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Forme canonique d'une forme binaire

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1278)

Abstract

The space of polynomials in one variable x of odd degree 2n+1 is 2n+2-dimensional. A linear combination of n+1 polynomials (x−β)2n+1 takes care of the required number of parameters. Such an expression has been called the canonical form of a binary form. Sylvester has shown that this reduction is obtained through another polynomial, the catalecticant, when it has the taste of having all its roots distinct. It happens, and this is not by coincidence, that the catalecticant is an orthogonal polynomial for a certain linear functional associated to the polynomial; the required relations are given by the theory of symmetric functions, supplemented by a little amount of divided differences and Lagrange interpolation formula. Having recovered with these tools the classical case, one can go further and treat as well the case where all the roots of the catalecticant are the same; this is what we do in Theorem 3.4.

Keywords

  • Orthogonal Polynomial
  • Divided Difference
  • Lagrange Interpolation Formula
  • Sont Nuls
  • Relation Suivante

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  • C.BREZINSKI-Padé-type Approximants, Birhaüser 1980

    Google Scholar 

  • A. CAYLEY-Journal de Crelle 54(1858) 48–58, 292

    MathSciNet  Google Scholar 

  • J. EISENSTEIN-Journal de Crelle 27(1844) 75–79 & 89–104

    Google Scholar 

  • FAA DE BRUNO-Théorie des formes binaires, Turin 1876

    Google Scholar 

  • L&S 1=A.LASCOUX & M.P.SCHÜTZENBERGER-in Invariant theory, SpringerL.N. 996

    Google Scholar 

  • L&S 2=A.LASCOUX & M.P.SCHÜTZENBERGER=in Séminaire d'algèbre M.P.Malliavin 1984, Springer L.N. 1146

    Google Scholar 

  • A. LASCOUX & SHI HE-Comptes Rendus Ac.Sc.Paris, 300(1985) 681

    MathSciNet  Google Scholar 

  • I.G.MACDONALD-Symmetric Functions and Hall Polynomials, Oxford Mat.Mono. 1979

    Google Scholar 

  • P. SONDAT-Nouv.Ann.Math. 19 3ème série (1900) 25–28

    Google Scholar 

  • J.J.SYLVESTER-Collected Work, Chelsea reprint: Tome I, p. 203–216, 265–283, Tome II, p.18–27

    Google Scholar 

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© 1987 Springer-Verlag

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Lascoux, A. (1987). Forme canonique d'une forme binaire. In: Koh, S.S. (eds) Invariant Theory. Lecture Notes in Mathematics, vol 1278. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078805

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  • DOI: https://doi.org/10.1007/BFb0078805

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18360-0

  • Online ISBN: 978-3-540-47908-6

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