Re: Proposed math coding scheme

[Alan Jeffrey <jeffrey@cs.chalmers.se>]

Apologies for broadcasting this on two lists at once.  Perhaps I
should have sent my initial message to dcfonts-l instead.  Oh well...

Summarizing some off-line chatter, there seems to be three problems:

1. New symbols.  Collecting new candidate symbols shouldn't be too
hard---finding character positions for them will be the usual
nightmare...  I'll mail barbara with more details about my
suggestions. 

2. Lining vs non-lining numerals.  This is something of a headache,
since non-lining numerals are only in the math fonts for historical
reasons.  One sensible suggestion (from Don Hosek and Chris Rowley) is
that the text fonts should have whichever numerals are considered
appropriate by the designer, and that the math fonts should contain
math digits (which will almost always be the lining digits for the
text roman).

Unfortunately, there is at least one exception to this rule, which is
the Concrete text family with Euler math.  In this case, the math
digits have nothing to do with the text lining digits, so (for
example) document styles that used math digits for footnote markers
would be in trouble.

There may be other examples where the math fonts bear little
resemblance to the text fonts, so this scheme will break down---Jeremy
Gibbons ran his thesis with Baskerville text and a variant CM humanist
sans for mathematics.

So, unfortunately, document style designers shouldn't always assume
that the math font and the text font have anything to do with one
another.  In passing, this raises a side-issue---should we expect all
document designs to be font-specific (in which case we can expect
document designers to do the work of making sure the correct digits
are used) or as font-independent as possible (so the same document
should TeX as well as possible with different fonts)?

3. Math fonts.  In chatting with Yannis Haralambous, I wondered
whether we could classify math symbols as:

   Geometrics (such as \oplus, \bot, etc) which are relatively
      independent of the text font, and

   Humanists  (such as \Gamma, \S, etc) which are very dependent on
      the text font.

the idea being that Geometrics should be adaptable (by varying
x-height, weight, etc.) to most fonts, whereas Humanists would have to
be adapted for each text font.  On further thought, we probably need
Text Humanists (such as \S and \dagger) which are designed to blend
with the text fonts, and Math Humanists (such as \Gamma and \emptyset)
that should blend with the math fonts.

The line between Geometrics and Humanists (sorry about misusing the
terms by the way---all better suggestions welcome) is rather vague,
and probably depends on the font.  For example, [ is a Geometric in
CMR, whereas in Monotype Baskerville it's a Humanist.

There's also the problem of other letter-forms in mathematics.  At a
first guess, the following are reasonably common in mathematics
setting:

   Roman, Italic, Sans, Typewriter, Upright Greek, Italic Greek, 
   Geometric symbols, Humanist symbols, Black letter, Copperplate, 
   Calligraphic, Open face, and all again in bold.

At the moment, some of these (Roman, Italic, Sans and Typewriter) have
their own text fonts, whereas the others are included in math fonts.
Is there some way of sytematizing this?  In an ideal world, perhaps
they should all be full text fonts (or dingbat fonts, in the case of
the symbols), and the math fonts should be VFs.  But that sounds like
a lot of work (although at the end of the day we'd also be able to TeX
our wedding invitations in CMcopperplate and newspaper mastheads in
CMRopen :-).

Well, that should be enough to be going on with...

Cheers,

Alan.

Alan Jeffrey         Tel: +46 31 72 10 59         jeffrey@cs.chalmers.se
Department of Computer Sciences, Chalmers University, Gothenburg, Sweden