.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | -4729x_1^4-10226x_1^3x_2-10744x_1^2x_2^2-13356x_1x_2^3+4372x_2^4-
------------------------------------------------------------------------
10972x_1^3x_3+7598x_1^2x_2x_3+9279x_1x_2^2x_3-9818x_2^3x_3-2833x_1^2x_3^
------------------------------------------------------------------------
2+8959x_1x_2x_3^2-4184x_2^2x_3^2-2486x_1x_3^3-14085x_2x_3^3-13253x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3+3045x_1x_3^2+5508x_2x_3^2-3699x_3^3
------------------------------------------------------------------------
x_1x_2x_3+3067x_1x_3^2-6460x_2x_3^2-4875x_3^3
------------------------------------------------------------------------
x_1^2x_3+11317x_1x_3^2+1298x_2x_3^2-15574x_3^3
------------------------------------------------------------------------
x_2^3+8520x_1x_3^2+13875x_2x_3^2-5039x_3^3
------------------------------------------------------------------------
x_1x_2^2-952x_1x_3^2+14186x_2x_3^2-3898x_3^3
------------------------------------------------------------------------
x_1^2x_2-4040x_1x_3^2+8623x_2x_3^2+6131x_3^3
------------------------------------------------------------------------
x_1^3+854x_1x_3^2-3915x_2x_3^2+4432x_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
|