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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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
id todo:paper_00243795_v565_n_p123_DAndrea
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spelling todo:paper_00243795_v565_n_p123_DAndrea2023-10-03T14:34:50Z Closed formula for univariate subresultants in multiple roots D'Andrea, C. Krick, T. Szanto, A. Valdettaro, M. 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 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00243795_v565_n_p123_DAndrea
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic 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
spellingShingle 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
D'Andrea, C.
Krick, T.
Szanto, A.
Valdettaro, M.
Closed formula for univariate subresultants in multiple roots
topic_facet 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
description 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.
format JOUR
author D'Andrea, C.
Krick, T.
Szanto, A.
Valdettaro, M.
author_facet D'Andrea, C.
Krick, T.
Szanto, A.
Valdettaro, M.
author_sort D'Andrea, C.
title Closed formula for univariate subresultants in multiple roots
title_short Closed formula for univariate subresultants in multiple roots
title_full Closed formula for univariate subresultants in multiple roots
title_fullStr Closed formula for univariate subresultants in multiple roots
title_full_unstemmed Closed formula for univariate subresultants in multiple roots
title_sort closed formula for univariate subresultants in multiple roots
url http://hdl.handle.net/20.500.12110/paper_00243795_v565_n_p123_DAndrea
work_keys_str_mv AT dandreac closedformulaforunivariatesubresultantsinmultipleroots
AT krickt closedformulaforunivariatesubresultantsinmultipleroots
AT szantoa closedformulaforunivariatesubresultantsinmultipleroots
AT valdettarom closedformulaforunivariatesubresultantsinmultipleroots
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