 0}});
o2 : Ideal of W
i3 : cc = {ideal W => 1};
Caveat
The module has to be a regular holonomic complex-analytic module; while the holomicity can be checked by isHolonomic there is no algorithm to check the regularity.