.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | -13229x_1^4+5837x_1^3x_2-8355x_1^2x_2^2-6915x_1x_2^3-14855x_2^4+4400x_
------------------------------------------------------------------------
1^3x_3+1852x_1^2x_2x_3-13277x_1x_2^2x_3+3694x_2^3x_3+1557x_1^2x_3^2+
------------------------------------------------------------------------
6811x_1x_2x_3^2-597x_2^2x_3^2-8568x_1x_3^3+14940x_2x_3^3-9451x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3+7707x_1x_3^2-7451x_2x_3^2-2085x_3^3
------------------------------------------------------------------------
x_1x_2x_3+14671x_1x_3^2-6923x_2x_3^2+801x_3^3
------------------------------------------------------------------------
x_1^2x_3-14392x_1x_3^2+8553x_2x_3^2-481x_3^3
------------------------------------------------------------------------
x_2^3-7086x_1x_3^2+838x_2x_3^2+8301x_3^3
------------------------------------------------------------------------
x_1x_2^2+4473x_1x_3^2-1520x_2x_3^2+4661x_3^3
------------------------------------------------------------------------
x_1^2x_2-12499x_1x_3^2-7490x_2x_3^2-7149x_3^3
------------------------------------------------------------------------
x_1^3+10288x_1x_3^2-3769x_2x_3^2+9181x_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
|