.
i1 : R = ZZ/32003[x_1..x_3];
|
i2 : g = random(R^1, R^{-4})
o2 = | 251x_1^4-6135x_1^3x_2-15846x_1^2x_2^2+11255x_1x_2^3+1409x_2^4+9246x_1^
------------------------------------------------------------------------
3x_3-12362x_1^2x_2x_3-1789x_1x_2^2x_3-13068x_2^3x_3+11704x_1^2x_3^2+
------------------------------------------------------------------------
11586x_1x_2x_3^2-10231x_2^2x_3^2-13763x_1x_3^3+11306x_2x_3^3-7118x_3^4 |
1 1
o2 : Matrix R <--- R
|
i3 : f = fromDual g
o3 = | x_2^2x_3+393x_1x_3^2-4320x_2x_3^2+1441x_3^3
------------------------------------------------------------------------
x_1x_2x_3-12113x_1x_3^2+14704x_2x_3^2+8557x_3^3
------------------------------------------------------------------------
x_1^2x_3+7746x_1x_3^2-1690x_2x_3^2-476x_3^3
------------------------------------------------------------------------
x_2^3+704x_1x_3^2-7805x_2x_3^2+798x_3^3
------------------------------------------------------------------------
x_1x_2^2-1020x_1x_3^2+11847x_2x_3^2+4626x_3^3
------------------------------------------------------------------------
x_1^2x_2+14648x_1x_3^2-11098x_2x_3^2+5411x_3^3
------------------------------------------------------------------------
x_1^3+15x_1x_3^2-4005x_2x_3^2+12337x_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
|