.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | -14831x_1^4-11326x_1^3x_2-2950x_1^2x_2^2+10279x_1x_2^3-6359x_2^4+8547x
------------------------------------------------------------------------
_1^3x_3+8156x_1^2x_2x_3-10861x_1x_2^2x_3+15753x_2^3x_3-7991x_1^2x_3^2-
------------------------------------------------------------------------
13769x_1x_2x_3^2-13133x_2^2x_3^2+4344x_1x_3^3-3758x_2x_3^3+3843x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-13188x_1x_3^2+5407x_2x_3^2-5351x_3^3
------------------------------------------------------------------------
x_1x_2x_3-8328x_1x_3^2+8905x_2x_3^2+3069x_3^3
------------------------------------------------------------------------
x_1^2x_3-325x_1x_3^2+9272x_2x_3^2-6028x_3^3
------------------------------------------------------------------------
x_2^3+14697x_1x_3^2-15454x_2x_3^2+4704x_3^3
------------------------------------------------------------------------
x_1x_2^2-6701x_1x_3^2+14485x_2x_3^2+2880x_3^3
------------------------------------------------------------------------
x_1^2x_2-4341x_1x_3^2-14005x_2x_3^2+11912x_3^3
------------------------------------------------------------------------
x_1^3+13485x_1x_3^2+4675x_2x_3^2+9754x_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
|