Sparse resultants and straight-line programs

Autores
Jeronimo, Gabriela Tali; Sabia, Juan Vicente Rafael
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove that the sparse resultant, redefined by D'Andrea and Sombra and by Esterov as a power of the classical sparse resultant, can be evaluated in a number of steps which is polynomial in its degree, its number of variables and the size of the exponents of the monomials in the Laurent polynomials involved in its definition. Moreover, we design a probabilistic algorithm of this order of complexity to compute a straight-line program that evaluates it within this number of steps.
Fil: Jeronimo, Gabriela Tali. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Sabia, Juan Vicente Rafael. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
ALGORITHMS
SPARSE RESULTANTS
STRAIGHT-LINE PROGRAMS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/89011
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/89011
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Sparse resultants and straight-line programsJeronimo, Gabriela TaliSabia, Juan Vicente RafaelALGORITHMSSPARSE RESULTANTSSTRAIGHT-LINE PROGRAMShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove that the sparse resultant, redefined by D'Andrea and Sombra and by Esterov as a power of the classical sparse resultant, can be evaluated in a number of steps which is polynomial in its degree, its number of variables and the size of the exponents of the monomials in the Laurent polynomials involved in its definition. Moreover, we design a probabilistic algorithm of this order of complexity to compute a straight-line program that evaluates it within this number of steps.Fil: Jeronimo, Gabriela Tali. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Sabia, Juan Vicente Rafael. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaAcademic Press Ltd - Elsevier Science Ltd2018-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/89011Jeronimo, Gabriela Tali; Sabia, Juan Vicente Rafael; Sparse resultants and straight-line programs; Academic Press Ltd - Elsevier Science Ltd; Journal Of Symbolic Computation; 87; 7-2018; 14-270747-7171CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0747717117300561info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsc.2017.05.005info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:14:54Zoai:ri.conicet.gov.ar:11336/89011instacron: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:34982025-09-29 10:14:54.459CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Sparse resultants and straight-line programs
title Sparse resultants and straight-line programs
spellingShingle Sparse resultants and straight-line programs
Jeronimo, Gabriela Tali
ALGORITHMS
SPARSE RESULTANTS
STRAIGHT-LINE PROGRAMS
title_short Sparse resultants and straight-line programs
title_full Sparse resultants and straight-line programs
title_fullStr Sparse resultants and straight-line programs
title_full_unstemmed Sparse resultants and straight-line programs
title_sort Sparse resultants and straight-line programs
dc.creator.none.fl_str_mv Jeronimo, Gabriela Tali
Sabia, Juan Vicente Rafael
author Jeronimo, Gabriela Tali
author_facet Jeronimo, Gabriela Tali
Sabia, Juan Vicente Rafael
author_role author
author2 Sabia, Juan Vicente Rafael
author2_role author
dc.subject.none.fl_str_mv ALGORITHMS
SPARSE RESULTANTS
STRAIGHT-LINE PROGRAMS
topic ALGORITHMS
SPARSE RESULTANTS
STRAIGHT-LINE PROGRAMS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We prove that the sparse resultant, redefined by D'Andrea and Sombra and by Esterov as a power of the classical sparse resultant, can be evaluated in a number of steps which is polynomial in its degree, its number of variables and the size of the exponents of the monomials in the Laurent polynomials involved in its definition. Moreover, we design a probabilistic algorithm of this order of complexity to compute a straight-line program that evaluates it within this number of steps.
Fil: Jeronimo, Gabriela Tali. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Sabia, Juan Vicente Rafael. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description We prove that the sparse resultant, redefined by D'Andrea and Sombra and by Esterov as a power of the classical sparse resultant, can be evaluated in a number of steps which is polynomial in its degree, its number of variables and the size of the exponents of the monomials in the Laurent polynomials involved in its definition. Moreover, we design a probabilistic algorithm of this order of complexity to compute a straight-line program that evaluates it within this number of steps.
publishDate 2018
dc.date.none.fl_str_mv 2018-07
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/11336/89011
Jeronimo, Gabriela Tali; Sabia, Juan Vicente Rafael; Sparse resultants and straight-line programs; Academic Press Ltd - Elsevier Science Ltd; Journal Of Symbolic Computation; 87; 7-2018; 14-27
0747-7171
CONICET Digital
CONICET
url http://hdl.handle.net/11336/89011
identifier_str_mv Jeronimo, Gabriela Tali; Sabia, Juan Vicente Rafael; Sparse resultants and straight-line programs; Academic Press Ltd - Elsevier Science Ltd; Journal Of Symbolic Computation; 87; 7-2018; 14-27
0747-7171
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0747717117300561
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsc.2017.05.005
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Ltd - Elsevier Science Ltd
publisher.none.fl_str_mv Academic Press Ltd - Elsevier Science Ltd
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
_version_ 1844614080635076608
score 13.070432

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