.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | 11753x_1^4-8489x_1^3x_2-10263x_1^2x_2^2-8210x_1x_2^3-5170x_2^4+13283x_
------------------------------------------------------------------------
1^3x_3-2835x_1^2x_2x_3+9906x_1x_2^2x_3-5725x_2^3x_3+15330x_1^2x_3^2-
------------------------------------------------------------------------
7474x_1x_2x_3^2-14761x_2^2x_3^2-916x_1x_3^3-9677x_2x_3^3-3824x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-694x_1x_3^2+2504x_2x_3^2+8982x_3^3
------------------------------------------------------------------------
x_1x_2x_3-14272x_1x_3^2-2492x_2x_3^2-5927x_3^3
------------------------------------------------------------------------
x_1^2x_3+13693x_1x_3^2+15219x_2x_3^2+9655x_3^3
------------------------------------------------------------------------
x_2^3-10837x_1x_3^2+12813x_2x_3^2+6508x_3^3
------------------------------------------------------------------------
x_1x_2^2+6284x_1x_3^2-11086x_2x_3^2-564x_3^3
------------------------------------------------------------------------
x_1^2x_2-6733x_1x_3^2-5392x_2x_3^2+8202x_3^3
------------------------------------------------------------------------
x_1^3-1347x_1x_3^2+7635x_2x_3^2-14777x_3^3 |
1 7
o3 : Matrix R <--- R
|
i4 : res ideal f
1 7 7 1
o4 = R <-- R <-- R <-- R <-- 0
0 1 2 3 4
o4 : ChainComplex
|
i5 : betti oo
0 1 2 3
o5 = total: 1 7 7 1
0: 1 . . .
1: . . . .
2: . 7 7 .
3: . . . .
4: . . . 1
o5 : BettiTally
|