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

[Paul Libbrecht]

On Tuesday, December 12, 2000, at 05:30 PM, Richard Fateman wrote:

> I could not parse the note from Paul Libbrecht, but the point as 
> taken up by Manfred Riem suggests that the OpenMath CD is going 
> to include a specification of all algorithms, and that CAS 
> are free to either implement them or not.  Thus by carefully 
> specifying certain operations, one could exclude certain CAS 
> implementations entirely. Gor example a reasonable spec 
> for floating-point operations would either have to exclude 
> all arithmetic of Mathematica or all of Maple, since their 
> models are, I believe, incompatible.   

But one could mention a precision context-variable which might make them compatible. Is it too stupid ??

Being exclusive on the implementations will be timed-bomb I believe
(don't we want some implementations, at least of wrappers ?)

>   Since people who have better ideas than either of 
> these do not always agree, what is the role of OpenMath, 
> to state what is correct? 

It should be "semantically" correct.
(this is what has to be defined and where OpenMath can reign)

> 1. CAS even disagree on whether x+1 or 1+x is simpler. 

But not when used "as a polynomial".

> 2. For fun, assume that my indefinite integration program 
> always returns the same as yours, except that I add to 
> the result  C=(arctan(x)+arctan(1/x)).   Does my 
> program conform to the same openmath CD? 

The good questions are starting.
I hope it becomes possible that this ambiguity is covered by a simplification of some sort.

> Note that derivative of C wrt x is 0 in any CAS. Therefore 
> it must be a constant, and one can always add a constant 
> to the result of indefinite integration, right?. But it is not. 

This ambiguity is exactly what has to be specified by an "indefinite integration" operation.

> Plot it. 

Ah, come on, that's user related ;>>

> I also think it is unreasonable to 
> expect that some small group of essentially 
> self-appointed standardizers will be able to 
> dictate an abstract specification to which  
> programmers must comply. 

I have the feeling some implementors are not too far away,
that makes the view more valid.

> If I wanted to actually do a computation, I 
> would undoubted choose  
> the most appropriate single 
> ONE computer algebra system X  
> for nearly all the computations.  If I decided 
> I needed another facility only  in some other computer 
> algebra system Y, I would have to study that 
> computer algebra system carefully, and see 
> if the facility was what I wanted.  Studying 
> the OpenMath CD would probably not be helpful, 
> according to what I've just read here. 
Hopes...

Paul
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