[om] Reference vs. Referent: solution to an old problem

[Paul Libbrecht]

Sir Andrew,
All,


I think this need for a kind of standardization of CAS systems seems fair.

After all, the formulation in OpenMath seems appropriate as sooner or 
later a "mathematical reality" will have the same semantics the  CAS 
operations. Just read the start of all good books, the operations 
like simplifications, equality, solutions and so on are all defined 
in a very precise manner (eg the "solution" to a differential 
equation, or the sum of two polynomials, or the cartesian product of 
two topological spaces).

The thing is... indeed... no two books are the same in their start 
just as OpenMath doesn't necessarily define a polynomial as a 
sequence of numbers, a function in the generated ring of x and the 
base-field or as... a syntactic writing.

So accepting OpenMath can only carefully set the standard in a world 
where still the cultures are a bit different... it really seems that, 
from Computer Algebra Systems, we can't expect a uniform result.

And that's my only point here. For a CD on elementary 
openmath-objects- mutations, I'd twice vote yes. But just as OpenMath 
needs to be made on a consensus, this CD describing operations will 
need to be made on a consensus and I definitely feel the implementors 
of these CAS systems will feel like worried or concerned.

The latter point is a great thing, actually, that could shake them 
sufficiently (or get them indifferent completely, who knows). One 
thing seems sure for me, MathML with its lack of semantics is lost 
there (whereas many CAS implementors think it is the way). That could 
very well be the revenge of OpenMath.

Go ahead Andrew, you've got my vote and I might even spend some time on it...

Paul


At 11:34 -0800 08/12/00, Andrew Solomon wrote:
>I think that if one subscribes to this view of the future, then it's necessary
>to have *some* way to define, in a standard way, the behaviour of a
>compute engine which is part of this cooperative network. Whether you want to
>define this system/standard with OpenMath CDs (like the CAS CD)
>seems to me to be a matter of taste, but to my mind, to exclude this kind of
>work from the OpenMath effort would be bizarre since I thought it 
>was one of the goals
>of OpenMath.
>
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