.
i1 : R = ZZ/32003[x_1..x_3];
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i2 : g = random(R^1, R^{-4})
o2 = | 11200x_1^4+12039x_1^3x_2+7829x_1^2x_2^2+9006x_1x_2^3+4867x_2^4-12902x_
------------------------------------------------------------------------
1^3x_3+15030x_1^2x_2x_3+4702x_1x_2^2x_3-278x_2^3x_3+6817x_1^2x_3^2-7154x
------------------------------------------------------------------------
_1x_2x_3^2+5293x_2^2x_3^2+12025x_1x_3^3-9956x_2x_3^3-7876x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-12355x_1x_3^2+6934x_2x_3^2+8739x_3^3
------------------------------------------------------------------------
x_1x_2x_3+1235x_1x_3^2-6478x_2x_3^2-9069x_3^3
------------------------------------------------------------------------
x_1^2x_3-9518x_1x_3^2-1516x_2x_3^2-13464x_3^3
------------------------------------------------------------------------
x_2^3-12650x_1x_3^2+9513x_2x_3^2-1693x_3^3
------------------------------------------------------------------------
x_1x_2^2+2975x_1x_3^2+1053x_2x_3^2-14663x_3^3
------------------------------------------------------------------------
x_1^2x_2+9718x_1x_3^2+1703x_2x_3^2-9857x_3^3
------------------------------------------------------------------------
x_1^3-13349x_1x_3^2+2226x_2x_3^2+15068x_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
|