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<div class="ChapSects"><a href="chapB_mj.html#X7BC2C62E7A8CC2B9">B <span class="Heading">Leisure and Recreation: Cohomology Rings
of all Groups of Size 16</span></a>
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<h3>B <span class="Heading">Leisure and Recreation: Cohomology Rings
of all Groups of Size 16</span></h3>

<p>Below is the output of the test file <code class="keyw">tst/batch.g</code>. The file runs through all groups of size <span class="SimpleMath">\(n\)</span>, which is initially set to <span class="SimpleMath">\(16\)</span>, calls <code class="keyw">ProjectiveResolution</code>, <code class="keyw">CohomologyGenerators</code>, and <code class="keyw">CohomologyRelators</code> 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 <a href="chapA_mj.html#X82113B3184F76F58"><span class="RefLink">A</span></a>. The example below was computed on a 2.4 GHz AMD64 processor with 12 GB of RAM. See the file <code class="keyw">tst/README</code> for suggestions on dealing with other users when running long-running batch processes.</p>

<div class="example"><pre>
SmallGroup(16,1)
Betti Numbers: [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]
Generators in degrees: [ 1, 2 ]
Relators: [ [ z, y ], [ z^2 ] ]

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

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

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

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

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

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

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

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

SmallGroup(16,10)
Betti Numbers: [ 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66 ]
Generators in degrees: [ 1, 1, 1, 2 ]
Relators: [ [ z, y, x, w ], [ z^2 ] ]

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

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

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

SmallGroup(16,14)
Betti Numbers: [ 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286 ]
Generators in degrees: [ 1, 1, 1, 1 ]
Relators: [ [ z, y, x, w ], [  ] ]

</pre></div>

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