Extract the terms which under the U-functor defined in Tate Resolutions on Products of Projective Spaces contributed to the Beilinson complex U(T) of T, i.e. W is the smallest free subquotient complex of T such that U(W) = U(T)
i1 : n={1,1};
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i2 : (S,E) = productOfProjectiveSpaces n; |
i3 : W=(chainComplex {map(E^0,E^1,0),map(E^1,E^0,0)})[1]
1
o3 = 0 <-- E <-- 0
-1 0 1
o3 : ChainComplex
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i4 : time T=tateExtension W;
-- used 0.272329 seconds
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i5 : cohomologyMatrix(T,-{3,3},{3,3})
o5 = | 8h 4h 0 4 8 12 16 |
| 6h 3h 0 3 6 9 12 |
| 4h 2h 0 2 4 6 8 |
| 2h h 0 1 2 3 4 |
| 0 0 0 0 0 0 0 |
| 2h2 h2 0 h 2h 3h 4h |
| 4h2 2h2 0 2h 4h 6h 8h |
7 7
o5 : Matrix (ZZ[h, k]) <--- (ZZ[h, k])
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i6 : W=beilinsonWindow T
1
o6 = 0 <-- E <-- 0
-1 0 1
o6 : ChainComplex
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i7 : cohomologyMatrix(W,-{2,2},{2,2})
o7 = | 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 1 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
5 5
o7 : Matrix (ZZ[h, k]) <--- (ZZ[h, k])
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i8 : a={2,-3}
o8 = {2, -3}
o8 : List
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i9 : W2=beilinsonWindow (T**E^{a}[sum a])
4 11 6
o9 = E <-- E <-- E
-1 0 1
o9 : ChainComplex
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i10 : cohomologyMatrix(W2,-{2,2},{2,2})
o10 = | 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 8h 4h 0 0 |
| 0 6h 3h 0 0 |
| 0 0 0 0 0 |
5 5
o10 : Matrix (ZZ[h, k]) <--- (ZZ[h, k])
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i11 : cohomologyMatrix(tateExtension W2,-{2,2},{2,2})
o11 = | 18h 12h 6h 0 6 |
| 15h 10h 5h 0 5 |
| 12h 8h 4h 0 4 |
| 9h 6h 3h 0 3 |
| 6h 4h 2h 0 2 |
5 5
o11 : Matrix (ZZ[h, k]) <--- (ZZ[h, k])
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