.
i1 : R = ZZ/32003[x_1..x_3];
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i2 : g = random(R^1, R^{-4})
o2 = | 15536x_1^4-11977x_1^3x_2-15352x_1^2x_2^2-337x_1x_2^3-2489x_2^4-2668x_1
------------------------------------------------------------------------
^3x_3+360x_1^2x_2x_3-5879x_1x_2^2x_3-15875x_2^3x_3-4454x_1^2x_3^2+10175x
------------------------------------------------------------------------
_1x_2x_3^2+70x_2^2x_3^2-8410x_1x_3^3+14818x_2x_3^3-11472x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-15929x_1x_3^2-5875x_2x_3^2+3291x_3^3
------------------------------------------------------------------------
x_1x_2x_3-14231x_1x_3^2+12475x_2x_3^2+12953x_3^3
------------------------------------------------------------------------
x_1^2x_3+6641x_1x_3^2+6122x_2x_3^2+9879x_3^3
------------------------------------------------------------------------
x_2^3-13394x_1x_3^2+9467x_2x_3^2-12002x_3^3
------------------------------------------------------------------------
x_1x_2^2-13167x_1x_3^2+15613x_2x_3^2-7995x_3^3
------------------------------------------------------------------------
x_1^2x_2+4736x_1x_3^2-13469x_2x_3^2+5214x_3^3
------------------------------------------------------------------------
x_1^3-7093x_1x_3^2-11243x_2x_3^2+15762x_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
|