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The upright "d" (was: Re: math fonts)

Commenting on Barbara Beeton and Ulrik Viet,
regarding the inclusion of the upright "d" in
the math core font:

> this is not arbitrary, and is there for the same reason that an
> upright partial sign is included among the "extra greek-like
> material" -- it is to represent the differential operator, which
> is upright according to an iso standard for math notation (whose
> reference number i don't remember at the moment).  since that
> standard was developed by engineers, not mathematicians, actual
> practice in those two communities may differ, but the fact remains
> that the upright "d" is standardized and the (more familiar to me)
> italic "d" is not.

Ulrik Viet:
> NO!!!  The upright "d" and upright \partial are despartely needed for
> differentials, at least according to typesetting rules applicable in
> physics.  The reason to have them in the MC font is kerning: If you
> run the math test of the MFbook testfont.tex program, you'll find that
> there are numerous kern pairs between italics "d" and other italics or
> greek letters.  Kerning between upright "d" and other letters may not
> be as critical as for the italics "d", but one shouldn't rule out this
> possibility by banning the upright "d" from the MC font prematurely.
> BTW, from the point of view of physics requirements, I'd also like to
> have an upright "i" (and perhaps also "j") in the MC font for kerning
> reasons.  I'm afraid that this suggestion somehow never made it into
> Justin's report.  Just look closely at

I fully agree on Barbara Beeton.
I use and like to use it myself and I don't like the
italic "d", in mathematics or elsewhere, but there are other
symbols to be set upright which aren't included. That was my point.
So chosing "d" but not chosing "i" or "e" is arbitrary.
Or "D", which is also used as a differential operator in certain cases.
The upright partial (in fact a variant delta) is not available
in other fonts, and so has a right to reside here (it has so
anyway as a Greek letter, hasn't it?)
  But math italic should match the text font of a document, and so
the upright sybols could well be taken from there, if available.
The only problem here is kerning, and it seems impossible to come up
with a font of 256 characters which could include all needed glyphs.
(So we'll have to change to Omega...)


[Special Laplace symbol]

> Very good idea!  Reserving a slot for \Laplacian would allow the font
> designer to choose between different styles for \Laplacian and \nabla,
> either in ``Greek'' style (upright and inverted \Delta) or geometric
> (upright and inverted triangle of uniform line thickness).  Another
> symbol in this grooup would be the d'Alembert operator (a.k.a. quabla),
> usually just a geometric square, but it should match the size of
> the Laplacian.

I got the idea of creating a special \Lapla (to match my \Nabla as a control
sequence) by the Duden, which in some cases shows glyph variant, the
variant used in the DIN rules indicated by an asterisk. Now, it showed here
such a triangle. Only later I realizes that DIN uses sans serif (which
looks terrible for math), so may be this was just a sans serif Delta...
Anyway, I think these symbols should be a little larger than a Delta,
somewhere in between uppercase and things like \sum (in textmode) in
height, thus "reigning" the following formula just as \sum does (and
thus increasing readability). They don't need to be as large as \sum,
as normally they don't have such a large scope (the parts following
them an belonging to them are often composed only of a single symbol).

> Question: Are these really math characters, or just greek text characters?
> Remember, we want to do a math font not a greek text font, so if they are
> never ever used in math, I'd suggest to get rid of them.

At least they were used as number signs in historic Greece. But they don't
have to reside in the core, they could be somewhere in the fourth or
seventh symbol font...

Johannes Kuester

Johannes Kuester                    kuester@mathematik.tu-muenchen.de
Mathematisches Institut der
Technischen Universitaet Muenchen