%0 Journal Article 
%A Recio, Tomás
%A Sendra Pons, Juan Rafael
%A Tabera, Luis Felipe
%A Villarino Cabellos, Carlos
%T Factoring analytic multivariate polynomials and non-standard Cauchy-Riemann conditions
%D 2014
%@ 0378-4754
%U http://hdl.handle.net/10017/20443
%X 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.
%K Cauchy-Riemann conditions
%K Analytic polynomials
%K Factorization
%K Ciencia
%K Matemáticas
%K Science
%K Mathematics
%~ Biblioteca Universidad de Alcala