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diff --git a/info/ltx3pub/l3d007.tex b/info/ltx3pub/l3d007.tex new file mode 100644 index 0000000000..8816b1cd44 --- /dev/null +++ b/info/ltx3pub/l3d007.tex @@ -0,0 +1,5583 @@ +%%% ==================================================================== +%%% @LaTeX3-report { LaTeX3-L3-007 +%%% filename = "l3d007.tex", +%%% archived = "ctan:/tex-archive/info/ltx3pub/", +%%% 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. +%%% ", +%%% keywords = "Math fonts encoding", +%%% project-address = "LaTeX3 Project \\ +%%% c/o Dr. Chris Rowley \\ +%%% The Open University \\ +%%% Parsifal College \\ +%%% Finchley Road \\ +%%% London NW3 7BG, England, UK", +%%% project-tel = "+44 20 7794 0575", +%%% project-FAX = "+44 20 7556 6196", +%%% project-email = "latex-team@latex-project.org", +%%% copyright = "Copyright (C) 1994 LaTeX3 Project. +%%% All rights reserved. +%%% +%%% Permission is granted to make and distribute +%%% verbatim copies of this publication or of +%%% coherent parts from this publication provided +%%% this copyright notice and this permission +%%% notice are preserved on all copies. +%%% +%%% Permission is granted to copy and distribute +%%% translations of this publication or of +%%% individual items from this publication into +%%% another language provided that the translation +%%% is approved by the original copyright holders. +%%% +%%% No other permissions to copy or distribute this +%%% publication in any form are granted and in +%%% particular no permission to copy parts of it +%%% in such a way as to materially change its +%%% meaning.", +%%% generalinfo = "To subscribe to the LaTeX3 discussion list: +%%% +%%% Send mail to listserv@urz.uni-heidelberg.de +%%% with the following line as the body of the +%%% message (substituting your own name): +%%% +%%% subscribe LaTeX-L First-name Surname +%%% +%%% To find out about volunteer work: +%%% +%%% look at the document vol-task.tex which can +%%% be obtained electronically, see below. +%%% +%%% To retrieve project publications electronically: +%%% +%%% Project publications are available for +%%% retrieval by anonymous ftp from ctan hosts: +%%% cam.ctan.org +%%% dante.ctan.org +%%% tug.ctan.org +%%% in the directory /tex-archive/info/ltx3pub. +%%% +%%% The file ltx3pub.bib in that directory gives +%%% full bibliographical information including +%%% abstracts in BibTeX format. A brief history +%%% of the project and a description of its aims +%%% is contained in l3d001.tex. +%%% +%%% If you only have access to email, and not ftp +%%% You may use the ftpmail service. +%%% Send a message just containg the word +%%% help +%%% to ftpmail@dante.ctan.org +%%% for more information about this service. +%%% +%%% For offers of financial contributions or +%%% contributions of computing equipment or +%%% software, contact the project at the above +%%% address, or the TeX Users Group. +%%% +%%% For offers of technical assistance, contact the +%%% project at the above address. +%%% +%%% For technical enquiries and suggestions, send +%%% e-mail to the latex-l list or contact the +%%% project at the above address.", +%%% checksum = "23322 5582 30455 207129", +%%% docstring = "The checksum field above contains a CRC-16 +%%% checksum as the first value, followed by the +%%% equivalent of the standard UNIX wc (word +%%% count) utility output of lines, words, and +%%% characters. This is produced by Robert +%%% Solovay's checksum utility.", +%%% } +%%% ==================================================================== + +\NeedsTeXFormat{LaTeX2e} + +\begin{filecontents}{l3d007.sty} +%%% Action macros for this document +%%% + +%%% table stuff from testfont whole thing need wrapup!!!!!! + +\tracinglostchars=0 + +\newcount\mcnt \newcount\ncnt \newcount\pcnt \newdimen\dim +%JWZ the next two counters can be changed for 128 glyphs or 256 glyphs. +\newcount\maxz \maxz=128 +\newcount\maxiz \maxiz=127 +\newif\ifskipping +\def\setbaselineskip{\setbox0=\hbox{\ncnt=0 +\loop\char\ncnt \ifnum \ncnt<\maxiz \advance\ncnt 1 \repeat} +\baselineskip=6pt \advance\baselineskip\ht0 \advance\baselineskip\dp0 } +\def\hours{\ncnt=\time \divide\ncnt 60 + \mcnt=-\ncnt \multiply\mcnt 60 \advance\mcnt \time + \twodigits\ncnt\twodigits\mcnt} +\def\twodigits#1{\ifnum #1<10 0\fi \number#1} +\def\startfont#1{\font\testfont=#1 +% \leftline{\scriptsize Test of #1\unskip\ on \today\ at \hours} +% \medskip + \testfont \setbaselineskip + \ifdim\fontdimen6\testfont<10pt \rightskip=0pt plus 20pt + \else\rightskip=0pt plus 2em \fi + \spaceskip=\fontdimen2\testfont % space between words (\raggedright) + \xspaceskip=\fontdimen2\testfont \advance\xspaceskip + by\fontdimen7\testfont} + +\def\oct#1{\hbox{\rm\'{}\kern-.2em\it#1\/\kern.05em}} % octal constant +\def\hex#1{\hbox{\rm\H{}\tt#1}} % hexadecimal constant +\def\setdigs#1"#2{\gdef\h{#2}% \h=hex prefix; \0\1=corresponding octal + \mcnt=\ncnt \divide\mcnt by 64 \xdef\0{\the\mcnt}% + \multiply\mcnt by-64 \advance\mcnt by\ncnt \divide\mcnt by 8 + \xdef\1{\the\mcnt}} +\def\testrow{\setbox0=\hbox{\penalty 1\def\\{\char"\h}% + \\0\\1\\2\\3\\4\\5\\6\\7\\8\\9\\A\\B\\C\\D\\E\\F% + \global\pcnt=\lastpenalty}} % \pcnt=1 if none of the characters exist +\def\oddline{\cr + \noalign{\nointerlineskip} + \multispan{19}\hrulefill& + \setbox0=\hbox{\lower 2.3pt\hbox{\hex{\h x}}}\smash{\box0}\cr + \noalign{\nointerlineskip}} +\def\evenline{\loop\skippingfalse + \ifnum\ncnt<\maxz \mcnt=\ncnt \divide\mcnt 16 \chardef\next=\mcnt + \expandafter\setdigs\meaning\next \testrow + \ifnum\pcnt=1 \skippingtrue \fi\fi + \ifskipping \global\advance\ncnt 16 \repeat + \ifnum\ncnt=\maxz \let\next=\endchart\else\let\next=\morechart\fi + \next} +\def\morechart{\cr\noalign{\hrule\penalty5000} + \chartline \oddline \mcnt=\1 \advance\mcnt 1 \xdef\1{\the\mcnt} + \chartline \evenline} +\def\chartline{&\oct{\0\1x}&&\:&&\:&&\:&&\:&&\:&&\:&&\:&&\:&&} +\def\chartstrut{\lower4.5pt\vbox to14pt{}} +\def\dofonttable#1{\startfont{#1}$$\global\ncnt=0 + \halign to\hsize\bgroup + \chartstrut##\tabskip0pt plus10pt& + &\hfil##\hfil&\vrule##\cr + \lower6.5pt\null + &&&\oct0&&\oct1&&\oct2&&\oct3&&\oct4&&\oct5&&\oct6&&\oct7&\evenline} +\def\endchart{\cr\noalign{\hrule} + \raise11.5pt\null&&&\hex 8&&\hex 9&&\hex A&&\hex B& + &\hex C&&\hex D&&\hex E&&\hex F&\cr\egroup$$\par} +\def\:{\setbox0=\hbox{\char\ncnt}% + \ifdim\ht0>7.5pt\reposition + \else\ifdim\dp0>2.5pt\reposition\fi\fi + \box0\global\advance\ncnt 1 } +\def\reposition{\setbox0=\vbox{\kern2pt\box0}\dim=\dp0 + \advance\dim 2pt \dp0=\dim} +\def\centerlargechars{ + \def\reposition{\setbox0=\hbox{$\vcenter{\kern2pt\box0\kern2pt}$}}} + +%%% use of code example + +%\begin{figure} +%\dofonttable{msbm7} +%\caption{Output of the \texprog{nfssfont.tex} program for the font +% \texttt{msbm7}} +%\label{fig:testfontmsbm} +%\end{figure} + + +\newcommand\textem[1]{\emph{#1}} + +\newcommand{\note}[1]{% + \par \vskip .25cm \textbf{Note:\ }#1 \par \vskip .25cm} + +\chardef\bslash=`\\ +% Command name +\newcommand{\cn}[1]{$\mathchar"026E${\tt#1}} +% File name +\newcommand{\fn}[1]{{\tt#1}} + +\def\jzitem#1{\item{\bf #1\\}} + +\def\thisisnew{\marginpar {\textbf + {\textsl {\begin{raggedright}This part is + new.\end{raggedright}}}}} + +\def\changedabit{\marginpar {\textbf + {\textsl {\begin{raggedright}Changed this a little + bit. + \end {raggedright}}}}} + +\def\seeappendix{\marginpar {\textbf + {\textsl {\begin{raggedright}Here is an + appendix reference. + \end {raggedright}}}}} + +% don't warn about bold typewriter +\DeclareFontShape{OT1}{cmtt}{bx}{n}{ <-> ssub * cmtt/m/n }{} +% \DeclareFontShape {T1}{cmtt}{bx}{n}{ <-> ssub * cmtt/m/n }{} +\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 <ovee> and <owedge> as well as + <bigovee> and <bigowedge> 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} + + + +\documentclass{l3ms002} + +\usepackage{l3d007} +\usepackage{ifthen} + +\setlength{\emergencystretch}{2em} + +\hyphenation{pre-sent fa-mi-ly} + +\renewcommand{\abstractname}{\Large Acknowledgement} + + +\typeout{******************************************} +\typeout{* } +\typeout{* This document makes use of three fonts} +\typeout{* which you might not have on your system.} +\typeout{* These are:} +\typeout{* \space\space ecrm1000 \space\space T1 encoded Computer Modern} +\typeout{* \space\space msam10 \space\space AMS symbol font A} +\typeout{* \space\space msbm10 \space\space AMS symbol font B} +\typeout{* } +\typeout{* In that case type <RETURN> to the error message} +\typeout{* The output will not contain the font charts but} +\typeout{* but will otherwise be readable.} +\typeout{* } +\typeout{* The document will also produce a number of underfull} +\typeout + {* and overfull boxes. Please ignore them (or volunteer to help)} +\typeout{* } +\typeout{******************************************} + +\newcounter{sleep} +\whiledo{\value{sleep}<1000}{\stepcounter{sleep}} + +\begin{document} + + + + + +\title{Technical Report on Math Font Encoding} +\author{Justin Ziegler} +\date{Started on June 13, 1993\\ + Last change: June 1, 1994\\ + Organisational updates: August 23, 2000\\ + Printed: \today \\ + Filename: \fn{l3d007.tex} } + +\maketitle + + + +\newcommand{\NFSS}{\textsf{NFSS}} + +\chapter*{Foreword} + +I'm pleased to present the final report on ``Math Font Encoding'' +produced by Justin Ziegler for the \LaTeX3 project to the public. + +Justin has worked for three months at the Johannes Gutenberg +University Mainz. His work was generously sponsored by GUTenberg +(The French \TeX{} Users Group) and by the ZDV of the University +of Mainz (Data Processing Center), the latter providing Justin with +office space and taking care of the administrative details. + +In the past years a lot of work went into integrating new fonts into +the \TeX{} system. Only five years ago, typesetting with \TeX{} +basically meant typesetting in Computer Modern. Nowadays many users can +choose (at least theoretically) from several thousands of fonts. +Today, \NFSS{} is the standard font selection in \LaTeX{} and due to +this mechanism and the fontinst-package by Alan Jeffrey virtually every +PostScript font, in fact, every font for which a \texttt{tfm}-file can +be obtained, can be used, out of the box, with \LaTeX. + +But for these thousand text fonts there are only five font families for +use in math formulas +to go with them. Even