Two places to start:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.2680http://www.math.fsu.edu/~hoeij/papers/comments/jsc1997a.html
I haven't read these articles. According to the Maple 10 user
documentation, Maple uses the method in the 1997
paper of van Hoeij. I hope that you will consider writing Maxima code for
determining parametric representations
of curves.
Barton
maxima-bounces at math.utexas.edu wrote on 10/06/2008 12:00:51 AM:
> [image removed]
>
> [Maxima] Parameterization of implicit equation
>
> Bowo Prasetyo
>
> to:
>
> maxima
>
> 10/06/2008 12:00 AM
>
> Sent by:
>
> maxima-bounces at math.utexas.edu
>
> Hi all,
>
> Suppose, I have an implicit equation of Cayley Cubic as below:
>
> x^2 + y^2 - x^2*z + y^2*z + z^2 - 1 = 0
>
> How could I rewrite it in parametric equation of x, y and z?
> I have googled around about parameterization and found that there is
> no definitive way to do that, rather it is a trial and error process.
>
> Could we use Maxima to help doing parameterization?
>
> Thank you
> ~ bowo ~
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