#LyX 1.6.5svn created this file. For more info see http://www.lyx.org/ \lyxformat 345 \begin_document \begin_header \textclass scrartcl \begin_preamble \usepackage[all]{xy} % define new commands used in sec. 5.1 \newcommand{\xyR}[1]{ \xydef@\xymatrixrowsep@{#1}} \newcommand{\xyC}[1]{ \xydef@\xymatrixcolsep@{#1}} \newdir{|>}{!/4.5pt/@{|}*:(1,-.2)@^{>}*:(1,+.2)@_{>}} % a pdf-bookmark for the TOC is added \let\myTOC\tableofcontents \renewcommand\tableofcontents{% \pdfbookmark[1]{\contentsname}{} \myTOC } % redefine the \LyX macro for PDF bookmarks \def\LyX{\texorpdfstring{% L\kern-.1667em\lower.25em\hbox{Y}\kern-.125emX\@} {LyX}} \end_preamble \options BCOR7.5mm \use_default_options false \language english \inputencoding auto \font_roman ae \font_sans default \font_typewriter default \font_default_family default \font_sc false \font_osf false \font_sf_scale 100 \font_tt_scale 100 \graphics default \paperfontsize 12 \spacing single \use_hyperref true \pdf_title "Using XY-pc in LyX" \pdf_author "H. Peter Gumm" \pdf_subject "LyX's XY-pic manual" \pdf_keywords "LyX, documentation" \pdf_bookmarks true \pdf_bookmarksnumbered true \pdf_bookmarksopen true \pdf_bookmarksopenlevel 2 \pdf_breaklinks false \pdf_pdfborder false \pdf_colorlinks true \pdf_backref false \pdf_pdfusetitle false \pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue,pdfpagelayout=OneColumn, pdfnewwindow=true,pdfstartview=XYZ, plainpages=false, pdfpagelabels" \papersize a4paper \use_geometry false \use_amsmath 1 \use_esint 0 \cite_engine basic \use_bibtopic false \paperorientation portrait \secnumdepth 3 \tocdepth 3 \paragraph_separation indent \defskip medskip \quotes_language english \papercolumns 1 \papersides 2 \paperpagestyle default \tracking_changes false \output_changes false \author "" \author "" \author "" \end_header \begin_body \begin_layout Title Using \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -pic in LyX \end_layout \begin_layout Author H. Peter Gumm \end_layout \begin_layout Abstract With the recent versions of LyX and with the \family typewriter preview \family default -style installed in the LaTeX-System, the graph drawing package \family typewriter \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset \family default -pic can be conveniently used inside LyX. Diagrams can be edited and displayed inside the main LyX editing window. Here, we shall describe how to use the \family typewriter \backslash xymatrix \family default command from \family typewriter xypic \family default inside LyX in order to draw, to edit and to preview diagrams as typically used in category theory, algebra, and related fields. \end_layout \begin_layout Abstract \begin_inset CommandInset toc LatexCommand tableofcontents \end_inset \end_layout \begin_layout Section Introduction \end_layout \begin_layout Standard The \family typewriter xypic \family default -package has long served as a convenient tool for easily constructing graphs and diagrams in LaTeX. Unfortunately, its use in LyX had long been restricted to the infamous TeX code boxes, meaning that the LyX editor could only display the LaTeX-source and not the finished diagram. The new \family typewriter preview \family default -style of LaTeX which is part of the AUCTeX project \begin_inset CommandInset citation LatexCommand cite key "AUCTeX" \end_inset , finally enables the editing and displaying of \family typewriter xypic \family default -diagrams, constructed, displayed and interactively edited inside LyX. \end_layout \begin_layout Standard \begin_inset VSpace defskip \end_inset \end_layout \begin_layout Standard \align center \begin_inset Graphics filename xyfigure.png scale 50 BoundingBox 0bp 0bp 580bp 440bp clip \end_inset \end_layout \begin_layout Standard \begin_inset VSpace defskip \end_inset \end_layout \begin_layout Standard In this note, we describe how \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -pic can be used from inside LyX, how diagrams can be created and edited. We have tested the following using LyX versions 1.3.7 up to 1.6, running under Windows \begin_inset space \thinspace{} \end_inset XP and under Windows Vista. \end_layout \begin_layout Standard There are two modes of operations: For a start, and for some first tests, it may be easiest to first enter the \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -pic code inside the LyX-window, select it all and convert it to a graphical representation by pressing \family sans Ctrl-m \family default or \family sans Ctrl-M \family default . If you use \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -pic more frequently, or if you want to modify your initial figure, you will want to assemble and modify your figures using LyX's math editor. \end_layout \begin_layout Standard Once the cursor is moved over a diagram, this is displayed as an array of nodes and arrow-commands. These can be changed interactively. When the cursor leaves the editing area, the diagram reappears. \end_layout \begin_layout Standard In the first two sections of this documentation, we explain how to use LyX in the first mentioned mode and we introduce all \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -pic features that might be of use for drawing commutative diagrams, graphs or automata. Section \begin_inset CommandInset ref LatexCommand ref reference "sec:math-editor" \end_inset explains how to use the \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -pic commands inside a math-editing area. \end_layout \begin_layout Standard It is not our intention to write another introduction to \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -pic, rather our motivation is to give an introduction how the most important commands work inside LyX, since the keystrokes as explained in the \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -pic manual \begin_inset CommandInset citation LatexCommand cite key "xypic manual" \end_inset will not always function correctly inside LyX. \end_layout \begin_layout Section Preparation \end_layout \begin_layout Standard The following requires that the LaTeX-packages \family typewriter xypic \family default and \family typewriter preview \family default are installed in the LaTeX system. They are available from CTAN, see at \begin_inset CommandInset citation LatexCommand cite key "instant-preview" \end_inset , resp. at \begin_inset CommandInset citation LatexCommand cite key "xypic" \end_inset . After freshly installing them, it may be necessary, to run \family sans Tools\SpecialChar \menuseparator Reconfigure \family default from the main LyX menu. The steps to a first diagram output in LyX are then: \end_layout \begin_layout Enumerate Activate and test \family typewriter preview \end_layout \begin_deeper \begin_layout Enumerate Open LyX, choose \family sans Tools\SpecialChar \menuseparator Preferences\SpecialChar \menuseparator Look and Feel\SpecialChar \menuseparator Display \family default and turn \emph on Instant Preview \emph default on. \end_layout \begin_layout Enumerate In \family sans Document\SpecialChar \menuseparator Settings\SpecialChar \menuseparator Math \begin_inset space ~ \end_inset Options \family default , uncheck \emph on Use AMS Math package automatically \emph default and check \emph on Use AMS Math package \emph default . \end_layout \begin_layout Enumerate Test, if \family typewriter instant-preview \family default works by opening a LyX-document and entering any math-formula, e. \begin_inset space \thinspace{} \end_inset g. \begin_inset Formula $a+b=c$ \end_inset . \end_layout \begin_layout Enumerate Move the cursor out of the formula, and watch it change its appearance to look just like in the finished DVI- or PostScript document. \end_layout \end_deeper \begin_layout Enumerate Activate and test \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -pic \family typewriter : \end_layout \begin_deeper \begin_layout Enumerate Inside your LyX-Document, enter the text \family typewriter \begin_inset Newline newline \end_inset \backslash xymatrix{A \backslash ar[r] & B} \family default . \end_layout \begin_layout Enumerate Select the whole text and choose \family sans Insert\SpecialChar \menuseparator Math\SpecialChar \menuseparator Display Formula \family default , or use the corresponding keyboard shortcut \family sans Ctrl-M \family default . \end_layout \begin_layout Enumerate Move the mouse cursor out of the editing box and wait for a split second to see an arrow appear: \begin_inset Formula $\xymatrix{A\ar[r] & B} $ \end_inset . \end_layout \end_deeper \begin_layout Section Commutative diagrams \end_layout \begin_layout Standard The following diagram, which is taken from the documentation of \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -pic \begin_inset CommandInset citation LatexCommand cite key "xypic manual" \end_inset by its creator Kristoffer H. Rose, will provide an example for many of the features available with that package. Its source code is: \end_layout \begin_layout LyX-Code \backslash xymatrix{ \begin_inset Newline newline \end_inset U \backslash ar@/_{1pc}/[ddr]_ \backslash psi \backslash ar@/^{1pc}/[drr]^ \backslash varphi \begin_inset Newline newline \end_inset \backslash ar@{.>}[dr]|-{(x,y)} \backslash \backslash \begin_inset Newline newline \end_inset & X \backslash times_Z Y \backslash ar[d]^q \backslash ar[r]_p & X \backslash ar[d]_f \backslash \backslash \begin_inset Newline newline \end_inset & Y \backslash ar[r]^g & Z } \end_layout \begin_layout LyX-Code \end_layout \begin_layout Standard Again, to turn this code into a graphical output, select it all at once starting from the \family typewriter \backslash xymatrix{ \family default \SpecialChar \ldots{} up to the closing brace \SpecialChar \ldots{} \family typewriter } \family default and turn it into display-math as explained above. A moment after the cursor leaves the math-area, you should see the diagram in its full graphical glory as shown below. \end_layout \begin_layout Standard \begin_inset Formula $\xymatrix{U\ar@/_{1pc}/[ddr]_{\psi}\ar@/{}^{1pc}/[drr]^{\varphi}\ar@{.>}[dr]|-{(x,y)}\\ & X\times_{Z}Y\ar[d]^{q}\ar[r]_{p} & X\ar[d]_{f}\\ & Y\ar[r]^{g} & Z} $ \end_inset \end_layout \begin_layout Subsection The matrix layout of diagrams \end_layout \begin_layout Standard \family typewriter xymatrix \family default uses a matrix to define the layout of the vertices of a diagram. For the above example, we need a \begin_inset Formula $3\times3$ \end_inset -matrix of which 5 entries are used for the vertices \begin_inset Formula $U$ \end_inset , \begin_inset Formula $X\times_{Z}Y$ \end_inset , \begin_inset Formula $X$ \end_inset , \begin_inset Formula $Y$ \end_inset , \begin_inset Formula $Z$ \end_inset , the other positions remaining empty. In this case, the following matrix determines the layout: \end_layout \begin_layout LyX-Code \backslash xymatrix{ \begin_inset Newline newline \end_inset U \backslash \backslash \begin_inset Newline newline \end_inset & X \backslash times_Z Y & X \backslash \backslash \begin_inset Newline newline \end_inset & Y & Z } \end_layout \begin_layout Standard The pattern should be familiar from LaTeX: We see three rows, the first two being terminated by the end-of-line-marker \family typewriter \backslash \backslash \family default . Each line consists of entries, separated by the ampersand \family typewriter & \family default . \end_layout \begin_layout Subsection Arrows \end_layout \begin_layout Standard Having entered the vertices, we add arrows between them. The basic \family typewriter xypic \family default -command to produce an arrow is \family typewriter \backslash ar \family default , it is entered into the cell of the matrix where the arrow is to start. The target of the arrow is defined by direction commands \family typewriter u \family default (up) \family typewriter d \family default (down) \family typewriter l \family default (left), or \family typewriter r \family default (right). These can be combined to a path and enclosed in square brackets. As an example, the arrows from the vertex \begin_inset Formula $U$ \end_inset in the upper left corner down and right to the vertices \begin_inset Formula $X\times_{Z}Y$ \end_inset , \begin_inset Formula $Y$ \end_inset , and \begin_inset Formula $X$ \end_inset are, respectively, defined as \family typewriter \backslash ar[dr] \family default , \family typewriter \backslash ar[ddr] \family default and \family typewriter \backslash ar[drr] \family default . Thus the above diagram