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 [H99] in 1999, but was not made generally available.

Version, kan~0.91, was prepared to run under GAP~4.4.6, in July 2005.

This version, kan~0.94, differs in three ways:

3.2 What needs doing next?

There are too many items to list here, but some of the most important are as follows.

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.



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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