Dissertation/ Thesis
On the Extended Hensel Construction and its Application to the Computation of Real Limit Points
| Title: | On the Extended Hensel Construction and its Application to the Computation of Real Limit Points |
|---|---|
| Authors: | Ataei Jaliseh, Masoud |
| Contributors: | Marc Moreno Maza |
| Publication Year: | 2025 |
| Collection: | The University of Western Ontario: Scholarship@Western |
| Subject Terms: | Computer Algebra, Extended Hensel Construction, Limit of a multivariate rational function |
| Description: | The thesis cover page in the PDF document includes references to Western University’s previous institutional repository platform, known as Scholarship@Western, and links to that platform (beginning with ir.lib.uwo.ca). In citing or referring to this thesis, use the DOI or handle from this page instead. Sample citation: Author name, "Thesis title." (Year). Western University Open Repository. https://doi.org/10.71858/123456. ; The Extended Hensel Construction (EHC) is a procedure which, for an input bivariate polyno- mial with complex coefficients, can serve the same purpose as the Newton-Puiseux algorithm. We show that the EHC requires only linear algebra and univariate polynomial arithmetic. We deduce complexity estimates and report on a software implementation together with experimental results. This work is motivated and illustrated by two applications. The first one is the computation of real branches of space curves. The second one is the computation of limits of real multivariate rational function. For the latter, we present an algorithm for determining the existence of the limit of a real multivariate rational function q at a given point p which is an isolated zero of the denominator of q. When the limit exists, the algorithm computes it, without making any assumptions on the number of variables. |
| Document Type: | thesis |
| File Description: | application/pdf |
| Language: | English |
| Relation: | https://hdl.handle.net/20.500.14721/27848 |
| Availability: | https://hdl.handle.net/20.500.14721/27848 |
| Accession Number: | edsbas.7FAA55B2 |
| Database: | BASE |
| FullText | Text: Availability: 0 CustomLinks: – Url: https://hdl.handle.net/20.500.14721/27848# Name: EDS - BASE (ns324271) Category: fullText Text: View record from BASE |
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| RecordInfo | BibRecord: BibEntity: Languages: – Text: English Subjects: – SubjectFull: Computer Algebra Type: general – SubjectFull: Extended Hensel Construction Type: general – SubjectFull: Limit of a multivariate rational function Type: general Titles: – TitleFull: On the Extended Hensel Construction and its Application to the Computation of Real Limit Points Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Ataei Jaliseh, Masoud – PersonEntity: Name: NameFull: Marc Moreno Maza IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2025 Identifiers: – Type: issn-locals Value: edsbas |
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