.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | 107x_1^4+4376x_1^3x_2+3187x_1^2x_2^2+8570x_1x_2^3+10359x_2^4-5570x_1^
------------------------------------------------------------------------
3x_3+3783x_1^2x_2x_3-15344x_1x_2^2x_3-7464x_2^3x_3-5307x_1^2x_3^2+8444x_
------------------------------------------------------------------------
1x_2x_3^2-8251x_2^2x_3^2-10480x_1x_3^3+2653x_2x_3^3+5071x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-1990x_1x_3^2+422x_2x_3^2-602x_3^3
------------------------------------------------------------------------
x_1x_2x_3-6143x_1x_3^2+11220x_2x_3^2+3149x_3^3
------------------------------------------------------------------------
x_1^2x_3-9615x_1x_3^2+1977x_2x_3^2-1176x_3^3
------------------------------------------------------------------------
x_2^3-7928x_1x_3^2+5677x_2x_3^2+7191x_3^3
------------------------------------------------------------------------
x_1x_2^2+10146x_1x_3^2-6442x_2x_3^2+6898x_3^3
------------------------------------------------------------------------
x_1^2x_2-6929x_1x_3^2-14079x_2x_3^2+896x_3^3
------------------------------------------------------------------------
x_1^3-2708x_1x_3^2-1803x_2x_3^2+9150x_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
|