.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | -5774x_1^4+13584x_1^3x_2-13078x_1^2x_2^2-4592x_1x_2^3+13785x_2^4-6265x
------------------------------------------------------------------------
_1^3x_3-233x_1^2x_2x_3+349x_1x_2^2x_3+14358x_2^3x_3-2774x_1^2x_3^2-6506x
------------------------------------------------------------------------
_1x_2x_3^2+3721x_2^2x_3^2+12013x_1x_3^3-7745x_2x_3^3+5260x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-9750x_1x_3^2-918x_2x_3^2-10802x_3^3
------------------------------------------------------------------------
x_1x_2x_3+5190x_1x_3^2+7959x_2x_3^2+10472x_3^3
------------------------------------------------------------------------
x_1^2x_3+7875x_1x_3^2-3409x_2x_3^2-11067x_3^3
------------------------------------------------------------------------
x_2^3+2655x_1x_3^2+7118x_2x_3^2-3854x_3^3
------------------------------------------------------------------------
x_1x_2^2-8957x_1x_3^2+2497x_2x_3^2-1293x_3^3
------------------------------------------------------------------------
x_1^2x_2+2794x_1x_3^2-1677x_2x_3^2+5618x_3^3
------------------------------------------------------------------------
x_1^3+4036x_1x_3^2+12873x_2x_3^2+40x_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
|