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\input mynfss.tex

\title{Towards a list of mathematical glyphs\thanks{This is not a
    finished document. It contains many spelling mistakes, many typing
    mistakes, and many brain mistakes. Things have been forgoten. All
    comments are welcome.}\\ This is not a finished document}

\author{Justin Ziegler\\ \texttt{\small
    ziegler@goofy.zdv.uni-mainz.de} \\ \texttt{\small
    ziegler@educ.emse.fr} }

\date{Started: 9 July 1993\\Printed: \today
  \\Version: 3.00
  \\Filename: agreed.tex}


  The idea here is to try and list the contents of the new math
  encoding.  For this I have tried to make logical glyph groupings.
  Please remember that this is a draft, and I used as my workbench.
  Some of it is out of date, and usually the comments are only for me.
  There are lots of spelling mistakes I know!

\section{A global rule for boldface}
We have decided not to mix ligthface and bold face symbols, in the same
encoding, but to generate a separate parallel boldface versions of all
lightface math encoded fonts.  This does not make it impossible to mix the
two. For this, either one can use the \texttt{\string\boldsymbol} approch,
or one can load an extra bold face font in a given family,
and have it directly and permanently accessible.

\section{Sans serif and typewriter fonts}
Extra fonts could be designed in sans serif, or in typewriter using
some of the new math encodings. An other solution is to load the Cork
encoded sans fonts (or typewriter fonts) in a free family. In any
case, the new math encoding will not have any slots containing
specifically sans serif or typewriter glyphs.

\section{Concerning the Euler shapes}

Euler shapes could be a good example implementation of the new math

On the other hand all the Euler shapes could be grouped in a single
font table. But this would not be part of the math encoding. It would
just be an extra font that could be loaded in an extra family, just
like the Dingbats could be.

%something added by bb for euler:
%\item Cursive (normal) capital letters. not often used.
%\item Cursive (normal) lowercase letters.
%\item Script uppercase.
%\item (Some) script lowercase.
%\item Fraktur (old german) uppercase.
%\item Fraktur (old german) lowercase.
%\item Digits.
%% bb --
%[bb: I will be happy to make a proposal for this.]

\section{The 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 mathchardefs.

\section{Extra font dimensions}
\item The disign 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

\section{The kerning}
We \textem{will} make better kerning possible in the latin math
italic, {\tiny if possible.} 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 every thing that must be kerned
as beeing ordinary, old documents may very well start looking
different. To avoid this, the user interface could define a macro
\texttt{\string\mathkerning\{...\}} that would use the kerning
specified in the \texttt{.tfm} file.

This needs more thinking, but so far we can produce the following
list of items that should be kerned:
\item A bit of ajusting with [ and ( and ) and ] in order to produce
  better spacing when folowed by letters. (Memo: Transforming into
  mathord, and italic correction.)
\item A bit of ajusting for the situation when letters are folowed by
  [ ] ( ). 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 Introduce kerning of the integral with itself. This would only
  be available via the \texttt{\string\mathkerning} macro (see
  previous comment).
\item Introduce kerning of the period with its self,
\item Introduce kerning of the centered period with its self.
\item Spivak and Jan M.R. are adament that kerning is needed between
  Latin and Greek. More precise information is needed.

\subsection{Document compatibility}
We will not aim in beeing totaly compatible. A lot of positions will
change, so direct math chardefs will not always work. We will make
sure that documented names from AMSLA\TeX\ (this includes names from
LA\TeX, \TeX, and AMS\TeX, and LAMS\TeX) are still suported.

\subsection{Compatibility with other encodings}
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) in every font table encoding.

If there is a lot of free space, we may consider leaving positions
from 0 to 32 empty.

\section{Will be taken out of the present math encoding}
\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,
\item The musical signs: $\flat, \natural, \sharp$
\item The maltese cross. (AMS)
\item The checkmark (AMS)
\item the funy tie accent: $\mathchar"017F$
\item The $\mathchar"017F$ seems not to be needed in maths. It could be put
in the text companion font.
\item The circled R must come out of the math symbols. (AMS)
\item The raised asterisc is comming out of math.
\item More ... ?

