.
i1 : R = ZZ/32003[x_1..x_3];
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i2 : g = random(R^1, R^{-4})
o2 = | 14949x_1^4+10776x_1^3x_2-13665x_1^2x_2^2-9294x_1x_2^3-8425x_2^4+3945x_
------------------------------------------------------------------------
1^3x_3-5848x_1^2x_2x_3-449x_1x_2^2x_3+2478x_2^3x_3+12855x_1^2x_3^2+
------------------------------------------------------------------------
12661x_1x_2x_3^2-15133x_2^2x_3^2+8350x_1x_3^3+8861x_2x_3^3+13954x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3+9978x_1x_3^2-15027x_2x_3^2-10789x_3^3
------------------------------------------------------------------------
x_1x_2x_3-12986x_1x_3^2-554x_2x_3^2-5513x_3^3
------------------------------------------------------------------------
x_1^2x_3+8512x_1x_3^2+5097x_2x_3^2-15184x_3^3
------------------------------------------------------------------------
x_2^3+1039x_1x_3^2-11569x_2x_3^2+10823x_3^3
------------------------------------------------------------------------
x_1x_2^2+14910x_1x_3^2-13847x_2x_3^2-7491x_3^3
------------------------------------------------------------------------
x_1^2x_2-12457x_1x_3^2+10866x_2x_3^2+4958x_3^3
------------------------------------------------------------------------
x_1^3-12352x_1x_3^2-11020x_2x_3^2+15882x_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
|