From f07bb53970ee2ecc53f81a206a3d3a67ef665e4a Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Mon, 9 Jan 2006 00:56:57 +0000 Subject: doc 6 git-svn-id: svn://tug.org/texlive/trunk@85 c570f23f-e606-0410-a88d-b1316a301751 --- .../texmf-dist/doc/generic/borceux/Diagram_Read_Me | 580 +++++++++++++++++++++ 1 file changed, 580 insertions(+) create mode 100644 Master/texmf-dist/doc/generic/borceux/Diagram_Read_Me (limited to 'Master/texmf-dist/doc/generic/borceux/Diagram_Read_Me') diff --git a/Master/texmf-dist/doc/generic/borceux/Diagram_Read_Me b/Master/texmf-dist/doc/generic/borceux/Diagram_Read_Me new file mode 100644 index 00000000000..e811bd0fe9d --- /dev/null +++ b/Master/texmf-dist/doc/generic/borceux/Diagram_Read_Me @@ -0,0 +1,580 @@ +\documentstyle{article} + +\textheight520pt +\textwidth349pt +\footskip15pt + +\hoffset-35mm +\voffset-35mm + +\title{User's guide for {\em Diagram 3}\thanks{With respect +to versions 1 and 2, the shape of arrows has been improved, the variety of +directions and arrows available has been more than doubled, all diagram arrows +admit an optional length argument, the typing of diagrams has been shortened, error +and help messages have been introduced. To typeset with {\em Diagram~3}, diagrams +prepared with versions~1 or~2, read the file {\em OldDiagram} after the file {\em +Diagram}.}} +\author{Francis Borceux, Louvain-la-Neuve} +\date{borceux@agel.ucl.ac.be} + +\font\bldfc=cmmib10 +\def\boldface#1{\mbox{\bldfc#1}} + +\newcommand{\XA}% +{\truex{300}% +\begin{picture}(0,0)% +\put(0,0){\circle{\value{x}}}% +\end{picture}} + +\newcommand{\XB}% +{\truex{500}% +\begin{picture}(0,0)% +\put(0,0){\circle*{\value{x}}}% +\end{picture}} + +\newcommand{\V}[3]{\cross{\XB}{\movevertex(#1,#2){\scriptstyle#3}}} + +\begin{document} + +\maketitle + +\section{The {\em Diagram} macros} + +The {\em Diagram macros} realize the construction of diagrams as +those appearing in category theory texts. The user gives the list +of vertices and arrows to be included, just as when composing a +matrix, and the program takes care of computing the dimensions of +the arrows and realizing the pagesetting. All the user has to do +about the arrows is precising their type (monomorphism, pair of +adjoint arrows,\ldots) and their direction (north, +south-east,\ldots): 12 types and 32 directions are available; see +figures~1 and~3 for exhaustive lists. + +A file {\em MultipleArrows} exists, producing additional +triple, quadruple and quintuple arrows, parallel or adjoint, but +the size of those pictures is so big that severe restrictions apply +to them. + +The {\em Diagram macros} make a big use of \LaTeX\ commands and +cannot work without \LaTeX\ being loaded. + +Some small implementations of \TeX, essentially those limited to +$2^{16}$ words of memory, are unable to handle the {\em Diagram +macros}. For those cases, two levels of restricted files have been +created, where the restriction applies just to the number of types +of arrows: +\begin{itemize} +\item {\em MicroDiagram} is only able to design plain arrows; +\item {\em MiniDiagram} designs plain arrows, pairs of +plain arrows and adjoint pairs of plain arrows. +\end{itemize} +The restriction is even more subtle, since arrows are