I have a system of equations for algebraic curve given by the zero locus of some polynomial encoded in the system of equations (I want to eliminate variable z and get algebraic curve in terms of x and y, C12 and C22 can be assumed to be integers and even positive if that helps):
Eliminate[{y == z^(2 + 2 C12)/(-x^2 + z^2),
1 == ((x - z) (x/z)^(2 C12) z^(-2 - 2 C12 + 2 C22) (x + z))/(-1 +
z^2)}, {z}]
Eliminate::ifun: Inverse functions are being used by Eliminate, so some solutions may not be found; use Reduce for complete solution information.
However Mathematica can't eliminate z.
When I use Solve I get:
Solve::nsmet: This system cannot be solved with the methods available to Solve.
Maple gives some answers but they aren't very useful, for instance they don't give algebraic curve that I want.
Is there any smart way to do what I want?
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