Closed formula for univariate subresultants in multiple roots

We generalize Sylvester single sums to multisets and show that these sums compute subresultants of two univariate polynomials as a function of their roots independently of their multiplicity structure. This is the first closed formula for subresultants in terms of roots that works for arbitrary poly...

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Detalles Bibliográficos
Autores principales: D'Andrea, C., Krick, T., Szanto, A., Valdettaro, M.
Formato: JOUR
Materias:
Exchange lemma
Formulas in roots
Schur functions
Subresultants
Linear algebra
Mathematical techniques
Arbitrary polynomial
Multiple roots
Multiplicity structures
Schur function
Schur polynomials
Polynomials
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00243795_v565_n_p123_DAndrea
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario:We generalize Sylvester single sums to multisets and show that these sums compute subresultants of two univariate polynomials as a function of their roots independently of their multiplicity structure. This is the first closed formula for subresultants in terms of roots that works for arbitrary polynomials, previous efforts only handled special cases. Our extension involves in some cases confluent Schur polynomials and is obtained by using multivariate symmetric interpolation via an Exchange Lemma. © 2018 Elsevier Inc.

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