All these will be put in to the ``Text symbols'' encoding, that would
come in many faces, and be text dependent.
Other things will be put in this ``Text symbols'' font:
\item More numerals,
\item The perthousand sign.
\item Maybe this is a good place for the `fraction' characters from
\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)
\item ...

Alan jeffrey has work on the text symbol font. Actually it is now
called the companion text font. He has written more about the subject.

\section{The Greek glyphs: 124}
We will include the following shapes:
\item All the Uppercase in upright. 24
\item All the Uppercase in italic. 24
\item All the Lowercase in upright. 24
\item All the Lowercase in italic face. 24. So far: $24*4=96$
\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
  problems, prefer the italic shapes to the upright ones. 3. 
\item Some control glyphs: 2

\subsection{Variable shapes: 10}
This list comes basicaly from: J\"org Knappen.  All listed here
including the ones that are already in the cm:
\item Lowercase Phi, 
\item Lowercase Pi, 
\item Lowercase Kappa, (AMS)
\item Lowercase beta (new), 
\item Lowercase Rho, 
\item Lowercase Epsilon, 
\item Lowercase Sigma, 
\item Lowercase Theta. 
\item Upper case chi (new),
\item Upper case for upsilon.

\subsection{Extra letters for numerals: 3}
Source: J\"org Knappen.  All listed here including the ones that are
already in the cm, and the ams. Must be given in uppercase\footnote
{Uppercase greek numerals exist, allthough extremely rare. For the
  sake of completeness one could fill them in. But they are surely not
  the hottest characters needed. J\"org}, and lowercase.
\item Qoppa (new),
\item Sampi/Sanpi (new) (J\"org Knappen),
\item Digamma (AMS).

\subsection{Some control glyphs to access the different greek faces: 2}
\item An italic control glyph, i.e. the folowing 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 maybe not a good idea.

\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 effect the kerning. But one could use them
  differently from what you suggested.  Although i'm not sure it is
  interesting, the ligature mecanism does not have to be visible for
  the user. (ei, 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.
  \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 no very good. Better in the
    dcmr'136. (J\"org)
  \item An italic partial sign with a ? bar, ??. J\"org says no. ??????
  \item A barred upright lambda, ?????? (probably not J\"org)
  \item A barred italic lambda, this is prefered. (J\"org)
  \item An upright mho sign (upside down Omega),
  \item The back to front epsilon: AMS "7F \cn{backepsilon},
  \item The Weierstrass symbol: $\wp$ only in one style,
  \item Arabic letter dal: looks something like a back to front $c$.
  \item Hebrew letter '151 in msbm,
  \item Hebrew letter '152 in msbm,
  \item Hebrew letter '153 in msbm,
  \item The $\aleph$ or \cn{aleph} in position '100 of CMSY,
  \item The Nabla, $\nabla$ in CMSY'162
  \item More ?

The barred partial signs may be obtained by ligatures, or could be
constructed with kerning. In any case some slots for ligatures must be
left free.

\section{The latin letters: One set$=54$ glyphs}

We shall assume here that all lower case alphabets contain an `i' and
a `j' without dots, so that they can take other accents if wanted.
\item The usual cmmi italic shape. Uppercase and lowercase.
\item The calligraphic shapes. Uppercase and lowercase. I believe
  that the lowercase shapes are presently not available.
\item The script shapes. Uppercase and lowercase. Here as well I believe
  that the lowercase shapes are presently not available.
\item The black board bold shapes. Uppercase and lowercase.
\item The Fraktur style. Uppercase, and lowercase.

  \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.''

  We will include the two if there is not enough space for symbols.
  Otherwise we will only have one. i.e: putting the two instead of one
  means adding an extra family in which case there would be more place
  for symbols. The reason why that means adding an extra family, is
  because the letters should be in the usual Cork letter position.

  \subsection{A hyphen char ?} These Latin letters are not ment for
  typeseting words. We shall assume that all multiletter words will be
  typeset using the text fonts, not the math fonts. Thus we will not
  have any hyphen character 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 their long

  \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. But on top of that they need a special
  mode for writing their chemical equations. One of the
  particularities of this chemical mode is the different placing of
  sub- and superscript. A possible implementation is something like
  \textem{enter-chemical-mode} and textem{exit-chemical-mode}, which
  would in actual fact load a new set of fonts (or only th font in
  family 2), in order to have a different value for the font
  dimensions in family 2.

