[om] Re: [om-a] critique of OpenMath

[Andrew Solomon]

On Wed, Jan 17, 2001 at 02:16:58PM -0800, Richard Fateman wrote:
> For some concepts there may be only one translation. For integers I hope
> that there will be general agreement.
> 
> I don't think anyone else will be able to describe adequately what
> is meant by a Mathematica floating point number except to say that
> it is a number with inputformat ......  and it comes from Mathematica.
> In some other systems it is kind of like an interval.  It is not
> enough to point out that Mathematica's ArcTan(x,y) function is to
> most other systems atan2(y,x).  It has different semantics as to
> what to do about special values, numerical evaluation etc.  So it
> is not a common meaning shared by anyone else, in reality.
> Certainly Maple's understanding of sin(x) is not the same as (say)
> NAG's numerical version.

As Richard pointed out in previous emails, there are some 
objects in computer algebra systems which can only be
defined in a zen-like fashion by reference to the 
code which implements them. Floats in Mathematica may be such 
objects and there are probably very good internal reasons why this should 
be so. However, this should not deter us from:

a) Making definitions in OM cds which are as elegant as possible and 
as close as possible to the usual mathematical conceptualization;

b) Writing interfaces to Mathematica and other programs which
deal in these less peculiar definitions.

Surely this is the only way to
ease the process of getting different pieces of software to 
work together?

What one can deduce is that it is almost certainly not possible
to expose the full functionality of a CA system through a single OpenMath
interface since then the "internal reasons" mentioned above would
make adherence to more idealized definitions impossible.

Andrew



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