- Usage:
`populateCechComplexCC(I,cc)`

- Function: populateCechComplexCC
- Outputs:
- a mutable hash table, with entries corresponding to the direct summands of the chains in the Cech complex

For the ideal I=(f_{1},...,f_{k}) the routine computes the characteristic cycles of the localized modules M_{fi1,...,fik} and places them in the corresponding places in the Cech complex.

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}; |

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.

- BMM -- the characteristic cycle of the localized $D$-module
- pruneCechComplexCC -- reduction of the Cech complex that produces characteristic cycles of local cohomology modules