Development History
Versions of the package The first version of the package, written for &GAP; 3, formed part of Anne Heyworth's thesis 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. The manual was produced using the GAPDoc package. The test file kan/tst/kan_manual.tst set the AssertionLevel to 0 to avoid recursion in the &Automata; package.

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. The latest version is 1.34 of March 2022.

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. 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 ]);;