.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | -15870x_1^4-10462x_1^3x_2+4168x_1^2x_2^2+12857x_1x_2^3+8899x_2^4+6621x
------------------------------------------------------------------------
_1^3x_3+10859x_1^2x_2x_3+9544x_1x_2^2x_3+15505x_2^3x_3-3604x_1^2x_3^2-
------------------------------------------------------------------------
12949x_1x_2x_3^2-6703x_2^2x_3^2+13728x_1x_3^3+13489x_2x_3^3+3096x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3+12925x_1x_3^2+6009x_2x_3^2-13550x_3^3
------------------------------------------------------------------------
x_1x_2x_3-10340x_1x_3^2-14226x_2x_3^2-13283x_3^3
------------------------------------------------------------------------
x_1^2x_3+2511x_1x_3^2-3679x_2x_3^2-9255x_3^3
------------------------------------------------------------------------
x_2^3+10973x_1x_3^2+6947x_2x_3^2+5297x_3^3
------------------------------------------------------------------------
x_1x_2^2-1785x_1x_3^2+13133x_2x_3^2-9955x_3^3
------------------------------------------------------------------------
x_1^2x_2-3662x_1x_3^2-8500x_2x_3^2-6717x_3^3
------------------------------------------------------------------------
x_1^3-8314x_1x_3^2-9653x_2x_3^2+3337x_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
|