Description
By definition, this is the same as computing HH_(-i) C.
i1 : R = ZZ/101[x,y]
o1 = R
o1 : PolynomialRing
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i2 : C = chainComplex(matrix{{x,y}},matrix{{x*y},{-x^2}})
1 2 1
o2 = R <-- R <-- R
0 1 2
o2 : ChainComplex
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i3 : M = HH^1 C
o3 = 0
o3 : R-module
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i4 : prune M
o4 = 0
o4 : R-module
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Here is another example computing simplicial cohomology (for a hollow tetrahedron):
i5 : needsPackage "SimplicialComplexes"
o5 = SimplicialComplexes
o5 : Package
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i6 : R = QQ[a..d]
o6 = R
o6 : PolynomialRing
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i7 : D = simplicialComplex {a*b*c,a*b*d,a*c*d,b*c*d}
o7 = simplicialComplex | bcd acd abd abc |
o7 : SimplicialComplex
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i8 : C = chainComplex D
1 4 6 4
o8 = QQ <-- QQ <-- QQ <-- QQ
-1 0 1 2
o8 : ChainComplex
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i9 : HH_2 C
o9 = image | -1 |
| 1 |
| -1 |
| 1 |
4
o9 : QQ-module, submodule of QQ
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i10 : prune oo
1
o10 = QQ
o10 : QQ-module, free
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