[Om] Upcoming OpenMath communication

Lars Hellström lars.hellstrom at mdu.se
Mon Oct 23 14:43:00 CEST 2023

Having heard no objections, James, Michael, and myself will continue as we conspired, which means that Friday next week I will give an OpenMath talk via Zoom, tentatively titled

   "Complex complex domains, 
    and self-documentation of Formal Mathematical Properties"

From a strict logical perspective those are two separate topics, but work on one inspired the other, so it makes sense to use the first as a case to be studied using the latter.

I'm expecting a mixed audience, so I'll take care to both introduce the math we'll see in the first part — concretely Riemann surfaces as domains of complex extensions of e.g. elementary functions — and the OpenMath features that we encounter; in the second part we will give attributions some (much needed?) exercise.

PRACTICAL ISSUE: Should we strive for a recurring Zoom link, or generate a new one every meeting? (Need to decide before sending out the announcement proper.)

This particular talk is traditional OM workshop material — presenting work one might publish as a paper in the workshop proceedings (had there been any of those) — but looking forward we don't have to stick to that formula. We could alternatively name a particular area as the topic for a meeting and combine surveys of best practices (or tutorials) with discussions on how to move forward.

One area I think needs some attention is that of associating notation with OM symbols. Consider the case of Dr. A. M. Athmatician, who has a history of using computers to carry out major calculations on pure math problems; recently he completed an impressive enumeration of all regular widgets of order 17 (or rather, he wrote a program that did this). Being a modern scientist in the era of Open Research Data, Dr. Athmatician seeks to adhere to the FAIR principles by having his widget-enumerating program generate the output in OpenMath format. (This isn't too hard, even without any OM phrasebook library, because OM-XML is just text with a specific recursive syntax. You could generate it even from programming languages with very primitive string processing and no dynamic memory to speak of, if you're fine with the program being as recursive as the output it is tasked with generating. (Of course, *parsing* OM is a very different matter.)) This does require inventing some new symbols to state the whole thing, but that makes sense to Dr. Athmatician: these widgets of his are rather advanced concepts, so one cannot expect a standard to have them pre-defined — there are professors at his department who don't grasp the finer points of this! Having defined new symbols, Dr. Athmatician wishes to also lay down the notation for these symbols, however for all that he looks he cannot find any documentation of how to do that… So what would our community advise Dr. Athmatician to do?

I suspect sTeX is by now quite big in how much notation it has associated to semantics, so is that how we do this nowadays, or is the de facto solution to hack XSLTs? Are we comfortable with whatever the state of the art is in this matter? What even is the state of the art? Perhaps early February we can hear some opinions on the matter. Or perhaps we will hear something else.

Lars Hellström

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