\section{Latin like material: 5}
This group should live next to the Latin letter set.
  \item An uright d. This is needed for the standard for mathematical
  \item A horizontally barred italic h, for physicists.
  \item A slanted barred italic h, for physicists.
  \item An italic uppercase Vee with a bar, the bar is ment to be
  \item An upright uppercase Vee with a bar, the bar is ment to be
    horizontal, and extends through both sides of the Vee almost like
    a strikeout.
  \item ??????? The powerset symbol from Martin.Ward@durham.ac.uk.
    Something like this:
    XXXXX           XXXX
    XXXXX           XXXX
  XXXXXXXX          XXXX
  XXX  XXX          XX
  XX    XXXX
  XX    XXXX
  XX      XXXX
  XX      XXXX

\section{The different ways needed to write numbers}
  \item The normal set of numbers in the cmmi: upright lining.
  \item The black board bold numbers. (This is used in physics. And a
    field of maths. See alan J. for more details.) [Note: I think that
    presently no satisfactory bbb numbers exist.]

\section{Empty slots?} 
We can include some free slots 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.

We shall enable this sort of construction. 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.  That sort of thing just has to be thought of, and
forecasted. What this does mean, is that those construction blocks
will not be used for any other purpose --- like for instance the equal
or minus sign.

All arrows from cm, and from ms, will be taken if necessary. Maybe
some others too.

  \subsection{The ``Plain horizontal arrows'' group: 14}
  The next 6 are in cmmi'050 to '055
    \item leftharpoonup
    \item leftharpoondown
    \item rightharpoondown
    \item rightharpoonup
    \item lhook
    \item rhook
      Now we are in 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

  \subsection{Extra arrows for use with plain arrows: 5}

    \item I think it would be reasonable to add a \cn{mapsfromchar} in
      order to build things like: $<\!\!-\!|$: 1

    \item I think it would be reasonnable to add a \cn{Mapstochar}
      that could go with the double arrows to build things like
      $|\!=\!>$ : 1

    \item I think it would be reasonnable 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


  \subsection{The ``Plain vertical arrows'' group: 6}
    \item CMSY'154 to '155: 2
    \item CMSY'42 to '43 :2
    \item CMSY'52 to '53 :2

  \subsection{The ``Plain oblique arrows'' group: 4 }
  \item CMSY'45
  \item CMSY'46
  \item CMSY'55
  \item CMSY'56

  \subsection{The ``Ams obliques'' group: 2}
  \item msbm'36
  \item msbm'37

  \subsection{The ``Latex arrows heads'' group: 4}
  LASY: The four characters in position '50 to '53 from the lasy font
  (These apear in the wasy font as well) must be put with the arrows.
  They are arrow heads. 4

  \subsection{The ``Ams arrows'' group: 12}
    \item MSAM: '10 to '11 :2
    \item MSAM:'24 to '27 : 4
    \item MSAM:'30, '31 '36, '37 :4
    \item MSAM:'113 '114 : 2 ??

  \subsection{AMS horizontal arrows: 22}
  This includes all the arrows horizontal arrows and the negated ones,
  that are listed page 280 of ``The joy of tex''.
  \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

  \subsection{The slashed and bared arrow}
  Alan J. is dealing with the arrows, and the possibility of baring
  them with a slah. Different slants and sizes of the slash should be
  available, depending on the the glyph that is being slashed. It can
  be done with kerning, and/or ligatures. I guess we can count for 4
  different types of slashing glyphs.

