.
i1 : R = ZZ/32003[x_1..x_3];
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i2 : g = random(R^1, R^{-4})
o2 = | -11560x_1^4+10268x_1^3x_2-11893x_1^2x_2^2+6705x_1x_2^3+1711x_2^4+
------------------------------------------------------------------------
12260x_1^3x_3+10051x_1^2x_2x_3+9368x_1x_2^2x_3+1739x_2^3x_3-6383x_1^2x_3
------------------------------------------------------------------------
^2-12746x_1x_2x_3^2-8708x_2^2x_3^2+1292x_1x_3^3+7594x_2x_3^3+13474x_3^4
------------------------------------------------------------------------
|
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-13198x_1x_3^2-4757x_2x_3^2+14683x_3^3
------------------------------------------------------------------------
x_1x_2x_3-5086x_1x_3^2+10729x_2x_3^2+5434x_3^3
------------------------------------------------------------------------
x_1^2x_3-5418x_1x_3^2+9043x_2x_3^2-14550x_3^3
------------------------------------------------------------------------
x_2^3+8571x_1x_3^2+2439x_2x_3^2+4822x_3^3
------------------------------------------------------------------------
x_1x_2^2+8454x_1x_3^2-12206x_2x_3^2+9417x_3^3
------------------------------------------------------------------------
x_1^2x_2-7907x_1x_3^2+10022x_2x_3^2-13843x_3^3
------------------------------------------------------------------------
x_1^3-4443x_1x_3^2+3174x_2x_3^2-4822x_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
|