produced +here in a more economical way. + +Big diagrams require much \TeX\ memory when typesetting; if you are +badly limited, try to produce them as separate one-page documents. To save +memory, you can also cancel from a file those macros you are not intending to +use. Do not copy macros from {\em Diagram} to {\em MiniDiagram} or {\em +MicroDiagram}\/: this would not work. + +The {\em Diagram macros} have been designed to give optimal results +on printers with resolutions up to 300dpi. In the case of printers +with higher resolutions, the parameter {\em printerresolution} +given as a first instruction of the file {\em Diagram} must be changed +accordingly. Notice that reducing this parameter is another way of +saving \TeX\ memory. This parameter does not exist in the files +{\em MicroDiagram} and {\em Minidiagram}. + +\section{Arrows in formulas} + +Arrows can be introduced in formulas, thus in a line of +text between single dollars or in a displayed formula, between +double dollars. While the command to be given is the same, the +effect which is produced is different in the text and in a +displayed formula. The variety of arrows available is described in +figure~1. +\begin{figure} +\settextarrowlength{45} +\begin{center} +\begin{tabular}{|l|c|l|} +\hline +{\bf Name}&{\bf Arrow}&{\bf Code}\\ +\hline\hline +plain arrow&$\ar$&ar\\ +dotted arrow&$\dotar$&dotar\\ +distributor&$\dist$&dist\\ +monomorphism&$\mono$&mono\\ +epimorphism&$\epi$&epi\\ +bimorphism&$\bimo$&bimo\\ +isomorphism&$\iso$&iso\\ +equality&$\eql$&eql\\ & & \\ +pair of arrows&$\biar$&biar\\ & & \\ +adjoint arrows&$\adjar$&adjar\\ & & \\ +pair of distributors&$\bidist$&bidist\\ & & \\ +adjoint distributors&$\adjdist$&adjdist\\ +\hline +\end{tabular} +\hspace{5mm} +\begin{minipage}{30mm} +The codes {\em iso, dist, bidist, adjdist} are generic: +the marks $\cong$, $\circ$ can be changed anywhere in the document via the +instructions \verb+\isomark{...}+, \verb+\distmark{...}+, +where \verb+...+ are the new marks. The default marks are \verb+\cong+ and +\verb+\distcircle+. +\end{minipage} +\end{center} +\caption{The various types of arrows.} +\settextarrowlength{20} +\end{figure} +\begin{itemize} +\item To produce a given type of formula arrow +in the forward direction (as in figure~1), just type a {\em +backslash} followed by the code for this type of arrow: thus +\verb+$f \colon A \mono B$+ will produce $f \colon A \mono B$. +\item To produce a given type of formula arrow in the ``backward'' direction, type a +command starting with \verb+\bk+ and ending with the code for the type of +arrow: thus \verb+$g \colon B \bkepi C$+ produces $g \colon B \bkepi C$. +\item To give an upper name to one of the previous arrows, just use +a first uppercase letter and give the name as an argument: thus +\verb+$C \Dist h D$+ will produce $C \Dist h D$. Of course, when +the picture consists of two arrows, two names must be given, first +the top one and next the bottom one; for example +\verb+$D \Bkadjar ij E$+ to produce $D \Bkadjar ij E$. As usual, when +the names are not single tokens, use curly brackets to delimit them. +\end{itemize} +To let you appreciate the difference between {\em textstyle} and +{\em displaystyle}, here are the previous