We compute all points in the Boij-Soederberg cone of resolution which would minimally lead to matrix factorization of format the (18x(15+3), (15+3)x18 of a cubic in P4, its tranposed, its syzygy or the transpose of its syzygy. This trivial but lengthly computation takes a lot of time. The version allCandidates(0) reproduces a pre-calculated list.
i1 : cands=allCandidates(0);#cands o2 = 39 |
i3 : tally apply(cands,b->codim b)
o3 = Tally{3 => 39}
o3 : Tally
|
i4 : cands1=reverse apply(cands,b-> (degree b, b)); |
i5 : netList apply(13,i->apply(3,j->cands1_(j+3*i)))
+------------------------+------------------------+------------------------+
| 0 1 2 3 | 0 1 2 3 | 0 1 2 3 |
o5 = |(20, total: 3 10 15 8) |(20, total: 8 15 10 3) |(17, total: 4 11 14 7) |
| 0: 3 . . . | 0: 8 15 . . | 0: 2 . . . |
| 1: . 10 . . | 1: . . 10 . | 1: 2 11 1 . |
| 2: . . 15 8 | 2: . . . 3 | 2: . . 13 7 |
+------------------------+------------------------+------------------------+
| 0 1 2 3 | 0 1 2 3 | 0 1 2 3 |
|(17, total: 7 14 11 4) |(16, total: 3 14 15 4) |(16, total: 4 15 14 3) |
| 0: 7 13 . . | 0: 3 . . . | 0: 4 3 . . |
| 1: . 1 11 2 | 1: . 14 12 . | 1: . 12 14 . |
| 2: . . . 2 | 2: . . 3 4 | 2: . . . 3 |
+------------------------+------------------------+------------------------+
| 0 1 2 3 | 0 1 2 3 4 | 0 1 2 3 |
|(14, total: 5 12 13 6) |(14, total: 3 9 14 9 1) |(14, total: 6 13 12 5) |
| 0: 1 . . . | 0: 2 . . . . | 0: 6 11 . . |
| 1: 4 12 2 . | 1: 1 9 . . . | 1: . 2 12 4 |
| 2: . . 11 6 | 2: . . 14 9 1 | 2: . . . 1 |
+------------------------+------------------------+------------------------+
| 0 1 2 3 | 0 1 2 3 | 0 1 2 3 |
|(13, total: 4 15 14 3) |(13, total: 3 14 15 4) |(11, total: 6 13 12 5) |
| 0: 2 . . . | 0: 3 1 . . | 1: 6 13 3 . |
| 1: 2 15 13 . | 1: . 13 15 2 | 2: . . 9 5 |
| 2: . . 1 3 | 2: . . . 2 | |
+------------------------+------------------------+------------------------+
| 0 1 2 3 4 | 0 1 2 3 | 0 1 2 3 4 |
|(11, total: 4 10 13 8 1)|(11, total: 5 12 13 6) |(11, total: 6 12 11 6 1)|
| 0: 1 . . . . | 0: 5 9 . . | 0: 6 12 . . . |
| 1: 3 10 1 . . | 1: . 3 13 6 | 1: . . 11 3 . |
| 2: . . 12 8 1 | | 2: . . . 3 1 |
+------------------------+------------------------+------------------------+
| 0 1 2 3 4 | 0 1 2 3 4 | 0 1 2 3 4 |
|(10, total: 3 13 14 5 1)|(10, total: 3 13 14 5 1)|(8, total: 2 8 15 10 1) |
| 0: 2 . . . . | 0: 3 2 . . . | 0: 2 . . . . |
| 1: 1 13 12 . . | 1: . 11 14 1 . | 1: . 8 1 . . |
| 2: . . 2 5 1 | 2: . . . 4 1 | 2: . . 14 10 . |
| | | 3: . . . . 1 |
