The Crime Package

Version 1.1

Marcus Bishop
e-mail: marcus.bishop@gmail.com

Copyright

(C) 2006 Marcus Bishop

We adopt the copyright regulations of GAP as detailed in the copyright notice in the GAP manual.

Acknowledgements

This project would not have been possible without Jon Carlson. Jon devised the algorithms used by ProjectiveResolution, CohomologyGenerators, and CohomologyRelators, having already implemented them in Magma and sharing these programs with me.

Contents

1. Installation and Loading
2. Usage
   2.1 Cohomology Objects
      2.1-1 CohomologyObject
   2.2 Minimal Projective Resolutions
      2.2-1 ProjectiveResolution
      2.2-2 BoundaryMap
   2.3 Cohomology Generators and Relators
      2.3-1 CohomologyGenerators
      2.3-2 CohomologyRelators
   2.4 Tests for Completion
   2.5 Cohomology Rings
      2.5-1 CohomologyRing
      2.5-2 IsHomogeneous
      2.5-3 Degree
      2.5-4 LocateGeneratorsInCohomologyRing
   2.6 What Happens if n Isn't Big Enough?
   2.7 Induced Maps
      2.7-1 InducedHomomorphismOnCohomology
      2.7-2 Inclusion
   2.8 Massey Products
      2.8-1 MasseyProduct
3. Leisure and Recreation: Cohomology Rings of all Groups of Size 16




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