-#LyX 1.6.0beta3 created this file. For more info see http://www.lyx.org/\r
-\lyxformat 335\r
-\begin_document\r
-\begin_header\r
-\textclass article\r
-\begin_preamble\r
-\usepackage[all]{xy}\r
-\r
-\r
-\makeatletter\r
-\newcommand{\xyR}[1]{\r
- \makeatletter\r
- \xydef@\xymatrixrowsep@{#1}\r
- \makeatother\r
-}\r
-\makeatletter\r
-\newcommand{\xyC}[1]{\r
- \makeatletter\r
- \xydef@\xymatrixcolsep@{#1}\r
- \makeatother\r
-}\r
-\r
-\newdir{|>}{!/4.5pt/@{|}*:(1,-.2)@^{>}*:(1,+.2)@_{>}}\r
-\end_preamble\r
-\language english\r
-\inputencoding auto\r
-\font_roman ae\r
-\font_sans default\r
-\font_typewriter default\r
-\font_default_family default\r
-\font_sc false\r
-\font_osf false\r
-\font_sf_scale 100\r
-\font_tt_scale 100\r
-\graphics default\r
-\paperfontsize default\r
-\spacing single\r
-\use_hyperref false\r
-\papersize a4paper\r
-\use_geometry false\r
-\use_amsmath 1\r
-\use_esint 0\r
-\cite_engine basic\r
-\use_bibtopic false\r
-\paperorientation portrait\r
-\secnumdepth 3\r
-\tocdepth 3\r
-\paragraph_separation indent\r
-\defskip medskip\r
-\quotes_language english\r
-\papercolumns 1\r
-\papersides 1\r
-\paperpagestyle default\r
-\tracking_changes false\r
-\output_changes false\r
-\author "" \r
-\author "" \r
-\end_header\r
-\r
-\begin_body\r
-\r
-\begin_layout Title\r
-Using \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--pic in LyX\r
-\end_layout\r
-\r
-\begin_layout Author\r
-H.\r
- Peter Gumm\r
-\end_layout\r
-\r
-\begin_layout Abstract\r
-With the recent versions of LyX and with the \r
-\family typewriter\r
-preview\r
-\family default\r
--style installed in the LaTeX-System, the graph drawing package \r
-\family typewriter\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\family default\r
--Pic can be conveniently used inside LyX.\r
- Diagrams can be edited and displayed inside the main LyX editing window.\r
- Here, we shall describe how to use the \r
-\family typewriter\r
-\r
-\backslash\r
-xymatrix\r
-\family default\r
- command from \r
-\family typewriter\r
-xypic\r
-\family default\r
- inside LyX in order to draw, to edit and to preview diagrams as typically\r
- used in category theory, algebra, and related fields.\r
- \r
-\end_layout\r
-\r
-\begin_layout Abstract\r
-\begin_inset CommandInset toc\r
-LatexCommand tableofcontents\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Introduction \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The \r
-\family typewriter\r
-xypic\r
-\family default\r
--package has long served as a convenient tool for easily constructing graphs\r
- and diagrams in LaTeX.\r
- Unfortunately, its use in LyX had long been restricted to the infamous\r
- ERT-boxes, meaning that the LyX editor could only display the LaTeX-source\r
- and not the finished diagram.\r
- The new \r
-\family typewriter\r
-preview\r
-\family default\r
--style of LaTeX which is part of the AUCTeX project\r
-\begin_inset CommandInset citation\r
-LatexCommand cite\r
-key "AUCTeX"\r
-\r
-\end_inset\r
-\r
-, finally enables the editing and displaying of \r
-\family typewriter\r
-xypic\r
-\family default\r
--diagrams, constructed, displayed and interactively edited inside LyX.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace defskip\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Graphics\r
- filename xyfigure.png\r
- scale 50\r
- BoundingBox 0bp 0bp 580bp 440bp\r
- clip\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset VSpace defskip\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In this note, we describe how \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--pic can be used from inside LyX, how diagrams can be created and edited.\r
- We have tested the following using LyX versions 1.3.7 up to 1.6, running under\r
- WindowsXP and under Windows Vista.\r
- \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-There are two modes of operations: For a start, and for some first tests,\r
- it may be easiest to first enter the \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--Pic code inside the LyX-window, select it all and convert it to a graphical\r
- representation by pressing \r
-\family sans\r
-Ctrl-m\r
-\family default\r
- or \r
-\family sans\r
-Ctrl-M\r
-\family default\r
-.\r
- If you use \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--Pic more frequently, or if you want to modify your initial figure, you\r
- will want to assemble and modify your figures using LyX's math editor.\r
- \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Once the cursor is moved over a diagram, this is displayed as an array of\r
- nodes and arrow-commands.\r
- These can be changed interactively.\r
- When the cursor leaves the editing area, the diagram reappears.\r
- \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-In the first two sections of this documentation, we explain how to use LyX\r
- in the first mentioned mode and we introduce all \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--Pic features that might be of use for drawing commutative diagrams, graphs\r
- or automata.\r
- Section 3 explains how to use the \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--Pic commands inside a math-editing area.\r
- \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-It is not our intention to write another introduction to \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--Pic, rather our motivation is to give an introduction how the most important\r
- commands work inside LyX, since the keystrokes as explained in the \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--Pic manual\r
-\begin_inset CommandInset citation\r
-LatexCommand cite\r
-key "xypic manual"\r
-\r
-\end_inset\r
-\r
- will not always function correctly inside LyX.\r
- \r
-\end_layout\r
-\r
-\begin_layout Section\r
-Preparation\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The following requires that the LaTeX-packages \r
-\family typewriter\r
-xypic\r
-\family default\r
- and \r
-\family typewriter\r
-preview\r
-\family default\r
- are installed in the LaTeX system.\r
- They are available from CTAN, see at \r
-\begin_inset CommandInset citation\r
-LatexCommand cite\r
-key "instant-preview"\r
-\r
-\end_inset\r
-\r
-, resp.\r
- at \r
-\begin_inset CommandInset citation\r
-LatexCommand cite\r
-key "xypic"\r
-\r
-\end_inset\r
-\r
-.\r
- After freshly installing them, it may be necessary, to run \r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Reconfigure\r
-\family default\r
- from the main LyX menu.\r
- The steps to a first diagram output in LyX are then:\r
-\end_layout\r
-\r
-\begin_layout Enumerate\r
-Activate and test \r
-\family typewriter\r
-preview\r
-\end_layout\r
-\r
-\begin_deeper\r
-\begin_layout Enumerate\r
-Open LyX, choose \r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Preferences\SpecialChar \menuseparator\r
-Look and Feel\SpecialChar \menuseparator\r
-Graphics\r
-\family default\r
- and place a check-mark at \r
-\emph on\r
-Instant Preview\r
-\emph default\r
-.\r
- \r
-\end_layout\r
-\r
-\begin_layout Enumerate\r
-Test, if \r
-\family typewriter\r
-instant-preview\r
-\family default\r
- works by opening a LyX-document and entering any math-formula, e.g.\r
- \r
-\begin_inset Formula $a+b=c$\r
-\end_inset\r
-\r
-.\r
- \r