arrows in {\em display +style} +$$ A \Mono f B \Bkepi g C \Dist h D \Bkadjar ij E $$ +introduced via the commands +\begin{verbatim} +$$ A \Mono f B \Bkepi g C \Dist h D \Bkadjar ij E $$ +\end{verbatim} + +The default length of a {\em text arrow} is 20pt while the names +are processed in {\em scriptstyle}; the default length of a {\em display +arrow} is 30 pt and the names are processed in {\em textstyle}. The +default lengthes can be changed at any time in the document via +instructions of the form +\begin{verbatim} +\settextarrowlength{25} +\setdisplayarrowlength{40} +\end{verbatim} +where 25 and 40 express the new lengthes in points. + +\section{Constructing a diagram} + +To construct a 2-dimensional diagram, imagine a pattern of +points, visualized by circles and bullets as in figure~2: +\begin{figure} +\begin{diagram} +\XB¤\XA¤\XB¤\XA¤\XB¤\XA¤\XB¤¤ +\XA¤\cross{\XA}{\sear}¤\cross{\XA}{\esear}¤\cross{\XA}{\eesear}¤\XA¤\XA¤\XA¤¤ +\XB¤\cross{\XA}{\ssear}¤\XB¤\cross{\XA}{\ear}¤\XB¤\cross{\XA}{\ear}¤\XB¤¤ +\XA¤\XA¤\cross{\XA}{\sar}¤\XA¤\cross{\XA}{\sar}¤\XA¤\cross{\XA}{\sar}¤¤ +\XB¤\XA¤\XB¤\cross{\XA}{\ear}¤\XB¤\cross{\XA}{\ear}¤\XB¤¤ +\end{diagram} +\caption{Conceiving a 2-dimensional diagram.} +\end{figure} +the bullets indicate the points of this pattern where vertices +could be expected. Each vertex and each arrow is attached by its center at a +point of the pattern. It suffices now to enumerate the items, line by line and +column by column, like for a matrix; in particular when all actual items of a +line have been enumerated, you can pass directly to the next line. All items are +processed in math mode. The program will take care of choosing correctly the +length of each arrow. + +A vertex is typed as any mathematical formula. The rules for typing +an arrow are completely analogous to those of section~2: +the various types of arrows are again those of figure~1 while +the possible directions and their codes are given in figure~3. +\begin{figure} +\begin{diagram}[60] +\XB¤\XA¤\V{0}{10}{nwnnw}¤\XA¤\V{0}{10}{nnnw}¤\XA¤\XB¤\XA¤\V{0}{10}{nnne}¤ +\XA¤\V{0}{10}{nenne}¤\XA¤\XB¤¤ +\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤¤ +\V{-10}{0}{\makebox[0pt][r]{$\scriptstyle nwwnw$}}¤\XA¤\XB¤\XA¤ +\V{-5}{10}{\boldface{nnw}}¤\XA¤\XB¤\XA¤\V{5}{10}{\boldface{nne}}¤\XA¤\XB¤\XA¤ +\V{10}{0}{\makebox[0pt][l]{$\scriptstyle +neene$}}¤¤ +\XA¤\XA¤\XA¤\XA¤\cross{\XA}{\nwnnwar}¤\cross{\XA}{\nnnwar}¤\XA¤\cross{\XA}{\nnnear}¤ +\cross{\XA}{\nennear}¤\XA¤\XA¤\XA¤\XA¤¤ +\V{-10}{0}{\makebox[0pt][r]{$\scriptstyle +wwnw$}}¤\XA¤\V{-10}{10}{\boldface{wnw}}¤\cross{\XA}{\nwwnwar}¤ +\V{-5}{10}{\boldface{nw}}¤\cross{\XA}{\bold\nnwar}¤\V{0}{10}{\boldface{n}}¤ +\cross{\XA}{\bold\nnear}¤\V{5}{10}{\boldface{ne}}¤\cross{\XA}{\neenear}¤ +\V{10}{10}{\boldface{ene}}¤\XA¤\V{10}{0}{\makebox[0pt][l]{$\scriptstyle +eene$}}¤¤ +\XA¤\XA¤\XA¤\cross{\XA}{\wwnwar}¤\cross{\XA}{\bold\wnwar}¤\cross{\XA}{\bold\nwar}¤ +\cross{\XA}{\bold\nar}¤\cross{\XA}{\bold\near}¤\cross{\XA}{\bold\enear}¤ +\cross{\XA}{\eenear}¤\XA¤\XA¤\XA¤¤ +\XB¤\XA¤\XB¤\XA¤\V{-10}{0}{\boldface{w}}¤\cross{\XA}{\bold\war}¤\XB¤ +\cross{\XA}{\bold\ear}¤\V{10}{0}{\boldface{e}}¤\XA¤\XB¤\XA¤\XB¤¤ +\XA¤\XA¤\XA¤\cross{\XA}{\wwswar}¤\cross{\XA}{\bold\wswar}¤\cross{\XA}{\bold\swar}¤ +\cross{\XA}{\bold\sar}¤\cross{\XA}{\bold\sear}¤\cross{\XA}{\bold\esear}¤ +\cross{\XA}{\eesear}¤\XA¤\XA¤\XA¤¤ +\V{-10}{0}{\makebox[0pt][r]{$\scriptstyle +wwsw$}}¤\XA¤\V{-10}{-10}{\boldface{wsw}}¤\cross{\XA}{\swwswar}¤ +\V{-5}{-10}{\boldface{sw}}¤\cross{\XA}{\bold\sswar}¤\V{0}{-10}{\boldface{s}}¤ +\cross{\XA}{\bold\ssear}¤\V{5}{-10}{\boldface{se}}¤\cross{\XA}{\seesear}¤ +\V{10}{-10}{\boldface{ese}}¤\XA¤\V{10}{0}{\makebox[0pt][l]{$\scriptstyle +eese$}}¤¤ +\XA¤\XA¤\XA¤\XA¤\cross{\XA}{\swsswar}¤\cross{\XA}{\ssswar}¤\XA¤\cross{\XA}{\sssear}¤ +\cross{\XA}{\sessear}¤\XA¤\XA¤\XA¤\XA¤¤ +\V{-10}{0}{\makebox[0pt][r]{$\scriptstyle +swwsw$}}¤\XA¤\XB¤\XA¤\V{-5}{-10}{\boldface{ssw}}¤\XA¤\XB¤\XA¤ +\V{5}{-10}{\boldface{sse}}¤\XA¤\XB¤\XA¤ +\V{10}{0}{\makebox[0pt][l]{$\scriptstyle seese$}}¤¤ +\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤¤ +\XB¤\XA¤\V{0}{-10}{swssw}¤\XA¤\V{0}{-10}{sssw}¤\XA¤\XB¤\XA¤\V{0}{-10}{ssse}¤ +\XA¤\V{0}{-10}{sesse}¤\XA¤\XB¤¤ +\end{diagram} +\caption{The 32 directions for {\em Diagram} arrows.} +\end{figure} +Taking some +liberty with geography and trigonometry, the 32 directions considered +by the {\em Diagram macros} are named after those of the compass card. +\begin{itemize} +\item To produce a type of arrow in a given direction, type a {\em +backslash} followed by the code of the direction and the code of +the arrow. For example \verb+\nemono+ draws a north-east +monomorphism. +\item To give an upper name to a diagram arrow, use a first upper case +letter and give the name as an argument. For example +\verb+\Ssedist f+ draws a south-sout-east distributor with upper +name $f$. Of course, when the picture consists in two arrows, +two names must be given: first the upper one and next the lower one. +In the case of vertical arrows, read {\em left} instead of {\em +upper}. +\item The procedure for giving a lower name is analogous, but uses +a last uppercase letter. Thus \verb+\wbimO f+ produces a west +bimorphism with lower name $f$. In the case of vertical arrows, +read {\em right} instead of {\em lower}. For two-arrow pictures, +both naming procedures are equivalent. +\end{itemize} +All 12 types of arrows exist in all 16 principal directions printed in bold +in figure~3; just plain arrows are provided in the 16 other +directions. + +It remains to explain the syntax\footnote{This syntax uses the character \S. If +this is a problem for you, just replace \S\ by any character you are unlikely to +use in a digram, for example ?; you can safely make this change globally and +automatically in the file {\em Diagram}.} for typing diagrams. This is just +\begingroup% +\catcode`\¤=\active\def¤{{\S}}% +\begin{verbatim} +\begin{diagram} +...¤...¤...¤¤ +...¤...¤...¤...¤¤ +...¤...¤...¤...¤¤ +\end{diagram} +\end{verbatim}% +\endgroup% +\noindent where \verb+...