Factoring analytic multivariate polynomials and non-standard Cauchy–Riemann conditions
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AuthorRecio Muñiz, Tomás; Sendra Pons, Juan Rafael; Tabera Alonso, Luis Felipe; Villarino Cabellos, Carlos
Copyright © 2013 IMACS. Published by Elsevier Ltd. All rights reserved. This is the author’s version of a work that was accepted for publication in Mathematics and Computers in Simulation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Mathematics and Computers in Simulation, vol. 104, Pp. 43-57, DOI:10.1016/j.matcom.2013.03.013
Mathematics and Computers in Simulation, vol. 104, Pp. 43-57
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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 → x + iy on a univariate polynomial View the MathML source, i.e. p (z ) → p (x + iy ) = P (x , y )) to other finite field extensions, beyond the classical case of View the MathML source. In this general setting we obtain different properties on the factorization, 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.