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
|
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 = | 47 23 27 -45 2 -2 35 -24 -5 -5 35 26 -48 -10 -32 9 8 24 -33 -11 25
-----------------------------------------------------------------------
-38 21 -8 -41 19 39 -24 -29 19 -29 -29 -30 -36 -16 -22 |
1 36
o14 : Matrix kk <--- kk
|
i15 : pt2 = randomPointOnRationalVariety compsJ_1
o15 = | 2 15 28 -14 38 31 26 -39 24 28 -12 48 30 -13 -46 -7 -36 -47 27 -47 34
-----------------------------------------------------------------------
-21 16 -43 38 -18 22 6 19 -39 38 -28 0 34 2 -15 |
1 36
o15 : Matrix kk <--- kk
|
i16 : F1 = sub(F, (vars S)|pt1)
2 2 2
o16 = ideal (a - 32b*c - 5c + 26a*d - 2b*d + 27c*d + 47d , a*b - 41b*c -
-----------------------------------------------------------------------
2 2 2
33c + 25a*d - 48b*d - 5c*d + 23d , a*c - 29b*c + 19c - 24a*d - 11b*d
-----------------------------------------------------------------------
2 2 2 2 2
- 10c*d + 2d , b - 16b*c - 29c - 30a*d - 38b*d + 9c*d + 35d , b*c +
-----------------------------------------------------------------------
2 2 2 2 3 3 2
19b*c*d + 21c d + 39a*d + 8b*d + 35c*d - 45d , c - 22b*c*d - 29c d
-----------------------------------------------------------------------
2 2 2 3
- 36a*d - 8b*d + 24c*d - 24d )
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 - 46b*c + 28c + 48a*d + 31b*d + 28c*d + 2d , a*b + 38b*c +
-----------------------------------------------------------------------
2 2 2
27c + 34a*d + 30b*d + 24c*d + 15d , a*c - 28b*c - 18c + 6a*d - 47b*d
-----------------------------------------------------------------------
2 2 2 2 2
- 13c*d + 38d , b + 2b*c + 19c - 21b*d - 7c*d + 26d , b*c - 39b*c*d
-----------------------------------------------------------------------
2 2 2 2 3 3 2
+ 16c d + 22a*d - 36b*d - 12c*d - 14d , c - 15b*c*d + 38c d +
-----------------------------------------------------------------------
2 2 2 3
34a*d - 43b*d - 47c*d - 39d )
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
|