.
i1 : R = ZZ/32003[x_1..x_3];
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i2 : g = random(R^1, R^{-4})
o2 = | 5964x_1^4+14557x_1^3x_2+12372x_1^2x_2^2+9316x_1x_2^3-7349x_2^4-13169x_
------------------------------------------------------------------------
1^3x_3+10457x_1^2x_2x_3-9638x_1x_2^2x_3+3093x_2^3x_3-5770x_1^2x_3^2+
------------------------------------------------------------------------
12354x_1x_2x_3^2+1761x_2^2x_3^2-3046x_1x_3^3+9313x_2x_3^3-12469x_3^4 |
1 1
o2 : Matrix R <--- R
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i3 : f = fromDual g
o3 = | x_2^2x_3+11164x_1x_3^2-15645x_2x_3^2+5248x_3^3
------------------------------------------------------------------------
x_1x_2x_3-12579x_1x_3^2+6267x_2x_3^2-1865x_3^3
------------------------------------------------------------------------
x_1^2x_3+2129x_1x_3^2+13873x_2x_3^2+6620x_3^3
------------------------------------------------------------------------
x_2^3-8361x_1x_3^2-4790x_2x_3^2-8167x_3^3
------------------------------------------------------------------------
x_1x_2^2-4885x_1x_3^2+11045x_2x_3^2-13293x_3^3
------------------------------------------------------------------------
x_1^2x_2-15400x_1x_3^2+13129x_2x_3^2+10340x_3^3
------------------------------------------------------------------------
x_1^3-4960x_1x_3^2-8557x_2x_3^2+5014x_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
|