Symbolic Treatment of Trigonometric Parametrizations: The General Unirational Case and Applications

Abstract

In this paper, we consider symbolic (hybrid trigonometric) parametrizations defined as tuples of real rational expressions involving circular and hyperbolic trigonometric functions as well as monomials, with the restriction that variables in each block of functions are different. We prove that the varieties parametrizable in this way are exactly the class of real unirational varieties of any dimension. In addition, we provide symbolic algorithms to implicitize and to convert a hybrid trigonometric parametrization into a unirational one, and vice versa. We illustrate by some examples the applicability of having these different types of parametrizations, namely, hybrid trigonometric and unirational.

Keywords

Trigonometric parametrization / Hyperbolic parametrization / Implicitization algorithm / Unirational algebraic variety / Applications / Symbolic computation

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Funding

Universidad de Alcalá

RIGHTS & PERMISSIONS

The Author(s)