.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | 10021x_1^4+314x_1^3x_2+6757x_1^2x_2^2-10752x_1x_2^3-15335x_2^4-8035x_1
------------------------------------------------------------------------
^3x_3+4140x_1^2x_2x_3-2018x_1x_2^2x_3+5687x_2^3x_3-13556x_1^2x_3^2-
------------------------------------------------------------------------
13385x_1x_2x_3^2+15248x_2^2x_3^2-1374x_1x_3^3+1581x_2x_3^3+10627x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-14454x_1x_3^2+251x_2x_3^2-5952x_3^3
------------------------------------------------------------------------
x_1x_2x_3+3432x_1x_3^2+7642x_2x_3^2-10943x_3^3
------------------------------------------------------------------------
x_1^2x_3+10145x_1x_3^2-7765x_2x_3^2+9506x_3^3
------------------------------------------------------------------------
x_2^3-12274x_1x_3^2+1741x_2x_3^2+15596x_3^3
------------------------------------------------------------------------
x_1x_2^2+6332x_1x_3^2+737x_2x_3^2+10617x_3^3
------------------------------------------------------------------------
x_1^2x_2+7358x_1x_3^2-7827x_2x_3^2-10578x_3^3
------------------------------------------------------------------------
x_1^3-13125x_1x_3^2+14037x_2x_3^2-14138x_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
|