Re: help on Rewrite rules

• To: mathgroup at smc.vnet.net
• Subject: [mg50882] Re: [mg50875] help on Rewrite rules
• From: DrBob <drbob at bigfoot.com>
• Date: Sun, 26 Sep 2004 05:31:43 -0400 (EDT)
• References: <200409250555.BAA05054@smc.vnet.net>
• Reply-to: drbob at bigfoot.com
• Sender: owner-wri-mathgroup at wolfram.com

```Here's one approach:

s = Solve[x^2 + y^2 == 1, y];
f = Union[Simplify[#1 /.s]] & ;

f[3*x^2 + 2*y^2]
{2 + x^2}

f[(x^2 + y^2)^(1/2)]
{1}

A[x^2] + B[y^2] + f@C[x^2 + y^2]
{A[x^2] + B[y^2] + C[1]}

I don't know if the last example will work for every C function one could possibly specify.

Bobby

On Sat, 25 Sep 2004 01:55:17 -0400 (EDT), Jon Palmer <Jonathan.palmer at new.ox.ac.uk> wrote:

> 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.
>
>
>
>
>

--
DrBob at bigfoot.com
www.eclecticdreams.net

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From: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>
To: mathgroup at smc.vnet.net
References: <cj322j\$542\$1 at smc.vnet.net>
Subject: [mg50882] Re: Simple questions with Complex Numbers
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Organization: Customer of PlusNet plc (http://www.plus.net)

Use ComplexExpand thus:

z = s+ I t;
zbar = s- I t;
Re[1/(z zbar)]//ComplexExpand//Simplify

Steve Luttrell

"Sunil Pinnamaneni" <pinnama at cims.nyu.edu> wrote in message
news:cj322j\$542\$1 at smc.vnet.net...
> I'm having difficulty getting mathematica to do simplifications with
> Complex
> Numbers. For instance,
>
> z = s+ I t;
> zbar = s- I t;
> FullSimplify[Re[1/(z zbar)]]
>
> yields
>
> Re[1/(s^2 +t^2)]
>
> Is there any way to get Mathematica to yield the result 1/(s^2 +t^2)
> without
> the Re? It seems like Mathematica should have been programmed to do easy
> simplifications using Complex Numbers.
>
> I'm interested in finding the Real part of expressions like 1/z^5, but
> Mathematica doesn't seem to want to multiply the denominator by the
> conjugate, and carry out the simpification.
>
> Can Mathematica do such things, or does one have to specifically program
> it
> to handle these simplifications.
>
> Thanks,
> Sunil
>
>

```

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