Factoring analytic multivariate polynomials and non-standard Cauchy-Riemann conditions
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/20443DOI: 10.1016/j.matcom.2013.03.013
ISSN: 0378-4754
Publisher
Elsevier
Date
2014Funders
Ministerio de Ciencia e Innovación
Bibliographic citation
Mathematics and Computers in Simulation, 2014, v. 104, p. 43-57
Keywords
Cauchy-Riemann conditions
Analytic polynomials
Factorization
Description / Notes
The journal version of this paper appears in Mathematics
and Computers in Simulation 104 (2014) 43-57.
(http://dx.doi.org/10.1016/j.matcom.2013.03.013/)
∗ Corresponding author: fax +34 942 201 402
Email addresses: tomas.recio@unican.es (Tomas Recio),
rafael.sendra@uah.es (J. Rafael Sendra), taberalf@unican.es (Luis Felipe
Tabera), carlos.villarino@uah.es (Carlos Villarino).
URLs: http://www.recio.tk (Tomas Recio), http://www2.uah.es/rsendra/
(J. Rafael Sendra), http://personales.unican.es/taberalf/ (Luis Felipe
Tabera).
Second and fourth authors
belong to the Research Group ASYNACS (Ref. CCEE2011/R34).
Project
info:eu-repo/grantAgreement/MICINN//MTM2011-25816-C02-01/ES/ALGORITMOS Y APLICACIONES EN GEOMETRIA DE CURVAS Y SUPERFICIES/
info:eu-repo/grantAgreement/MICINN//MTM2008-04699-C03-01/ES/VARIEDADES PARAMETRICAS: ALGORITMOS Y APLICACIONES/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/submittedVersion
Publisher's version
http://dx.doi.org/10.1016/j.matcom.2013.03.013Rights
© IMACS/Elsevier B.V., 2014
Access rights
info:eu-repo/semantics/openAccess
Abstract
Motivated by previous work on the simplification of parametrizations of curves, in this paper we generalize the well known notion of analytic polynomial (a bivariate polynomial $P(x,y)$, with complex coefficients, which arises by substituting $z \rightarrow x+\ii y$
on a univariate polynomial $p(z)\in \mathbb{C}[z]$, i.e. $p(z)\rightarrow
p(x+\ii y)=P(x, y)$) to other finite field extensions, beyond the classical case of $\mathbb{R}\subset \mathbb{C}$. In this general setting we obtain different properties on the factorization, {\it gcd}'s and
resultants of analytic polynomials, which seem to be new even in the context of Complex Analysis. Moreover, we extend the well-known Cauchy-Riemann
conditions (for harmonic conjugates) to this algebraic framework, proving that the new conditions also characterize the components of generalized analytic polynomials.
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