worse, every of these math font sets are encoded +in a different way making it nearly impossible even for an expert \TeX{} +user to use different fonts for math in different jobs. + +The work undertaken by Justin is the first of several steps to solve +the problems at hand, the final goal being the development of a system +that allows the user +to change math fonts as painlessly as it is now possible with text +fonts. + +Based on Justin's analysis and his proposal, the \LaTeX3 Project is now +undertaking to provide a prototype implementation for math fonts, +starting with the Computer Modern fonts as well as the Euler Math fonts. +We expect this implementation to be available for public usage +during 1995. + + +\begin{flushright} +Mainz, December 6, 1994\\[5pt] +Frank Mittelbach\\ +Technical Director \LaTeX3 Project +\end{flushright} + + + + +\begin{abstract} + +\vskip1cm + I wish to thank the many people without whom my stay in + Germany would not have been possible, and the work I did would not + have been done. This includes: + + \begin{description} + \item[GUTenberg] who financed my stay; + + \item[Ehoud Ahronovitz] for helping me with the administrative side + of things, for giving me the opportunity of coming here, and + spending extra time with me to make sure that everything went + all right; + + \item[Frank Mittelbach] for his friendly welcome, for the + organization, time and guidance; + + \item[Bernard Gaulle] the past president of GUTenberg, for the + organization and logistics; + + \item[Klaus Merle] for lending all the material that I used; + + \item[Chris Rowley] for the organization, and help; + + \item[Stefan Steffens] for answering patiently all my stupid + questions, and helping me integrate Mainz and the university; + + \item[The \LaTeX3 project] which partially financed my stay in England + for the Aston conference; + + \begin{sloppypar} + \item[Barbara Beeton and Alan Jeffrey] who commented my papers, and + answered more stupid questions; + \end{sloppypar} + + \item[J\"org Knappen] who gave me advice on the project, and + with whom I discovered the Mainz night life; + + \item[All the computer center employees] for making my stay more + pleasant; + + \begin{sloppypar} + \item[All the people who took the trouble to answer my mail,] for + their time and effort; + \end{sloppypar} + + \item[Donald E. Knuth] who created \TeX. + + \end{description} + +\end{abstract} + + +\setcounter{tocdepth}{1} +\tableofcontents + + + + +% This is the introduction + + + + +\chapter{Introduction / Overview} + +\section{The technical environment} +I worked in the ZDV of the university of Mainz in Germany. In German +ZDV stands for ``Zentrum f\"ur Daten Verarbeitung''. Which means: Data +Processing Center. +This is where the main --- soft and hardware --- maintenance team +works. + +I worked on an X-terminal like a lot of other people in the university. +For writing my documents I used GNU Emacs together with the +AUC\TeX\ package. + + + +\section{A few Definitions}% ***************** first section + %jwzinria: one could get rid of this subsection ? + \subsection{\TeX: a page description language} + The best definition I can find for \TeX\ is: ``one third compiler, + one third interpreter, and one third word processor''. It was + written in $\fam 1 1975$ by D.~E.~Knuth and a group of students. + One of its main features is its portability. A document written + on one machine can be used on another machine. Knuth also + insisted that \TeX\ would not change. So a document written in $\fam + 1 1980$ + is still usable in $\fam 1 1990$. + + The language defined by \TeX\ is very specific, in so far as it is + designed to describe a page layout. \TeX\ processes the page like a + rectangle, or more exactly like a box, that can be filled with + smaller boxes. These smaller boxes can similarly be filled with + smaller boxes, and etc... The smallest box one can get is a + vertical~/~horizontal line, or a character (a glyph), or just some + space. \TeX\ has variables in which one can put boxes, or different + types of numbers. One can define functions ---~usually called + macros~--- in a way similar to lisp. The if-then-else statement is + there, and combined with recursion it can be used to make loops. + + In spite of its limitations due to its specificity, \TeX{} defines + a Turing machine. The syntax is very disagreeable, but one can get + used to it: somebody wrote a basic interpreter in \TeX. The only + difference between \TeX{} and a usual compiler, is that \TeX{} stops + the compilation when it gets to the pcode, and just puts it into a + file. This file, called the device independant file, can then be + sent to a printer, a screen, or any other printing device. + + Today many people use \TeX. All \TeX\ users have got together and + created TUG: \TeX\ Users Group. + + \subsection{Plain \TeX} \label{plain-tex} + %jwzinria: one could get rid of this subsection ? + Plain \TeX\ is the standard set of macros and definitions that comes + with \TeX. It is written in \TeX. + + \subsection{\LaTeX{}: a document description language} + %jwzinria: one could get rid of this subsection ? + Just as \TeX\ is a language to describe pages, \LaTeX\ is a + language designed for describing whole documents, and their logical + structure. The idea is that it lets the user concentrate on the + contents of the document rather than the formating commands + necessary for the document to look good. Thus it uses the + logical mark-up concept. It was written by Leslie Lamport in 1985. + Technicaly, \LaTeX\ is ``only'' a cluster of macros written in \TeX. + This means that a \LaTeX\ user has still got access to most of the + \TeX\ language. \LaTeX\ includes the following facilities: + \begin{itemize} + \item Cross referencing. + \item Automatic construction of a table of contents. + \item Automatic construction of an index. + \item Bibliography referencing. + \item Basically the same math mode as \TeX. + \end{itemize} + + + + \subsection{The \LaTeX3 project} + %jwzinria: one could get rid of this subsection ? + During the 1989 TUG conference at Stanford, the decision was taken + to produce an improved and expanded version of \LaTeX, that was + going to be called \LaTeX3. + + The major difference in the new version will be the addition of a + good interface through which designers can specify how classes of + documents should be formated. + + Frank Mittelbach is the technical director of the project; he and + Chris Rowley are responsible for the management. + + + \subsection{Fonts, glyphs, and slots} + \TeX\ would not be able to produce any nice documents if it did not + have any fonts. One cannot get a nice looking `A' or `$\mathcal{A}$', + or any other letter if nobody has previously designed it. + + All \TeX\ really does, is produce a file that contains a set of + instructions. Each instruction looks like the following: ``place + here the picture that is in such and such a file, in position number + $x$.'' \textem{The files that contain all the pictures (the letters + and other symbols), are called ``fonts''. All the pictures that are + in a font are called ``glyphs''.} Every glyph in a given font has + a specific and known position. \textem{I shall use the word ``slot'' + to refer to a given position in a font.} Some slots can be empty, + but most of them contain a glyph. + + + + + \subsection{Font encodings} \label {about-encoding} + When \TeX\ refers to the glyph number $x$, it must know which glyph + is in position number $x$. This knowledge is contained in the + encoding. In some cases one could say that the letters are in the + ASCII order. But this is not sufficient, because the + ASCII code does not include all the glyphs that people wish + to put in their documents. Therefore, one must link every single + font with a given encoding, and make the encoding known by \TeX. + Many different encodings exist, sometimes even for the same group + of glyphs. But there are also many fonts that use the same encoding. + + A mathematical definition of an encoding could be the following: + \textem{An encoding is a set of glyph names in a given order.} + + \subsection{The ``Computer Modern Fonts''} + When D.~E.~Knuth created \TeX, he also created a set of fonts called + the + \textem{Computer Modern Fonts}. Most of them were based on an encoding + that is called the Computer Modern Encoding throughout this document. + + All file names of Computer Modern Fonts start with the two + letters `\texttt{cm}'. + + + \subsection{Metafont: a font description language} + Metafont is a language / program especially designed to describe glyph + shapes, and more generally whole fonts. It was used to generate all + the ``Computer modern'' fonts. The Metafont user must describe or + ``program'' the curves for each glyph. Then Metafont produces an array + of black and white dots for each glyph. The dots can be made as small + as necessary to fit the precision of the printing device. + + + \subsection{\TeX\ version 3} + In the beginning of $\fam 1 1990$, under a lot of pressure (from the + \TeX\ User Community), D.~E.~Knuth produced a new version of \TeX. + \TeX\ version 3 was born. The main improvements were the following: + + \begin{itemize} + \item Up to 256 glyphs per font. The previous versions of \TeX\ could + only use the first 128 glyphs of a font. + + + \item Virtual fonts. A normal font has all its + glyphs in a file, and this file is in actual fact the font. + Virtual fonts enable people to group 256 glyphs taken from many + different fonts, and make \TeX\ think it is using one normal font. + For instance, one could make a virtual font with lowercase letters + in bold, and uppercase letters in italic. The user would work as + if he was using one font, but the results would in actual fact be + a combination of two fonts. A very good example implementation of + virtual fonts is the creation of ``Small Caps'' fonts: the + uppercase letters could come from a roman upright font at 12 + points, whereas the lowercase ones could come from a roman + upright at 10 points. + + Virtual fonts enable still more ingenious things, like replacing + glyphs with a set of \TeX\ macros. One can then + consider, for example, automatic raising or lowering of some + letters. + + \item Better hyphenation. \TeX\ version 3 can have up to 256 + different hyphenation tables, and can produce good automatic + hyphenation even when a word contains accents. The latter was not + possible in previous versions. More generally the hyphenation + mecanisms have been improved. + + \item The new ligature mecanism is more powerful. The result of a + ligature is no longer only one glyph, but can be a set of + glyphs... + + \item Special ligatures can be done at the beginning and at the end + of words. Thus when a given letter is at the end of a word, its + shape can be different from the shape it would have in the middle + of a word. + + \item Better automatic adjusting of interword space. + + \item More little details that make everybody happy... + \end{itemize} + + + \subsection{The ``DC Fonts''} + Although D.