.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | 141x_1^4+8998x_1^3x_2+4869x_1^2x_2^2-1560x_1x_2^3+2250x_2^4+1077x_1^3x
------------------------------------------------------------------------
_3+2749x_1^2x_2x_3+12955x_1x_2^2x_3-7948x_2^3x_3-497x_1^2x_3^2+12508x_1x
------------------------------------------------------------------------
_2x_3^2-12049x_2^2x_3^2+8392x_1x_3^3+1417x_2x_3^3+8016x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3+15772x_1x_3^2-8049x_2x_3^2-643x_3^3
------------------------------------------------------------------------
x_1x_2x_3+4639x_1x_3^2-6777x_2x_3^2-14771x_3^3
------------------------------------------------------------------------
x_1^2x_3+1291x_1x_3^2+7125x_2x_3^2-15722x_3^3
------------------------------------------------------------------------
x_2^3+7825x_1x_3^2+9389x_2x_3^2+1819x_3^3
------------------------------------------------------------------------
x_1x_2^2-13151x_1x_3^2+2689x_2x_3^2+13243x_3^3
------------------------------------------------------------------------
x_1^2x_2-5387x_1x_3^2-283x_2x_3^2+4308x_3^3
------------------------------------------------------------------------
x_1^3-10829x_1x_3^2+10095x_2x_3^2-4453x_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
|