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

[Andrew Solomon]

Dear Richard, 

Thank you for your comments.

Richard Fateman wrote:
> 
> I think it is a mistake to define any behavior whatsoever
> in "an open math compliant CAS" other than its results syntactically
> correspond to a certain grammar.

Let's leave aside for the moment the question of *what label* defines CAS
behaviour, whether it be "openmath compliant CAS" or "Andrew compliant CAS"
and refer back to the big picture to see that it is desirable to have
*some label* defining CAS behaviour.

The Big Picture: It's 2002 and I'm sitting back playing with my new 
version of OMGAP-i 1.0 (OpenMath compliant and Internet enabled). 
I've just got an enormous characteristic polynomial from of a matrix
and when I type "Factorization(p)" OMGAP-i knows full well it doesn't
have a chance of doing the job in a reasonable time frame and 
would be better off subcontracting the job to a more specialized polynomial engine.  
So, OMGAP-i hits openmath.napster.com asking for the nearest OM server which does
[cd="PolyZ" name="Factorization"], and gets a selection of servers to try. The
one it chooses is cas.maple.com (but it could have been cas.mathematica.com).

OMGAP-i asks cas.maple.com to evaluate the object:

<OMOBJ>
  <OMA>
    <OMS cd="cas" name="referent"/>
    <OMSTR some/>
    <OMA>
      <OMS cd="polyZ" name="Factorization"/>
      < the polynomial >
    </OMA>
  </OMA>
</OMOBJ>

and gets back an openmath list of polynomials which are irreducible factors of p.

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.
 
> In the particular example, changing 3! to 6 is certainly not
> a required, compulsory, or necessarily desirable transformation.

I don't see what else 3! refers to. If you want to 
keep 3! then you can simply not ask for the referent.
i.e 
3! = [cd="integer1" name="factorial"](3) 
while
[cd="cas" name="referent"]([cd="integer1" name="factorial"](3)) = 6

> 
> Transmitting the concept of 3! is NOT the same as transmitting
> the concept of 6.  consider:
> 
> x+x^2/2+x^3/6+...  versus    x+x^2/2+x^3/3!+ ...

I completely agree. I don't understand what you're getting at here.

Andrew


-- 
PIMS/MITACS/CECM                       http://www.cecm.sfu.ca
Simon Fraser University
Personal homepage:                     http://www.illywhacker.net

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