with all arrows added becomes: \end_layout \begin_layout LyX-Code \backslash xymatrix{ \begin_inset Newline newline \end_inset U \backslash ar[ddr] \backslash ar[drr] \backslash ar[dr] \backslash \backslash \begin_inset Newline newline \end_inset & X \backslash times_Z Y \backslash ar[d] \backslash ar[r]& X \backslash ar[d] \backslash \backslash \begin_inset Newline newline \end_inset & Y \backslash ar[r] & Z } \end_layout \begin_layout Standard \begin_inset Formula \xymatrix{ U \ar[ddr] \ar[drr] \ar[dr]\\ & X \times_{Z} Y \ar[d] \ar[r] & X \ar[d]\\ & Y \ar[r] & Z } \end_inset \end_layout \begin_layout LyX-Code \end_layout \begin_layout LyX-Code \end_layout \begin_layout Subsection Labels \end_layout \begin_layout Standard Labels are attached to arrows by affixing them as upper or lower indices to the \family typewriter \backslash ar \family default -command. Thus, \family typewriter \backslash ar[drr]^ \backslash varphi \family default defines an arrow going one cell down, two to the right and having the label \begin_inset Formula $\varphi$ \end_inset attached above. To attach a label below the arrow, make it a lower index as in \family typewriter \backslash ar[ddr]_ \backslash psi \family default . This explanation is correct only for arrows pointing to the right. More precisely, imagine looking along the arrow in the direction it is pointing. Then an upper index places a label to the left and a lower index places it to the right. Consequently, an arrow pointing from right to left, such as \family typewriter \backslash ar[l]^ \backslash alpha_ \backslash beta \family default will have label \begin_inset Formula $\alpha$ \end_inset below and label \begin_inset Formula $\beta$ \end_inset above the arrow, e. \begin_inset space \thinspace{} \end_inset g. \begin_inset space \space{} \end_inset \begin_inset Formula $\xymatrix{\ & \ \ar[l]_{\beta}^{\alpha}.} $ \end_inset Using the character | instead of ^ or _ , it is even possible to place the label right onto the arrow, obscuring part of its shaft. \end_layout \begin_layout Standard Normally, a label is placed halfway between an arrow's start and target objects. In the first diagram, the central arrow starting in \begin_inset Formula $U$ \end_inset has the label \begin_inset Formula $(x,y)$ \end_inset in the middle of the arrow's shaft, rather than in the middle between the two objects it connects. This is achieved by prefixing the label with a minus sign, here: \family typewriter \backslash ar[dr]|-{(x,y)} \family default . \end_layout \begin_layout LyX-Code \backslash xymatrix{ \begin_inset Newline newline \end_inset U \backslash ar[ddr]_ \backslash psi \backslash ar[drr]^ \backslash varphi \backslash ar[dr]|-{(x,y)} \backslash \backslash \begin_inset Newline newline \end_inset & X \backslash times_Z Y \backslash ar[d]^q \backslash ar[r]_p& X \backslash ar[d]_f \backslash \backslash \begin_inset Newline newline \end_inset & Y \backslash ar[r]^g & Z } \end_layout \begin_layout LyX-Code \begin_inset Formula \xymatrix{ U \ar[ddr]_{\psi}\ar[drr]^{\varphi}\ar[dr]|-{(x,y)}\\ & X \times_{Z} Y \ar[d]^{q} \ar[r]_{p} & X \ar[d]_{f}\\ & Y \ar[r]^{g} & Z } \end_inset \end_layout \begin_layout Standard \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -pic normally permits labels to be shifted towards the tip or towards the start of an arrow by prefixing the label with a ratio, such as e. \begin_inset space \thinspace{} \end_inset g. \family typewriter (.3) \family default . In LyX this works only for labels which are placed on top of the arrow, such as \family typewriter \backslash ar[r]|(0.3){ \backslash phi} \family default . \end_layout \begin_layout Standard For labels placed to the left or to the right of the arrow this does not work. The corresponding \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -pic code such as e. \begin_inset space \thinspace{} \end_inset g. \family typewriter \backslash ar[r]^(.3) \backslash phi \family default or \family typewriter \backslash ar[r]_(.3) \backslash psi \family default is not correctly interpreted by LyX's math editor. Two workarounds are suggested in the last section of this note. \end_layout \begin_layout Subsection Arrow modification \end_layout \begin_layout Standard Modification of the design, the form or the positioning of arrows are introduced by the \family typewriter @ \family default -character. This is followed by a pair of matching brackets, where the form of the bracket pair, \family typewriter { } \family default or \family typewriter < > \family default or \family typewriter / / \family default indicates, whether we want to modify the design, the or the curvature of the arrow. Various modifications can be applied to an arrow at the same time. \end_layout \begin_layout Subsubsection Arrow design \end_layout \begin_layout Standard Various designs such as \emph on solid \emph default , \emph on dotted \emph default , \emph on dashed \emph default or \emph on double \emph default are possible for the shaft of an arrow. These can be combined with various ends and various tips. In general, the design of an arrow is described by following the command \family typewriter \backslash ar \family default immediately by an \family typewriter @ \family default -sign and a pair of braces {\SpecialChar \ldots{} } containing characters describing the end, the shaft and the tip of the arrow. These characters are chosen to give some form of ASCII-rendering of the real thing. For instance \family typewriter \backslash ar@{>..>>} \family default produces an arrow with split end, a dotted shaft and double head. A number of other arrow designs is given in the table below. Note that the ends of embedding arrows \begin_inset Formula $\xymatrix{A\ar@{^{(}->}[r] & B} $ \end_inset are described by raising or lowering opening parentheses, such as in \family typewriter \backslash ar@{^(->}[r]. \begin_inset Newline newline \end_inset \end_layout \begin_layout Standard \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout Result \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Source code in LyX \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula \xymatrix{\ \ar[r] & \ } \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \family typewriter \backslash ar \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula \xymatrix{\ \ar@{-->}[r] & \ } \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \family typewriter \backslash ar@{-->} \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula \xymatrix{\ \ar@{..