An elementary proof of Sylvester's double sums for subresultants

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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 using multi-Schur functions and divided differences. In this paper, we provide a...

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Autores principales: D'Andrea, C., Hong, H., Krick, T., Szanto, A.
Formato: JOUR
Materias:
Double-sum formula
Subresultants
Vandermonde determinant
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_07477171_v42_n3_p290_DAndrea
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_07477171_v42_n3_p290_DAndrea
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spelling todo:paper_07477171_v42_n3_p290_DAndrea2023-10-03T15:38:55Z An elementary proof of Sylvester's double sums for subresultants D'Andrea, C. Hong, H. Krick, T. Szanto, A. Double-sum formula Subresultants Vandermonde determinant 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 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 determinants. © 2006 Elsevier Ltd. All rights reserved. Fil:D'Andrea, C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Krick, T. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_07477171_v42_n3_p290_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 Double-sum formula
Subresultants
Vandermonde determinant
spellingShingle Double-sum formula
Subresultants
Vandermonde determinant
D'Andrea, C.
Hong, H.
Krick, T.
Szanto, A.
An elementary proof of Sylvester's double sums for subresultants
topic_facet Double-sum formula
Subresultants
Vandermonde determinant
description 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 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 determinants. © 2006 Elsevier Ltd. All rights reserved.
format JOUR
author D'Andrea, C.
Hong, H.
Krick, T.
Szanto, A.
author_facet D'Andrea, C.
Hong, H.
Krick, T.
Szanto, A.
author_sort D'Andrea, C.
title An elementary proof of Sylvester's double sums for subresultants
title_short An elementary proof of Sylvester's double sums for subresultants
title_full An elementary proof of Sylvester's double sums for subresultants
title_fullStr An elementary proof of Sylvester's double sums for subresultants
title_full_unstemmed An elementary proof of Sylvester's double sums for subresultants
title_sort elementary proof of sylvester's double sums for subresultants
url http://hdl.handle.net/20.500.12110/paper_07477171_v42_n3_p290_DAndrea
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AT szantoa anelementaryproofofsylvestersdoublesumsforsubresultants
AT dandreac elementaryproofofsylvestersdoublesumsforsubresultants
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AT szantoa elementaryproofofsylvestersdoublesumsforsubresultants
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