Re: Simplification to Partial Fractions
- To: mathgroup at smc.vnet.net
- Subject: [mg59700] Re: [mg59676] Simplification to Partial Fractions
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Thu, 18 Aug 2005 00:16:33 -0400 (EDT)
- References: <001c01c5a383$320181d0$6901a8c0@JonathanPalmer>
- Sender: owner-wri-mathgroup at wolfram.com
I don't think you will be able to do it since your representation is
not unique. Given your u2 you can produce lot's of different
representations of the form u1. For exmple, here is another one:
(B*(x^2 - 3*y^2)*(x^2 + z^2) + C*(y^2 + z^2)*(x^2 + z^2) +
D*(5*x^4 + 2*z^2*x^2 + z^4))/(x^2 + z^2) + A -
(4*(D*x^4 + C*y^2*x^2 + D*y^2*x^2 - B*y^4 + C*y^4))/(x^2 + y^2) +
(4*C*y^4)/(y^2 + z^2)
It is less nice than yours but has "the same form". In order to be
able to reverse the process of expanding your original expression
should be in some sense unique (unless you want to find all such
representations, which will probably be computationally v. hard) and
unless you can specify more usable information this won't be possible.
Andrzej Kozlowski
On 18 Aug 2005, at 01:27, Jon Palmer wrote:
> At first glance I can't make PolynomialReduce do what I need.
>
> Here is an example problem. Take the expression:
>
> u1 = A + (B*(x^2 - y^2)^2)/(x^2 + y^2) + (C*(y^2 - z^2)^2)/(y^2 +
> z^2)
> + (D*(-x^2 + z^2)^2)/(x^2 + z^2)
>
> Now
>
> u2 = Factor[u1]
>
>
>
> How do you Simplify u2 back to the form of u1?
>
> Many thanks
> Jon Palmer
>
>
>
>
>
>> -----Original Message-----
>> From: Andrzej Kozlowski [mailto:akoz at mimuw.edu.pl]
To: mathgroup at smc.vnet.net
>> Sent: Wednesday, August 17, 2005 11:14 AM
>> Subject: [mg59700] Re: [mg59676] Simplification to Partial Fractions
>>
>>
>> On 17 Aug 2005, at 10:00, Jon Palmer wrote:
>>
>>
>>> I was wondering if someone can help with a Partial Fraction problem.
>>>
>>> I have a calculated expression, u, which is a quotient of two
>>> polynomials in
>>> three variables x, y & z.
>>>
>>>
>>> u = P(x,y,z)/Q(x,y,z)
>>>
>>>
>>> I know that the quotient, when simplified, is a sum of partial
>>> fractions of
>>> the form
>>>
>>> u = R(x,y,z) + S(x,y,z)/(x^2 +y^2) + T(x,y,z)/(y^2 +z^2) + U
>>> (x,y,z)/(z^2
>>> +x^2)
>>>
>>>
>>> Is there a way to simplify the expression into the parial fraction
>>> form?
>>>
>>> I have tried various combinations of Simplify, Apart, Collect etc.
>>> and can't
>>> find a method that works. Any help would be much appreciated.
>>>
>>> Thanks
>>> Jon Palmer
>>>
>>>
>>>
>>
>> It should be possible to do this using PolynomialReduce but you would
>> have to post the actual problem before I could tell for sure.
>>
>> Andrzej Kozlowski
>>
>
>
>