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Abstract:

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.

Registro:

Documento: Artículo
Título:Closed formula for univariate subresultants in multiple roots
Autor:D'Andrea, C.; Krick, T.; Szanto, A.; Valdettaro, M.
Filiación:Department de Matemàtiques i Informàtica, Facultat de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via de les Corts Catalanes, 58508007, Spain
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, IMAS, CONICET, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
Palabras clave:Exchange lemma; Formulas in roots; Schur functions; Subresultants; Linear algebra; Mathematical techniques; Arbitrary polynomial; Exchange lemma; Formulas in roots; Multiple roots; Multiplicity structures; Schur function; Schur polynomials; Subresultants; Polynomials
Año:2019
Volumen:565
Página de inicio:123
Página de fin:155
DOI: http://dx.doi.org/10.1016/j.laa.2018.12.010
Título revista:Linear Algebra and Its Applications
Título revista abreviado:Linear Algebra Its Appl
ISSN:00243795
CODEN:LAAPA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00243795_v565_n_p123_DAndrea

Referencias:

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  • D'Andrea, C., Hong, H., Krick, T., Szanto, A., An elementary proof of Sylvester's double sums for subresultants (2007) J. Symbolic Comput., 42 (3), pp. 290-297
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  • Diaz-Toca, G.M., Gonzalez-Vega, L., Various new expressions for subresultants and their applications (2004) Appl. Algebra Engrg. Comm. Comput., 15 (3-4), pp. 233-266
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  • Valdettaro, M., Fórmulas en raíces para las subresultantes (2017), http://cms.dm.uba.ar/academico/carreras/doctorado/tesis-Valdettaro.pdf, Ph.D. Thesis University of Buenos Aires

Citas:

---------- APA ----------
D'Andrea, C., Krick, T., Szanto, A. & Valdettaro, M. (2019) . Closed formula for univariate subresultants in multiple roots. Linear Algebra and Its Applications, 565, 123-155.
http://dx.doi.org/10.1016/j.laa.2018.12.010
---------- CHICAGO ----------
D'Andrea, C., Krick, T., Szanto, A., Valdettaro, M. "Closed formula for univariate subresultants in multiple roots" . Linear Algebra and Its Applications 565 (2019) : 123-155.
http://dx.doi.org/10.1016/j.laa.2018.12.010
---------- MLA ----------
D'Andrea, C., Krick, T., Szanto, A., Valdettaro, M. "Closed formula for univariate subresultants in multiple roots" . Linear Algebra and Its Applications, vol. 565, 2019, pp. 123-155.
http://dx.doi.org/10.1016/j.laa.2018.12.010
---------- VANCOUVER ----------
D'Andrea, C., Krick, T., Szanto, A., Valdettaro, M. Closed formula for univariate subresultants in multiple roots. Linear Algebra Its Appl. 2019;565:123-155.
http://dx.doi.org/10.1016/j.laa.2018.12.010