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Hans Aberg wrote:

>   If you write a paper with say a Levi-Civita connection, then the best way
> is to first make a macro-name, say \LC, \LeviCivita, or \connection, or
> something, which could expand to any makeshift symbol. At a later point,
> one could substitute something better (like
>     \def\LC{\hbox{\raise2pt\hbox{$\bigtriangledown$}}}
> or something).
>
>   This sort of follows the same principle as typing \em for emphasis, or
> the principles for choosing an international set of characters. (One
> difference thou, is that new math concepts are being invented, so one would
> need pay special attention to that.)
>
>   TeX consists of a jumble of these two different ideas, selecting a glyph,
> that is a typeset output, and choosing a semantically correct typing input.
> =46or example $\emptyset$ produces a specific rendering of the empty set
> symbol, but now, there is another AMS-fonts alternative, $\varnothing$. So
> here one should really have one name for the empty set concept, and then
> one could choose rendering of it.
>
>   This sort of bring us back to ideas presented here earlier, by J=F6rg
> Knappen, Barbara Beeton, and others, (discussions about standard for gcd,
> differentials, etc) but then it was not very explicit. Has one discussed of
> introducing such a feature in the LaTeX3 project?

TeX's math control sequences are mixing two different concepts: partly
they describe the shape of the glyph, partly they desribe the mathematical
meaning and/or concept behind the symbol (\otimes is an example of the
former, \sum an example of the latter). A good' author would of course
choose his macro names according to their mathematical meaning (e.g.
using \tensor and not \otimes, when using this glyph to denote a tensor
product) thus rendering his source code much more readable, sometimes
even more readable than the actual output: if the same glyph is used
for different concepts, a careful author could use different control
sequences for these concepts. For existing glyphs, this could easily be
done with a suitable set of \let commands. May be some rather standard
ways could be added here to TeX's standard, e.g. something like
\tensor as an alternative way to get the \otimes glyph, as this is
standard mathematical usage. I think that in general control sequences
are preferable which describe the mathematical meaning rather than those
which describe the outlook of the glyph.

It should be clear that a mathematical concept is always developed
before its proper notation, but this should not hinder a user to choose
a proper control sequence for it, even if the needed glyph doesn't exist
yet (or even if the user couldn't yet think of a matching notation), so
this could later be added (or the source code could be easily searched
and changed, e.g. if something entered as a product is later decided to
be written by a single symbol or something like that). So I think
LaTeX could provide some control sequences even for not yet existing
or not yet universally available glyphs, as -- I think -- this would
be helpful: existing documents could then be easily updated to match
better' standards (e.g. for a next edition), or a publishing house
which has some special glyphs in its own fonts could insert these by
simply changing some macro definitions. It seems to be more important
to set math documents to the best standard and with the best available
glyphs rather than keeping their looks fixed for all time.

To give an explicit example: I'm using my own macros for intervals,
namely \ivc,\ivo,\ivco and \ivoc (closed, open, left-closed right-open,...,
with \bigivc etc. through all sizes and \Ivc etc. for automatic \left and
\right insertion), to be used like \ivc{a}{b} (as it has the further
feature of choosable separator: I'm using a semicolon instead of a comma,
as comma is the decimal separator in German notation, i.e. [a;b] etc.),
even as the author of the book I'm texing with these macros doesn't want
to use special delimiters here. For a later edition, this could easily
changed; and similarly for other documents and other control sequences.
Of course, this could be done by non-standard macros, too, but why
not adding some standard macros for agreed-upon concepts?

The danger here is to arrive at far too many macros, and all those
macros need to be well documented, and this then still relies on very
careful typists (to continue the above example: from this standpoint
using \ivc{a}{b} seems preferable, but it can't be avoided that a user
still enters [a,b] instead, thus making these macros useless to some degree).

Johannes

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