<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <head> <title>GAP (crime) - Chapter 3: Leisure and Recreation: Cohomology Rings of all Groups of Size 16</title> <meta http-equiv="content-type" content="text/html; charset=UTF-8" /> <meta name="generator" content="GAPDoc2HTML" /> <link rel="stylesheet" type="text/css" href="manual.css" /> </head> <body> <div class="chlinktop"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a> <a href="chap1.html">1</a> <a href="chap2.html">2</a> <a href="chap3.html">3</a> <a href="chapBib.html">Bib</a> <a href="chapInd.html">Ind</a> </div> <div class="chlinkprevnexttop"> <a href="chap0.html">Top of Book</a> <a href="chap2.html">Previous Chapter</a> <a href="chapBib.html">Next Chapter</a> </div> <p><a id="X7BC2C62E7A8CC2B9" name="X7BC2C62E7A8CC2B9"></a></p> <div class="ChapSects"><a href="chap3.html#X7BC2C62E7A8CC2B9">3. <span class="Heading">Leisure and Recreation: Cohomology Rings of all Groups of Size 16</span></a> </div> <h3>3. <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 n, which is initially set to 16, and runs <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 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 <span class="URL"><a href="http://www.math.uga.edu/~lvalero/cohointro.html">http://www.math.uga.edu/~lvalero/cohointro.html</a></span>. See also the file <code class="keyw">tst/README</code> for suggestions on dealing with other users when running long-running batch processes.</p> <table class="example"> <tr><td><pre> 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 </pre></td></tr></table> <div class="chlinkprevnextbot"> <a href="chap0.html">Top of Book</a> <a href="chap2.html">Previous Chapter</a> <a href="chapBib.html">Next Chapter</a> </div> <div class="chlinkbot"><span class="chlink1">Goto Chapter: </span><a href="chap0.html">Top</a> <a href="chap1.html">1</a> <a href="chap2.html">2</a> <a href="chap3.html">3</a> <a href="chapBib.html">Bib</a> <a href="chapInd.html">Ind</a> </div> <hr /> <p class="foot">generated by <a href="http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc">GAPDoc2HTML</a></p> </body> </html>