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

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:  0:00:05.864
Generators in degrees: [ 1, 2 ]
Time:  0:00:00.086
Relators: [ [ z, y ], [ z^2 ] ]
Time:  0:00:00.245

SmallGroup(16,2)
Betti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ]
Time:  0:00:00.931
Generators in degrees: [ 1, 1, 2, 2 ]
Time:  0:00:02.874
Relators: [ [ z, y, x, w ], [ z^2, y^2 ] ]
Time:  0:00:12.227

SmallGroup(16,3)
Betti Numbers: [ 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36 ]
Time:  0:00:05.292
Generators in degrees: [ 1, 1, 2, 2, 2 ]
Time:  0:00:21.770
Relators: [ [ z, y, x, w, v ], [ z^2, z*y, z*x, y^2*v+x^2 ] ]
Time:  0:01:26.166

SmallGroup(16,4)
Betti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ]
Time:  0:00:01.047
Generators in degrees: [ 1, 1, 2, 2 ]
Time:  0:00:03.253
Relators: [ [ z, y, x, w ], [ z^2, z*y+y^2, y^3 ] ]
Time:  0:00:14.294

SmallGroup(16,5)
Betti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ]
Time:  0:00:01.065
Generators in degrees: [ 1, 1, 2 ]
Time:  0:00:02.493
Relators: [ [ z, y, x ], [ z^2 ] ]
Time:  0:00:13.573

SmallGroup(16,6)
Betti Numbers: [ 1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 6 ]
Time:  0:00:00.446
Generators in degrees: [ 1, 1, 3, 4 ]
Time:  0:00:01.566
Relators: [ [ z, y, x, w ], [ z^2, z*y^2, z*x, x^2 ] ]
Time:  0:00:04.132

SmallGroup(16,7)
Betti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ]
Time:  0:00:01.076
Generators in degrees: [ 1, 1, 2 ]
Time:  0:00:02.495
Relators: [ [ z, y, x ], [ z*y ] ]
Time:  0:00:13.862

SmallGroup(16,8)
Betti Numbers: [ 1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 6 ]
Time:  0:00:00.465
Generators in degrees: [ 1, 1, 3, 4 ]
Time:  0:00:01.570
Relators: [ [ z, y, x, w ], [ z*y, z^3, z*x, y^2*w+x^2 ] ]
Time:  0:00:04.350

SmallGroup(16,9)
Betti Numbers: [ 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2 ]
Time:  0:00:00.140
Generators in degrees: [ 1, 1, 4 ]
Time:  0:00:00.255
Relators: [ [ z, y, x ], [ z*y, z^3+y^3, y^4 ] ]
Time:  0:00:00.718

SmallGroup(16,10)
Betti Numbers: [ 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66 ]
Time:  0:00:20.139
Generators in degrees: [ 1, 1, 1, 2 ]
Time:  0:01:04.158
Relators: [ [ z, y, x, w ], [ z^2 ] ]
Time:  0:06:27.688

SmallGroup(16,11)
Betti Numbers: [ 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66 ]
Time:  0:00:20.428
Generators in degrees: [ 1, 1, 1, 2 ]
Time:  0:01:04.678
Relators: [ [ z, y, x, w ], [ z*y ] ]
Time:  0:06:33.808

SmallGroup(16,12)
Betti Numbers: [ 1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17 ]
Time:  0:00:02.438
Generators in degrees: [ 1, 1, 1, 4 ]
Time:  0:00:08.927
Relators: [ [ z, y, x, w ], [ z^2+z*y+y^2, y^3 ] ]
Time:  0:00:44.464

SmallGroup(16,13)
Betti Numbers: [ 1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17 ]
Time:  0:00:02.389
Generators in degrees: [ 1, 1, 1, 4 ]
Time:  0:00:09.247
Relators: [ [ z, y, x, w ], [ z*y+x^2, z*x^2+y*x^2, y^2*x^2+x^4 ] ]
Time:  0:00:44.323

SmallGroup(16,14)
Betti Numbers: [ 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286 ]
Time:  0:07:00.973
Generators in degrees: [ 1, 1, 1, 1 ]
Time:  0:15:40.874
Relators: [ [ z, y, x, w ], [  ] ]
Time:  1:54:28.052

Total time:  2:38:14.841

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