Re: [EXTERNAL] Re: New writeup for intent examples

Note \varpi has been called \pomega by some people. (Re: Deyan's example)

The fundamental point is that very few symbols have anywhere
near unique mathematical semantics, whether this is a question
of tokens commonly used as variable names or as operators.

Patrick


On Thu, Nov 12, 2020 at 12:52 PM Neil Soiffer <soiffer@alum.mit.edu> wrote:

> The article is definitely WAY above my pay grade. Those are good examples.
> At the bottom of page one, the authors do distinguish between the double
> struck 'd' and the regular 'd', but you are correct that they both refer to
> a derivative -- one apparently is for a scalar and the other for a field.
> Not sure how one would distinguish that in speech other than to pronounce
> the double struck 'd' as such, and not as 'd' or 'differential d'.
>
> One other interesting thing is that early in the article they say
> "...here called ϖ (pronounced ‘var-PIE’)". That shows up in equations 7, 8,
> and 9. I believe that your proposal will handle this, but I felt this is a
> nice real world example where the authors say how to pronounce it.
> Hopefully if written in TeX, a marco is used that can get transferred into
> the MathML.
>
>     Neil
>
>
> On Thu, Nov 12, 2020 at 8:37 AM Deyan Ginev <deyan.ginev@gmail.com> wrote:
>
>> Hi Murray, all,
>>
>> If we could reliably defer to Unicode to provide all mathematical
>> intent for single glyphs, that would have been one task less to
>> consider, but of course that's not something we can commit to.
>>
>> An ascii "d" should be possible to remediate as a differential,
>> without requiring the authors to use the double-struck style.
>>
>> Similarly we can't expect separate Unicode entries for all
>> mathematical operations that use arrows, vertical bars, and even other
>> single letters. E.g. in lambda calculus one finds a "λx" that serves a
>> very similar purpose to "dx" (or "ⅆx"), but we only have one Unicode
>> lambda.
>>
>> So it would be nice if we can get to a place where we don't need to
>> re-examine Unicode reliance as a primary mechanism in the a11y spec.
>> Narrating the glyph is the baseline fallback, but taking it further
>> should be well-qualified in some limited scope of defaults, such as
>> subject areas (if we end up introducing such mechanisms).
>>
>> To get a real world example with fully developed complexity, take a
>> look at equations (1) through (9) on page 2 of this arXiv PDF:
>> https://arxiv.org/pdf/1804.01919.pdf
>>
>> You will find both "d" and "ⅆ" used as differential-d in integrals,
>> and you will also separately find both used as variables in the
>> equations for differential forms (which btw are way above my own
>> paygrade). They even make this distinction explicit in the same page -
>> the unicode glyph stands for "the deRahm differential", while the
>> simple d is used for "the space-time differential".
>>
>> All to say that we shouldn't over-rely on the unicode glyphs
>> themselves as a primary "intent" mechanism.
>>
>> Greetings,
>> Deyan
>>
>>
>> On Thu, Nov 12, 2020 at 10:27 AM Murray Sargent
>> <murrays@exchange.microsoft.com> wrote:
>> >
>> > The intent is conveyed in both cases by using 2146 for the d.
>> >
>> > Get Outlook for iOS
>> > ________________________________
>> > From: David Farmer <farmer@aimath.org>
>> > Sent: Thursday, November 12, 2020 4:05:52 AM
>> > To: public-mathml4@w3.org <public-mathml4@w3.org>
>> > Subject: [EXTERNAL] Re: New writeup for intent examples
>> >
>> >
>> > I'll repeat a point I made earlier about integrals with a
>> > weight function.
>> >
>> > The following expression is natural in the context of Chebyshev
>> > polynomials (similarly for any set of orthogonal polynomials):
>> >
>> > \int_{-1}^1 f(x) \frac{dx}{\sqrt{1-x^2}}
>> >
>> > The " 1/\sqrt{1-x^2} " is distinguished.  A similar situation
>> > arises in integral transforms.
>> >
>> > I suggest these "weighted integrals" should have a way of denoting
>> > the weight.
>> >
>> >
>> > I'd like to know how Sam's  "Differential alone in the numerator"
>> > compares to
>> >
>> > \int_0^1 \frac{1}{x^2 + 1} dx .
>> >
>> > Does that have the same intent?
>> >
>> >
>> > On Wed, 11 Nov 2020, Neil Soiffer wrote:
