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%%% @LaTeX3-report { LaTeX3-L3-007
%%% filename = "l3d007.tex",
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%%% author = "Justin Ziegler",
%%% doc-group = "Project core team",
%%% title = "Technical report on Math Font Encoding",
%%% version = "2.00",
%%% date = "June 1, 1994",
%%% time = "18:52:36 GMT",
%%% status = "Public, official",
%%% abstract = "This is a report of the \LaTeX3
%%% Project work on math font encoding.
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\NeedsTeXFormat{LaTeX2e}
\begin{filecontents}{l3d007.sty}
%%% Action macros for this document
%%%
%%% table stuff from testfont whole thing need wrapup!!!!!!
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%%% use of code example
%\begin{figure}
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%\caption{Output of the \texprog{nfssfont.tex} program for the font
% \texttt{msbm7}}
%\label{fig:testfontmsbm}
%\end{figure}
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\end{filecontents}
\begin{filecontents}{l3d007a.tex}
\section{Introduction}
This document aims to put on paper what could be the backbone or the
skeleton of a new math encoding for \TeX. This is not the complete
description of an encoding, but a sort of grid, or global picture of
what things could look like. This document refers to many glyph groups
defined in another document called ``Towards a list of math glyphs''.
Same author.
\section{A few definitions}
\begin{description}
\item[An ``encoding table''.] This conveys the
traditional meaning of an encoding. That is to say a set of 256
glyphs in a given order. The expression ``encoding table'' is usually
abbreviated to ``encoding''.
\item[A ``slot''.] It is the usual word used for referring
to a position in an encoding, that can contain a glyph. It is usually
an integer between 0 and 255. A slot is
certainly not a family, nor anything to do with it.
\item[A ``math kernel''.] This terminology is used to
specify the fonts that are necessary for the math facility to work
as it is described in most \TeX\ documentation\footnote{documentation
on LA\TeX, AMS\TeX, etc, also fits in here.}.
In DEK's implementation the math kernel consists of the
families from 0 to 3. On top of the kernel, many other fonts, with
whatever encoding is available, could be optionally loaded and used.
\item[A ``math encoding''.] It is considered here as a whole; not
just one 256-glyph encoding table, but a set of encoding tables.
This concept will be referd to as ``M-encoding''.
\item[The ``core symbols''.] They are made of two
groups. The group of symbols that must live with the default alphabet
for kerning reasons, and the group of symbols that must live with the
default alphabet for design reasons.
\item[The ``default alphabet''.] It is the alphabet that is
used when a user types \texttt{\$abc\$}. In the present encoding that
produces $abc$.
\item[``Glyph compatibility''.] Two encodings are glyph compatible
when they contain the same glyphs but not in the same positions. As well
as containing the same glyphs, it must also be possible for the
corresponding fonts to contain the same sidebearings and the same
kerning and ligaturing information.
\end{description}
\section{Global policy}
\subsection{Text in math mode}
It is generally agreed that for best quality documents, if one wants
to put text in a math formulae, one should switch back into text
mode, using something like the \cn{text} macro in the AMS
package. None of the encodings can be expected to support bad
usage. In a math encoded font, the letters are not kerned in the same
way as in a text encoded font, and there are no letter ligatures,
because they are not needed.
\subsection{A global rule for boldface}
It has been decided not to mix ligth face and bold face symbols in
the same encoding, but to generate a separate boldface version of all
lightface math encoded fonts when necessary. This does not make it
impossible to mix the two: either one can use the
\texttt{\string\boldsymbol} approach, or one can load an extra bold
face font in a given family, and have it directly and permanently
accessible.
\subsection{Sans serif and typewriter fonts}
Extra fonts could be designed in sans serif, or in typewriter using
some of the proposed new encodings. Another solution is to load the
Cork encoded sans serif fonts (or typewriter fonts) in free
families. In either case, the new math encoding will not have any
slots containing specifically sans serif or typewriter glyphs.
\subsection{Concerning the Euler shapes}
Euler shapes could be a good example implementation of the new math
encoding. Thus no Euler glyphs will be included in the new
encoding. However, it may be useful to use the Euler Fraktur for a
first implementation example, if the new encoding includes a Fraktur
or old German alphabet.
\section{Concerning Cyrillic letters}
These would be available, but not as part of the math encoding. They
would be loaded as an extra family, with whatever encoding exists,
together with suitable \cn{mathchardef}s.
\subsection{Compatibility with other typesetting systems}
\subsubsection{Grouping all \TeX\ specific glyphs in one font
encoding}
The present \texttt{cmex} font contains glyphs that cannot be used
by other typesetting systems, because they are set in a strange way.
The present \texttt{cmsy} font contains one glyph that is set in a
strange way --- the radical sign, and thus makes that whole font
unusable for the outer world. It would be a good idea to make sure
that this does not happen again.
The \LaTeX 3 project is hoping to set a new standard, that will not
only be used by \TeX, but by all systems that typeset mathematical
formulae. If every thing goes according to plan, in the next few years
many math fonts will exist, for many different systems, and they will
all use the same encoding.
The fact that they all use the same encoding means that it will be
very easy to exchange fonts from one system to another. So one day a
\TeX\ user will be able to take a math font used by Microsoft Word,
and convert it easily in order to use it with \TeX.
If \TeX\ specific glyphs are grouped in one font, there will only be
one problematic font. As it happens, all \TeX\ specific glyphs are
more or less geometric, so they could be used with more than one
math font.
On the other hand, if \TeX\ specific glyphs are spread around in
many fonts, then many ``imported'' fonts will not be usable by \TeX\
without major messing about.
Concerning this problem, the real question is: is the \LaTeX 3 project
setting a real standard for the next few years, or just
making another \TeX\ math font encoding?
If the answer is: ``the \LaTeX 3 project is setting a real standard
for the next few years'', then \TeX\ specific glyphs must be grouped
in one font. If that is really not possible,
then one can maybe consider putting them in two fonts.
If a font designer designs a math font for adobe, the work necessary
for adapting his font to the \TeX\ world should be reduced as much as
possible.
Otherwise nobody will provide any fonts for \TeX.
The \TeX\ specific glyphs that are concerned here could be visually
compatible with many math fonts.
Which are the \TeX\ specific glyphs? So far:
\begin{itemize}
\item The delimiters.
\item The large and small `bigops'.
\item The radicals.
\end{itemize}
\subsubsection{The space issue}
To enable easier font exchange between the \TeX\ world and the rest of
the world, the new math encoding will have a space in position 32
(decimal) of every encoding table, if it is possible.
\subsection{General document compatibility}
It is not worth beeing totaly compatible. A lot of glyph positions
will change, thus direct \cn{mathchardef}s will not always work.
Documented names from AMSLA\TeX\ (this includes names from
LA\TeX, \TeX, and AMS\TeX, and LAMS\TeX) ought to be kept.
\subsection{Grouping all Plain and \LaTeX\ glyphs in 4 fonts}
The main reason for this is compatibility. Let us consider a user
that has typed a document with the present math encoding and has
saturated the families for this document. If the new math encoding
does not guarantee Plain and \LaTeX\ glyph compatibility with a
minimum of 4 fonts, then that document cannot run with the new math
encoding: not enough families. Thus one should make the first four
font encodings of the new math encoding glyph compatible with
the group made by: cmr, cmmi, cmex, cmsy.
\subsection{Grouping all AMS\TeX\ and AMS\LaTeX\ glyphs in less than
6 fonts} The main reason for this is compatibility. Let us consider
a user that has typed a document with the existant AMS\TeX\ or
\LaTeX\ package, and has saturated the families for this document.
If the new math encoding does not guarantee AMS\LaTeX\ and AMS\TeX\
glyph compatibility with less than 6 fonts, then that document cannot
run with the new math encoding: not enough families. The first 6
font encodings must be one way glyph compatible with the fonts
provided in the AMS package.
\subsection{Replacing \texttt {cmex}}
The math font group has decided that the encoding due to replace the
\texttt {cmex} encoding will be designed in such a way that the
corresponding font can be loaded in three sizes or in one size.
Loading such a font in three sizes produces better typesetting. But
the resulting page and line-breaks will not be the same as
when the font was loaded in one size only. Some people will not like
that change, in their old documents. But for new documents loading
the extensibles font in three sizes will be better.
\subsection{Accents in maths}
There seems to be an agreement that math accents should not change
with the font or style of the letter. But it is not a problem to keep
the accents that are already in plain \TeX\ (and the \fn{cm} fonts) in
the same position as in the T1 encoding. That will allow them to be
variable family; thus any T1 encoding could be loaded, and its
accents used. Since there will be millions of documents using
bold hats this possibility must be preserved even if by default
all math accents are non-variable family.
\section{The base: a Cork encoded text font}
Main use: things like \texttt{\string\log}. This would generally be a
Latin font.
If it is a Latin upright font, it would probably also be used by
physicists (and chemists) for operators, and more generally whenever
upright letters are needed.
\textbf{Separating this set from the rest} enables the user to decide
how `log' and `sin', etc. should be typeset. Thus the multiletter
operators can be compatible with the text font, or with the rest of
the math glyphs, or even set in yet another font.
Math mode should not be used for setting text phrases in mathematical
material. For example:
\begin{verbatim}
$$x=y \quad {\rm is\ a\ direct\ consequence\ of} \quad y=x$$
\end{verbatim}
would be better input as:
\begin{verbatim}
$$x=y \quad\hbox{\rm is a direct consequence of}\quad y=x$$
\end{verbatim}
or, better still:
\begin{verbatim}
$$x=y \quad\text{is a direct consequence of}\quad y=x$$
\end{verbatim}
where \verb|\text| is a macro which sets its argument in horizontal
mode. This avoids unpleasant surprises such as:
\begin{verbatim}
$$X \quad{\rm is\ a\ sub-object\ of}\quad Y$$
\end{verbatim}
However, for upward compatibility with existing plain \TeX\
documents, it will still be possible to set text phrases in math mode,
as long as they only contain $\langle\mbox{character}\rangle$s of type
Variable.
\section{The ``text symbol'' encoding: the TS encoding}
Here one would put the old style numerals, and most of what
is comming out of the present math encoding. Other symbols could
be added. The Text Symbol encoding is definetly \textem{not part of
the math kernel.} But since it will contain symbols that
previously were accessed via the math fonts, its
encoding must be supplied. This font will not be loaded in a family. It
will just be loaded as a normal text font\footnote{If some users really
feel the need to load it in a math family, they can.}.
\section{The core: the MC encoding (263)}
Counting: 1,10,1 , 54,5 , 124,14 , 12,24,9 ,9= 263 glyphs
The accents are no longer here. They had no real reason to be here.
Most of them are geometrics anyway. But they do have reasons to be
elsewhere. One of the main consequences of taking these accents out
is that the core can be made more coherent, and more complete. The MC
encoding would contain:
\begin{itemize}
\itemsep -0.1cm
\item The skewchar in position 0: 1
\item The core digits: 10
\item The space character in position 32: 1
\item The core Latin alphabet, which is the default alphabet, in
uppercase, and lowercase, together with the dotless i and j: 54
\item The Latin friends: 5
\item All the Greek material: 124
\item The Greek friends, next to the Greek: 14
\item The core symbols for kerning reasons (punctuation and
delimiters): 12
\item The core symbols for design reasons: 24
More for kerning reasons:
\item The basic geometric delimiters: 9
Some new glyphs:
\item New basic delimiters: 9
\end{itemize}
Sacrifices can be made in the greek material, and in the core symbols
for design reasons.
\section{The MX encoding: 243}
Count up: 1 1 78 8 10 24 6 16 7 7 26 47 = 230
The usual extensible characters, together with some new ones, would live
here. Here any characters that have strange \TeX\ features, like big
descenders are included, thus grouping glyphs that are not compatible
with the outer world.
For various reasons discussed in ``Replacing \texttt {cmex}?'' (Same
author), the math font group has decided that the MX encoding will be
designed in a way such that when it is loaded in one size (like in the
present \TeX), every thing works OK, and the user can still have
access to the new symbols. However, the MX encoding will produce better
quality typesetting when loaded in three sizes.
Detailed contents of MX:
\begin{itemize}
\itemsep -0.1cm
\item Maybe a skewchar: 1
The space is questionable here, because MX will not be usable by
other typesetting systems, see comment:
\item Maybe a space: 1
\item Big and extensible \TeX\ delimiters from cmex: 78
Any characters that have strange \TeX\ features like big descenders:
\item The radicals: 8
Technically the following can come out, but then they must go in
MSP.
To make this possible one could take the bar accent out of MSP.
\item Horizontal curly braces: 10
\item All existant big and small ``bigops'' except the integrals: 24
\item The existant Plain vertical extensible arrows: 6
One has to limit the number of wide accents, otherwise there is not
enough place.
\item The wide tildes, and the wide hats: 16
New glyphs:
It is a little bothering that the following will be separated from
their small versions, but there is nothing much that can be done
about it:
\item The big ``big integral'' family: 7
\item The small ``big integral'' family: 7
\item The new big and small `bigops': 26
\item New multisized and extensible delimiters: 47
\end{itemize}
Note: all integral glyphs must be kerned with themselves, so that two
integrals following each other can be kerned easily with a little
care. Same for various other glyphs.
\section{The math symbol `privilege' font ``MSP'': 250}
Count up: 1,1, 54 , 18,7,3 , 23 , 8,4,2,4,4 , 20,7, 10 , 8,8,12 , 14 ,
6,4,5,4,5 , 8,2 , 16 = 250
\begin{itemize}
\itemsep -0.1cm
\item A skewchar in position 0: 1
\item A spacechar in position 32: 1
\item The script/calligraphic Latin letter set:54
According to AMS statistics, the script/cal are
used more often than the Blackboard bold.
Having the script/calligraphic here also achieves backward
compatibility with the existing \TeX, without loading MS1 and MS2.
