i6 : keys H
o6 = {(3, 4), (3, 5), (4, 6), (2, 3)}
o6 : List
|
i7 : H#(2,3)
o7 = {3} | -t_8-t_20t_13 t_7t_20-t_14t_20+t_20t_13t_19
{3} | -t_7+t_14-t_13t_19 -t_8-t_20t_13+t_7t_19-t_14t_19+t_13t_19^2
------------------------------------------------------------------------
-t_2-t_14^2+t_20t_13^2 -t_8t_14+t_1t_20+t_7t_20t_13 |
-t_1-2t_14t_13+t_13^2t_19 -t_2-t_7t_14-t_8t_13+t_1t_19+t_7t_13t_19 |
2 4
o7 : Matrix (kk[t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t ]) <-- (kk[t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t ])
6 12 5 30 18 4 24 36 11 2 29 3 10 17 1 23 28 35 8 16 9 22 26 34 7 14 27 15 20 25 32 13 21 33 19 31 6 12 5 30 18 4 24 36 11 2 29 3 10 17 1 23 28 35 8 16 9 22 26 34 7 14 27 15 20 25 32 13 21 33 19 31
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i8 : H#(3,4)
o8 = {4} | -t_20
{4} | -1
{4} | t_8+t_20t_13-t_7t_19+t_14t_19-t_13t_19^2
{4} | -t_7+t_14-t_13t_19
{4} | 0
------------------------------------------------------------------------
-t_8 |
t_13 |
t_2+t_7t_14+t_8t_13-t_1t_19-t_7t_13t_19 |
-t_1-2t_14t_13+t_13^2t_19 |
t_7-t_14+t_13t_19 |
5 2
o8 : Matrix (kk[t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t ]) <-- (kk[t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t ])
6 12 5 30 18 4 24 36 11 2 29 3 10 17 1 23 28 35 8 16 9 22 26 34 7 14 27 15 20 25 32 13 21 33 19 31 6 12 5 30 18 4 24 36 11 2 29 3 10 17 1 23 28 35 8 16 9 22 26 34 7 14 27 15 20 25 32 13 21 33 19 31
|
i9 : H#(3,5)
o9 = {5} | -1 t_13 -t_14 |
1 3
o9 : Matrix (kk[t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t ]) <-- (kk[t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t ])
6 12 5 30 18 4 24 36 11 2 29 3 10 17 1 23 28 35 8 16 9 22 26 34 7 14 27 15 20 25 32 13 21 33 19 31 6 12 5 30 18 4 24 36 11 2 29 3 10 17 1 23 28 35 8 16 9 22 26 34 7 14 27 15 20 25 32 13 21 33 19 31
|
i10 : H#(4,6)
o10 = {6} | -1 |
1 1
o10 : Matrix (kk[t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t ]) <-- (kk[t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t ])
6 12 5 30 18 4 24 36 11 2 29 3 10 17 1 23 28 35 8 16 9 22 26 34 7 14 27 15 20 25 32 13 21 33 19 31 6 12 5 30 18 4 24 36 11 2 29 3 10 17 1 23 28 35 8 16 9 22 26 34 7 14 27 15 20 25 32 13 21 33 19 31
|
i11 : J = trim(minors(1, H#(2,3)) + groebnerStratum F);
o11 : Ideal of kk[t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t , t ]
6 12 5 30 18 4 24 36 11 2 29 3 10 17 1 23 28 35 8 16 9 22 26 34 7 14 27 15 20 25 32 13 21 33 19 31
|
i12 : compsJ = decompose J;
|
i13 : #compsJ
o13 = 2
|
i14 : pt1 = randomPointOnRationalVariety compsJ_0
o14 = | -36 -24 -35 11 -49 -45 35 28 -36 11 -28 -30 8 -22 21 5 34 21 -10 23
-----------------------------------------------------------------------
27 19 -10 -30 38 -29 -8 19 39 -24 -29 -36 -16 -38 -29 24 |
1 36
o14 : Matrix kk <-- kk
|
i15 : pt2 = randomPointOnRationalVariety compsJ_1
o15 = | -20 7 11 -14 -31 20 -47 -46 -37 28 -3 -38 -23 -28 22 10 -36 16 -38
-----------------------------------------------------------------------
-47 -48 31 -15 -39 -2 -47 -43 -2 2 22 -18 19 0 38 -13 34 |
1 36
o15 : Matrix kk <-- kk
|
i16 : F1 = sub(F, (vars S)|pt1)
2 2 2
o16 = ideal (a + 21b*c + 11c - 30a*d - 45b*d - 35c*d - 36d , a*b + 38b*c -
-----------------------------------------------------------------------
2 2 2
10c + 27a*d + 8b*d - 36c*d - 24d , a*c - 36b*c - 29c + 19a*d + 23b*d
-----------------------------------------------------------------------
2 2 2 2 2
- 22c*d - 49d , b - 29b*c + 39c - 16a*d + 19b*d + 5c*d + 35d , b*c -
-----------------------------------------------------------------------
2 2 2 2 3 3 2
24b*c*d - 10c d - 8a*d + 34b*d - 28c*d + 11d , c + 24b*c*d - 29c d
-----------------------------------------------------------------------
2 2 2 3
- 38a*d - 30b*d + 21c*d + 28d )
o16 : Ideal of S
|
i17 : betti res F1
0 1 2 3
o17 = total: 1 6 8 3
0: 1 . . .
1: . 4 4 1
2: . 2 4 2
o17 : BettiTally
|
i18 : F2 = sub(F, (vars S)|pt2)
2 2 2
o18 = ideal (a + 22b*c + 28c - 38a*d + 20b*d + 11c*d - 20d , a*b - 2b*c -
-----------------------------------------------------------------------
2 2 2
38c - 48a*d - 23b*d - 37c*d + 7d , a*c + 19b*c - 47c - 2a*d - 47b*d -
-----------------------------------------------------------------------
2 2 2 2 2
28c*d - 31d , b - 13b*c + 2c + 31b*d + 10c*d - 47d , b*c + 22b*c*d -
-----------------------------------------------------------------------
2 2 2 2 3 3 2 2
15c d - 43a*d - 36b*d - 3c*d - 14d , c + 34b*c*d - 18c d + 38a*d -
-----------------------------------------------------------------------
2 2 3
39b*d + 16c*d - 46d )
o18 : Ideal of S
|
i19 : betti res F2
0 1 2 3
o19 = total: 1 6 8 3
0: 1 . . .
1: . 4 4 1
2: . 2 4 2
o19 : BettiTally
|