  \subsection{Some control glyphs for access to arrows }
  These do not appear in the dvi file, they just enable the
  construction of some arrows and slahsed arrows using the ligature

  \subsection{Free space for special arrow ligatures: }

\section{Accents: approx 85} 

  \subsection{Basic size accents: 19}
  \item All those that have been created by macros in the ams: the 3
    doted accent, and the 4 doted 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\char'175 ? e$\mathchar"017E$. They all come from cmr except for
    the last two from cmmi. \quad 12

  \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

  \note {J\"org says that e\char'175\ is not needed in math. ?????? }

  \note {The $\mathchar"017F$ seems not to be needed in maths. It
    could be put in the text companion font.}

  \subsection{Some double accents: 7}
    \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,

  \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 ment 5 different sizes until today, we could raise
  that number to 8.  
  \note {If the accents are in a font that is
    loaded in three different sizes, the choice mecanism of
    \cn{mathaccent} will only look in the current style size (unlike
    the delimiter choice mecanism). Thus although one could hope to
    multiply the number of available sizes by three, in actual fact in
    a given style the number of automaticaly available sizes would not
    be multiplied.  All the same this \textem{would} give different
    results in each style.  I can forsee better quality typesetting,
    but \textem{problems of compatibility} e.i.~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 redefine mathaccent to
    a mathchoice. Thus the accents could always come from textstyle,
    and the accented material could come from the durrent 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}?'' by
    the same author.}

    \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

  \subsection{Underaccents: 3 so far}
  So far I have had requests for:
    \item A tilde,
    \item A breve (\char'25)
    \item A bar

  Like for the double accents, research could be done at the AMS...

\section{Core symbols}

This is the only name I thought of to identify 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: 14}
  \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 an 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 cmmi.}, and as
    fraction sign, CMR


  \subsection{Basic geometric delimiters: 12}
  Should go in the core, for kerning reasons, like the other ( ) and [
  ].  I 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.
    \item $\rangle$
    \item $\langle$
    \item $|$
    \item $\|$
    \item $\rceil$
    \item $\lceil$
    \item $\rfloor$
    \item $\lfloor$
    \item The $\mathchar"026E$ in position '156
      In actual fact maybe this does not belong here:
    \item We could add the smallsetminus from msbm'162
    \item The msbm nmid '055
    \item The msbm nparallel '054


     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 neede here, where as it is necessary for
     the bracket.

  \subsection{For design similarity reasons: 23}
    \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 \& don't know where to find this.

    \item The $\ell$ as a rounded `l'. CMMI
    \item The centered dot $\cdot$ for use 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 wiht @, \%, $\ell$. In position
      '057 of CMSY.
    \item The $'$ or prime in position '060 of CMSY, one can not
      separate the prime from the slots for the prime ligatures. (2
      ligatures) Kerning of the prome letters in not possible, because
      tjhe prime is set in superscript. ????????

    \item The backprime form 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 $\Re$,
    \item and the $\Im$ in position '074, and '075 of CMSY,
    \item The $\dagger$ or dagger in CMSY'171, ?????
    \item The smile, ???????
    \item and the frown form CMMI ????????
    \item Could maybe include the circled S from MSAM'163. ?????

\section{Symbols from lasy that must be kept: }
The first four lasy symbols are in the msam. The ones in positions '50
through '53 are arrow heads, and are counted as such. Character '60 is
in the msam. '61 is not in the msam, and should be kept.  Char'62:
same as msam'03 ?  Char'63: same as msam'06?  Lasy'72: same as
msbm'163 or msam'166 ?  Lasy'73: same as msam'40 ?

A list of what we shall keep of lasy:
\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 sim glyph.}

  \subsection{The ``subset plain'' group: 4}
    \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,

  \subsection{The ``subset ams'' group: 12}
    \item From MSBM'040 to MSBM'43 : 12

  \subsection{The ``Inni plain'' group: 2}
    \item The $\in$ sign in position CMSY'062,
    \item The $\ni$ sign in position CMSY'063,

  \subsection{The ``sqsubset plain \& ams'' group: 4}
  Don't know where else to put these,
    \item The $\sqsubseteq$, cmsy'166,
    \item The $\sqsupseteq$, cmsy'167,
    \item The sqsubset from MSAM'100,
    \item The sqsupset from MSAM'101,

\section{The ``Greater than'' group}

  \subsection{The ``Greater than Plain'' group: 8}
    \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 form CMMI'074,
    \item $>$ Greater than: CMMI'076,
    \item The alternative leq: msam'66
    \item The alternative geq: msam'76

  \subsection{The ``greater than ams'' group: 30}
    \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

  \subsection{The ``greater than with sim'' group: 8}
    \item MSBM'022, 
    \item MSBM'023,
    \item MSBM'032,
    \item MSBM'033.
    \item MSAM'046,
    \item MSAM'047,
    \item MSAM'056,
    \item MSAM'057

  The shapee sim, and the geometric sim are now considered to be the
  same glyph.

