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Re: [Axiom-developer] Re: hyperdoc

From: C Y
Subject: Re: [Axiom-developer] Re: hyperdoc
Date: Fri, 14 Jan 2005 17:57:21 -0800 (PST)

--- root <address@hidden> wrote:

> > Do you have any experience with OpenMath?
> The point of debate with openmath is as follows... Consider axiom and
> maple or mathematica. Ideally openmath would allow you to take an
> axiom expression, export it to maple, and get back an answer so that
> the computation was transparent. But in Axiom most of the semantics 
> of an equation is embedded in the type. Thus, 
>  x:POLY(FRAC(INT)):=1
> is not the same as
> or 
>  x:FRAC(POLY(INT)):=1
> or any other variation. I don't know how to design a
> system-independent way that Maple can take an axiom computation 
> involving 'x' and return the correctly typed result. 

In fact, might this not in fact be impossible in general, since Maple
won't be keeping track of the things Axiom wants to know?

Perhaps I'm wrong, but I always thought the fundamental problem with
OpenMath was it assumed a feature and logical lineup within all CASs
that doesn't seem to exist.

That's one of the things I'll be interested to see how CATS deals with
- there (as I understand it, please correct me if I'm wrong Tim) the
goal is not to be able to swap inputs and outputs, but to have as
nearly as possible the same question posed, and see if the systems
agree mathematically?

> In fact, until we get our act together it is not always clear what 
> the return type of an expression will be even within axiom. 
> Eventually we will write out the coerce/convert tree and
> be able to tell, of course, but that won't help us with openmath.

That will be an impressive accomplishment. :-)

Thanks as always guys for your hard work!


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