\item The basic accents: 18 % all basic accents should stay here
\item The double accents: 7 % could go elsewhere
\item The underaccents: 3 % could go elsewhere
The following must stay here:
\item The ``Basic symbols'' group: 23
The next 5 are needed for compatibility with plain:
\item The ``Greater than plain'' group: 8
\item The ``Subset plain'' group: 4
\item The ``In / ni plain'' group: 2
\item The ``Sqsubset plain \& ams'' group: 4
\item The ``Succ without sim plain'' group: 4
\item The ``Small binops plain'' group: 20
\item The small ints: 7
These should probably live with the other `succ' members for design
reasons:
\item The ``Succ without sim ams'' group: 10
The next three make a homogenous group, and must live with sim.
Sim itself must live here because of compatibility with Plain:
\item The ``Greater than with sim'' group: 8
\item The ``Succ with sim'' group: 8
\item The ``Sim'' group: 12
The arrows, for compatibility, (improved a little though):
\item ``Plain horizontal arrows'': 14 or 10
\item ``Plain vertical arrows'' : 6 \\
Does not include the extensible arrows.
The latter are in MX as before.
\item ``Plain oblique arrows'': 4\\
Also called ``Plain other arrows''.
\item ``Latex arrows'': 5
\item Plain miscellaneous geometric symbols: 4
Extras ---~these are new glyphs~--- to improve a little what \TeX\
can already do:
\item Extra arrows for use with plain: 5
The ``lasy'' triangles are included in the AMS fonts and thus are
included in the following group:
\item AMS left-right open triangles: 8
Should live with the ``Plain oblique arrows'':
\item ``AMS obliques'':2
Some new glyphs: Some of this could come out.
\item Wide accents bar: 8
\end{itemize}
\section{The MS1, MS2, Math-Symbol encodings}
Each of these encodings will contain a set of Latin letters, like for
instance fraktur or blackboard bold, in uppercase or lowercase or
both. In some cases a place should be reserved for a set of matching
numbers too (i.e. Open). The rest would be filled up with symbols.
An MS$_i$ encoding is needed for:
\begin{itemize}
\item An extra script/calligraphic, (see below comment on script and
calligraphic) the default caligraphic is in the MSP encoding.
\item Open + (Arrows or relations) + other geometrics.
\item Old german,
\end{itemize}
\textbf{Note:} Barbara Beeton writes ``Regarding script vs.
calligraphic, I do understand the difference; however, at AMS I believe
we only very rarely get a request to use both styles in the same paper.
For that there are two possibilities:
\begin{enumerate}
\item designing one encoding table where the positions A-Z (and
probably a-z and 0-9 even if they are not all filled) are
supposed to contain a ``calligraphy/script'' set of characters.
Then there would be instances of that encoding that would
contain script chars and others that would contain calligraphic
chars. Suppose our standard would say that this encoding is to
be used as family 4. A designer would then choose one such
font with this encoding for family 4 (thereby effectively
deciding what \texttt{\string\cal} and a lot of other symbols
look like (the ones whose \cn {mathchardef} points into family
4)). For those who in addition would like to use another
script/call math alphabet: they can then just allocate one of
the free families. Access to this would then be trivial.
\item Having two different encodings; one for cal, and one for
script. The remaining symbols in both encodings would be
different too. Thus both encodings would need to be part of the
standard suite of math encoding tables.
Which solution is preferable depends a bit on the number of
symbols that ought to go in the standard.''
\end{enumerate}
Also J\"org Knappen writes: ``I strongly support having two different
encodings, one for cal and one for script. If users have the choice
between cal and script, they prefer script (at least in
Mainz\footnote{Maybe Americans prefer it the other way
round.}). However, the old calligraphic alphabet still
needs to be supported for compatibility reasons.''
\section{The MS1 encoding: 232}
Count up: 1 1 54 10 32 36 30 12 10 21 10 15= 232
\begin{enumerate}
\itemsep -0.1cm
\item A skewchar in position 0: 1
\item A spacechar in position 32: 1
\item The BBB alphabet uppercase and lowercase: 54
\item The BBB digits: 10
\item The last WIDE ACCENTS: arc, back-to-front vector, and
double-sided vector, normal vector: 32
For AMS inclusion:
\item The ``AMS horizontal arrows'' group: 22
\item The AMS other arrows group: 12
\item The ``Greater than AMS'' group: 30
\item The ``Subset AMS'' group: 12
\item ``AMS Equals friends'': 10
\item ``AMS Miscellaneous geometric symbols'': 21
\item ``AMS Vdash group'': 10
\item ``AMS boxes and friends: 15
For fun if there is place to spare:
\item Alan's arrow construction set: ?
\end{enumerate}
\section{Other requested typefaces}
\begin{itemize}
\item In general, users may want MC fonts in arbitrary styles (bold
sans serif MC for instance) in order to get the Greek letters in
their favourite styles.
\item A ``text-like'' italic or slanted for computer science
identifier names and the like. This would be Cork encoded and
optionally loaded.
\item A ``bold upright'' for use as variables -- e.g. vectors in
physics notation rather than the arrow over an italic letter. This
would be Cork encoded, and optionally loaded or accessed via the
\texttt{\string\boldsymbol} concept in which case no family would be
required.
\item Bold italic for use as variables: either optionally loaded as
a second font with MC or cork encoding (using only variable family
symbols) or accessed via something like
\texttt{\string\boldsymbol}.
\item Bold Old german (occasional) suggested
\texttt{\string\boldsymbol} approach.
\item Bold script (occasional) suggested \texttt{\string\boldsymbol}
approach.
\item Sans serif lightface (occasional): optionally loaded cork
encoded font.
\item Sans serif boldface (occasional): optionally loaded cork
encoded font.
\item Bold symbols: either \texttt{\string\boldsymbol} or optionally
loaded in remaining slots.
\item Ultra bold symbols: either \texttt{\string\boldsymbol} or
optionally loaded in remaining slots.
\item An MC-encoded bold font containing upright bold Latin glyphs,
plus bold upright and bold slanted Greek. This would contain all
of the most commonly requested bold glyphs in one font (rather
than many more).
\item A cyrillic alphabet. Loaded as an extra family, or in text.
\end{itemize}
\section{Summarising the families used by the proposed YAASP M-encoding}
\begin{enumerate}
\item Family $0$: A Cork encoded upright text font.
\item Family $2$: An MC encoded font containing the default Latin and
Greek italic+upright, and core symbols...
\item Family $1$: An MSP encoded font containing cal/script and
accents...
\item Family $3$: An MX encoded font including all extensible glyphs,
and double sized operators...
\item Family $y$: An MS$1$ encoded symbol font for Open, and arrows
or relations.
\item Family $z$: An MS$2$ encoded symbol font for Old German.
\end{enumerate}
\textbf{Comments:}
\begin{itemize}
\item This leaves 10 families free for anything else, (like bold
or sans...) and makes many symbols available.
\item The first four encoding tables put together give total
\TeX, La\TeX\ compatibility.
\item The first six give total \TeX, \LaTeX, AMS\TeX,
AMS\LaTeX, LAMS\TeX\ compatibility.
\item The six put together: do wonders, using no more font
families than the present AMS\TeX.
\end{itemize}
\section{Discussion}
\subsection{Advantages}
For MC: A big advantage here, is kerning. In this encoding kerning
is possible between the Latin default alphabet, and both italic and
upright Greek alphabets. This is necessary for compatibility, and for
tidyness. On top of this both letter sets (in actual fact there are
three) can be kerned with the core symbols that are in the MC
encoding. This last point is the most important, and gives new and
better automatic math spacing. (For compatibility reasons,
the Greek italic must be kerned with the period, the comma, and the
slash.)
The bold version of the MC encoding gives the user access to a lot of
bold letter sets in one go. The global family consumption is therefore
largely reduced: 1 bold font instead of 2 or 3.
Taking the accents away from the letters, means that the accents do
not change when the text face changes, i.e. bold letters and medium
letters get the same accents.
One can get more than compatibility with plain \TeX\ only using 4
families (the same number as standard \TeX\ currently uses).
One can get more than compatibility with AMS\TeX\ using 6 families.
This is less or equal than the number of families used by AMS\TeX.
The calligraphic alphabet is more used than the open, so putting it
with the accents is a step towards grouping most used glyphs together.
This proposal gives a little room in the MC for free spaces, and good
core material.
With the MSP encoding concept, the MSi encodings can really be
considered as (optional) extensions. Thus somebody who knows he
does not need the arrow kit and the Blackboard bold letter set does not
have to load them. Same for Fraktur.
All the \TeX\ specific glyphs are grouped in MX. Thus all the other
fonts could be used by other typesetting systems.
Using the Cork encoded font in family 0 for things like \cn{log} and
\cn{sin}, means that the Greek users can replace it by a Greek font.
(Apparently Greek mathematicians set these function names
using a Greek alphabet).
\subsection{Disadvantages}
If there is not enough space for all the required symbols,
one can make an MS3 encoding that would contain the other
version of script/cal, together with extra symbols.
\subsection{Comments}
In this proposal the core is really made of two fonts, and the kernel is
made of four.
Comments from Alan about the space slot in MX:
\begin{quote}
``MX will be used by \TeX, and the dvi drivers may be outputting to a
device that does not accept anything but a space in position 32. So
if you don't include a space here, then the MX-encoded fonts have to
be split into two device fonts by the drivers.''
\end{quote}
Comment from Alan about the Cork encoded font:
\begin{quote}
``I think it would be good to specify that this is family 0, for
compatiblity with current \TeX\ documents containing explicit
\cn{fam 0}
(naughty them!) and in order to have filled up slots 0 to 3 rather
than leaving a gap in family 0.''
\end{quote}
\end{filecontents}
\begin{filecontents}{l3d007b.tex}
\section{Introduction}
The goal of this document is to try and list the future contents of
the new math encoding. The glyphs have been divided into groups and
subgroups.
\textem {This is a draft and a workbench document. Some of it is out
of date, and usually the comments are not for the public. There are
lots of spelling mistakes, I know! The reader should be indulgent.}
%something added by bb for euler:
%begin{enumerate}
%\item Cursive (normal) capital letters. not often used.
%\item Cursive (normal) lower-case letters.
%\item Script upper-case.
%\item (Some) script lower-case.
%\item Fraktur (old german) upper-case.
%\item Fraktur (old german) lower-case.
%\item Digits.
%\end{enumerate}
%% bb --
%[bb: I will be happy to make a proposal for this.]
\section{Extra font dimensions}
\begin{itemize}
\itemsep -0.15cm
\item The design size,
\item The default script size,
\item The default scriptscript size,
\item Suggested value for mathsurround (in MC)
\item Math\_axis (in every font)
\item Thin mu skip,
\item Med mu skip,
\item Thick mu skip,
\item Recommended rule weight
\item Baselineskip: leadingheight,
\item Baselineskip: leadingdepth
\item Suggested by JMR: the big and bigg params.
\end{itemize}
\section{Kerning}
Better kerning should be made possible in the Latin math
italic, if it is possible. Normal kerning information is put in the
\fn{.tfm}
file. But in math mode, for things to get kerned as specified in the
\texttt{.tfm} file the left atom must be of ordinary type. If the user
interface redefines everything that must be kerned as being ordinary,
old documents will start looking different, and this is not wanted. To
avoid this, the user interface could define a macro
\texttt{\string\mathkerning\{...\}} that would use the kerning specified
in the \texttt{.tfm} file, without globally making all characters
ordinary.
The following glyphs should be kerned:
\begin{itemize}
\itemsep -0.15cm
\item The spacing of [ and ( and ) and ] followed by letters should
be adjusted.
\item The spacing of letters followed by [ ] ( ) should be
adjusted. This is an important one.
\item Keep the kerning with\quad . \quad , \quad / \quad for most
letters !
%\item Keep kerning between = and upright $\Gamma$ ! (I must have
%dreamt this one) Maybe add kerning for other punctuation characters.
\item At least keep the kerning between d and Y,Z,j,f. Maybe add some
others: dx, dy, d$\alpha$, d$\theta$, d$\phi$ ...
\item New kerning of the integral with itself. This would only
be available via a \texttt{\string\mathkerning} macro (see
previous comment).
\item Kerning of the period with itself,
\item Kerning of the centered period with itself.
\item Jan M.R. is sure that kerning is needed between
Latin and Greek. More precise information is needed.
\end{itemize}
\section{The following should be taken out of the present math encoding}
\begin{itemize}
\itemsep -0.15cm
\item The old digits: 10.
\item The 2 paragraph signs: \P, \S.
\item The Yen sign: Y.
\item The double dagger sign \ddag.
\item The four card families: $\clubsuit, \heartsuit, \diamondsuit,
\spadesuit$.
\item The musical signs: $\flat, \natural, \sharp$ ?????????
\item The maltese cross. (AMS)
\item The $\mathchar"017F$ seems not to be needed in maths.
\item The circled R must come out of the math symbols. (AMS)
\item The raised asterisk,
\item The two triangles in cmmi: cmmi'56 '57 ???????
\end{itemize}
All these will be put in to the ``Text symbols'' encoding, that would
come in many faces, and be text dependent.
Other glyphs could be put in the ``Text symbols'' font:
\begin{itemize}
\itemsep -0.15cm
\item More numerals,
\item The perthousand sign.
\item Maybe this is a good place for the `fraction' characters from
adobe.
\item $<$florin$>$, $<$ellipsis$>$ etc.
\item The superior and inferior digits, and put in kerning so that
$<$onesuperior$>$ $<$fraction$>$ $<$twoinferior$>$ produces a 1/2.
\item The single dagger finds a place here although it is in
maths as well. This makes them two different symbols, and enables both
to have more specific shapes.
\item A real copyright symbol, TM (trademark) and SM (service mark).
\item An interrabang (a combination of ? and !) new. (bb)
\end{itemize}
Alan Jeffrey has worked on the `text symbol font'. Actually it is now
called the companion text font. He has written more on this topic.
