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Original Articles

Symmetric interpolation, Exchange Lemma and Sylvester sums

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Pages 3231-3250 | Received 23 Mar 2016, Published online: 09 Jan 2017

References

  • Chen, W. Y. C., Louck, J. D. (1996). Interpolation for symmetric functions. Adv. Math. 117:147–156.
  • D’Andrea, C., Hong, H., Krick, T., Szanto, A. (2007). An elementary proof of Sylvester’s double sums for subresultants. J. Symb. Comput. 42:290–297.
  • D’Andrea, C., Hong, H., Krick, T., Szanto, A. (2009). Sylvester’s double sums: the general case. J. Symb. Comput. 44:1164–1175.
  • D’Andrea, C., Krick, T., Szanto, A. (2015). Subresultants, Sylvester sums and the rational interpolation problem. J. Symb. Comput. 68:72–83.
  • Krick, T., Szanto, A. (2012). Sylvester’s double sums: An inductive proof of the general case. J. Symb. Comput. 47: 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).
  • Lascoux, A. Notes on Interpolation in one and several variables. Available at: http://igm.univ-mlv.fr/ãl/ARTICLES/interp.dvi.gz. Accessed on 13 June 2003.
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  • Roy, M.-F., Szpirglas, A. (2011). Sylvester double sums and subresultants. J. Symb. Comput. 46:385–395.
  • 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).

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