.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | -13760x_1^4-12372x_1^3x_2+10273x_1^2x_2^2+14679x_1x_2^3-2058x_2^4-
------------------------------------------------------------------------
6359x_1^3x_3+9330x_1^2x_2x_3+2905x_1x_2^2x_3+2031x_2^3x_3-12846x_1^2x_3^
------------------------------------------------------------------------
2-1094x_1x_2x_3^2-8399x_2^2x_3^2-496x_1x_3^3-12606x_2x_3^3+3913x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3+11082x_1x_3^2+11133x_2x_3^2+11240x_3^3
------------------------------------------------------------------------
x_1x_2x_3+8075x_1x_3^2+1732x_2x_3^2+12116x_3^3
------------------------------------------------------------------------
x_1^2x_3+11624x_1x_3^2+6929x_2x_3^2+10844x_3^3
------------------------------------------------------------------------
x_2^3+6893x_1x_3^2+7078x_2x_3^2-6152x_3^3
------------------------------------------------------------------------
x_1x_2^2+5339x_1x_3^2-12700x_2x_3^2-14557x_3^3
------------------------------------------------------------------------
x_1^2x_2+14340x_1x_3^2+6938x_2x_3^2+12283x_3^3
------------------------------------------------------------------------
x_1^3-9027x_1x_3^2+4749x_2x_3^2+3140x_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
|