# Drinfeld modules and their application to factor polynomials

 dc.contributor.advisor Breuer, Florian en_ZA dc.contributor.author Randrianarisoa, Tovohery Hajatiana en_ZA dc.contributor.other Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. en_ZA dc.date.accessioned 2012-11-29T14:37:07Z en_ZA dc.date.accessioned 2012-12-12T08:15:53Z dc.date.available 2012-11-29T14:37:07Z en_ZA dc.date.available 2012-12-12T08:15:53Z dc.date.issued 2012-12 en_ZA dc.identifier.uri http://hdl.handle.net/10019.1/71872 dc.description Thesis (MSc)--Stellenbosch University, 2012. en_ZA dc.description.abstract ENGLISH ABSTRACT: Major works done in Function Field Arithmetic show a strong analogy between en_ZA the ring of integers Z and the ring of polynomials over a nite eld Fq[T]. While an algorithm has been discovered to factor integers using elliptic curves, the discovery of Drinfeld modules, which are analogous to elliptic curves, made it possible to exhibit an algorithm for factorising polynomials in the ring Fq[T]. In this thesis, we introduce the notion of Drinfeld modules, then we demonstrate the analogy between Drinfeld modules and Elliptic curves. Finally, we present an algorithm for factoring polynomials over a nite eld using Drinfeld modules. dc.description.abstract AFRIKAANSE OPSOMMING: 'n Groot deel van die werk wat reeds in funksieliggaam rekenkunde voltooi af_ZA is toon 'n sterk verband tussen die ring van heelgetalle, Z; en die ring van polinome oor 'n eindige liggaam, F[T]: Terwyl daar alreeds 'n algoritme, wat gebruik maak van elliptiese kurwes, ontwerp is om heelgetalle te faktoriseer, het die ontdekking van Drinfeld modules, wat analoog is aan elliptiese kurwes, dit moontlik gemaak om 'n algoritme te konstrueer om polinome in die ring F[T] te faktoriseer. In hierdie tesis maak ons die konsep van Drinfeld modules bekend deur sekere aspekte daarvan te bestudeer. Ons gaan voort deur 'n voorbeeld te voorsien wat die analoog tussen Drinfeld modules en elliptiese kurwes illustreer. Uiteindelik, deur gebruik te maak van Drinfeld modules, bevestig ons hierdie analoog deur die algoritme vir die faktorisering van polinome oor eindige liggame te veskaf. dc.format.extent 70 p. dc.publisher Stellenbosch : Stellenbosch University en_ZA dc.subject Drinfeld modules en_ZA dc.subject Factorization (Mathematics) en_ZA dc.subject Polynomials en_ZA dc.subject Dissertations -- Mathematics en_ZA dc.subject Theses -- Mathematics en_ZA dc.subject Modules (Algebra) en_ZA dc.title Drinfeld modules and their application to factor polynomials en_ZA dc.type Thesis en_ZA dc.rights.holder Stellenbosch University en_ZA
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