

\title%[\textsf{yhmath}]
      {Large brackets and accents: the \textsf{yhmath} package}
\author[Yannis Haralambous]{Yannis Haralambous\\
                           187, rue Nationale,
                           59800 Lille, France\\
                           \texttt{haralambous@univ-lille1.fr}}
\begin{Article} 


\section{Abstract}
This package\footnote{This article describes the currently available
         version. An extended package with more symbols is planned.}
 provides a set of big delimiters, intermediate to those
of the original \TeX{}, and also much bigger. It also provides very
wide accents (including two new ones: parenthesis and triangle). These
symbols are included in a font which has Don's \File|cmex10| as
lower ASCII part. 


\section{Installation}

This package consists of (a) a font, written in Metafont, (b) a \LaTeX{}
style file, (c) an \texttt{fd} file for the OMX encoding using the new
font.
To build the font put all the Metafont files somewhere where your 
Metafont can find them (for example in 
\path|texmf/fonts/src/public/yhmath|)

Then launch Metafont at least once on \File|yhcmex10| so that at least
one \texttt{tfm} file exists when you'll start typesetting
(\File|dvips| and similar programs will create the \texttt{pk}s, don't
worry).

Then take the \File|OMXyhex.fd| file and put it together with your other
\texttt{fd} (Font Definition) files; and \File|yhmath.sty| together
with your other \LaTeX{} styles. Have fun!

\section{Availability}

Don Knuth's code is included in Metafont files, so this code is under
the usual \TeX ware copyright conditions. My code is
postcard-ware. (If you like it and find it is worth a
postcard + a stamp + the mental effort of writing a word
[optional!] and the physical effort
of going to the nearest mailbox, then do it!)

Everything is on \textsc{ctan},
and if there are upgrades you will be informed in the usual way. 

\section{Very big delimiters}
I never liked those parentheses of matrices which become almost
immediately straight. In traditional math typography, parentheses stay
curved, even if they are very big. So I decided to play around with 
\TeX's \texttt{charlist} font property, and make some more of those
big delimiters.
I also did intermediate sizes (for all ``big'' delimiters).
Here are some examples :

%\begin{figure*}
\begingroup
\begin{gather}\label{p1}
\begin{pmatrix} a & b & c\\ d & e & f\\ g & h & i
\end{pmatrix}
\begin{pmatrix} a & b & c\\ d & e & f\\ g & h & i\\ j & k & l
\end{pmatrix}
\begin{pmatrix} a & b & c\\ d & e & f\\ g & h & i\\ j & k & l\\
m & n & o
\end{pmatrix}
\end{gather}

\mathversion{yh}\setbox0\hbox{$$}

\begin{gather}\label{p2}
\begin{pmatrix} a & b & c\\ d & e & f\\ g & h & i
\end{pmatrix}
\begin{pmatrix} a & b & c\\ d & e & f\\ g & h & i\\ j & k & l
\end{pmatrix}
\begin{pmatrix} a & b & c\\ d & e & f\\ g & h & i\\ j & k & l\\
m & n & o
\end{pmatrix}
\end{gather}
\eqref{p1} is produced using the standard \TeX\ fonts, \eqref{p2} shows
the result of using this package.

\endgroup
%\end{figure*}

\section{A new \AmS-\LaTeX{}-like matrix-like environment}

Since I also did ``very big'' versions of the ``left angle'' and ``right
angle'' symbols, why not make ``matrices'' with them as delimiters?
I have never seen such a mathematical object, but perhaps was it just
because this construction wasn't available yet?
(This is a chicken and egg story).


I called this new \AmS-\LaTeX-like environment \texttt{amatrix}
(``a'' for ``angle'').
I hope AMS people will just love it and include it into 
\AmS-\LaTeX!\footnote{Talking of \AmS-\LaTeX{}
there are a few more macros I would like to see included,
see next section.}

Here are the same matrices as above, with angles instead of parentheses:

\begingroup
\begin{gather}\label{a1}
\begin{amatrix} a & b & c\\ d & e & f\\ g & h & i
\end{amatrix}
\begin{amatrix} a & b & c\\ d & e & f\\ g & h & i\\ j & k & l
\end{amatrix}
\begin{amatrix} a & b & c\\ d & e & f\\ g & h & i\\ j & k & l\\
m & n & o\end{amatrix}
\end{gather}

\mathversion{yh}\setbox0\hbox{$$}

\begin{gather}\label{a2}
\begin{amatrix} a & b & c\\ d & e & f\\ g & h & i
\end{amatrix}
\begin{amatrix} a & b & c\\ d & e & f\\ g & h & i\\ j & k & l
\end{amatrix}
\begin{amatrix} a & b & c\\ d & e & f\\ g & h & i\\ j & k & l\\
m & n & o
\end{amatrix}
\end{gather}
\eqref{a1} is produced using the standard \TeX\ fonts, \eqref{a2} shows
the result of using this package.