-\end_layout\r
-\r
-\begin_layout Enumerate\r
-Move the cursor out of the formula, and watch it change its appearance to\r
- look just like in the finished dvi- or postscript document.\r
- \r
-\end_layout\r
-\r
-\end_deeper\r
-\begin_layout Enumerate\r
-Activate and test \r
-\family typewriter\r
-xypic\r
-\end_layout\r
-\r
-\begin_deeper\r
-\begin_layout Enumerate\r
-Choose \r
-\family sans\r
-Layout\SpecialChar \menuseparator\r
-Document\SpecialChar \menuseparator\r
-Preamble\r
-\family default\r
- and type \r
-\family typewriter\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\backslash\r
-usepackage[all]{xy}.\r
-\end_layout\r
-\r
-\begin_layout Enumerate\r
-Inside your LyX-Document, enter the text \r
-\family typewriter\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\backslash\r
-xymatrix{A \r
-\backslash\r
-ar[r] & B}\r
-\family default\r
- .\r
-\end_layout\r
-\r
-\begin_layout Enumerate\r
-Select the whole text and choose \r
-\family sans\r
-Insert\SpecialChar \menuseparator\r
-Math\SpecialChar \menuseparator\r
-Display Formula\r
-\family default\r
-, or use the corresponding keyboard shortcut \r
-\family sans\r
-Ctrl-M\r
-\family default\r
-.\r
- \r
-\end_layout\r
-\r
-\begin_layout Enumerate\r
-Move the mouse cursor out of the editing box and wait for a split second\r
- to see an arrow appear: \r
-\begin_inset Formula $\xymatrix{A\ar [r] & B}\r
-$\r
-\end_inset\r
-\r
-.\r
- \r
-\end_layout\r
-\r
-\end_deeper\r
-\begin_layout Section\r
-Commutative diagrams\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The following diagram, which is taken from the documentation of \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--Pic\r
-\begin_inset CommandInset citation\r
-LatexCommand cite\r
-key "xypic manual"\r
-\r
-\end_inset\r
-\r
- by its creator Kristoffer H.\r
- Rose, will provide an example for many of the features available with that\r
- package.\r
- Its source code is: \r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
-\r
-\backslash\r
-xymatrix{\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
- U \r
-\backslash\r
-ar@/_{1pc}/[ddr]_\r
-\backslash\r
-psi\r
-\backslash\r
-ar@/^{1pc}/[drr]^\r
-\backslash\r
-varphi\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\backslash\r
-ar@{.>}[dr]|-{(x,y)}\r
-\backslash\r
-\r
-\backslash\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
- & X \r
-\backslash\r
-times_Z Y \r
-\backslash\r
-ar[d]^q \r
-\backslash\r
-ar[r]_p & X \r
-\backslash\r
-ar[d]_f\r
-\backslash\r
-\r
-\backslash\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
- & Y \r
-\backslash\r
-ar[r]^g & Z }\r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Again, to turn this code into a graphical output, select it all at once\r
- starting from the \r
-\family typewriter\r
-\r
-\backslash\r
-xymatrix{\r
-\family default\r
- \SpecialChar \ldots{}\r
- up to the closing brace \SpecialChar \ldots{}\r
- \r
-\family typewriter\r
-}\r
-\family default\r
- and turn it into display-math as explained above.\r
- A moment after the cursor leaves the math-area, you should see the diagram\r
- in its full graphical glory as shown below.\r
- \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Formula $\xymatrix{U\ar @/_{1pc}/[ddr]_{\psi}\ar @/{}^{1pc}/[drr]^{\varphi}\ar @{.>}[dr]|-{(x,y)}\\\r
- & X\times_{Z}Y\ar [d]^{q}\ar [r]_{p} & X\ar [d]_{f}\\\r
- & Y\ar [r]^{g} & Z}\r
-$\r
-\end_inset\r
-\r
- \r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-The matrix layout of diagrams\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\family typewriter\r
-xymatrix\r
-\family default\r
- uses a matrix to define the layout of the vertices of a diagram.\r
- For the above example, we need a \r
-\begin_inset Formula $3\times3$\r
-\end_inset\r
-\r
--matrix of which 5 entries are used for the vertices \r
-\begin_inset Formula $U$\r
-\end_inset\r
-\r
-, \r
-\begin_inset Formula $X\times_{Z}Y$\r
-\end_inset\r
-\r
-, \r
-\begin_inset Formula $X$\r
-\end_inset\r
-\r
-, \r
-\begin_inset Formula $Y$\r
-\end_inset\r
-\r
-, \r
-\begin_inset Formula $Z$\r
-\end_inset\r
-\r
-, the other positions remaining empty.\r
- In this case, the following matrix determines the layout:\r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
-\r
-\backslash\r
-xymatrix{\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
- U \r
-\backslash\r
-\r
-\backslash\r
- \r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
- & X\r
-\backslash\r
-times_Z Y & X \r
-\backslash\r
-\r
-\backslash\r
- \r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
- & Y & Z } \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The pattern should be familiar from LaTeX: We see three rows, the first\r
- two being terminated by the end-of-line-marker \r
-\family typewriter\r
-\r
-\backslash\r
-\r
-\backslash\r
-\r
-\family default\r
- .\r
- Each line consists of entries, separated by the ampersand \r
-\family typewriter\r
-&\r
-\family default\r
-.\r
- \r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Arrows\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Having entered the vertices, we add arrows between them.\r
- The basic \r
-\family typewriter\r
-xypic\r
-\family default\r
--command to produce an arrow is \r
-\family typewriter\r
-\r
-\backslash\r
-ar\r
-\family default\r
- , it is entered into the cell of the matrix where the arrow is to start.\r
- The target of the arrow is defined by direction commands \r
-\family typewriter\r
-u\r
-\family default\r
- (up) \r
-\family typewriter\r
-d\r
-\family default\r
- (down) \r
-\family typewriter\r
-l\r
-\family default\r
- (left), or \r
-\family typewriter\r
-r\r
-\family default\r
- (right).\r
- These can be combined to a path and enclosed in square brackets.\r
- As an example, the arrows from the vertex \r
-\begin_inset Formula $U$\r
-\end_inset\r
-\r
- in the upper left corner down and right to the vertices \r
-\begin_inset Formula $X\times_{Z}Y$\r
-\end_inset\r
-\r
-, \r
-\begin_inset Formula $Y$\r
-\end_inset\r
-\r
-, and \r
-\begin_inset Formula $X$\r
-\end_inset\r
-\r
- are, respectively, defined as \r
-\family typewriter\r
-\r
-\backslash\r
-ar[dr]\r
-\family default\r
-, \r
-\family typewriter\r
-\r
-\backslash\r
-ar[ddr]\r
-\family default\r
- and \r
-\family typewriter\r
-\r
-\backslash\r
-ar[drr]\r
-\family default\r
-.\r
- Thus the above diagram with all arrows added becomes:\r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
-\r
-\backslash\r
-xymatrix{\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
- U \r
-\backslash\r
-ar[ddr] \r
-\backslash\r
-ar[drr] \r
-\backslash\r
-ar[dr]\r
-\backslash\r
-\r
-\backslash\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
- & X \r
-\backslash\r
-times_Z Y \r
-\backslash\r
-ar[d] \r
-\backslash\r
-ar[r]& X \r
-\backslash\r
-ar[d]\r
-\backslash\r
-\r
-\backslash\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
- & Y \r
-\backslash\r
-ar[r] & Z }\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Formula \xymatrix{ U \ar [ddr] \ar [drr] \ar [dr]\\\r
- & X \times_{Z} Y \ar [d] \ar [r] & X \ar [d]\\\r
- & Y \ar [r] & Z }\r
-\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
-\r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Labels\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Labels are attached to arrows by affixing them as upper or lower indices\r
