[Om] Tutorial or example collection for OpenMath?

[Lars Hellström]

Konrad Hinsen skrev 2014-02-21 16.31:
> Dear all,
>
> I discovered OpenMath a while ago and I am trying to figure out how to
> use it. The documentation looks quite complete in the sense of
> defining the meaning of OpenMath objects, but what I need is the
> inverse: find out how to encode a certain formula in OpenMath. In
> theory, I could study all the content dictionaries, but I'd probably
> give up before completing that task.
>
> So what I am looking for is either a tutorial, or at least a list of
> examples. I don't need anything particularly exotic, but I don't even
> see immediately how to express something like "a sum over all pairs of
> indices".

One resource I've found useful is the "Index of all symbols" 
(http://www.openmath.org/cdindex.html). Searching in this page has a good 
chance of turning up something relevant, even if it's in a content 
dictionary you didn't expect.

As for encoding a sum over all pairs of indices, there is the complication 
that the official OMCDs aren't fond of expressing things using binder 
symbols (even if the standard supports the concept of such), so one 
typically has to wrap the body up in a lambda before feeding it to a 
summation symbol; sort of like writing $\sum_{[a,b]} f$ rather than 
$\sum_{k=a}^b f(k)$. Thus we get

<OMA>
   <OMS cd="arith1" name="sum"/>
   <OMA> <!-- the set of pairs of indices: -->
     <OMS cd="set1" name="cartesian_product"/>
     <OMV name="my_index_set"/>
     <OMV name="my_index_set"/>
   </OMA>
   <OMBIND>
     <OMS cd="fns1" name="lambda"/>
     <OMBVAR> <OMV name="i"/> <OMV name="j"/> </OMBVAR>

     <!-- Insert expression you're summing here. -->

   </OMBIND>
</OMA>

(with reservation for typing errors) as the basic idiom for summing over all 
pairs $(i,j)$ of indices. It's the same with integrals.

Lars Hellström

> Version 2.0 of the OpenMath standard refers to "OpenMath primer" at
> http://www.openmath.org/standard/primer/, but the contents are a bit
> disappointing.
>
> For a bit of background information, I intend to use OpenMath for
> describing potential energies in molecular modelling. I am working on
> a data model for computational chemistry
> (http://mosaic-data-model.github.io/), which is to molecular modelling
> what OpenMath is to maths: a data model with multiple encodings
> designed for exchanging data between programs.
>
> Konrad.
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