Re: [Axiom-mail] Type of Expression Problem

[Martin Rubey]

Hans Peter Würmli <address@hidden> writes:

> But even checking that some summand is a hypergeometric term causes the
> greatest pain. So in fact, the last thing I tried was trying to check wether
> a quotient
> 
> F(n-1,k)/F(n,k) ,
> 
> primarily given by an Expression Integer could be "coerced" / "converted" / 
> "retracted" (certainly not) to, say, a 
> 
> Fraction Polynomial Integer.

Indeed, "retractIfCan(argument)@Domain" is your friend. What it does is to
check whether "argument" can be regarded as an element of "Domain".

Well, in this particular case not quite, since you want rationality only in
k, and unfortunately there is no such domain in Axiom...

To see how it is done see the function notRF? in combfunc.spad.pamphlet.

A suggestion: as you probably know, Gospers method is already implemented in
Axiom. Maybe you could implement a simple version of Zeilbergers algorithm?
Very similar problems are involved, and the mathematics are no more difficult.

If you do, you will need to have a method of representing recurrences, with
which I can help.

Martin