.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | 12771x_1^4+4571x_1^3x_2+1498x_1^2x_2^2+458x_1x_2^3+14376x_2^4+6687x_1^
------------------------------------------------------------------------
3x_3-15343x_1^2x_2x_3+3747x_1x_2^2x_3-7359x_2^3x_3-12664x_1^2x_3^2+4490x
------------------------------------------------------------------------
_1x_2x_3^2+8217x_2^2x_3^2+7994x_1x_3^3-3319x_2x_3^3+11080x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-14071x_1x_3^2+8928x_2x_3^2-4571x_3^3
------------------------------------------------------------------------
x_1x_2x_3+3319x_1x_3^2+3372x_2x_3^2+15356x_3^3
------------------------------------------------------------------------
x_1^2x_3+248x_1x_3^2-10721x_2x_3^2+6746x_3^3
------------------------------------------------------------------------
x_2^3-258x_1x_3^2+742x_2x_3^2+11665x_3^3
------------------------------------------------------------------------
x_1x_2^2-4482x_1x_3^2+4526x_2x_3^2-13622x_3^3
------------------------------------------------------------------------
x_1^2x_2-5270x_1x_3^2+4302x_2x_3^2+10040x_3^3
------------------------------------------------------------------------
x_1^3+3126x_1x_3^2+14894x_2x_3^2-8207x_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
|