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 |
| Mathematics Department | |
| Michigan State University | telephone: 517-355-9684 |
| E. Lansing, MI 48824-1027 USA | FAX: 517-432-1562 |
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