[om] DefMP elements

[Professor James Davenport]

On Tue, 9 Dec 2003, Richard Fateman wrote:

> And is pi a numerical value?  How about  pi^2+e ?
> And what about sin(1)?  
> thus   sin(1)  means   sin(1)    looks ok to computer algebra systems.
> so does tan(x) means sin(x)/cos(x).  Is x a numerical value?
That is why we have the words
"Denotes an OpenMath object that is to be thought of as something that
represents a numerical value, or a numerical value". While I am not proud 
of these words, I would see that pi (as in <OMS name="pi" cd="nums1"/> is 
a numerical value, and that in <OMS name="sin" cd="transc1"/>(x), x should 
be a variable that represents a numerical value, and not, say, a matrix or 
tensor. Infinity, as you point out, is a very curious case, and I see the 
OpenMath CDs as not really legislating here,
> In a CAS, there is typically a definition for a function Q that
> looks like this:
> 
>  Q(x):=   case
In some CAS, in others the type of the argument would determine the code 
to be obeyed. 
> Q could be sin.
> 
> I'm sure that one could elaborate on the cases above; I am just writing this
> freehand.
> 
> If you insist than sin be given an explicit numerical value, you are 
> describing something like BASIC.
I certainly don't think the definition above of NumericalValue implies 
that. But if some-one comes along and defines hexonions on which their 
definition of tan(x) is not equal to sin(x)/cos(x), they cannot claim that 
the OpenMath transc1 CD is broken, since OpenMath never said that transc1 
applied to hexonions.
James
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