Quelle history.xml Sprache: XML

<?xml version="1.0" encoding="UTF-8"?>

<Chapter Label="chap-history">
<Heading>Development History</Heading>

<Section><Heading>Versions of the package</Heading>

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.
<P/>
Version 0.91 was prepared to run under &GAP; 4.4.6, in July 2005.
<P/>
Version 0.94 differed in two significant ways.
<List>
<Item>
The manual was produced using the <Package>GAPDoc</Package> package.
</Item>
<Item>
The test file <F>kan/tst/kan_manual.tst</F> set the <C>AssertionLevel</C>
to <C>0</C> to avoid recursion in the &Automata; package.
</Item>
</List>
<P/>
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.
<P/>
&kan; became an accepted &GAP; package in May 2015.
<P/>
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.
<P/>
Only minor changes have been made in recent years.
<P/>
</Section>

<Section><Heading>What needs doing next?</Heading>

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

<List>
<Item>
Implement iterators and enumerators for double cosets.
</Item>
<Item>
At present the methods for <C>DoubleCosetsNC</C> and <C>RightCosetsNC</C>
in this package return automata, rather than lists of cosets
or coset enumerators.  This needs to be fixed.
</Item>
<Item>
Provide methods for operations such as <C>DoubleCosetRepsAndSizes</C>.
</Item>
<Item>
Convert the rest of the original &GAP; 3 version of &kan; to &GAP; 4.
</Item>
</List>

<ManSection>
   <Oper Name="DoubleCosetsAutomaton"
         Arg="G, U, V" />
   <Oper Name="RightCosetsAutomaton"
         Arg="G, V" />
<Description>
Alternative methods for <C>DoubleCosetsNC(G,U,V)</C>
and <C>RightCosetsNC(G,V)</C> <E>should be</E> provided in the cases
where the group <C>G</C> has a rewriting system or is known to be infinite.
At present the functions <C>RightCosetsAutomaton</C> and
<C>DoubleCosetsAutomaton</C> return minimized automata,
and <C>Iterators</C> for these are not yet available.
</Description>
</ManSection>
<Example>
<![CDATA[
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 ]);;
]]>
</Example>
</Section>
</Chapter>

quality97%

¤ Dauer der Verarbeitung: 0.24 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.