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 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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