From e0c6872cf40896c7be36b11dcc744620f10adf1d Mon Sep 17 00:00:00 2001
From: Norbert Preining <norbert@preining.info>
Date: Mon, 2 Sep 2019 13:46:59 +0900
Subject: Initial commit

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+
+\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}
+
-- 
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