- to the \r
-\family typewriter\r
-\r
-\backslash\r
-ar\r
-\family default\r
--command.\r
- Thus, \r
-\family typewriter\r
-\r
-\backslash\r
-ar[drr]^\r
-\backslash\r
-varphi\r
-\family default\r
- defines an arrow going one cell down, two to the right and having the label\r
- \r
-\begin_inset Formula $\varphi$\r
-\end_inset\r
-\r
- attached above.\r
- To attach a label below the arrow, make it a lower index as in \r
-\family typewriter\r
-\r
-\backslash\r
-ar[ddr]_\r
-\backslash\r
-psi\r
-\family default\r
-.\r
- This explanation is correct only for arrows pointing to the right.\r
- More precisely, imagine looking along the arrow in the direction it is\r
- pointing.\r
- Then an upper index places a label to the left and a lower index places\r
- it to the right.\r
- Consequently, an arrow pointing from right to left, such as \r
-\family typewriter\r
-\r
-\backslash\r
-ar[l]^\r
-\backslash\r
-alpha_\r
-\backslash\r
-beta\r
-\family default\r
- will have label \r
-\begin_inset Formula $\alpha$\r
-\end_inset\r
-\r
- below and label \r
-\begin_inset Formula $\beta$\r
-\end_inset\r
-\r
- above the arrow, i.e.\r
-\begin_inset Formula $\xymatrix{\ & \ \ar [l]_{\beta}^{\alpha}.}\r
-$\r
-\end_inset\r
-\r
-Using the character | instead of ^ or _ , it is even possible to place the\r
- label right onto the arrow, obscuring part of its shaft.\r
- \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Normally, a label is placed halfway between an arrow's start and target\r
- objects.\r
- In the first diagram, the central arrow starting in \r
-\begin_inset Formula $U$\r
-\end_inset\r
-\r
- has the label \r
-\begin_inset Formula $(x,y)$\r
-\end_inset\r
-\r
- in the middle of the arrow's shaft, rather than in the middle between the\r
- two objects it connects.\r
- This is achieved by prefixing the label with a minus sign, here: \r
-\family typewriter\r
-\r
-\backslash\r
-ar[dr]|-{(x,y)}\r
-\family default\r
-.\r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
-\r
-\backslash\r
-xymatrix{\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
- U \r
-\backslash\r
-ar[ddr]_\r
-\backslash\r
-psi \r
-\backslash\r
-ar[drr]^\r
-\backslash\r
-varphi\r
-\backslash\r
-ar[dr]|-{(x,y)}\r
-\backslash\r
-\r
-\backslash\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
- & X \r
-\backslash\r
-times_Z Y \r
-\backslash\r
-ar[d]^q \r
-\backslash\r
-ar[r]_p& X \r
-\backslash\r
-ar[d]_f\r
-\backslash\r
-\r
-\backslash\r
-\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
- & Y \r
-\backslash\r
-ar[r]^g & Z }\r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
-\begin_inset Formula \xymatrix{ U \ar [ddr]_{\psi}\ar [drr]^{\varphi}\ar [dr]|-{(x,y)}\\\r
- & X \times_{Z} Y \ar [d]^{q} \ar [r]_{p} & X \ar [d]_{f}\\\r
- & Y \ar [r]^{g} & Z }\r
-\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--pic normally permits labels to be shifted towards the tip or towards the\r
- start of an arrow by prefixing the label with a ratio, such as e.g.\r
- \r
-\family typewriter\r
-(.3)\r
-\family default\r
-.\r
- In LyX this works only for labels which are placed on top of the arrow,\r
- such as \r
-\family typewriter\r
-\r
-\backslash\r
-ar[r]|(0.3){\r
-\backslash\r
-phi}\r
-\family default\r
-.\r
- \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-For labels placed to the left or to the right of the arrow this does not\r
- work.\r
- The corresponding \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--pic code such as e.g.\r
- \r
-\family typewriter\r
-\r
-\backslash\r
-ar[r]^(.3)\r
-\backslash\r
-phi\r
-\family default\r
- or \r
-\family typewriter\r
-\r
-\backslash\r
-ar[r]_(.3)\r
-\backslash\r
-psi\r
-\family default\r
- is not correctly interpreted by LyX's math editor.\r
- Two workarounds are suggested in the last section of this note.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Arrow modification \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Modification of the design, the form or the positioning of arrows are introduced\r
- by the \r
-\family typewriter\r
-@\r
-\family default\r
--character.\r
- This is followed by a pair of matching brackets, where the form of the\r
- bracket pair, \r
-\family typewriter\r
-{ }\r
-\family default\r
- or \r
-\family typewriter\r
-< >\r
-\family default\r
- or \r
-\family typewriter\r
-/ /\r
-\family default\r
- indicates, whether we want to modify the design, the or the curvature of\r
- the arrow.\r
- Various modifactions can be applied to an arrow at the same time.\r
-\end_layout\r
-\r
-\begin_layout Subsubsection\r
-Arrow design \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Various designs such as \r
-\emph on\r
-solid\r
-\emph default\r
-, \r
-\emph on\r
-dotted\r
-\emph default\r
-, \r
-\emph on\r
-dashed\r
-\emph default\r
- or \r
-\emph on\r
-double\r
-\emph default\r
- are possible for the shaft of an arrow.\r
- These can be combined with various ends and various tips.\r
- In general, the design of an arrow is described by following the command\r
- \r
-\family typewriter\r
-\r
-\backslash\r
-ar\r
-\family default\r
- immediately by an \r
-\family typewriter\r
-@\r
-\family default\r
--sign and a pair of braces {\SpecialChar \ldots{}\r
-} containing characters describing the end,\r
- the shaft and the tip of the arrow.\r
- These characters are chosen to give some form of ASCII-rendering of the\r
- real thing.\r
- For instance \r
-\family typewriter\r
-\r
-\backslash\r
-ar@{>..>>}\r
-\family default\r
- produces an arrow with split end, a dotted shaft and double head.\r
- A number of other arrow designs is given in the table below.\r
- Note that the ends of embedding arrows \r
-\begin_inset Formula $\xymatrix{A\ar @{^{(}->}[r] & B}\r
-$\r
-\end_inset\r
-\r
- are described by raising or lowering opening parentheses, such as in \r
-\family typewriter\r
-\r
-\backslash\r
-ar@{^(->}[r].\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="11" columns="2">\r
-<features islongtable="true">\r
-<column alignment="center" valignment="top" width="0">\r
-<column alignment="center" valignment="top" width="0">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Source code in LyX\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula \xymatrix{\ \ar [r] & \ }\r
-\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-ar \r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula \xymatrix{\ \ar @{-->}[r] & \ }\r
-\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-ar@{-->}\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula \xymatrix{\ \ar @{..>}[r] & \ }\r
-\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-ar@{..>}\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula \xymatrix{\ \ar @{~>}[r] & \ }\r
-\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-ar@{~>}\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula \xymatrix{\ \ar @{->>}[r] & \ }\r
-\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-ar@{->>}\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula \xymatrix{\ \ar @{-->>}[r] & \ }\r
-\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-ar@{-->>}\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula \xymatrix{\ \ar @{>->>}[r] & \ }\r
