| products/Sources/formale Sprachen/GAP/pkg/groupoids/doc/ (MySQL Server Version 8.1-8.4©) Datei vom 11.8.2025 mit Größe 2 kB |
|
Quelle intro.xml Sprache: XML |
|||||||||
|
<?xml version="1.0" encoding="UTF-8"?>
<Chapter Label="chap-intro"> <Heading>Introduction</Heading> Groupoids are mathematical categories in which every arrow is invertible. The &groupoids; package provides functions for the computation with groupoids and their morphisms; for graphs of groups and graphs of groupoids. The package is far from complete, and development continues. <P/> It was used by Emma Moore in her thesis <Cite Key="emma-thesis" /> to calculate normal forms for <E>free products with amalgamation</E>, and for <E>HNN-extensions</E> when the initial groups have rewriting systems. <P/> The package may be obtained as a compressed tar file <File>groupoids-version.number.tar.gz</File> by ftp from one of the following sites: <List> <Item> the &groupoids; GitHub site: <URL>https://github.com/gap-packages.github.io/groupoids/</URL>. </Item> <Item> any &GAP; archive, e.g. <URL>https://www.gap-system.org/Packages/packages.html</URL>; </Item> </List> The package also has a GitHub repository at: <URL>https://github.com/gap-packages/groupoids/</URL>. <P/> The information parameter <C>InfoGroupoids</C> takes default value <C>1</C> which, for the benefit of new users, causes more messages to be printed out when operations fail. When raised to a higher value, additional information is printed out. <P/> Help is available in the usual way. <P/> <Example> <![CDATA[ gap> LoadPackage( "groupoids" ); ]]> </Example> For version 1.05 the package was completely restructured, starting with <E>magmas with objects</E> and their mappings, and building up to groupoids via semigroups with objects and monoids with objects. From version 1.07 the package includes some functions to implement constructions for automorphisms and homotopies, as described in <Cite Key="AlWe" />. More functions will be released when time permits. <P/> Once the package is loaded, it is possible to check the installation has proceeded correctly by running the test suite of the package with the command <C> ReadPackage("groupoids","tst/testing.g"); </C>. Additional tests may be run using <C> ReadPackage("groupoids","tst/testextra.g");.</C> (The file <C>"tst/testall.g"</C> is used for automated testing.) <P/> You may reference this package by mentioning <Cite Key="BrMoPoWe" />, <Cite Key="emma-thesis" /> and <Cite Key="AlWe" />. <P/> Additional information on <E>Computational Higher Dimensional Algebra</E> can be found in the notes on crossed modules at: <URL>https://github.com/cdwensley/xmod-notes</URL>. </Chapter> ¤ Dauer der Verarbeitung: 0.15 Sekunden (vorverarbeitet) ¤*© Formatika GbR, Deutschland |
|
2026-03-28