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ConvexInterface :: mHomology

mHomology -- Compute the homology.

Synopsis

Description

Returns a list of FinitelyGeneratedAbelianGroups with the homology with closed support of C with integer coefficients.

C does not have to be simplicial.

This uses the Convex functions convHull, simplicialsubdiv, pcomplex and homology.

Remark: One should also implement the relative version from Convex.

i1 : C={{{}}, {{{-1, -1, -1, -1}}, {{1, 0, 0, 0}}, {{0, 1, 0, 0}}, {{0, 0, 1,0}}, {{0, 0, 0, 1}}}, {{{-1, -1, -1, -1}, {0, 1, 0, 0}}, {{-1, -1, -1,-1}, {0, 0, 1, 0}}, {{1, 0, 0, 0}, {0, 0, 1, 0}}, {{1, 0, 0, 0}, {0, 0, 0,1}}, {{0, 1, 0, 0}, {0, 0, 0, 1}}}, {}, {}, {}};
i2 : mHomology(C)

o2 = {}

o2 : List

RP2:

i3 : C= {{{}}, {{{-1, -1, -1, -1, -1}}, {{1, 0, 0, 0, 0}}, {{0, 1, 0, 0, 0}}, {{0, 0, 1, 0, 0}}, {{0, 0, 0, 1, 0}}, {{0, 0, 0, 0, 1}}}, {{{-1, -1, -1, -1,-1}, {1, 0, 0, 0, 0}}, {{-1, -1, -1, -1, -1}, {0, 1, 0, 0, 0}}, {{1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}}, {{-1, -1, -1, -1, -1}, {0, 0, 1, 0, 0}}, {{1, 0, 0, 0, 0}, {0, 0, 1, 0, 0}}, {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}}, {{-1, -1, -1, -1, -1}, {0, 0, 0, 1, 0}}, {{1, 0, 0, 0, 0}, {0, 0, 0, 1, 0}}, {{0, 1, 0, 0, 0}, {0, 0, 0, 1, 0}}, {{0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}}, {{-1, -1, -1, -1, -1}, {0, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0}, {0, 0, 0, 0, 1}}, {{0, 1, 0, 0, 0}, {0, 0, 0, 0, 1}}, {{0, 0, 1, 0, 0}, {0, 0, 0, 0, 1}}, {{0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}}}, {{{-1, -1, -1, -1, -1}, {1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}}, {{1, 0, 0, 0, 0}, {0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}}, {{-1, -1, -1, -1, -1}, {1, 0, 0, 0, 0}, {0, 0, 0, 1, 0}}, {{-1, -1, -1, -1, -1}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}}, {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}}, {{-1, -1, -1, -1, -1}, {0, 1, 0, 0, 0}, {0, 0, 0, 0, 1}}, {{-1, -1, -1, -1, -1}, {0, 0, 1, 0, 0}, {0, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 0, 1}}, {{1, 0, 0, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}}, {{0, 1, 0, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}}}, {}, {}, {}};
i4 : mHomology(C)

o4 = {}

o4 : List

Ways to use mHomology :

For the programmer

The object mHomology is a method function.