``alanje@cogs.susx.ac.uk''
\section{The Greek glyphs: 124}
The following shapes must be included:
\begin{itemize}
\itemsep -0.15cm
\item All the Upper-case in upright. 24
\item All the Upper-case in italic. 24
\item All the Lower-case in upright. 24
\item All the Lower-case in italic face. 24. So far: $24\times 4=96$
\item All the variable shapes in upright. 10
\item All the variable shapes in italic. 10
\item All the special numeric letters in upright. 3
\item All the special numeric letters in italic. If lack of space
prefer the italic shapes to the upright ones. 3.
\item Some control glyphs: 2 (probably useless)
\end{itemize}
\subsection{Variable shapes: 10}
This list comes basically from: J\"org Knappen. They are all listed
here including the ones that are already in the \fn{cm} fonts:
\begin{enumerate}
\itemsep -0.15cm
\item Lower-case Phi,
\item Lower-case Pi,
\item Lower-case Kappa, (AMS)
\item Lower-case beta (new),
\item Lower-case Rho,
\item Lower-case Epsilon,
\item Lower-case Sigma,
\item Lower-case Theta.
\item Upper case chi (new),
\item Upper case for upsilon.
\end{enumerate}
\subsection{Extra letters for numerals: 3}
Source: J\"org Knappen. They are all listed here including the ones
that are already in the \fn{cm} and \fn{ams} fonts. Must be given in
lower-case.
Upper-case Greek numerals exist, although extremely rare. For the
sake of completeness one could fill them in. But they are surely not
the hottest characters needed. (J\"org)
\begin{enumerate}
\itemsep -0.15cm
\item Qoppa (new),
\item Sampi (Sanpi?) (new) (J\"org Knappen),
\item Digamma (AMS).
\end{enumerate}
\subsection{Control glyphs: 2}
\begin{enumerate}
\itemsep -0.15cm
\item An italic control glyph, i.e. the following Greek letter is not
taken from the upright, but from the italic Greek,
\item A variable shape control glyph, i.e. the following Greek letter
is not taken from the normal set of letters, but form the variant shape
set. This will not work for all letters. Thus may not be a good idea.
\end{enumerate}
\note {From Alan about the control slots for Greek, ``Er, I'm not very
sure about those, since they'll affect kerning. I'd prefer to have
the choice between italic / upright made by the document designer.
And I'm not sure why anyone would want to get at an upper case $\xi$
by a macro \texttt{\string\uppercasegreek}\{\texttt{\string\xi}\}!''
--- ``True they will affect the kerning. But one could use them
differently from what you suggested. Although I'm not sure it is
interesting, the ligature mechanism does not have to be visible for
the user, i.e. he can still type \texttt{\string\Gamma}, which is
expanded to \texttt{\string\up \string\gamma}.''}
\section{Extra Greek-like material: 14}
This group of glyphs should not really be separated from the rest of
the Greek material.
\begin{enumerate}
\itemsep -0.15cm
\item An upright partial sign,
\item An italic partial sign,
\item An upright partial sign with a slanted bar, AMS \cn{eth}
\item A \cn{thorn} WASY'151 but this one is not very good. There is a
better one in dcmr'136. There is one is wslipa10'102 (J\"org)
\item A barred upright lambda, ?????? (probably not J\"org)
\item A barred italic lambda, this is preferred. (J\"org)
\item An upright mho sign (upside down Omega),
\item The back to front epsilon: AMS "7F \cn{backepsilon},
\item Arabic letter dal: looks something like a back to front $c$.
\item Hebrew letter msbm'151,
\item Hebrew letter msbm'152,
\item Hebrew letter msbm'153,
\item The $\aleph$ or \cn{aleph} in position CMSY'100,
\item The Nabla, $\nabla$ in CMSY'162
\end{enumerate}
The barred signs may be obtained by ligatures, or could be
constructed with kerning. In any case some slots for ligatures must be
left free if possible.
\section{The Latin letters: One set$=54$ glyphs}
We shall assume here that all lower case alphabets contain a dotless `i'
and a dotless `j', so that they can take accents other than a dot.
\begin{itemize}
\itemsep -0.15cm
\item The usual \fn{cmmi} italic shapes. Upper-case and lower-case.
\item The calligraphic shapes. Upper-case and lower-case.
The lower-case shapes are presently maybe not available.
\item The script shapes. Upper-case and lower-case.
The lower-case shapes are presently maybe not available.
\item The black board bold shapes. Upper-case and lower-case.
\item The Fraktur style. Upper-case, and lower-case.
\end{itemize}
\subsection{The calligraphic and/or script styles}
BB: ``How are ``calligraphic'' and ``script'' different here? I've
never seen what Knuth calls calligraphic and what most
mathematicians call script (the ``curly'' style) used in the same
context, so they are presumably not distinct from one another in
actual usage.''
The two should be included if there is enough space.
Otherwise one is enought.
\subsection{A hyphen char ?} These Latin letters are not meant for
typesetting words. It is assumed that all multi-letter words should be
typeset using the text fonts, not the math fonts. Thus
the hyphen character is not needed in the math encoding.
\subsection{Computer science and identifiers}
It looks as though the new math encoding will not contain anything
specially designed for computer science. Computer scientists will have
to use \texttt {cmti*} in an extra family for long identifiers.
\subsection{Chemists and chemical formulae} Considering the fact that
chemists do use a lot of mathematical expressions, they need the total
math mode as it is. On top of that they need a special mode for
writing chemical equations. One of the particularities of this
chemical mode would be the different placing of sub- and
superscript. A possible implementation is something like
\cn{EnterChemicalMode} and \cn{ExitChemicalMode}, which would
in actual fact load a new set of fonts (or only the font in family 2),
in order to have a different font dimensions in family 2.
\section{Latin-like material: 5}
This group should live next to the Latin letter set.
\begin{enumerate}
\itemsep -0.15cm
\item An upright d. This is needed for standard mathematical
typesetting.
\item A horizontally barred italic h, for physicists.
\item A slanted barred italic h, for physicists.
\item An italic upper-case Vee with a bar, the bar is meant to be
horizontal. \texttt{jvpurcel@vela.acs.oakland.edu}
\item An upright upper-case Vee with a bar, the bar is meant to be
horizontal, and extends through both sides of the Vee almost like
a strikeout. \texttt{jvpurcel@vela.acs.oakland.edu}
\end{enumerate}
\section{The different ways needed to write numbers}
\begin{itemize}
\itemsep -0.15cm
\item The normal set of numbers in \fn{cmmi}: upright lining.
\item The blackboard bold numbers. (Used in physics and a field of
maths. See Alan J. for more details.) [Note: presently no
satisfactory bbb numbers seem to exist.]
\end{itemize}
\section{Empty slots?}
Some free slots could be included, so that people can put their
ligatures in when they are trying to convert fonts coming from other
worlds.
Alan J. can give good explanations for this.
\section{Arrows}
Arrow construction should be possible. But to make sure it does not fail
when used in different sizes, every single glyph used for this purpose,
will be \textem{specifically} designed for this use. \textem{All of
them will be in the same font table}. This does not mean that a given
construction block can't be used for different types of arrows. This
sort of thing has to be thought of, and forecasted. These construction
blocks must not be used for any other purpose --- like for instance the
equal or minus sign.
All arrows from \fn{cm}, and from \fn{msam/msbm}, should be taken if
necessary. Maybe some others too.
\subsection{The ``Plain horizontal arrows'' group: 14 (Alan:10)}
The first 6 are in cmmi'050 to '055:
\begin{enumerate}
\itemsep -0.15cm
\item leftharpoonup
\item leftharpoondown
\item rightharpoondown
\item rightharpoonup
\item lhook
\item rhook
From \fn{cmsy}:
\item leftarrow '40
\item Leftarrow '50
\item leftrightarrow '44
\item Leftrightarrow '54
\item rightarrow '41
\item Rightarrow '51
\item CMSY'67 this is the \cn{mapstochar}
\item CMSY'66 the negation sign/slash: 1
\end{enumerate}
\subsection{Extra arrows for use with plain arrows: 5 (Alan 5)}
\begin{enumerate}
\itemsep -0.15cm
\item It would be reasonable to add a \cn{mapsfromchar} in order to
build things like: $<\!\!-\!|$: 1
\item It would be reasonable to add a \cn{Mapstochar} that could go
with the double arrows to build things like $|\!=\!>$ : 1
\item It would be reasonable to add a \cn{Mapsfromchar}
that could go with the double arrows to build things like
$<\!=\!\!|$ : 1
\item A - for extending arrows: 1
\item A = for extending arrows: 1
\end{enumerate}
\subsection{The ``Plain vertical arrows'' group: 6 (Alan 6)}
\begin{itemize}
\itemsep -0.15cm
\item updownarrow cmsy'154
\item Updownarrow cmsy'155
\item uparrow cmsy'042
\item downarrow cmsy'043
\item Uparrow cmsy'052
\item Downarrow cmsy'053
\end{itemize}
\subsection{Plain vertical extensible arrows: 6 (Alan 6)}
\begin{enumerate}
\itemsep -0.15cm
\item Top sing arrow: cmex'170
\item Bottom single arrow cmex'171
\item Top double arrow cmex'176
\item Bottom double arrow cmex'177
\item Middle double arrow cmex '167
\item Middle single arrow cmex '077
\end{enumerate}
\subsection{Plain extra vertical arrows: 0}
Nothing added here.
\subsection{The plain other arrows: 8 (Alan)}
First the oblique arrows:
\begin{enumerate}
\itemsep -0.15cm
\item CMSY'45
\item CMSY'46
\item CMSY'55
\item CMSY'56
What else: ?
\end{enumerate}
\subsection{The ``Ams obliques'' group: 2}
\begin{enumerate}
\itemsep -0.15cm
\item msbm'36
\item msbm'37
\end{enumerate}
\subsection{The ``Latex arrows'' group: 5}
The four characters in position LASY'50 to '53 from the lasy font
(These appear in the wasy font as well) must be put with the arrows.
They are arrow heads. The squig \cn{arrow} in position '73
of lasy should also be included: 5
\subsection{The ``Ams other arrows'' group: 4}
\begin{itemize}
\itemsep -0.15cm
\item Circle arrows MSAM: '10 to '11 :2
\item Horizontal arrows MSAM:'113 '114 :2
\end{itemize}
\subsection{AMS horizontal arrows: 22 (Alan 23)}
This includes all the horizontal arrows and the negated ones,
that are listed page 280 of ``The joy of tex''.
\begin{enumerate}
\itemsep -0.15cm
\item leftarrowtail
\item leftleftarrows
\item leftrightarrows
\item leftrightsquigarrow
\item lefttrightharpoons
\item Lleftarrow
\item looparrowleft
\item looparrowright
\item nleftarrow
\item nLeftarrow
\item nLeftrightarrow
\item nleftrightarrow
\item nrightarrow
\item nRightarrow
\item rightarrowtail
\item rightleftarrows
\item rightleftharpoons
\item rightrightarrows
\item rightsquigarrow
\item Rrightarrow
\item twoheadleftarrow
\item twoheadrightarrow
\end{enumerate}
\subsection{Ams vertical arrows (Alan: 6) (here: 8)}
\begin{enumerate}
\itemsep -0.15cm
\item MSAM:'24 upuparrows
\item MSAM:'25 downdownarrows
\item MSAM:'26 upharpoonright
\item MSAM:'27 downharpoonright
\item MSAM:'30 upharpoonleft
\item MSAM:'31 downharpoonleft
\item MSAM:'36 Lsh
\item MSAM:'37 Rsh
\end{enumerate}
\subsection{Some control glyphs for access to arrows }
These do not appear in the \fn{.dvi} file, they simply enable the
construction of some arrows and slahsed arrows using the ligature
mechanism.
% end of arrows
\section{All sorts of accents}
\subsection{Basic size accents: 18}
\begin{itemize}
\itemsep -0.15cm
\item All those that are created by macros in the Ams package: the 3
dotted accent, and the 4 dotted accent.\quad 2
\item The ones in \TeX: e\char'22\ e\char'23\ e\char'24\ e\char'25
e\char'26\ e\char'27\ e\char'136\ e\char'137\ e\char'177\ e\char'176
e$\mathchar"017E$. They all come from \fn{cmr} except for
the last two from \fn{cmmi}. \quad 11
\item Extra: a back-to-front vector arrow, \quad 1
\item Extra: a double sided type vector arrow, \quad 1
\item Extra: a square bracket used as an accent, \quad 1
\item Extra: The previous one turned upside down, \quad 1
\item Extra: an arc is requested by AMS, \quad 1
\end{itemize}
\note {The e\char'175\ in \fn{cmr} is not needed in maths, it is just
a Hungarian accent.}
\note {The $\mathchar"017F$ seems not to be needed in maths. It
could be put in the text companion font.}
\subsection{Double accents: 7}
\begin{enumerate}
\itemsep -0.15cm
\item A bar and a dot on top,
\item A dot and a bar on top,
\item 2 dots with a bar on top,
\item A bar with 2 dots on top,
\item A hat and a tilde on top,
\item A hat and bar on top,
\item A double bar,
\end{enumerate}
\note {For the double accents, Spivak and Ralf Rey could do some
archive research at the AMS. Similar research could be done at the
APS, and the CUP.}
\subsection{Variable size accents: $7*8=56$}
Variable size has meant 5 different sizes until today.
That number could be raised to 8.
\note {If the accents are in a font
loaded in three different sizes, the choice mechanism of
\cn{mathaccent} will only look in the current style size (unlike
the delimiter choice mechanism). Thus although one could hope to
multiply the number of available sizes by three, in actual fact in
a given style the number of automatically available sizes would not
be multiplied. All the same this \textem{would} give better
results in each style,
but it would also create \textem{compatibility problems}
i.e.~formulae heights and widths may change. Even if not done in an
automatic way, the user would still have a larger range of accents
to choose from.
Compatibility problems could be avoided by redefining
\cn{mathaccent} to a \cn{mathchoice}. Thus the accents could always
come from text style, and the accented material could come from the
current style. But this does not work either. In doing so one would
no longer be able to take the base accents from the current style.