\section{The ``Succ'' groups}

  \subsection{The ``Succ without sim plain'' group: 4}
      \item CMSY'026,
      \item CMSY'027,
      \item CMSY'036,
      \item CMSY'037

  \subsection{The ``Succ without sim ams'' group: 10}
      \item MSBM'006, '007: 2
      \item MSBM'016, '017: 2
      \item MSBM'026, '027: 2
      \item MSAM'062 - '064: 3
      \item MSAM'074: 1

  \subsection{The ``Succ with sim ams'' group: 8}
    \item MSBM'020, '021: 2
    \item MSBM'030, '031: 2
    \item MSBM'166, '167: 2
    \item MSAM'45,
    \item MSAM'55,

  The shapee sim, and the geometric sim are now considered to be the
  same glyph.

\section{The ``Sim'' group: 12}
    \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

  \subsection{The ``Small binops plain'' group: 20}
    \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

  \subsection{Small plain left right triangles: 2}
  I think these should be replaced by the ones in ams
    \item triangle left: CMMI'56
    \item triangle right CMMI'57

  \subsection{AMS left right open triangles: 8}
  These are also in LASY.
  \item vartriangle left
  \item vartriangle right
  \item triangle left eq
  \item triangle right eq

    The previous four are in msam
  \item Same 4 negated msbm: 4

\section{Basic Symbols: 23}
A group of symbols that are used for typesetting basic mathematics.
These are mainly geometrics, some have been added for alikeness
  \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 nexists sign from msbm'100
  \item The $\neg$ sign CMSY'072,
  \item The \cn{varpropto} from AMS "5F. ????? or should we leave this
    as 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 personnally
    think it should be shorter.

  \item The \cn{varnothing} from MSBM'77,

  \item The $\perp$ perp or bot sign in position '077,
  \item top sign CMSY'076

\section{The radicals: 8}
Currently available in cmex are:
  \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

  \item In cmsy there is the basic size of the radical. This is
    always, and has always been loaded in three sizes. If we take the
    radical sign out of cmsy, and put in MX, then we must take that
    into consideration. I remind the reader here that MX should be
    designed in such a way that it can be loaded in one size, and
    everything works as before. So we must add three sizes of the
    radical sign in MX: 3


\section{The integrals family: 18}

  \subsection{Big `bigops' size: 7}
    \item The single integral.
    \item The double integral. Could be done with kerning.
    \item The triple integral. Could be done with kenring.
    \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.

  \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.
  \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.
  \item Triple normal integral ???? (J\"org thinks yes) Could be done
    with kerning.
  \item The sigma integral. ?????
  \item The slash integral. ?????

  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 cmsy), i suggested this solely for
    reasons of completeness. The need for it is less now that 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 there.

    YH also pointed out, the upright versions of integrals are very
    common in textbooks. since the integral sign is one of the most
    common symbols used in math, it may not be a bad idea to include
    upright versions of *all* integral signs in cmex (with
    corresponding small versions in cmsy) again for reasons of


\section{Ams Vdash group: 10}
\item MSBM'056
\item MSBM'057
\item MSBM'061
\item MSBM'062
\item MSBM'063
\item MSBM'160
\item MSBM'161
\item MSAM'015
\item MSAM'016
\item MSAM'017

\section{Plain miscellaneous geometric symbols: 5}
\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

\section{AMS equals friends: 10}
  \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

\section{Ams miscellaneous geometric symbols: 21}
\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

\section{AMS boxes and friends: 15}
\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

\section{The curly braces: 8}

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.

\section{Non classified existing symbols}
Here are listed some symbols that do not have a place elsewhere:
  \item The diferent shapes of \# should find a place, although one is
    already in the core.

\section{A list of new glyphs}

The following symbols should be added in the mathfonts. Some have
already been designed by various people, so it should be possible to
find them...

