.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | -10367x_1^4-11577x_1^3x_2+10826x_1^2x_2^2-5904x_1x_2^3+15506x_2^4+162x
------------------------------------------------------------------------
_1^3x_3-7364x_1^2x_2x_3-7760x_1x_2^2x_3+10081x_2^3x_3+8570x_1^2x_3^2+
------------------------------------------------------------------------
8161x_1x_2x_3^2-13625x_2^2x_3^2+7458x_1x_3^3+9784x_2x_3^3-4629x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3+15275x_1x_3^2-8823x_2x_3^2+1299x_3^3
------------------------------------------------------------------------
x_1x_2x_3-14557x_1x_3^2+531x_2x_3^2-14358x_3^3
------------------------------------------------------------------------
x_1^2x_3+15251x_1x_3^2-8289x_2x_3^2-11703x_3^3
------------------------------------------------------------------------
x_2^3+7049x_1x_3^2-10100x_2x_3^2+15972x_3^3
------------------------------------------------------------------------
x_1x_2^2-6735x_1x_3^2+9152x_2x_3^2-6774x_3^3
------------------------------------------------------------------------
x_1^2x_2-1413x_1x_3^2-7552x_2x_3^2+5259x_3^3
------------------------------------------------------------------------
x_1^3-11639x_1x_3^2-10102x_2x_3^2-9062x_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
|