.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | 12464x_1^4-3x_1^3x_2+2750x_1^2x_2^2-295x_1x_2^3-5655x_2^4+6303x_1^3x_3
------------------------------------------------------------------------
-3345x_1^2x_2x_3-8646x_1x_2^2x_3-6594x_2^3x_3+12894x_1^2x_3^2-6011x_1x_
------------------------------------------------------------------------
2x_3^2-7778x_2^2x_3^2-12073x_1x_3^3+13644x_2x_3^3-13132x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-2174x_1x_3^2-7138x_2x_3^2+5022x_3^3
------------------------------------------------------------------------
x_1x_2x_3+5531x_1x_3^2+7118x_2x_3^2+11137x_3^3
------------------------------------------------------------------------
x_1^2x_3-1165x_1x_3^2+4550x_2x_3^2+650x_3^3
------------------------------------------------------------------------
x_2^3-5551x_1x_3^2-7245x_2x_3^2-12336x_3^3
------------------------------------------------------------------------
x_1x_2^2+12814x_1x_3^2-10428x_2x_3^2-7906x_3^3
------------------------------------------------------------------------
x_1^2x_2+7681x_1x_3^2+13358x_2x_3^2-9321x_3^3
------------------------------------------------------------------------
x_1^3-15836x_1x_3^2+15617x_2x_3^2+10926x_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
|