Below is the output of the test file tst/batch.g
. The file runs through all groups of size n, which is initially set to 16, and runs ProjectiveResolution
, CohomologyGenerators
and CohomologyRelators
for each group, and prints the results as well as the timings for each operation to a file. The output below was computed on a 1.8 GHz Intel processor with 2 GB of RAM. The projective resolutions are calculated initially to degree 10 and the generators and relators to degree 6, due to the fact that I already knew all the generators and relators to be of degree less than 6, see http://www.math.uga.edu/~lvalero/cohointro.html. See also the file tst/README
for suggestions on running long-running batch processes.
SmallGroup(16,1) Betti Numbers: [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] Time: 0:00:03.290 Generators in degrees: [ 1, 2 ] Time: 0:00:00.030 Relators: [ [ z, y ], [ z^2 ] ] Time: 0:00:00.000 SmallGroup(16,2) Betti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ] Time: 0:00:04.750 Generators in degrees: [ 1, 1, 2, 2 ] Time: 0:00:01.050 Relators: [ [ z, y, x, w ], [ y^2, z^2 ] ] Time: 0:00:00.000 SmallGroup(16,3) Betti Numbers: [ 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36 ] Time: 0:01:18.190 Generators in degrees: [ 1, 1, 2, 2, 2 ] Time: 0:00:06.780 Relators: [ [ z, y, x, w, v ], [ z*y, z^2, z*v, y^2*x+v^2 ] ] Time: 0:00:00.000 SmallGroup(16,4) Betti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ] Time: 0:00:14.020 Generators in degrees: [ 1, 1, 2, 2 ] Time: 0:00:01.080 Relators: [ [ z, y, x, w ], [ z^2, z*y+y^2, y^3 ] ] Time: 0:00:00.000 SmallGroup(16,5) Betti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ] Time: 0:00:06.640 Generators in degrees: [ 1, 1, 2 ] Time: 0:00:00.800 Relators: [ [ z, y, x ], [ z^2 ] ] Time: 0:00:00.000 SmallGroup(16,6) Betti Numbers: [ 1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 6 ] Time: 0:00:02.990 Generators in degrees: [ 1, 1, 3, 4 ] Time: 0:00:00.310 Relators: [ [ z, y, x, w ], [ z^2, z*y^2, z*x, x^2 ] ] Time: 0:00:00.000 SmallGroup(16,7) Betti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ] Time: 0:00:05.330 Generators in degrees: [ 1, 1, 2 ] Time: 0:00:00.790 Relators: [ [ z, y, x ], [ z*y ] ] Time: 0:00:00.000 SmallGroup(16,8) Betti Numbers: [ 1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 6 ] Time: 0:00:02.970 Generators in degrees: [ 1, 1, 3, 4 ] Time: 0:00:00.310 Relators: [ [ z, y, x, w ], [ z*y, z^3, z*x, y^2*w+x^2 ] ] Time: 0:00:00.000 SmallGroup(16,9) Betti Numbers: [ 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2 ] Time: 0:00:00.670 Generators in degrees: [ 1, 1, 4 ] Time: 0:00:00.070 Relators: [ [ z, y, x ], [ z*y, z^3+y^3, y^4 ] ] Time: 0:00:00.000 SmallGroup(16,10) Betti Numbers: [ 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66 ] Time: 0:07:29.440 Generators in degrees: [ 1, 1, 1, 2 ] Time: 0:00:22.680 Relators: [ [ z, y, x, w ], [ z^2 ] ] Time: 0:00:00.000 SmallGroup(16,11) Betti Numbers: [ 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66 ] Time: 0:08:22.950 Generators in degrees: [ 1, 1, 1, 2 ] Time: 0:00:22.640 Relators: [ [ z, y, x, w ], [ z*y ] ] Time: 0:00:00.000 SmallGroup(16,12) Betti Numbers: [ 1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17 ] Time: 0:01:13.200 Generators in degrees: [ 1, 1, 1, 4 ] Time: 0:00:03.720 Relators: [ [ z, y, x, w ], [ z^2+z*y+y^2, y^3 ] ] Time: 0:00:00.000 SmallGroup(16,13) Betti Numbers: [ 1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17 ] Time: 0:00:23.330 Generators in degrees: [ 1, 1, 1, 4 ] Time: 0:00:03.430 Relators: [ [ z, y, x, w ], [ z*y+x^2, z*x^2+y*x^2, y^2*x^2+x^4 ] ] Time: 0:00:00.000 SmallGroup(16,14) Betti Numbers: [ 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286 ] Time: 6:37:11.670 Generators in degrees: [ 1, 1, 1, 1 ] Time: 0:04:17.050 Relators: [ [ z, y, x, w ], [ ] ] Time: 0:00:00.000 |
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