OM-services was "[om] Reference vs. Referent: solution to an old problem"

[Manfred Riem]

Hi all,

> Since I started this discussion, I think I should make my own position
> a bit clearer. 

[snip]

> 1. I don't hope to construct a computer algebra system for 
>    all mathematics or even a specification for one. I know 
>    that each computer algebra system has its own motivations 
>    and that for self consistent reasons it will define some 
>    mathematical operations differently to another CAS.

No question about that!

> 2. I believe that in the future, people will continue to do 
>    most of their computing in the specific CAS which is oriented 
>    toward their interests.
> 
> 3. I don't think that an OM CAS CD should place any constraints on
>    computer algebra systems as such. Computer algebra systems 
>    should be permitted to continue doing as they do.

A CD does not meddle with the internals of a CAS, only with how it
can be externally invoked to perform a certain function. Like
calculation, simplification, solving etc.

> 4. I do see a network of microservers with traditional CASs 
>    as possible clients: Suppose we have an algorithm which computes 
>    function f:A->B, and it hasn't been coded yet. The first thing 
>    you do will be to write it in the native code of the most 
>    appropriate CAS, say Maypole. Then when you're working in another 
>    CAS and you need the algorithm, what do you do? Code it again? 
>    and possibly a whole lot of other guff which the first system gave 
>    you for free? Of course not. OpenMath is about doing it smarter.
>    Rather, create a server running on the "OpenMath port" which 
>    is advertised in a centralized or distributed OpenMath database as 
>    computing f:A->B. This "microserver" does just that one task and 
>    does it in a way which is defined precisely by the OpenMath symbol 
>    for f. The symbol for "f" should be written with as much 
>    mathematical good will as possible, and without any particular 
>    leaning towards Maypole. This means that while the microserver does
>    computations with Maypole in the background, it might also do 
>    further processing on the result in order to obtain a mathematically 
>    clean object, perhaps even using other CAS for further processing. 
>    Then any other internet/OM enabled software can contact this 
>    microserver to have this computation done. [I just got an email from 
>    Paul, using the word "wrapper" - this certainly captures an aspect 
>    of what I'm getting at with "microserver".]

That's what I've been meaning to say all along, but the general picture
got clouded by other issues (like context etc). The function to perform
would have to be specified, described by either a CD, or something else.
Because this microserver is just delivering a service why don't we just
can it a service ;-).

[snip]

> I hope a result of this will be a bit of standard behaviour 
> (which is the power behind the networked world, after all). Remember, 
> I'm not proposing a standard across all mathematics, just a symbol 
> here and there as we need it. Ultimately it will be the people who 
> write the microservers who decide what that semantics is.
> 
> > 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.
> 
> I hope it's clear now that isn't where I was heading.

Neither was I! I was NOT suggesting one OpenMath CD, but rather a
set of CDs that would define the functions a particular service
implements and each service could have its own set of CDs, which
would have to be published at a central location.


> > If the CD requires that the results of integration be
> > cognizant of special values (e.g. to avoid dividing by
> > zero or computing log(0).) then certain CAS would have
> > to be avoided, too.
> 
> If guess this problem goes away when you stop thinking of 
> existing CASs as the servers.

See comment above, I view the CAS as a way of delivering a service,
for which you don't necessarily know which CAS is doing the job.

[snip]

> I hope that it won't be necessary to write a microserver
> for rational arithmetic, but if it is, then I hope the people who
> write it, together with the rest of the OM community can 
> agree on a behaviour, acknowledging that there's no canonical 
> answer but realizing that if we can agree on a *standard* answer, 
> we'll all be better off.

Agreed, and shouldn't that be defined by an OpenMath CD then?

[snip]

> > 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.
> 
> I hope we can make it helpful.

As am I, it's all in the world of services, which do a job
for you, so that you don't have to do it from scratch!

Manfred.

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