.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | 7108x_1^4+12879x_1^3x_2-3125x_1^2x_2^2+1492x_1x_2^3-9587x_2^4+5598x_1^
------------------------------------------------------------------------
3x_3+6143x_1^2x_2x_3+13606x_1x_2^2x_3-1064x_2^3x_3+15767x_1^2x_3^2+4344x
------------------------------------------------------------------------
_1x_2x_3^2+3194x_2^2x_3^2+10949x_1x_3^3-6437x_2x_3^3-15482x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-42x_1x_3^2+6104x_2x_3^2-6098x_3^3
------------------------------------------------------------------------
x_1x_2x_3-2667x_1x_3^2+5350x_2x_3^2-1793x_3^3
------------------------------------------------------------------------
x_1^2x_3-7425x_1x_3^2+9792x_2x_3^2-1921x_3^3
------------------------------------------------------------------------
x_2^3+12885x_1x_3^2+61x_2x_3^2-3725x_3^3
------------------------------------------------------------------------
x_1x_2^2-8741x_1x_3^2+7215x_2x_3^2-3124x_3^3
------------------------------------------------------------------------
x_1^2x_2+2232x_1x_3^2-15502x_2x_3^2+8018x_3^3
------------------------------------------------------------------------
x_1^3+15168x_1x_3^2-13482x_2x_3^2-12028x_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
|