+ denote the various items of the diagram. So a +single \S\ is the delimiter between two items of a same line, while +a double \S\S\ indicate the end of a line. Typing the double \S\S\ at the end of the last line is +compulsory and nothing should stand between this double \S\S\ and the +\verb+\end{diagram}+ instruction (well, there is a single exception to this rule, +explained in section~6). Do not forget a blank space to indicate an empty item, +since two consecutive \S\S\ would be interpreted as an {\em end of line} symbol; of +course several blank spaces are always equivalent to a single one. + +So diagram~1, +\begin{floatingdiagram} +A¤¤ + ¤\Sedotar x¤\eseaR y ¤\Eesear z¤¤ + ¤\sseaR u ¤A ¤\Eepi a ¤B ¤\Emono b¤C ¤¤ + ¤ ¤\saR c ¤ ¤\Sadjar de¤ ¤\seqL{1_C}¤¤ + ¤ ¤D ¤\waR g ¤D\oplus E ¤\eaR h ¤C ¤¤ +\end{floatingdiagram} +which has the precise shape of the diagram conceived in figure~2, is produced by +the following commands: +\begingroup% +\catcode`\¤=\active\def¤{{\S}}% +\begin{verbatim} +\begin{diagram} +A¤¤ + ¤\Sedotar x¤\eseaR y ¤\Eesear z¤¤ + ¤\sseaR u ¤A ¤\Eepi a ¤B ¤\Emono b¤C ¤¤ + ¤ ¤\saR c ¤ ¤\Sadjar de¤ ¤\seqL{1_C}¤¤ + ¤ ¤D ¤\waR g ¤D\oplus E ¤\eaR h ¤C ¤¤ +\end{diagram} +\end{verbatim}% +\endgroup% + +There is a second, completely analogous environment for producing +diagrams; it has the form +\begingroup% +\catcode`\¤=\active\def¤{{\S}}% +\begin{verbatim} +\begin{floatingdiagram} +...¤...¤...¤¤ +...¤...¤...¤...¤¤ +...¤...¤...¤...¤¤ +\end{floatingdiagram} +\end{verbatim}% +\endgroup% +\noindent As the name indicates, the diagram is then introduced as +a floating body and will automatically receive a numbered label +(cf.~diagrams~1~to~3). The default is to number successively the +diagrams through all the document. You can prefer +a number 3.12 for, let us say, the twelfth diagram of chapter~3 +(in a style which contains chapters!). This is forced +by the instruction +\begin{verbatim} +\setdiagramcounter{chapter} +\end{verbatim} +where, of course, {\em chapter} can be replaced by any sectioning +level, for example {\em part, section,\ldots} For non-English texts, you +will also want to ``translate'' the word {\em Diagram} in the label: this +is achieved by an instruction like +\begin{verbatim} +\diagramlabel{Diagramme} +\end{verbatim} +given anywhere in the text, but not inside a diagram. + +Every diagram, floating or not, can be given a caption. This is done +by the instruction +\begin{verbatim} +\diagramcaption{...} +\end{verbatim} +which can be introduced anywhere in the diagram, but before the last two +\S\S. In the case of a floating diagram, this caption completes the automatic +label, as in diagram~4. + +\section{Changing the sizes} + +The step of the pattern +underlying a diagram is 40~units, where the default value of the unit is 1pt. +This default value can be ``scaled'' at any time in the document by giving an +instruction like +\begin{verbatim} +\setdefaultscale{75} +\end{verbatim} +(scaling factor of 75\%); this instruction applies to all subsequent diagrams +and must be given outside a diagram environment. +If you want to apply a scaling factor to just one specific diagram, give the +scaling factor as an optional argument of the corresponding environment; thus +type +\begin{verbatim} +\begin{diagram}[125] +........ +\end{diagram} +\end{verbatim} +for an enlargement of 125\%, and correspondingly for floating diagrams. The +scaling factor given for a specific diagram overrides the {\em defaultscale} +value just for this specific diagram. For example, diagram~1 is not scaled and +diagram~2 is the same diagram, scaled at 75\%. Observe the precise +effect of the scaling option: this is by no way a brute homothetic process. +\begin{floatingdiagram}[75] +A¤¤ + ¤\Sedotar x¤\eseaR y ¤\Eesear z¤¤ + ¤\sseaR u ¤A ¤\Eepi a ¤B ¤\Emono b¤C ¤¤ + ¤ ¤\saR c ¤ ¤\Sadjar de¤ ¤\seqL{1_C}¤¤ + ¤ ¤D ¤\waR g ¤D\oplus E ¤\eaR h ¤C ¤¤ +\end{floatingdiagram} + +To motivate the next features, consider the conception of a +3-dimensional diagram, as in figure~4. Compare first the subpattern of bullets +with that of figure~2. +\begin{figure} +\begin{diagram}[50] +\XB¤\XA¤\cross{\XA}{\ear[130]}¤\XA¤\XB¤\XA¤\cross{\XA}{\ear[130]}¤\XA¤\XB¤\XA¤\XA¤¤ +\XA¤\cross{\XA}{\sear}¤\XA¤\XA¤\XA¤\cross{\XA}{\sear}¤\XA¤\XA¤\XA¤\cross{\XA}{\sear}¤\XA¤¤ +\cross{\XA}{\sar[130]}¤\XA¤\XB¤\XA¤\cross{\XA}{\cross{\ear[130]}{\sar[130]}}¤\XA + ¤\XB¤\XA¤\cross{\XA}{\cross{\ear[130]}{\sar[130]}}¤\XA¤\XB¤¤ +\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤\XA¤¤ +\XB¤\XA¤\cross{\XA}{\cross{\ear[130]}{\sar[130]}}¤\XA¤\XB¤ + ¤\cross{\XA}{\cross{\ear[130]}{\sar[130]}}¤\XA¤\XB¤\XA¤\cross{\XA}{\sar[130]}¤¤ +\XA¤\cross{\XA}{\sear}¤\XA¤\XA¤\XA¤\cross{\XA}{\sear}¤\XA¤\XA¤\XA¤\cross{\XA}{\sear}¤\XA¤¤ +\XA¤\XA¤\XB¤\XA¤\cross{\XA}{\ear[130]}¤\XA¤\XB¤\XA¤\cross{\XA}{\ear[130]}¤\XA¤\XB¤¤ +\end{diagram} +\caption{Conceiving a 3-dimensional diagram} +\end{figure} +In this case, not only you must +``cross'' different arrows at a same point of the pattern, +but you must also consider arrows which cross several points +of the pattern before reaching the objects they connect. In fact, the {\em +Diagram macros} assume that an arrow attached at some point of the +pattern connects the two adjacent points of the pattern, in the direction of the +arrow. When this is not the case, it is left on you to determine the length of +the corresponding arrow. + +To impose a specific length to a diagram arrow, just give the corresponding extent as +an optional argument\footnote{This argument should be an actual positive +integer; anything else, including the value of a counter, could put \TeX\ in +deep trouble. The formula arrows (section~2) do not admit this optional +argument.}:the extent of vertical and horizontal arrows is their length; the extent +of other arrows is the length of their horizontal projection (see \LaTeX\ manual, +{\em Picture environment}, for further explanations). Thus \verb+\Near[60]f+ draws a +north-east arrow of horizontal extent 60 units with upper name $f$. Here are +the basic default extents of diagram arrows: 50 in the directions n, s, e, w; +59 in the directions ne, nw, se, sw; 133 in the directions ene, ese, wnw, +wsw; 67 in the directions nne, sse, nnw, ssw; 211 in the directions +eene, eese, wwnw, wwsw; 71 in the directions nnne, ssse, nnnw, +sssw; 215 in the direction neene, seese, nwwnw, swwsw; 143 in the +directions nenne, sesse, nwnnw, swssw. In most circumstances, you will obtain +the required extent by augmenting the basic default extent by 40 for +each additional point of the formal pattern crossed by the arrow. + +As far as ``crossing arrows'' is concerned, the command +\begin{verbatim} +\cross{item 1}{item 2} +\end{verbatim} +allows you to introduce at the same time {\em item~1} and {\em +item~2} at the same point of the pattern; those two items can be +indifferently vertices or arrows. Diagram~3, +conceived