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, calls `ProjectiveResolution`

, `CohomologyGenerators`

, and `CohomologyRelators`

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. The example below was computed on a 2.4 GHz AMD64 processor with 12 GB of RAM. See 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 ] 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 ], [ ] ]

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