.
i1 : R = ZZ/32003[x_1..x_3];
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i2 : g = random(R^1, R^{-4})
o2 = | 4816x_1^4+3777x_1^3x_2+3711x_1^2x_2^2+6295x_1x_2^3+15024x_2^4+11156x_1
------------------------------------------------------------------------
^3x_3+9677x_1^2x_2x_3-11667x_1x_2^2x_3+513x_2^3x_3-14649x_1^2x_3^2-
------------------------------------------------------------------------
10246x_1x_2x_3^2-15307x_2^2x_3^2+1349x_1x_3^3-11410x_2x_3^3+9008x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3+14659x_1x_3^2-1458x_2x_3^2+6561x_3^3
------------------------------------------------------------------------
x_1x_2x_3+11699x_1x_3^2+4464x_2x_3^2+15965x_3^3
------------------------------------------------------------------------
x_1^2x_3-8417x_1x_3^2+6639x_2x_3^2+2097x_3^3
------------------------------------------------------------------------
x_2^3-9613x_1x_3^2+1254x_2x_3^2+x_3^3
------------------------------------------------------------------------
x_1x_2^2+13974x_1x_3^2+6951x_2x_3^2-3636x_3^3
------------------------------------------------------------------------
x_1^2x_2-10045x_1x_3^2-2689x_2x_3^2+2396x_3^3
------------------------------------------------------------------------
x_1^3-11647x_1x_3^2-485x_2x_3^2+7385x_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
|