On Sep 18, 1:01 am, "John Cremona" <[EMAIL PROTECTED]> wrote:
> 2008/9/18 John H Palmieri <[EMAIL PROTECTED]>:
>
> > On Sep 17, 9:09 pm, "William Stein" <[EMAIL PROTECTED]> wrote:
> >> On Wed, Sep 17, 2008 at 8:59 PM, John H Palmieri <[EMAIL PROTECTED]> wrote:
>
> >> > Along the same lines, partial fraction decomposition should work for
> >> > rational numbers; this would work if elements of QQ were instances of
> >> > FractionFieldElement, right?
>
> >> Or you could just implement it, which would likely be a good idea.
>
> > It might be a good idea, but I don't know how to do it.  How do I
> > produce, given 1/20, the output 1/4 - 1/5?  That is, how do I tell
> > sage to output 1/4 - 1/5, as an element in QQ, I suppose, without
> > evaluating it and just printing 1/20?
>
> I used to set this as an exercise in my undergaduate number theory
> class.  Shall I look for my model solution ? ;)

It wasn't the mathematics I was looking for, but how to output the
answer once I find it. If Sage computes that 1/20 = 1/4 - 1/5, how do
I get it to print the expression 1/4 - 1/5 without simplifying it to
1/20?  For example, if I compute the various parts and store them in a
list 'parts', then something naive like 'return sum(parts)' won't
work. How do I return an expression made up of rational numbers, +'s,
and -'s, with no simplification?

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