>> >
>> > > I figured I should read more carefully what you wrote in
>> > >
>> https://nam06.safelinks.protection.outlook.com/?url=https%3A%2F%2Fmathml-refresh.github.io%2Fmathml%2Fdocs%2Fintent.html&amp;data=04%7C01%7Cmurrays%40exchange.microsoft.com%7Ccedd31445d00400b07b508d887035c21%7C72f988bf86f141af91ab2d7cd011db47%7C0%7C0%7C637407795789448872%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&amp;sdata=k3yMvi3zTKaDzc0gGXyfHusMMI7omdNYO2e4we%2BkQUk%3D&amp;reserved=0
>> even though you hadn't done an update yet.
>> > > In case you didn't fix it, the MathML for "Binomial as stacked
>> numbers" is not right. Probably you
>> > > want it to be an mfrac, but an mtable could also be used. Kind of
>> garbled in the version I read.
>> > >
>> > > I still don't like the way you handle plus/minus, but that's not
>> really a criticism of the intent
>> > > idea...
>> > >
>> > > I don't think the "Differential alone in the numerator" is correct.
>> The 'intent' on the mfrac should
>> > > block the higher level intent from seeing the 'x' inside it. Further,
>> the 'x' should not be in an
>> > > <mtext>. Same issues for the next differential examples.
>> > >
>> > >     Neil
>> > >
>> > >
>> > >
>> > >
>> > > On Wed, Oct 21, 2020 at 12:41 PM Sam Dooley <samdooley64@gmail.com>
>> wrote:
>> > >       Hello all,
>> > >
>> > >       Regrets for tomorrow's meeting, I will be having cataract
>> surgery.
>> > >
>> > >
>> https://nam06.safelinks.protection.outlook.com/?url=https%3A%2F%2Fmathml-refresh.github.io%2Fmathml%2Fdocs%2Fintent.html&amp;data=04%7C01%7Cmurrays%40exchange.microsoft.com%7Ccedd31445d00400b07b508d887035c21%7C72f988bf86f141af91ab2d7cd011db47%7C0%7C0%7C637407795789448872%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&amp;sdata=k3yMvi3zTKaDzc0gGXyfHusMMI7omdNYO2e4we%2BkQUk%3D&amp;reserved=0
>> > >
>> > >       On the plus side, I did my homework, and created a new document
>> to describe as best I
>> > >       can what I believe is the latest consensus on the intent
>> attribute.  Not the final word,
>> > >       as there are still things to discuss, and it is certainly
>> biased toward my preferences,
>> > >       but hopefully not too badly.
>> > >
>> > >       I was able to include examples that should address Bruce's
>> concerns with the handling of
>> > >       transpose.  To be continued.
>> > >
>> > >       If an element has sub elements with intent, then intent="fn"
>> will collect them as
>> > >       arguments to fn.  If an element has no such sub elements, then
>> intent="transpose" gives
>> > >       the intent of the transpose function itself, with no
>> arguments.  If an operator has no
>> > >       arguments, and you want the intent of the application of the
>> function, use
>> > >       intent="fn()".  Easy as pi, but we should discuss.
>> > >
>> > >       The operator name can be placed on the enclosing element for
>> the apply, or on an element
>> > >       that gives markup for the operator.  This should allow for what
>> folks want, but we
>> > >       should discuss.
>> > >
>> > >       I've included examples with both argument index references, and
>> argument name
>> > >       references.  I'd really like to avoid XPath references.
>> > >
>> > >       I was able to expand on Bruce's examples where multiple
>> infix/prefix/postfix operators
>> > >       appear in a single mrow, and I marked up both minimal-mrow and
>> complete-mrow versions of
>> > >       each example.  To be discussed.
>> > >
>> > >       I've included examples with integrals of fractions where the
>> differential is included in
>> > >       the fraction.  We should discuss scoping of argument name
>> references.
>> > >
>> > >       I've not said anything about literal references, which I intend
>> to add.
>> > >
>> > >       Oh yes, and I still need to convert this to markdown, once we
>> stop adding examples to
>> > >       it.  I've not gone through the entire encyclopaedia.
>> > >
>> > >       This version is intended to be more descriptive than
>> prescriptive.  The examples are
>> > >       informally grouped to illustrate how to use the syntax.
>> > >
>> > >       Enjoy,
>> > >       Sam
>> > >
>> > >
>> > >
>>
>>