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## Re: [Axiom-math] Decomposition of rationnal fractions

 From: Raymond Rogers Subject: Re: [Axiom-math] Decomposition of rationnal fractions Date: Thu, 13 May 2010 20:16:21 -0500 User-agent: Thunderbird 2.0.0.24 (X11/20100411)

I don't know about a specialized solution (outside of Taylor series),
but as I recall making change and counting such is the first example in:
http://www.msri.org/communications/vmath/special_productions/production1/index_html
Sturmfel's excellent elementary introduction to Grobner Bases; which
Axiom does have support for.

Ray

Nicolas FRANCOIS wrote:
> Hi.
>
> Is there any way to obtain the decomposition in simple elements (don't
> know exactly how to say this in english) of a fraction of the form :
>
>           1
>   -------------------
>   (1-X)(1-X^2)(1-X^5)
>
> (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 !)).
>
> I'd like to obtain the C-decomposition, what do I have to do ?
>
> More precisely : is there a way to force the use of an extension of
> Q(X), by adding roots like exp(2*I*PI/5) or sqrt(2) ?
>
> \bye
>
> PS : clearly I'm not very good at using Axiom documentation !
>
>