Artículo
Krick, T.; Szanto, A. "Sylvester's double sums: An inductive proof of the general case" (2012) Journal of Symbolic Computation. 47(8):942-953
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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. 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.
Registro:
| Documento: | Artículo |
| Título: | Sylvester's double sums: An inductive proof of the general case |
| Autor: | Krick, T.; Szanto, A. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS, CONICET, 1428 Buenos Aires, Argentina Department of Mathematics, North Carolina State University, Raleigh NC 27695, United States |
| Palabras clave: | Subresultants; Sylvester's double sums |
| Año: | 2012 |
| Volumen: | 47 |
| Número: | 8 |
| Página de inicio: | 942 |
| Página de fin: | 953 |
| DOI: | http://dx.doi.org/10.1016/j.jsc.2012.01.003 |
| Título revista: | Journal of Symbolic Computation |
| Título revista abreviado: | J. Symb. Comput. |
| ISSN: | 07477171 |
| PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_07477171_v47_n8_p942_Krick.pdf |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v47_n8_p942_Krick |
Referencias:
- Apéry, F., Jouanolou, J.-P., Résultants et sous-résultants: le cas d'une variable (2005), Monographie, Cours DESS 1995-1996, 322 pages; Collins, G., Suresultants and reduced polynomial remainder sequences (1967) J. ACM, 142, pp. 128-142
- D'Andrea, C., Hong, H., Krick, T., Szanto, A., An elementary proof of Sylvester's double sums for subresultants (2007) J. Symbolic Comput., 42, pp. 290-297
- D'Andrea, C., Hong, H., Krick, T., Szanto, A., Sylvester's double sums: the general case (2009) J. Symbolic Comput., 44, pp. 1164-1175
- von zur Gathen, J., Gerhard, J., (2003) Modern Computer Algebra, , Cambridge University Press, Cambridge, UK, 800 pages
- Geddes, K., Czapor, S., Labahn, G., (1992) Algorithms for Computer Algebra, , Kluwer Academic Publishers, 585 pages
- Ilyuta, G.G., Sylvester sub-resultants, rational Cauchy approximations, Thiele's continued fractions, and higher Bruhat orders (2005) Uspekhi Mat. Nauk, 60, pp. 165-166
- Kós, G., Rónyai, L., (2011), arxiv:1008.2901, Alon's Nullstellensatz for multisets; Lascoux, A., Pragacz, P., Double Sylvester sums for subresultants and multi-Schur functions (2003) J. Symbolic Comput., 35, pp. 689-710
- Roy Marie-Françoise, Szpirglas, A., Sylvester double sums and subresultants (2011) J. Symbolic Comput., 46, pp. 385-395
- 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) Philosophical Transactions of the Royal Society of London, Part III, pp. 407-548. , Appears also in Collected Mathematical Papers of James Joseph Sylvester, Vol. 1, Chelsea Publishing Co. (1973) 429-586
Citas:
---------- APA ----------
Krick, T. & Szanto, A. (2012) . Sylvester's double sums: An inductive proof of the general case. Journal of Symbolic Computation, 47(8), 942-953.http://dx.doi.org/10.1016/j.jsc.2012.01.003
---------- CHICAGO ----------
Krick, T., Szanto, A. "Sylvester's double sums: An inductive proof of the general case" . Journal of Symbolic Computation 47, no. 8 (2012) : 942-953.http://dx.doi.org/10.1016/j.jsc.2012.01.003
---------- MLA ----------
Krick, T., Szanto, A. "Sylvester's double sums: An inductive proof of the general case" . Journal of Symbolic Computation, vol. 47, no. 8, 2012, pp. 942-953.http://dx.doi.org/10.1016/j.jsc.2012.01.003
---------- VANCOUVER ----------
Krick, T., Szanto, A. Sylvester's double sums: An inductive proof of the general case. J. Symb. Comput. 2012;47(8):942-953.http://dx.doi.org/10.1016/j.jsc.2012.01.003
