[Om] Tutorial or example collection for OpenMath?

[Konrad Hinsen]

Michael Kohlhase writes:

 > The OM CDs at openmath.org are made with general maths (the K14
 > fragment) in mind. They are quite vague, since they try to cover the
 > general case.
 > 
 > If you need more specific "semantics", then you can always use
 > (your own) more specific CDs. You just have to agree on them with
 > your communication partners, and you can even submit them to the
 > OpenMath Society for distribution and canonicalization.

That's always one way out, but if everyone makes their own CDs, then
OpenMath is reduced to hardly more than an XML schema for representing
expression trees. On the other hand, I see the difficulty of agreeing
on semantics for "general" mathematics. Perhaps the right level of
standardization is somewhere in between? I could well imagine
consensual yet precise semantics for a wide domain such as
"mathematical and computational physics and chemistry". Of course,
getting people in such a field to agree on anything is a different
matter.

Lars Hellström writes:

 > Users should be more disturbed by their results being inaccurate than by 
 > those inaccuracies not being fully reproducible.

Definitely. But that's pretty much my point: the inaccuracies are due
to a lack of understanding of the numerical aspects, one of which is
the frequent assumption of associativity for addition.

 > Also, didn't you state that you are now at the stage of formulating
 > models?  Surely it should be the responsibility of an
 > implementation to accurately implement a model defined with respect
 > to exact arithmetic, rather than of the model to record all quirks
 > that may turn up in an implementation.

Numerical models are the result of a sequence of assumptions and
approximations, which at some point involves the transition from exact
arithmetic to whatever the computer allows to do - and that's floating
point in most of today's computational science. There is no point in
formulating a model in exact arithmetic if it cannot be implemented on
a real-life computer.

Konrad.