Description
Returns a surjective ChainComplexMap that is a quasi-isomorphism from a (generally non-minimal) ChainComplex of free modules. resolution C is the same as resolutionOfChainComplex C. The quasi-isomorphism is computed by the method of iterated mapping cones. (For the computation of the Cartan-Eilenberg resolution, which is usually slower and results in a larger complex, use cartanEilenbergResolution C
i1 : R = ZZ/32003[a..d]
o1 = R
o1 : PolynomialRing
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i2 : I = monomialCurveIdeal(R,{1,2,3})
2 2
o2 = ideal (c - b*d, b*c - a*d, b - a*c)
o2 : Ideal of R
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i3 : C = koszulComplex(ideal vars R) ** (R^1/I);
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i4 : m = res C;
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i5 : isQuasiIsomorphism m
o5 = true
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i6 : betti source m
0 1 2 3 4 5 6
o6 = total: 1 7 20 30 25 11 2
0: 1 4 6 4 1 . .
1: . 3 14 26 24 11 2
o6 : BettiTally
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i7 : C == target m
o7 = true
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