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# Hap Programming – An experimental framework for objectifying the data structures of Hap

( development version of 02.12.2008 )

Marc Röder
e-mail: marc.roeder(at)nuigalway.ie

Address:
Marc Röder, Department of Mathematics, NUI Galway, Irleland

### Abstract

This extension does not change the behaviour of Hap and is fully backwards-compatible. It is not a part of Hap and there is no guarantee that it will at any point be supported by Hap. Use at your own risk.

### Copyright

© 2007 Marc Röder.

This package is distributed under the terms of the GNU General Public License version 2 or later (at your convenience). See the file `LICENSE.txt` or http://www.gnu.org/copyleft/gpl.html

### Acknowledgements

This work was supported by Marie Curie Grant No. MTKD-CT-2006-042685

### Contents

1. Resolutions in Hap
1.1 The Standard Representation `HapResolutionRep`
1.2 The `HapLargeGroupResolutionRep` Representation
2. Accessing and Manipulating Resolutions
2.1 Representation-Independent Access Methods
2.1-1 StrongestValidRepresentationForLetter
2.1-2 StrongestValidRepresentationForWord
2.1-3 PositionInGroupOfResolution
2.1-4 IsValidGroupInt
2.1-5 GroupElementFromPosition
2.1-6 MultiplyGroupElts
2.1-7 MultiplyFreeZGLetterWithGroupElt
2.1-8 MultiplyFreeZGWordWithGroupElt
2.1-9 BoundaryOfFreeZGLetter
2.1-10 BoundaryOfFreeZGWord
2.2 Converting Between Representations
2.2-1 ConvertStandardLetter
2.2-2 ConvertStandardWord
2.2-3 ConvertLetterToStandardRep
2.2-4 ConvertWordToStandardRep
2.3 Special Methods for `HapResolutionRep`
2.3-1 IsFreeZGLetter
2.3-2 IsFreeZGWord
2.3-3 MultiplyGroupEltsNC
2.3-4 MultiplyFreeZGLetterWithGroupEltNC
2.3-5 MultiplyFreeZGWordWithGroupEltNC
2.3-6 BoundaryOfFreeZGLetterNC
2.3-7 BoundaryOfFreeZGWordNC
2.4 The `HapLargeGroupResolutionRep` Representation
2.4-1 GroupRingOfResolution
2.4-2 MultiplyGroupElts_LargeGroupRep
2.4-3 IsFreeZGLetterNoTermCheck_LargeGroupRep
2.4-4 IsFreeZGWordNoTermCheck_LargeGroupRep
2.4-5 IsFreeZGLetter_LargeGroupRep
2.4-6 IsFreeZGWord_LargeGroupRep
2.4-7 MultiplyFreeZGLetterWithGroupElt_LargeGroupRep
2.4-8 MultiplyFreeZGWordWithGroupElt_LargeGroupRep
2.4-9 GeneratorsOfModuleOfResolution_LargeGroupRep
2.4-10 BoundaryOfGenerator_LargeGroupRep
2.4-11 BoundaryOfFreeZGLetterNC_LargeGroupRep
2.4-12 BoundaryOfFreeZGWord_LargeGroupRep
3. Contracting Homotopies
3.1 The `PartialContractingHomotopy` Data Type
3.1-1 ResolutionOfContractingHomotopy
3.1-2 PartialContractingHomotopyLookup
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