Re: help on Rewrite rules

• To: mathgroup at smc.vnet.net
• Subject: [mg50896] Re: [mg50875] help on Rewrite rules
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sun, 26 Sep 2004 05:32:16 -0400 (EDT)
• Reply-to: hanlonr at cox.net
• Sender: owner-wri-mathgroup at wolfram.com

```Use an assumption in Simplify.

assumption = x^2+y^2==1;

soln = Simplify[#,assumption]&/@
{3x^2+2y^2,
(x^2+y^2)^(1/2),
A[x^2]+B[y^2]+C[x^2+y^2]}

{3 - y^2, 1, A[x^2] + B[y^2] + C[1]}

In the first case Mathematica eliminated x rather than y.  You can use a
replacement rule to convert the expression.

rr = Solve[assumption,y]//Last;

soln[[1]] /. rr

x^2 + 2

Bob Hanlon

>
> From: "Jon Palmer" <Jonathan.palmer at new.ox.ac.uk>
To: mathgroup at smc.vnet.net
> Date: 2004/09/25 Sat AM 01:55:17 EDT
> To: mathgroup at smc.vnet.net
> Subject: [mg50896] [mg50875] 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[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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