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: 0:00:05.864 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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