From e0c6872cf40896c7be36b11dcc744620f10adf1d Mon Sep 17 00:00:00 2001 From: Norbert Preining Date: Mon, 2 Sep 2019 13:46:59 +0900 Subject: Initial commit --- usergrps/uktug/baskervi/6_1/bv61yh.tex | 251 +++++++++++++++++++++++++++++++++ 1 file changed, 251 insertions(+) create mode 100644 usergrps/uktug/baskervi/6_1/bv61yh.tex (limited to 'usergrps/uktug/baskervi/6_1/bv61yh.tex') diff --git a/usergrps/uktug/baskervi/6_1/bv61yh.tex b/usergrps/uktug/baskervi/6_1/bv61yh.tex new file mode 100644 index 0000000000..68a6d97727 --- /dev/null +++ b/usergrps/uktug/baskervi/6_1/bv61yh.tex @@ -0,0 +1,251 @@ + + +\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} + -- cgit v1.2.3