>}[r] & \ } \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \family typewriter \backslash ar@{..>} \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula \xymatrix{\ \ar@{~>}[r] & \ } \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \family typewriter \backslash ar@{~>} \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula \xymatrix{\ \ar@{->>}[r] & \ } \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \family typewriter \backslash ar@{->>} \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula \xymatrix{\ \ar@{-->>}[r] & \ } \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \family typewriter \backslash ar@{-->>} \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula \xymatrix{\ \ar@{>->>}[r] & \ } \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \family typewriter \backslash ar@{>->>} \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula \xymatrix{\ \ar@{_{(}->}[r] & \ } \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \family typewriter \backslash ar@{_(->} \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula \xymatrix{\ \ar@{^{(}->}[r] & \ } \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \family typewriter \backslash ar@{^(->} \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula \xymatrix{\ \ar@{|-|}[r] & \ } \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \family typewriter \backslash ar@{|-|} \end_layout \end_inset \end_inset \end_layout \begin_layout Standard \noindent Following the @-character by either a 2, 3, _,or a ^, we can produce arrows with double, triple shaft or arrows showing only the lower or upper half of their tips and ends. Arrows need not have tips nor ends, as the last example shows : \begin_inset Newline newline \end_inset \end_layout \begin_layout Standard \begin_inset Tabular \begin_inset Text \begin_layout Plain Layout Result \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout Source code for LyX \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula \xymatrix{\ \ar@2[r] & \ } \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \family typewriter \backslash ar@2 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula \xymatrix{\ \ar@3[r] & \ } \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \family typewriter \backslash ar@3 \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula \xymatrix{\ \ar@_{->}[r] & \ } \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \family typewriter \backslash ar@_{->} \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula \xymatrix{\ \ar@^{->}[r] & \ } \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \family typewriter \backslash ar@^{->} \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula \xymatrix{\ \ar@^{>>->>}[r] & \ } \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \family typewriter \backslash ar@^{>>->>} \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula \xymatrix{\ \ar@{^{<}-_{>}}[r] & \ } \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \family typewriter \backslash ar@{^<-_>} \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \begin_inset Formula \xymatrix{\ \ar@2{--}[r] & \ } \end_inset \end_layout \end_inset \begin_inset Text \begin_layout Plain Layout \family typewriter \backslash ar@2{--} \end_layout \end_inset \end_inset \end_layout \begin_layout Subsubsection Designing your own arrows \end_layout \begin_layout Standard Within certain limits there is even a way to design your own arrows. Using some the characters \family typewriter ><|ox+/()[ \family default one can even design one's own arrow tips using the \family typewriter \backslash newdir \family default command in the preamble. For explanations, we refer to the \family typewriter \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset \family default -manual, from which we take the example: \end_layout \begin_layout Standard \family typewriter \backslash newdir{|>}{!/4.5pt/@{|}*:(1,-.2)@^{>}*:(1,+.2)@_{>}} \family default . \end_layout \begin_layout Standard \noindent This defines a new arrow tip, referred to as \family typewriter |> \family default in \family typewriter \backslash ar@{-|>}[r] \family default and which displays correctly in LyX as: \begin_inset Formula \[ \xymatrix{A\ar@{-|>}[r] & \ \ B} \] \end_inset \end_layout \begin_layout Subsection Arrow positioning \end_layout \begin_layout Standard Arrows are shifted sideways with the modifier \family typewriter @< \family default \begin_inset Formula $\ldots$ \end_inset \family typewriter > \family default where the ellipsis is replaced by a positive or negative measure. For instance, to design a pair of mutually opposing arrows between two nodes, we shift them to see them apart. Note that the direction of the shift (positive) is to the left if one looks along the arrow. Thus \end_layout \begin_layout Standard \family typewriter \backslash xymatrix{ \backslash circ \backslash ar@<1ex>[r]& \backslash circ \backslash ar@<1ex>[l]} \end_layout \begin_layout Standard \noindent produces \begin_inset space ~ \end_inset \begin_inset space ~ \end_inset \begin_inset Formula \[ \xymatrix{\circ\ar@<1ex>[r] & \circ\ar@<1ex>[l]} \] \end_inset \end_layout \begin_layout Subsubsection Inline or centered diagrams \end_layout \begin_layout Standard Arrows and diagrams can be used inline, such as this one: \begin_inset Formula $\xymatrix{\circ\ar@<1ex>[r] & \circ\ar@<1ex>[l]} $ \end_inset . When their code is written inside LyX as above, select it and choose either \family sans Ctrl-m \family default for inline appearance or \family sans Ctrl-M \family default for displaystyle. Diagrams constructed inline can later be centered, or, conversely, centered diagrams can be changed to inline formulas with \family sans Edit\SpecialChar \menuseparator Math \family default \family sans \SpecialChar \menuseparator Change Formula Type. \end_layout \begin_layout Subsection Bending arrows \end_layout \begin_layout Standard There are two simple methods to make arrows bend. The first is giving an explicit value by