  \subsection{New basic size delimiters: 8}
  Basic size means the same size as the parentheses and brackets in cmr.
    \item a $|||$ for use as $|||f|||$ a norme: 
    \item Unicode contains another style of brackets,
        they call them tortoise shell brackets. They look like\\ 
        \verb+/ \+\\ \verb+| |+\\ \verb+\ /+\\ These are like
        parentheses, but with straight lines. No curves !
    \item The previous ones in Bbb.
    \item Multi set brackets $\{|$ and $|\}$


  \subsection{Basic size operators: 2}
  Basic size means the same size as the operators in cmsy.
    \item Something like \cn{cupdot} and 
    \item Something like \cn{capdot} See Frank to justify these.

  \subsection{New multi-sized, and extensible delimiters: 60}
  A multi-sized delimiter means: 4 sizes for each side : 8 glyphs.
  Plus and extensible version: top botom extension module for both
  sides:6 glyphs. Sometimes also a middle: 8 glyphs. Total: 16 or 14.

    \item Semantic brakets $[\![$ and $]\!]$ must be extensible: 14

    \item An extensible version of $|||$ for use as $|||f|||$ (a
      norme). Just the extension module: 1

    \item {\tt Unicode contains another style of brackets,
        they call them tortoise shell brackets. They look like\\ 
        \verb+/ \+\\ \verb+| |+\\ \verb+\ /+\\}: 14

    \item The previous ones in Bbb: 14

    \item Multi set brackets $\{|$ and $|\}$: 16

    \item For both multisized curly braces there is only one
      extensible module.  This works for DEK's curly braces, probably
      because they are symetrical. But this may not be the case for an
      other design. So we must include a slot for the other extensible
      module: 1


  \subsection{New double sized `bigops': 26 }
  All these would 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.


    \item A double sized sqcap $\sqcap$ \cn{bigsqcap} cspex

    \item Two sized $\bigcirc$ with $\vee$ inside.  $\bigcirc
      \!\!\!\!\!\vee$ proposed name: \cn{ovee}, and \cn{bigovee}.
      cspex and stmary

    \item Two sized $\bigcirc$ with $\wedge$ inside.  $\bigcirc 
      cspex \!\!\!\!\!\wedge$ proposed name \cn{owedge}, and
      \cn{bigowedge}.  comment from Alan:
        ``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.)''

    \item Dijkstra choice: $[\!]$ CSPEX

    \item A wide Dijkstra choice. CSPEX . Comment from alan:
        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...

    \item Parallel \cn{bigparallel} just a double sized version of

    \item Interleaving $|\!|\!|$ : \cn{biginterleaving} [bb: I'm not
      sure about the spacing or meaning but we've had requests for
      triple verts as delimiters.]
        `Interleaving' and `parallel' are used in (at least) three
        different ways:
        \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 textstyle and
          display style versions.
      The big operators aren't the same glyphs as the extensible

  \item \cn{bigcupdot}: A `U' with a dot in it. Something like:

  \item \cn{bigcapdot}: an upside down `U' with a dot in it. Something
    like: $\bigcap\!\!\!\!\cdot$

  \item An inverted \& . \cn{dnasrepma}

  \item Large operator symbols based on, asterisk sign.

  \item Large operator symbols based on, a hash sign.
  \item Large operator symbols based on, an ampersand sign.


\subsection{Geometrics: 21}

  \item Don't forget the ams smaller or equal and greater or equal.

  \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 this: $\raise .1cm \hbox{$|$}\!\_$
    maybe the same upside down.
  \item From JMR: Something like this: $\_\!\raise .1cm \hbox{$|$}$
    maybe the same upside down.
  \item More ?


\subsection{New arrows}
\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 wrote as well: Add
  the `building blocks' for the AMS negated relations, for example a
  \cn{arrownot} to build \cn{nlongrightarrow} and
  \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.

\subsection{Non geometrics: 19}

%  \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 cmr is appropriate.

  \item lightning (wasy) --- I don't think this 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 A nice powerset symbol:
%  \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 Joerg. 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 lowercase sigma with a long tail that goes a little bit below the

  \item Must not forget the two versions of the \# hash sign. I
    believe one is geometric, and one isn't: 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. (Joerg)

  \item More ?


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