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MathGroup Archive 1998

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Re: Altering terms of an Expression


  • To: mathgroup@smc.vnet.net
  • Subject: [mg11866] Re: Altering terms of an Expression
  • From: "C. Woll" <carlw@u.washington.edu>
  • Date: Fri, 3 Apr 1998 03:45:26 -0500
  • Organization: University of Washington
  • References: <6fsjtm$gpn@smc.vnet.net>

Hi,

How about the following.

1) If your terms are being added together, why don't you just do

Do[ answer=Expand[gm[[k,l]]*f[k]*f[l]];,
	{k,1,n},{l,k+1,n}]

To answer you specific question about Length, you could try creating
your own function

SRlength[a_Plus]:=Length[a]
SRlength[_]:=1

2,3) I think the following code does what you ask. Define a function g
which takes two arguments, the index and the string, with the following
properties

g /: g[n_,"newstring"] g[n_,a_] := g[n,a] g /: g[n_,a_] g[n_,b_] := g[n,
a<>b]

You could also use format to have the output appear the way you wanted,
that is

Format[g[n_,a_]] := a[n]

Then, define a fill variable

fill = Product[g[n,"newstring"],{n,4}]

where you can replace 4 with the maximum allowed index.

Now,

g[3,"astring"] g[1,"bstring"] g[1,"cstring"] fill

produces

bstringcstring[1] newstring[2] astring[3] newstring[4]

Internally, the output is represented as

g[1,"bstringcstring"] g[2,"newstring"] g[3,"astring"] g[4,"newstring"]

Is this what you were looking for?

Carl Woll
Dept. of Physics
U. of Washington

On 1 Apr 1998, S. Rempe wrote:

> Hi,
> 	There are 3 things I want to do with an expression.
>         The expression may have 1 or more terms added together, each
> term is composed of a product of elements.
> 
> 
> 1).  I want to multiply each term in the expression by a product of
>      functions.  For example,  the expression labelled by integers k,l
>      might look like
> 
> 	gm[[k,l]]= a*b*c
>   
>      I want it to become
> 
> 	gm[[k,l]]= a*b*c*f[k]*f[l]
> 
>     
>      I have written a Do loop that doesn't work because I wish that
>      Length would output the number of terms added in the expression
>      (1 term in above expression), but Length gives 3 for the expression
>      above.
> 
> 	Do[{
> 	     answer=gm[[k,l]][[i]]*f[k]*f[l];
>             },{k,1,n},{l,k+1,n},{i,1,Length[gm[[k,l]]]} ];
> 
>     
>      This works fine when the expression contains 2 or more terms.
>      How do I make it work (automatically) even in the case of 1
>      term in the expression?
> 
> 2).  I want to order each term in the expression by the index.
>      For example, say the expression is in alphabetical order,
> 
>            astring[3]*bstring[1]
> 
>      I want it ordered numerically 
> 
>           bstring[1]*astring[3]
> 
> 
> 3). Then in each term of the expression, I want to combine
>     the strings that refer to the same index and multiply in
>     a new string if the index is missing.  
> 
>     For example, the expression in numerical order from the
>     last step might be,
> 
>         bstring[1]*cstring[1]*astring[3]
> 
>     I want it to become
> 
> 	bstringcstring[1]*newstring[2]*astring[3]	   
> 
> 
>     To summarize:
>   
>     In Step 1 Length[expression] gives the number of terms
>     summed together in expression except when there is only 1 term.
>     I need to know how to get around that.
> 
>     The result of Step 3, merging strings with the same index, is the
>     other thing I want.  Numerical ordering of the indices is not
>     required in the result, I just thought it might make Step 3 
>     easier to accomplish.
> 
>     Thanks.
> 
>     Susan Rempe
>     rempe@u.washington.edu
> 
> 
> 




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