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.
  
  ---------------------------  Example  ----------------------------
    
    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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