Article ID Journal Published Year Pages File Type
1139091 Mathematics and Computers in Simulation 2014 15 Pages PDF
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 → x + iy on a univariate polynomial p(z)∈ℂ[z], i.e. p(z) → p(x + iy) = P(x, y)) to other finite field extensions, beyond the classical case of ℝ⊂ℂ. 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.
Related Topics
Physical Sciences and Engineering Engineering Control and Systems Engineering
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