Although one could make two macros. See paper ``Repacing
\texttt{cmex}?'', same author.}
\begin{enumerate}
\itemsep -0.15cm
\item e$\mathchar"017E$ the vector. \quad 8
\item e\char'176\ the tilde. \quad 8
\item e\char'136\ the hat. \quad 8
\item e\char'26\ the bar. \quad 8
\item Some people request a variable size arc. \quad 8
\item The back to front vector arrow, \quad 8
\item The double sided vector arrow, \quad 8
\end{enumerate}
\subsection{Under accents: 3 so far}
Requests exist for the following:
\begin{enumerate}
\itemsep -0.15cm
\item A tilde,
\item A breve (\char'25)
\item A bar
\end{enumerate}
Like for the double accents, research could be done at the AMS...
???????
\section{Core symbols}
The symbols that have some reason to live with the default math
material. There are mainly two reasons for them to be there: one is
kerning, and the other is design similarity.
\subsection{For kerning reasons: 12}
\begin{enumerate}
\itemsep -0.15cm
\item The period . CMMI
\item The coma , CMMI
\item The semi colon ; CMR
\item The colon : CMR
\item The exclamation mark ! CMR
\item The (
\item and the ) respectively opening-class and closing-class, CMR
\item The [
\item and the ] respectively opening-class and closing-class, CMR
\item The $\{$,
\item And the $\}$ (design similarity reasons also) in positions '146
and '147 of CMSY,
\item The `/' as a delimiter\footnote {This is not accessible via a
single key. The key `/' produces the sign $/$ taken from
\fn{cmmi}.}, and as a fraction sign, CMR
\end{enumerate}
\subsection{Basic geometric delimiters: 9}
Should go in the core, for kerning reasons, like the other ( ) and [
]. If they don't fit in the core, they must go with the basics. The
ones listed here are all in CMSY, around '142, and '150.
\begin{enumerate}
\itemsep -0.15cm
\item $\rangle$
\item $\langle$
\item $|$
\item $\|$
\item $\rceil$
\item $\lceil$
\item $\rfloor$
\item $\lfloor$
\item The $\mathchar"026E$ in position '156
\end{enumerate}
Test: $|f|,\|f\|,\lfloor f\rfloor,$$\lceil f\rceil,\langle
f\rangle$ $f\lceil,f\lfloor,$$f\langle,f\backslash$ strange that
no kerning seems to be needed here, where as it is necessary for
the bracket.
\subsection{New basic size delimiters: 9}
Basic size means the same size as the parentheses and brackets in
\fn{cmr}. The following is a preference order list of desired new
delimiters:
\begin{enumerate}
\itemsep -0.15cm
\item A $|||$ for use as $|||f|||$ a norme,
Semantic brackets: $[\![$ and $]\!]$
\item The opening semantic bracket,
\item The closing semantic bracket,
\item Opening multi set brackets $\{|$
\item Closing multi set bracket $|\}$
Unicode contains another style of brackets, they call them
tortoise shell brackets. They look like:
\begin{verbatim}
/
/
/
|
|
|
\
\
\
\end{verbatim}
These are like parentheses, but with straight lines. No curves.
\item The opening tortoise shell bracket,
\item The closing turtoise shell bracket,
Triangle brackets, something like:
\begin{verbatim}
/|
/ |
/ |
\ |
\ |
\|
\end{verbatim}
\item The opening triangle bracket,
\item The closing triangle bracket.
% \item The opening turtoise shell in Bbb.
% \item The closing turtoise shell in Bbb.
\end{enumerate}
\subsection{For design similarity reasons: 24}
All this group must live with the default alphabet for design
similarity reasons.
\begin{enumerate}
\itemsep -0.15cm
\item The question mark ? must live with the ! CMR
\item The percent sign \% must live with the ! and ? CMR
\item The at sign @ must live with the \% CMR
\item The \$ sign must live with the @ \% ? ! CMR
\item The \& must live with \$, \% .. CMR
\item The \# in CMR
\item The inverted \&: must be found.
\item The $\ell$ as a rounded `l'. CMMI
\item The centered dot $\cdot$ for use as a multiplication sign,
must live with the period. CMSY
\item The asterisk $\mathchar"0203$ for use as a multiplication
sign, in position '003 in CMSY.
\item The $\propto$ sign must live with @, \%, $\ell$. In position
'057 of CMSY.
\item The $'$ or prime in position '060 of CMSY, one cannot
separate the prime from the the prime ligature slots. (2
ligatures) Kerning of letters with the prime is
not possible, because
the latter is set in superscript. ????????
\item The backprime from MSAM'070 should live with the prime. ??????
\item The $\infty$ sign in position '061,
\item The $\emptyset$ in position '073 of CMSY,
\item The \cn{check} mark in MSAM'130, ?????
\item The \cn{between} double parentheses in MSAM'107
should go with the normal parentheses.
\item The $\Re$, could come out if necessary,
\item The $\Im$ in position '074, and '075 of CMSY, could also
come out if necessary.
\item The $\dagger$ or dagger in CMSY'171, ?????
\item The smile, ???????
\item The frown form CMMI ????????
\item Could maybe include the circled S from MSAM'163. ?????
\item The Weierstrass symbol: $\wp$ only in one style, (could come
out)
\item The powerset symbol from
\texttt{Martin.Ward@durham.ac.uk}. (could come out if necessary)
It looks something like this:
\begin{verbatim}
XXXXXXXXXXX
XXXXXXXX XXXX
XXXXX XXXX
XXXXX XXXX
XXXXXXXX XXXX
XXX XXX XX
XX XXXXXXX XXXXXX
XX XXXXXXXXXXXX
XX XXXX
XX XXXX
XX XXXX
XX XXXX
XXXX XXXX
XXXX XXXX
XXXX XXXX
XXXXXX
\end{verbatim}
\end{enumerate}
\section{Symbols from \fn{lasy} that must be kept: }
The first four \fn{lasy} symbols are in \fn{msam}.
The ones in positions '50 through '53 are arrow heads, and are counted
as such in the corresponding group.
Character '60 is in the \fn{msam}.
'61 is not in the \fn{msam}, and should be kept.
Char'62: same as \fn{msam}'03 ?
Char'63: same as \fn{msam}'06?
Lasy'72: same as \fn{msbm}'163 or \fn{msam}'166 ?
Lasy'73: same as \fn{msam}'40 ?
A list of what should be kept from \fn{lasy}:
\begin{itemize}
\itemsep -0.15cm
\item Character '61: \quad 1
\item ???
\end{itemize} \textbf{This makes a total of 1.}
\section{The ``Subset'' groups}
\note {None of these have anything to do with the \cn{sim} glyph.}
\subsection{The ``subset plain'' group: 4}
\begin{itemize}
\itemsep -0.15cm
\item The $\subseteq$ in position CMSY'022
\item The $\supseteq$ in position CMSY'023
\item The $\subset$ in position CMSY'032,
\item The $\supset$ in position CMSY'033,
\end{itemize}
\subsection{The ``subset Ams'' group: 12}
\begin{itemize}
\itemsep -0.15cm
\item From MSBM'040 to MSBM'43 : 12
\end{itemize}
\subsection{The ``In/ni plain'' group: 2}
\begin{enumerate}
\itemsep -0.15cm
\item The $\in$ sign in position CMSY'062,
\item The $\ni$ sign in position CMSY'063,
\end{enumerate}
\subsection{The ``sqsubset plain \& Ams'' group: 4}
These do not have a place any where else:
\begin{enumerate}
\itemsep -0.15cm
\item The $\sqsubseteq$, cmsy'166,
\item The $\sqsupseteq$, cmsy'167,
\item The sqsubset from MSAM'100,
\item The sqsupset from MSAM'101,
\end{enumerate}
\section{The ``Greater than'' group}
\subsection{The ``Greater than Plain'' group: 8}
\begin{itemize}
\itemsep -0.15cm
\item The $\leq$ in position CMSY'024,
\item The $\geq$ in position CMSY'025,
\item The $\ll$ in position CMSY'34,
\item The $\gg$ in position CMSY'35
\item $<$ less than CMMI'074,
\item $>$ Greater than: CMMI'076,
\item The alternative leq: msam'66
\item The alternative geq: msam'76
\end{itemize}
\subsection{The ``Greater than AMS'' group: 30}
\begin{itemize}
\itemsep -0.15cm
\item From MSBM'000 to '005: 6
\item From MSBM'010 to '015: 6
\item From MSBM'024 to '025: 4
\item From MSBM'154 to '155: 2
\item From MSAM'060 to '061: 2
\item From MSAM'065 and '067: 2
\item From MSAM'075 and '077: 2
\item From MSAM'121 to '124: 4
\item From MSAM'156 to '157: 2
\end{itemize}
\subsection{The ``greater than with sim'' group: 8}
\begin{enumerate}
\itemsep -0.15cm
\item MSBM'022,
\item MSBM'023,
\item MSBM'032,
\item MSBM'033.
\item MSAM'046,
\item MSAM'047,
\item MSAM'056,
\item MSAM'057
\end{enumerate}
The `shapee' \cn{sim}, and the geometric \cn{sim} are considered to be
the same glyph, i.e. the difference that is sometimes visible is
considered to be a bug.
\section{The ``Succ'' groups}
\subsection{The ``Succ without sim plain'' group: 4}
\begin{enumerate}
\itemsep -0.15cm
\item CMSY'026,
\item CMSY'027,
\item CMSY'036,
\item CMSY'037
\end{enumerate}
\subsection{The ``Succ without sim AMS'' group: 10}
\begin{itemize}
\itemsep -0.15cm
\item MSBM'006, '007: 2
\item MSBM'016, '017: 2
\item MSBM'026, '027: 2
\item MSAM'062 - '064: 3
\item MSAM'074: 1
\end{itemize}
\subsection{The ``Succ with sim Ams'' group: 8}
\begin{itemize}
\itemsep -0.15cm
\item MSBM'020, '021: 2
\item MSBM'030, '031: 2
\item MSBM'166, '167: 2
\item MSAM'45,
\item MSAM'55,
\end{itemize}
The `shapee' \cn{sim}, and the geometric \cn{sim} are considered to be
the same glyph, i.e. the difference that is sometimes visible is
considered to be a bug.
\section{The ``Sim'' group: 12}
\begin{enumerate}
\itemsep -0.15cm
\item sim CMSY'030
\item approx CMSY '31
\item simeq CMSY'047
\item wr CMSY'157
\item The bold MSBM'034
\item MSBM'035
\item MSBM'150
\item The bold MSBM'163
\item The bold MSBM'164
\item MSBM'165
\item MSAM'166, backsim
\item MSAM'167, backsimeq
\end{enumerate}
\section{Binops}
\subsection{The ``Small binops plain'' group: 20}
\begin{enumerate}
\itemsep -0.15cm
\item cap CMSY
\item cup CMSY
\item uplus CMSY
\item sqcap CMSY
\item sqcup CMSY
\item big circle CMSY
\item big triangle up CMSY
\item big triangle down CMSY
\item vee CMSY
\item wedge CMSY
\item oplus CMSY
\item ominus CMSY
\item otimes CMSY
\item oslash CMSY
\item odot CMSY
\item amalg CMSY
\item bullet CMSY
\item circ CMSY
\item diamond CMSY
\item star (5 branches): CMMI'77
\end{enumerate}
\subsection{Small plain left right triangles: 2}
These should be replaced by the ones in the AMS fonts for math usage.
They are also used as bullets, and should go in the text symbol
encoding for such a usage.
\begin{enumerate}
\itemsep -0.15cm
\item triangle left: CMMI'56
\item triangle right CMMI'57
\end{enumerate}
\subsection{AMS left right open triangles: 8}
These are also in LASY.
\begin{itemize}
\itemsep -0.15cm
\item vartriangle left
\item vartriangle right
\item triangle left eq
\item triangle right eq
The previous four are in \fn{msam}
\item Same 4 negated in \fn{msbm}: 4
\end{itemize}
\section{Basic Symbols: 24}
A group of symbols used for typesetting basic mathematics.
These are mainly geometrics. Some have been added for similarity
reasons:
\begin{enumerate}
\itemsep -0.15cm
\item = The equals sign, CMR'075
\item - The minus sign, CMSY'00
\item + The plus sign, CMR'053
\item The $\times$ multiplication sign CMSY'002,
\item The \cn{divide} sign $\div$ CMSY'004
\item The \cn{divideontimes} from msbm'076 should live with divide
and times.
\item The rtimes from msbm'157 should live with the times.
\item The ltimes from msbm'156 should live with the times.
\item The $\pm$ sign in position CMSY'006,
\item The $\mp$ sign in position CMSY'007,
\item The $\equiv$ in position CMSY'021, Difficult to separate from
other similar relations.
\item The $\forall$ sign in position '070,
\item The $\exists$ sign in position '071,
\item The \cn{nexists} sign from msbm'100
\item The $\neg$ sign CMSY'072,
\item The \cn{varpropto} from AMS "5F. ????? or should this be left
as a geometric?????
\item The varemptyset from MSBM'77, ????
\item Could go here: the upside down F: Finv from msbm'140 ???????
\item And the back to front G: Game from Msbm'141 ???????
\item Unary minus like en dash, could be CMR'173 but I personally
think it should be shorter.
\item The \cn{varnothing} from MSBM'77,
\item smallsetminus from msbm'162
\item The $\perp$ perp or bot sign in position '077,
\item top sign CMSY'076
\end{enumerate}
\section{Radical}
\subsection{The \TeX\ radicals: 10}
Currently available in \fn{cmex} are:
\begin{itemize}
\itemsep -0.15cm
\item Five radical signs: 5
\item The vertical bit needed to construct the big
radical '165 : 1
\item The top bit of the constructed radical. '166 : 1
\end{itemize}
\fn{cmsy} includes the basic size of the radical. It
has always been loaded in three sizes, and must remain so.
