.
i1 : R = ZZ/32003[x_1..x_3];
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i2 : g = random(R^1, R^{-4})
o2 = | 4028x_1^4-12805x_1^3x_2+2475x_1^2x_2^2-15333x_1x_2^3-8850x_2^4-5657x_1
------------------------------------------------------------------------
^3x_3-9731x_1^2x_2x_3-11652x_1x_2^2x_3+5709x_2^3x_3-4943x_1^2x_3^2-1799x
------------------------------------------------------------------------
_1x_2x_3^2+14366x_2^2x_3^2+8046x_1x_3^3-12352x_2x_3^3+5553x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3+10253x_1x_3^2+7132x_2x_3^2-9443x_3^3
------------------------------------------------------------------------
x_1x_2x_3-13476x_1x_3^2+490x_2x_3^2-4298x_3^3
------------------------------------------------------------------------
x_1^2x_3-13098x_1x_3^2-4986x_2x_3^2-14248x_3^3
------------------------------------------------------------------------
x_2^3-2272x_1x_3^2-7000x_2x_3^2-13392x_3^3
------------------------------------------------------------------------
x_1x_2^2-11056x_1x_3^2-11351x_2x_3^2-7994x_3^3
------------------------------------------------------------------------
x_1^2x_2-13918x_1x_3^2-12107x_2x_3^2-11932x_3^3
------------------------------------------------------------------------
x_1^3+2515x_1x_3^2+1968x_2x_3^2-32x_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
|