.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | -7442x_1^4-13790x_1^3x_2-1750x_1^2x_2^2-11743x_1x_2^3-12133x_2^4+7541x
------------------------------------------------------------------------
_1^3x_3-4759x_1^2x_2x_3-10310x_1x_2^2x_3-7x_2^3x_3+11280x_1^2x_3^2+3139x
------------------------------------------------------------------------
_1x_2x_3^2+6389x_2^2x_3^2-11148x_1x_3^3-5691x_2x_3^3+8175x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3+563x_1x_3^2+12400x_2x_3^2+15193x_3^3
------------------------------------------------------------------------
x_1x_2x_3+3285x_1x_3^2+5513x_2x_3^2+14843x_3^3
------------------------------------------------------------------------
x_1^2x_3+10145x_1x_3^2-13187x_2x_3^2-14220x_3^3
------------------------------------------------------------------------
x_2^3-3625x_1x_3^2-11727x_2x_3^2+5488x_3^3
------------------------------------------------------------------------
x_1x_2^2+3304x_1x_3^2+13517x_2x_3^2+3707x_3^3
------------------------------------------------------------------------
x_1^2x_2-4335x_1x_3^2-1373x_2x_3^2-4467x_3^3
------------------------------------------------------------------------
x_1^3+14199x_1x_3^2+15460x_2x_3^2-11693x_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
|