Decomposition of rationnal fractions



Nicolas FRANCOIS wrote:

> Le Thu, 13 May 2010 23:05:12 +0100,
> Jaime Villate <villate at fe.up.pt> a ?crit :
> 
>> On Thu, 2010-05-13 at 23:00 +0100, Jaime Villate wrote:
>> > (to obtain its formal series equivalent \sum a_nX^n, a_n being the
>> > > number of ways to pay n? using 1, 2 and 5? corners (no, there
>> > > is no such thing as a 5? corner, but there's a 5? banknote !)).
>> Oops, sorry; I did not read this part before my previous reply to your
>> message. Then the partial fractions expansion that I told you is not
>> what you need.
> 
> Yes it is, and I'm aware of the partfrac function. My problem is it
> does only work in Q[X] : I would like to force the use of complex
> roots, to decompose 1+x+x^2+x^3+x^4 into a product of factors X-w,
> where w is one of the fifth roots of 1 distinct from 1.
> 
> So my question is : is there a way to work in an extension of Q(X) ?
> 
> \bye
> 

You can work in an extension by first using "factor" in an extension.
For example:

(%i6) factor(x^4+1,w^2+1);
                                 2        2
(%o6)                          (x  - w) (x  + w)

So all you need is first adjoint the appropriate roots.


--

Michel Talon