.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | 12073x_1^4-7067x_1^3x_2+11656x_1^2x_2^2+6962x_1x_2^3+5238x_2^4+7785x_1
------------------------------------------------------------------------
^3x_3-13086x_1^2x_2x_3+10017x_1x_2^2x_3-11415x_2^3x_3+14458x_1^2x_3^2-
------------------------------------------------------------------------
4097x_1x_2x_3^2+6054x_2^2x_3^2-2091x_1x_3^3-1076x_2x_3^3+11149x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3+3219x_1x_3^2-9052x_2x_3^2-11029x_3^3
------------------------------------------------------------------------
x_1x_2x_3+3531x_1x_3^2+3404x_2x_3^2-12902x_3^3
------------------------------------------------------------------------
x_1^2x_3-11304x_1x_3^2-11254x_2x_3^2-11308x_3^3
------------------------------------------------------------------------
x_2^3-1048x_1x_3^2-4553x_2x_3^2-4490x_3^3
------------------------------------------------------------------------
x_1x_2^2-11489x_1x_3^2-4017x_2x_3^2-7848x_3^3
------------------------------------------------------------------------
x_1^2x_2+1396x_1x_3^2+15999x_2x_3^2-1006x_3^3
------------------------------------------------------------------------
x_1^3-415x_1x_3^2+3603x_2x_3^2+13815x_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
|