If it is taken out of \fn{cmsy}, and put in a \fn{cmex}
replacement,
then this point must be taken into consideration.
If the new \fn{cmex} is loaded in one size, it must contain
three different sizes of the radical in order to stay compatible
with plain: 3
\subsection{New radicals: 2}
Request made by: \texttt { HITT\% USOUTHAL.BITNET@SHSU.edu }.
One can overload the little vertical extensible module of the
radical, in order to produce a left quantum operator. For the right
quantum operator, the glyphs could be available, but the radical
macro can't be used.
A specific macro could be designed and it would need two glyphs:
the top right hand corner, and the repeatable
vertical bit: 2
\section{The integrals family: 18}
\subsection{Big `bigops' size: 7}
\begin{enumerate}
\itemsep -0.15cm
\item The single integral.
\item The double integral. Could be done with kerning if there is
not enough space.
\item The triple integral. Could be done with kerning if there is
not enough space.
\item The single O integral.
\item The double O integral.
% \item The triple O integral. ??????? J\"org says no.
\item The sigma integral. For physics: J\"org.
\item The slash integral. For physics: J\"org.
\end{enumerate}
\subsection{Small `bigops' size: 7}
The same as in big `bigops' size.
\subsection{Small size: 7 }
This refers to the size of the \cn{smallint} in CMSY.
\begin{enumerate}
\itemsep -0.15cm
\item The single normal integral.
\item The single O integral.
\item Double O integral. ???? (J\"org thinks yes)
\item Double normal integral ???? (J\"org thinks yes) Could be done
with kerning if there is not enough space.
\item Triple normal integral ???? (J\"org thinks yes) Could be done
with kerning if there is not enough space.
\item The sigma integral.
\item The slash integral.
\end{enumerate}
Mail from HSS:
\begin{quote} %\fontsize{7}{7}\selectfont
\cn{doubleoint} is used by Becker in "electromagnetic fields and
interactions" (Dover). I also saw \cn{tripleoint} used in
electromagnetic theory books although both are somewhat archaic.
Concerning the small version (in \fn{cmsy}), I suggested this solely
for reasons of completeness. The need for it is less now that
\fn{cmex} will be loaded in three sizes. But the small version of
\cn{int}
\& \cn{oint} look a bit large when used in inline formulas. The
\cn{smallint} \& \cn{smalloint} etc. may be a choice for some
authors in the latter case.
YH also pointed out, that the upright versions of integrals are very
common in textbooks. since the integral sign is one of the most
common symbols used in maths, it may not be a bad idea to include
upright versions of *all* integral signs in \fn{cmex} (with
corresponding small versions in \fn{cmsy}) again for reasons of
completeness.
\end{quote}
\section{AMS Vdash group: 10}
\begin{enumerate}
\itemsep -0.15cm
\item MSBM'054 nparallel
\item MSBM'055 nmid
\item MSBM'056 nshortmid
\item MSBM'057 nshortparallel
\item MSBM'061 nVdash
\item MSBM'062 nvDash
\item MSBM'063 nVDash
\item MSBM'160 shortmid
\item MSBM'161 shortparallel
\item MSAM'015 Vdash
\item MSAM'016 Vvdash
\item MSAM'017 vDash
\end{enumerate}
\section{Plain and \fn{lasy} miscellaneous symbols: 6}
\begin{enumerate}
\itemsep -0.15cm
\item CMSY'20
\item CMSY'140
\item CMSY'141
Should live with the two previous:
\item MSBM'060 What about the back to front version of this ?????
\item LASY'061 the bow tie,
\item LASY'62 the small box. It is smaller than the one in the AMS
fonts. ????
\end{enumerate}
\section{AMS equals friends: 10}
\begin{enumerate}
\itemsep -0.15cm
\item msam'155
\item msam'154
\item msam'120
\item msam'73
\item msam'72
\item msam'54
\item msam'53
\item msam'52
\item msam'51
\item msam'44
\end{enumerate}
\section{AMS miscellaneous geometric symbols: 21}
\begin{enumerate}
\itemsep -0.15cm
\item msam'174
\item msam'173
\item msam'171
\item msam'170
\item msam'165
\item msam'164
\item msam'161
\item msam'160
\item msam'151
\item msam'150
\item msam'147
\item msam'146
\item msam'141
\item msam'140
\item msam'136
\item msam'135
\item msam'134
\item msam'133
\item msam'132
\item msam'131
\item msam'050
\item msam'005
\end{enumerate}
\section{AMS boxes and friends: 15}
\begin{enumerate}
\itemsep -0.15cm
\item MSAM'000
\item MSAM'001
\item MSAM'002
\item MSAM'003
\item MSAM'004
\item MSAM'006
\item MSAM'007
\item MSAM'014
\item MSAM'106
\item MSAM'110
\item MSAM'111
\item MSAM'112
\item MSAM'115
\item MSAM'116
\item MSAM'117
\end{enumerate}
\section{The horizontal curly braces: 10}
Their design should be the same as the vertical braces. Add two
horizontal extension modules for them, since if they are drawn with
rules, digitization errors may cause them not to line up with the
horizontal brace glyphs. What's more, this would enable the designer
to choose there boldness.
Plus two extra middle bits. So that the designer is not restricted by
the number of slots. Knuths design could use that little amount of
glyphs, but maybe other will need more.
Count: for the downwards brace: 2 end bits, 1 middle bit, 2 extensible
modules. That makes a total of 5 per curly brace. One up, and one
down: makes 10.
\section{Big and extensible \TeX\ delimiters from \fn{cmex}: 78}
This group includes delimiters that are in \fn{cmex}. And an extra
little extensible module for the \{ and \}.
\begin{itemize}
\itemsep -0.15cm
\item Four different sizes of ( and ): 8
\item Extensible versions of ( and ): 6 \\
Left and right extensible modules are '102 and '103. Top and bottom
are '060, '061, '100, '101.
\item Four different sizes of [ ]: 8
\item Extensible version of [ and ]: 6 \\
The extensible modules, one for the right bracket, and one for the
left bracket are: '066, '067. The top and bottom pieces are: '062
to '065.
\item Four different sizes of \{ and \}\,: 8
\item Extensible module for \{ and \}\,: 7 \\
The extensible module ('76) used for the curly braces is very small,
because it is added twice: once above the middle piece, and once
below the middle piece. Its height is half that of the parentheses
extensible module. Other pieces are: '070 - '075.
\item An extra extensible module for the \{ and \}\,: 1\\
There is only one extensible module for both the left and the
right curly brace in \fn{cm}. This is because the left-right spread
of a curly brace is symmetrical in \fn{cm}, unlike the parentheses
for example.
This may not be the case for other designs.
\item Four different sizes of $\langle$ and $rangle$: 8
\item Four different sizes of $\backslash$ and $/$: 8
\item Four different sizes of $\lfloor$ and $\rfloor$: 8 \\
The extensible version is build with the same pieces as the
extensible brackets.
\item Four different sizes of $\lceil$ and $\rceil$: 8 \\
The extensible version is build with the same pieces as the
extensible brackets.
\item Extensible vert and parallel: 2 \\
Extensible versions of the vertical bar and the double vertical
bar. They are their own extensible modules: '014 and '015.
\end{itemize}
\section{Bigops}
\subsection{Old bigops from \TeX: 28}
There are two glyphs for each bigop.
\begin{enumerate}
\itemsep -0.15cm
\item The sqcup
\item The circled integral
\item The circled dot
\item The circled plus
\item The circled times
\item The sums
\item The prods
\item The normal integrals
\item The bigcups
\item The bigcaps
\item The U plus
\item The wedges
\item The vees
\item The coprods
\end{enumerate}
\subsection{New double sized `bigops': 26 }
All these should come in two sizes, in the same font, like the present
\cn{bigcup}. One for display style, and one for text style. That
makes two glyphs for each one.
\begin{enumerate}
\itemsep -0.15cm
\item A double sized sqcap $\sqcap$ \cn{bigsqcap} (can be found in
\fn{cspex})
\item Two sized $\bigcirc$ with $\vee$ inside. $\bigcirc
\!\!\!\!\!\vee$ proposed name: \cn{ovee}, and \cn{bigovee}.
Can be found in \fn{cspex} and \fn{stmary}.
\item Two sized $\bigcirc$ with $\wedge$ inside. $\bigcirc
\!\!\!\!\!\wedge$ proposed name \cn{owedge}, and
\cn{bigowedge}. Comment from Alan:
\begin{quote}
``As far as I'm aware nobody has *ever* used these glyphs in a
paper. I put them in St Mary's Road because I needed them at
the time, but I shortly abandoned writing the paper they were
going to be used in. Please don't include them! (If we are
going to, we need to include and as well as
and which are the ones you described.)''
\end{quote}
\item Dijkstra choice: $[\!]$ CSPEX
\item A wide Dijkstra choice. CSPEX . Comment from Alan:
\begin{quote}
If this is the glyph I think it is, it's not quite a wide
Dijkstra choice in shape (although mathematically it's the
same thing as Dijkstra choice). The two glyphs are:
$<$dijkstrachoice$>$ looks remarkably like [ and ] glued
together.
$<$oblong$>$ looks like $<$sqcap$>$ but with the square
completed.
$<$oblong$>$ is used in CSP in conjunction with $<$sqcap$>$,
so it's quite important that they look the same. In
particular, they need to be of the same width because if they're
not, formulae sometimes don't line up properly...
\end{quote}
\item Parallel \cn{bigparallel} just a double sized version of
parallel.
\item Interleaving $|\!|\!|$ : \cn{biginterleaving}
\begin{quote}
`Interleaving' and `parallel' are used in (at least) three
different ways:
\begin{itemize}
%\itemsep -0.15cm
\item As delimiters $||$foo$||$ and $|||$foo$|||$. These
should come in basic-sized and extensible versions.
\item As binary operators p $||$ q and p $|||$ q. These can
be the same glyphs as for the basic-sized delimiters.
\item As `big' operators $||_i \;p_i$ and $|||_i \;p_i$
similar to \cn{bigcup}. These should come in text style and
display style versions.
\end{itemize}
The big operators are not the same glyphs as the extensible
delimiters.
\end{quote}
\item \cn{bigcupdot}: A `U' with a dot in it. Something like:
$\bigcup\!\!\!\!\cdot$
\item \cn{bigcapdot}: an upside down `U' with a dot in it. Something
like: $\bigcap\!\!\!\!\cdot$
\item An inverted \& called \cn{dnasrepma}
\item Large operator symbol based on, an asterisk sign.
\item Large operator symbol based on a times sign.
\item Large operator symbol based on, a hash sign.
\item Large operator symbol based on, an ampersand sign.
\end{enumerate}
\section{Non classified existing symbols}
Here is a list of some symbols that do not have a place elsewhere:
\begin{itemize}
\itemsep -0.15cm
\item The different shapes of \# should find a place, although one is
already in the core group.
\end{itemize}
\section{A list of new glyphs}
The following symbols should be added in the math fonts. Some have
already been designed by various people, so it should be possible to
find them...
\subsection{Basic size operators: 2}
Basic size means the same size as the operators in \fn{cmsy}.
\begin{enumerate}
\itemsep -0.15cm
\item Something like \cn{cupdot} and
\item Something like \cn{capdot} Frank M. can justify these.
\end{enumerate}
\subsection{New multi-sized, and extensible delimiters: 47}
Count: 8, 6, 1, 8, 8, 8, 8, makes 47 .
A multi-sized delimiter means: 4 sizes for each side : 8 glyphs.
Plus and extensible version: top, bottom, extension module for both
sides: 6 glyphs. Sometimes also a middle: 8 glyphs. Total: 16 or 14.
\begin{enumerate}
\itemsep -0.15cm
\item Four sizes of the semantic brackets $[\![$ and $]\!]$: 8
\item An extensible version of the semantic brackets: 6 \\
(Top - Middle - Bottom) * 2 makes 6.
\item An extensible version of $|||$ for use as $|||f|||$ (a
norme). Just the extension module: 1
\item 4 sizes of multiset brackets $\{|$ and $|\}$: 8
\item An extensible version of multi-set brackets: 8 \\
(Top - Bottom - Middle - extensible module) *2 makes 8.
Unicode contains another style of brackets, they are called
tortoise shell brackets. They look like
\begin{verbatim}
/
/
/
|
|
|
|
|
\
\
\
\end{verbatim}
\item Four sizes of tortoise shell brackets: 8 \\
No extensible version. could add them in.
\item Four sizes of triangle brackets: 8 \\
They look like:
\begin{verbatim}
/|
/ |
/ |
\ |
\ |
\|
\end{verbatim}
\end{enumerate}
\subsection{Geometrics: 21}
\begin{enumerate}
\itemsep -0.15cm
\item The \fn{ams} smaller or equal and greater or equal must not be
forgotten.
\item Linear `is implied by' if o-- and o--o [bb: There are also
versions of these with filled-in circles.]
\item From JMR: something like: $\raise .1cm \hbox{$|$}\!\_$
maybe the same upside down.
\item From JMR: Something like: $\_\!\raise .1cm \hbox{$|$}$
maybe the same upside down.
\item \texttt{Here are some other symbol I once needed: \cn{opm},
\cn{omp}. Why? There is \cn{oplus} and \cn{ominus} and there
is +, -, \cn{pm} and \cn{mp}, but there's no \cn{opm} and
\cn{omp}.}
\texttt {I once needed them in a context, where \cn{oplus} and
\cn{ominus} were used as subscripts to indicate symmetric and
antisymmetric wave functions that were normalized. It is easy to
specify formulae that include both cases using \cn{pm} and
\cn{mp}, but suddenly there was no \cn{opm} and \cn{omp}. I
constructed symbols using the circle from the copyright sign,
but that was not actually the perfect size.}
\end{enumerate}
\subsection{New arrows}
\begin{itemize}
\itemsep -0.15cm
\item Alan J. wrote: \cn{arrownot} and \cn{Arrownot}, so that for
example \cn{arrownot}\cn{mapsto} is visually compatible with
\cn{nrightarrow}. Describing the same thing he also wrote: Add
the `building blocks' for the AMS negated relations, for example a
\cn{arrownot} to build \cn{nlongrightarrow} and
\cn{nrightarrowfill}.