~E.~Knuth included a lot of ``European glyphs'' in his + Computer + Modern fonts, more were needed. In $\fam 1 1989$ \TeX\ users got + together in Cork, and designed some new fonts called the \textem{DC + Fonts}. + Thanks to the new features of \TeX\ version 3 (256 glyphs per font + encoding), + DC fonts included for example more special letters for Catalan and + Scandinavian languages. + + The DC Fonts used what is now called the \textem{Cork encoding.} + All DC fonts file names start with `\texttt{dc}'. + + +\section{My work} +%\section{My work} +One of \TeX's nicest features is its ability to typeset mathematical +formulae. There has now been over ten years of experience typesetting +mathematical material with \TeX. During this time, \TeX's math mode +has been used to set a wide variety of material, including traditional +mathematics, categorical diagrams, chemical reactions, computer +programs and textual material such as `$5\frac12\%$ or $\fam0M^{lle}$. + +In recent years, with the arrival of the Cork standard for typesetting +European text, and the Virtual Font standard, the fonts available for +use in \TeX\ have radically changed. The current situation is that +there are over 14,000 text fonts available for use in \TeX, but only +five math fonts: +\begin{itemize} +\item Computer Modern +\item Computer Concrete with Euler +\item Lucida Math +\item Lucida New Math +\item Math Time +\end{itemize} +Each of these fonts use different encodings, and each comes with its own +selection of \TeX\ macros. + +Although the Cork encoding is rapidly being established as the +standard encoding for European Latin text, there is no similar +encoding for mathematics. The result is: +\begin{itemize} +\item complex macro packages for using each math font. +\item it is difficult to set mathematics with Cork text, since the Cork + encoding does not include the uppercase Greek. +\item installing PostScript math fonts such as Mathematical Pi is very + difficult. +\end{itemize} + +Furthermore, the present math encoding includes glyphs like old-style +digits, and game card suits $(\spadesuit)$ that just do not belong in +a math encoding. On the other hand, many new glyphs have been +designed and should be included in the math encoding. + +To solve these problems, a new math encoding, using all the power of +\TeX\ version 3, is needed. For this reason I have been trying to +re-organize all the glyphs that are needed to typeset mathematical +formulae with \TeX, according to various technical constraints. + +The new math encoding that I am helping to produce is hopefully going +to be part of the \LaTeX3 package, and comes as one of the general +improvements of \LaTeX. + +First I learnt to use \TeX. In a second stage, I had to study and +understand the technical constraints that apply on the grouping of +mathematical glyphs in a font. Only then could I actually start +thinking about which glyphs should go where. I intensively used \LaTeX\ +---~so that I permanently had an up to date record of what had been +done ---~and email, to communicate with the people I +was working with. + + + + + + + + + + + + + + + + + + +\chapter{The \TeX nicalities of math typesetting} + + + +\section{A brief description of \TeX's math facility} + \begin{description} + \item[Logical markup like \LaTeX.] For the design of \TeX's user + interface, one of Knuth's concerns was that in the source code of + a mathematical document the formulae should be readable in a + linear manner. Thus when a mathematician thinks, he says to + himself: ``$n$ over $n-1$'', and when a \TeX nician works, in order + to produce the result $\frac{n}{n-1}$ he just has to type: + \verb|n \over {n-1}|. + + The user is no longer bothered by trying to get this bit of text + higher than this other bit of text. He just gives \TeX\ the + logical meaning of what should be typeset, and it is correctly + placed. + + \item[The two math modes.] There are two ways to enter \TeX's math + mode, which produce slightly different results with the same + input. One mode is called the \textem{display mode,} and produces + \textem{display style,} while the other is called \textem{text + mode,} and produces \textem{text style.} The following input:\\ + \verb| $ \int_0^1 \frac{1}{x}\;dx $| \\ produces + \textem{text style:} $\int_0^1 \frac{1}{x}\;dx$, which can be + mixed with text, whereas \\ + \verb| $$ \int_0^1 \frac {1}{x} \;dx $$| \\ produces \textem + {display style:} + $$ \int_0^1 \frac {1}{x} \;dx $$ which is automatically + centered and surrounded by space. + + \item[Automatic size change according to meaning.] When the user + says to \TeX: ``this letter is a superscript'', or ``this number is + a subscript'', \TeX\ automatically typesets the letter (or the + number) in a smaller font size. \TeX\ does that same size adjustment + for setting limits on glyphs like $\sum$, or $\smallint$. + + \item[Automatic placing for sub/superscript and for limits.] At the + same time as \TeX\ changes size automatically when the user + specifies a sub- or superscript, \TeX\ also raises and lowers the + resulting text. When placing limits over a $\sum$, for example, + \TeX\ automatically centers them over the sum: + $$\sum_{i=0}^{i=n} i = \frac {n(n+1)} {2}$$ + + \item[Size change for big operators.] One can see in the previous + example that the two $\sum$ signs (one in the text and one in the + example), are not set in the same size. \TeX\ changes the size of + some big operators when they are set in a centered environment + like that example is. The integral also changes size. + + \item[Automatic spacing and math classes.] As one can see in the + previous example, \TeX\ also spaces various glyphs in a special + way. For instance the space around the $+$ sign is quite large, + whereas the space between the $n$ and the open parentheses is + comparatively reduced. Turning off the automatic mathematical + spacing for the $+$ sign would produce the following: $(n \mathord + + 1)$ versus $(n+1)$. + + On a \TeX nical point of view, the math spacing is done by + dividing all mathematical glyphs into classes. For each class + \TeX\ has different spacing rules. Thus a class 1 glyph followed + by a class two glyph would not induce the same spacing as a class + 1 followed by a class 3. There is no point in giving all the spacing + rules here. The different classes are listed below\footnote{Thanks + to Victor Eijkout for the comments.}: + \begin{enumerate} + \item \textem{Ordinary:} lowercase Greek characters, and those + symbols that are just `symbols'; + \item \textem{Large operators:} integral and sum signs, and `big' + objects such as \cn{bigcap}, or \cn{bigotimes}. Large operators + are centered vertically, and they may behave differently in text + style, and in display style\footnote{See below for + explanations.}. + \item \textem{Binary operators:} plus, minus, and look + alikes; + \item \textem{Binary relations:} equal, less than, subset, and + friends; + \item \textem{Opening symbol:} opening brace, bracket, + parentheses, etc$\ldots$ + \item \textem{Closing symbol:} closing brace, etc$\ldots$ + \item \textem{Punctuation:} most punctuation marks, with an + exception or two; + \item \textem{Variable family:} described further on in section + \ref {var-fam}. + \end{enumerate} + + \item[More symbols/glyphs.] Last but not least, \TeX's math facility + gives the user easy access to special symbols: Greek letters, + $\aleph$\footnote{$\aleph$ is a Hebrew letter, not a Greek one.} + $\cap$, $\subset$, and many others that are often used in + mathematical formulae. + + \end{description} + + +\section{Math styles} + When Knuth wrote ``The \TeX book'', he extended the `display', and + `text style' terminology. If \TeX\ is typesetting sub- or superscript + material, one says that it is in \textem{script style.} Furthermore, + if \TeX\ is typesetting sub- or superscript when it is already in + script style, one says that it is in \textem {scriptscript style.} The + style terminology must not be confused with the size terminology that + is described further on: text size, script size, and scriptscript + size. + + +\section{Font families} + \subsection{What are font families? / a definition} + In math mode, \TeX\ does not load fonts in the same way as it does + in text mode. For maths, Knuth thought best to organize the fonts in + families, and give each family a number. One font family can contain + three fonts. + + The normal use is to load in a single family the same font in + three different sizes. One size for the main text, one size for + superscript and subscript, and one size for the exceptional + super-superscript, or super-subscript. A good example ought to make + things clear: $$\int_0^\infty\;e^{\alpha.x^\alpha}\;dx = \;\;?$$ It is + clear that the $x$ is smaller than the $e$, and that the second + $\alpha$ is smaller than the first, which is the same size as the $x$. + + \subsection{The organization of mathematical glyphs} + In the present version of \TeX\ the mathematically used glyphs are + organized in 4 families: + \begin{description} + \item[Family 0: Computer Modern Roman (\texttt {cmr})] This is a + normal upright roman text font. It is loaded in a math family + in order to typeset things like $\log$ or $\sin$. The other reason + for which it is loaded into a math font family is that it + contains the uppercase Greek alphabet, so that the user can + typeset $\Psi$ and $\Gamma$, or even $\Upsilon$. A few other + symbols are also taken from \texttt{cmr}: `;' `=' `( )' `[ ]' `:' + `+' $\ldots$ See figure in appendix \ref + {app-fonts}. + + \item[Family 1: Computer Modern Math Italic (\texttt {cmmi})] The + \texttt {cmmi} font is one of the special math fonts. For a + non-expert user, its letters look just like normal \textit {italic} + letters. But in actual fact they are slightly different in their + shapes, especially the lowercase. The reason for the letters being + different is so that the variable $a$ can be easily differenciated + from the article `a' used in ``a horse'' for example. + + Whereas \texttt {cmit}\footnote {The normal italic Computer + Modern font.