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## [Axiom-developer] Re: [Axiom-mail] beginner question about sum(...)

 From: Martin Rubey Subject: [Axiom-developer] Re: [Axiom-mail] beginner question about sum(...) Date: Wed, 2 Feb 2005 10:08:44 +0100

```Kostas Oikonomou writes:
> Hello Martin,
>
> course the sum 1/(k*(k+a)) is hypergeometric. And indeed Axiom evaluates it
> if you give "a" a positive integral value.  Now wouldn't you expect that if
> you declared "a" to be a positive integer the summation would be evaluated?
> It is not.  Instead Axiom says that "a" has not been given a value.

This is correct. In fact, this is a good example: Gosper's algorithm cannot
work with "indefinite" values. It needs the value, not only the information
that "a" is an integer or whatever.

> situation.  That if you make a certain type declaration, you would expect
> Axiom to act accordingly, but it does not appear to do so.

No it does not, by design. Declaring "a" to be of type Integer tells axiom that
the memory slot "a" will contain an Integer, i.e. a number.

There is a proposal (on the WishList) to provide for domains like Indefinite
Integers, thus enabling assumptons in Mathematicas sense.

In fact, there has been done a lot of work already, but it appears that the
code is lost: I recently sent a mail to address@hidden,

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If you happen to know how Mathematica, Maple or MuPad handle these sums, please
share your knowledge and add an appropriate entry on the WishList on
Mathaction.

If you happen to be mainly interested in hypergeometric sums, there is such an
entry already: porting Christian Krattenthalers Mathematica packages Hyp and
Hypq to Axiom. I think that this would not be too difficult, once you decided
on an appropriate design. Note that Krattenthalers package is quite
interactive, which is not Axioms style. On the other hand, hypergeometric
functions clearly form a domain, which is not Mathematicas style...

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Concerning Mathematica versus Axiom: I don't think that Axiom can serve as a
replacement for Mathematica. However, maybe you can use Axiom for some tasks
(especially programming) and Mathematica for those Axiom cannot handle yet.

In some areas, I'd say that Axiom is superior to any of the available CAS, with
the exception of MuPad maybe. For me, the greatest advantage of Axiom is its
programming language, especially the Aldor dialect.

Martin

```