Determine the positions, where the non-zero numbers in both lists which coincide up to a threshold. This is needed in the Laplacian method to compute the SVD normal form of a complex
i1 : needsPackage "RandomComplexes" o1 = RandomComplexes o1 : Package |
i2 : setRandomSeed "a good example"; |
i3 : h={2,3,5,3}
o3 = {2, 3, 5, 3}
o3 : List
|
i4 : r={4,3,5}
o4 = {4, 3, 5}
o4 : List
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i5 : elapsedTime C=randomChainComplex(h,r,Height=>100,ZeroMean=>true)
-- 0.00379691 seconds elapsed
6 10 13 8
o5 = ZZ <-- ZZ <-- ZZ <-- ZZ
0 1 2 3
o5 : ChainComplex
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i6 : C.dd^2
6 13
o6 = 0 : ZZ <----- ZZ : 2
0
10 8
1 : ZZ <----- ZZ : 3
0
o6 : ChainComplexMap
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i7 : D=disturb(C**RR_53,1e-4)
6 10 13 8
o7 = RR <-- RR <-- RR <-- RR
53 53 53 53
0 1 2 3
o7 : ChainComplex
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i8 : Delta=laplacians D; |
i9 : L0=(SVD Delta#0)_0, L1=(SVD Delta#1)_0,L2=(SVD Delta#2)_0,L3=(SVD Delta#3)_0
o9 = ({60648900}, {28210500000}, {28210500000}, {2056900000})
{55489200} {9617270000 } {9617270000 } {1028620000}
{29990300} {3132530000 } {3132530000 } {754460000 }
{9100710 } {60649000 } {2056900000 } {484906000 }
{.327165 } {55489300 } {1028620000 } {49026600 }
{.0102018} {29990300 } {754460000 } {3.7497 }
{9100740 } {484906000 } {2.9526 }
{38.8744 } {49026600 } {1.35595 }
{21.2473 } {51.0793 }
{5.85738 } {29.3294 }
{20.8771 }
{3.48837 }
{2.04772 }
o9 : Sequence
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i10 : commonEntries(L0,L1)
o10 = ({0, 1, 2, 3}, {3, 4, 5, 6})
o10 : Sequence
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i11 : commonEntries(L1,L2)
o11 = ({0, 1, 2}, {0, 1, 2})
o11 : Sequence
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i12 : commonEntries(L2,L3)
o12 = ({3, 4, 5, 6, 7}, {0, 1, 2, 3, 4})
o12 : Sequence
|