\endgroup

\section{New roots}

Roots got bigger as well, so that now the ``vertical root'' comes
much later. Example :
\begin{equation}\label{r1}
\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{%
\sqrt{\sqrt{\sqrt{\sqrt{\sqrt x}}}}}}}}}}}}
\end{equation}
{\mathversion{yh}
\begin{equation}\label{r2}
\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{%
\sqrt{\sqrt{\sqrt{\sqrt{\sqrt x}}}}}}}}}}}}
\end{equation}}
\eqref{r1} is produced using the standard \TeX\ fonts, \eqref{r2} shows
the result of using this package.


\section{A few things missing from \AmS-\LaTeX{} v1.2}

In \AmS-\LaTeX{} there is a \verb|\ddots| command for diagonal dots.
How about antidiagonal ones? There are matrices called anti-symmetric,
and for them we need the notation ``dots going up''.
I define a \verb|\adots| macro, with a code symmetric to \verb|\ddots|,
here is the result: \smash{$\adots$}.

Another thing missing in all \TeX{} \& Co\@. packages: the ring accent,
used in topology for the interior of a space.
I define a macro \verb|\ring| to be used in math mode.
Here is the result: if $X=[0,1]$ then $\ring{X}=]0,1[$.

\section{Very wide accents}

I added some more hats and tildes (accessed by the standard
\verb|\widehat| and \verb|\widetilde| commands).
so that you can get really wide accents now; see the examples below:
\begin{gather}
\label{h1}
\widehat{A},\widehat{ABC},\widehat{ABCDE},\widehat{ABCDEFG}\\
\label{h2}
\amswidehat{A},\amswidehat{ABC},\amswidehat{ABCDE},
\amswidehat{ABCDEFG}\\
\label{h3}
\mbox{\mathversion{yh}$\displaystyle
\widehat{A},\widehat{ABC},\widehat{ABCDE},\widehat{ABCDEFG}$}
\end{gather}
\begin{gather}
\label{h4}
\widetilde{A},\widetilde{ABC},\widetilde{ABCDE},\widetilde{ABCDEFG}\\
\label{h5}
\amswidetilde{A},\amswidetilde{ABC},\amswidetilde{ABCDE},
\amswidetilde{ABCDEFG}\\
\label{h6}
\mbox{\mathversion{yh}$\displaystyle
\widetilde{A},\widetilde{ABC},\widetilde{ABCDE},\widetilde{ABCDEFG}$}
\end{gather}
\eqref{h1} and \eqref{h4} show the standard \TeX\ font. 
\eqref{h2} and \eqref{h5}
show the larger accents possible using the AMS fonts,
as defined in the \AMS-\LaTeX\ package \textsf{amsfonts}.
\eqref{h3} and \eqref{h6} show the larger accents produced by the new 
\texttt{yhcmex10} font.


\mathversion{yh}
I also designed two new
accents: the triangle accent \verb|\widetriangle|
and the parenthesis accent \verb|\wideparen|:
$$
\widetriangle{A}, 
\widetriangle{ABC},
\widetriangle{ABCDE},
\widetriangle{ABCDEFG}
$$
$$
\wideparen{A}, 
\wideparen{ABC},
\wideparen{ABCDE},
\wideparen{ABCDEFG}
$$



The former is used (in France only??) to show that the notation $ABC$,
where $A,B,C$ are three points, means a triangle and not an angle.
See what I mean? $\widetriangle{ABC}$ is a triangle, $\widehat{ABC}$
is an angle.

The latter is used when we want a non-expansible accent to be applied
to more than one letters at once. Of course \AmS-\LaTeX{} has given a
solution to this (place the symbols between parentheses and the accent
as an exponent of the right parenthesis), by I happen not to like that
solution. For example if I want to write ``the interior of $[0,1]$''
$$\textrm{I prefer to see}\quad\widering{[0,1]}
\quad
\textrm{than}
\quad
([0,1])\ring{}
\quad
\textrm{don't you?}
$$
Of course this notation is not my invention, I saw it in many French
math books (ever heard of Nick Bourbaki?).


I call this macro \verb|\widering|, because it plays the r\^ole of a
wide symbol (and since the ring can't be widened, a parenthesis
is used).
Here are some more examples (the first one coded as \verb|\ring{A}|):
$$
\ring{A},
\widering{ABC},
\widering{ABCDE},
\widering{ABCDEFG}
$$


\end{Article}

