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Sylvester's Double Sums: the general case

2007/01/24 by Carlos D’Andrea, Carlos D'Andrea, D'Andrea, Carlos +8
Mathematics · #14Q10 #68W30 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #History and Theory of Mathematics #Mathematical and Theoretical Analysis #Mathematics and Applications #math.AC #math.AG #msc:14Q10 #msc:68W30

paper · pdf · doi:10.48550/arxiv.math/0701721

16 pages, uses academic.cls and yjsco.sty. Revised version accepted for publication in the special issue of the Journal of Symbolic Computation on the occasion of the MEGA 2007 Conference

openalex publication_date 2007/01/24 · arxiv created 2008/03/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1853 Sylvester introduced a family of double sum expressions for two finite sets of indeterminates and showed that some members of the family are essentially the polynomial subresultants of the monic polynomials associated with these sets. A question naturally arises: What are the other members of the family? This paper provides a complete answer to this question. The technique that we developed to answer the question turns out to be general enough to charactise all members of the family, providing a uniform method.

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