3. Leisure and Recreation: Cohomology Rings of all Groups of Size 16

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 3.06 GHz Intel processor with 3.71 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 dealing with other users when running long-running batch processes.



SmallGroup(16,1)
Betti Numbers: [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
Time:  0:00:04.209
Generators in degrees: [ 1, 2 ]
Time:  0:00:00.037
Relators: [ [ z, y ], [ z^2 ] ]
Time:  0:00:00.101

SmallGroup(16,2)
Betti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ]
Time:  0:00:03.055
Generators in degrees: [ 1, 1, 2, 2 ]
Time:  0:00:09.322
Relators: [ [ z, y, x, w ], [ z^2, y^2 ] ]
Time:  0:00:23.386

SmallGroup(16,3)
Betti Numbers: [ 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36 ]
Time:  0:00:54.653
Generators in degrees: [ 1, 1, 2, 2, 2 ]
Time:  0:03:29.691
Relators: [ [ z, y, x, w, v ], [ z^2, z*y, z*x, y^2*v+x^2 ] ]
Time:  0:06:33.189

SmallGroup(16,4)
Betti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ]
Time:  0:00:03.163
Generators in degrees: [ 1, 1, 2, 2 ]
Time:  0:00:09.873
Relators: [ [ z, y, x, w ], [ z^2, z*y+y^2, y^3 ] ]
Time:  0:00:25.149

SmallGroup(16,5)
Betti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ]
Time:  0:00:03.080
Generators in degrees: [ 1, 1, 2 ]
Time:  0:00:07.356
Relators: [ [ z, y, x ], [ z^2 ] ]
Time:  0:00:22.859

SmallGroup(16,6)
Betti Numbers: [ 1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 6 ]
Time:  0:00:00.674
Generators in degrees: [ 1, 1, 3, 4 ]
Time:  0:00:02.575
Relators: [ [ z, y, x, w ], [ z^2, z*y^2, z*x, x^2 ] ]
Time:  0:00:03.675

SmallGroup(16,7)
Betti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ]
Time:  0:00:03.071
Generators in degrees: [ 1, 1, 2 ]
Time:  0:00:07.282
Relators: [ [ z, y, x ], [ z*y ] ]
Time:  0:00:22.786

SmallGroup(16,8)
Betti Numbers: [ 1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 6 ]
Time:  0:00:00.676
Generators in degrees: [ 1, 1, 3, 4 ]
Time:  0:00:02.584
Relators: [ [ z, y, x, w ], [ z*y, z^3, z*x, y^2*w+x^2 ] ]
Time:  0:00:03.825

SmallGroup(16,9)
Betti Numbers: [ 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2 ]
Time:  0:00:00.087
Generators in degrees: [ 1, 1, 4 ]
Time:  0:00:00.139
Relators: [ [ z, y, x ], [ z*y, z^3+y^3, y^4 ] ]
Time:  0:00:00.374

SmallGroup(16,10)
Betti Numbers: [ 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66 ]
Time:  0:05:37.603
Generators in degrees: [ 1, 1, 1, 2 ]
Time:  0:16:52.067
Relators: [ [ z, y, x, w ], [ z^2 ] ]
Time:  0:52:54.579

SmallGroup(16,11)
Betti Numbers: [ 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66 ]
Time:  0:05:30.506
Generators in degrees: [ 1, 1, 1, 2 ]
Time:  0:16:29.940
Relators: [ [ z, y, x, w ], [ z*y ] ]
Time:  0:52:04.624

SmallGroup(16,12)
Betti Numbers: [ 1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17 ]
Time:  0:00:10.051
Generators in degrees: [ 1, 1, 1, 4 ]
Time:  0:00:43.703
Relators: [ [ z, y, x, w ], [ z^2+z*y+y^2, y^3 ] ]
Time:  0:02:02.128

SmallGroup(16,13)
Betti Numbers: [ 1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17 ]
Time:  0:00:09.991
Generators in degrees: [ 1, 1, 1, 4 ]
Time:  0:00:43.443
Relators: [ [ z, y, x, w ], [ z*y+x^2, z*x^2+y*x^2, y^2*x^2+x^4 ] ]
Time:  0:01:59.953

SmallGroup(16,14)
Betti Numbers: [ 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286 ]
Time:  5:03:44.290
Generators in degrees: [ 1, 1, 1, 1 ]
Time:  8:14:32.187





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