in figure~4, must thus be typed as +\begingroup +\catcode`\¤=\active\def¤{{\S}} +\begin{verbatim} +\begin{floatingdiagram}[50] +A¤ ¤\ear[130]¤ ¤B¤ ¤\ear[130]¤ ¤C¤¤ +¤\sear¤ ¤ ¤ ¤\sear¤ ¤ ¤ ¤\sear ¤¤ +\sar[130]¤ ¤D¤ ¤\cross{\ear[130]}{\sar[130]}¤ + ¤E¤ ¤\cross{\ear[130]}{\sar[130]}¤ ¤F¤¤ ¤¤ +G¤ ¤\cross{\ear[130]}{\sar[130]}¤ ¤H¤ + ¤\cross{\ear[130]}{\sar[130]}¤ ¤I¤ ¤\sar[130]¤¤ +¤\sear¤ ¤ ¤ ¤\sear¤ ¤ ¤ ¤\sear¤¤ +¤ ¤J¤ ¤\ear[130]¤ ¤K¤ ¤\ear[130]¤ ¤L¤¤ +\end{floatingdiagram} +\end{verbatim} +\endgroup +\begin{floatingdiagram}[50] +A¤ ¤\ear[130]¤ ¤B¤ ¤\ear[130]¤ ¤C¤¤ +¤\sear¤ ¤ ¤ ¤\sear¤ ¤ ¤ ¤\sear ¤¤ +\sar[130]¤ ¤D¤ ¤\cross{\ear[130]}{\sar[130]}¤ + ¤E¤ ¤\cross{\ear[130]}{\sar[130]}¤ ¤F¤¤ ¤¤ +G¤ ¤\cross{\ear[130]}{\sar[130]}¤ ¤H¤ + ¤\cross{\ear[130]}{\sar[130]}¤ ¤I¤ ¤\sar[130]¤¤ +¤\sear¤ ¤ ¤ ¤\sear¤ ¤ ¤ ¤\sear¤¤ +¤ ¤J¤ ¤\ear[130]¤ ¤K¤ ¤\ear[130]¤ ¤L¤¤ +\end{floatingdiagram} + +Finally you can change the thickness of a diagram arrow by typing first the command +\verb+\bold+; thus \verb+\bold\nar+ produces a bold north arrow. This +\verb+\bold+ option will be cancelled by the next \S\ sign; you can cancel its +effects earlier (for example during a \verb+\cross+ command) by the +instruction \verb+\unbold+. See figure~3 for examples of bold arrows. + +\section{Curved arrows} + +The {\em Diagram macros} provide also eight curved arrows which can be used +for connecting two rather distant points lying on a same edge of a diagram; +the code for curved arrows is {\em curvar}. +These arrows are presented in figure~5, scaled at 50\%, +\begin{figure} +\begin{diagram}[50] +\cdot¤\ear¤\cross{\XB}{\Necurvar{ne}}¤\ear¤\cdot¤ ¤ ¤ ¤ ¤ +\cdot¤\ear¤\cross{\XB}{\Nwcurvar{nw}}¤\ear¤\cdot¤¤ +\sar¤ ¤\sar¤ ¤\sar¤ ¤ ¤ ¤ ¤\sar¤ ¤\sar¤ ¤\sar¤¤ +\cross{\XB}{\Wncurvar{wn}}¤\ear¤\cdot¤\ear¤\cross{\XB}{\Escurvar{es}}¤ ¤ ¤ ¤ ¤ +\cross{\XB}{\Wscurvar{ws}}¤\ear¤\cdot¤\ear¤\cross{\XB}{\Encurvar{en}}¤¤ +\sar¤ ¤\sar¤ ¤\sar¤ ¤ ¤ ¤ ¤\sar¤ ¤\sar¤ ¤\sar¤¤ +\cdot¤\ear¤\cross{\XB}{\Swcurvar{sw}}¤\ear¤\cdot¤ ¤ ¤ ¤ ¤ +\cdot¤\ear¤\cross{\XB}{\Securvar{se}}¤\ear¤\cdot¤¤ +\spacing(15,0,15) +\end{diagram} +\caption{The eight curved arrows} +\end{figure} +together with the +corresponding direction codes. The first +letter of the direction code indicates the position of the arrow with respect to the +diagram; the second letter indicates the global direction of the arrow. So +\verb+\wscurvar+ draws a curved arrow, on the west side of the diagram, oriented +to the south. As for the other arrows, a first (or last) upper case letter allows you +to name the curved arrows. + +Curved arrows are a typical example of items which are generally introduced +via the \verb+\cross+ command of section~4, at a formal point of the pattern +which they share with a vertex or another arrow. In figure~5, the bullets +indicate the formal ``center'' of the curved arrows; i.e.