which the midpoint of the arrow's shaft is raised or depressed, the other is by forcing the arrow to leave its origin in a prescribed compass direction and to make him enter the target at another direction. The necessary bending of the arrow is determined automatically. We describe both methods. \end_layout \begin_layout Subsubsection Raising the shaft \end_layout \begin_layout Standard For bending arrows we use the modifier @/ \begin_inset Formula $\ldots$ \end_inset / . The ellipsis stands for a TeX-measure which needs to be entered as a lower or upper index. Whereas in \family typewriter xypic \family default , we could simply write, e. \begin_inset space \thinspace{} \end_inset g. \family typewriter \backslash ar@/_1pc/ \family default for an arrow bending \family typewriter 1pc \family default downwards, this cannot directly be done in LyX. It is necessary, to enclose the measure in a pair of braces, such as e. \begin_inset space \thinspace{} \end_inset g. \family typewriter \backslash ar@/_{1pc}/ \family default . As an example, here are two opposing arrows between \begin_inset Formula $A$ \end_inset and \begin_inset Formula $B$ \end_inset , each bending by .5 pica, given by the following source code: \end_layout \begin_layout Standard \family typewriter \backslash xymatrix{A \backslash ar@/_{.5pc}/[r] & B \backslash ar@/_{.5pc}/[l]} \end_layout \begin_layout Standard \begin_inset Formula \[ \xymatrix{A\ar@/{}_{.5pc}/[r] & B\ar@/{}_{.5pc}/[l]} \] \end_inset \end_layout \begin_layout Subsubsection Specifying exit- and entrance directions \end_layout \begin_layout Standard An alternative for making arrows bend is by specifying their compass direction as they are leaving their source and their direction from which they enter their target. Instead of north, north-east, east, etc., the directions are named \family typewriter u \family default , \family typewriter ur \family default , \family typewriter r \family default , \family typewriter dr \family default , \family typewriter d \family default , \family typewriter dl \family default , \family typewriter l \family default , \family typewriter ul \family default , standing for up, up-right, right, down-right, etc.. A direction is specified as @( \emph on out \emph default , \emph on in \emph default ) where \emph on out \emph default stands for the direction the first object is left and \emph on in \emph default stands for the direction from which the target is entered. As an example, we show some bending arrows and a loop, which arises when we do not specify a target for an arrow, just its incoming and outgoing direction: \end_layout \begin_layout Standard \begin_inset Formula \[ \xymatrix{A\ar@(dr,dl)[r]\ar@(dr,dl)[rr] & B\ar@(d,r)[dl] & C\\ E\ar@(ul,ur)} \] \end_inset \end_layout \begin_layout LyX-Code \backslash xymatrix{A \backslash ar@(dr,dl)[r] \backslash ar@(dr,dl)[rr] \begin_inset Newline newline \end_inset &B \backslash ar@(d,r)[dl] &C \backslash \backslash \begin_inset Newline newline \end_inset E \backslash ar@(ul,ur)} \end_layout \begin_layout Subsection Modifying vertices \end_layout \begin_layout Standard The above example is reminiscent of an automata diagram, except that in such a diagram states would be enclosed in small circles, with double circles denoting final states. \end_layout \begin_layout Subsubsection Framing objects \end_layout \begin_layout Standard With \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -pic, entries can obtain a single or a double frame, such as \begin_inset Formula $\xymatrix{*+[F]{A}} $ \end_inset or \begin_inset Formula $\xymatrix{*+[F=]{B}} $ \end_inset by prefixing an entry with \family typewriter *[F-] \family default or \family typewriter *[F=] \family default and enclosing the portion of the entry to be framed in braces. Normally, the frame will be very tight so that it must be widened by prefixing with \family typewriter + \family default or with \family typewriter ++ \family default . Round frames, such as \begin_inset Formula $\xymatrix{*++[o][F]{A}} $ \end_inset and \begin_inset Formula $\xymatrix{*++[o][F=]{B}} $ \end_inset are obtained by specifying the shape as \family typewriter [o]. \family default So the latter figure was constructed as *++[o][F=]{B}. This way, the following automaton \end_layout \begin_layout Standard \begin_inset Formula \[ \xymatrix{\txt{start}\ar[r] & *++[o][F]{1}\ar[r] & *++[o][F=]{2}\ar@(ur,dr)\ar@(ur,ul)[l]} \] \end_inset \end_layout \begin_layout Standard \noindent can be typeset as \end_layout \begin_layout LyX-Code \backslash xymatrix{ \backslash txt{start} \backslash ar[r] \end_layout \begin_layout LyX-Code & *++[o][F]{1} \backslash ar[r] \end_layout \begin_layout LyX-Code & *++[o][F=]{2} \backslash ar@(ur,dr) \backslash ar@(ur,ul)[l] \end_layout \begin_layout LyX-Code }. \end_layout \begin_layout Standard The LaTeX command \family typewriter \backslash entrymodifiers={ \family default \SpecialChar \ldots{} \family typewriter } \family default will make a certain entry style the default, that can, of course be overridden for individual entries. Thus, after \family typewriter \backslash entrymodifiers={++[o][F-]} \family default , all following entries inside \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -matrices would be encircled. \end_layout \begin_layout Subsubsection Framing rectangles \end_layout \begin_layout Standard Framing a whole rectangle inside an xymatrix is done with the macro pair \family typewriter \backslash save ... \backslash restore \family default . \family roman \series medium \shape up \size normal \emph off \bar no \noun off \color none The dimension of the rectangle is given as a dotted pair \begin_inset Formula $P_{0}.P_{1}$ \end_inset of points denoting the top left and lower right corners of the rectangle. Each point, in turn,is given as a doubly quoted comma separated pair \begin_inset Quotes eld \end_inset \begin_inset Formula $x,y$ \end_inset \begin_inset Quotes erd \end_inset specifying row \begin_inset Formula $x$ \end_inset and column \begin_inset Formula $y$ \end_inset . These are followed by the framing commands, to produce figures such as the following: \begin_inset Formula \[ \xymatrix{A & B\ar@(d,r)[dl]\sp(0.2)\phi\sp(0.7)\psi\save"1,1"."2,1"*+[F=]\frm{}\restore\,\\ C & \save"1,1"."1,2"*++[F]\frm{}\restore} \] \end_inset Here, the code \family typewriter \series default \shape default \size default \emph default \bar default \noun default \color inherit \backslash save"1,1"."2,1"*+[F=] \backslash frm{} \backslash restore \family roman \series medium \shape up \size normal \emph off \bar no \noun off \color none produces the doubly framed rectangle, and the code for the extra wide horizonta l rectangle is \family typewriter \series default \shape default \size default \emph default \bar default \noun default \color inherit \backslash save"1,1"."1,2"*++[F] \backslash frm{} \backslash restore \family roman \series medium \shape up \size normal \emph off \bar no \noun off \color none . This code can be placed in arbitrary cells of the xymatrix. \end_layout \begin_layout Section Using LyX's math editor \begin_inset CommandInset label LatexCommand label name "sec:math-editor" \end_inset \end_layout \begin_layout Standard As an alternative to writing the \family typewriter xypic \family default code, then transforming it into a math-editing environment by marking it and applying \family sans Ctrl-m \family default , or \family sans Ctrl-M \family default , one may construct and modify the whole xypic-diagram inside LyX's math editor. We describe the editing steps for a figure just like the one above. \end_layout \begin_layout Subsection Caveat - how to enter braces \end_layout \begin_layout Standard Recall that in LyX's math-editor any pair of braces \family typewriter { \family default and \family typewriter } \family default that are to enclose a macro-parameter must be entered by typing just \family typewriter \backslash { \family default . The closing brace is automatically supplied and in between a box into which to the parameter is entered. In connection with \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -diagrams, this applies in particular to arrow modifications that are normally given in the form \family typewriter @{ \family default \SpecialChar \ldots{} \family typewriter } \family default with the ellipsis standing for the description of end, shaft and tip of the arrow. Inside the math-editor, enter just \family typewriter @ \backslash { \family default and let LyX provide the closing brace and the box into which to enter the description of the arrow. \end_layout \begin_layout Standard Braces that are entered without the backslash \family typewriter \backslash \family default will just appear as typed, but cannot be used to receive a macro parameter. They are useful, for instance to denote sets, e. \begin_inset space \thinspace{} \end_inset g. \family typewriter {x \backslash in X \backslash mid x \backslash notin x} \family default will display as \begin_inset Formula $\{x\in X\mid x\notin x\}$ \end_inset . \end_layout \begin_layout Subsection Setting up the matrix \end_layout \begin_layout Standard With \family sans Ctrl-m \family default or \family sans Ctrl-M \family default open a formula environment and enter: \family typewriter \backslash xymatrix \family default . This produces a 1 \begin_inset Formula $\times$ \end_inset 1- \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -matrix. Add extra rows by typing \family sans Ctrl-Enter \family default and add columns by typing \family sans Alt-m c i. \end_layout \begin_layout Standard At any time, further rows or columns can be entered or deleted using commands available from \family sans Edit\SpecialChar \menuseparator Math, \family default resp. their shortcuts, beginning with \family sans Alt-m c \family default for the column commands or \family sans Alt-m w \family default for the row commands. A more direct way uses the icons in the math toolbar once it has been activated via \family sans View\SpecialChar \menuseparator Toolbars. \end_layout \begin_layout Subsection Entering nodes, arrows and labels \end_layout \begin_layout Standard Type the nodes into the correct positions of the matrix. If you move the cursor out of the matrix, you should see a first rendering of the node layout. Next, add the arrows at the nodes from where they should emanate by typing \family typewriter \backslash ar[ \family default \emph on p \family typewriter \emph default ] \family default , where \emph on p \emph default can be any path made up from the characters \family typewriter u \family default , \family typewriter d \family default , \family typewriter l \family default , \family typewriter r \family default . Make sure that the path indeed leads to an existing node within the matrix. Otherwise, the figure will not display when the cursor leaves the editing area. \end_layout \begin_layout Standard Next, label the arrows by attaching a label text as upper or lower indices to the end of the arrow's path. As always in LyX's math editor, an underscore \family typewriter _ \family default opens a box for a lower index and a \family typewriter ^ \family default followed by a space opens a box for an upper index. You can enter any LaTeX-code as a label. \end_layout \begin_layout Subsection Modifying arrows \end_layout \begin_layout Standard Finally, you can modify the appearance of the arrows by entering @-modifiers \family typewriter @{ \family default \SpecialChar \ldots{} \family typewriter } \family default , \family typewriter @< \family default \SpecialChar \ldots{} >, \family typewriter @( \family default \SpecialChar \ldots{} ,\SpecialChar \ldots{} ) or \family typewriter @/ \family default \SpecialChar \ldots{} \family typewriter / \family default . The above caveat applies to the first form only. It must be entered as \family typewriter @ \backslash { \family default with the arrow description entered inside the LyX-supplied box. If this box remains empty, you have specified an empty arrow. This is a useful construction, too, as you will see in the next section. \end_layout \begin_layout Standard The other modifiers, \family typewriter @< \family default \SpecialChar \ldots{} \family typewriter > \family default , \family typewriter @( \family default \SpecialChar \ldots{} ,\SpecialChar \ldots{} \family typewriter ) \family default and \family typewriter @/ \family default \SpecialChar \ldots{} \family typewriter / \family default