The Canny–Emiris Conjecture for the Sparse Resultant
- Autores
- D'Andrea, Carlos; Jeronimo, Gabriela Tali; Sombra, Martín
- Año de publicación
- 2022
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We present a product formula for the initial parts of the sparse resultant associated with an arbitrary family of supports, generalizing a previous result by Sturmfels. This allows to compute the homogeneities and degrees of this sparse resultant, and its evaluation at systems of Laurent polynomials with smaller supports. We obtain an analogous product formula for some of the initial parts of the principal minors of the Sylvester-type square matrix associated with a mixed subdivision of a polytope. Applying these results, we prove that under suitable hypothesis, the sparse resultant can be computed as the quotient of the determinant of such a square matrix by one of its principal minors. This generalizes the classical Macaulay formula for the homogeneous resultant and confirms a conjecture of Canny and Emiris.
Fil: D'Andrea, Carlos. Centre de Recerca Matemàtica; España. Universidad de Barcelona; España
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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Sombra, Martín. Centre de Recerca Matemàtica; España. Institució Catalana de Recerca I Estudis Avançats; España. Universidad de Barcelona; España - Materia
-
INITIAL PART
MACAULAY FORMULA
MIXED SUBDIVISION
SPARSE RESULTANT - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/213781
Ver los metadatos del registro completo
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The Canny–Emiris Conjecture for the Sparse ResultantD'Andrea, CarlosJeronimo, Gabriela TaliSombra, MartínINITIAL PARTMACAULAY FORMULAMIXED SUBDIVISIONSPARSE RESULTANThttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We present a product formula for the initial parts of the sparse resultant associated with an arbitrary family of supports, generalizing a previous result by Sturmfels. This allows to compute the homogeneities and degrees of this sparse resultant, and its evaluation at systems of Laurent polynomials with smaller supports. We obtain an analogous product formula for some of the initial parts of the principal minors of the Sylvester-type square matrix associated with a mixed subdivision of a polytope. Applying these results, we prove that under suitable hypothesis, the sparse resultant can be computed as the quotient of the determinant of such a square matrix by one of its principal minors. This generalizes the classical Macaulay formula for the homogeneous resultant and confirms a conjecture of Canny and Emiris.Fil: D'Andrea, Carlos. Centre de Recerca Matemàtica; España. Universidad de Barcelona; EspañaFil: 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Sombra, Martín. Centre de Recerca Matemàtica; España. Institució Catalana de Recerca I Estudis Avançats; España. Universidad de Barcelona; EspañaSpringer2022-03info: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/11336/213781D'Andrea, Carlos; Jeronimo, Gabriela Tali; Sombra, Martín; The Canny–Emiris Conjecture for the Sparse Resultant; Springer; Foundations Of Computational Mathematics; 23; 3; 3-2022; 741-8011615-3375CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10208-021-09547-3info:eu-repo/semantics/altIdentifier/doi/10.1007/s10208-021-09547-3info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:34:54Zoai:ri.conicet.gov.ar:11336/213781instacron: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 10:34:54.39CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
The Canny–Emiris Conjecture for the Sparse Resultant |
title |
The Canny–Emiris Conjecture for the Sparse Resultant |
spellingShingle |
The Canny–Emiris Conjecture for the Sparse Resultant D'Andrea, Carlos INITIAL PART MACAULAY FORMULA MIXED SUBDIVISION SPARSE RESULTANT |
title_short |
The Canny–Emiris Conjecture for the Sparse Resultant |
title_full |
The Canny–Emiris Conjecture for the Sparse Resultant |
title_fullStr |
The Canny–Emiris Conjecture for the Sparse Resultant |
title_full_unstemmed |
The Canny–Emiris Conjecture for the Sparse Resultant |
title_sort |
The Canny–Emiris Conjecture for the Sparse Resultant |
dc.creator.none.fl_str_mv |
D'Andrea, Carlos Jeronimo, Gabriela Tali Sombra, Martín |
author |
D'Andrea, Carlos |
author_facet |
D'Andrea, Carlos Jeronimo, Gabriela Tali Sombra, Martín |
author_role |
author |
author2 |
Jeronimo, Gabriela Tali Sombra, Martín |
author2_role |
author author |
dc.subject.none.fl_str_mv |
INITIAL PART MACAULAY FORMULA MIXED SUBDIVISION SPARSE RESULTANT |
topic |
INITIAL PART MACAULAY FORMULA MIXED SUBDIVISION SPARSE RESULTANT |
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 present a product formula for the initial parts of the sparse resultant associated with an arbitrary family of supports, generalizing a previous result by Sturmfels. This allows to compute the homogeneities and degrees of this sparse resultant, and its evaluation at systems of Laurent polynomials with smaller supports. We obtain an analogous product formula for some of the initial parts of the principal minors of the Sylvester-type square matrix associated with a mixed subdivision of a polytope. Applying these results, we prove that under suitable hypothesis, the sparse resultant can be computed as the quotient of the determinant of such a square matrix by one of its principal minors. This generalizes the classical Macaulay formula for the homogeneous resultant and confirms a conjecture of Canny and Emiris. Fil: D'Andrea, Carlos. Centre de Recerca Matemàtica; España. Universidad de Barcelona; España 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina Fil: Sombra, Martín. Centre de Recerca Matemàtica; España. Institució Catalana de Recerca I Estudis Avançats; España. Universidad de Barcelona; España |
description |
We present a product formula for the initial parts of the sparse resultant associated with an arbitrary family of supports, generalizing a previous result by Sturmfels. This allows to compute the homogeneities and degrees of this sparse resultant, and its evaluation at systems of Laurent polynomials with smaller supports. We obtain an analogous product formula for some of the initial parts of the principal minors of the Sylvester-type square matrix associated with a mixed subdivision of a polytope. Applying these results, we prove that under suitable hypothesis, the sparse resultant can be computed as the quotient of the determinant of such a square matrix by one of its principal minors. This generalizes the classical Macaulay formula for the homogeneous resultant and confirms a conjecture of Canny and Emiris. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-03 |
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/11336/213781 D'Andrea, Carlos; Jeronimo, Gabriela Tali; Sombra, Martín; The Canny–Emiris Conjecture for the Sparse Resultant; Springer; Foundations Of Computational Mathematics; 23; 3; 3-2022; 741-801 1615-3375 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/213781 |
identifier_str_mv |
D'Andrea, Carlos; Jeronimo, Gabriela Tali; Sombra, Martín; The Canny–Emiris Conjecture for the Sparse Resultant; Springer; Foundations Of Computational Mathematics; 23; 3; 3-2022; 741-801 1615-3375 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://link.springer.com/article/10.1007/s10208-021-09547-3 info:eu-repo/semantics/altIdentifier/doi/10.1007/s10208-021-09547-3 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by/2.5/ar/ |
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openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by/2.5/ar/ |
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application/pdf application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Springer |
publisher.none.fl_str_mv |
Springer |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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13.070432 |