  
  
                                    [1X walrus [101X
  
  
                   [1X A new approach to proving hyperbolicity [101X
  
  
                                      0.99
  
  
                                19 February 2019
  
  
                                Markus Pfeiffer
  
  
  
  Markus Pfeiffer
      Email:    [7Xmailto:markus.pfeiffer@st-andrews.ac.uk[107X
      Homepage: [7Xhttp://www.morphism.de/~markusp/[107X
      Address:  [33X[0;14YSchool of Computer Science[133X
                [33X[0;14YUniversity of St Andrews[133X
                [33X[0;14YJack Cole Building, North Haugh[133X
                [33X[0;14YSt Andrews, Fife, KY16 9SX[133X
                [33X[0;14YUnited Kingdom[133X
  
  
  
  -------------------------------------------------------
  
  
  [1XContents (walrus)[101X
  
  1 [33X[0;0YOverview[133X
    1.1 [33X[0;0YExamples[133X
      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 [33X[0;0YTesting Hyperbolicity[133X
    1.3 [33X[0;0YThe MAGMA-compatible interface[133X
  2 [33X[0;0YPregroups[133X
    2.1 [33X[0;0YCreating Pregroups[133X
      2.1-1 PregroupByTable
      2.1-2 PregroupByRedRelators
      2.1-3 PregroupOfFreeProduct
      2.1-4 PregroupOfFreeGroup
    2.2 [33X[0;0YFilters and Representations[133X
      2.2-1 IsPregroup
      2.2-2 IsPregroupTableRep
      2.2-3 IsPregroupOfFreeGroupRep
      2.2-4 IsPregroupOfFreeProductRep
    2.3 [33X[0;0YAttributes, Properties, and Operations[133X
      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 [33X[0;0YElements of Pregroups[133X
      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 [33X[0;0YSmall Pregroups[133X
      2.5-1 NrSmallPregroups
      2.5-2 SmallPregroup
  3 [33X[0;0YPregroup Presentations[133X
    3.1 [33X[0;0YConcepts[133X
      3.1-1 [33X[0;0YLocations[133X
      3.1-2 [33X[0;0YPlaces[133X
    3.2 [33X[0;0YAttributes[133X
      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 [33X[0;0YCreating Pregroup Presentations[133X
      3.3-1 NewPregroupPresentation
      3.3-2 PregroupPresentationFromFp
      3.3-3 PregroupPresentationToFpGroup
    3.4 [33X[0;0YFilters, Attributes, and Properties[133X
      3.4-1 IsPregroupPresentation
      3.4-2 
    3.5 [33X[0;0YHyperbolicity testing for pregroup presentations[133X
      3.5-1 RSymTestOp
      3.5-2 RSymTest
      3.5-3 IsHyperbolic
    3.6 [33X[0;0YInput and Output of Pregroup Presentations[133X
      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
  
  
  [32X
