I didn't understand this question at all, I'm afraid. Where you wrote "loci", I think you probably meant "foci". The "radii" presumably refers to major and minor radius of an ellipse. The coefficients are presumably those of the parameters in the coordinate functions. A circle is rationally parameterised by [w,x,y] = [1+t^2, 1-t^2, 2t], the Cartesian coordinates of the conic then being [x/w, y/w]. Why should this not disprove your assertion? A reference to the relevant background might be of some assistance! Fred Lunnon On 8/5/11, James Cloos <cloos@jhcloos.com> wrote:
AIUI, in order to form conic setion curves using rational parametric polynomials such that the (Cartesian) coordinates of the loci, the radii and the coefficients are all in Q, the polymonials have to be at least quintic. Otherwise, at least one of the loci, radii or coefficients are radicals.
Presuming that is true, is there any relation between that and the fact that quintics are the lowest degree polys which are not always solvable in terms of radicals (given coefficients in Q)?
-JimC -- James Cloos <cloos@jhcloos.com> OpenPGP: 1024D/ED7DAEA6
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