On mixed polynomials of bidegree (n, 1)
| Autor: | Mohamed Elkadi, André Galligo |
|---|---|
| Přispěvatelé: | Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Géométrie , Algèbre, Algorithmes (GALAAD2), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire Jean Alexandre Dieudonné (LJAD), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Université Nice Sophia Antipolis (... - 2019) (UNS), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS) |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
[INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC] General Computer Science Discrete orthogonal polynomials 010102 general mathematics Polynomial arithmetic 01 natural sciences Vandermonde matrix Theoretical Computer Science Classical orthogonal polynomials Macdonald polynomials Difference polynomials [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] 0103 physical sciences Orthogonal polynomials ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION 010307 mathematical physics 0101 mathematics Mathematics Complex conjugate root theorem |
| Popis: | Specifying the bidegrees (n, m) of mixed polynomials P (z, ¯ z) of the single complex variable z, with complex coefficients, allows to investigate interesting roots structures and counting; intermediate between complex and real algebra. Multivariate mixed polynomials appeared in recent papers dealing with Milnor fibrations, but in this paper we focus on the univariate case and m = 1, which is closely related to the important subject of harmonic maps. Here we adapt, to this setting, two algorithms of computer algebra: Vandermonde interpolation and a bissection-exclusion method for root isolation. Implemented in Maple, they are used to explore some interesting classes of examples. |
| Databáze: | OpenAIRE |
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