} contains ligatures, \texttt{cmmi} does not, and + includes instead the Greek lowercase and uppercase alphabets in + italic. + + A strange feature of \fn{cmmi} is that it contains some + old style digits. Thus one can write $\fam1 1789$ or $\fam1 1942$ + which are quite different from 1789 and 1942. But these digits are + never used in maths, so they do not belong in a font that is + designed for use in maths. + + The \fn{cmmi} font also includes some other useful\footnote + {Only for scientists though.} symbols / glyphs that one can see on + the corresponding figure in appendix \ref {app-fonts}. + + \item[Family 2: Computer Modern Symbols (\texttt {cmsy})] One can + find in this font the calligraphic alphabet that some scientists + use: $\cal{A B C D E F G H}$ $\cal{ I J K L M N O}$ $\cal{ P Q R S + T U V X Y Z}$; plus lots of other symbols that only + mathematicians could want to use: $\cap \cup \ominus \otimes + \bigtriangleup \exists \; \forall \subset \le \succ \leftarrow + \ldots$ See figure in appendix \ref + {app-fonts}. + + \item[Family 3: Computer Modern Extensibles (\texttt {cmex})] All + three sizes in this family are the same. \texttt {cmex} mainly + contains symbols that change size, automatically. + One can produce: + \[ \left\{ + \begin{array}{ll} + u(x,y,z,t) & = u_{0}(x,y,t) + U(x,y,z,t) \\ + v(x,y,z,t) & = v_{0}(x,y,t) + V(x,y,z,t) \\ + w(x,y,z,t) & = w_{0}(x,y,t) + W(x,y,z,t) \\ + w'(x,y,z,t) & = w'_{0}(x,y,t) + W'(x,y,z,t) + \end{array} + \right. \]\label {extens-example}% + with four or ten lines, and the `\{' will get bigger and bigger of + its own accord, without the user specifying anything more. \texttt + {cmex} also contains wide accents, so one can produce: $\widehat{a}$ + $\widehat{ar}$ $\widehat{arg}$. I have previously spoken about the + automatic size change of some operators, whether in text, or in + display, style. These double sized `big operators' are in \texttt + {cmex}: + $\bigcap\ and\ \coprod$ in text style, and in display style: + $$\bigcup \ and\ \coprod\ and \ldots$$ + The total contents of \fn {cmex} is + shown in a figure appendix \ref {app-fonts}. + + Most of the glyhs in \texttt{cmex} have a stange metric + particularity, that makes them \TeX\ specific. Thus no other + typesetting system can use those glyphs. Vice versa \TeX\ could not + use those glyphs if they were made for another typesetting system. + I spent a certain amount of time trying to understand all the + triks hidden in \texttt {cmex}, and wrote a document on the topic + (see appendix \ref {app-rep-cmex}). The math font group was then + able to take decisions concerning the replacement of \fn + {cmex}. + + \item[The AMS symbol fonts: \texttt {msam} and \texttt {msbm}.] Many + more mathematical glyphs, and an extra blackboard bold alphabet. + They are not part of the standard \TeX, and are not loaded + automatically in a family, but they are used on many sites. They + were designed for the AMS: American Math Society, for use with + \TeX, and are now very widely spread. Their contents is shown in + figures, appendix \ref {app-fonts}. + + \end{description} + + + \subsection {How does \TeX\ identify glyphs? } + \begin{description} + + \item[Glyph names.] In Plain (see section \ref {plain-tex}) many + glyph names are defined. They refer to some of the numerous + glyphs \TeX\ can typeset. + + The user can also define his own names for glyphs. To a + glyph name must be associated a family number, and a position + in the given family. On top of that \TeX\ likes to know which + class the glyph belongs to. As well as the classes that have + already been defined, there is an extra one: + + \item[The \textem {`variable family'} class and the \cn{fam} + variable.] \label{var-fam} This class has nothing to do with + spacing, and, to my mind, treating it as a class is one of + Knuth's mistakes. It is used in particular for letters, but it + could have other uses. If the calligraphic, upright, and italic + letters all have the same position in their respective fonts, + one does not want to define a different name for each letter in + each shape. Instead, \TeX\ has a \cn{fam} variable, that + contains the number of the current family where glyphs should be + taken from. So when a glyph is of class \textem {`variable + family'}, it is taken from the family number \cn{fam}. But + that is not enough. Some times the \cn{fam} variable can be + equal to $-1$, and there is no family number $-1$. In such a + case a default family number is used. So together with the class + and the position, one can assign the default family number for + each glyph name. When a glyph is not defined as being variable + family, it always comes from the same family, and its family + number is linked to its name in the same way as the class + number. + + Example: when the user enters math mode, \cn{fam} is equal to + $-1$, the letters come from the default family. By typing: + \verb|$abda$| which produces `$abda$', one can see that the + default family for letters is family number 1 (See family + descriptions). If the user assigns the family variable to $0$ + then the letters will come from family $0$. Thus + \verb|$\fam0 abda$| produces `$\fam0 abda$'. (See family + descriptions). + \end{description} + + + + + + + +\section{Font metric files: The ``\texttt{.tfm}'' files} + \subsection{A theoretical overview} + When \TeX\ is typesetting a page, and making all the calculations + that are necessary for this, it does not need the actual picture of + the glyphs. All \TeX\ needs at this stage is the dimensions of the + glyphs, and other numerical data. That information is in the + ``\texttt{.tfm}''\footnote{\texttt{tfm} stands for ``\TeX\ font metric + file.''} files, and every font has one. Without it, the font is + unusable as far as \TeX\footnote{There are some slight exceptions to + this rule: in some cases a given font can use another font's + ``\texttt{.tfm}'' file. But the visual results are not very good.} + is concerned. + + For mathematical typesetting \TeX\ uses all the information that a + ``\texttt {.tfm}'' file can give. One of the first things I had to do + was to study and understand the machinery hidden in the math fonts + ``\texttt {.tfm}'' files. From a general point of view a font metrics + file can contain the following data: \footnote {This is not + restricted to \TeX. Although the file formats maybe slightly + different, Postscript type fonts and others use similar + metric files. One can find programs to convert the files + from one format to another.} + + \begin{description} + \item [Font dimensions.] These are global parameters + for the whole font. In a normal text font one would find the + slant (positive on an italic or slanted font), the size of the + interword space, other interword spacing parameters, more general + spacing parameters, and the x-height. The latter is the height of + the `x' glyph, and is used for correct accent positioning. + + The fonts in family 2 and 3 are a little special as far as font + dimensions are concerned. \TeX\ looks in family 2 and 3 for more + font dimensions than usual. This extra information is used for + special math spacing. + + \item [Glyph dimensions.] Each glyph has a height, a width and a + depth specified in the ``\texttt{.tfm}'' file. The height of the + box that surrounds a glyph is equal to the height of the glyph + plus the depth of the glyph, whereas the width is that of the + glyph. I think it is important to say that \textem{these values + are theoretical, and can be quite different from the real size + of the glyph.} Thus some glyphs are bigger than their box. A + good example of this is the italic `f': \textit{f}. The top right + end, and the bottom left end stick out of the box. The right hand + side of a given glyph box is also the left hand side of the + next\footnote{The box on the right of the first one.} glyph box. + + \item [Kerns.] \label {about-kerning} They are necessary for the + \textem{automatic adjustment } of the spacing between two glyphs. + Many non professional electronic typesetting systems have for a + long time ignored this refinement of traditional typesetting. The + problem is the following: for visual comfort all the letters of + the alphabet cannot be spaced in the same manner. For instance + when an `A' is followed by a `V', the two letters must be brought + closer together to produce `AV' versus `A{V}'. In other cases + letters must be separated a little to produce `aj' versus `a{j}', + or `f!' versus `f{!}'. Otherwise the spacing does not look correct + compared to the spacing of surrounding letters. In the + ``\texttt{.tfm}'' file, for each glyph one can specify kerns with + every other glyph \textem{of the font}. \textem{When two glyphs + that are kerned in the ``\texttt{.tfm}'' file are found side by + side in the right order, \TeX\ automatically brings them closer + together, or farther away.} + + \item [Ligatures.] \label {about-ligs} Here again, the idea is to + improve visual comfort, and reading. Some letters when followed by + other particular letters do not look right. In this case the two + glyphs side by side must be replaced by another glyph that will + look much better. This is called a ligature. The best and very + well known example occurs when an `f' glyph is followed by an `i' + glyph. The non-ligatured glyphs look like `f{i}', and + \textem{\TeX\ automatically replaces} them with the ligature that + looks like `fi'. In the ``Collection La Pleiade'', one can see many + other ligatures if one looks hard enough. + + In \TeX\ version 3 the concept of ligatures is more general. It + can use more than two letters, and has other interesting new + features. + + \item [Italic corrections.] For this I can only quote Frank + Mittelbach: + \begin{quote} + ``At the points where one switches from slanted or italic to + upright, the glyphs usually come too close together, especially + if the last slanted/italic glyph has an ascender\footnote{Here + is something that has not been defined. The following letters + have ascenders: l,k,h,f,t,b,d, in lowercase. One can guess + what descenders are.