# [Maxima] intersections of curves

Daniel Lakeland dlakelan at street-artists.org
Fri Jul 13 16:40:24 CDT 2007

On Fri, Jul 13, 2007 at 05:29:33PM -0400, David Joyner wrote:
> On 7/13/07, sen1 at math.msu.edu <sen1 at math.msu.edu> wrote:
> > Hello,
> >   Using the function 'find_root' one can find an intersection of
> >   two explicit curves
> >     x -> [x, g(x)]
> >     x -> [x, h(x)]
> >
> > in an interval [a,b] such that g - h have different signs at the
> > endpoints.
> >
> > Does maxima have an analogous routine to find the intersection of two
> > parametrized curves
> >
> > g:  t -> [x(t), y(t)], 0 < t < 1
> > h:  s -> [u(s), v(s)], 0 < s < 1
> >
> > where it is known that such an intersection exists?
>
> In many cases, I'm guessing the answer is  "yes", for the following reasons.
> If x,y,u,v are polynomials in t then Grobner bases will
> put these curves in algebraic form. Maxima has some Grobner bases routines.
> An example is in
> Once they are in algebraic form, again Grobner bases can be used
> to find 0-dimensional solutions.
> Does this make sense?

x and y depend on t, but u, and v are parameterized by s which is
unrelated to t.

--
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan