Deprecated: $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372
Applications of Rewriting Systems and Groebner Bases to Computing Kan Extensions and Identities Among Relations - MaRDI portal

Deprecated: Use of MediaWiki\Skin\SkinTemplate::injectLegacyMenusIntoPersonalTools was deprecated in Please make sure Skin option menus contains `user-menu` (and possibly `notifications`, `user-interface-preferences`, `user-page`) 1.46. [Called from MediaWiki\Skin\SkinTemplate::getPortletsTemplateData in /var/www/html/w/includes/Skin/SkinTemplate.php at line 691] in /var/www/html/w/includes/Debug/MWDebug.php on line 372

Deprecated: Use of MediaWiki\Skin\BaseTemplate::getPersonalTools was deprecated in 1.46 Call $this->getSkin()->getPersonalToolsForMakeListItem instead (T422975). [Called from Skins\Chameleon\Components\NavbarHorizontal\PersonalTools::getHtml in /var/www/html/w/skins/chameleon/src/Components/NavbarHorizontal/PersonalTools.php at line 66] in /var/www/html/w/includes/Debug/MWDebug.php on line 372

Deprecated: Use of QuickTemplate::(get/html/text/haveData) with parameter `personal_urls` was deprecated in MediaWiki Use content_navigation instead. [Called from MediaWiki\Skin\QuickTemplate::get in /var/www/html/w/includes/Skin/QuickTemplate.php at line 131] in /var/www/html/w/includes/Debug/MWDebug.php on line 372

Applications of Rewriting Systems and Groebner Bases to Computing Kan Extensions and Identities Among Relations

From MaRDI portal
Publication:6501126

arXivmath/9812097MaRDI QIDQ6501126

Author name not available (Why is that?)


Abstract: This thesis concentrates on the development and application of rewriting and Groebner basis methods to a range of combinatorial problems. Chapter Two contains the most important result, which is the application of Knuth-Bendix procedures to Kan extensions, showing how rewriting provides a useful method for attempting to solve a variety of combinatorial problems which can be phrased in terms of Kan extensions. Chapter Three shows that the standard Knuth-Bendix algorithm is step-for-step a special case of Buchberger's algorithm. The one-sided cases and higher dimensions are considered. Chapter Four relates rewrite systems, Groebner bases and automata. Automata which only accept irreducibles, and automata which output reduced forms are discussed for presentations of Kan extensions. Reduction machines for rewrite systems are identified with standard output automata and the reduction machines devised for algebras are expressed as Petri nets. Chapter Five uses the completion of a group rewriting system to algorithmically determine a contracting homotopy necessary in order to compute the set of generators for the module of identities among relations using the covering groupoid methods devised by Brown and Razak Salleh. Reducing the resulting set of submodule generators is identified as a Groebner basis problem. Algorithms are implemented in GAP3.





Mathematics Subject Classification ID

No records found.








This page was built for publication: Applications of Rewriting Systems and Groebner Bases to Computing Kan Extensions and Identities Among Relations

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6501126)

Retrieved from "https://mardi.schubotz.org/w/index.php?title=Publication:6501126&oldid=37958594"
Powered by MediaWiki