}. The proper amount of extra + white space that should be added at this boundary is called the + `italic correction'. Its value depends on individual glyph + shape, and is therefore stored in the ``\texttt{.tfm}'' file for + each glyph. [...] For an upright font the italic corrections + are usually null. [...] In slanted and italic fonts, the italic + corrections are usually positif...'' + \end{quote} + Example: in the word {\it dif}ferent, the first f runs into the + second one. Whereas in the word \textem{dif}ferent, a little space + is left between the two f's. That space is the f's italic + correction. + + \item [`Skewchar' kerning.] The skewchar is a specific character + that is used for placing mathematical accents. In math mode, when + an accent is placed on a glyph, the accent is first centered on + top of the glyph's box, and then shifted rightwards by the amount + of the kern between the glyph and the skewchar. + + Each font should have its own skewchar. For most characters, the + ``{\tt .tfm}'' file specifies the kerning of each letter with its + skewchar. This is true for the computer modern fonts, but other + font designers may have chosen not to use 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 not usually subject to kerning from + other glyphs.'' + + + \begin{sloppypar} + \item[Charlists.] \label {about-charlists} Charlists enable several + characters in a font to be linked together. The \texttt {cmex} + font uses charlists a lot: by just typing \texttt{charlist oct + "000": oct "020": oct "022": oct "040": oct "060"} in the + metafont source code, one links in order of increasing size all + the left parenthesis that are in the font. Thus with this + information contained in the ``\texttt {.tfm}'' file, \TeX\ can + find the parentheses that has the correct size for what is + currently being typeset. + + Charlists are used for: + \begin{itemize} + \item Linking variable-size delimiters, + \item Linking variable-width accents, + \item Pairing the ``big operators'' that are typeset in + different sizes in display style, and text style. + \end{itemize} + \end{sloppypar} + + \item[Extensibles.] \label {about-extens} Extensible glyphs can + change size vertically (not horizontally), according to the + context. A good example is given in section \ref {extens-example} + where the \{ grows automatically. + + \begin{sloppypar} + An extensible glyph is identified with one of its pieces. One simply + has to decide which piece is going to be used for this + identification. In the following example: \texttt {extensible + oct"060": oct"060", 0, oct"100", oct"102";} --- which appears in + the metafont code of \texttt {cmex}, the first oct"060" is the + identifier of the whole extensible glyph. The next three + characters are the top, middle, and bottom pieces of the glyph + whose identifier is oct"060". The last character code 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 + pieces are optional except the repeatable piece. + \end{sloppypar} + + This mecanism is also used for the construction of the radical + sign. But it only works for glyphs that grow vertically. + Therefore the horizontal braces and the horizontal extendable + arrows cannot use this facility. + +\end{description} + + + + + \subsection{Example: analysis of `\texttt{cmmi}' metrics} + %\footnotetext{\texttt{cmmi} stands for Computer Modern Math italic, + % and is the default font for typesetting mathematics.} + I shall use here the usual \TeX\ notation for writing octal numbers. + Thus all numbers preceeded by a little quote sign like '77 are in + octal. + \begin{itemize} + \item Most characters in `\texttt{cmmi}' are kerned with the + skewchar. + + \item Many Greek uppercase and lowercase letters are kerned to: `.' + `,' and `/' respectivly '72, '73, and '75. This takes us right up + to position '50. + + \item Characters from '50 to '73 are not kerned at all. This + includes: funny horizontal half arrows, two hooks for the arrow + construction set, two triangles, the old style digits, the `.', the + `,' and the `$<$'. + + \item The `$/$' sign is kerned with 1\footnote {The digit.}, A, M, + N, Y, Z. Nothing to say about `$<$' and $*$ and $\partial$. + + \item Then come the uppercase Latin letters. They are not kerned + among each other. They are not kerned either with the lowercase + letters. Just like the Greek letters, some of them are kerned with + `.' `,' `$/$'. + + \item In my \fn{.pl} file, it looks as though N and X have got two + different kerns with '75. (Not yet any explanation for this.) The + 3 musical signs are not kerned with anything. The horizontal + parentheses are not either. + + \item The lowercase Latin letters are not kerned with each other, + except `$d$' that is kerned with $Y, Z, j, f$. Some of them are + kerned with `,' `.' `$/$' in a way similar to that of uppercase + letters. + + \item The last characters are not kerned at all. + \end{itemize} + + For compatibility reasons, all these kerns will have to be in the + new encoding. + + See appendix \ref {app-rep-cmex} for a complete description and + analyses of \fn{cmex10.tfm}. + + +% \subsection{Large operators} +% \subsection{Delimiters} + + + + + + + + + + + + + + + + + + +\chapter{Dividing all the glyphs into groups} + +\section{More vocabulary}\label{MoreVocab} + \begin{description} + \item[An ``encoding table''.] This conveys the traditional meaning + of an encoding (see section \ref {about-encoding}). That is to say + a set of 256 glyphs in a given order. The expression ``encoding + table'' is usually abbreviated: ``encoding''. + + \item[A ``slot'':] the usual word used for referring to a + position in an encoding. A slot can contain a glyph, or be empty. + It is represented by an integer between 0 and 255. A slot is + \textem{not} a family in spite of the usage some people make of this + word. + + \item[The ``math kernel''.] This terminology is used to specify the + minimal group of fonts that is necessary for the math facility to + work, as described in the \TeX\ documentation\footnote{And + LA\TeX, AMS\TeX, etc, documentation.}. In D.~E.~K.'s + package (Plain) the math kernel consists of the families + numbered from 0 to 3. Together with the kernel, many other fonts can + optionally be loaded and used. + + \item[A ``math encoding'':] considered here as a + whole. Not just one 256-glyph encoding table, but a set of $x$ + encoding tables, where $x$ is greater or equal to the number of + fonts in the math kernel. I will sometimes refer to this concept + with the abbreviation ``M-encoding''. + + \item[The ``default alphabet'':] the alphabet that is used + when a user types \texttt{\$abc\$}. With Plain \TeX's math + encoding that produces $abc$. + + \item[``Glyph compatibility'':] two encodings (or M-encodings) are + glyph compatible, if they contain the same glyphs. The latter do + not systematically have to be in the same positions. However + identical glyphs must have the same + metrics. The kerning and ligaturing information must + also be identical in both M-encodings. + + +\end{description} + +\section{General approach} +Taking all the glyphs one by one, and putting them in a font encoding +would have been to easy, and above all not satisfactory. Instead one +must divide all the necessary glyphs into groups and subgroups, and then +tried to match groups in individual encoding tables according to all +the constraints. + +For instance, a typical group is the Latin alphabet: it includes the +uppercase letters A-Z, and the lowercase letters a-z. +Mathematicians often use accents on letters. For this they +need a dotless `i' (looks like: `$\i$') and a dotless `j' +(looks like: `$\j$') with every Latin alphabet. Thus the Latin +alphabet group contains the uppercase and lowercase letters, the +dotless `i' and the dotless `j'. + +The grouping is based on different types of constraints: some +technical, and some based on glyph usage. These are detailed in the next +section. + +\section{Grouping constraints} +Before being able to group the glyphs, grouping rules had to be +established. \footnote {I've put in appendix +\ref {app-accents}, \ref {app-rep-cmex}, and \ref {app-delims}, three +of the documents that I wrote for this purpose.} + +At first I did not realise the importance of the design similarity +constraint for the person designing the font. Thus the first two +proposals did not really take it into account at all. + + \begin{description} + \item [Kerning.] See section \ref {about-kerning} for a definition + of kerning. The kerning information for a given font can be found + in it's \texttt{tfm} file. Thus two glyphs from the same + encoding table can be kerned together, but the letter `f' + belonging in a given encoding table, cannot be kerned with a + glyph (the open parenthesis for instance) belonging in another + encoding table. A group resulting from this constraint is: the + group of glyphs that must be kerned with the default alphabet. + This group and the alphabet will have to live in the same + encoding table. This constraint is considered to be one of the + most important. + + In fact this type of grouping is not so much grouping together + all the glyphs that must be kerned, but putting together in one + group the glyphs that need to be kerned with another group. In + order to facilitate the counting. + + \item[Ligaturing.] See section \ref {about-ligs} for a definition of + ligaturing. In a similar manner to kerning, ligatures request + that various glyphs live in the same encoding. If the letter + `f' is to be ligatured with the letter `i' and produce the `fi' + ligature, then those three glyphs `f',`i', and `fi' must live + in the same encoding. In actual fact ligatures are not really + used in math fonts. But they may be necessary one day. So + empty slots should be left for ligatures where possible. + + \item[Design similarity:] another reason for which the letter A must + live in the same font encoding as the letter B, and all the other + letters. All the glyphs in a normal text encoding are designed to be + visually compatible with each other. This should also be the case in a + math encoding. But all the compatible glyphs cannot live in the same + font. There are simply too many of them. So one has to make a + choice. Which glyphs must be alike? A lot of groups result from this + constraint, which even comes into play when putting the groups + together into encodings. A good example is the sim group. `Sim' is + the name given to the glyph: $\sim$. Many mathematical symbols contain + such a sim. $\approx$ cannot be separated from $\sim$ because they + must look alike, and for that they must be designed by the same + person. Even more, the $\sim$ and the $\approx$ should be produced in + metafont using the same sub-routine, with the same parameters. This + also explains why it is important that the letters of a given style + all live together. + + + \item[Charlists.] The reader is advised to re-read section \ref + {about-charlists} if he no longer remembers what charlists are. The + information that such and such a glyph is part of a charlist is in + the \texttt{tfm} file. Therefore charlists are also restricted to + one font. Because of this all glyphs that are intended to be + linked in a charlist must be put in the same font. Concerned + by this restriction are: + \begin{itemize} + \item Wide accents, which are linked with a charlist in order of + increasing size, + \item Big delimiters: same as accents, + \item The two sizes of big operators which are linked, + \item All the different sized radicals. + \end{itemize} + + \item[Extensibles.] In case of memory deficiency the reader is + advised to take another look at the relevant passage in section + \ref {about-extens} again. As for charlists, the extensible + information is part of the \texttt {tfm} file. The different + pieces of an extensible glyph must therefore live in the same + font. Concerned by this restriction are: + + \begin{itemize} + \item Extensible delimiters (not all delimiters are extensible). + This constraint is doubled by the fact that an extensible + delimiter is often the last element of a charlist. Thus many + glyphs must live together. + + \item Radicals: the last element of the radical charlist is an + extensible: it grows as high as necessary. In + the same way as delimiters, the glyphs used to + build the extensible radical are a subgroup of + the radical charlist group, and therefore must + live with the other members of the charlist. + + \item Vertical arrows or bars\footnote {But not horizontal + arrows.}. + \end{itemize} + + \item[Constructed symbols.] Some glyphs in a font are especially + designed to be put next to each other. Good examples are the + horizontal arrows, and the horizontal curly braces. Because of + their horizontal characteristic, the extensible mechanism cannot + be used. So the $$\underbrace {\mathrm {horizontal\ curly\ brace}}$$ + is built up with abbuting glyphs. These glyphs must be of the same + weight, and very well adjusted in order to fit together properly. + They must therefore live in the same font. + +\end{description} + + + +\section {Constraint importance} +The design constraint is less important than the kerning constraint. +Whereas keeping empty slots for ligaturing has very little +importance compared to the two former constraints. + +Charlists' and extensible lists' members \textbf {must} stay together, +without exception. One could establish the following order of +importance: + + \begin{enumerate} + \item Extensibles, + \item Charlists, + \item Constructed symbols, + \item Kerning, + \item Ligatures, + \item Design similarities, + \item Empty slots for ligatures. + \end{enumerate} + + + +\section{A few groups} + +\begin{itemize} +\item The Greek letter sets, +\item The Greek-like glyphs, +\item The Latin letter set, +\item The Latin-like material +\item The digits, +\item The vertical arrows, +\item The horizontal arrows, +\item The accents, wide, double, underaccents, +\item The core symbols: must live with the default alphabet, +\item The subset group, +\item The greater than group, +\item etc ... +\end{itemize} + +A lot of the above groups were still divided into smaller groups in +order to make things fit in the encoding tables. Compromises had to be +made, in order to respect the constraints set by compatibility. + + + +\chapter{Making encoding tables} +Similarly to the constraints governing the grouping, the constraints +governing the division into encoding tables listed below were not at +all obvious, and had to be thought of, and fully understood. + +The construction of encoding tables largely depends on the main goals of +a new math encoding. + +\section{The constraints of group grouping} +\begin{description} + + \item[Glyphs access.] (alphabets, variable family) This is + another technical constraint due to the way \TeX\ accesses glyphs. + It is also a user interface constraint, because the idea is to + make alphabets easily accessible to the user. + + Due to the variable family mechanism (explained in section \ref + {var-fam}), It is very practical for the user that font + encodings contain only one alphabet. Thus when the fonts are + loaded into the families, different letters can be accessed by + changing the \cn{fam} variable, and typing the usual letters on + the keyboard. For instance, when \cn{fam} is equal to $-1$, the + default family is used. When \cn{fam} equals 2 the user can + get the script alphabet. For this the user need only type + \verb|$\fam=2 A,B,C$| and the letters $\cal{A,B,C}$ are + produced. + + The alternative would be to have many alphabets in one encoding. + In that case, to access script letters A,B,C for example, the user + would have to type \verb|$\scriptA,\scriptB$|. That would be much more + difficult to read, and less practical. + + This constraint --~due to glyph access~-- sets the shape of the whole + M-encoding and has a very high priority. + + \item[Font access.] This only concerns the font that will replace + \texttt {cmex}. For compatibility reasons, the math font group + decided that it would be reasonable to try and replace \texttt + {cmex} by a font that can be loaded in one size, \textem {and} in + three sizes. Therefore the \texttt{cmex} replacement can only + take: + \begin{itemize} + \item Wide accents, + \item Big delimiters, + \item Big Operators, + \item Radicals (with a small change), + \item Vertical extensible arrows. + \end{itemize} + It would be too long to justify the decision here, but the relevant + document is in appendix \ref {app-rep-cmex}. One of the consequences + of this is that one cannot put an alphabet in \texttt {cmex}'s + replacement encoding. An aphabet must be available in all three + sizes. + Other glyphs are also victims of this limitation. + + \item[Kerning.] Obviously, if glyphs in two separate groups must be + kerned, then those two groups must live together. + + \item[Design similarity.] This is a designor's constraint and + therefore has low priority. Because of this low priority, it often + happens that big design similarity groups are subdivided into smaller + ones. In such case one must try in sofar as is possible to put the + smaller groups back together. + + \item[Bold face.] Mathematicians and physicists often use boldface + glyphs. These can either be directly available in some of the + encodings, whereby the encoding will specify: here should go a + bold uppercase `A' ---~and that could be next to a non-bold glyph; + or none of the encoding tables specify whether or not the glyphs + are bold, and a bold version of the whole M-encoding or of each + encoding table can be made ---~as with text fonts. + + To reduce the total number of glyphs in the M-encoding, the + second possibility has been chosen. But this induces another + constraint on the global M-encoding: the individual encoding + tables must be designed in such a way that the most commonly + used bold glyphs are put together. + + \begin{sloppypar} + \item[Compatibility with other font-using programs.] Since the + invention of ASCII code, the first 32 slots of fonts were + often not used for glyphs, but reserved for control + codes. Today many programs are still not designed to use the + first 32 slots of a font. Thus fonts should not contain any + glyphs in those slots. + But this would be a big waste for \TeX, because it can use + glyphs in slots below 32. + + However, if the glyphs in the critical slots do not have any + kerning relation-ship with other glyphs in the font, then the + former can be put in another font, and be used with little + difficulty even in problematic software. This seemed a fairly + good compromise, so it was decided to fill slots below 32 + with glyphs that do not have any kerning with the others, and + could thus be separated from them. + + On the same lines: some programs are unable to use fonts that do + not have a space in position 32. To solve this problem, only one + slot in concerned, so it was decided to include a space in every + font. This should not be a problem. + + \item[Grouping \TeX\ specific glyphs: another compatibility + issue.] \hfil + The present \texttt{cmex} font/encoding contains glyphs + that cannot be used by other typesetting systems, because they + are set in a strange way. Similarly \texttt{cmsy} contains one + glyph that is set in a strange way: the radical sign. Therefore + the whole of \texttt{cmsy} is unusable for other programs. Such a + mistake must not be reproduced. + + It is hoped that the new \TeX\ math encoding will set a + standard, that will not only be used by \TeX, but by all + systems that typeset mathematical formulae. If everything 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 M-encoding. Thus it will be very easy to use the same + fonts on different systems. One day a \TeX\ user will be able + to take a mathematical font from 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 next to + different math fonts. 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 changes. + + From a commercial point of view, if a font designer creates a math + font for Adobe, the work necessary for adapting it to \TeX\ must + be reduced to the minimum. Otherwise nobody will provide any new + math fonts for \TeX. + + \TeX\ specific glyphs are the following: + \begin{itemize} + \item The delimiters, + \item The large and small `bigops', + \item The radicals. + \end{itemize} + + + \item[Compatibility with Plain and \LaTeX.] Let us consider a user + that has typed a document with the present math encoding, and in + so doing has saturated the available families. If the new math + encoding does not garantee Plain and \LaTeX\ glyph compatibility + with a \textem {maximum of 4 fonts,} then the document will + not be able to run with the new math encoding: not enough + families. Thus one should make the first four encoding tables of + the global M-encoding glyphs compatible with the Computer + Modern cluster: cmr, cmmi, cmex, and cmsy. + + + \item[Compatibility with AMS\TeX, AMS\LaTeX, and LAMS\TeX.] Let us + consider this time a user that has typed a document with the + existant AMS\TeX\ or AMS\LaTeX\ package, and in so doing has + saturated the available families. If the new math encoding does + not give AMS\LaTeX\ and AMS\TeX\ glyph compatibility with less + than 6 encoding tables, then that document will not run with the + new math encoding, for lack of family reasons. + + The first 6 encoding tables must be one way glyph compatible with + the fonts provided in the AMS packages. + \end{sloppypar} + + \item[Trying to give the Plain \TeX\ user a logical cluster of new + glyphs.] No comment. + +\end{description} + +\section{The Aston-LC math encoding} +This is one of the proposals first thought of, but it is +not the one finally chosen, because it had many problems. + +LC stands for latin core. The main characteristic is the separation of +the Greek letter sets from the Latin ones. In keeping these two sets +separate, we give the greek letters an identity of their own, thus +making them quite independent of the rest. The idea goes in the +direction of orthogonal grouping. All the encodings that contain +letters would have them in the Cork encoding positions, thus making +access very simple. In fact this positioning concept will be taken +farther: Cork encoded glyphs that are in the new encoding, will keep +their Cork position. + +\subsection{The encoding tables} + \begin{description} + \item[The text symbols: the TS encoding.] Here would be included the + old style numerals, and most of what is to be taken out of the + present math encoding, because it does not belong with the rest of the + math glyphs. Other symbols could be added in this encoding. + + This encoding is not part of the M-encoding, but it will contain + symbols that previously were accessed via the math fonts. In + normal usage, this font will not be loaded in a family. It will + simply be loaded as a normal text font. + + \item[The base: a Cork encoded latin text font.] The main use of + this font would be to typeset function names like \texttt + {\string\log}. The idea being that the user can actually choose + this font among the existing Cork encoded fonts. Thus `sin' can + actually be typeset in the same style as the text, or in another + special style to match the rest of the math glyphs. + + \item[The core: the MC encoding.] It would not contain any Greek + glyphs (unlike \texttt {cmmi}). The basic accents (only one size) + would be here, next to the default numerals. It would also include + all the upper and lowercase default latin alphabet, all + of the symbols that are most commonly used, and glyphs that must + be kerned with the default alphabet. + + \item[The Greek alphabets: the MG encoding.] This encoding table + would contain all the upper and lowercase Greek letters in + upright and italic, plus some variable shape Greek letters, also + in upright and italic, and some numeric Greek letters. Any other + Greek related glyphs would also live in MG. If place is still + available, one could include some symbols. An advantage of + putting the italic Greek and upright Greek together, is that both + are often requested in medium and in bold weight. + + \item[The extensibles: the MX encoding.] This encoding would look + very much like the present \texttt {cmex} encoding: the usual + extensible characters, together with some new ones. It could + include any characters that have strange \TeX\ features like big + descenders. Thus glyphs that are not compatible with the + outer world would be kept together. + + \begin{sloppypar} + \item[The math symbols: the MS1, MS2, MS3... encodings.] Each of + these encodings would contain a set of Latin letters, like for + instance script or blackboard bold, in upper or lowercase, or + both, together with a set of matching accents if needed. In some + cases a place should also be reserved for a set of matching + numbers. The rest would be filled up with symbols. There could be + an MS$_i$ encoding for: + \begin{itemize} + \item Calligraphic, + \item Script, + \item Open, + \item Old german, (Fraktur) + \end{itemize} + \end{sloppypar} + + \end{description} + + + +\subsection{Other requested typefaces} + \begin{itemize} + \item A ``text-like'' italic or slanted font for computer science + identifier-names and the like. This would be Cork encoded. + \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. + \item Bold italic for use as variables: an MC or Cork encoding. + \item Bold Old german (occasional). + \item Bold script (occasional). + \item Sans serif lightface (occasional): Cork encoded font. + \item Sans serif boldface (occasional): Cork encoded font. + \item Bold symbols: the same encodings loaded in bold. + \item Ultra bold symbols: the same encodings loaded in bold. +\end{itemize} + + + +\subsection{Summarizing the family occupation} +The following encodings are needed in the kernel: + +\begin{enumerate} +\item A Cork encoded upright text font. +\item An MC encoded font containing the default alphabet, digits, + accents, and symbols. +\item An MS$_1$ encoded symbol font for calligraphic/script. +\item An MX encoded extensible font. +\item An MG encoded font for Greek italic and upright. +\item An MS$_2$ encoded symbol font for Open and symbols. +\item An MS$_3$ encoded symbol font for Old german and symbols. +\end{enumerate} + +This occupies 7 families, and leaves 9 free for anything else, (like +bold or sans...) and makes many symbols available. + + + + +\subsection{Pros and cons} +This proposal did not respect the limit of 4 and 6 families +(compatibility with Plain\TeX\ and AMS\TeX), nor did it enable the Latin +and Greek to be kerned together, nor could the Greek be kerned with the +same symbols as the Latin alphabet, unless these were +repeated. Generally, to get the equivalent of Plain \TeX, one would have +had to load 5 families, and to get the functionalities of AMS\TeX, one +would have needed to load 7 families. + +One of the advantages was the orthogonality of the individual encoding +tables, i.e. there were no strange mixes like Latin and Greek, or +anything of the sort. + +The main reasons for rejecting this proposal are: +\begin{itemize} +\item it is a big family consumer. In particular bold Latin and Greek + would occupy two extra families, and they are frequently requested. +\item it does not enable kerning between the Greek and punctuation + which is needed for compatibility ---~the punctuation is in + a separate encoding table from the Greek. +\end{itemize} + +The next proposal is more attractive... + + + +\section{The Aston LGC math encoding} + +LGC stands for Latin Greek core. One of the main features of this +proposal is that the Greek and Latin alphabets have been put +together. In one font they could be upright, and in the other they could +be italic. A good reason for doing things this way is that the font +dimension called slant may give a few unexpected problems if italic and +non italic glyphs are mixed in the way that they would have been in the +Aston LC math encoding. + + +\subsection{The encoding tables} +\begin{description} + +\begin{sloppypar} +\item[The text symbols: the TS encoding.] This would be the same as in + the previous proposal, and would be used in a similar manner. + +\item[The base: a Cork encoded latin text font.] This would be the same + as in the previous proposal, and they would be used in a similar + manner. +\end{sloppypar} + +\item[The core: the LG encoding.] Instead of the MC encoding (in the + previous proposal), the core could be duplicated. Once in upright, + and once in uppercase. The LG encoding would contain one instance + of both Latin and Greek letter sets. So two LG encoded fonts would + be used (upright, and italic). + + As far as the other slots are concerned, they could be filled in + with the most used math symbols (similarly to the MC encoding), + these would then appear once in upright, and once in bold. An + alternative to such a duplication would be to make an LG1 encoding + that would contain different symbols from an LG2 encoding, and these + would always be in upright, whereas the letters would be specified + as italic in LG1, and upright in LG2. + + \textbf{Note.} The user could choose whether he wants to load both LG1 + and LG2, or only one of the two. + + +\item[The extensibles: the MX encoding.] It would be the same as in + the previous proposal, and it would be used in a similar manner. + +\item[The math symbols: the MS1, MS2, MS3... encodings.] {\sloppy These + would be the same as in the previous proposal, and they would be + used in a similar manner.} + +\end{description} + +\subsection{And the rest?} +Similarly to the previous proposal, many other fonts could be loaded +in all the free families. + + +\subsection{Summarising the Family occupation} +\begin{enumerate} + \item An LG encoded font containing Latin and Greek italic. (This + could be LG1 if necessary. See explanations above.) + \item An MS$_1$ encoded symbol font for calligraphic/script. + \item An MX encoded extensibles font. + \item An LG encoded font containing latin and Greek upright. (This + could be LG2 if necessary. See explanations above.) + \item An MS$_2$ encoded font for Open and symbols. + \item An MS$_3$ encoded font for Old German and symbols. +\end{enumerate} + +Only 6 families are occupied. This leaves 10 families free for +anything else, (like bold or sans...) and makes many symbols +available. + + + +\subsection{Pros and cons} + +One of the advantages of this proposal is that kerning can be done +between Latin and Greek (as long as they are in the same shape), and +between Greek and other symbols present in the encoding such as +punctuation. Also when bold is requested, one gets the bold Latin and +the bold Greek in the same font table, which again consumes less +families than having the two separate. + +This proposal occupies less families than the previous one. + +Reasons for abandoning the Aston LGC math encoding: +\begin{itemize} + \item The user must be able to choose the look of his log, sin, and + friends. He may want them to be either text compatible, or + compatible with the other math alphabets and the rest of the math + glyphs in general. The choice must be left open, and the math font + designer must not impose his decision on the user. + \item A solution to the previous problem is to include another + font for this purpose, as in the previous proposal. But then the + family occupation rises up to 7, and three Latin alphabets are + loaded, of which one (the LG upright) is probably not going to be + used much. Thus a lot of precious space is wasted. + \item The `Yaasp' proposal is much more attractive. +\end{itemize} + + + + +\chapter{The proposed YAASP encoding} +\label{app-yaasp} +\begin{quote} + This chapter is the final proposal that was made. It is also the body + of the official document that was produced. The reader may find some + similarities with the previous sections, for instance some of the + definitions can be found in section \ref {MoreVocab}. Also a lot of + the points discussed in the global policy section have already been + discussed. + +\end{quote} + +\input{l3d007a.tex} + + + +\chapter{The glyph groups} + +\input{l3d007b.tex} + + + + +\chapter{Final conclusions} + +The `Yaasp' proposal, which is the final proposal made, is given in +chapter \ref{app-yaasp}. + +Working on the \LaTeX3 project in Mainz was very interesting for many +reasons: +\begin{itemize} +\item People next to me were working on net management and system + maintenance. I used email intensively for communicating + with other people working on the project. I used tar files and + other programs to send large amounts of information to other people. + + It was a very good introduction to the network oriented studies I + will be doing in my last year. I don't think that I really knew before + what the network was. Now I have a better idea. + +\item I installed a test version of NFSS2. It was a good + introduction to software installing, and enabled me to discover a + few more UNIX tools. I hope I will be able to use this knowledge for + installing various packages for \TeX\ and especially emacs in the + Ecole des Mines de Saint Etienne. + + +\item The work I did was to a large extent research work and thus + involved many topics for which no previous experience was + available. For this reason the work seemed to go slowly, and we often + had to go back to the drawing board and re-think points that we + thought were already finished and done with. All of this, of course, + was made worse by the fact that a lot of the communication was done + via email. + + However, the final result was very positive. By the end of the three + months, a complete proposal for a new math font set-up was produced. + For Frank Mittelbach technical director of the \LaTeX 3 project, + this is a good achievement, and a big step forward. The next stage is + to try and implement the proposal, and start testing it. + + +\item Last but not least, I greatly improved my English and my German. + I learnt about another country, about its educational system, and + about its habits, which one can only grasp by working in the country. + I learnt how to integrate in a foreign environment, and how to deal + with a few distressing problems: it was not easy to keep calm when + my car packed up the week-end before I had planned to go back to + France. In one's own country garage mechanics aren't easy people to + deal with; matters get even worse when it is in a foreign country. + +\end{itemize} + +The whole experience was very enriching in many domains. The difficulty +I had in speaking German proved to me that the teaching of languages in +the \textem {Ecole des Mines de Saint Etienne} is not good enough, and +must be improved and given more importance. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% appendix starts here. +\appendix + + +\chapter{Analysing \TeX's positioning of \cn{mathaccent}s} +\label {app-accents} +\input{l3d007c.tex} + + +\chapter{A close look at extensible characters} +\label {app-delims} +\input{l3d007d.tex} + + +\chapter{Replacing \texttt{cmex} ?} +\label{app-rep-cmex} +\input{l3d007e.tex} + + + + + + +\chapter{Fonts and font encodings} +\label{app-fonts} + +The first 4 figures given on the next few pages are the standard fonts +used in plain \TeX\ for maths. +\begin{itemize} +\item \textbf{Computer Modern Roman:} loaded in family 0 shown on figure + \ref {fnt-tbl-cmr}. +\item \textbf{Computer Modern Math Italic:} loaded in family 1 shown on + figure \ref {fnt-tbl-cmmi}. +\item \textbf{Computer Modern SYmbols:} loaded in family 2 shown on + figure \ref {fnt-tbl-cmsy}. +\item \textbf{Computer Modern EXtensibles:} loaded in family 3 shown on + figure \ref {fnt-tbl-cmex}. +\end{itemize} +% +Figure \ref {fnt-tbl-dcr} shows the DC-encoding with which the new +math encoding is designed to live. Unlike the \fn{cmr} encoding, the +Cork encoding does not include any Greek glyphs, this prevents its use +in family 0 for maths. But an upright text font is needed in family 0, +for mixing sub- and super-script in text. This problem has until now +prevented the wide spreading of the DC-fonts. + +The next two fonts shown in figures \ref {fnt-tbl-msam} and \ref +{fnt-tbl-msbm} are the AMS fonts, designed especially for use in +maths. +% +\begin{figure}[b] + \dofonttable{cmr10} + \caption{The \fn{cmr} encoding: 128 glyphs.} + \label{fnt-tbl-cmr} +\end{figure} +% +\begin{figure}[b] + \dofonttable{cmmi10} + \caption{The \fn{cmmi} encoding: 128 glyphs.} + \label{fnt-tbl-cmmi} +\end{figure} +% +\begin{figure}[b] + \dofonttable{cmsy10} + \caption{The \fn{cmsy} encoding: 128 glyphs.} + \label{fnt-tbl-cmsy} +\end{figure} +% +\begin{figure}[b] + \dofonttable{cmex10} + \caption{The \fn{cmex} encoding: 128 glyphs.} + \label{fnt-tbl-cmex} +\end{figure} +% +\begin{figure}[b] + \dofonttable{msam10} + \caption{The \fn{msam} encoding: 128 glyphs.} + \label{fnt-tbl-msam} +\end{figure} +% +\begin{figure}[b] + \dofonttable{msbm10} + \caption{The \fn{msbm} encoding: 128 glyphs.} + \label{fnt-tbl-msbm} +\end{figure} +% +\maxz=256 \maxiz=255 +\begin{figure}[b] + \dofonttable{ecrm1000} + %\dofonttable{cmssdc10} + \caption{The \fn{dcr} encoding: 256 glyphs.} + \label{fnt-tbl-dcr} +\end{figure} +% + +%\begin{figure}[b] +% \dofonttable{cspex10} +% \caption{The \fn{cspex} and Saint Mary Road encodings.} +% \label{fnt-tbl-mary} +%\end{figure} + + + +%\chapter{Requirements analysis} +%\label{app-require} + + + + + + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% end +\end{document} +\chapter{Daily detail of what I did (for personal record)} + +\begin{itemize} + +\jzitem{First week} +A lot of reading: Tex for the impatient... +Getting accustamed to the local environment: Emacs Bash Mwm... +Getting Telnet and mail connection with France. +Started my social report. +Looked a little at the code of latex. +Played around with latex. (wrote two letters) +Played around with the Tex boxes. +Read the chapter 7 from Frank's coming book. +Started to read a little more about the math fonts in \TeX. + +\jzitem{Sunday 13th June} +Started this report. Got familiar with Frank's integrated documenting +system. Got to letter f in the tex index of commands. (evening) + +\jzitem{Monday 14th June} +Trying to install NFSS2 in my environment. +Read a lot of the installation documentation. +Found the punk font, it was here. +Read to letter k of the tex index.(evening) + +\jzitem{Tuesday 15th June} +Last details of installing nfss2. +Testing various features of NFSS2. +Playing with nfss2: first page of my report. +Read to letter p of the tex index. + +\jzitem{Wednesday 16th June} +Still correcting a few problems with the installation of nfss2. +Installing the punk font in NfSS2: +made file nfpunk.dst based on nfpandor.dst. + +\jzitem{Thursday 17th June} +Still installing the punk font in NfSS2. +Read mail about maths. +Went to get my car. +End of afternoon with Frank. +Read to letter t of the tex index. + +\jzitem{Friday 18th June : time flies} +Ended the installation of the punk fonts. +Read the article from tugboat about the punk fonts. +Did the documentation for the pk fonts. +Played around with NFSS2 and texlatex: getting my presentation page ok. + +\jzitem{Saturday 19th June} +Ended the tex index. +Read more about char in the Tex by topic. + +\jzitem{Sunday 20th June} +Read still more about the Tex fonts and math fonts. +Tested char and loops =$>$ loops make problems in latex. +Tried postcript fonts. + +\jzitem{Monday 21st June} Tried to install the dunhill font with +nfss2: OK. Maybe make a ``\texttt{.sty}'' file like punk. I find it +is a nice font. Used raise and negative kerns for a joke. Reading +more on math fonts. + +\jzitem{Tuesday 22nd June} +Still more reading on mathfonts.-Families-mathcode-mathchar-greek +and testing. Finaly solved all problems due to the loop. + +\jzitem{Wednesday 23rd June} +Testing on skewchar, and more reading about maths. + +\jzitem{Thursday 24th June} +More testing with skewchar. +Meeting with FMI + +\jzitem{Friday 25th June} +All day : writing the paper about accents. + +\jzitem{Week end} +nothing about tex or latex +oh yes: reading about fonts. (cahier gutenberg) + +\jzitem{Monday 28th June} +Morning more testing with accents. +Afternoon: Meeting with FMI and Jorg K. + +\jzitem{Tuesday 29th June} +Writing a summary of yesterday, and trying to figure out how to do the +work. + +\jzitem{Wednesday 30th June} +Reinstalling NFSS2. Sending NFSS2 to Estonia. Reading all the mail +printed by Joerg. + +\jzitem{Thursday 1st July} +More thinking about maths. Sending mail to people. Reading about the +Tex files. + +\jzitem{Friday 2nd July} +More mailing. + +\jzitem{monday 5th July} +More mailing, meeting with Frank. + +\jzitem{Tuesday 6th July} +More mailing, reading about the extensible chars. + +\jzitem{Wednesday 7th July} +More mailing. Sending stuff to joerg. Dealing with Aston. +Continuing The paper on extensible chars. + +\end{itemize} +\end{document} + + +% Local Variables: +% mode: latex +% TeX-master: t +% TeX-command-default: "LaTeX2+" +% End: |