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1. Closed formula for univariate subresultants in multiple roots.

Author

D'Andrea, Carlos, Krick, Teresa, Szanto, Agnes, and Valdettaro, Marcelo

Subjects
*UNIVARIATE analysis, *POLYNOMIALS, *SCHUR functions, *MATHEMATICAL models, *MULTIVARIATE analysis
Abstract

Abstract 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. [ABSTRACT FROM AUTHOR]

Published
2019
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2. Closed formula for univariate subresultants in multiple roots

Author

Teresa Krick, Carlos D'Andrea, Agnes Szanto, and Marcelo Valdettaro

Subjects
Matemáticas, SUBRESULTANTS, MathematicsofComputing_NUMERICALANALYSIS, 0211 other engineering and technologies, 02 engineering and technology, EXCHANGE LEMMA, Commutative Algebra (math.AC), 01 natural sciences, Matemática Pura, Combinatorics, purl.org/becyt/ford/1 [https], Mathematics - Algebraic Geometry, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, FOS: Mathematics, Discrete Mathematics and Combinatorics, Computer Science::Symbolic Computation, 0101 mathematics, SCHUR FUNCTIONS, Algebraic Geometry (math.AG), Mathematics, Numerical Analysis, Algebra and Number Theory, 010102 general mathematics, Univariate, purl.org/becyt/ford/1.1 [https], 021107 urban & regional planning, Multiplicity (mathematics), Mathematics - Commutative Algebra, Schur polynomial, FORMULAS IN ROOTS, Geometry and Topology, CIENCIAS NATURALES Y EXACTAS
Abstract

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. Fil: D'Andrea, Carlos. Universidad de Barcelona; España Fil: Krick, Teresa Elena Genoveva. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina Fil: Szanto, Agnes. North Carolina State University; Estados Unidos Fil: Valdettaro, Marcelo Alejandro. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina

Published
2019

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