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Re: Expression manipulation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg88740] Re: [mg88722] Expression manipulation
  • From: John Fultz <jfultz at wolfram.com>
  • Date: Thu, 15 May 2008 06:52:11 -0400 (EDT)
  • Reply-to: jfultz at wolfram.com

I'm no expert at this, but I've seen other experts within Wolfram using the
AlgebraicManipulation palette to do simplifications on pieces of a large 
expression similar to the ones you describe.  Basically, they select a piece by 
hand, apply the appropriate button from the palette, possibly re-evaluate to
combine like terms and/or save the current state of the expression, and iterate 
again with the palette until they're satisfied.

To aid in this, you may find structured selection in the user interface useful.  
The user interface is aware of the structure of expressions and responds to
multi-clicking by selecting successively larger structurally complete elements 
(important since the buttons in the palette would fail on structurally 
incomplete elements).  For example, double-clicking on an open or close 
parenthesis will select the entire parenthesized contents. Double-click-drag 
from there will then allow you to drag-select neighboring terms in their 
entirety.  Triple-click, quadruple-click, quintuple-click, and so on from any 
given point will select successively larger structural elements.  It's difficult 
to explain in words, but easy to understand once you've observed it in action, 
so feel free to experiment.

The AlgebraicManipulation palette is available in both 5.2 and 6.0.

Sincerely,
 
John Fultz
jfultz at wolfram.com
User Interface Group
Wolfram Research, Inc.


On Wed, 14 May 2008 06:04:50 -0400 (EDT), 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
> license, I have access to more recent versions. Would it help to
> 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



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