.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | -5277x_1^4-15725x_1^3x_2+12454x_1^2x_2^2+15272x_1x_2^3+336x_2^4-4349x_
------------------------------------------------------------------------
1^3x_3+3152x_1^2x_2x_3-8611x_1x_2^2x_3-1344x_2^3x_3-13531x_1^2x_3^2-
------------------------------------------------------------------------
4179x_1x_2x_3^2+10136x_2^2x_3^2-4908x_1x_3^3-2005x_2x_3^3+9458x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-14763x_1x_3^2-7882x_2x_3^2-5198x_3^3
------------------------------------------------------------------------
x_1x_2x_3+2838x_1x_3^2-818x_2x_3^2-3319x_3^3
------------------------------------------------------------------------
x_1^2x_3+13848x_1x_3^2-11812x_2x_3^2+13004x_3^3
------------------------------------------------------------------------
x_2^3+127x_1x_3^2+4105x_2x_3^2-9137x_3^3
------------------------------------------------------------------------
x_1x_2^2+2633x_1x_3^2-575x_2x_3^2+1110x_3^3
------------------------------------------------------------------------
x_1^2x_2-13137x_1x_3^2-917x_2x_3^2-4782x_3^3
------------------------------------------------------------------------
x_1^3+14298x_1x_3^2+14844x_2x_3^2-10138x_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
|