+------------------------+------------------------+------------------------+
| 0 1 2 3 4 | 0 1 2 3 4 | 0 1 2 3 4 |
|(8, total: 3 8 13 10 2) |(8, total: 5 11 12 7 1) |(8, total: 5 11 12 7 1) |
| 0: 1 . . . . | 1: 5 11 2 . . | 0: 5 10 . . . |
| 1: 2 8 . . . | 2: . . 10 7 1 | 1: . 1 12 5 . |
| 2: . . 13 10 2 | | 2: . . . 2 1 |
+------------------------+------------------------+------------------------+
| 0 1 2 3 4 | 0 1 2 3 4 | 0 1 2 3 4 |
|(7, total: 4 14 13 4 1) |(7, total: 2 11 14 7 2) |(7, total: 2 12 15 6 1) |
| 0: 1 . . . . | 0: 2 . . . . | 0: 2 . . . . |
| 1: 3 14 13 . . | 1: . 11 11 . . | 1: . 12 15 3 . |
| 2: . . . 4 1 | 2: . . 3 7 2 | 2: . . . 3 1 |
+------------------------+------------------------+------------------------+
| 0 1 2 3 4 | 0 1 2 3 4 | 0 1 2 3 4 |
|(7, total: 3 12 13 6 2) |(5, total: 4 9 12 9 2) |(5, total: 3 9 14 9 1) |
| 0: 3 3 . . . | 1: 4 9 1 . . | 0: 1 . . . . |
| 1: . 9 13 . . | 2: . . 11 9 2 | 1: 2 9 2 . . |
| 2: . . . 6 2 | | 2: . . 12 9 . |
| | | 3: . . . . 1 |
+------------------------+------------------------+------------------------+
| 0 1 2 3 4 | 0 1 2 3 4 | 0 1 2 3 4 |
|(5, total: 4 10 13 8 1) |(4, total: 2 12 15 6 1) |(4, total: 3 12 13 6 2) |
| 0: 4 8 . . . | 0: 2 . . . . | 0: 1 . . . . |
| 1: . 2 13 7 . | 1: . 12 13 . . | 1: 2 12 12 . . |
| 2: . . . 1 1 | 2: . . 2 6 . | 2: . . 1 6 2 |
| | 3: . . . . 1 | |
+------------------------+------------------------+------------------------+
| 0 1 2 3 4 | 0 1 2 3 4 | 0 1 2 3 4 |
|(4, total: 2 11 14 7 2) |(2, total: 3 7 12 11 3) |(2, total: 2 7 14 11 2) |
| 0: 2 1 . . . | 1: 3 7 . . . | 0: 1 . . . . |
| 1: . 10 14 2 . | 2: . . 12 11 3 | 1: 1 7 1 . . |
| 2: . . . 5 2 | | 2: . . 13 11 1 |
| | | 3: . . . . 1 |
+------------------------+------------------------+------------------------+
| 0 1 2 3 4 | 0 1 2 3 4 | 0 1 2 3 4 |
|(2, total: 4 10 13 8 1) |(2, total: 3 9 14 9 1) |(2, total: 4 9 12 9 2) |
| 1: 4 10 3 . . | 0: 3 6 . . . | 0: 4 9 . . . |
| 2: . . 10 8 . | 1: . 3 14 9 . | 1: . . 12 6 . |
| 3: . . . . 1 | 2: . . . . 1 | 2: . . . 3 2 |
+------------------------+------------------------+------------------------+
| 0 1 2 3 4 | 0 1 2 3 4 | 0 1 2 3 4 |
|(1, total: 3 13 14 5 1) |(1, total: 2 10 13 8 3) |(1, total: 2 10 13 8 3) |
| 0: 1 . . . . | 0: 1 . . . . | 0: 2 2 . . . |
| 1: 2 13 14 . . | 1: 1 10 11 . . | 1: . 8 13 1 . |
| 2: . . . 5 . | 2: . . 2 8 3 | 2: . . . 7 3 |
| 3: . . . . 1 | | |
+------------------------+------------------------+------------------------+
|