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walrus

A new approach to proving hyperbolicity

0.9991

21 February 2022

Markus Pfeiffer
Email: markus.pfeiffer@st-andrews.ac.uk
Homepage: http://www.morphism.de/~markusp/
Address:
School of Computer Science
University of St Andrews
Jack Cole Building, North Haugh
St Andrews, Fife, KY16 9SX
United Kingdom

Contents

1 Overview
 1.1 Examples

  1.1-1 TriangleGroup
  1.1-2 TriangleCommutatorQuotient
  1.1-3 RandomTriangleQuotient
  1.1-4 JackButtonGroup
  1.1-5 RandomPregroupPresentation
  1.1-6 RandomPregroupWord
 1.2 Testing Hyperbolicity
 1.3 The MAGMA-compatible interface
2 Pregroups
 2.1 Creating Pregroups

  2.1-1 PregroupByTable
  2.1-2 PregroupByRedRelators
  2.1-3 PregroupOfFreeProduct
  2.1-4 PregroupOfFreeGroup
 2.2 Filters and Representations

  2.2-1 IsPregroup
  2.2-2 IsPregroupTableRep
  2.2-3 IsPregroupOfFreeGroupRep
  2.2-4 IsPregroupOfFreeProductRep
 2.3 Attributes, Properties, and Operations

  2.3-1 []
  2.3-2 IntermultPairs
  2.3-3 One
  2.3-4 MultiplicationTable
  2.3-5 SetPregroupElementNames
  2.3-6 PregroupElementNames
 2.4 Elements of Pregroups

  2.4-1 IsElementOfPregroup
  2.4-2 IsElementOfPregroupRep
  2.4-3 IsElementOfPregroupOfFreeGroupRep
  2.4-4 PregroupOf
  2.4-5 IsDefinedMultiplication
  2.4-6 IsIntermultPair
  2.4-7 PregroupInverse
 2.5 Small Pregroups

  2.5-1 NrSmallPregroups
  2.5-2 SmallPregroup
3 Pregroup Presentations
 3.1 Concepts

  3.1-1 Locations
  3.1-2 Places
 3.2 Attributes

  3.2-1 IsPregroupLocation
  3.2-2 InLetter
  3.2-3 OutLetter
  3.2-4 Places
  3.2-5 NextLocation
  3.2-6 PrevLocation
  3.2-7 __ID
 3.3 Creating Pregroup Presentations

  3.3-1 NewPregroupPresentation
  3.3-2 PregroupPresentationFromFp
  3.3-3 PregroupPresentationToFpGroup
 3.4 Filters, Attributes, and Properties

  3.4-1 IsPregroupPresentation
  3.4-2
 3.5 Hyperbolicity testing for pregroup presentations

  3.5-1 RSymTestOp
  3.5-2 RSymTest
  3.5-3 IsHyperbolic
 3.6 Input and Output of Pregroup Presentations

  3.6-1 PregroupPresentationToKBMAG
  3.6-2 PregroupPresentationToStream
  3.6-3 PregroupPresentationFromStream
  3.6-4 PregroupPresentationToSimpleStream
  3.6-5 PregroupPresentationToFile
  3.6-6 PregroupPresentationFromFile
  3.6-7 PregroupPresentationToSimpleFile
Index

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