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### 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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