Symmetric interpolation, Exchange Lemma and Sylvester sums
The theory of symmetric multivariate Lagrange interpolation is a beautiful but rather unknown tool that has many applications. Here we derive from it an Exchange Lemma that allows to explain in a simple and natural way the full description of the double sum expressions introduced by Sylvester in 185...
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| Otros Autores: | , |
| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
Taylor and Francis Inc.
2017
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| Sumario: | The theory of symmetric multivariate Lagrange interpolation is a beautiful but rather unknown tool that has many applications. Here we derive from it an Exchange Lemma that allows to explain in a simple and natural way the full description of the double sum expressions introduced by Sylvester in 1853 in terms of subresultants and their Bézout coefficients. © 2017 Taylor & Francis. |
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| Bibliografía: | Chen, W.Y.C., Louck, J.D., Interpolation for symmetric functions (1996) Adv. Math., 117, pp. 147-156 D’Andrea, C., Hong, H., Krick, T., Szanto, A., An elementary proof of Sylvester’s double sums for subresultants (2007) J. Symb. Comput., 42, pp. 290-297 D’Andrea, C., Hong, H., Krick, T., Szanto, A., Sylvester’s double sums: the general case (2009) J. Symb. Comput., 44, pp. 1164-1175 D’Andrea, C., Krick, T., Szanto, A., Subresultants, Sylvester sums and the rational interpolation problem (2015) J. Symb. Comput., 68, pp. 72-83 Krick, T., Szanto, A., Sylvester’s double sums: An inductive proof of the general case (2012) J. Symb. Comput., 47, pp. 942-953 Lascoux, A., (2003) Symmetric Functions and Combinatorial Operators on Polynomials, , CBMS Regional Conference Series in Mathematics, Vol. 99, Providence, RI: American Mathematical Society (Published for the Conference Board of the Mathematical Sciences, Washington, DC) Notes on Interpolation in one and several variables, , http://igm.univ-mlv.fr/ãl/ARTICLES/interp.dvi.gz, Lascoux, A. Accessed on 13 June 2003 Lascoux, A., Pragacz, P., Double Sylvester sums for subresultants and multi-Schur functions (2003) J. Symb. Comput., 35, pp. 689-710 Roy, M.-F., Szpirglas, A., Sylvester double sums and subresultants (2011) J. Symb. Comput., 46, pp. 385-395 Sylvester, J.J., (1853), On a theory of syzygetic relations of two rational integral functions, comprising an application to the theory of Sturm’s function and that of the greatest algebraical common measure. Phi. Trans. R. Soc. Lond. 1 January 1853, vol. 407–548 (appears also in Collected Mathematical Papers of James Joseph Sylvester, Vol. 1, Chelsea Publishing Co., 1973, pp. 429–586) |
| ISSN: | 00927872 |
| DOI: | 10.1080/00927872.2016.1236121 |