In this procedure we work over the coordinate ring SQ where Q ⊂ ℙ11 is the complete intersection of the four quadratic relations. For i=1,2, we resolve the matrices li and litr in both directions and put this together to a chain complex Ci. Very surprisingly, in the case "1111" the resolution of l1 and l2 over the non-regular ring SQ is finite in both directions. So far, we have studied these chain complexes mainly for the case "1111". The resulting complexes C1 and C2 are exact outside a codimension 3 respectively 2 subscheme of Q. These loci are determined in the procedure homologyLocus.
i1 : kk = ZZ/197; |
i2 : s = "1111"; |
i3 : (relLin,relPfaf,d1',d2,Ms) = setupGodeaux(kk,s); |
i4 : (C1,C2) = getChainComplexes(relLin,relPfaf); |
i5 : betti C1, betti C2
0 1 2 3 0 1 2 3
o5 = (total: 4 12 12 4, total: 12 30 20 2)
-3: 4 12 12 4 -4: 12 30 20 .
-3: . . . .
-2: . . . 2
o5 : Sequence
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i6 : prune HH C1
o6 = 0 : cokernel {-3} | a_(3,0,3) a_(3,1,3) a_(3,2,3) 0 0
{-3} | 0 0 0 a_(2,0,2) a_(2,1,2)
{-3} | 0 0 0 0 0
{-3} | 0 0 0 0 0
0 0 0 0 0 0
a_(2,2,3) 0 0 0 0 0
0 a_(1,0,1) a_(1,1,2) a_(1,1,3) 0 0
0 0 0 0 a_(0,0,1) a_(0,0,2)
0 |
0 |
0 |
a_(0,0,3) |
1 : 0
2 : 0
3 : 0
o6 : GradedModule
|
i7 : apply(4,i-> (pH = prune HH_i(C1); (dim pH,degree pH)))
o7 = {(5, 64), (-1, 0), (-1, 0), (-1, 0)}
o7 : List
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i8 : dim ring C1 o8 = 8 |
i9 : apply(4,i-> (pH = prune HH_i(C2); (dim pH,degree pH)))
o9 = {(6, 72), (6, 72), (-1, 0), (-1, 0)}
o9 : List
|