-\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-ar@{>->>}\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula \xymatrix{\ \ar @{_{(}->}[r] & \ }\r
-\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-ar@{_(->}\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula \xymatrix{\ \ar @{^{(}->}[r] & \ }\r
-\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-ar@{^(->}\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula \xymatrix{\ \ar @{|-|}[r] & \ }\r
-\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-ar@{|-|}\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-noindent\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- Following the @-character by either a 2, 3, _,or a ^, we can produce arrows\r
- with double, triple shaft or arrows showing only the lower or upper half\r
- of their tips and ends.\r
- Arrows need not have tips nor ends, as the last example shows :\r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Tabular\r
-<lyxtabular version="3" rows="8" columns="2">\r
-<features islongtable="true">\r
-<column alignment="center" valignment="top" width="0">\r
-<column alignment="center" valignment="top" width="0">\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Result\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-Source code for LyX\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula \xymatrix{\ \ar @2[r] & \ }\r
-\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-ar@2\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula \xymatrix{\ \ar @3[r] & \ }\r
-\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-ar@3\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula \xymatrix{\ \ar @_{->}[r] & \ }\r
-\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-ar@_{->}\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula \xymatrix{\ \ar @^{->}[r] & \ }\r
-\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-ar@^{->}\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula \xymatrix{\ \ar @^{>>->>}[r] & \ }\r
-\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-ar@^{>>->>}\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula \xymatrix{\ \ar @{^{<}-_{>}}[r] & \ }\r
-\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-ar@{^<-_>}\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-<row>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\begin_inset Formula \xymatrix{\ \ar @2{--}[r] & \ }\r
-\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">\r
-\begin_inset Text\r
-\r
-\begin_layout Plain Layout\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-ar@2{--}\r
-\end_layout\r
-\r
-\end_inset\r
-</cell>\r
-</row>\r
-</lyxtabular>\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsubsection\r
-Designing your own arrows\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Within certain limits there is even a way to design your own arrows.\r
- Using some the characters \r
-\family typewriter\r
-><|ox+/()[\r
-\family default\r
- one can even design one's own arrow tips using the \r
-\family typewriter\r
-\r
-\backslash\r
-newdir\r
-\family default\r
- command in the preample.\r
- For explanations, we refer to the \r
-\family typewriter\r
-\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\family default\r
--manual, from which we take the example: \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-newdir{|>}{!/4.5pt/@{|}*:(1,-.2)@^{>}*:(1,+.2)@_{>}}\r
-\family default\r
-.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-noindent \r
-\end_layout\r
-\r
-\end_inset\r
-\r
-This defines a new arrow tip, referred to as \r
-\family typewriter\r
-|>\r
-\family default\r
- in \r
-\family typewriter\r
-\r
-\backslash\r
-ar@{-|>}[r]\r
-\family default\r
- and which displays correctly in LyX as:\r
-\begin_inset Formula \[\r
-\xymatrix{A\ar @{-|>}[r] & \ \ B}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Arrow positioning\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Arrows are shifted sideways with the modifier \r
-\family typewriter\r
-@<\r
-\family default\r
-\r
-\begin_inset Formula $\ldots$\r
-\end_inset\r
-\r
- \r
-\family typewriter\r
->\r
-\family default\r
- where the ellipsis is replaced by a positive or negative measure.\r
- For instance, to design a pair of mutually opposing arrows between two\r
- nodes, we shift them to see them apart.\r
- Note that the direction of the shift (positive) is to the left if one looks\r
- along the arrow.\r
- Thus\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-xymatrix{\r
-\backslash\r
-circ \r
-\backslash\r
-ar@<1ex>[r]& \r
-\backslash\r
-circ \r
-\backslash\r
-ar@<1ex>[l]}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-noindent\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- produces\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-\r
-\begin_inset space ~\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula \[\r
-\xymatrix{\circ\ar @<1ex>[r] & \circ\ar @<1ex>[l]}\r
-\]\r
- \r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsubsection\r
-Inline or centered diagrams\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Arrows and diagrams can be used inline, such as this one: \r
-\begin_inset Formula $\xymatrix{\circ\ar @<1ex>[r] & \circ\ar @<1ex>[l]}\r
-$\r
-\end_inset\r
-\r
-.\r
- When their code is written inside LyX as above, select it and choose either\r
- \r
-\family sans\r
-Ctrl-m\r
-\family default\r
- for inline appearence or \r
-\family sans\r
-Ctrl-M\r
-\family default\r
- for displaystyle.\r
- Diagrams constructed inline can later be centered, or, conversely, centered\r
- diagrams can be changed to inline formulas with \r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math\r
-\family default\r
- \r
-\family sans\r
-\SpecialChar \menuseparator\r
-Alignment.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Bending arrows \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-There are two simple methods to make arrows bend.\r
- The first is giving an explicit value by which the midpoint of the arrow's\r
- shaft is raised or depressed, the other is by forcing the arrow to leave\r
- its origin in a prescribed compass direction and to make him enter the\r
- target at another direction.\r
- The necessary bending of the arrow is determined automatically.\r
- We describe both methods.\r
-\end_layout\r
-\r
-\begin_layout Subsubsection\r
-Raising the shaft\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-For bending arrows we use the modifier @/\r
-\begin_inset Formula $\ldots$\r
-\end_inset\r
-\r
-/ .\r
- The ellipsis stands for a TeX-measure which needs to be entered as a lower\r
- or upper index.\r
- Whereas in \r
-\family typewriter\r
-xypic\r
-\family default\r
-, we could simply write, e.g.\r
- \r
-\family typewriter\r
-\r
-\backslash\r
-ar@/_1pc/\r
-\family default\r
- for an arrow bending \r
-\family typewriter\r
-1pc\r
-\family default\r
- downwards, this cannot directly be done in LyX.\r
- It is necessary, to enclose the measure in a pair of braces, such as e.g.\r
- \r
-\family typewriter\r
-\r
-\backslash\r
-ar@/_{1pc}/\r
-\family default\r
-.\r
- As an example, here are two opposing arrows between \r
-\begin_inset Formula $A$\r
-\end_inset\r
-\r
- and \r
-\begin_inset Formula $B$\r
-\end_inset\r
-\r
