- Usage:
`BMM(cc,f), BMM(I,cc)`

- Outputs:
`List`, the characteristic cycle of the localized module*M*_{f}= M[f^{-1}]

Provided a characteristic cycle in the form `{I_1 => m_1, ..., I_k => m_k}` with associated prime ideals I_{1},...,I_{k} and the multiplicities m_{1},...,m_{k} of M along them, the routine computes the characteristic cycle of M_{f}.

The method is based on a geometric formula given by V.Ginsburg in *Characteristic varieties and vanishing cycles, Invent. Math. 84 (1986), 327--402.* and reinterpreted by J.Briancon, P.Maisonobe and M.Merle in *Localisation de systemes differentiels, stratifications de Whitney et condition de Thom, Invent. Math. 117 (1994), 531--550*.

i1 : A = QQ[x_1,x_2,a_1,a_2] o1 = A o1 : PolynomialRing |

i2 : cc = {ideal A => 1} -- the characteristic ideal of R = CC[x_1,x_2] o2 = {ideal () => 1} o2 : List |

i3 : cc1 = BMM(cc,x_1) -- cc of R_{x_1} o3 = {ideal () => 1, ideal(x ) => 1} 1 o3 : List |

i4 : cc12 = BMM(cc1,x_2) -- cc of R_{x_1x_2} o4 = {ideal () => 1, ideal(x ) => 1, ideal(x ) => 1, ideal (x , x ) => 1} 2 1 2 1 o4 : List |

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.

- pruneCechComplexCC -- reduction of the Cech complex that produces characteristic cycles of local cohomology modules
- populateCechComplexCC -- Cech complex skeleton for the computation of the characteristic cycles of local cohomology modules

- BMM(Ideal,RingElement)
- BMM(List,RingElement)