~the point of the +pattern where to attach them. + +The default extent of curved arrows is 160 units, yielding the situation of +figure~5. As for other diagram arrows, an arbitary extent can be imposed as a +first optional argument (again an actual positive integer!). + +Curved arrows are also part of the {\em MicroDiagram} and {\em Minidiagram} +packages. + +\section{Spacing adjustments} + +The {\em Diagram macros} determine the dimensions of a diagram by counting the +number of rows and columns in the formal pattern. When the actual dimensions +are rather different from those estimated in this way, for example when you +introduce curved arrows along a diagram, a spacing correction can be needed. +This is realized via the command \verb+\spacing(t,l,b)+ +which must imperatively be given between the \S\S\ of the last line and the +instruction \verb+\end{diagram}+ (or \verb+\end{floatingdiagram}+). This +command\footnote{Do not +abbreviate that command, this would put \TeX\ in deep trouble.} +adds $t$ points space at the top of the diagram, $l$ points space at the left and +$b$ points space at the bottom. $t$, $l$, $b$ should be positive or negative +integers. +\begingroup% +\catcode`\¤=\active\def¤{{\S}}% +\begin{verbatim} +\begin{diagram}[80] +\diagramcaption{What a nice diagram!} +...¤...¤...¤¤ +...¤...¤...¤...¤¤ +...¤...¤...¤...¤¤ +\spacing(10,-15,10) +\end{diagram} +\end{verbatim}% +\endgroup% + +When using the \verb+\cross+ command, it can also happen that an arrow +collides with the name of another arrow. To take care of this and other +unusual situations, commands exist to move elements of a diagram without +disturbing the general construction. +\begin{itemize} +\item \verb+\movename(n,m){f}+ moves the name $f$ of an arrow $n$ points right +and $m$ points up. +\item \verb+\movearrow(n,m){\arrow}+ moves the arrow \verb+\arrow+ (and its +name when there is one) $n$ points right and $m$ points up. +\item \verb+\movevertex(n,m){XXX}+ moves the vertex $XXX$ $n$ points right and +$m$ points up. +\item \verb+\movevertexleft{XXX}+ moves a too long vertex $XXX$ +positioned on the left edge of a diagram, +so that the next horizontal arrow keeps maximal length. +\item \verb+\movevertexright{XXX}+ moves a too long vertex $XXX$ +positioned on the right edge of a diagram, +so that the previous horizontal arrow keeps a maximal length. +\end{itemize} + +For example, diagram~4 +\begin{floatingdiagram} +(A\oplus B)\otimes(C\oplus D) ¤ \Ear f¤ X\oplus V ¤¤ +\Sar g¤ ¤ \saR h¤¤ +Y\oplus W ¤ \eaR i¤ (E\oplus F)\otimes(G\oplus H) ¤¤ +\movevertexleft{(A\oplus B)\otimes(C\oplus D)} ¤ \Ear f¤ X\oplus V ¤¤ +\Sar g¤ ¤ \saR h¤¤ +Y\oplus W ¤ \eaR i¤ \movevertexright{(E\oplus F)\otimes(G\oplus H)} +\diagramcaption{Automatic and manual adjustments} ¤¤ +\end{floatingdiagram} +has been obtained by just typing +\begingroup +\catcode`\¤=\active\def¤{{\S}} +\begin{verbatim} +\begin{floatingdiagram} +(A\oplus B)\otimes(C\oplus D)¤\Ear f¤X\oplus V¤¤ +\Sar g¤ ¤ \saR h¤¤ +Y\oplus W¤\eaR i¤(E\oplus F)\otimes(G\oplus H)¤¤ +\movevertexleft{(A\oplus B)\otimes(C\oplus D)}¤\Ear f¤ X\oplus V¤¤ +\Sar g¤ ¤\saR h¤¤ +Y\oplus W¤\eaR i¤\movevertexright{(E\oplus F)\otimes(G\oplus H)} +\diagramcaption{Automatic and manual adjustments}¤¤ +\end{floatingdiagram} +\end{verbatim} +\endgroup +The upper square is thus produced automatically by the {\em Diagram macros}, +while the lower square has been adjusted by the user. Make your choice. +\vfill + +\mbox{}\hfill{\footnotesize Une version fran\c caise de ce mode d'emploi est +\'egalement disponible.} + + +\end{document} \ No newline at end of file -- cgit v1.2.3