suggestion to use 'semantics' for handling alignment

At the core meeting yesterday, there was discussion of
maligngroup/malignmark and what to do about alignment in MathML given the
difficulty of using and implementing the spec. Only Office and MathPlayer
ever implemented them, and Murray is unsure how much of the spec Office
implements.

I have some vague un-worked-out ideas about extending elementary math to
handle this because:
1. Elementary math aligns digits
2. An obvious extension to long division is to allow it to handle long
division of polynomials. This ends up aligning terms in the polynomial
3. Aligning terms (and a relational operator) is what most people want to
do for alignment, so this would 'naturally' happen and little special
markup would be needed -- probably just mstack and msrow would work (with
direct children <mo>s becoming the column markers). Still just a vague idea
though and I'm not sure it works.

The group bemoaned that alignment now mostly is done by splitting things
apart into columns in a table (the TeX way of alignment) and this destroys
the semantics. It's definitely not good for a11y. David Carlise had an
interesting suggestion: maybe 'semantics' can be used to restore
semantics/a11y when a table is used. No details were discussed.

Currently, semantics is used to resolve ambiguous notation like specifing
what some superscripted quantity means or what ⊕ means. Using semantics for
"undoing" alignment is a bit different. I think it merits some discussion
so I will add it to the Thursday meeting's agenda.

As an opening shot, we could:
1. On <mtable> add semantics="system-of-equations(@1, @2, @3)" for 3
equations (not quite the same as 'linear-system
<https://docs.google.com/spreadsheets/d/1EsWou1K5nxBdLPvQapdoA9h-s8lg_qjn8fJH64g9izQ/edit#gid=1818558895&range=2137:2137>'
in the list Deyan created)
2  On <mtr> add semantics=" equals( plus(@1, @3, @5), @7) if you have
something like
       2x + 3y + 1 = 4

[still not clear what we really should do if it had ' - 3y' instead of ' +
3y', but that's a different issue we haven't resolved yet]

There are many different uses of mtable, so "system-of-equations" is just
one example of what might be used on 'mtable'. 'piecewise' would be another
potential value.

Labeling the 'mtr' could be tricky for programs that generate 'semantics'.
For example, a TeX to MathML generator would likely need to strip out the
'&'s and figure out what 'semantics' should be but generate the actual
presentation with the '&' in (they map to columns). Something to discuss.
If it is a problem, what we really want to be able to say is "ignore the
'mtd's and just concatenate the row together, but having a special case
isn't good.

Food for thought for a discussion on Thursday.

    Neil


<http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail>
Virus-free.
www.avg.com
<http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail>
<#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>