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Re: Rearranging the Terms of a Polynomial

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  • Subject: [mg131325] Re: Rearranging the Terms of a Polynomial
  • From: David Bailey <dave at removedbailey.co.uk>
  • Date: Fri, 28 Jun 2013 04:14:33 -0400 (EDT)
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On 27/06/2013 11:23, PiMan wrote:
> Hi, I have another formatting question.
>
> I have a polynomial as the output of an expression, and I would like to rearrange the terms of the polynomial in the output.  The current output I am getting is x1*x3-\[Alpha]2*x2-x3.  However, I wish the output to read x1*x3 - x3 - \[Alpha]2*x2, that is, rearrange the second and third terms.  Does anyone have an idea of how I might be able to do this for this polynomial or any polynomial in general?  Thanks.
>
Your desired form seems to already be the canonical form coming out of 
Mathematica, so let me answer this question more generally.

Mathematica always rearranges sums and products of terms into one form. 
This makes it easier for it to do algebra, but can be a nuisance, as you 
have found out. There are lots of ways to rearrange terms, but their 
effects are instantly cancelled out if you apply them directly to such 
expressions. For example:

expr = Series[Exp[x], {x, 0, 5}] // Normal

Out[6]= 1 + x + x^2/2 + x^3/6 + x^4/24 + x^5/120

In[7]:= Reverse[expr]

Out[7]= 1 + x + x^2/2 + x^3/6 + x^4/24 + x^5/120

The key to manipulating such expressions into a desired form, is to use 
Hold or HoldForm to stop all evaluation (which includes rearrangements). 
Thus, to rearrange the contents or expr ( polynomial) you can do:

In[8]:= Reverse[Hold[Evaluate[expr]], 2]

Out[8]= Hold[x^5/120 + x^4/24 + x^3/6 + x^2/2 + x + 1]

Notice that Hold[expr] wouldn't even evaluate expr - which is why I used 
Evaluate - you can also use With to achieve something similar.

Hold is easy to use when exploring this sort of process, but once you 
understand what you are doing, you may want to switch to HoldForm. This 
works the same way, but HoldForm doesn't actually show, so the output 
looks nicer. You just need to understand clearly that expressions 
wrapped in HoldForm may look the same as normal ones, but won't evaluate 
properly in expressions unless you remove that outer wrapper.

Finally, you can even create your own wrapper to make things more 
explicit, e.g.

SetAttributes[wrapped,HoldAll]

David Bailey
http://www.dbaileyconsultancy.co.uk




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