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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| Autores principales: | , |
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| Formato: | Artículo publishedVersion |
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2012
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| 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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| Sumario: | 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. |
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