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Topic: Finding Vertices
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Alex Tabarrok

Posts: 3
Registered: 12/12/04
Finding Vertices
Posted: Jun 17, 1996 9:00 PM
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Perhaps someone has an idea or reference for solving the following
problem. I am solving equations using Mathematica which have
multi-dimensional solutions. By this I mean that I have more variables
than equations so the solution has several free parameters. One free
parameter indicates a line of solutions, two a plane of solutions and so
forth.

For example, suppose the free parameters are x and y and I know that
0<=x<=1, 0<=y<=1. I am interesting in using this information to find the
vertices of the solution area. As a simple example we might have x->1-y
and y->y thus the solution defines a line with vertices {0,1} and {1,0}.
Things get more complicated with more free parameters of course!
(Usually I have six variables with two or three free so the solution is a
plane or surface and there are a number of permutations of free
parameters which lead to vertices.)

I am interested in a routine that will take the solution from
Mathematica's solve procedure and return the vertices of the solution
area when given some constraints as above. I've written such a routine
for a specific case but wonder if there is not a more general procedure.
If someone has a reference on this type of problem it would also be
appreciated.

Thanks

Alex Tabarrok
Department of Economics
University of Virginia

at5q@virginia.edu










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