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Drinfeld modules and their application to factor polynomials
Thesis (MSc)--Stellenbosch University, 2012.
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Stellenbosch : Stellenbosch University
2012
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| _version_ | 1867613907530547200 |
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| access_status_str | Open Access |
| author | Randrianarisoa, Tovohery Hajatiana |
| author2 | Breuer, Florian |
| author_browse | Breuer, Florian Randrianarisoa, Tovohery Hajatiana |
| author_facet | Breuer, Florian Randrianarisoa, Tovohery Hajatiana |
| author_sort | Randrianarisoa, Tovohery Hajatiana |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2012. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/71872 |
| institution | Stellenbosch University (South Africa) |
| last_indexed | 2026-06-10T12:43:36.390Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2012 |
| publishDateRange | 2012 |
| publishDateSort | 2012 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/71872 Drinfeld modules and their application to factor polynomials Randrianarisoa, Tovohery Hajatiana Breuer, Florian Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Drinfeld modules Factorization (Mathematics) Polynomials Dissertations -- Mathematics Theses -- Mathematics Modules (Algebra) Thesis (MSc)--Stellenbosch University, 2012. ENGLISH 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. AFRIKAANSE 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. 2012-11-29T14:37:07Z 2012-12-12T08:15:53Z 2012-11-29T14:37:07Z 2012-12-12T08:15:53Z 2012-12 Thesis http://hdl.handle.net/10019.1/71872 Stellenbosch University 70 p. application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Drinfeld modules Factorization (Mathematics) Polynomials Dissertations -- Mathematics Theses -- Mathematics Modules (Algebra) Randrianarisoa, Tovohery Hajatiana Drinfeld modules and their application to factor polynomials |
| title | Drinfeld modules and their application to factor polynomials |
| title_full | Drinfeld modules and their application to factor polynomials |
| title_fullStr | Drinfeld modules and their application to factor polynomials |
| title_full_unstemmed | Drinfeld modules and their application to factor polynomials |
| title_short | Drinfeld modules and their application to factor polynomials |
| title_sort | drinfeld modules and their application to factor polynomials |
| topic | Drinfeld modules Factorization (Mathematics) Polynomials Dissertations -- Mathematics Theses -- Mathematics Modules (Algebra) |
| url | http://hdl.handle.net/10019.1/71872 |
| work_keys_str_mv | AT randrianarisoatovoheryhajatiana drinfeldmodulesandtheirapplicationtofactorpolynomials |