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Re: Re: Expression manipulation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg88791] Re: [mg88738] Re: Expression manipulation
  • From: Syd Geraghty <sydgeraghty at mac.com>
  • Date: Fri, 16 May 2008 05:35:21 -0400 (EDT)
  • References: <g0edhe$9eq$1@smc.vnet.net> <200805151051.GAA21816@smc.vnet.net>

David,

As a very satisfied user of your Presentations package may I suggest a  
possible interface addition to a future release.

It would be nice to have your additional manipulations (discussed  
below by you) in a new palette "PresentationsAlgebraicManipulation".

This would supplement the standard release palette  
AlgebraicManipulation and enable use of one very interactive style of  
expression manipulation.

As I write this it strikes me that this might not be a very easy thing  
to do and I would appreciate your response.

This thought was prompted by John Fulz's contribution to this thread.

	From: 	jfultz at wolfram.com
	Subject: 	[mg88740] Re: [mg88722] Expression manipulation

Best wishes,

Syd




Syd Geraghty B.Sc, M.Sc.

sydgeraghty at mac.com

My System

Mathematica 6.0.2.1 for Mac OS X x86 (64 - bit) (March 13, 2008)
MacOS X V 10.5.2
MacBook Pro 2.33 Ghz Intel Core 2 Duo  2GB RAM






On May 15, 2008, at 3:51 AM, David Park wrote:

> David,
>
> You should be able to do all the manipulations using Mathematica.  
> You should
> learn how to use rule based programming, commands such as MapAt,  
> Apart,
> Together, Cancel. HoldForm and of course Simplify.
>
> Still, Mathematica is often very theoretically oriented and lacks  
> some of
> the practical operations often used. The Presentations package, at  
> my web
> site below, has a 'Manipulations' section that contains some practical
> additions. Sometimes these are useful in manipulating expressions and
> sometimes useful to get expressions in particular standard forms for  
> display
> in reports or to match a textbook expression.
>
> If you want to keep a particular subexpression together as a unit  
> you can
> wrap it in a HoldForm. This prevents routines like Simplify from  
> splitting
> it up. Presentations has a CreateSubexpression and a  
> ReleaseSubexpressions
> routines that allow you to wrap a subexpression in a tagged Tooltip.  
> This
> works just as well as a HoldForm and allows you to see what the
> subexpressions are.
>
> FactorOut can be used to remove a factor from an expression - even  
> if the
> factor is  not initially in the expression. For example, you can  
> pull a
> factor out of a matrix and wrap the matrix in a HoldForm all in one
> operation.
>
> MultiplyByOne will multiply the numerator and denominator of an  
> expression
> by the same factor and Simplify, or perform any other specified  
> operations
> on the numerator and denominator, so the factor won't cancel back out.
>
> MapLevelParts and MapLevelPatterns will map an operation onto a  
> subset of
> level parts in an expression. The most common use is to apply some  
> function
> to a selected subset of terms in a sum.
>
> LinearBreakout[f1,f2,...][v1,v2,..][expr] will break out the linear  
> terms of
> any expressions within expr that have heads matching the patterns fi  
> over
> variables matching the patterns vj.
>
> PushOnto is a much improved version of the Through command that will  
> push a
> list of arguments onto specific functions.
>
> HoldOp[operation][expr] will prevent an explicit operation in expr  
> from
> being evaluated but will evaluate the arguments of the operation. It  
> is
> useful when operation has a number of definitions with it, but you  
> want to
> see what the expression looks like before these definitions are  
> applied.
>
> EvaluateAtPattern will evaluate specific patterns in held expressions.
>
> Here is an example of using some of these routines to manipulate an
> expression as you might do it 'by hand':
>
> a + b + c
> % // MapLevelParts[CreateSubexpression, {{1, 3}}]
> d % // Expand
> % // FactorOut[sub]
> % // ReleaseSubexpressions[]
>
> a + b + c
>
> b + (a + c)         where (a+c) has a tag and Tooltip 'held'.
>
> b d+d (a + c)      where d did not Distribute across the  
> subexpression.
>
> (d+(b d)/(a+c)) (a+c)  factoring out the subexpression (a+c), even  
> though it
> is not a true 'factor'.
>
> (a+c) (d+(b d)/(a+c))   releasing the subexpression keeps the overall
> structure.
>
> Finally, I might mention the annoying tendency of Mathematica to get  
> more
> minus signs into standard expressions than you might wish. One way to
> correct this is just to Map Minus onto two factors in a product. For
> example:
>
> 3 - a (c - b)
> MapAt[Minus, %, {{2, 1}, {2, 3}}]
> 3 - a (-b + c)
> 3 + a (b - c)
>
> -- 
> David Park
> djmpark at comcast.net
> http://home.comcast.net/~djmpark/
>
>
> "David" <David.B.A.Epstein at googlemail.com> wrote in message
> news:g0edhe$9eq$1 at smc.vnet.net...
>> 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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