On 7/13/07, Daniel Lakeland <dlakelan at street-artists.org> wrote:
> 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
> > http://cadigweb.ew.usna.edu/~wdj/book/node86.html
> > 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.
Sorry. Typo. I meant of course
"If x,y are polynomials in t and u,v polynomials in s then Grobner bases will
put these curves in algebraic form. "
>
>
>
> --
> Daniel Lakeland
> dlakelan at street-artists.org
> http://www.street-artists.org/~dlakelan
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