.
i1 : R = ZZ/32003[x_1..x_3];
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i2 : g = random(R^1, R^{-4})
o2 = | 8110x_1^4-3561x_1^3x_2-6917x_1^2x_2^2+6905x_1x_2^3+10322x_2^4+1731x_1^
------------------------------------------------------------------------
3x_3+1686x_1^2x_2x_3-14427x_1x_2^2x_3+10867x_2^3x_3-1199x_1^2x_3^2+
------------------------------------------------------------------------
12140x_1x_2x_3^2+12150x_2^2x_3^2-9689x_1x_3^3-14379x_2x_3^3+8904x_3^4 |
1 1
o2 : Matrix R <--- R
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i3 : f = fromDual g
o3 = | x_2^2x_3+5022x_1x_3^2+7971x_2x_3^2+5817x_3^3
------------------------------------------------------------------------
x_1x_2x_3-13505x_1x_3^2-6478x_2x_3^2+14770x_3^3
------------------------------------------------------------------------
x_1^2x_3-373x_1x_3^2+9449x_2x_3^2+5742x_3^3
------------------------------------------------------------------------
x_2^3+4144x_1x_3^2-1337x_2x_3^2-10468x_3^3
------------------------------------------------------------------------
x_1x_2^2-7405x_1x_3^2+8229x_2x_3^2-15984x_3^3
------------------------------------------------------------------------
x_1^2x_2+15214x_1x_3^2-14201x_2x_3^2+5846x_3^3
------------------------------------------------------------------------
x_1^3+5007x_1x_3^2+5848x_2x_3^2+9242x_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
|