.
i1 : R = ZZ/32003[x_1..x_3];
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i2 : g = random(R^1, R^{-4})
o2 = | 8814x_1^4-2212x_1^3x_2-6952x_1^2x_2^2+15554x_1x_2^3+3339x_2^4-3220x_1^
------------------------------------------------------------------------
3x_3+5589x_1^2x_2x_3-7234x_1x_2^2x_3+11557x_2^3x_3+12406x_1^2x_3^2+1950x
------------------------------------------------------------------------
_1x_2x_3^2+13808x_2^2x_3^2+3170x_1x_3^3-6359x_2x_3^3+13683x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-7089x_1x_3^2-6415x_2x_3^2+2152x_3^3
------------------------------------------------------------------------
x_1x_2x_3+6289x_1x_3^2-9466x_2x_3^2-7676x_3^3
------------------------------------------------------------------------
x_1^2x_3+221x_1x_3^2+4015x_2x_3^2-4424x_3^3
------------------------------------------------------------------------
x_2^3+10805x_1x_3^2-8110x_2x_3^2+5281x_3^3
------------------------------------------------------------------------
x_1x_2^2-14488x_1x_3^2+1252x_2x_3^2+14237x_3^3
------------------------------------------------------------------------
x_1^2x_2+9631x_1x_3^2+5397x_2x_3^2-8927x_3^3
------------------------------------------------------------------------
x_1^3-12642x_1x_3^2-12965x_2x_3^2-15200x_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
|