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

[Andreas Strotmann]

On Thu, 18 Jan 2001, Andrew Solomon wrote:

> 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.
> 
> 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?

I agree completely here, Andrew.  Indeed, from the OpenMath exercises that
I have been doing with by now about half a dozen implementations of
subsets of OpenMath functionality in a very diverse set of systems I can
report that it always takes some effort to fix bugs or circumvent features
of these system wrt. their "understanding" of maths.  I can also report
that it is quite possible to get such a diverse group of systems to
actually understand the same thing (in a global sense) for given formulas,
provided their actual mathematical concepts are sufficiently clear.

This will usually take some reformulation.  As an example, in one
implementation I needed to rephrase equations produced by Maple that
involved expressions of the form x = root_of(p(x)) into equations of the
form p(x) = 0.  This kind of semantic adjustment is more than likely to be
necessary when importing or exporting OpenMath (in whichever syntactic
form it might come).

So, the point of OpenMath is not to make every system understand all the
minutiae of Mathematica, Maple, MuPad, REDUCE,...  -- an obvious n^2
problem.  The point is to have these systems speak a common language with
common meanings even if the translation will require some work on all
sides.

Incidentally - exposing the full functionality of any given CA system via
OpenMath would be trivial.  Just define, say, a Mathematica CD (plus one
each for all the Mathematica packages out there) listing the symbols
Mathematica knows.  OpenMath explicitly does not do that, because that's
not its point.


   --  Andreas


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