.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | 3982x_1^4+11660x_1^3x_2+11822x_1^2x_2^2+13760x_1x_2^3-8451x_2^4+4334x_
------------------------------------------------------------------------
1^3x_3-11099x_1^2x_2x_3+9670x_1x_2^2x_3+240x_2^3x_3-2405x_1^2x_3^2+1365x
------------------------------------------------------------------------
_1x_2x_3^2-2498x_2^2x_3^2+903x_1x_3^3-11890x_2x_3^3-2480x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-13376x_1x_3^2-2365x_2x_3^2-11186x_3^3
------------------------------------------------------------------------
x_1x_2x_3+11958x_1x_3^2+15251x_2x_3^2-14088x_3^3
------------------------------------------------------------------------
x_1^2x_3-13352x_1x_3^2+680x_2x_3^2+4872x_3^3
------------------------------------------------------------------------
x_2^3-14821x_1x_3^2+12635x_2x_3^2+13144x_3^3
------------------------------------------------------------------------
x_1x_2^2-12540x_1x_3^2-10589x_2x_3^2+1556x_3^3
------------------------------------------------------------------------
x_1^2x_2+5846x_1x_3^2-4732x_2x_3^2+12255x_3^3
------------------------------------------------------------------------
x_1^3-13032x_1x_3^2-10x_2x_3^2+12261x_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
|