<?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) - Appendix B: 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="chapA.html">A</a> <a href="chapB.html">B</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="chapA.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="chapB.html#X7BC2C62E7A8CC2B9">B. <span class="Heading">Leisure and Recreation: Cohomology Rings of all Groups of Size 16</span></a> </div> <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 n, which is initially set to 16, 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.html#X82113B3184F76F58"><b>A.</b></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> <table class="example"> <tr><td><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></td></tr></table> <div class="chlinkprevnextbot"> <a href="chap0.html">Top of Book</a> <a href="chapA.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="chapA.html">A</a> <a href="chapB.html">B</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>