• To: support@YandY.com
• From: Ulrik Vieth <vieth@thphy.uni-duesseldorf.de>
• Date: Tue, 20 Jan 1998 17:34:49 +0100
• Cc: clasen@pong.mathematik.uni-freiburg.de, math-font-discuss@cogs.susx.ac.uk


> At 02:22 PM 1/20/98 +0100, Ulrik Vieth wrote:
>> - What to do abuot missing sets of upright or italic Greek?

> Does anyone have some information on whether upright lower case
> Greek (regular weight)  is ever used in math?

> I know it used by physicists for elementary particles, but I haven't
> seen it in math. Also, the bold upright lower case Greek is used for
> vectors (I suppose in anology with math italic becoming upright bold
> when we turn a symbol into one denoting a vector).  But regular weight
> upright lower case Greek?

I thought we were doing something that was supposed to be usable for
physicists as well as for mathematicians.  Besides there are certain
differences in the typographic traditions in various coutries.

The American tradition uses upright Greek capitals and lowercase
italic Greek, which has become the default in TeX.  Unfortunately,
other conventions applicable in their countries or their specific
fields of sciences.

Two examples:

1.) The French tradition, according to Thierry Bouche, uses upright
Greek captials as well as upright Greek lowercase in math.  This
point was brought up here a few month ago (see the archives), when
I experimented with an upright version of the lowercase CM Greek.
Perhaps Thierry could provide some references.

2.) The typesetting rules applicable for physics imply using italic
shape for all symbols denoting physical quantities, which applies to
Greek capitals as well as Greek lowercase, but upright Greek is used
for certain operators (e.g. upright \Delta for the Laplacian, upright
\delta for variational quantities, upright \partial for partial
differentials, upright \pi for the meathematical constant, etc).

As for vectors becoming upright bold, this is indeed a widely-used
convention, but not excactly what they should be like according to
the rules.  Strictly speaking, vectors in physics should be typeset
in bold italics (not bold upright) and tensors of the second rank
in bold sans serif oblique.  In theory, this convention should apply
to all letters denoting physical quantities, regardless of whether
Latin or Greek, upper- or lowercase, but many authors or publishers
use something else, such as upright bold or upright sans serif bold.

One obvious reason might have been the lack of support for bold math
italics as a math alphabet (i.e. no \mathbm analogous to \mathbf)
or simply the lack of knowlege how to change the default alphabet
for the Greek capitals.

> Mike Spivak felt strongly that this was an abomination, and so MathTime
> has only bold upright lower case Greek (and heavy). Although there is
> separate font with upright lower case regular weight Greek meant for
> the physicists (which curiously is not meant to be used in math or
> for Greek text).

I wouldn't hesitate to build an implementation of the MC encoding by
combining glyphs from MTMI and MTGU as a first approximation, provided
that both sets are available.  Of course, for a final release some
the glyph metrics.  Even if I will use them only for particle symbols,
I would prefer to use a markup like \particle{\alpha} and take them
from a math font using a more or less standard encoding rather than
taking them from MTGU with a weird encoding, where \alpha = a,
\beta = b, but \gamma = g and \varepsilon = ve (ligature), etc.

> Chuck Bigelow followed more the model of four styles regular, bold,
> italic, bold italic and let the user decide what is appropriate (given
> enough rope...)

As explained above, this seems to be a better approach if you want
to support various conventions applicable in various fields.
If all the Greek alphabets are available in four styles, it's fine.
If not, then some users in some fields will get a missing glyph
warning, and they'll have to figure out how to find a work-around.

Cheers, Ulrik.

P.S. Personally, I find "MathTime Complete" one of the better examples
in that it does at least provide a lowercase upright Greek alphabet,
quite unlike the original CM.