• To: mathgroup at smc.vnet.net
• Subject: [mg31916] Re: Simple questions about Mathematica
• From: "Alan Mason" <swt at austin.rr.com>
• Date: Wed, 12 Dec 2001 04:13:56 -0500 (EST)
• References: <9uvhm2\$ibq\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hello,
Your first question isn't as straightforward as it sounds, because of the
way Mathematica stores expressions internally (you can always find out how
it does this by using FullForm[]).
For instance, the simplest rule rl=Sqrt[a^2+b^2]\[Rule]R fails to work in a
lot of cases, e.g., 1/Sqrt[a^2+b^2].

The best simple rule I can think of is
rl2 = (a^2 + b^2)^Rational[p_, 2] :> R^p.
This works on things like Log[(a^2+b^2)^(3/2)]
in[ Sqrt[a^2+b^2]]/Sqrt[a^2+b^2].
For example,
Log[(a^2+b^2)^(3/2)] Sin[ Sqrt[a^2+b^2]]/Sqrt[a^2+b^2] //. rl2 gives
Log[R^3]Sin[R]/R.

"Stephen Gray" <stevebg at adelphia.net> wrote in message
news:9uvhm2\$ibq\$1 at smc.vnet.net...
> 1. Suppose I solve some equations and get a complicated
> expression containing multiple identical elements such as
> sqrt(a^2+b^2). To make the expression smaller, clearer, and
> easier to deal with, I want to substitute say R=sqrt(a^2+b^2)
> everywhere in the main expression and have R available as
> a symbol from then on. I see nothing in Help or anywhere
> else about how to do this. But it's such a standard thing to
> do that there must be an easy answer.
>
> 2. I'm not sure how a "batch" file is suppposed to be
> prepared and fed to Mathematica. That is, I want to
> prepare a bunch of operations and variables in advance
> and feed it in, preferably having mathematica give me
> line-by-line output as it would if I were typing each line
> in  one by one.
>
>     As a new user I really need answers to these questions.
> Thanks in advance for any information.
>

```

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