-, each bending by .5 pica, given by the following source code: \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\r
-\family typewriter\r
-\r
-\backslash\r
-xymatrix{A \r
-\backslash\r
-ar@/_{.5pc}/[r] & B \r
-\backslash\r
-ar@/_{.5pc}/[l]}\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Formula \[\r
-\xymatrix{A\ar @/{}_{.5pc}/[r] & B\ar @/{}_{.5pc}/[l]}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsubsection\r
-Specifying exit- and entrance directions.\r
- \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-An alternative for making arrows bend is by specifying their compass direction\r
- as they are leaving their source and their direction from which they enter\r
- their target.\r
- Instead of north, north-east, east, etc., the directions are named \r
-\family typewriter\r
-u\r
-\family default\r
-, \r
-\family typewriter\r
-ur\r
-\family default\r
-, \r
-\family typewriter\r
-r\r
-\family default\r
-, \r
-\family typewriter\r
-dr\r
-\family default\r
-, \r
-\family typewriter\r
-d\r
-\family default\r
-, \r
-\family typewriter\r
-dl\r
-\family default\r
-, \r
-\family typewriter\r
-l\r
-\family default\r
-, \r
-\family typewriter\r
-ul\r
-\family default\r
-, standing for up, up-right, right, down-right, etc..\r
- A direction is specified as @(\r
-\emph on\r
-out\r
-\emph default\r
-,\r
-\emph on\r
-in\r
-\emph default\r
-) where \r
-\emph on\r
-out\r
-\emph default\r
- stands for the direction the first object is left and \r
-\emph on\r
-in\r
-\emph default\r
- stands for the direction from which the target is entered.\r
- As an example, we show some bending arrows and a loop, which arises when\r
- we do not specify a target for an arrow, just its incoming and outgoing\r
- direction:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Formula \[\r
-\xymatrix{A\ar @(dr,dl)[r]\ar @(dr,dl)[rr] & B\ar @(d,r)[dl] & C\\\r
-E\ar @(ul,ur)}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
-\r
-\backslash\r
-xymatrix{A \r
-\backslash\r
-ar@(dr,dl)[r]\r
-\backslash\r
-ar@(dr,dl)[rr] \r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
- &B\r
-\backslash\r
-ar@(d,r)[dl] &C \r
-\backslash\r
-\r
-\backslash\r
- \r
-\begin_inset Newline newline\r
-\end_inset\r
-\r
- E \r
-\backslash\r
-ar@(ul,ur)}\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Modifying vertices\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The above example is reminiscent of an automata diagram, except that in\r
- such a diagram states would be enclosed in small circles, with double circles\r
- denoting final states.\r
- \r
-\end_layout\r
-\r
-\begin_layout Subsubsection\r
-Framing objects \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-With \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--Pic, entries can obtain a single or a double frame, such as \r
-\begin_inset Formula $\xymatrix{*+[F]{A}}\r
-$\r
-\end_inset\r
-\r
- or \r
-\begin_inset Formula $\xymatrix{*+[F=]{B}}\r
-$\r
-\end_inset\r
-\r
- by prefixing an entry with \r
-\family typewriter\r
-*[F-]\r
-\family default\r
- or \r
-\family typewriter\r
-*[F=]\r
-\family default\r
- and enclosing the portion of the entry to be framed in braces.\r
- Normally, the frame will be very tight so that it must be widened by prefixing\r
- with \r
-\family typewriter\r
-+\r
-\family default\r
- or with \r
-\family typewriter\r
-++\r
-\family default\r
-.\r
- Round frames, such as \r
-\begin_inset Formula $\xymatrix{*++[o][F]{A}}\r
-$\r
-\end_inset\r
-\r
- and \r
-\begin_inset Formula $\xymatrix{*++[o][F=]{B}}\r
-$\r
-\end_inset\r
-\r
- are obtained by specifying the shape as \r
-\family typewriter\r
-[o].\r
-\r
-\family default\r
- So the latter figure was constructed as *++[o][F=]{B}.\r
- This way, the following automaton \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Formula \[\r
-\xymatrix{\txt {start}\ar [r] & *++[o][F]{1}\ar [r] & *++[o][F=]{2}\ar @(ur,dr)\ar @(ur,ul)[l]}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-noindent\r
-\end_layout\r
-\r
-\end_inset\r
-\r
- can be typeset as\r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
-\r
-\backslash\r
-xymatrix{\r
-\backslash\r
-txt{start}\r
-\backslash\r
-ar[r]\r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
- & *++[o][F]{1}\r
-\backslash\r
-ar[r]\r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
- & *++[o][F=]{2}\r
-\backslash\r
-ar@(ur,dr)\r
-\backslash\r
-ar@(ur,ul)[l]\r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
- }.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The LaTeX command \r
-\family typewriter\r
-\r
-\backslash\r
-entrymodifiers={\r
-\family default\r
-\SpecialChar \ldots{}\r
-\r
-\family typewriter\r
-}\r
-\family default\r
- will make a certain entry style the default, that can, of course be overridden\r
- for individual entries.\r
- Thus, after \r
-\family typewriter\r
-\r
-\backslash\r
-entrymodifiers={++[o][F-]}\r
-\family default\r
-, all following entries inside \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--matrices would be encircled.\r
-\end_layout\r
-\r
-\begin_layout Subsubsection\r
-Framing rectangles\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Framing a whole rectangle inside an xymatrix is done with the macro pair\r
- \r
-\family typewriter\r
-\r
-\backslash\r
-save ...\r
- \r
-\backslash\r
-restore\r
-\family default\r
-.\r
- \r
-\family roman\r
-\series medium\r
-\shape up\r
-\size normal\r
-\emph off\r
-\bar no\r
-\noun off\r
-\color none\r
-The dimension of the rectangle is given as a dotted pair \r
-\begin_inset Formula $P_{0}.P_{1}$\r
-\end_inset\r
-\r
- of points denoting the top left and lower right corners of the rectangle.\r
- Each point, in turn,is given as a doubly quoted comma separated pair \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-\r
-\begin_inset Formula $x,y$\r
-\end_inset\r
-\r
-\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- specifying row \r
-\begin_inset Formula $x$\r
-\end_inset\r
-\r
- and column \r
-\begin_inset Formula $y$\r
-\end_inset\r
-\r
-.\r
- These are followed by the framing commands, to produce figures such as\r
- the following: \r
-\begin_inset Formula \[\r
-\xymatrix{A & B\ar @(d,r)[dl]\sp (0.2)\phi\sp (0.7)\psi\save "1,1"."2,1"*+[F=]\frm {}\restore \,\\\r
-C & \save "1,1"."1,2"*++[F]\frm {}\restore }\r
-\]\r
-\r
-\end_inset\r
-\r
- Here, the code \r
-\family typewriter\r
-\series default\r
-\shape default\r
-\size default\r
-\emph default\r
-\bar default\r
-\noun default\r
-\color inherit\r
-\r
-\backslash\r
-save"1,1"."2,1"*+[F=]\r
-\backslash\r
-frm{}\r
-\backslash\r
-restore\r
-\family roman\r
-\series medium\r
-\shape up\r
-\size normal\r
-\emph off\r
-\bar no\r
-\noun off\r
-\color none\r
- produces the doubly framed rectangle, and the code for the extra wide horizonta\r
-l rectangle is \r
-\family typewriter\r
-\series default\r
-\shape default\r
-\size default\r
-\emph default\r
-\bar default\r
-\noun default\r
-\color inherit\r
-\r
-\backslash\r
-save"1,1"."1,2"*++[F]\r
-\backslash\r
-frm{}\r
-\backslash\r
-restore\r
-\family roman\r
-\series medium\r
-\shape up\r
-\size normal\r
-\emph off\r
-\bar no\r
-\noun off\r
-\color none\r
-.\r
- This code can be placed in arbitrary cells of the xymatrix.\r
- \r
-\end_layout\r
-\r
-\begin_layout Section\r
