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help on Rewrite rules
I am having trouble simplifying expressions in mathematica. My epxerissions involve two parameters x & y that parameterise a unit circle so that x^2 + y^2 =1 Without chosing a particular parameterization for x and y I want to simplify epxpertions of the form: 3x^2 + 2y^2 -----> 2 + x^2 or (x^2 + y^2)^(1/2) -----> 1 and more importantly for should perform the simplification A[x^2] + B [y^2] + C[x^2+y^2] -----> A[ x^2] + B[ y^2] + C where A,B&C are functions. I assume that this can me achieved with a relatively simple rewrite rule but I have had very limited success making this work. Can anyone suggest a solution, Many thanks Jon Palmer P.S. I also want to expand the problem to that of three variables x,y&z parameterizing a unit sphere but I suspect that this will be obvious form the solution of the unit circle problem.