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MathGroup Archive 2005

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Re: Re: Re: how to have a blind factorization of a polinomial?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54192] Re: [mg54151] Re: [mg54123] Re: how to have a blind factorization of a polinomial?
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Sun, 13 Feb 2005 00:21:24 -0500 (EST)
  • References: <cud789$2t3$1@smc.vnet.net> <cuf453$gfb$1@smc.vnet.net> <200502110833.DAA09170@smc.vnet.net> <200502120656.BAA21687@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 12 Feb 2005, at 06:56, Andrzej Kozlowski wrote:

> On 11 Feb 2005, at 08:33, foice wrote:
>
>> On Thu, 10 Feb 2005 07:57:23 +0000 (UTC), "Jens-Peer Kuska"
>> <kuska at informatik.uni-leipzig.de> wrote:
>>
>>> Sqrt[x + y] /. a_ + x :> x*(a/x + 1)
>> Thanks for your help. Probably is a viable method, but is a little
>> less than you expect
>> for a WorldWideFamous software as Mathematica.
>> In this way you can chose the form of the output, you can also do
>> mistaques typing
>> something like
>> Sqrt[x^3 + y^2] /. a_ + x :> x^3*(a/x + 1)
>> and mathematica will not prevent you from the error giving an output
>> in the form
>> Sqrt[x^3*(y^2/x+1)]
>>
>> Is mathematica so feature poor to allow only a "requested form"
>> factorization?
>> I can't belive it.
>> Why there isn't somethig as Collect but that can use also negatieve
>> powers to collect?
>>
>> i.e. Collect[x+y,x,Blind] giving x(1+y/x)
>>
>> Or better, at least for my task, a Mathematica command converting a
>> function f(x,y) into a
>> function f(x,y/x) (if possible)
>>
>> Thanks
>>
> Such a function does not exist because there are infinitely many
> similar "factorizations" that might be useful to some users but not to
> 99% of others. Besides, it is easy to define it yourself:
>
> CollectBlind[expr_, {x_, y_}] := Block[{
>      u}, MapAll[Factor, (expr /. y -> u x)] /. u -> y/x]
>
>
> Then
>
>
> CollectBlind[x + y, {x, y}]
>
>
> x*(y/x + 1)
>
> and also, for example,
>
>
> CollectBlind[x^2 + y, {x, y}]
>
>
> x*(x + y/x)
>
>
> CollectBlind[x^2 + y, {x^2, y}]
>
>
> x^2*(y/x^2 + 1)
>
>
>
> Andrzej Kozlowski
> Chiba, Japan
> http://www.akikoz.net/~andrzej/
> http://www.mimuw.edu.pl/~akoz/
>
>
>

I just noticed that my definition of CollectBlind does not work 
properly in the case Sqrt[x^3+y]. The reason and the fix are possibly 
interesting. The definition I gave above was:

CollectBlind[expr_, {x_, y_}] := Block[{
      u}, MapAll[Factor, (expr /. y -> u x)] /. u -> y/x]


This will work fine in cases like:


CollectBlind[Sin[x^3 + y], {x^3, y}]


Sin[x^3*(y/x^3 + 1)]


CollectBlind[f[x^3 + y], {x^3, y}]


f[x^3*(y/x^3 + 1)]

But not for:


CollectBlind[Sqrt[x^3 + y], {x^3, y}]


Sqrt[x^3 + y]

It actually works as an intermediate step, but the last use of Factor 
returns the expression to the original form:



Factor[Sqrt[x^3*(y/x^3 + 1)]]


Sqrt[x^3 + y]

So we need to change the definition as follows:

Clear[CollectBlind]

CollectBlind[expr_, {x_, y_}] := Block[{
      u}, Map[Factor, (expr /. y -> u x), Infinity] /. u -> y/x]

Now


CollectBlind[Sqrt[x^3 + y], {x^3, y}]


Sqrt[x^3*(y/x^3 + 1)]

Of course the name CollectBlind is terrible, I only used it because 
that was what the original poster wanted.

Andrzej Kozlowski


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