.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | -11947x_1^4-5952x_1^3x_2+15465x_1^2x_2^2-13424x_1x_2^3+9850x_2^4+2218x
------------------------------------------------------------------------
_1^3x_3+14343x_1^2x_2x_3+3008x_1x_2^2x_3-4508x_2^3x_3+1495x_1^2x_3^2+
------------------------------------------------------------------------
11634x_1x_2x_3^2-15505x_2^2x_3^2+4721x_1x_3^3+2735x_2x_3^3+2846x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3+3841x_1x_3^2+2966x_2x_3^2+5357x_3^3
------------------------------------------------------------------------
x_1x_2x_3+10389x_1x_3^2+8580x_2x_3^2-15936x_3^3
------------------------------------------------------------------------
x_1^2x_3+3781x_1x_3^2-4363x_2x_3^2-11874x_3^3
------------------------------------------------------------------------
x_2^3-10896x_1x_3^2+9706x_2x_3^2+5735x_3^3
------------------------------------------------------------------------
x_1x_2^2-4689x_1x_3^2+7526x_2x_3^2-5134x_3^3
------------------------------------------------------------------------
x_1^2x_2-15347x_1x_3^2-11361x_2x_3^2-1131x_3^3
------------------------------------------------------------------------
x_1^3+13178x_1x_3^2-15779x_2x_3^2+14567x_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
|