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3 Development History
 3.1 Versions of the package
 3.2 What needs doing next?

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

Version 0.94 differed in two significant ways.

Version 1.11, of December 2014 was required when the Kan website moved yet again. At the same time a bitbucket repository for the package was started.

Kan became an accepted GAP package in May 2015.

Version 1.28, of May 2017, saw a great many changes to the examples, with the various rewriting systems used to perform reduction of words to reduced form.

Only minor changes have been made in recent years.

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> G5 := F/rels;;
gap> genG5 := GeneratorsOfGroup( G5 );;
gap> a := genG5[1];  b := genG5[2];;
gap> U := Subgroup( G5, [a^2] );;
gap> V := Subgroup( G5, [b] );;
gap> L := [2,1,4,3];; 
gap> rws5 := ReducedConfluentRewritingSystem( G5, L, "shortlex", 0, "aAbB" );; 
gap> dc5 := DoubleCosetsAutomaton( G5, U, V );;
gap> Print( dc5 );
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> rc5 := RightCosetsAutomaton( G5, V );;
gap> Print( rc5 );
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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