[om] OpenMath and Imaging

[Michael Kohlhase]

> The argument that all CAS will talk to each other in the future is
> probably
> not so convincing:   There are really very
> few  CAS and in the (somewhat unlikely) case that you really
> want to communicate between 2 of them, it is probably because
> they don't share some capability and you will have to program
> some special translation mechanisms.

Well the chance that two computer algebra systems will want to talk to each
other might not be so great, but then there is more mathematics computation
than computer algebra. For instance in the OMEGA Project[1] in Saarbr"ucken
we are routinely using computer algebra systems to help our system with
proving mathematical theorems (admittedly very simple theorems, and very
simple queries to Maple and GAP, but without being able to call CAS we
would not be able to prove them at all).

We are currently changing our communication language from POST (our home
brew) to OpenMath, in the hope to reduce communication and translation
costs. 

> Take your favorite textbook or table of integrals and see 
> how much of that can be typed in to Mathematica and via 
> MathML transmitted to Maple.  Indexing info? side-conditions?  
> provenance?  

That is true, since OpenMath concentrates on representing mathematical
OBJECTS, instead of definitions, theorems, theories, that are used in
mathematics to do these things. In the long run, OpenMath will have to
broaden its scope to include these, if it wants to be successful as a
communication langauge for mathematics. Since in the automated theorem
proving business are more tuned towards these structures anyhow (in fact
they are at the heart of our computation), we are working on an extension
of OpenMath [2] that will be powerful enough to specify the information you
are alluding to. BTW, today, you would want to encode most of this in the
OpenMath CDs (not that there is much support for doing this, but that would
be the place things should go IMO).

> But then I seem to be in a skeptical mood.

Cheer up, there is more than Computer Algebra :-)


[1] http://www.ags.uni-sb.de/~omega
[2] http://www.ags.uni-sb.de/~omega/www/projects/openmath/omdoc

     Michael
--------------------------------------------------------------------------
   Priv. Doz. Dr. Michael Kohlhase, FB Informatik,  Bau 36, Zi. 220.1
   Universit"at des Saarlandes, 66041 Saarbr"ucken, Germany    
   tel/fax: (49)-681-302-4628/2235 net: <kohlhase at cs.uni-sb.de> 
   http://www.ags.uni-sb.de/~kohlhase/
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