Artículo
D'Andrea, C.; Hong, H.; Krick, T.; Szanto, A. "Sylvester's double sums: The general case" (2009) Journal of Symbolic Computation. 44(9):1164-1175
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Abstract:
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. A question naturally arises: What are the other members of the family? This paper provides a complete answer to this question. The technique that we developed to answer the question turns out to be general enough to characterize all members of the family, providing a uniform method. © 2009 Elsevier Ltd. All rights reserved.
Registro:
| Documento: | Artículo |
| Título: | Sylvester's double sums: The general case |
| Autor: | D'Andrea, C.; Hong, H.; Krick, T.; Szanto, A. |
| Filiación: | Department d'Àlgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Via de les Corts Catalanes, 585, Gran, 08007, Spain Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina CONICET, Argentina |
| Palabras clave: | Double sums; Subresultants; Vandermonde determinants |
| Año: | 2009 |
| Volumen: | 44 |
| Número: | 9 |
| Página de inicio: | 1164 |
| Página de fin: | 1175 |
| DOI: | http://dx.doi.org/10.1016/j.jsc.2008.02.011 |
| Título revista: | Journal of Symbolic Computation |
| Título revista abreviado: | J. Symb. Comput. |
| ISSN: | 07477171 |
| PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_07477171_v44_n9_p1164_DAndrea.pdf |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v44_n9_p1164_DAndrea |
Referencias:
- Apéry, F., Jouanolou, J.-P., (2006) Résultant et sous-résultant: le cas d'une variable avec exercices corrigés, , Hermann, Paris 477 p
- Borchardt, C.W., Uber eine Interpolationsformel für eine Art symmetrischer Funktionen und über deren Anwendung (1860) Math. Abh. Akad. Wiss. zu Berlin, pp. 1-20
- Borchardt, C.W., Zur Theorie der Elimination und Kettenbruchentwicklung (1878) Math. Abh. Akad. Wiss. zu Berlin, pp. 1-17
- D'Andrea, C., Hong, H., Krick, T., Szanto, A., An elementary proof of Sylvester's double sums for subresultants (2007) J. Symbolic Comput., 42 (3), pp. 290-297
- Lascoux, A., Pragacz, P., Double Sylvester sums for subresultants and multi-Schur functions (2003) J. Symbolic Comput., 35 (6), pp. 689-710
- Sylvester, J.J., 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 (1853) Philos. Trans. Roy. Soc. London Part III, pp. 407-548. , Appears also in Collected Mathematical Papers of James Joseph Sylvester, vol. 1, Chelsea Publishing Co., 1973, pp. 429-586
- Sylvester, J.J., On a generalization of the Lagrangian theorem of interpolation (1858) Phil. Mag., , Appears also in Collected Mathematical Papers of James Joseph Sylvester, vol. 1, Chelsea Publishing Co., 1973, pp. 645-646
Citas:
---------- APA ----------
D'Andrea, C., Hong, H., Krick, T. & Szanto, A. (2009) . Sylvester's double sums: The general case. Journal of Symbolic Computation, 44(9), 1164-1175.http://dx.doi.org/10.1016/j.jsc.2008.02.011
---------- CHICAGO ----------
D'Andrea, C., Hong, H., Krick, T., Szanto, A. "Sylvester's double sums: The general case" . Journal of Symbolic Computation 44, no. 9 (2009) : 1164-1175.http://dx.doi.org/10.1016/j.jsc.2008.02.011
---------- MLA ----------
D'Andrea, C., Hong, H., Krick, T., Szanto, A. "Sylvester's double sums: The general case" . Journal of Symbolic Computation, vol. 44, no. 9, 2009, pp. 1164-1175.http://dx.doi.org/10.1016/j.jsc.2008.02.011
---------- VANCOUVER ----------
D'Andrea, C., Hong, H., Krick, T., Szanto, A. Sylvester's double sums: The general case. J. Symb. Comput. 2009;44(9):1164-1175.http://dx.doi.org/10.1016/j.jsc.2008.02.011
