.
i1 : R = ZZ/32003[x_1..x_3];
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i2 : g = random(R^1, R^{-4})
o2 = | 7918x_1^4-12499x_1^3x_2+6849x_1^2x_2^2-12376x_1x_2^3+15953x_2^4-12640x
------------------------------------------------------------------------
_1^3x_3-9768x_1^2x_2x_3-14116x_1x_2^2x_3+7943x_2^3x_3-5993x_1^2x_3^2+
------------------------------------------------------------------------
14485x_1x_2x_3^2-11606x_2^2x_3^2+11742x_1x_3^3-6229x_2x_3^3-11315x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3+12095x_1x_3^2-2414x_2x_3^2+586x_3^3
------------------------------------------------------------------------
x_1x_2x_3-5841x_1x_3^2+6193x_2x_3^2-12855x_3^3
------------------------------------------------------------------------
x_1^2x_3+6434x_1x_3^2+6181x_2x_3^2-13773x_3^3
------------------------------------------------------------------------
x_2^3+1452x_1x_3^2+7452x_2x_3^2-5856x_3^3
------------------------------------------------------------------------
x_1x_2^2-6494x_1x_3^2+1596x_2x_3^2-14984x_3^3
------------------------------------------------------------------------
x_1^2x_2+1472x_1x_3^2-6853x_2x_3^2+163x_3^3
------------------------------------------------------------------------
x_1^3-3916x_1x_3^2+15128x_2x_3^2+2620x_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
|