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

( development version of 10.02.2020 )

Marc Röder
Email: 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 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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