# Proposed math coding scheme

I received a copy of barbara's proposed extended TeX font encoding
scheme for math fonts at the Nordic TUG meeting.  Mostly it seems
quite sensible, but I've got a few comments:

a) Extra symbols.  We could take the opportunity of issuing new fonts
to plug some of the gaps in the current symbol set.  I realise that
most people will have their own pet symbols they're dying to
introduce, but some of the standard theoretical CS symbols that are
missing are:

Dijkstra choice (often written as [\!])
Semantic brackets (often written as [\![ and ]\!])
With and par (ampersand and inverted ampersand)
General least upper bound (\bigsqcap)
Blackboard bold numerals
\arrownot and \Arrownot, so that (for example) \arrownot\mapsto is
visually compatible with \nrightarrow.

in addition, my personal wish list would include:

General parallel (\bigparallel)
Interleaving (|\!|\!|) and general interleaving (\biginterleaving)
Linear implied and iff ( o-- and o--o )
Lightning
The building blocks to make \mapsfrom <-|, \Mapsto |=>, and
\Mapsfrom <=|
Lfloor, Rfloor, Lceil and Rceil (\lfloor\!\lfloor, etc.)
Multiset brackets (usually written {| and |})
Arrows with triangles on the end: <|--, --|> and <|--|>
Dutch bisimulation, which is an equals-like symbol:

<-->
----

b) Digitization fixes.  At the moment, many of the characters do not
digitize symmetrically.  The worst offenders are \oplus, \otimes, etc.
which at 11pt on a CanonCX are egg-shaped and asymmetric.  There also
needs to be digitization hacks to make the pens that symbols are drawn
with symmetric---for example \sqcup in cmsy10 for a CanonCX digitizes
as:

**   **
**   **
**   **
*******
******

because the pen it was drawn with has the shape:

**
*

c) Font encoding.  At the moment, there are two copies of the Greek
lower case letters---is one of these going to become an upright Greek?
Is there a font encoding for math italic?  The black letter glyphs
>From the Euler font seem to fit well enough with CMR that they should
be included in one of the symbol fonts for CM---then the Euler
math fonts could use the same encoding as the CM math fonts.

Non-lining numerals really should have been in the text font encoding,
but I suppose we're stuck with including them in the math encodings
now.  This means that the math fonts have to include:

math numerals    (lining and non-lining)
text numerals    (non-lining)
italic numerals  (non-lining)
oblique numerals (non-lining)

The other non-lining numerals (bold, typewriter, sans, etc) can come
>From variant math fonts.  Perhaps a more sensible suggestion would be
that fonts with non-lining numerals should be variants, but this means

a) *every* font is going to have to come in two versions---lining or
non-lining.

b) designers who specify both lining and non-lining digits in the same
document are going to have problems.  (And yes, this does
happen---it's very common for folios and numerals in textual matter
to be set non-lining, and footnote markers to be set lining.)

This is the situation with Adobe fonts, and it is rather sad that
we're probably going to be landed with it too.

Sorry to carp on, but using mathematics is my livelihood, and I'd like
to see TeX's excellent setting of mathematics get just that little bit
better.

Cheers,

Alan.

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