Software Engineering and complexity in effective Algebraic Geometry

Autores
Heintz, Joos Ulrich; Kuijpers, Bart; Rojas Paredes, Andres Avelino
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
One may represent polynomials not only by their coefficients but also by arithmetic circuits which evaluate them. This idea allowed in the past fifteen years considerable complexity progress in effective polynomial equation solving. We present a circuit based computation model which captures all known symbolic elimination algorithms in effective Algebraic Geometry and exhibit a class of simple elimination problems which require exponential size circuits to be solved in this model. This implies that the known, circuit based elimination algorithms are already optimal.
Fil: Heintz, Joos Ulrich. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Universidad de Cantabria; España. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Kuijpers, Bart. Hasselt University; Bélgica
Fil: Rojas Paredes, Andres Avelino. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Robust Parameterized Arithmetic Circuit
Isoparametric Routine
Branching Parsimonious Algorithm
Flat Family of Zero Dimensional Elimination Problems
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/15847
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/15847
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Software Engineering and complexity in effective Algebraic GeometryHeintz, Joos UlrichKuijpers, BartRojas Paredes, Andres AvelinoRobust Parameterized Arithmetic CircuitIsoparametric RoutineBranching Parsimonious AlgorithmFlat Family of Zero Dimensional Elimination Problemshttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1One may represent polynomials not only by their coefficients but also by arithmetic circuits which evaluate them. This idea allowed in the past fifteen years considerable complexity progress in effective polynomial equation solving. We present a circuit based computation model which captures all known symbolic elimination algorithms in effective Algebraic Geometry and exhibit a class of simple elimination problems which require exponential size circuits to be solved in this model. This implies that the known, circuit based elimination algorithms are already optimal.Fil: Heintz, Joos Ulrich. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Universidad de Cantabria; España. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Kuijpers, Bart. Hasselt University; BélgicaFil: Rojas Paredes, Andres Avelino. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaElsevier Inc2013-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/15847Heintz, Joos Ulrich; Kuijpers, Bart; Rojas Paredes, Andres Avelino; Software Engineering and complexity in effective Algebraic Geometry; Elsevier Inc; Journal Of Complexity; 29; 1; 2-2013; 92-1380885-064Xenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jco.2012.04.005info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0885064X1200043Xinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:01:46Zoai:ri.conicet.gov.ar:11336/15847instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-10 13:01:46.978CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Software Engineering and complexity in effective Algebraic Geometry
title Software Engineering and complexity in effective Algebraic Geometry
spellingShingle Software Engineering and complexity in effective Algebraic Geometry
Heintz, Joos Ulrich
Robust Parameterized Arithmetic Circuit
Isoparametric Routine
Branching Parsimonious Algorithm
Flat Family of Zero Dimensional Elimination Problems
title_short Software Engineering and complexity in effective Algebraic Geometry
title_full Software Engineering and complexity in effective Algebraic Geometry
title_fullStr Software Engineering and complexity in effective Algebraic Geometry
title_full_unstemmed Software Engineering and complexity in effective Algebraic Geometry
title_sort Software Engineering and complexity in effective Algebraic Geometry
dc.creator.none.fl_str_mv Heintz, Joos Ulrich
Kuijpers, Bart
Rojas Paredes, Andres Avelino
author Heintz, Joos Ulrich
author_facet Heintz, Joos Ulrich
Kuijpers, Bart
Rojas Paredes, Andres Avelino
author_role author
author2 Kuijpers, Bart
Rojas Paredes, Andres Avelino
author2_role author
author
dc.subject.none.fl_str_mv Robust Parameterized Arithmetic Circuit
Isoparametric Routine
Branching Parsimonious Algorithm
Flat Family of Zero Dimensional Elimination Problems
topic Robust Parameterized Arithmetic Circuit
Isoparametric Routine
Branching Parsimonious Algorithm
Flat Family of Zero Dimensional Elimination Problems
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv One may represent polynomials not only by their coefficients but also by arithmetic circuits which evaluate them. This idea allowed in the past fifteen years considerable complexity progress in effective polynomial equation solving. We present a circuit based computation model which captures all known symbolic elimination algorithms in effective Algebraic Geometry and exhibit a class of simple elimination problems which require exponential size circuits to be solved in this model. This implies that the known, circuit based elimination algorithms are already optimal.
Fil: Heintz, Joos Ulrich. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Universidad de Cantabria; España. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Kuijpers, Bart. Hasselt University; Bélgica
Fil: Rojas Paredes, Andres Avelino. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description One may represent polynomials not only by their coefficients but also by arithmetic circuits which evaluate them. This idea allowed in the past fifteen years considerable complexity progress in effective polynomial equation solving. We present a circuit based computation model which captures all known symbolic elimination algorithms in effective Algebraic Geometry and exhibit a class of simple elimination problems which require exponential size circuits to be solved in this model. This implies that the known, circuit based elimination algorithms are already optimal.
publishDate 2013
dc.date.none.fl_str_mv 2013-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/15847
Heintz, Joos Ulrich; Kuijpers, Bart; Rojas Paredes, Andres Avelino; Software Engineering and complexity in effective Algebraic Geometry; Elsevier Inc; Journal Of Complexity; 29; 1; 2-2013; 92-138
0885-064X
url http://hdl.handle.net/11336/15847
identifier_str_mv Heintz, Joos Ulrich; Kuijpers, Bart; Rojas Paredes, Andres Avelino; Software Engineering and complexity in effective Algebraic Geometry; Elsevier Inc; Journal Of Complexity; 29; 1; 2-2013; 92-138
0885-064X
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jco.2012.04.005
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0885064X1200043X
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Inc
publisher.none.fl_str_mv Elsevier Inc
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.993085

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