Re: Expression manipulation

• To: mathgroup at smc.vnet.net
• Subject: [mg88737] Re: [mg88722] Expression manipulation
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Thu, 15 May 2008 06:51:34 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200805141004.GAA09601@smc.vnet.net>

```You might find David Park's no-cost Expression Manipulation package
useful. It includes a nice tutorial notebook on its use.  (If you're
running it with Mathematica 6.0, you'll need to let the Version Advisory
scan locate two places in the tutorial notebook that need the
compatibility updating it suggests.)

Another possibility, although not no-cost, is Park's big Presentations
bundle. It includes a Manipulations package that includes, I believe,
some or all of the functionality of that Expression Manipulation
package.  Among the dozen or so functions it defines or extends are:

CompleteTheSquare
FactorOut
MultiplyByOne

This last directly accomplishes one of the tasks you listed --
multiplying numerator and denominator by the same quantity.

For both, see:

http://home.comcast.net/~djmpark/Mathematica.html

David wrote:
> When trying to simplify an expression by hand, one carries out various
> kinds of steps:
> 1. Replace a subexpression that occurs repeatedly by a single symbol.
> 2. Multiply numerator and denominator of some subexpression by the
> same factor.
> 3. Cancel particular factors in numerator and denominator of some
> subexpression.
> 4. Gather together two subexpressions that were added together, and
> rewrite with a common denominator.
> 5. Remove common factors.
>
> etc. etc. etc.
>
> Using Part, one can of course access any particular subexpression. But
> this is time-consuming and clumsy. I find that I need trial and error
> to access the correct subexpression. Once I've accessed it, I often
> have difficulty in persuading Mathematica to perform the desired
> operation. And then I have trouble putting the subexpression back into
> place. It's something like 20 times slower than working with pencil
> and paper. HOWEVER pencil and paper calculations are more prone to
> stupid arithmetic errors, particularly if the computation is a long
> one.
>
> I have been unable to find a convenient way of doing this in
> Mathematica. I use version 5.2, but because of my University's site
> change?
>
> Can anyone point me to a tutorial where experts use Mathematica to do
> a typical pencil and paper computation?
>
> Thanks a lot. Please copy replies to my personal email address as I
> don't look at the newsgroup very often.
>
> David
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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