.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | -8492x_1^4-8692x_1^3x_2-9690x_1^2x_2^2-9527x_1x_2^3+7093x_2^4+13840x_1
------------------------------------------------------------------------
^3x_3+9055x_1^2x_2x_3-5856x_1x_2^2x_3-9379x_2^3x_3+11417x_1^2x_3^2+7958x
------------------------------------------------------------------------
_1x_2x_3^2+14593x_2^2x_3^2-11361x_1x_3^3-8564x_2x_3^3+7934x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-4264x_1x_3^2+3936x_2x_3^2+13973x_3^3
------------------------------------------------------------------------
x_1x_2x_3+9798x_1x_3^2+2535x_2x_3^2+13958x_3^3
------------------------------------------------------------------------
x_1^2x_3+8930x_1x_3^2+8946x_2x_3^2-9936x_3^3
------------------------------------------------------------------------
x_2^3+5820x_1x_3^2-10505x_2x_3^2+13667x_3^3
------------------------------------------------------------------------
x_1x_2^2+9250x_1x_3^2+13782x_2x_3^2+371x_3^3
------------------------------------------------------------------------
x_1^2x_2+9038x_1x_3^2+5063x_2x_3^2-8293x_3^3
------------------------------------------------------------------------
x_1^3-8471x_1x_3^2-9906x_2x_3^2+14007x_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
|