Semialgebraic sets and real binary forms decompositions

The Waring Problem over polynomial rings asks how to decompose a homogeneous polynomial p of degree d as a linear combination of d-th powers of linear forms. In this work we give an algorithm to obtain a real Waring decomposition of any given real binary form p of length at most its degree. In fact,...

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Detalles Bibliográficos
Autores: Ansola Fernández-Enríquez, María Macarena, Díaz-Cano Ocaña, Antonio, Zurro, María Ángeles
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/8046
Acceso en línea:https://hdl.handle.net/20.500.14352/8046
Access Level:acceso abierto
Palabra clave:512.622
512.7
Real binary forms
Waring decompositions
Semialgebraic sets
Álgebra
Geometria algebraica
1201 Álgebra
1201.01 Geometría Algebraica
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spelling Semialgebraic sets and real binary forms decompositionsAnsola Fernández-Enríquez, María MacarenaDíaz-Cano Ocaña, AntonioZurro, María Ángeles512.622512.7Real binary formsWaring decompositionsSemialgebraic setsÁlgebraGeometria algebraica1201 Álgebra1201.01 Geometría AlgebraicaThe Waring Problem over polynomial rings asks how to decompose a homogeneous polynomial p of degree d as a linear combination of d-th powers of linear forms. In this work we give an algorithm to obtain a real Waring decomposition of any given real binary form p of length at most its degree. In fact, we construct a semialgebraic family of Waring decompositions for p. We illustrate our results with some examples.ElsevierUniversidad Complutense de Madrid20212021-01-0120212021-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/8046reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/80462026-06-02T12:44:21Z
dc.title.none.fl_str_mv Semialgebraic sets and real binary forms decompositions
title Semialgebraic sets and real binary forms decompositions
spellingShingle Semialgebraic sets and real binary forms decompositions
Ansola Fernández-Enríquez, María Macarena
512.622
512.7
Real binary forms
Waring decompositions
Semialgebraic sets
Álgebra
Geometria algebraica
1201 Álgebra
1201.01 Geometría Algebraica
title_short Semialgebraic sets and real binary forms decompositions
title_full Semialgebraic sets and real binary forms decompositions
title_fullStr Semialgebraic sets and real binary forms decompositions
title_full_unstemmed Semialgebraic sets and real binary forms decompositions
title_sort Semialgebraic sets and real binary forms decompositions
dc.creator.none.fl_str_mv Ansola Fernández-Enríquez, María Macarena
Díaz-Cano Ocaña, Antonio
Zurro, María Ángeles
author Ansola Fernández-Enríquez, María Macarena
author_facet Ansola Fernández-Enríquez, María Macarena
Díaz-Cano Ocaña, Antonio
Zurro, María Ángeles
author_role author
author2 Díaz-Cano Ocaña, Antonio
Zurro, María Ángeles
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 512.622
512.7
Real binary forms
Waring decompositions
Semialgebraic sets
Álgebra
Geometria algebraica
1201 Álgebra
1201.01 Geometría Algebraica
topic 512.622
512.7
Real binary forms
Waring decompositions
Semialgebraic sets
Álgebra
Geometria algebraica
1201 Álgebra
1201.01 Geometría Algebraica
description The Waring Problem over polynomial rings asks how to decompose a homogeneous polynomial p of degree d as a linear combination of d-th powers of linear forms. In this work we give an algorithm to obtain a real Waring decomposition of any given real binary form p of length at most its degree. In fact, we construct a semialgebraic family of Waring decompositions for p. We illustrate our results with some examples.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-01-01
2021
2021-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/8046
url https://hdl.handle.net/20.500.14352/8046
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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