i1 : n={1,1};
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i2 : (S,E) = productOfProjectiveSpaces n;
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i3 : T1 = (dual res trim (ideal vars E)^2)[1];
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i4 : a=-{2,2};T2=T1**E^{a}[sum a];
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i6 : W=beilinsonWindow T2,cohomologyMatrix(W,-2*n,2*n)
15 16 4
o6 = (E <-- E <-- E , | 0 0 0 0 0 |)
| 0 0 0 0 0 |
0 1 2 | 0 8 15 0 0 |
| 0 4 8 0 0 |
| 0 0 0 0 0 |
o6 : Sequence
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i7 : T=tateExtension W;
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i8 : cohomologyMatrix(T,-{3,3},{3,3})
o8 = | 12h 4 20 36 52 68 84 |
| 10h 3 16 29 42 55 68 |
| 8h 2 12 22 32 42 52 |
| 6h 1 8 15 22 29 36 |
| 4h 0 4 8 12 16 20 |
| 2h h 0 1 2 3 4 |
| 0 2h 4h 6h 8h 10h 12h |
7 7
o8 : Matrix (ZZ[h, k]) <-- (ZZ[h, k])
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i9 : c={1,0}
o9 = {1, 0}
o9 : List
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i10 : rT0=regionComplex(T,c,({},{0,1},{})); --a single position
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i11 : cohomologyMatrix(rT0,-{3,3},{3,3})
o11 = | 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 22 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
7 7
o11 : Matrix (ZZ[h, k]) <-- (ZZ[h, k])
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i12 : rT1=regionComplex(T,c,({0},{1},{})); --a horizontal half line
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i13 : cohomologyMatrix(rT1,-{3,3},{3,3})
o13 = | 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 6h 1 8 15 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
7 7
o13 : Matrix (ZZ[h, k]) <-- (ZZ[h, k])
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i14 : rT2=regionComplex(T,c,({},{0},{})); -- a vertical line
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i15 : cohomologyMatrix(rT2,-{3,3},{3,3})
o15 = | 0 0 0 0 52 0 0 |
| 0 0 0 0 42 0 0 |
| 0 0 0 0 32 0 0 |
| 0 0 0 0 22 0 0 |
| 0 0 0 0 12 0 0 |
| 0 0 0 0 2 0 0 |
| 0 0 0 0 8h 0 0 |
7 7
o15 : Matrix (ZZ[h, k]) <-- (ZZ[h, k])
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i16 : rT3=regionComplex(T,c,({},{},{1})); -- a upper half plane
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i17 : cohomologyMatrix(rT3,-{3,3},{3,3})
o17 = | 12h 4 20 36 52 68 84 |
| 10h 3 16 29 42 55 68 |
| 8h 2 12 22 32 42 52 |
| 6h 1 8 15 22 29 36 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
7 7
o17 : Matrix (ZZ[h, k]) <-- (ZZ[h, k])
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i18 : rT4=regionComplex(T,c,({0},{},{1})); --a north east quadrant
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i19 : cohomologyMatrix(rT4,-{3,3},{3,3})
o19 = | 12h 4 20 36 0 0 0 |
| 10h 3 16 29 0 0 0 |
| 8h 2 12 22 0 0 0 |
| 6h 1 8 15 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
7 7
o19 : Matrix (ZZ[h, k]) <-- (ZZ[h, k])
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i20 : rT5=regionComplex(T,c,({1},{},{0})); --a south west quadrant
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i21 : cohomologyMatrix(rT5,-{3,3},{3,3})
o21 = | 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 12 16 20 |
| 0 0 0 0 2 3 4 |
| 0 0 0 0 8h 10h 12h |
7 7
o21 : Matrix (ZZ[h, k]) <-- (ZZ[h, k])
|