.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | -14788x_1^4+15540x_1^3x_2-13296x_1^2x_2^2+8852x_1x_2^3+14623x_2^4+
------------------------------------------------------------------------
1851x_1^3x_3+12538x_1^2x_2x_3+1190x_1x_2^2x_3+6498x_2^3x_3+15771x_1^2x_3
------------------------------------------------------------------------
^2-4450x_1x_2x_3^2-5133x_2^2x_3^2+7694x_1x_3^3+12093x_2x_3^3+14218x_3^4
------------------------------------------------------------------------
|
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3+14246x_1x_3^2+7886x_2x_3^2-15922x_3^3
------------------------------------------------------------------------
x_1x_2x_3+15717x_1x_3^2+12939x_2x_3^2-9856x_3^3
------------------------------------------------------------------------
x_1^2x_3-11160x_1x_3^2-3330x_2x_3^2+5996x_3^3
------------------------------------------------------------------------
x_2^3-12803x_1x_3^2+14663x_2x_3^2-5753x_3^3
------------------------------------------------------------------------
x_1x_2^2-2323x_1x_3^2-4575x_2x_3^2+3935x_3^3
------------------------------------------------------------------------
x_1^2x_2+7131x_1x_3^2+1066x_2x_3^2-7418x_3^3
------------------------------------------------------------------------
x_1^3-3683x_1x_3^2-11762x_2x_3^2-11626x_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
|