Automatic Rational Parameterization of Curves and Surfaces I: Conics and Conicoids
نویسندگان
چکیده
We describe algorithms to obtain rational parametric equations, (a polynomial equation divided by another), for degree two curves (conics) and degree two surfaces (conicoids), given the implicit equations. We further consider the rational parameterizations over t':~ fields of rationals, reals and complex numbers. In doing so, solutions are given to important subproblems of finding rational, real or complex points on the given conic curve or conicoid surt'ace. Polynomial parameterizations are obtained whenever they exist for the conics and conicoids. These algorithms have been implemented on a VAX-780 using VAXIMA. t Department of Mathematics. Purdue Universiry, West Lafayene.:IN
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تاریخ انتشار 2013