\item The building blocks to make \cn{mapsfrom} $<\!\!-\!|$
\cn{Mapsto} $|\!=\!>$ and \cn{Mapsfrom} $<\!=\!\!|$
\item Lfloor, Rfloor, Lceil, Rceil like $\lfloor\!\lfloor$
\item Arrows with triangles on the end.
$$<\!\!\!|\!\!-\!\!-,\ -\!\!-\!\!|\!\!\!>,\ <\!\!\!|\!\!-\!\!-|\!\!\!>$$
\item Equals like symbol: $<\!--\!>$ with $==$ underneath.
\end{itemize}
\subsection{Non geometrics: 19}
\begin{enumerate}
\itemsep -0.15cm
% \item The double circled integral, or the surface integral for
% physicists.
% \item A single integral with on top a $\Sigma$:
% $\displaystyle\int\!\!\!\!\!\!\textstyle\Sigma$ (J\"org)
% \item A single integral with a slanted dash:
% $\displaystyle\int\!\!\!\!\!\textstyle-$
% \item A triple, circled integral.
\item Possibly something like $\bar{}\!\!($ and $\bar{}\!\!)$ if the
bar was touching the parentheses.
\item Banana brackets: look (sort of) like $(\!|$ and $|\!)$. Or
they look like bananas if you believe Jeremy... Alan: The St. Mary
Road font includes samples of them, in a line-drawing style. Since
I have not seen them in real use, I cannot comment, if this style
or rather the look of \& in \fn{cmr} is appropriate.
\item lightning (\fn{wasy}) --- probably does not belongs in maths.
Alan: It is actually used though! It means `interrupt' in process
theory, c.f. Communicating Sequential Processes, Hoare, Prentice
Hall 1985. I don't know how widely used outside process theory it
is though...
% \item Upright partial derivation sign. In the Greek-like stuff.
% \item Arabic letter dal: looks something like a back to front $c$.
% This should live with the Hebrew letters.
% \item Remember that message forwarded by J\"org. The V-bar, and the
% parenthesis-bar. jvpurcel@vela.acs.oakland.edu. The V-bar is in
% with the Latin like stuff.
\item Katakana character that looks like a spiral. (bb)
% \item Here is a proposal from J\"org: Mylona's and Whitney's
% ligatures: two extra symbs. These would come in italic, and
% upright like the rest of the Greek stuff. J\"org himself does not
% like this. [bb: But we're not talking about text! Why put these
% in a math font?] It now looks as though this is not going to be
% included in the new math encoding.
\item A lower-case sigma with a long tail that goes a little bit below
the baseline.
\item The two versions of the \# hash sign must not be forgotten. It
seems that one is geometric, and one is not: the slanted
hash sign and the upright hash sign.
\item An \cn{inviota} is sometimes requested on the net. I'll send
you a reference file for it. (J\"org)
\item More ?
\end{enumerate}
\end{filecontents}
\begin{filecontents}{l3d007c.tex}
%a macro to put a frame round a box
\newcommand{\frameit}[1]{\vbox{\hrule\hbox{\vrule
\hskip .1cm\vbox{\vskip .1cm\hbox{#1}\vskip .1cm}\hskip .1cm
\vrule}\hrule}}
\begin{quote} \small
The placing of mathematical accents in \TeX{} is done with
the following control sequence: {\tt\string
\mathaccent"xyzz\{box\}}. {\tt"xyzz} is the code that
identifies the accent, and `{\tt box}' is the entity to come
under the accent. The box can be any type of box known by \TeX{}: a
single letter, a vbox, an hbox, etc... The accent code used is a
usual math code (refer to any book on \TeX\ for more details). The
accent is basicaly centered over the given box, but there are ways
of influencing the way the centering is done. The vertical placement
is as we shall see a little more tricky.
\end{quote}
\section{The accent choosing}
Let us call $x$ the box that is due to be accentuated, and $u$ its
width.
We shall first suppose that $x$ is a single character.\\
\vskip .05cm
\centerline{$x:\qquad \rightarrow$\lower .2cm%
\hbox{\frameit{\huge x}}$\leftarrow$u}
\vskip .2cm
If the accent is part of a list of successors\footnote{See document on
charlist for more details about successors.}, \TeX{} chooses the one
whose total width is {\em as close as possible} to $u$, but still
{\em smaller or equal} to $u$.
\vskip .25cm \textbf{Note.} A list of successors can only take place
in one and one font only, and Knuth reminds us of this fact in rule 12:
``[...] has a successor in its font [...]'' This makes me wonder...
The hat and tilde come in their smallest size in cmr position '136 and
'176. The other sizes are in cmex position '142 - '147. The
following:\\
\verb| $\mathaccent"005E{e}$, ... ,$\mathaccent"005E{eeee}$|\\
produces: $\mathaccent"005E{e}$ and
$\mathaccent "005E{ee}$ and $\mathaccent "005E{eee}$ and
$\mathaccent "005E{eeee}$. So as expected there is no automatic sizing,
seeing as the hat in cmr is not part of a charlist. Same test with
tilde: \\
\verb| $\mathaccent "007E{e}$, ... ,$\mathaccent"007E{eeee}$|\\
produces: $\mathaccent"007E{e}$ and $\mathaccent
"007E{ee}$ and $\mathaccent "007E{eee}$ and $\mathaccent "007E{eeee}$.
In order to get a hat that changes size automatically one must
call the smallest hat in \texttt{cmex} directly , like \cn{widehat}
does. \cn{widehat} is defined as: \cn{mathaccent} \texttt{"0362}.
Family three indicates cmex, and 62 is the hex position of the
smallest hat in \texttt{cmex}. Thus \cn{widehat}\verb|{abda}|
produces: $\widehat{abda}$.
\section{The horizontal placing}
The accent followed by its italic correction is put into a box $y$
whose width we shall call $w$.\\
\vskip .05cm
\centerline{$y:\qquad \rightarrow$\lower .2cm\hbox{\frameit{ acc
{\tt \string\/}}}$\leftarrow\ w$}
\vskip .2cm
Let us call $s$ the kern between the character in box $x$ and the {\em
skewchar\/}\footnote{See below for more details about the skewchar.}
---~taken in that order. The box $y$ is first centered on top of the
box $x$ and then shifted rightwards by the amount $s$.
\textsl {If the box $x$ is {\em not a single character}, the amount
$s$ is taken equal to zero, therefore the skewchar is ignored and
the box $y$ is normally centered\footnote{But the box $y$
contains the italic correction, which influences the centering.}
over the box $x$.
}
%
%
%
\subsection{The `skewchar'}
The \textem {skewchar} is a specific character that D.E.~Knuth decided
to use ---~in the way described above~--- for placing accents. Each font
should have its own skewchar.
For most characters, the {\tt .tfm} file specifies a particular
kerning of each letter with the skewchar. This is true for the
computer modern fonts, but other font designers may not have used this
feature.
Why choose one skewchar rather than another? This is because the
character $\mathchar"017F$ chosen by Knuth does not have any other
kerning that could have been disturbed by the skewchar kerning. This
choice may not always be good for all fonts, because it depends on
what the character in position '127 is. Thus a font designer might
choose another skewchar and put the necessary kernings in the {\tt
.tfm} file. Accent glyphs can be used as skewchars, because they
are usually not subject to kerns from other glyphs.
As long as one uses the {\tt cm} fonts, it does not make much sense to
change the skewchar, unless one wants to get strange effects, or
unless one intends to change the {\tt .tfm file}. One should remember
that an assignment to skewchar is not undone at the end of the group,
but is a part of the global font information. A local change
therefore involves saving the original value, and then restoring it.
\subsection{The italic correction}
The presence of the italic correction here is a little mysterious.
Its effect is to shift the accent to the left compared to the position
it would have without it. One should note that it is still added when
the $x$ box is more than one character.
%My personal theory is that
%whereas the skewchar-kerning enables a general positioning of all
%accents on one character, the italic correction enables an adjustment
%of a particular accent over all characters.
\subsection{Conclusions}
It is useless changing the skewchar unless one also modifies the
{\tt .tfm} file(s), which contain(s) the info for the skewchar kerning,
and for the italic correction.
Accents from any font can be positioned on characters from any other
font if there is a skewchar in the character font.
%
%
%
%
%
%
\section{The vertical placing}
This is a little more tricky. Here as well one can start
by supposing that the character to be put under the accent is single.
All previous notations are kept. $\chi$ is the x-height
of the accent's font i.e. {\tt\string \fontdimen5}. Let us call $h_x$
the height of the $x$ box:\\
%
\vskip .1cm
\centerline{\vbox{\hbox{$\ \downarrow$} \frameit{\huge x} \kern
-.2cm\hbox{$\ \uparrow$}
\hbox{$h_x$}}}
\noindent
and $h'_x$ the height of a box $x'$ containing the character to be put
under the accent, together with an empty superscript, and an empty
subscript.\\
\centerline{%
$x':\qquad $ \lower 1.5cm \vbox{\hbox{$\ \downarrow$}%
\frameit{$\mathop{\frameit{\huge x}}\limits^{\frameit{\scriptsize%
super}}_{\frameit{\scriptsize sub}}$}%
\kern-.2cm
\hbox{$\ \uparrow$}%
\hbox{$h'_x$}}%
}%end of centerline
%
\noindent
Now set $\delta$ with the minimum of $\chi$ and $h_x$, and increase it
by $h'_x-h_x$.
The end result is a \cn{vbox} $z$ containing box $y$ (the accent
correctly positioned lateraly), followed by a (vertical) kern of
$-\delta$, and then box $x'$ . A normal accent char has the folowing
aspect:
\frameit{\char127}. This explains why the kern of $-\delta$ is needed.
Without it the gap under the accent would be to big. One can now
understand why an `O' used as an accent over an `e' produces the
following: $\mathaccent"714F{e}$.
If the height $h_z$ of $z$ is smaller than $h_x$ then a kern
is added on top of $z$ in order to make the end height that of $x$.
Finally, the width of $z$ is set to the width of $x$.
%
\textsl{If the character to be accentuated is not single, $\delta$ is
not increased by $h'_x-h_x$. In other words, one can forget about
the subscript and superscript.
}%end of textsl
\subsection{Conclusions}
The x-height is used for the vertical placing of accents. This means
that one cannot mix in the same font table glyphs designed with
different x-heights.
\end{filecontents}
\begin{filecontents}{l3d007d.tex}
\begin{quote}\small
The re-encoding of the math fonts cannot be thought of without a
closer look at \TeX's mechanisms for dealing with extensible
characters. This includes all characters that come in different sizes,
all characters that are constructed, and the operators that usually
come in two sizes. The ultimate questions are: how
to implement these characters? What sort of kerning can be
done with them?
\end{quote}
\section{Let us start with the easiest: The operators}
A large operator like $\sum$ will be vertically centered with respect
to the axis when it is typeset. Thus, large operators can be used
with different sizes of text. This vertical adjustment is not made for
symbols of other classes. [The \TeX book p.155]
This is a sum in tex: $\sum_{i=0}^{i=n} i$ and this is a prod in text:
$\prod_{j=0}^{i=m} j$.
Same test in display maths:$$ \sum_{i=0}^{i=n}
vi\quad \prod_{j=0}^{j=m} j$$
The sum is defined as follows:
\begin{verbatim}\mathchardef\sum = "1350 \end{verbatim}
If \TeX\ is in display style, it looks to see if the character in
position "50 of family 3 (The extensible \fn{cmex} family) has a
successor\footnote{See below for explanations on successors.}. If it
does then the successor is taken. When not in display style, \TeX\
just takes character "50 from family 3.
\subsection{Conclusions for operators}
Both occurrencies of a double sized operator must be in the same font
table, because they are linked by the successor mechanism.
%JWZ commented this out: don't understand.
%It would be a good idea to try and make them all similar sizes so that
%they don't require many different sizes. This is due to font
%restrictions.
%\subsection{Going further}
%One wonders if the choosing is recursive, but presumably it isn't,
%because of the ``if we are in display mode'', which does not do any
%size testing.
\section{How characters can be linked}
\subsection{\texttt{charlists}}
They enable several characters of the same font to be linked together.
By simply typing \texttt{charlist oct"000": oct"020": oct"022":
oct"040": oct"060"} in the metafont source, one links all the
occurrences (in the \fn{cmex} font) of the left parentheses in
increasing size-order.
They are used for:
\begin{itemize}
\item Linking variable-size delimiters,
\item Linking variable-width accents,
\item Making pairs of operators that come in textsize and
display size.
\end{itemize}
\subsection{The \texttt{extensible} lists p318 metafont book.}
An extensible glyph is identified with one of its pieces. One has
to decide which piece is going to be used for this identification.
For instance, in \texttt{extensible oct"060": oct"060", 0, oct"100",
oct"102";} the first \texttt{oct"060"} is the identifier of the whole
glyph.
The next three characters are the top, middle, and bottom pieces. The
last character position is that of the piece to be repeated as many
times as necessary between the top
and middle, and between the bottom and middle pieces. All three pieces
are optional. When they are not needed, they are replaced with `0'.
But if a zero is put in the repeater position, then character `0' will
effectively be used as a repeater.
\subsection{Restrictions compiled from p318 of the Metafont book}
\begin{itemize}
\item An \texttt{extensible} identifier can only appear at the end of a
\texttt{charlist}.
\item A kerning/ligtable label can only appear at the end of a charlist.
\item One cannot use an extensible identifier as a kerning label.
\item One cannot use an extensible identifier as a ligature label.
%JWZ commented out the next two lines.
%\item this restriction explains why one specifies the kerning and the
% ligatures in the same table.
\end{itemize}
\subsection{Conclusions}
Kerning with parentheses is going to be very tricky...
