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Re: Re: Getting the small parts right or wrong. Order and Collect

  • To: mathgroup at smc.vnet.net
  • Subject: [mg63649] Re: [mg63631] Re: Getting the small parts right or wrong. Order and Collect
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Mon, 9 Jan 2006 04:48:25 -0500 (EST)
  • References: <dpg11e$pm4$1@smc.vnet.net> <dplhq9$em8$1@smc.vnet.net> <200601070729.CAA06924@smc.vnet.net> <6FCF3227-C4E1-418A-BAC1-F3981F969878@mimuw.edu.pl> <dpo3gp$gaq$1@smc.vnet.net> <200601080832.DAA02327@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 8 Jan 2006, at 17:32, Richard Fateman wrote:

>
> "Andrzej Kozlowski" <akoz at mimuw.edu.pl> wrote in message
> news:dpo3gp$gaq$1 at smc.vnet.net...
>> On 7 Jan 2006, at 18:04, Andrzej Kozlowski wrote:
>>
>>>
>>>
>>> There is one very simple thing you can do, which I think completely
>>> deals with your problem.
>>> You can convert the output to TraditionalForm.
>>>
>
> No,  because TraditionalForm is only a hack on the display.  If you  
> pick
> out the parts of the expression in sequence by  using %[[1]]   etc,  
> you find
> that the coefficients of the different powers of x  are picked out  
> in the
> StandardForm order, not the TraditionalForm order.

What's "right" and "wrong" here is a matter of opinion. In my opinion  
there is nothing wrong with what Mathematica does here.  I assumed  
you were concerned with "typesetting' and in this respect Mathematica  
behaves correctly in TraditionalForm.
Since I always work with TraditionalForm for display I have no  
problems here.
On the other hand I would never try to pick terms of a polynomial  
with %[[1]] as you suggest. This is indeed "entirely wrong". The  
"right" thing is, of course,  to use Coefficient or for this sort of  
thing CoefficientList. Please observe carefull:


CoefficientList[(1 + x + y)^3, x]


{y^3 + 3*y^2 + 3*y + 1, 3*y^2 + 6*y + 3, 3*y + 3, 1}

Who needs all the typing? Now you can pick terms as you like.  You  
can even Reverse the list. The only thing you can't do is Apply Plus:  
which is of course what I though you wanted to do, for typesetting  
reasons.


>
> Putting the coefficients in an array is plausible, but Andrzej other
> solution, which
> is 1 + Plus @@ Table[Coefficient[(1 + x + y)^3, x^i]*x^i, {i, 1, 3}]
>
> is wrong because it results in answers in the order 1, x^3, x^2, x.
> And of course picking out the coefficient of "1".

Of course I only suggested this assuming you were working in  
TraditionalForm, like I do, and were concerned with the way things  
looked.

>
> Along those lines it is
> better to do ... Table[Coefficient[(1+x+y)^3,x,i] ,{i,0,3}] where i  
> can also
> be 0.
> And the table keeps the coefficients from being randomly sorted.
>
> "Of course there is no way to make the powers of x ascend as you
> originally seems to have wanted but then we can't have everything
> even where Mathematica is concerned."    Eh, this one can be solved
> with Table and Coefficient.  It is just that the EXAMPLE IN THE BOOK
> is the mistake.
>

All of the above is a waste of time and effort  because the obvious  
thing to do is to use CoefficientList.

Andrzej Kozlowski


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