.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | -15363x_1^4+5050x_1^3x_2-6070x_1^2x_2^2+7890x_1x_2^3-9511x_2^4-14695x_
------------------------------------------------------------------------
1^3x_3-9649x_1^2x_2x_3+2389x_1x_2^2x_3+6247x_2^3x_3-12738x_1^2x_3^2-
------------------------------------------------------------------------
4306x_1x_2x_3^2+5785x_2^2x_3^2+6828x_1x_3^3-11610x_2x_3^3+12253x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3+13207x_1x_3^2+3599x_2x_3^2+4724x_3^3
------------------------------------------------------------------------
x_1x_2x_3+11273x_1x_3^2+14943x_2x_3^2-15154x_3^3
------------------------------------------------------------------------
x_1^2x_3-11350x_1x_3^2+5263x_2x_3^2+7818x_3^3
------------------------------------------------------------------------
x_2^3-7559x_1x_3^2-2935x_2x_3^2+6947x_3^3
------------------------------------------------------------------------
x_1x_2^2+1400x_1x_3^2-1626x_2x_3^2-4609x_3^3
------------------------------------------------------------------------
x_1^2x_2-4928x_1x_3^2-14425x_2x_3^2-2524x_3^3
------------------------------------------------------------------------
x_1^3-13038x_1x_3^2+11771x_2x_3^2-1182x_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
|