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Finding Vertices
Posted:
Jun 17, 1996 9:00 PM


Perhaps someone has an idea or reference for solving the following problem. I am solving equations using Mathematica which have multidimensional 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>1y 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



