.
i1 : R = ZZ/32003[x_1..x_3];
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i2 : g = random(R^1, R^{-4})
o2 = | 7560x_1^4+14085x_1^3x_2-6272x_1^2x_2^2+13637x_1x_2^3-13542x_2^4-7995x_
------------------------------------------------------------------------
1^3x_3-626x_1^2x_2x_3-2123x_1x_2^2x_3-248x_2^3x_3+6204x_1^2x_3^2-4216x_
------------------------------------------------------------------------
1x_2x_3^2-3315x_2^2x_3^2+1638x_1x_3^3-15134x_2x_3^3+7131x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-5257x_1x_3^2-14126x_2x_3^2+13271x_3^3
------------------------------------------------------------------------
x_1x_2x_3-1334x_1x_3^2-13597x_2x_3^2+15970x_3^3
------------------------------------------------------------------------
x_1^2x_3+3329x_1x_3^2-13705x_2x_3^2+1806x_3^3
------------------------------------------------------------------------
x_2^3-9755x_1x_3^2+1862x_2x_3^2-3811x_3^3
------------------------------------------------------------------------
x_1x_2^2-10154x_1x_3^2-7490x_2x_3^2-8833x_3^3
------------------------------------------------------------------------
x_1^2x_2-14177x_1x_3^2-2179x_2x_3^2+2927x_3^3
------------------------------------------------------------------------
x_1^3-12337x_1x_3^2-4450x_2x_3^2+8111x_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
|