Re: "They Use ∂ Differently in Math and Physics. Which is Better?"

On 20/06/2024 15:21, Deyan Ginev wrote:
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Hi Abbas, all,

Interesting additions, thank you.

For k-forms, since those are "differential forms", I wonder if the use already fits in the conventions described in the video.

I see you are referring to overloading the notational use of "∂" with the boundary example in homology.
I wasn't familiar with it until now, wikipedia has a nice overview here:
https://en.wikipedia.org/wiki/Homology_(mathematics)#Construction_of_homology_groups

Different "named concept" uses of ∂ would be relevant additions for the Intent Open list, especially in cases where - quoting you - "it would be nice to say boundary". That is useful for accessibility.

The original youtube video is closer to the OpenMath questions, as it reveals how an operator with the appearance of full formalization - "partial derivative" - may represent (at least) two different formal definitions.
In OpenMath terms, one could have cast the video exposition as two symbols "convention-m:partial-derivative" and "convention-p:partial-derivative".

But I doubt generator tools can realistically infer these without some very purposeful additional help from authors - such as a brand new notational convention.

Deyan


On Thu, Jun 20, 2024 at 8:56 AM Abbas Jaffary <abbas.jaffary2@gmail.com<mailto:abbas.jaffary2@gmail.com>> wrote:
Very interesting!  There is also the differential geometry use of derivatives as one-forms (and k-forms), and the as boundary operator in algebraic topology. In homology, for example, one could likely infer "partial x" as the "boundary of x", though it would be nice to have it say "boundary".

I imagine there will be some crowdsourced effort to accommodate the most popular use cases for fundamental symbols.  Not sure where OpenMath is with this?

On Wed, Jun 19, 2024 at 8:49 AM Deyan Ginev <deyan.ginev@gmail.com<mailto:deyan.ginev@gmail.com>> wrote:
Hello everyone,

I stumbled on a very well-made exposition video, which covers a subtlety in the meaning of  "partial derivative" between mathematics and physics:

https://youtu.be/QFHSHhpbo00


Aside: This topic is not directly related to current conversations about derivative syntax for "intent".

Instead, the presenter has some well-reasoned general discussion, a community proposal for adding yet-another notation, and showcases some of the problems that our generator tools also face when trying to infer Content MathML expressions from human-authored math syntax.

Greetings,
Deyan

use of ∂  for boundary (read as "boundary") is already flagged in an example in the draft open concept list

https://w3c.github.io/mathml-docs/intent-open-concepts/#boundary1function


this list of course is never complete or correct but it's a start....

David






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