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

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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Detalles Bibliográficos
Autor principal: Krick, Teresa Elena Genoveva
Publicado: 2012
Materias:
Subresultants
Sylvester's double sums
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v47_n8_p942_Krick
http://hdl.handle.net/20.500.12110/paper_07477171_v47_n8_p942_Krick
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_07477171_v47_n8_p942_Krick
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spelling paper:paper_07477171_v47_n8_p942_Krick2023-06-08T15:45:11Z Sylvester's double sums: An inductive proof of the general case Krick, Teresa Elena Genoveva Subresultants Sylvester's double sums 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. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v47_n8_p942_Krick http://hdl.handle.net/20.500.12110/paper_07477171_v47_n8_p942_Krick
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Subresultants
Sylvester's double sums
spellingShingle Subresultants
Sylvester's double sums
Krick, Teresa Elena Genoveva
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.
author Krick, Teresa Elena Genoveva
author_facet Krick, Teresa Elena Genoveva
author_sort Krick, Teresa Elena Genoveva
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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v47_n8_p942_Krick
http://hdl.handle.net/20.500.12110/paper_07477171_v47_n8_p942_Krick
work_keys_str_mv AT krickteresaelenagenoveva sylvestersdoublesumsaninductiveproofofthegeneralcase
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