are typed as shown with the arrow description replacing the ellipsis. The code for bending arrows, which in \family typewriter xypic \family default is \family typewriter @/_ \family default \emph on measure \family typewriter \emph default / \family default or \family typewriter @/ \emph on ^ \family default measure \family typewriter \emph default / \family default where \emph on measure \emph default is any valid TeX-measure that should be entered as upper or lower index to the first slash /. Make sure that the ending slash does not end up being part of the upper or lower index. \end_layout \begin_layout Subsection What if something goes wrong \end_layout \begin_layout Standard When constructing a diagram, you should at times check it by just moving the cursor out of the editing area to see whether instant preview can successfu lly convert it into graphical output. If this does not happen, it may either be that instant preview for some reason is not aware that it should retranslate the graphics. Moving the cursor into the editing area and out again sometimes wakes up instant preview. \end_layout \begin_layout Standard A more serious reason could be a syntactical error in your input (in that case, the math edition area disappears completely). If necessary, undo the last editing steps, using \family sans Ctrl+Z \family default , or try to translate the LyX-file into \family sans DVI \family default using \family sans Ctrl+D \family default or \family sans View\SpecialChar \menuseparator DVI \family default . There should be some error generated, which hopefully gives you a hint as to the source of the mistake. \end_layout \begin_layout Section Hacks \end_layout \begin_layout Standard Certain things do not work correctly inside LyX. The ones that we (used to) miss most are the horizontal and vertical scaling of diagrams, and the correct positioning of arrows. There are some workarounds that we are explaining here. \end_layout \begin_layout Subsection Horizontal and vertical scaling \end_layout \begin_layout Standard It is often convenient to stretch the horizontal or the vertical dimensions of an entire diagram by using spacing commands for rows and/or columns. According to the \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -manual, for instance, \family typewriter \backslash xymatrix@R=1pc{ \family default \SpecialChar \ldots{} \family typewriter } \family default defines an \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -matrix with row spacing of 1 pica. Similarly, \family typewriter \backslash xymatrix@C= \family default \SpecialChar \ldots{} \family typewriter { \family default \SpecialChar \ldots{} \family typewriter } \family default allows to modify the space between columns. Unfortunately, these commands do currently not work inside LyX, as the @-character is interpreted by LyX as ending the \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -matrix-macro. \end_layout \begin_layout Standard Knowing that \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset \begin_inset space ~ \end_inset stores the values for row-spacing and column-spacing in the variables \family typewriter \backslash xymatrixrowsep@ \family default and \family typewriter \backslash xymatrixrowsep@ \family default , add the following macro to the preamble ( \family sans Layout\SpecialChar \menuseparator Document\SpecialChar \menuseparator Preamble \family default ): \begin_inset Newpage pagebreak \end_inset \end_layout \begin_layout LyX-Code \backslash newcommand{ \backslash xyR}[1]{% \end_layout \begin_layout LyX-Code \backslash xydef@ \backslash xymatrixrowsep@{#1}} \end_layout \begin_layout LyX-Code \end_layout \begin_layout Standard A macro \family typewriter \backslash xyC \family default can be defined correspondingly by replacing \family typewriter \backslash xymatrixrowsep@ \family default with \family typewriter \backslash xymatrixcolsep@ \family default . Now, a figure can be scaled by entering \backslash xyR{...} into the \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -matrix. Place the cursor inside the matrix, just before the first entry. Then enter \family typewriter \backslash xyR \backslash { \family default or \family typewriter \backslash xyC \backslash { \family default or both. Don't forget the backslashes and remember, that the closing brace is automatica lly supplied by LyX. Inside the braces enter the dimensions. The default is \family typewriter 2pt \family default . Here you see a diagram which is squashed vertically and stretched horizontally with \family typewriter \backslash xyR{9pc} \backslash xyC{.5pc} \family default : \end_layout \begin_layout Standard \begin_inset Formula \[ \xyC{.5pc}\xyC{9pc}\xymatrix{A\ar[r]\ar[d] & B\\ C\ar@{}[ur]|{\text{{horizontal stretch}}}} \] \end_inset \end_layout \begin_layout Subsection Label positioning \end_layout \begin_layout Standard Another useful \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -command allows the correct positioning of labels along the shaft of arrows. This feature is sometimes necessary, when the default position of a label would otherwise clutter the picture, or would even coincide with other items, such as the intersection of the arrows in the figure below. In order to shift a label position alongside the shaft of an arrow, \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset \begin_inset space ~ \end_inset allows to prefix the label by a decimal number in parentheses, specifying the fraction of distance alongside the arrow where the label is to be placed. For instance, the code \family typewriter \backslash ar[r]|(0.3) \backslash varphi \family default , will place the label on the shaft, but only about one third of the way. \end_layout \begin_layout Standard Doing the same with labels above or below arrows as \family typewriter \backslash ar[dr]^(0.3) \backslash varphi, \family default respectively \family typewriter \backslash ar[ur]_(0.3) \backslash phi \family default , does not work from inside LyX. Instead, one has to replace the hat-symbol ^, resp. the underscore _ , by the macros \family typewriter \backslash sp \family default , resp. \family typewriter \backslash sb \family default , obtaining \family typewriter \backslash ar[dr] \backslash