Torsion points on elliptic curves

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dc.contributor.advisorKeet, A. P.en_ZA
dc.contributor.authorNyirenda, Darlisonen_ZA
dc.contributor.otherStellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.en_ZA
dc.date.accessioned2013-02-25T11:00:37Zen_ZA
dc.date.accessioned2013-03-15T07:36:10Z
dc.date.available2013-02-25T11:00:37Zen_ZA
dc.date.available2013-03-15T07:36:10Z
dc.date.issued2013-03en_ZA
dc.descriptionThesis (MSc)--Stellenbosch University, 2013.en_ZA
dc.description.abstractENGLISH ABSTRACT: The central objective of our study focuses on torsion points on elliptic curves. The case of elliptic curves over finite fields is explored up to giving explicit formulae for the cardinality of the set of points on such curves. For finitely generated fields of characteristic zero, a presentation and discussion of some known results is made. Some applications of elliptic curves are provided. In one particular case of applications, we implement an integer factorization algorithm in a computer algebra system SAGE based on Lenstra’s elliptic curve factorisation method.en_ZA
dc.description.abstractAFRIKAANSE OPSOMMING: Die hoofdoel van ons studie is torsiepunte op elliptiese krommes. Ons ondersoek die geval van elliptiese krommes oor ‘n eindige liggaam met die doel om eksplisiete formules vir die aantal punte op sulke krommes te gee. Vir ‘n eindig-voortgebringde liggaam met karakteristiek nul bespreek ons sekere bekende resultate. Sommige toepassings van elliptiese krommes word gegee. In een van hierdie toepassings implementeer ons ‘n heeltallige faktoriseringalgoritme in die rekenaar-algebrastelsel SAGE gebaseer op Lenstra se elliptiese krommefaktoriseeringmetode.af_ZA
dc.format.extent103 p.
dc.identifier.urihttp://hdl.handle.net/10019.1/80120
dc.language.isoen_ZAen_ZA
dc.publisherStellenbosch : Stellenbosch Universityen_ZA
dc.rights.holderStellenbosch Universityen_ZA
dc.subjectDissertations -- Mathematical sciencesen_ZA
dc.subjectTheses -- Mathematical sciencesen_ZA
dc.subjectTorsion theory (Algebra)en_ZA
dc.subjectCurves, Ellipticsen_ZA
dc.titleTorsion points on elliptic curvesen_ZA
dc.typeThesisen_ZA
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