3 Development History
  
  
  3.1 Versions of the package
  
  The  first  version  of  the package, written for GAP 3, formed part of Anne
  Heyworth's thesis [Hey99] in 1999, but was not made generally available.
  
  Version, kan 0.91, was prepared to run under GAP 4.4.6, in July 2005.
  
  Version, kan 0.94, differed in two significant ways.
  
  --    This manual is prepared using the GAPDoc package.
  
  --    The  test file kan/tst/kan\_manual.tst sets the AssertionLevel to 0 to
        avoid recursion in the Automata package.
  
  Version  0.95,  of 9th October 2007, just fixed file protections and added a
  CHANGES file.
  
  Version 0.96 was required because the kan website moved with the rest of the
  Mathematics website at Bangor.
  
  Version  0.97,  of November 18th 2008, deleted temporary fixes which were no
  longer needed once version 1.12 of Automata became available.
  
  
  3.2 What needs doing next?
  
  There are too many items to list here, but some of the most important are as
  follows.
  
  --    Implement iterators and enumerators for double cosets.
  
  --    At  present  the  methods for DoubleCosetsNC and RightCosetsNC in this
        package  return  automata,  rather  than  lists  of  cosets  or  coset
        enumerators. This needs to be fixed.
  
  --    Provide methods for operations such as DoubleCosetRepsAndSizes.
  
  --    Convert the rest of the original GAP 3 version of kan to GAP 4.
  
  3.2-1 DoubleCosetsAutomaton
  
  > DoubleCosetsAutomaton( G, U, V ) ________________________________operation
  > RightCosetsAutomaton( G, V ) ____________________________________operation
  
  Alternative  methods for DoubleCosetsNC(G,U,V) and RightCosetsNC(G,V) should
  be  provided  in  the  cases  where the group G has a rewriting system or is
  known  to  be  infinite.  At  present the functions RightCosetsAutomaton and
  DoubleCosetsAutomaton return minimized automata, and Iterators for these are
  not yet available.
  
  ---------------------------  Example  ----------------------------
    
    gap> F := FreeGroup(2);;
    gap> rels := [ F.2^2, (F.1*F.2)^2 ];;
    gap> G4 := F/rels;;
    gap> genG4 := GeneratorsOfGroup( G4 );;
    gap> a := genG4[1];  b := genG4[2];;
    gap> U := Subgroup( G4, [a^2] );;
    gap> V := Subgroup( G4, [b] );;
    gap> dc4 := DoubleCosetsAutomaton( G4, U, V );;
    gap> Print( dc4 );
    Automaton("det",5,"HKaAbB",[ [ 2, 2, 2, 5, 2 ], [ 2, 2, 1, 2, 1 ], [ 2, 2, 2, \
    2, 3 ], [ 2, 2, 2, 2, 2 ], [ 2, 2, 2, 2, 2 ], [ 2, 2, 2, 2, 2 ] ],[ 4 ],[ 1 ])\
    ;;
    gap> rc4 := RightCosetsAutomaton( G4, V );;
    gap> Print( rc4 );
    Automaton("det",6,"HKaAbB",[ [ 2, 2, 2, 6, 2, 2 ], [ 2, 2, 1, 2, 1, 1 ], [ 2, \
    2, 3, 2, 2, 3 ], [ 2, 2, 2, 2, 5, 5 ], [ 2, 2, 2, 2, 2, 2 ], [ 2, 2, 2, 2, 2, \
    2 ] ],[ 4 ],[ 1 ]);;
    
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