.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | -3234x_1^4+4618x_1^3x_2-13318x_1^2x_2^2-4658x_1x_2^3-14781x_2^4-14421x
------------------------------------------------------------------------
_1^3x_3+8624x_1^2x_2x_3+15741x_1x_2^2x_3+8026x_2^3x_3-11173x_1^2x_3^2+
------------------------------------------------------------------------
3526x_1x_2x_3^2+8153x_2^2x_3^2-2545x_1x_3^3+11063x_2x_3^3-3987x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-8182x_1x_3^2-7065x_2x_3^2-14403x_3^3
------------------------------------------------------------------------
x_1x_2x_3+2295x_1x_3^2-5986x_2x_3^2+1616x_3^3
------------------------------------------------------------------------
x_1^2x_3-5270x_1x_3^2+3297x_2x_3^2-12189x_3^3
------------------------------------------------------------------------
x_2^3+13817x_1x_3^2-13999x_2x_3^2+13262x_3^3
------------------------------------------------------------------------
x_1x_2^2-13314x_1x_3^2+2995x_2x_3^2+14710x_3^3
------------------------------------------------------------------------
x_1^2x_2+9535x_1x_3^2+6099x_2x_3^2-13402x_3^3
------------------------------------------------------------------------
x_1^3-11909x_1x_3^2-4152x_2x_3^2-6122x_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
|