A delimiter is made of two sets of characters that can be in two
separate font tables. The glyphs in these two sets (the delimiters),
can be kerned with the characters that accompany them in their font. So
one must place them correctly.
\note {There are no parentheses in the \fn{cmmi} fonts, so this
possibility has not been used.}
There is a list of all \fn{cm} extensibles, and charlists in ``Computer
modern typefaces'' p66.
\section{The vertical constructables, or ``those that come in pieces''
--- \textit{Delimiters}}
\subsection{A few notes}
First information about delimiters p.171 of the \TeX book. They are not
all of the same type. Some are (bigl,bigr) Open/close atoms, and
others are (bigm) rel and (big) ord atoms. On the other hand, a
\texttt{\string\left} \texttt{\string\right} grouping is inner.
When a delimiter gets larger, its height and depth both grow by the
same amount.
In the \fn{cmex} font, most of the vertical constructable glyphs are
below the baseline, in the \texttt{.tfm} file.
\subsection{A first description of the choice mechanism}
A delimiter is defined by a small ``character'' and a ``large
character''. \textbf{These characters can be in different families,
and therefore in different font tables.} We shall call the small
character $a$ in family $f_a$, and the large character $b$ in family
$f_b$.
The search first starts by considering the three different sizes of
char a in its family\footnote{i.e. the scriptscriptsize then the
scriptsize and finaly the textsize. This is done in an optimized
way: if the current size is bigger than scripscriptsize, no point
looking in the scriptscriptsize font, same goes for the other two
sizes.}. When testing a character in a given font table, its
successors are tested before going to the next bigger font. In other
words, for each member of a family, starting with the smallest, and
going to the biggest, \TeX{} first looks at char $a$ and then at its
successors\footnote{See later explanations.} in the same
font table. If nothing suitable is actually found within the family
$f_a$ a similar search is done in the family $f_b$ based on character
$b$.
The search stops when the character being tested has a sufficient
height plus depth, or when it is extensible\footnote{Obviously in this
case the appropriate delim has been found, seeing as it can be made
to any given size bigger than the non-extensible characters.}.
If either of the couples $(a,f_a)$, and $(b,f_b)$ are set to
$(0,0)$ then the corresponding part of the search is bypassed.
If none of the characters actually found are suitable, the biggest is
taken, i.e. the one with the greatest height plus depth.
\subsection{A second description of the choice mechanism by Victor E.}
\TeX\ first tries the small variant, and if that is not satisfactory
(or if the left part of the delimiter code is 000) it tries the large
variant. If trying the large variant does not meet with succes \TeX
takes the largest delimiter encountered in this search. If no
delimiter at all is found, (which can happen if the right hand part is
also 000), an empty box of width \texttt{\string\nulldelimiterspace}
is taken.
Investigating a variant means in sequence:
\begin{itemize}
\item If the current style is scriptscript style, the scriptscript font
of the family is tried.
\item If the current style is script style or smaller the script font of
the family is tried.
\item Otherwise the text font of the family is tried.
\end{itemize}
Note: The plain format puts the \fn{cmex10} font in all three styles of
family three.
Looking for a delimiter at a certain position in a certain font means:
\begin{itemize}
\item If the character is large enough, accept it.
\item If the character is extensible, accept it.
\item Otherwise, if the character has a successor, (the same but
bigger), try the successor.
\end{itemize}
\subsection{The final width of the delimiter ?}
If the character chosen ends up to be an \textbf{extensible} one,
\textem{the resulting width is that of the repeatable piece.}
Otherwise (in the case of a normal character) the width is that of the
chosen character \textem{plus its italic correction.}
\subsection{Conclusions for delims}
\begin{itemize}
\item The different sizes of a delimiter can be spread in two font
tables if it is necessary.
\item A given delimiter does not absolutly have to have two sizes.
\item One can adjust the width of the repeatable piece for
extensibles.
\item One can adjust the italic correction of the normal ``single
glyph'' delimiters, in order to get it further away from things like
$f$, $j$, $g$ and $p$. In the present case of `(' (in text
size) it comes from the text font \fn{cmr*} so obviously has not got
any italic correction. The vertical bar has not got any either
(checked in the \fn{.pl} files). This is quite a global solution and
the italic correction will be added in all cases: if it is small it
may not bother anybody and should have the right effect
in most cases.
\end{itemize}
\section{References}
The \TeX book ``Construction of math symbols'':
151 mathchoice: no good;
152: about delimiters and size choosing;
178: using phantom and vphantom - no good;
358: how large operators are assigned in plain, and
some horizontal constructables;
359: all the 24 delims that can change size and the big and bigg macros;
360-361: nothing.
The \TeX book ``math symbols'': 127-128: nothing, 289: nothing, 290:
interesting things about delims.
The \TeX book ``Mathcode'':
134: tiny little bit at the bottom about mathcodes,
154: a list of the 8 classes and (3) about variable family and (bottom)
about mathcode,
155: the mathcode "8000 + mathchardef + mathinner,
156: delcodes and delimiter,
157: radical,
214: nothing,
271: nothing, 289: nothing,
319,326: answer to exercises,
344: where all the mathcodes are set so that `1' comes from fam 0 and
`a' from fam 1,
345: where the delcodes for plain tex are set.
The \TeX book ``mathop'': 155 cf mathcode, 178 cf construction of math
symbs, 291 a bit about mathaccent, radical 324-325 361
The \TeX book ``dilimiters'':
156: delcode;
157: radical;
214: nothing; 289: nothing; 271: nothing;
290: in the middle ``A delim...''; 345: see at the top;
359: Plain tex definitions of some delimiters;
146: A list of plain tex delims;
147: the bigs;
148-149: details for use of left right;
150: still more extensible chars (bottom not on growing delims);
171: info on the type of atoms made by big bigr bigl bigm;
437: openings and closings;
442: The search of the appropriate delimiter: good.
About radicals rule 11 page 443 appendix G. \TeX book
\TeX book: About operators rule 13 page 443, successors. Interesting
about italic corrections. The way limits are typeset rule 13a.
About parameter usage p447 \TeX book.
About math spacing p170 \TeX book.
\TeX\ for the impatient: p.126 nothing, p.194-196 a list of operators
and a few explanations.
\TeX\ by topic p.194: Large operators and their limits, the choosing
method: good.
\end{filecontents}
\begin{filecontents}{l3d007e.tex}
\begin{quote}\small
% jz -- a little change in the first sentence
While working on the new math encoding, the writer realised that
the fact the \texttt{cmex} font is only loaded in one size, and not in
three like the other math fonts, was going to create a few problems.
This paper deals with the following topics:
\begin{itemize}
\item What is in \texttt{cmex}?
\item Which special mechanisms does \TeX\ use to access glyphs from
\texttt{cmex}?
\item What could be added to \texttt{cmex}?
\item What could be taken out of \texttt{cmex}?
\end{itemize}
The aim of this paper is to help the MFG\footnote{Math Font Group.}
design the MX encoding as a replacement and improvement of the
\texttt{cmex} encoding. \note{Most of what is written in this paper
is pure theory, and has not been applied or tested.}
Acknowledgements: thanks to Alan Jeffrey and Barbara Beeton for
their constructive comments, and help.
\end{quote}
% bb -- suggest adding an introductory section 0 giving a bit of
% background on knuth and early history; i would make suggestions
% and vouch for the accuracy of the statements, or offer to be
% quoted as the source if something is conjecture.
\section{What is in \texttt{cmex}?}
\subsection{Delimiters}
\begin{itemize}
\item Four different sizes of ( ) and extensible versions. Left and
right extensible modules are '102 and '103.
\item Four different sizes of [ ] and extensible versions. The
extensible modules, one for the right bracket, and one for the left
bracket are: '066, '067.
\item Same for \{ and \}\,; the extensible module is: '076.
\note{The extensible module here is very small, because it is
added twice: once above the middle piece, and once below the
middle piece. Its height is half that of the parentheses'
extensible module. Interesting to see that there is only one
extensible module for both the left and the right curly brace.
This is because the left-right extension of a curly
brace is symmetrical, unlike the parentheses for example.}
\item Four different sizes of $\langle$ and $rangle$. No extensible
version.
\item Same for $\backslash$ and $/$. No extensible version.
\item Four different sizes of $\lfloor$ and $\rfloor$ and an
extensible version. Extensible modules: '066, and '067.
\item Same for $\lceil$ and $\rceil$. Same extensible modules as the
previous one.
\item Glyphs in positions '014 and '015 are the extensible versions
of the vertical bar and the double vertical bar. They are their
own extensible modules.
\end{itemize}
\subsection{Large operators}
Large operators come in pairs:
\begin{itemize}
\item The sqcup
% bb -- although the sqcap isn't here, might want to note that it
% isn't but could be added
\item The circled integral
\item The circled dot
\item The circled plus
\item The circled times
\item The sums
\item The prods
\item The normal integrals
\item The bigcups
\item The bigcaps
\item The U plus
\item The wedges
\item The vees
\item The coprods
\end{itemize}
\subsection{Wide accents}
\begin{itemize}
\item 3 sizes for the hat
\item 3 sizes for the tilde
\end{itemize}
\subsection{Radicals}
\begin{itemize}
\item Five radical signs
\item The vertical bit needed to construct the big radical: '165
\item The top bit of the constructed radical: '166
\end{itemize}
\subsection{Arrows}
\begin{itemize}
\item The three pieces for the construction of the vertical double
arrow: '167 '176 '177
\item The three pieces of the vertical single arrow: '077, '170,
'171
\end{itemize}
\subsection{Horizontal curly braces}
\begin{itemize}
\item The four pieces for the construction of horizontal curly
braces: '172 -- '175
\end{itemize}
\section{\TeX's behavior with \texttt{cmex} glyphs}
\subsection{Large operators}
\begin{itemize}
\item A large operator is vertically centered with respect to the
math axis. This means that, whatever the surrounding glyph size,
things will not look too bad.
\item With the following definition of a large operator:
\cn{mathchardef} \cn{sum} \texttt{= "1xyy}, if \TeX\ is in \textem
{display style}, it looks to see if the character in position
\texttt{"yy} of family \texttt{x} has a successor. If it does then
the successor is taken. When not in \textem {display style}, \TeX\
simply takes character \texttt{"yy} from family \texttt{x}. Thus in
text style, in script style and in scriptscript style the same
glyph is used.
\end{itemize}
\subsection{Vertical delimiters, and friends}
Radicals are delimiters, and vertical arrows also, so let us only
speak about delimiters. Here is a quote from Victor Eijkhout's book:
\begin{quote}
A delimiter has two codes: a small variant, and a large variant.
\TeX\ first tries the small variant, and if that is not
satisfactory (or if the left part of the delimiter code is 000) it
tries the large variant. If trying the large variant does not meet
with success \TeX\ takes the largest delimiter encountered in this
search. If no delimiter at all is found, (which can happen if the
right hand part is also 000), an empty box of width
\texttt{\string\nulldelimiterspace} is taken.
Investigating a variant means in sequence:
\begin{itemize}
\item If the current style is scriptscript style, the scriptscript
font of the family is tried.
\item If the current style is script style or smaller the script
font of the family is tried.
\item Otherwise the text font of the family is tried.
\end{itemize}
Looking for a delimiter at a certain position in a certain font
means:
\begin{itemize}
\item If the character is large enough, accept it.
\item If the character is extensible accept it.
\item Otherwise, if the character has a successor (the same but
bigger), try the successor.
\end{itemize}
\end{quote}
Using the three size mechanism probably did not seem necessary to
Knuth. Generally large delimiters are used in display style, and not
in script or scriptscript style. However, they can also be used in
the small styles.
\subsection{Wide accents}
For the choice of accents, \TeX\ only considers one font, but looks
to see if the current accent has a successor. Unlike the delimiter
choice mechanism, the accent choice mechanism does not go through all
three sizes. \TeX\ chooses the accent in such a way that the accent
width is as close as possible but smaller than the width of the box
to cover.
\subsection{First conclusion}
For operators, a distinction in size is made between text style and
display style, whereas with the usual automatic size choosing
mechanism, glyphs in text style and in display style are taken from
the text size font, and are therefore the same size.
\section{Consequences of loading \texttt{cmex} in 3 different sizes}
\subsection{Consequences for operators}
For operators, let us consider two completely separate policies. In
the one case \texttt{cmex} is unchanged, and loaded in three
sizes. In the other case, an imaginary font derived from \fn{cmex}
called \texttt{cmex}$'$ is loaded in three sizes. In \fn{cmex}$'$ the
operators no longer have two sizes, thus glyphs like \cn{bigcup} do
not have a successor in their font.
\textem {All the following supposes that no new macros have been
written. What would \TeX's automatic behavior would be?}
\begin{description}
\item[If \texttt{cmex}$'$ is loaded in three sizes.] In
such a situation \TeX\ has a large version of \cn{bigcup} (and
other operators) in text size, a small version in script size, and
yet a smaller version in scriptscript size.
The operators can be centered: no problem.
% jz -- change:
In script and scriptscript style the resulting `big operators' would
be smaller than if they were produced with today's standard \TeX,
and today's standard \texttt{cmex}. What is more, one would be
smaller than the other, which is also not the case with today's
standard \TeX, and today's standard \texttt{cmex}.
% ----
In display style one would get big operators from the text size
font: this is acceptable. \textem {But one would also get a big
operator in text style,} and that does not conform with today's
standard \TeX\ behavior.
% jz -- I added encoding:
\item[If the existing \texttt{cmex} encoding is loaded in three
sizes.]
The operators can be centered: no problem.
In script style, one would get the smallest version of a large
operator. But coming from a small size font, that will produce
something very small. In scriptscript style, same behavior as in
script style, but the result would be even smaller.
% jz -- Added this:
Thus in script, and in scriptscript style, the large `big
operators' would never automatically be used.
Hence the \texttt{cmex}$'$ encoding.
% -- maybe should have said that earlier :-)
In text style, \TeX\ would produce the small version taken from
the text size font. In display style \TeX\ would produce the big
version of operators taken from the text size font.
