intersections of curves



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?

Note: the parameters are different, so any intersection requires the
solution of a pair of equations If not, does anyone know a good
reference for such a routine.

I am interested in the case of transcendental functions or high degree
polynomials.  In the cases of interest to me, newton's method has degeneracies or
numerical overflows and does not work.  So, I would prefer some sort
of 'bisection' method.

One special case of interest to me is the one in which the curves have
a non-degenerate crossing; i.e., have linearly independent tangent
vectors at the crossing.

TIA,

-sen


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  | Sheldon E. Newhouse            |    e-mail: sen1 at math.msu.edu           |
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