Homotopy gets real
This thesis presents the development of a new module for the Julia programming language, designed to decompose the real part of complex curves within the field of computational algebraic geometry. The work leverages homotopic approaches to bridge gaps in existing tools. The core objective is to impl...
- Autores:
-
González Cabrera, Juan Camilo
- Tipo de recurso:
- Trabajo de grado de pregrado
- Fecha de publicación:
- 2024
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/75053
- Acceso en línea:
- https://hdl.handle.net/1992/75053
- Palabra clave:
- Julia
Homotopy methods
Programming language
Computational algebraic geometry
Ingeniería
- Rights
- openAccess
- License
- Attribution-NonCommercial-ShareAlike 4.0 International
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Homotopy gets real |
| title |
Homotopy gets real |
| spellingShingle |
Homotopy gets real Julia Homotopy methods Programming language Computational algebraic geometry Ingeniería |
| title_short |
Homotopy gets real |
| title_full |
Homotopy gets real |
| title_fullStr |
Homotopy gets real |
| title_full_unstemmed |
Homotopy gets real |
| title_sort |
Homotopy gets real |
| dc.creator.fl_str_mv |
González Cabrera, Juan Camilo |
| dc.contributor.advisor.none.fl_str_mv |
Cardozo Álvarez, Nicolás Barrero Rosero, Daniel Ricardo |
| dc.contributor.author.none.fl_str_mv |
González Cabrera, Juan Camilo |
| dc.subject.keyword.none.fl_str_mv |
Julia Homotopy methods Programming language Computational algebraic geometry |
| topic |
Julia Homotopy methods Programming language Computational algebraic geometry Ingeniería |
| dc.subject.themes.spa.fl_str_mv |
Ingeniería |
| description |
This thesis presents the development of a new module for the Julia programming language, designed to decompose the real part of complex curves within the field of computational algebraic geometry. The work leverages homotopic approaches to bridge gaps in existing tools. The core objective is to implement a Julia package inspired by BertiniReal, aiming to efficiently handle the decomposition of algebraic sets into their real components. Julia’s robust features and growing prominence in scientific computing motivate the choice of the language. The thesis details the foundational concepts, the implementation of the new module, and its validation through comparative analysis, demonstrating the reliability and utility. |
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2024 |
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2024-08-09T16:44:46Z |
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2024-08-09T16:44:46Z |
| dc.date.issued.none.fl_str_mv |
2024-06-11 |
| dc.type.none.fl_str_mv |
Trabajo de grado - Pregrado |
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info:eu-repo/semantics/bachelorThesis |
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https://hdl.handle.net/1992/75053 |
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reponame:Repositorio Institucional Séneca |
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instname:Universidad de los Andes reponame:Repositorio Institucional Séneca repourl:https://repositorio.uniandes.edu.co/ |
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eng |
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eng |
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Silviana Amethyst, Daniel J. Bates, Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler, Bertini real: Numerical decomposition of real algebraic curves and surfaces. Silviana Amethyst, Daniel J. Bates, Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler, Bertinireal: Software for numerical decomposition of real algebraic sets, 2024, Accessed: fecha de acceso. Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler, Bertini: Software for numerical algebraic geometry, 2023, Version actualizada. G.E. Bredon, Topology and geometry, Graduate texts in mathematics, Springer Verlag, 1993. Paul Breiding and Sascha Timme, Homotopycontinuation.jl, Julia Package, 2024. |
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Attribution-NonCommercial-ShareAlike 4.0 International |
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http://creativecommons.org/licenses/by-nc-sa/4.0/ |
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openAccess |
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40 páginas |
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application/pdf |
| dc.publisher.none.fl_str_mv |
Universidad de los Andes |
| dc.publisher.program.none.fl_str_mv |
Ingeniería de Sistemas y Computación |
| dc.publisher.faculty.none.fl_str_mv |
Facultad de Ingeniería |
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Departamento de Ingeniería de Sistemas y Computación |
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Universidad de los Andes |
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Universidad de los Andes |
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Cardozo Álvarez, Nicolásvirtual::18150-1Barrero Rosero, Daniel RicardoGonzález Cabrera, Juan Camilo2024-08-09T16:44:46Z2024-08-09T16:44:46Z2024-06-11https://hdl.handle.net/1992/75053instname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/This thesis presents the development of a new module for the Julia programming language, designed to decompose the real part of complex curves within the field of computational algebraic geometry. The work leverages homotopic approaches to bridge gaps in existing tools. The core objective is to implement a Julia package inspired by BertiniReal, aiming to efficiently handle the decomposition of algebraic sets into their real components. Julia’s robust features and growing prominence in scientific computing motivate the choice of the language. The thesis details the foundational concepts, the implementation of the new module, and its validation through comparative analysis, demonstrating the reliability and utility.Pregrado40 páginasapplication/pdfengUniversidad de los AndesIngeniería de Sistemas y ComputaciónFacultad de IngenieríaDepartamento de Ingeniería de Sistemas y ComputaciónAttribution-NonCommercial-ShareAlike 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Homotopy gets realTrabajo de grado - Pregradoinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_7a1fTexthttp://purl.org/redcol/resource_type/TPJuliaHomotopy methodsProgramming languageComputational algebraic geometryIngenieríaSilviana Amethyst, Daniel J. Bates, Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler, Bertini real: Numerical decomposition of real algebraic curves and surfaces.Silviana Amethyst, Daniel J. Bates, Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler, Bertinireal: Software for numerical decomposition of real algebraic sets, 2024, Accessed: fecha de acceso.Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler, Bertini: Software for numerical algebraic geometry, 2023, Version actualizada.G.E. Bredon, Topology and geometry, Graduate texts in mathematics, Springer Verlag, 1993.Paul Breiding and Sascha Timme, Homotopycontinuation.jl, Julia Package, 2024.201911030Publicationhttps://scholar.google.es/citations?user=3iTzjQsAAAAJvirtual::18150-10000-0002-1094-9952virtual::18150-1a77ff528-fc33-44d6-9022-814f81ef407avirtual::18150-1a77ff528-fc33-44d6-9022-814f81ef407avirtual::18150-1CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-81031https://repositorio.uniandes.edu.co/bitstreams/f7507026-2f0d-4390-8e20-81cd275632ac/download934f4ca17e109e0a05eaeaba504d7ce4MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-82535https://repositorio.uniandes.edu.co/bitstreams/9eec017b-a2b5-42b3-8e8e-c68e4dabc841/downloadae9e573a68e7f92501b6913cc846c39fMD52ORIGINALHomotopy gets real.pdfHomotopy gets real.pdfapplication/pdf1655740https://repositorio.uniandes.edu.co/bitstreams/41c7a14d-c8f1-428a-9995-c2d1c6c4a51f/download37a73619799e587e1f8c14c4b9b1cef6MD52autorizacion tesis 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