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Studies on factoring polynomials over global fields
Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2007.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : University of Stellenbosch
2008
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| _version_ | 1867613879385718784 |
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| access_status_str | Open Access |
| author | Benzaoui, Ilhem |
| author2 | Green, Barry |
| author_browse | Benzaoui, Ilhem Green, Barry |
| author_facet | Green, Barry Benzaoui, Ilhem |
| author_sort | Benzaoui, Ilhem |
| collection | Thesis |
| dc_rights_str_mv | University of Stellenbosch |
| description | Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2007. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/2696 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:43:09.148Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2008 |
| publishDateRange | 2008 |
| publishDateSort | 2008 |
| publisher | Stellenbosch : University of Stellenbosch |
| publisherStr | Stellenbosch : University of Stellenbosch |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/2696 Studies on factoring polynomials over global fields Benzaoui, Ilhem Green, Barry University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. Dissertations -- Mathematics Theses -- Mathematics Polynomials Factorization (Mathematics) Mathematical Sciences Mathematics Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2007. In this thesis, we surveyed the most important methods for factorization of polynomials over a global field, focusing on their strengths and showing their most striking disadvantages. The algorithms we have selected are all modular algorithms. They rely on the Hensel factorization technique, which can be applied to all global fields giving an output in a local field that can be computed to a large enough precision. The crucial phase of the reconstruction of the irreducible global factors from the local ones, determines the difference between these algorithms. For different fields and cases, different techniques have been used such as residue class computations, ideal calculus, lattice techniques. The tendency to combine ideas from different methods has been of interest as it improves the running time. This appears for instance in the latest method due to van Hoeij, concerning the factorization over a number field. The ideas here can be used over a global function field in the form given by Belabas et al. using the logarithmic derivative instead of Newton sums. Complexity analysis was not our objective, nevertheless it was important to mention certain results as part of the properties of these algorithms. 2008-02-04T09:16:21Z 2010-06-01T08:55:53Z 2008-02-04T09:16:21Z 2010-06-01T08:55:53Z 2007-12 Thesis http://hdl.handle.net/10019.1/2696 en University of Stellenbosch 682166 bytes application/pdf application/pdf Stellenbosch : University of Stellenbosch |
| spellingShingle | Dissertations -- Mathematics Theses -- Mathematics Polynomials Factorization (Mathematics) Mathematical Sciences Mathematics Benzaoui, Ilhem Studies on factoring polynomials over global fields |
| title | Studies on factoring polynomials over global fields |
| title_full | Studies on factoring polynomials over global fields |
| title_fullStr | Studies on factoring polynomials over global fields |
| title_full_unstemmed | Studies on factoring polynomials over global fields |
| title_short | Studies on factoring polynomials over global fields |
| title_sort | studies on factoring polynomials over global fields |
| topic | Dissertations -- Mathematics Theses -- Mathematics Polynomials Factorization (Mathematics) Mathematical Sciences Mathematics |
| url | http://hdl.handle.net/10019.1/2696 |
| work_keys_str_mv | AT benzaouiilhem studiesonfactoringpolynomialsoverglobalfields |