[Om] Tutorial or example collection for OpenMath?

[Konrad Hinsen]

Alberto González Palomo writes:

 >    I'm not aware of any validation tool, but you can check the Simple
 > Type System (STS) used for symbol signatures in the OM CDs.
 > http://www.openmath.org/cd/sts.xhtml

Thanks, that looks interesting.

What's the status of these type signatures?  Are they part of the CD,
and thus of the standard? I don't remember seeing any reference to
them in the OpenMath Standard 2.0.

 >    For instance, arith1:sum has:
 > 
 > http://www.openmath.org/sts/arith1.xhtml#sum

That's bad news for me because it means I can't use OpenMath sums at
all for my application. Sums are defined only for Abelian monoids,
which excludes any expression containing floating-point numbers,
since floating-point addition is not associative. This is not
merely a theoretical concern as summation order definitely matters
in some of my use cases.

Exploring further, I note that arith1.plus also requires
commutativity.  Is there any CD that covers floating-point arithmetic?
OpenMath does provide floating-point numbers, so there should also be
something one can do with them.

 >    For the double sum you mentioned, that would be nested:

A bit verbose but perfectly fine - if I didn't need those floats.


Francis Wright writes:

 >> There is no definition of "range of summation", just an example. You use a set in
 >> your example, which is fine, but there's nothing in the definition of "sum" that
 >> tells me that sets are a valid specification for a "range of summation".

If by "set" you mean the use of { } in the example above then I think
that is part of the TeX syntax used to present the example and does
not imply a set.

Lars explicitly referred to set1.cartesian_product, so I do have a
set.  Reconsidering this, it wouldn't really help me because a
summation range defined by a set obviously implies that summation
order doesn't matter.


Konrad.