-Using LyX's math editor\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-As an alternative to writing the \r
-\family typewriter\r
-xypic\r
-\family default\r
- code, then transforming it into a math-editing environment by marking it\r
- and applying \r
-\family sans\r
-Ctrl-m\r
-\family default\r
-, or \r
-\family sans\r
-Ctrl-M\r
-\family default\r
-, one may construct and modify the whole xypic-diagram inside LyX's math\r
- editor.\r
- We describe the editing steps for a figure just like the one above.\r
- \r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Caveat - how to enter braces\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Recall that in LyX's math-editor any pair of braces \r
-\family typewriter\r
-{\r
-\family default\r
- and \r
-\family typewriter\r
-}\r
-\family default\r
- that are to enclose a macro-parameter must be entered by typing just \r
-\family typewriter\r
-\r
-\backslash\r
-{\r
-\family default\r
- .\r
- The closing brace is automatically supplied and in between a box into which\r
- to the parameter is entered.\r
- In connection with \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--diagrams, this applies in particular to arrow modifications that are normally\r
- given in the form \r
-\family typewriter\r
-@{\r
-\family default\r
- \SpecialChar \ldots{}\r
- \r
-\family typewriter\r
-}\r
-\family default\r
- with the ellipsis standing for the description of end, shaft and tip of\r
- the arrow.\r
- Inside the math-editor, enter just \r
-\family typewriter\r
-@\r
-\backslash\r
-{\r
-\family default\r
- and let LyX provide the closing brace and the box into which to enter the\r
- description of the arrow.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Braces that are entered without the backslash \r
-\family typewriter\r
-\r
-\backslash\r
-\r
-\family default\r
- will just appear as typed, but cannot be used to receive a macro parameter.\r
- They are useful, for instance to denote sets, e.g.\r
- \r
-\family typewriter\r
-{x\r
-\backslash\r
-in X \r
-\backslash\r
-mid x\r
-\backslash\r
-notin x}\r
-\family default\r
- will display as \r
-\begin_inset Formula $\{x\in X\mid x\notin x\}$\r
-\end_inset\r
-\r
-.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Setting up the matrix\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-With \r
-\family sans\r
-Ctrl-m\r
-\family default\r
- or \r
-\family sans\r
-Ctrl-M\r
-\family default\r
- open a formula environment and enter: \r
-\family typewriter\r
-\r
-\backslash\r
-xymatrix\r
-\family default\r
-.\r
- This produces a 1\r
-\begin_inset Formula $\times$\r
-\end_inset\r
-\r
-1- \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--matrix.\r
- Add extra rows by typing \r
-\family sans\r
-Ctrl-Enter\r
-\family default\r
- and add columns by typing \r
-\family sans\r
-Alt-m c i.\r
- \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-At any time, further rows or columns can be entered or deleted using commands\r
- available from \r
-\family sans\r
-Edit\SpecialChar \menuseparator\r
-Math,\r
-\family default\r
- resp.\r
- their shortcuts, beginning with \r
-\family sans\r
-Alt-m c\r
-\family default\r
- for the column commands or \r
-\family sans\r
-Alt-m w\r
-\family default\r
- for the row commands.\r
- \r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Entering nodes, arrows and labels\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Type the nodes into the correct positions of the matrix.\r
- If you move the cursor out of the matrix, you should see a first rendering\r
- of the node layout.\r
- Next, add the arrows at the nodes from where they should emanate by typing\r
- \r
-\family typewriter\r
-\r
-\backslash\r
-ar[\r
-\family default\r
-\emph on\r
-p\r
-\family typewriter\r
-\emph default\r
-]\r
-\family default\r
-, where \r
-\emph on\r
-p\r
-\emph default\r
- can be any path made up from the characters \r
-\family typewriter\r
-u\r
-\family default\r
-, \r
-\family typewriter\r
-d\r
-\family default\r
-, \r
-\family typewriter\r
-l\r
-\family default\r
-, \r
-\family typewriter\r
-r\r
-\family default\r
-.\r
- Make sure that the path indeed leads to an existing node within the matrix.\r
- Otherwise, the figure will not display when the cursor leaves the editing\r
- area.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Next, label the arrows by attaching a label text as upper or lower indices\r
- to the end of the arrow's path.\r
- As always in LyX's math editor, an underscore \r
-\family typewriter\r
-_\r
-\family default\r
- opens a box for a lower index and a \r
-\family typewriter\r
-^\r
-\family default\r
- followed by a space opens a box for an upper index.\r
- You can enter any LaTeX-code as a label.\r
- \r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Modifying arrows \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Finally, modify the appearance of the arrows by entering @-modifiers @{\SpecialChar \ldots{}\r
-},\r
- @<\SpecialChar \ldots{}\r
->, @(\SpecialChar \ldots{}\r
-,\SpecialChar \ldots{}\r
-) or @/\SpecialChar \ldots{}\r
-/.\r
- The above caveat applies to the first form only.\r
- It must be entered as \r
-\family typewriter\r
-@\r
-\backslash\r
-{\r
-\family default\r
- with the arrow description entered inside the LyX-supplied box.\r
- If this box remains empty, you have specified an empty arrow.\r
- This is a useful construction, too, as you will see in the next section.\r
- \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-The other modifiers, @<\SpecialChar \ldots{}\r
->, @(\SpecialChar \ldots{}\r
-,\SpecialChar \ldots{}\r
-) and @/\SpecialChar \ldots{}\r
-/ are typed as shown with the arrow\r
- description replacing the ellipsis.\r
- The code for bending arrows, which in \r
-\family typewriter\r
-xypic\r
-\family default\r
- is @/_\r
-\emph on\r
-measure\r
-\emph default\r
-/ or @/\r
-\emph on\r
-^measure\r
-\emph default\r
-/ where \r
-\emph on\r
-measure\r
-\emph default\r
- is any valid TeX-measure, should be entered as upper or lower index to\r
- the first slash / .\r
- Make sure that the ending slash does not end up being part of the upper\r
- or lower index.\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-What if something goes wrong\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-When constructing a diagram, you should at times check it by just moving\r
- the cursor out of the editing area to see whether instant preview can successfu\r
-lly convert it into graphical output.\r
- If this does not happen, it may either be that instant preview for some\r
- reason is not aware that it should retranslate the graphics.\r
- Moving the cursor into the editing area and out again sometimes wakes up\r
- instant preview.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-A more serious reason could be a syntactical error in your input.\r
- If necessary, redo the last editing steps, using Ctrl-z, or try to translate\r
- the LyX-file into dvi using Ctrl-d or \r
-\family sans\r
-View\SpecialChar \menuseparator\r
-Dvi\r
-\family default\r
-.\r
- There should be some error generated, which hopefully gives you a hint\r
- as to the source of the mistake.\r
-\end_layout\r
-\r
-\begin_layout Section\r
