.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | -8782x_1^4+12103x_1^3x_2+13533x_1^2x_2^2+2739x_1x_2^3-13356x_2^4+9533x
------------------------------------------------------------------------
_1^3x_3+7271x_1^2x_2x_3+10462x_1x_2^2x_3-11440x_2^3x_3+3691x_1^2x_3^2+
------------------------------------------------------------------------
14132x_1x_2x_3^2+8965x_2^2x_3^2-2918x_1x_3^3-2289x_2x_3^3+3725x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-676x_1x_3^2+7126x_2x_3^2-5406x_3^3
------------------------------------------------------------------------
x_1x_2x_3-8587x_1x_3^2-14819x_2x_3^2+13271x_3^3
------------------------------------------------------------------------
x_1^2x_3-6481x_1x_3^2+10604x_2x_3^2-13760x_3^3
------------------------------------------------------------------------
x_2^3-9853x_1x_3^2-13580x_2x_3^2-13457x_3^3
------------------------------------------------------------------------
x_1x_2^2+7687x_1x_3^2+3571x_2x_3^2-7174x_3^3
------------------------------------------------------------------------
x_1^2x_2+6678x_1x_3^2+8434x_2x_3^2-1427x_3^3
------------------------------------------------------------------------
x_1^3-5575x_1x_3^2-4282x_2x_3^2-7843x_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
|