sp(0.3) \backslash varphi \family default and \family typewriter \backslash ar[ur] \backslash sb(0.3) \backslash phi. \family default It is, in fact, possible to enter several labels this way and those labels are placed correctly, even if the arrow bends. In the following figure, the bending arrow with its four labels has been produced with \family typewriter \backslash ar@(r,r)[d] \backslash sp(0.2){ \backslash phi_{1}} \backslash sp(0.4){ \backslash phi_{2}} \backslash sb(0.6){ \backslash phi_{3}} \backslash sp(0.8){ \backslash phi_{4}}. \end_layout \begin_layout Standard \begin_inset Formula \[ \xyC{4pc}\xymatrix{\bullet\ar[dr]\sp(0.3)\varphi & \circ\ar@{}[d]|\vdots\ar@(r,r)[d]\sp(0.2){\phi_{1}}\sp(0.4){\phi_{2}}\sb(0.6){\phi_{3}}\sp(0.8){\phi_{4}}\\ \circ\ar[ur]\sb(0.3)\phi & \bullet} \] \end_inset \end_layout \begin_layout Subsection Invisible stretched arrows \end_layout \begin_layout Standard A more general trick uses invisible arrows to place any object almost anywhere inside a diagram. Produce an invisible arrow, shorten (or prolong) it past its goal by adding a decimal stretching ratio, e. \begin_inset space \thinspace{} \end_inset g. \family typewriter (0.6) \family default or \family typewriter (1.4) \family default to its path. Attach a label to this invisible arrow. \end_layout \begin_layout Standard Thus, the down pointing arrow with its label \begin_inset Formula $\varphi$ \end_inset at (0.3) of its way along the shaft might as well have been produced by adding to the regular arrow \family typewriter \backslash ar[dr] \family default an invisible \begin_inset Formula $\varphi$ \end_inset -labelled arrow \family typewriter \backslash ar@{}[dr(0.6)]^ \backslash varphi \family default , reaching only 0.6 of the way. Its label will now appear at 0.3 of the way of the original visible arrow. \end_layout \begin_layout Standard This workaround has two minor drawbacks: First, it does not work with bending arrows. Secondly, prolonging an invisible arrow beyond the normal dimension of the figure will invisibly extend the figure box, and thereby cause too much vertical space between the figure and the preceding or the following paragraph. \end_layout \begin_layout Standard Nevertheless, invisible arrows are an important tool, since they can, in principle, be used to place information at any chosen place in a diagram. In the above figure, for instance, we have used an invisible arrow to carry the \family typewriter \backslash vdots \family default as label and at the earlier figure we had used an invisible arrow to carry the text \begin_inset Quotes eld \end_inset \family typewriter horizontal stretch \family default \begin_inset Quotes erd \end_inset into the center of the figure. \end_layout \begin_layout Subsection Further \family typewriter \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset \family default -tricks \end_layout \begin_layout Standard Here we have focused only on the \family typewriter \backslash xymatrix \family default command, which is just one of the features available in Kris Rose's amazing \family typewriter \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset \family default -package. The \family typewriter \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset \family default -pic manual \begin_inset CommandInset citation LatexCommand cite key "xypic manual" \end_inset demonstrates many of the advanced possibilities of that package. Beware, that its style is rather terse and you will likely need a lot of experimenting and modifying the many worked examples. Lauda \begin_inset CommandInset citation LatexCommand cite key "Lauda" \end_inset explains how to use \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset -pic to make braids, cobordism, string diagrams, and much more. A good and rather systematic introduction to \family typewriter \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset \family default -matrix is \begin_inset CommandInset citation LatexCommand cite key "Ouvaton" \end_inset . Even if you share with me the disadvantage of not being fluent in Esperanto, you will be able to understand most of it. \end_layout \begin_layout Bibliography \begin_inset CommandInset bibitem LatexCommand bibitem label "1" key "xypic manual" \end_inset Kristoffer H. Rose: \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset \emph on -pic User's Guide \emph default . Version 3.7, Feb. 16, 1999. Available as part of the \family typewriter xypic \family default LaTeX package. \end_layout \begin_layout Bibliography \begin_inset CommandInset bibitem LatexCommand bibitem label "2" key "instant-preview" \end_inset \begin_inset Flex URL status collapsed \begin_layout Plain Layout http://www.tug.org/tex-archive/help/Catalogue/entries/preview-latex.html \end_layout \end_inset \end_layout \begin_layout Bibliography \begin_inset CommandInset bibitem LatexCommand bibitem label "3" key "xypic" \end_inset \begin_inset Flex URL status collapsed \begin_layout Plain Layout http://www.tug.org/tex-archive/help/Catalogue/entries/xypic.html \end_layout \end_inset \end_layout \begin_layout Bibliography \begin_inset CommandInset bibitem LatexCommand bibitem label "4" key "AUCTeX" \end_inset \begin_inset Flex URL status collapsed \begin_layout Plain Layout http://www.gnu.org/software/auctex/ \end_layout \end_inset \end_layout \begin_layout Bibliography \begin_inset CommandInset bibitem LatexCommand bibitem label "5" key "Lauda" \end_inset Aarlon Lauda: \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset \emph on -pic \emph default \emph on tutorial with an archive of examples \emph default . \begin_inset Flex URL status collapsed \begin_layout Plain Layout http://www.dpmms.cam.ac.uk/~al366/xytutorial.html \end_layout \end_inset \end_layout \begin_layout Bibliography \begin_inset CommandInset bibitem LatexCommand bibitem label "6" key "Ouvaton" \end_inset Filipp Ouvaton: \begin_inset ERT status collapsed \begin_layout Plain Layout \backslash Xy \end_layout \end_inset \emph on -pic \emph default : \emph on Enkonduko pri Xymatrix \emph default . \begin_inset Flex URL status collapsed \begin_layout Plain Layout http://filip.ouvaton.org/xypic/xymatrix/index.html \end_layout \end_inset \end_layout \end_body \end_document