-Hacks\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Certain things do not work correctly inside LyX.\r
- The ones that we (used to) miss most are the horizontal and vertical scaling\r
- of diagrams, and the correct positioning of arrows.\r
- There are some workarounds that we are explaining here.\r
- \r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Horizontal and vertical scaling\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-It is often convenient to stretch the horizontal or the vertical dimensions\r
- of an entire diagram by using spacing commands for rows and/or columns.\r
- According to the \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--manual, for instance, \r
-\family typewriter\r
-\r
-\backslash\r
-xymatrix@R=1pc{\r
-\family default\r
-\SpecialChar \ldots{}\r
-\r
-\family typewriter\r
-}\r
-\family default\r
- defines an \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--matrix with row spacing of 1 pica.\r
- Similarly, \r
-\family typewriter\r
-\r
-\backslash\r
-xymatrix@C=\r
-\family default\r
-\SpecialChar \ldots{}\r
-\r
-\family typewriter\r
-{\r
-\family default\r
-\SpecialChar \ldots{}\r
-\r
-\family typewriter\r
-}\r
-\family default\r
- allows to modify the space between columns.\r
- Unfortunately, these commands do currently not work inside LyX, as the\r
- @-character is interpreted by LyX as ending the \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--matrix-macro.\r
- \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Knowing that \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space ~\r
-\end_inset\r
-\r
- stores the values for row-spacing and column-spacing in the variables \r
-\family typewriter\r
-\r
-\backslash\r
-xymatrixrowsep@\r
-\family default\r
- and \r
-\family typewriter\r
-\r
-\backslash\r
-xymatrixrowsep@\r
-\family default\r
-, add the following macro to the preamble (\r
-\family sans\r
-Layout\SpecialChar \menuseparator\r
-Document\SpecialChar \menuseparator\r
-Preamble)\r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
-\r
-\backslash\r
-makeatletter\r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
-\r
-\backslash\r
-newcommand{\r
-\backslash\r
-xyR}[1]{% \r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
-\r
-\backslash\r
-makeatletter\r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
-\r
-\backslash\r
-xydef@\r
-\backslash\r
-xymatrixrowsep@{#1}\r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
-\r
-\backslash\r
-makeatother\r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
-} % end of \r
-\backslash\r
-xyR\r
-\end_layout\r
-\r
-\begin_layout LyX-Code\r
-\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-A macro \r
-\family typewriter\r
-\r
-\backslash\r
-xyC\r
-\family default\r
- can be defined correspondingly by replacing \r
-\family typewriter\r
-\r
-\backslash\r
-xymatrixrowsep@\r
-\family default\r
- with \r
-\family typewriter\r
-\r
-\backslash\r
-xymatrixcolsep@\r
-\family default\r
-.\r
- Now, a figure can be scaled by entering \r
-\backslash\r
-xyR{...} into the \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--matrix.\r
- Place the cursor inside the matrix, just before the first entry.\r
- Then enter \r
-\family typewriter\r
-\r
-\backslash\r
-xyR\r
-\backslash\r
-{\r
-\family default\r
- or \r
-\family typewriter\r
-\r
-\backslash\r
-xyC\r
-\backslash\r
-{\r
-\family default\r
- or both.\r
- Dont't forget the backslashes and remember, that the closing brace is automatic\r
-ally supplied by LyX.\r
- Inside the braces enter the dimensions.\r
- The default is \r
-\family typewriter\r
-2pt\r
-\family default\r
-.\r
- Here you see a diagram which is squashed vertically and stretched horizontally\r
- with \r
-\family typewriter\r
-\r
-\backslash\r
-xyR{9pc}\r
-\backslash\r
-xyC{.5pc}\r
-\family default\r
-:\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Formula \[\r
-\xyC {.5pc}\xyC {9pc}\xymatrix{A\ar [r]\ar [d] & B\\\r
-C\ar @{}[ur]|{\text{{horizontal stretch}}}}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Label positioning\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Another useful \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
--vcommand allows the correct positioning of labels along the shaft of arrows.\r
- This feature is sometimes necessary, when the default position of a label\r
- would otherwise clutter the picture, or would even coincide with other\r
- items, such as the intersection of the arrows in the figure below.\r
- In order to shift a label position alongside the shaft of an arrow, \r
-\begin_inset ERT\r
-status open\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset space ~\r
-\end_inset\r
-\r
- allows to prefix the label by a decimal number in parentheses, specifying\r
- the fraction of distance alongside the arrow where the label is to be placed.\r
- For instance, the code \r
-\family typewriter\r
-\r
-\backslash\r
-ar[r]|(0.3)\r
-\backslash\r
-varphi\r
-\family default\r
-, will place the label on the shaft, but only about one third of the way.\r
- \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Doing the same with labels above or below arrows as \r
-\family typewriter\r
-\r
-\backslash\r
-ar[dr]^(0.3)\r
-\backslash\r
-varphi,\r
-\family default\r
- respectively \r
-\family typewriter\r
-\r
-\backslash\r
-ar[ur]_(0.3)\r
-\backslash\r
-phi\r
-\family default\r
-, does not work from inside LyX.\r
- Instead, one has to replace the hat-symbol ^, resp.\r
- the underscore _ , by the macros \r
-\family typewriter\r
-\r
-\backslash\r
-sp\r
-\family default\r
-, resp.\r
- \r
-\family typewriter\r
-\r
-\backslash\r
-sb\r
-\family default\r
-, obtaining \r
-\family typewriter\r
-\r
-\backslash\r
-ar[dr]\r
-\backslash\r
-sp(0.3)\r
-\backslash\r
-varphi \r
-\family default\r
-and\r
-\family typewriter\r
- \r
-\backslash\r
-ar[ur]\r
-\backslash\r
-sb(0.3)\r
-\backslash\r
-phi.\r
- \r
-\family default\r
-It is, in fact, possible to enter several labels this way and those labels\r
- are placed correctly, even if the arrow bends.\r
- In the following figure, the bending arrow with its four labels has been\r
- produced with \r
-\family typewriter\r
-\r
-\backslash\r
-ar@(r,r)[d] \r
-\backslash\r
-sp(0.2){\r
-\backslash\r
-phi_{1}} \r
-\backslash\r
-sp(0.4){\r
-\backslash\r
-phi_{2}} \r
-\backslash\r
-sb(0.6){\r
-\backslash\r
-phi_{3}} \r
-\backslash\r
-sp(0.8){\r
-\backslash\r
-phi_{4}}.\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-\begin_inset Formula \[\r
-\xyC {4pc}\xymatrix{\bullet\ar [dr]\sp (0.3)\varphi & \circ\ar @{}[d]|\vdots\ar @(r,r)[d]\sp (0.2){\phi_{1}}\sp (0.4){\phi_{2}}\sb (0.6){\phi_{3}}\sp (0.8){\phi_{4}}\\\r
-\circ\ar [ur]\sb (0.3)\phi & \bullet}\r
-\]\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Subsection\r
-Invisible stretched arrows\r
-\end_layout\r
-\r
-\begin_layout Standard\r
-A more general trick uses invisible arrows to place any object almost anywhere\r
- inside a diagram.\r
- Produce an invisible arrow, shorten (or prolong) it past its goal by adding\r
- a decimal stretching ratio, e.g.\r
- \r
-\family typewriter\r
-(0.6)\r
-\family default\r
- or \r
-\family typewriter\r
-(1.4)\r
-\family default\r
- to its path.\r
- Attach a label to this invisible arrow.\r
- \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Thus, the down pointing arrow with its label \r
