.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | 6905x_1^4-3409x_1^3x_2+7791x_1^2x_2^2+11670x_1x_2^3-15961x_2^4-14399x_
------------------------------------------------------------------------
1^3x_3-4164x_1^2x_2x_3+2660x_1x_2^2x_3+6539x_2^3x_3-7781x_1^2x_3^2-
------------------------------------------------------------------------
10804x_1x_2x_3^2+152x_2^2x_3^2+12652x_1x_3^3+6641x_2x_3^3-15368x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3+5652x_1x_3^2-2927x_2x_3^2-5914x_3^3
------------------------------------------------------------------------
x_1x_2x_3-15359x_1x_3^2+11097x_2x_3^2+4222x_3^3
------------------------------------------------------------------------
x_1^2x_3-6234x_1x_3^2+3900x_2x_3^2+2323x_3^3
------------------------------------------------------------------------
x_2^3+12197x_1x_3^2+8989x_2x_3^2-14320x_3^3
------------------------------------------------------------------------
x_1x_2^2-4043x_1x_3^2+13542x_2x_3^2+11399x_3^3
------------------------------------------------------------------------
x_1^2x_2+10257x_1x_3^2+13316x_2x_3^2-1570x_3^3
------------------------------------------------------------------------
x_1^3+14385x_1x_3^2-12301x_2x_3^2+13873x_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
|