.
i1 : R = ZZ/32003[x_1..x_3];
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i2 : g = random(R^1, R^{-4})
o2 = | 6299x_1^4-170x_1^3x_2-12101x_1^2x_2^2+5874x_1x_2^3+7506x_2^4-10313x_1^
------------------------------------------------------------------------
3x_3-7126x_1^2x_2x_3-323x_1x_2^2x_3-13331x_2^3x_3-6415x_1^2x_3^2-7409x_
------------------------------------------------------------------------
1x_2x_3^2-10288x_2^2x_3^2+1333x_1x_3^3+15778x_2x_3^3+7090x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3+11697x_1x_3^2-7768x_2x_3^2+1832x_3^3
------------------------------------------------------------------------
x_1x_2x_3-11107x_1x_3^2-3794x_2x_3^2-1357x_3^3
------------------------------------------------------------------------
x_1^2x_3-8712x_1x_3^2+8499x_2x_3^2-10021x_3^3
------------------------------------------------------------------------
x_2^3+11272x_1x_3^2+3750x_2x_3^2-2270x_3^3
------------------------------------------------------------------------
x_1x_2^2+15066x_1x_3^2-8927x_2x_3^2-6154x_3^3
------------------------------------------------------------------------
x_1^2x_2+6777x_1x_3^2+2952x_2x_3^2-2620x_3^3
------------------------------------------------------------------------
x_1^3+5570x_1x_3^2+15339x_2x_3^2+13311x_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
|