So in text style and in display style, there would be no change
compared to what today's standard \TeX\ produces.
% jz -- changed the phrasing here:
But script and scriptscript style would produce different
results.
% --
\end{description}
In both cases, things could be improved if macros were written to
override the present behavior of \cn{bigsqcup}. One could think of
things like \cn{mathchoice}, but $\ldots$
\subsection{For vertical delimiters, radicals, vertical arrows}
Let us start by supposing \TeX\ is in scriptscript style, and it has
to typeset a large delimiter. One should consider two cases:
\begin{description}
\item[The delimiter has an extensible variant.] In this case the
search will start in scriptscript size, and continue until \TeX\
finds the extensible variant of scriptscript size. Then the search
will stop, and the extensible will be used. This extensible will
come from scriptscript size, and therefore probably not look the
same as it would in today's setup, where all extensibles come from
text size.
\item[The delimiter does not have an extensible variant.] As
previously, the search starts in scriptscript size. If nothing
big enough is found in scriptscript size, the search continues in
script size. If still nothing is found, the search then continues
in text size. If necessary the biggest delimiter from text size
will be used. If the search stops in text size, there is no
difference with what \TeX\ produces today. But if the search stops
before reaching text size, the chosen delimiter will be different
from the one \TeX\ would use in the present configuration. Its
strokes would be finer, and better adapted for use in script style.
\end{description}
If one supposes that \TeX\ is in script style, the previous two
cases also apply, except that every occurrence of `scriptscript' must
be replaced with `script'. If one supposes that \TeX\ is in text
style, the result of loading three different sizes of \texttt{cmex}
would be the same as it is in \TeX's current configuration.
\subsection{For horizontal curly braces}
If they are automatically taken from script size, or from script
script size when necessary, the spacing changes a little,
because the dimensions in the \texttt {.tfm} files would be
different. A consequence of this could be different line and page
breaks.
However, it would be nice if curly braces did come out
of the correctly sized fonts. Then their boldness would match the
surrounding text. But apparently from a macro programming
point of view things could be difficult, even if the glyphs are
available and loaded.
\subsection{For wide accents}
See first paragraph of previous section.
% jz --
% I guess that in actual fact, the wide accents were put in
% \texttt{cmex} because they could not fit any where else.
% jz -- I don't want to start any discussion on that topic so i'm
% taking it out
If accents were taken from the current size, things could only look
better.
The accent width would be closer to that of the material under the
accent, and the accent's boldness would be better adjusted.
\note {Unlike the delimiter choice mechanism, the accent choice
mechanism is restricted to one font, and one size. It will thus
not look in text size when it is in script size for instance. So
in script style, accents will always come out of the script size
font, and in scriptscript style, accents will always come out of
the scriptscript size font, etc.$\ldots$}
\subsection{Conclusion}
% jz -- Changed the conclusion
Nearly everything in \texttt{cmex} could have lived in a normal three
sized math font, and maybe that would have been better. The only
problems would have come from the specific ``big operator'' behavior
required by Knuth.
Also one must not forget that Knuth did not want to leave any empty
slots.
% jz -- added this:
The reduced amount of memory that was available on the machines with
which \TeX\ was first used could have been another reason for loading
\texttt{cmex} in one size only.
% jz -- This section has been changed a bit, and extended.
\section{What could be added to \texttt{cmex}?}
Let us now consider possible evolutions of \texttt{cmex}.
In spite of the terminology ``adding to \texttt{cmex}'', the font
resulting from these evolutions would have a different name.
\subsection{If the \texttt{cmex} encoded font is loaded in three
sizes}
In this case big operators would not produce the usual results, and
the rest would be slightly different, as stated above.
\begin{itemize}
\item One could add wide accents, but one would get slightly
different (better) results. Thus wide accents would match the
script and scriptscript styles. Macros could be made available
as a style option to keep the old behavior, if necessary.
\item One could increase the number of different sizes for accents.
\item One could add big delimiters and their extensible versions,
without any problem! Things will be slightly
better adjusted in script and scriptscript style. Macros could
be made (available as a style option) to keep the old behavior,
if necessary.
\item One could increase the number of different sizes for
delimiters, and one could probably reduce the height of the
extensible module in order to make the growing of delimiters
more gradual.
\item One could add some vertical extensible arrows! Things will be
slightly better adjusted in script and scriptscript style.
\item One can add small and large `big operators' without any
problem!
\item Big improvement: one could add loads of other glyphs (symbols,
etc.$\ldots$) that would come in all three sizes.
\end{itemize}
\subsection{If the \texttt{cmex} encoded font is only loaded in one
size}
\begin{itemize}
\item One could add big delimiters and their extensible versions
without any problem!
\item One could increase the number of different sizes for
delimiters, and one could reduce the height of the extensible
module in order to make the growing of delimiters more gradual.
\item One could add some vertical extensible arrows!
\item One could add large operators without any problem!
\item One could add wide accents without any problem, and the
present behavior of wide accents would not change. But if wide
accents are meant to match the script and scriptscript styles, then
wide accents must go in another font that would be loaded in
different sizes.
\item One could increase the number of different sizes for accents.
\item One could add other stuff, but it would only come in one
size.
\end{itemize}
\subsection {If a \texttt{cmex}$'$ encoded font is loaded in three
sizes}
The imaginary \texttt{cmex}$'$ encoded font, previously
described in this document is considered here.
One could add the same things as when \texttt{cmex} is loaded in three
sizes. The only difference is: if no macro programming were done, the
text style and display style will produce the same `big operators'.
In script and scriptscript style the `big operators' would be in
different sizes from one another and smaller than those in text
style.
\section{Conclusions}
If one loads \texttt{cmex} in three different sizes, many things are
improved, and with a \cn{mathchoice} the initial behaviour of large
operators could be kept, or available as a style option.
If \texttt{cmex} is kept in a single size, one must decide whether to
put wide accents in or not.
\section{The beginning of my \texttt{cmex10.pl} file}
\begin{verbatim}
(FAMILY CMEX)
(FACE O 352)
(CODINGSCHEME TEX MATH EXTENSION)
(DESIGNSIZE R 10.0)
(COMMENT DESIGNSIZE IS IN POINTS)
(COMMENT OTHER SIZES ARE MULTIPLES OF DESIGNSIZE)
(CHECKSUM O 37254272422)
(FONTDIMEN
(SLANT R 0.0)
(SPACE R 0.0)
(STRETCH R 0.0)
(SHRINK R 0.0)
(XHEIGHT R 0.430555)
(QUAD R 1.000003)
(EXTRASPACE R 0.0)
(DEFAULTRULETHICKNESS R 0.039999)
(BIGOPSPACING1 R 0.111112)
(BIGOPSPACING2 R 0.166667)
(BIGOPSPACING3 R 0.2)
(BIGOPSPACING4 R 0.6)
(BIGOPSPACING5 R 0.1)
)
(CHARACTER O 0 ...
\end{verbatim}
\subsection{Comments about the \texttt{cmex10.pl} file}
\begin{itemize}
\item The xheight is not equal to zero.
\item The space is equal to zero.
\item With the following:
\begin{verbatim}
(CHARACTER O 100
(CHARWD R 0.875003)
(CHARHT R 0.039999)
(CHARDP R 1.760019)
(VARCHAR
(TOP O 70)
(BOT O 73)
(REP O 76)
)
)
\end{verbatim}
that is in the \texttt{.pl} file, one can produce something that looks
like a growing integral:
$$ \left\lmoustache \frac{3.q}{\frac{3\pi.r^2}{3.q.b.c}} \right.$$
\item The pieces used to construct the horizontal curly braces are not
linked in any way.
\item The bottom pieces of the extensible parentheses are overloaded
for \cn{rmoustache} and \cn{lmoustache}. One of these could be linked
(charlisted) with the integrals, so that \cn{left}\cn{bigint} could
produce a growing integral like the delimiters.
\item The bottom pieces of the curly braces ('072 and '073) are also
overloaded for \cn{lgroup} and \cn{rgroup}.
\item The middle pieces of the curly braces are overloaded for
\cn{arrowvert} and \cn{Arrowvert}. Other single and double
extensible bars with different spacing.
\item The extensible module of the curly braces is overloaded for
\cn{bracevert}. A fat vertical bar.
\item The extensible modules of the parenthese are overloaded to
produce more fat vertical bars.
\item More overloading: the construction pieces of the extensible
brackets are also used for the $\lceil \rceil \lfloor \rfloor$. Thus
the top left bracket piece ('062) identifies the left bracket; the
top right bracket piece identifies the left bracket; the
bottom left bracket piece identifies the $\lfloor$ extensible
version; the bottom right piece identifies the $\rfloor$; the left
extensible module identifies the $\lceil$; and the right extensible
module identifies the $\rceil$. This over-loading may not be desired.
\item For the wide accents and the curly braces the depth is nil.
\item All the delimiter glyphs in \texttt{cmex} are set with a very
small height and a big depth. This is because the radical
primitive is also used for delimiters. For radicals, the \texttt
{.tfm} height of the glyph is used to determine the size of the
\cn{hrule}.
\item The extension modules do not have any height at all. Same for
the arrow heads.
\item The four integrals have italic corrections.
\item Small versions of operators have a nil height, whereas
big versions have a small height and a big depth:
\begin{verbatim}
(CHARACTER O 116
(COMMENT This is the small \bigotimes)
(CHARWD R 1.1111145)
(CHARDP R 1.000013)
(NEXTLARGER O 117)
)
(CHARACTER O 117
(COMMENT This is the big \bigotimes)
(CHARWD R 1.511116)
(CHARHT R 0.100001)
(CHARDP R 1.500012)
)
\end{verbatim}
What is more, in the metafont code,
both big and small versions of bigops are under the baseline.
\item There are no kerns or ligatures in \texttt{cmex}.
\end{itemize}
\section{Characters under the baseline}
\subsection{Which?}
It is understood and agreed that the radical glyphs need to be
virtually completely under the base line. \TeX\ uses their small
height to measure the thickness of the radical's over line. But
delimiters and `bigops' are also placed under the baseline for no
obvious reasons: both types of glyphs are just centered on the maths
axis.
\subsection{`Bigops' and metafont code}
\begin{description}
\item[The metafont padded operator.]
Although both big and small versions of bigops are placed completely
under the baseline (height=0), the big version ends up ---~in the
\texttt {tfm} file, with a non-nil height. Many people agree that the
reason for this is that the metafont code for the large version of
`bigops' contains the \cn {padded} macro. This last places some extra
space around the glyphs. This extra space would serve for separating
the `bigops' from the limits they may take.
Large integrals do not have any padded macro, and thus in the \texttt
{tfm} file, they are placed completely under the base line. The
reason for the difference between integrals, and other `bigops' could
be that the limits of the former are usually placed next to the glyph,
and not on top. Even when limits are placed on top of the integral,
the results do not look too bad, because the integral is very narrow.
The reason for `bigops' being set under the baseline is still unknown.
Whether or not they would be correctly centered on the math axis,
if they were placed over the base line is not sure either.
\item[Changing the metrics in the metafont code.] It is interesting to
see how \TeX\ would manage if the `bigops' were placed over the base
line.
The best way to find out, is to change the metafont code of \texttt
{cmex}, and see$\ldots$ I first did the test on \cn{bigoplus}
because it was a good candidate ---~simple metafont code. I have
never used metafont before. I copied all the necessary files into my
directory, and changed their names to `\texttt {my*}'. I then did
the following modifications in \texttt {mybigop.mf}
(look for \%\%\%\%):
\begin{verbatim}
cmchar "\textstyle circle-plus operator";
beginchar(oct"114",20u#,10/6dh#,0); %%%% was ,0,10/6dh#)
adjust_fit(0,0); pickup pencircle scaled stem;
lft x6=hround u; x2=w-x6; top y8=h; bot y4=-d; %%%% was top y8=0
...
cmchar "\displaystyle circle-plus operator";
beginchar(oct"115",27.2u#,14/6dh#,0); padded 1/6dh#;
%%%% was ,0,10/6dh#)
adjust_fit(0,0); pickup pencircle scaled curve;
lft x6=hround u; x2=w-x6; top y8=h; bot y4=-d; %%%% was top y8=0
...
\end{verbatim}
When I ran Metafont on it there were no problems. After having put
all the relevent files where they were meant to go, I gave the
following to \TeX:
\begin{verbatim}
Old cmex in text style: $\bigoplus i \coprod$
Old cmex in display style: $$-\bigoplus i\coprod \mathchar"034D$$
% change font:
\font\myfont=myex10
\textfont3=\myfont
\scriptfont3=\myfont
\scriptscriptfont3=\myfont
New myex in text style: $\bigoplus i \coprod$
New myex in display style: $$-\bigoplus i\coprod \mathchar"034D$$
The minus sign gives the height of the math axis, while the bottom
of the word `base' gives that of the baseline.
\bye
\end{verbatim}
Here is the output:
Old cmex in text style: $-\bigoplus i \coprod$ \\
Old cmex in display style:
$$-\bigoplus i\coprod \mathchar"034D base$$
% change font:
%\font\myfont=myex10
%\textfont3=\myfont
%\scriptfont3=\myfont
%\scriptscriptfont3=\myfont
New myex in text style: $-\bigoplus i \coprod$ \\
New myex in display style:
$$-\bigoplus i\coprod \mathchar"034D base$$
The minus sign gives the height of the math axis, while the bottom
of the word `base' gives the baseline.
The results are quite obvious: in both case the \cn{bigoplus} is
correctly centered. On the 300 dpi printer I have here there is no
visible difference. What is more the \cn{mathchar"034D} proves that
the metrics of the \cn{bigoplus} have changed: in the first case the
glyph is placed under the baseline, and in the second case it is
placed over the baseline. The difference is not visible if this
document is printed with the wrong fonts.
\end{description}
\end{filecontents}
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\renewcommand{\abstractname}{\Large Acknowledgement}
\typeout{******************************************}
\typeout{* }
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