First presenter Co-presenter(s)
Name :  Giovanna  Coral * Name:  Laureano Gonzalez-Vega
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Affiliation: Universidad de Cantabria Name:   
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Country: Spain Name:   
Talk
Number:
14-03  E-mail:    
Session: 14- Algorithms for Parametric Systems and their Applications Schedule:
 
Room:
Thursday, 11:30
 
B-3432
Related website:  
Title of
presentation:
Algorithms for hyperbolic and trigonometric curves: implicitization and parameterization
Abstract:
A hyperbolic poynomial is defined in the following way: ?k=0makcosh(k)+?k=0mbksinh(k), where ak???R and bk???R. A hyperbolic curve is a real plane curve where each coordinate is given parametrically by a hyperbolic poynomial:

x=?k=0makcosh(k)+?k=0mbksinh(k)

y=?k=0mckcosh(k)+?k=0mdksinh(k)
By adapting to hyperbolic curves the algorithms presented in [Hong and Schicho 98] for the trigonometric case, we give algorithms for simplifying a given parametric representation and for computing an implicit representation from a given parametric representation.

We show moreover that some of the algebraic curves arising from the implicitization of a hyperbolic curve have a very special structure containing both one hyperbolic part and one trigonometric part. For example:

2752x2-32x2y+2x4+310632-172y-130y2-y3=0
contains two curves, one trigonometric and the other hyperbolic.