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Torsion points on elliptic curves
Thesis (MSc)--Stellenbosch University, 2013.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2013
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| _version_ | 1867613923746775040 |
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| access_status_str | Open Access |
| author | Nyirenda, Darlison |
| author2 | Keet, Arnold P. |
| author_browse | Keet, Arnold P. Nyirenda, Darlison |
| author_facet | Keet, Arnold P. Nyirenda, Darlison |
| author_sort | Nyirenda, Darlison |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MSc)--Stellenbosch University, 2013. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/80120 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:43:51.865Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2013 |
| publishDateRange | 2013 |
| publishDateSort | 2013 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/80120 Torsion points on elliptic curves Nyirenda, Darlison Keet, Arnold P. Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Dissertations -- Mathematical sciences Theses -- Mathematical sciences Torsion theory (Algebra) Curves, Elliptics Thesis (MSc)--Stellenbosch University, 2013. ENGLISH 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. AFRIKAANSE 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. 2013-02-25T11:00:37Z 2013-03-15T07:36:10Z 2013-02-25T11:00:37Z 2013-03-15T07:36:10Z 2013-03 Thesis http://hdl.handle.net/10019.1/80120 en_ZA Stellenbosch University 103 p. application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Dissertations -- Mathematical sciences Theses -- Mathematical sciences Torsion theory (Algebra) Curves, Elliptics Nyirenda, Darlison Torsion points on elliptic curves |
| title | Torsion points on elliptic curves |
| title_full | Torsion points on elliptic curves |
| title_fullStr | Torsion points on elliptic curves |
| title_full_unstemmed | Torsion points on elliptic curves |
| title_short | Torsion points on elliptic curves |
| title_sort | torsion points on elliptic curves |
| topic | Dissertations -- Mathematical sciences Theses -- Mathematical sciences Torsion theory (Algebra) Curves, Elliptics |
| url | http://hdl.handle.net/10019.1/80120 |
| work_keys_str_mv | AT nyirendadarlison torsionpointsonellipticcurves |