.
i1 : R = ZZ/32003[x_1..x_3];
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i2 : g = random(R^1, R^{-4})
o2 = | 4421x_1^4+1931x_1^3x_2-13325x_1^2x_2^2-1388x_1x_2^3+9943x_2^4-15504x_1
------------------------------------------------------------------------
^3x_3-4457x_1^2x_2x_3-13650x_1x_2^2x_3+5177x_2^3x_3+4754x_1^2x_3^2+
------------------------------------------------------------------------
12023x_1x_2x_3^2+6770x_2^2x_3^2-15591x_1x_3^3-9378x_2x_3^3+14886x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-1899x_1x_3^2-6764x_2x_3^2-7590x_3^3
------------------------------------------------------------------------
x_1x_2x_3+3187x_1x_3^2+1586x_2x_3^2-2582x_3^3
------------------------------------------------------------------------
x_1^2x_3+6693x_1x_3^2+11150x_2x_3^2+6890x_3^3
------------------------------------------------------------------------
x_2^3-7508x_1x_3^2+10833x_2x_3^2+356x_3^3
------------------------------------------------------------------------
x_1x_2^2+4006x_1x_3^2+14302x_2x_3^2+3571x_3^3
------------------------------------------------------------------------
x_1^2x_2+9563x_1x_3^2+1921x_2x_3^2+6329x_3^3
------------------------------------------------------------------------
x_1^3-10981x_1x_3^2-11062x_2x_3^2-9949x_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
|