Sylvester double sums and subresultants
نویسندگان
چکیده
منابع مشابه
Sylvester double sums and subresultants
Sylvester double sums versus subresultants given two polynomials A and B first notion symmetric expression of the roots of two polynomials second notion defined through the coefficients polynomials main result of the lecture these two notions are very closely related (idea due to Sylvester [S]) see details and complete proofs in [RS]. 1 Definitions and main result. A and B two finite families o...
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J. J. Sylvester has announced formulas expressing the subresultants (or the successive polynomial remainders for the Euclidean division) of two polynomials, in terms of some double sums over the roots of the two polynomials. We prove Sylvester formulas using the techniques of multivariate polynomials involving multi-Schur functions and divided differences. Introduction and statement of the main...
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We present a solution for the classical univariate rational interpolation problem by means of (univariate) subresultants. In the case of Cauchy interpolation (interpolation without multiplicities), we give explicit formulas for the solution in terms of symmetric functions of the input data, generalizing the well-known formulas for Lagrange interpolation. In the case of the osculatory rational i...
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In 1853 Sylvester stated and proved an elegant formula that expresses the polynomial subresultants in terms of the roots of the input polynomials. Sylvester’s formula was also recently proved by Lascoux and Pragacz by using multi-Schur functions and divided differences. In this paper, we provide an elementary proof that uses only basic properties of matrix multiplication and Vandermonde determi...
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The alternate Sylvester sums are Tm(a, b) = ∑ n∈NR(−1)n, where a and b are coprime, positive integers, and NR is the Frobenius set associated with a and b. In this note, we study the generating functions, recurrences and explicit expressions of the alternate Sylvester sums. It can be found that the results are closely related to the Bernoulli polynomials, the Euler polynomials, and the (alterna...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2011
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2010.10.012