Drinfeld modules and their application to factor polynomials

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dc.contributor.advisorBreuer, Florianen_ZA
dc.contributor.authorRandrianarisoa, Tovohery Hajatianaen_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.en_ZA
dc.date.accessioned2012-11-29T14:37:07Zen_ZA
dc.date.accessioned2012-12-12T08:15:53Z
dc.date.available2012-11-29T14:37:07Zen_ZA
dc.date.available2012-12-12T08:15:53Z
dc.date.issued2012-12en_ZA
dc.descriptionThesis (MSc)--Stellenbosch University, 2012.en_ZA
dc.description.abstractENGLISH ABSTRACT: Major works done in Function Field Arithmetic show a strong analogy between 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.en_ZA
dc.description.abstractAFRIKAANSE OPSOMMING: 'n Groot deel van die werk wat reeds in funksieliggaam rekenkunde voltooi 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.af_ZA
dc.format.extent70 p.
dc.identifier.urihttp://hdl.handle.net/10019.1/71872
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.rights.holderStellenbosch Universityen_ZA
dc.subjectDrinfeld modulesen_ZA
dc.subjectFactorization (Mathematics)en_ZA
dc.subjectPolynomialsen_ZA
dc.subjectDissertations -- Mathematicsen_ZA
dc.subjectTheses -- Mathematicsen_ZA
dc.subjectModules (Algebra)en_ZA
dc.titleDrinfeld modules and their application to factor polynomialsen_ZA
dc.typeThesisen_ZA
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