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}}}, {}, {}, {}};
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i2 : mHomology(C)
o2 = {}
o2 : List
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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}}}, {}, {}, {}};
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i4 : mHomology(C)
o4 = {}
o4 : List
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The object mHomology is a method function.