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