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| HAL: hal-00578183, version 1 |
| DOI: 10.1016/j.jsc.2010.10.012 |
| Detailed view |  Export this paper |
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| Journal of Symbolic Computation 46, 4 (2011) 385-395 |
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| Sylvester double sums and subresultants |
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| Marie-Françoise Roy 1Aviva Szpirglas 2 |
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| (2011) |
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| Sylvester double sums, introduced first by Sylvester (see Sylvester (1840, 1853)), are symmetric expressions of the roots of two polynomials, while subresultants are defined through the coefficients of these polynomials (see Apery and Jouanolou (2006) and Basu et al. (2003) for references on subresultants). As pointed out by Sylvester, the two notions are very closely related: Sylvester double sums and subresultants are equal up to a multiplicative non-zero constant in the ground field. Two proofs are already known: that of Lascoux and Pragacz (2003), using Schur functions, and that of d'Andrea et al. (2007), using manipulations of matrices. The purpose of this paper is to give a new simple proof using similar inductive properties of double sums and subresultants. |
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| 1: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 2: | Laboratoire de Mathématiques et Applications |
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Université de Poitiers |
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| Subject | : | Mathematics/Commutative Algebra |
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| Resultants – Subresultants – Sylvester matrices – Sylvester sums |
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| hal-00578183, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00578183 | |
| oai:hal.archives-ouvertes.fr:hal-00578183 | |
| From: Marie-Annick Guillemer | |
| Submitted on: Friday, 18 March 2011 15:30:09 | |
| Updated on: Friday, 18 March 2011 15:30:09 | |
