Sylvester's double sums: An inductive proof of the general case

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In 1853, Sylvester introduced a family of double sum expressions for two finite sets of indeterminates and showed that some members of the family are essentially the polynomial subresultants of the monic polynomials associated with these sets. In 2009, in a joint work with C. D'Andrea and H. Ho...

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Autores principales: Krick, T., Szanto, A.
Formato: Artículo publishedVersion
Publicado: 2012
Materias:
Subresultants
Sylvester's double sums
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_07477171_v47_n8_p942_Krick
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_07477171_v47_n8_p942_Krick_oai
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Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires
id I28-R145-paper_07477171_v47_n8_p942_Krick_oai
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spelling I28-R145-paper_07477171_v47_n8_p942_Krick_oai2024-08-16 Krick, T. Szanto, A. 2012 In 1853, Sylvester introduced a family of double sum expressions for two finite sets of indeterminates and showed that some members of the family are essentially the polynomial subresultants of the monic polynomials associated with these sets. In 2009, in a joint work with C. D'Andrea and H. Hong we gave the complete description of all the members of the family as expressions in the coefficients of these polynomials. More recently, M.-F. Roy and A.Szpirglas presented a new and natural inductive proof for the cases considered by Sylvester. Here we show how induction also allows to obtain the full description of Sylvester's double-sums. © 2012 Elsevier Ltd. Fil:Krick, T. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. application/pdf http://hdl.handle.net/20.500.12110/paper_07477171_v47_n8_p942_Krick info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar J. Symb. Comput. 2012;47(8):942-953 Subresultants Sylvester's double sums Sylvester's double sums: An inductive proof of the general case info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_07477171_v47_n8_p942_Krick_oai
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-145
collection Repositorio Digital de la Universidad de Buenos Aires (UBA)
topic Subresultants
Sylvester's double sums
spellingShingle Subresultants
Sylvester's double sums
Krick, T.
Szanto, A.
Sylvester's double sums: An inductive proof of the general case
topic_facet Subresultants
Sylvester's double sums
description In 1853, Sylvester introduced a family of double sum expressions for two finite sets of indeterminates and showed that some members of the family are essentially the polynomial subresultants of the monic polynomials associated with these sets. In 2009, in a joint work with C. D'Andrea and H. Hong we gave the complete description of all the members of the family as expressions in the coefficients of these polynomials. More recently, M.-F. Roy and A.Szpirglas presented a new and natural inductive proof for the cases considered by Sylvester. Here we show how induction also allows to obtain the full description of Sylvester's double-sums. © 2012 Elsevier Ltd.
format Artículo
Artículo
publishedVersion
author Krick, T.
Szanto, A.
author_facet Krick, T.
Szanto, A.
author_sort Krick, T.
title Sylvester's double sums: An inductive proof of the general case
title_short Sylvester's double sums: An inductive proof of the general case
title_full Sylvester's double sums: An inductive proof of the general case
title_fullStr Sylvester's double sums: An inductive proof of the general case
title_full_unstemmed Sylvester's double sums: An inductive proof of the general case
title_sort sylvester's double sums: an inductive proof of the general case
publishDate 2012
url http://hdl.handle.net/20.500.12110/paper_07477171_v47_n8_p942_Krick
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_07477171_v47_n8_p942_Krick_oai
work_keys_str_mv AT krickt sylvestersdoublesumsaninductiveproofofthegeneralcase
AT szantoa sylvestersdoublesumsaninductiveproofofthegeneralcase
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