.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | -10741x_1^4-226x_1^3x_2+11103x_1^2x_2^2+6367x_1x_2^3-13686x_2^4+9517x_
------------------------------------------------------------------------
1^3x_3-7659x_1^2x_2x_3+422x_1x_2^2x_3+5727x_2^3x_3+14097x_1^2x_3^2-2976x
------------------------------------------------------------------------
_1x_2x_3^2+12443x_2^2x_3^2-4017x_1x_3^3-1610x_2x_3^3+14971x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3+5426x_1x_3^2+14602x_2x_3^2-5288x_3^3
------------------------------------------------------------------------
x_1x_2x_3+2413x_1x_3^2-49x_2x_3^2+14860x_3^3
------------------------------------------------------------------------
x_1^2x_3+14433x_1x_3^2+11225x_2x_3^2-4453x_3^3
------------------------------------------------------------------------
x_2^3-2512x_1x_3^2+13261x_2x_3^2+7278x_3^3
------------------------------------------------------------------------
x_1x_2^2+14073x_1x_3^2+15620x_2x_3^2-6327x_3^3
------------------------------------------------------------------------
x_1^2x_2+8398x_1x_3^2-11608x_2x_3^2-7372x_3^3
------------------------------------------------------------------------
x_1^3-7276x_1x_3^2-14602x_2x_3^2-5740x_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
|