  
  [1XB Leisure and Recreation: Cohomology Rings of all Groups of Size 16[0X
  
  Below  is the output of the test file [9Xtst/batch.g[0m. The file runs through all
  groups  of size n, which is initially set to 16, calls [9XProjectiveResolution[0m,
  [9XCohomologyGenerators[0m,  and [9XCohomologyRelators[0m for each group, and prints the
  results,  as well as the runtimes for each operation, to a file like the one
  shown  below.  The  runtimes  in this example have been deleted, having been
  presented  in  Appendix [14XA[0m. The example below was computed on a 2.4 GHz AMD64
  processor  with  12  GB  of  RAM. See the file [9Xtst/README[0m for suggestions on
  dealing with other users when running long-running batch processes.
  
  [4X---------------------------  Example  ----------------------------[0X
    [4X[0X
    [4XSmallGroup(16,1)[0X
    [4XBetti Numbers: [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ][0X
    [4XGenerators in degrees: [ 1, 2 ][0X
    [4XRelators: [ [ z, y ], [ z^2 ] ][0X
    [4X[0X
    [4XSmallGroup(16,2)[0X
    [4XBetti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ][0X
    [4XGenerators in degrees: [ 1, 1, 2, 2 ][0X
    [4XRelators: [ [ z, y, x, w ], [ z^2, y^2 ] ][0X
    [4X[0X
    [4XSmallGroup(16,3)[0X
    [4XBetti Numbers: [ 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36 ][0X
    [4XGenerators in degrees: [ 1, 1, 2, 2, 2 ][0X
    [4XRelators: [ [ z, y, x, w, v ], [ z^2, z*y, z*x, y^2*v+x^2 ] ][0X
    [4X[0X
    [4XSmallGroup(16,4)[0X
    [4XBetti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ][0X
    [4XGenerators in degrees: [ 1, 1, 2, 2 ][0X
    [4XRelators: [ [ z, y, x, w ], [ z^2, z*y+y^2, y^3 ] ][0X
    [4X[0X
    [4XSmallGroup(16,5)[0X
    [4XBetti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ][0X
    [4XGenerators in degrees: [ 1, 1, 2 ][0X
    [4XRelators: [ [ z, y, x ], [ z^2 ] ][0X
    [4X[0X
    [4XSmallGroup(16,6)[0X
    [4XBetti Numbers: [ 1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 6 ][0X
    [4XGenerators in degrees: [ 1, 1, 3, 4 ][0X
    [4XRelators: [ [ z, y, x, w ], [ z^2, z*y^2, z*x, x^2 ] ][0X
    [4X[0X
    [4XSmallGroup(16,7)[0X
    [4XBetti Numbers: [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ][0X
    [4XGenerators in degrees: [ 1, 1, 2 ][0X
    [4XRelators: [ [ z, y, x ], [ z*y ] ][0X
    [4X[0X
    [4XSmallGroup(16,8)[0X
    [4XBetti Numbers: [ 1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 6 ][0X
    [4XGenerators in degrees: [ 1, 1, 3, 4 ][0X
    [4XRelators: [ [ z, y, x, w ], [ z*y, z^3, z*x, y^2*w+x^2 ] ][0X
    [4X[0X
    [4XSmallGroup(16,9)[0X
    [4XBetti Numbers: [ 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2 ][0X
    [4XGenerators in degrees: [ 1, 1, 4 ][0X
    [4XRelators: [ [ z, y, x ], [ z*y, z^3+y^3, y^4 ] ][0X
    [4X[0X
    [4XSmallGroup(16,10)[0X
    [4XBetti Numbers: [ 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66 ][0X
    [4XGenerators in degrees: [ 1, 1, 1, 2 ][0X
    [4XRelators: [ [ z, y, x, w ], [ z^2 ] ][0X
    [4X[0X
    [4XSmallGroup(16,11)[0X
    [4XBetti Numbers: [ 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66 ][0X
    [4XGenerators in degrees: [ 1, 1, 1, 2 ][0X
    [4XRelators: [ [ z, y, x, w ], [ z*y ] ][0X
    [4X[0X
    [4XSmallGroup(16,12)[0X
    [4XBetti Numbers: [ 1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17 ][0X
    [4XGenerators in degrees: [ 1, 1, 1, 4 ][0X
    [4XRelators: [ [ z, y, x, w ], [ z^2+z*y+y^2, y^3 ] ][0X
    [4X[0X
    [4XSmallGroup(16,13)[0X
    [4XBetti Numbers: [ 1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 17 ][0X
    [4XGenerators in degrees: [ 1, 1, 1, 4 ][0X
    [4XRelators: [ [ z, y, x, w ], [ z*y+x^2, z*x^2+y*x^2, y^2*x^2+x^4 ] ][0X
    [4X[0X
    [4XSmallGroup(16,14)[0X
    [4XBetti Numbers: [ 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286 ][0X
    [4XGenerators in degrees: [ 1, 1, 1, 1 ][0X
    [4XRelators: [ [ z, y, x, w ], [  ] ][0X
    [4X[0X
  [4X------------------------------------------------------------------[0X
  
