The result is a hash table whose keys are the names of the 19 Betti table strata for quartenary quartics. For each, the value is a matrix wholse columns represent points. The quartic corresponding to this matrix is the sum of the 4th powers of the corresponding linear forms.
i1 : S = ZZ/101[a..d] o1 = S o1 : PolynomialRing |
i2 : bettiStrataExamples S
o2 = HashTable{[000] => {| 1 0 0 0 1 22 2 -37 -18 32 |, 10 general points} }
| 0 1 0 0 1 -47 29 -13 39 -9 |
| 0 0 1 0 1 -23 -47 -10 27 -32 |
| 0 0 0 1 1 -7 15 30 -22 -20 |
[100] => {| 1 0 0 0 1 39 48 -38 46 |, 9 general points}
| 0 1 0 0 1 43 36 33 -28 |
| 0 0 1 0 1 -17 35 40 1 |
| 0 0 0 1 1 -11 11 11 -3 |
[200] => {| 1 0 0 0 1 16 -48 -16 |, 8 general points}
| 0 1 0 0 1 22 -47 7 |
| 0 0 1 0 1 45 47 15 |
| 0 0 0 1 1 -34 19 -23 |
[210] => {| 1 0 0 0 1 1 0 1 |, 8 points with 6 in a plane, or five in a plane and three in a line}
| 0 1 0 0 1 0 1 1 |
| 0 0 1 0 0 1 1 1 |
| 0 0 0 1 0 0 0 1 |
[300a] => {| 1 1 1 1 1 1 1 1 |, 8 points which forms a CI}
| 2 2 2 2 -2 -2 -2 -2 |
| 3 3 -3 -3 3 3 -3 -3 |
| 1 -1 1 -1 1 -1 1 -1 |
[300b] => {| 1 0 0 0 1 19 -8 |, 7 general points}
| 0 1 0 0 1 19 -22 |
| 0 0 1 0 1 -10 -29 |
| 0 0 0 1 1 -29 -24 |
[300c] => {| 1 0 1 -38 34 -18 -28 |, 7 points, 3 on a line}
| 0 1 1 -16 19 -13 -47 |
| 0 0 0 39 -47 -43 38 |
| 0 0 0 21 -39 -15 2 |
[310] => {| 1 0 0 0 1 1 1 |, 7 points with 5 on a plane}
| 0 1 0 0 1 1 0 |
| 0 0 1 0 1 1 0 |
| 0 0 0 1 0 1 1 |
[320] => {| 1 0 0 0 1 1 1 |, 7 points on a twisted cubic curve}
| 0 1 0 0 1 0 0 |
| 0 0 1 0 0 1 0 |
| 0 0 0 1 0 0 1 |
[331] => {| 1 0 0 0 24 -15 33 |, 7 points with 6 on a plane}
| 0 1 0 0 -30 39 -49 |
| 0 0 1 0 -48 0 -33 |
| 0 0 0 1 0 0 0 |
[420] => {| 1 0 0 0 1 24 |, 6 general points}
| 0 1 0 0 1 -36 |
| 0 0 1 0 1 -30 |
| 0 0 0 1 1 -29 |
[430] => {| 1 0 0 0 1 1 |, 6 points, 3 on a line}
| 0 1 0 0 1 0 |
| 0 0 1 0 0 1 |
| 0 0 0 1 0 1 |
[441a] => {| 1 0 0 0 1 1 |, 6 points, 5 on a plane}
| 0 1 0 0 1 0 |
| 0 0 1 0 0 1 |
| 0 0 0 1 0 0 |
[441b] => {| 1 0 0 0 1 0 |, 6 points, 3 each on 2 skew lines}
| 0 1 0 0 1 0 |
| 0 0 1 0 0 1 |
| 0 0 0 1 0 1 |
[550] => {| 1 0 0 0 1 |, 5 general points}
| 0 1 0 0 1 |
| 0 0 1 0 1 |
| 0 0 0 1 1 |
[551] => {| 1 0 0 0 1 |, 5 points, 4 on a plane}
| 0 1 0 0 1 |
| 0 0 1 0 1 |
| 0 0 0 1 0 |
[562] => {| 1 0 0 0 1 |, 5 points, 3 on a line}
| 0 1 0 0 1 |
| 0 0 1 0 0 |
| 0 0 0 1 0 |
[683] => {| 1 0 0 0 |, 4 general points}
| 0 1 0 0 |
| 0 0 1 0 |
| 0 0 0 1 |
o2 : HashTable
|
The object bettiStrataExamples is a method function.