.
i1 : R = ZZ/32003[x_1..x_3];
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i2 : g = random(R^1, R^{-4})
o2 = | 10834x_1^4-8769x_1^3x_2-7106x_1^2x_2^2-11067x_1x_2^3+13131x_2^4+5059x_
------------------------------------------------------------------------
1^3x_3+8982x_1^2x_2x_3+14858x_1x_2^2x_3+782x_2^3x_3+12403x_1^2x_3^2-
------------------------------------------------------------------------
4329x_1x_2x_3^2-12022x_2^2x_3^2+5031x_1x_3^3-4346x_2x_3^3-195x_3^4 |
1 1
o2 : Matrix R <--- R
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i3 : f = fromDual g
o3 = | x_2^2x_3-2137x_1x_3^2-6180x_2x_3^2-7234x_3^3
------------------------------------------------------------------------
x_1x_2x_3-13465x_1x_3^2-5256x_2x_3^2+4575x_3^3
------------------------------------------------------------------------
x_1^2x_3-157x_1x_3^2+15473x_2x_3^2-250x_3^3
------------------------------------------------------------------------
x_2^3-10269x_1x_3^2+6529x_2x_3^2+10021x_3^3
------------------------------------------------------------------------
x_1x_2^2+12373x_1x_3^2-5434x_2x_3^2-13378x_3^3
------------------------------------------------------------------------
x_1^2x_2+14263x_1x_3^2+3791x_2x_3^2-4158x_3^3
------------------------------------------------------------------------
x_1^3+2690x_1x_3^2-2241x_2x_3^2+388x_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
|