i1 : R = ZZ/101[a..d, Degrees => {2:{1,0}, 2:{0,1}}];
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i2 : I = ideal random(R^1, R^{2:{-2,-2}, 2:{-3,-3}});
o2 : Ideal of R
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i3 : t = betti res I
0 1 2 3 4
o3 = total: 1 4 13 14 4
0: 1 . . . .
1: . . . . .
2: . . . . .
3: . 2 . . .
4: . . . . .
5: . 2 . . .
6: . . 1 . .
7: . . 8 6 .
8: . . 4 8 4
o3 : BettiTally
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i4 : peek t
o4 = BettiTally{(0, {0, 0}, 0) => 1 }
(1, {2, 2}, 4) => 2
(1, {3, 3}, 6) => 2
(2, {3, 7}, 10) => 2
(2, {4, 4}, 8) => 1
(2, {4, 5}, 9) => 4
(2, {5, 4}, 9) => 4
(2, {7, 3}, 10) => 2
(3, {4, 7}, 11) => 4
(3, {5, 5}, 10) => 6
(3, {7, 4}, 11) => 4
(4, {5, 7}, 12) => 2
(4, {7, 5}, 12) => 2
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The following three displays show the first degree, the second degree, and the total degree, respectively.
i5 : betti(t, Weights => {1,0})
0 1 2 3 4
o5 = total: 1 4 13 14 4
0: 1 . . . .
1: . 2 2 4 2
2: . 2 5 6 .
3: . . 4 . 2
4: . . . 4 .
5: . . 2 . .
o5 : BettiTally
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i6 : betti(t, Weights => {0,1})
0 1 2 3 4
o6 = total: 1 4 13 14 4
0: 1 . . . .
1: . 2 2 4 2
2: . 2 5 6 .
3: . . 4 . 2
4: . . . 4 .
5: . . 2 . .
o6 : BettiTally
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i7 : betti(t, Weights => {1,1})
0 1 2 3 4
o7 = total: 1 4 13 14 4
0: 1 . . . .
1: . . . . .
2: . . . . .
3: . 2 . . .
4: . . . . .
5: . 2 . . .
6: . . 1 . .
7: . . 8 6 .
8: . . 4 8 4
o7 : BettiTally
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i8 : peek oo
o8 = BettiTally{(0, {0, 0}, 0) => 1 }
(1, {2, 2}, 4) => 2
(1, {3, 3}, 6) => 2
(2, {3, 7}, 10) => 2
(2, {4, 4}, 8) => 1
(2, {4, 5}, 9) => 4
(2, {5, 4}, 9) => 4
(2, {7, 3}, 10) => 2
(3, {4, 7}, 11) => 4
(3, {5, 5}, 10) => 6
(3, {7, 4}, 11) => 4
(4, {5, 7}, 12) => 2
(4, {7, 5}, 12) => 2
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i9 : t' = multigraded t
0 1 2 3 4
o9 = 0: 1 . . . .
4: . 2a2b2 . . .
6: . 2a3b3 . . .
8: . . a4b4 . .
9: . . 4a5b4+4a4b5 . .
10: . . 2a7b3+2a3b7 6a5b5 .
11: . . . 4a7b4+4a4b7 .
12: . . . . 2a7b5+2a5b7
o9 : MultigradedBettiTally
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i10 : betti(t', Weights => {1,0})
0 1 2 3 4
o10 = 0: 1 . . . .
2: . 2a2b2 . . .
3: . 2a3b3 2a3b7 . .
4: . . 4a4b5+a4b4 4a4b7 .
5: . . 4a5b4 6a5b5 2a5b7
7: . . 2a7b3 4a7b4 2a7b5
o10 : MultigradedBettiTally
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i11 : betti(t', Weights => {0,1})
0 1 2 3 4
o11 = 0: 1 . . . .
2: . 2a2b2 . . .
3: . 2a3b3 2a7b3 . .
4: . . 4a5b4+a4b4 4a7b4 .
5: . . 4a4b5 6a5b5 2a7b5
7: . . 2a3b7 4a4b7 2a5b7
o11 : MultigradedBettiTally
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i12 : betti(t', Weights => {1,1})
0 1 2 3 4
o12 = 0: 1 . . . .
4: . 2a2b2 . . .
6: . 2a3b3 . . .
8: . . a4b4 . .
9: . . 4a5b4+4a4b5 . .
10: . . 2a7b3+2a3b7 6a5b5 .
11: . . . 4a7b4+4a4b7 .
12: . . . . 2a7b5+2a5b7
o12 : MultigradedBettiTally
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