help on Rewrite rules

• To: mathgroup at smc.vnet.net
• Subject: [mg50875] help on Rewrite rules
• From: "Jon Palmer" <Jonathan.palmer at new.ox.ac.uk>
• Date: Sat, 25 Sep 2004 01:55:17 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```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[1]

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.

```

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