.
i1 : R = ZZ/32003[x_1..x_3];
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i2 : g = random(R^1, R^{-4})
o2 = | 10797x_1^4+880x_1^3x_2+9357x_1^2x_2^2-2747x_1x_2^3-1725x_2^4-2778x_1^
------------------------------------------------------------------------
3x_3-1067x_1^2x_2x_3-14458x_1x_2^2x_3+15339x_2^3x_3+6277x_1^2x_3^2+
------------------------------------------------------------------------
11675x_1x_2x_3^2-12871x_2^2x_3^2-4842x_1x_3^3+9766x_2x_3^3+9931x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3-10938x_1x_3^2+3736x_2x_3^2-5029x_3^3
------------------------------------------------------------------------
x_1x_2x_3+554x_1x_3^2-7574x_2x_3^2+9019x_3^3
------------------------------------------------------------------------
x_1^2x_3+8910x_1x_3^2-8490x_2x_3^2-14235x_3^3
------------------------------------------------------------------------
x_2^3-8502x_1x_3^2-14301x_2x_3^2-4037x_3^3
------------------------------------------------------------------------
x_1x_2^2+2322x_1x_3^2+1086x_2x_3^2-9776x_3^3
------------------------------------------------------------------------
x_1^2x_2-4680x_1x_3^2-10086x_2x_3^2+14968x_3^3
------------------------------------------------------------------------
x_1^3+11460x_1x_3^2+14932x_2x_3^2+3823x_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
|