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Abstract:

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.

Registro:

Documento: Artículo
Título:Symmetric interpolation, Exchange Lemma and Sylvester sums
Autor:Krick, T.; Szanto, A.; Valdettaro, M.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales and IMAS, CONICET, Universidad de Buenos Aires, Buenos Aires, Argentina
Department of Mathematics, North Carolina State University, Raleigh, NC, United States
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
Palabras clave:Subresultants; Sylvester double sums; symmetric Lagrange interpolation
Año:2017
Volumen:45
Número:8
Página de inicio:3231
Página de fin:3250
DOI: http://dx.doi.org/10.1080/00927872.2016.1236121
ISSN:00927872
Registro:http://digital.bl.fcen.uba.ar/collection/paper/document/paper_00927872_v45_n8_p3231_Krick

Referencias:

  • 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)

Citas:

---------- APA ----------
Krick, T., Szanto, A. & Valdettaro, M. (2017) . Symmetric interpolation, Exchange Lemma and Sylvester sums, 45(8), 3231-3250.
http://dx.doi.org/10.1080/00927872.2016.1236121
---------- CHICAGO ----------
Krick, T., Szanto, A., Valdettaro, M. "Symmetric interpolation, Exchange Lemma and Sylvester sums" 45, no. 8 (2017) : 3231-3250.
http://dx.doi.org/10.1080/00927872.2016.1236121
---------- MLA ----------
Krick, T., Szanto, A., Valdettaro, M. "Symmetric interpolation, Exchange Lemma and Sylvester sums" , vol. 45, no. 8, 2017, pp. 3231-3250.
http://dx.doi.org/10.1080/00927872.2016.1236121
---------- VANCOUVER ----------
Krick, T., Szanto, A., Valdettaro, M. Symmetric interpolation, Exchange Lemma and Sylvester sums. 2017;45(8):3231-3250.
http://dx.doi.org/10.1080/00927872.2016.1236121