Closed formula for univariate subresultants in multiple roots
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Abstract
We generalize Sylvester single sums to multisets (sets with repeated elements), and show that these sums compute subresultants of two univariate polyomials 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.Keywords
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This publication has 11 references indexed in Scilit:
- Subresultants in multiple roots: An extremal caseLinear Algebra and its Applications, 2017
- Symmetric interpolation, Exchange Lemma and Sylvester sumsCommunications in Algebra, 2016
- Subresultants in multiple rootsLinear Algebra and its Applications, 2013
- Sylvester’s double sums: An inductive proof of the general caseJournal of Symbolic Computation, 2012
- Sylvester double sums and subresultantsJournal of Symbolic Computation, 2011
- An elementary proof of Sylvester’s double sums for subresultantsJournal of Symbolic Computation, 2007
- Various New Expressions for Subresultants and Their ApplicationsApplicable Algebra in Engineering, Communication and Computing, 2004
- LVII. Note on eliminationJournal of Computers in Education, 1840
- XXIII. A method of determining by mere inspection the derivatives from two equations of any degreeJournal of Computers in Education, 1840
- LXIII. Memoir on rational derivation from equations of coexistence, that is to say, a new and extended theory eliminationJournal of Computers in Education, 1839