GAP (crime) - Contents

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# The Crime Package

Version 1.0

Marcus Bishop
e-mail: marcus.bishop@epfl.ch

### 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.

Thank you also to Laurent Bartholdi for his helpful suggestions regarding the GAP implementation and the user interface, as well as for his proposal of the project in the first place. Laurent also tested the program extensively and uncovered several bugs.

### 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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