The function prints a precompiled list of the Betti candidates whose induced matrix factorizations have the same shape as the matrix factorization induced by a general curve of the input genus g and the degree as in the paper. The shape is computed assuming that every possible cancellation occurs
i1 : p=32009; |
i2 : Fp=ZZ/p; |
i3 : S=Fp[x_0..x_4]; |
i4 : beta=betti map(S^{22:0,6:-2},S^{0:-1,4:-2,24:-3},0)
0 1
o4 = total: 28 28
0: 22 .
1: . 4
2: 6 24
o4 : BettiTally
|
i5 : possMF=listOfPossibleMatFac(beta,4); |
i6 : precompiledListOfCandidates(20)
0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0
o6 = {total: 3 16 21 12 4, total: 4 13 22 15 2, total: 5 15 22 13 1, total: 3
0: 1 . . . . 1: 4 7 . . . 1: 5 9 . . . 2: 3
1: . . . . . 2: . . 2 . . 2: . . 4 . . 3: .
2: 2 16 17 . . 3: . 6 20 15 . 3: . 6 18 13 . 4: .
3: . . . 4 . 4: . . . . 2 4: . . . . .
4: . . 4 8 4 5: . . . . 1
------------------------------------------------------------------------
1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4
8 19 20 6, total: 6 16 21 12 1, total: 4 18 21 10 3, total: 7 21 18 7 3,
4 . . . 2: 6 12 6 . . 0: 1 . . . . 0: 1 . . . .
4 . . . 3: . 4 . . . 1: . . . . . 1: . 3 . . .
. 19 20 6 4: . . 15 12 . 2: 3 18 18 . . 2: 6 18 18 . .
5: . . . . . 3: . . . 4 . 3: . . . 1 .
6: . . . . 1 4: . . 3 6 3 4: . . . 6 3
------------------------------------------------------------------------
0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0
total: 2 16 23 12 3, total: 3 18 23 10 2, total: 4 9 18 19 6, total: 4
0: 1 . . . . 1: 3 . . . . 2: 4 6 . . . 2: 4
1: 1 . . . . 2: . 18 22 6 . 3: . 3 . . . 3: .
2: . 16 20 6 . 3: . . 1 . . 4: . . 18 18 6 4: .
3: . . 3 . . 4: . . . 4 2 5: . . . 1 .
4: . . . 6 3
------------------------------------------------------------------------
1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4
10 19 18 5, total: 5 20 21 8 2, total: 7 22 19 6 2, total: 5 12 19 16 4,
6 1 . . 0: 1 . . . . 0: 1 . . . . 2: 5 8 2 . .
4 . . . 1: . . . . . 1: . 2 . . . 3: . 4 . . .
. 18 18 5 2: 4 20 19 . . 2: 6 20 19 . . 4: . . 17 16 4
3: . . . 4 . 3: . . . 2 .
4: . . 2 4 2 4: . . . 4 2
------------------------------------------------------------------------
0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1
total: 6 22 21 6 1, total: 7 23 20 5 1, total: 6 16 21 12 1, total: 6 14
0: 1 . . . . 0: 1 . . . . 1: 6 10 . . . 2: 6 10
1: . . . . . 1: . 1 . . . 2: . . 3 . . 3: . 4
2: 5 22 20 . . 2: 6 22 20 . . 3: . 6 18 12 . 4: . .
3: . . . 4 . 3: . . . 3 . 4: . . . . 1
4: . . 1 2 1 4: . . . 2 1
------------------------------------------------------------------------
2 3 4 0 1 2 3 4 0 1 2 3 0 1 2 3 4
19 14 3, total: 2 16 23 12 3, total: 7 24 21 4, total: 2 17 24 11 2,
3 . . 0: 2 . . . . 0: 1 . . . 0: 2 . . . .
. . . 1: . . . . . 1: . . . . 1: . . . . .
16 14 3 2: . 16 17 . . 2: 6 24 21 . 2: . 17 20 6 .
3: . . . 4 . 3: . . . 4 3: . . 4 . .
4: . . 6 8 3 4: . . . 5 2
------------------------------------------------------------------------
0 1 2 3 4 0 1 2 3 0 1 2 3 4 0 1
total: 3 19 24 9 1, total: 4 21 24 7, total: 7 16 19 12 2, total: 3 18
0: 1 . . . . 1: 4 . . . 2: 7 12 4 . . 0: 2 .
1: 2 . . . . 2: . 21 24 6 3: . 4 . . . 1: . .
2: . 19 22 6 . 3: . . . . 4: . . 15 12 2 2: 1 18
3: . . 2 . . 4: . . . 1 3: . .
4: . . . 3 1 4: . .
------------------------------------------------------------------------
2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4
23 10 2, total: 8 18 19 10 1, total: 4 20 23 8 1, total: 8 24 19 4 1,
. . . 2: 8 14 5 . . 0: 2 . . . . 0: 2 . . . .
. . . 3: . 4 . . . 1: . . . . . 1: . 4 . . .
18 . . 4: . . 14 10 1 2: 2 20 19 . . 2: 6 20 19 . .
. 4 . 3: . . . 4 . 3: . . . . .
5 6 2 4: . . 4 4 1 4: . . . 4 1
------------------------------------------------------------------------
0 1 2 3 0 1 2 3 0 1 2 3 4 0 1 2
total: 8 19 20 9, total: 9 20 19 8, total: 2 14 21 14 5, total: 5 14 21
1: 8 13 . . 2: 9 16 6 . 0: 1 . . . . 2: 5 10 5
2: . . 4 . 3: . 4 . . 1: . . . . . 3: . 4 .
3: . 6 16 9 4: . . 13 8 2: 1 14 16 . . 4: . . 16
3: . . . 4 . 5: . . .
4: . . 5 10 5 6: . . .
------------------------------------------------------------------------
3 4 0 1 2 3 0 1 2 3 0 1 2 3 0 1
14 2, total: 5 22 23 6, total: 8 25 20 3, total: 3 20 25 8, total: 6 23
. . 0: 2 . . . 0: 2 . . . 0: 2 . . . 0: 2 3
. . 1: . . . . 1: . 3 . . 1: 1 . . . 1: 4 .
14 1 2: 3 22 20 . 2: 6 22 20 . 2: . 20 22 6 2: . 20
. . 3: . . . 4 3: . . . 1 3: . . 3 . 3: . .
. 1 4: . . 3 2 4: . . . 2 4: . . . 2 4: . .
------------------------------------------------------------------------
2 3 0 1 2 3 4 0 1 2 3 0 1 2 3
22 5, total: 7 23 20 5 1, total: 3 20 25 8, total: 8 25 20 3}
. . 0: 3 5 . . . 0: 3 . . . 0: 4 6 . .
. . 1: 4 . . . . 1: . . . . 1: 4 . . .
22 3 2: . 18 20 1 . 2: . 20 19 . 2: . 19 20 .
. . 3: . . . . . 3: . . . 4 3: . . . .
. 2 4: . . . 4 1 4: . . 6 4 4: . . . 3
o6 : List
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