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 = | 43 35 -43 7 38 31 47 48 46 21 8 10 6 -30 -40 10 -27 -10 -50 30 -21
-----------------------------------------------------------------------
-38 -16 -29 31 -36 39 -29 19 24 -24 -8 19 -29 21 -22 |
1 36
o14 : Matrix kk <-- kk
|
i15 : pt2 = randomPointOnRationalVariety compsJ_1
o15 = | 18 13 -48 10 27 -33 13 4 37 33 -15 46 42 -47 -35 23 45 -13 33 -43 1 7
-----------------------------------------------------------------------
2 -47 46 19 16 14 -18 34 38 -15 0 -39 22 -28 |
1 36
o15 : Matrix kk <-- kk
|
i16 : F1 = sub(F, (vars S)|pt1)
2 2 2
o16 = ideal (a - 40b*c + 21c + 10a*d + 31b*d - 43c*d + 43d , a*b + 31b*c -
-----------------------------------------------------------------------
2 2 2
50c - 21a*d + 6b*d + 46c*d + 35d , a*c - 8b*c - 36c - 29a*d + 30b*d -
-----------------------------------------------------------------------
2 2 2 2 2
30c*d + 38d , b + 21b*c + 19c + 19a*d - 38b*d + 10c*d + 47d , b*c +
-----------------------------------------------------------------------
2 2 2 2 3 3 2
24b*c*d - 16c d + 39a*d - 27b*d + 8c*d + 7d , c - 22b*c*d - 24c d -
-----------------------------------------------------------------------
2 2 2 3
29a*d - 29b*d - 10c*d + 48d )
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 - 35b*c + 33c + 46a*d - 33b*d - 48c*d + 18d , a*b + 46b*c +
-----------------------------------------------------------------------
2 2 2
33c + a*d + 42b*d + 37c*d + 13d , a*c - 15b*c + 19c + 14a*d - 43b*d -
-----------------------------------------------------------------------
2 2 2 2 2
47c*d + 27d , b + 22b*c - 18c + 7b*d + 23c*d + 13d , b*c + 34b*c*d +
-----------------------------------------------------------------------
2 2 2 2 3 3 2 2
2c d + 16a*d + 45b*d - 15c*d + 10d , c - 28b*c*d + 38c d - 39a*d -
-----------------------------------------------------------------------
2 2 3
47b*d - 13c*d + 4d )
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
|