.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | -8433x_1^4-5675x_1^3x_2-12017x_1^2x_2^2-15807x_1x_2^3-10927x_2^4+2741x
------------------------------------------------------------------------
_1^3x_3+1762x_1^2x_2x_3+14858x_1x_2^2x_3+10605x_2^3x_3+6698x_1^2x_3^2+
------------------------------------------------------------------------
7857x_1x_2x_3^2+15434x_2^2x_3^2-11440x_1x_3^3+13769x_2x_3^3-12015x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-8744x_1x_3^2+3087x_2x_3^2+14584x_3^3
------------------------------------------------------------------------
x_1x_2x_3+6403x_1x_3^2+4390x_2x_3^2+15039x_3^3
------------------------------------------------------------------------
x_1^2x_3+7011x_1x_3^2+15772x_2x_3^2+13312x_3^3
------------------------------------------------------------------------
x_2^3-383x_1x_3^2+7659x_2x_3^2-5579x_3^3
------------------------------------------------------------------------
x_1x_2^2-1547x_1x_3^2+8114x_2x_3^2-6482x_3^3
------------------------------------------------------------------------
x_1^2x_2+10014x_1x_3^2-1889x_2x_3^2-15487x_3^3
------------------------------------------------------------------------
x_1^3-12705x_1x_3^2-4903x_2x_3^2-15624x_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
|