-\begin_inset Formula $\varphi$\r
-\end_inset\r
-\r
- at (0.3) of its way along the shaft might as well have been produced by\r
- adding to the regular arrow \r
-\family typewriter\r
-\r
-\backslash\r
-ar[dr] \r
-\family default\r
-an invisible \r
-\begin_inset Formula $\varphi$\r
-\end_inset\r
-\r
--labelled arrow \r
-\family typewriter\r
-\r
-\backslash\r
-ar@{}[dr(0.6)]^\r
-\backslash\r
-varphi\r
-\family default\r
-, reaching only 0.6 of the way.\r
- Its label will now appear at 0.3 of the way of the original visible arrow.\r
- \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-This workaround has two minor drawbacks: First, it does not work with bending\r
- arrows.\r
- Secondly, prolonging an invisible arrow beyond the normal dimension of\r
- the figure will invisibly extend the figure box, and thereby cause too\r
- much vertical space between the figure and the preceding or the following\r
- paragraph.\r
- \r
-\end_layout\r
-\r
-\begin_layout Standard\r
-Nevertheless, invisible arrows are an important tool, since they can, in\r
- principle, be used to place information at any chosen place in a diagram.\r
- In the above figure, for instance, we have used an invisible arrow to carry\r
- the \r
-\family typewriter\r
-\r
-\backslash\r
-vdots\r
-\family default\r
- as label and at the earlier figure we had used an invisible arrow to carry\r
- the text \r
-\begin_inset Quotes eld\r
-\end_inset\r
-\r
-\r
-\family typewriter\r
-horizontal stretch\r
-\family default\r
-\r
-\begin_inset Quotes erd\r
-\end_inset\r
-\r
- into the center of the figure.\r
-\end_layout\r
-\r
-\begin_layout Bibliography\r
-\begin_inset CommandInset bibitem\r
-LatexCommand bibitem\r
-label "1"\r
-key "xypic manual"\r
-\r
-\end_inset\r
-\r
-Kristoffer H.\r
- Rose: \r
-\begin_inset ERT\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-\r
-\backslash\r
-Xy\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\emph on\r
--Pic User's Guide\r
-\emph default\r
-.\r
- Version 3.7, Feb.\r
- 16, 1999.\r
- Available as part of the \r
-\family typewriter\r
-xypic\r
-\family default\r
- LaTeX package.\r
- \r
-\end_layout\r
-\r
-\begin_layout Bibliography\r
-\begin_inset CommandInset bibitem\r
-LatexCommand bibitem\r
-label "2"\r
-key "instant-preview"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Flex URL\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-http://www.tug.org/tex-archive/help/Catalogue/entries/preview-latex.html\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Bibliography\r
-\begin_inset CommandInset bibitem\r
-LatexCommand bibitem\r
-label "3"\r
-key "xypic"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Flex URL\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-http://www.tug.org/tex-archive/help/Catalogue/entries/xypic.html\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\begin_layout Bibliography\r
-\begin_inset CommandInset bibitem\r
-LatexCommand bibitem\r
-label "4"\r
-key "AUCTeX"\r
-\r
-\end_inset\r
-\r
-\r
-\begin_inset Flex URL\r
-status collapsed\r
-\r
-\begin_layout Plain Layout\r
-\r
-http://www.gnu.org/software/auctex/\r
-\end_layout\r
-\r
-\end_inset\r
-\r
-\r
-\end_layout\r
-\r
-\end_body\r
-\end_document\r
+#LyX 2.0.0svn created this file. For more info see http://www.lyx.org/
+\lyxformat 382
+\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
+\maintain_unincluded_children false
+\language english
+\inputencoding auto
+\fontencoding global
+\font_roman ae
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\use_xetex false
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+
+\graphics default
+\default_output_format default
+\bibtex_command default
+\index_command 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
+\use_mhchem 1
+\cite_engine basic
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\quotes_language english
+\papercolumns 1
+\papersides 2
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_be_strict true
+\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
+ width 75col%
+ 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
+<lyxtabular version="3" rows="11" columns="2">
+<features islongtable="true" longtabularalignment="center">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Source code in LyX
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula \xymatrix{\ \ar[r] & \ }
+
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+
+\backslash
+ar
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula \xymatrix{\ \ar@{-->}[r] & \ }
+
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+
+\backslash
+ar@{-->}
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula \xymatrix{\ \ar@{..>}[r] & \ }
+
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+
+\backslash
+ar@{..>}
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula \xymatrix{\ \ar@{~>}[r] & \ }
+
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+
+\backslash
+ar@{~>}
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula \xymatrix{\ \ar@{->>}[r] & \ }
+
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+
+\backslash
+ar@{->>}
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula \xymatrix{\ \ar@{-->>}[r] & \ }
+
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+
+\backslash
+ar@{-->>}
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula \xymatrix{\ \ar@{>->>}[r] & \ }
+
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+
+\backslash
+ar@{>->>}
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula \xymatrix{\ \ar@{_{(}->}[r] & \ }
+
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+
+\backslash
+ar@{_(->}
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula \xymatrix{\ \ar@{^{(}->}[r] & \ }
+
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+
+\backslash
+ar@{^(->}
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula \xymatrix{\ \ar@{|-|}[r] & \ }
+
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+
+\backslash
+ar@{|-|}
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\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
+<lyxtabular version="3" rows="8" columns="2">
+<features islongtable="true" longtabularalignment="center">
+<column alignment="center" valignment="top" width="0">
+<column alignment="center" valignment="top" width="0">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Result
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+Source code for LyX
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula \xymatrix{\ \ar@2[r] & \ }
+
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+
+\backslash
+ar@2
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula \xymatrix{\ \ar@3[r] & \ }
+
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+
+\backslash
+ar@3
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula \xymatrix{\ \ar@_{->}[r] & \ }
+
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+
+\backslash
+ar@_{->}
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula \xymatrix{\ \ar@^{->}[r] & \ }
+
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+
+\backslash
+ar@^{->}
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula \xymatrix{\ \ar@^{>>->>}[r] & \ }
+
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+
+\backslash
+ar@^{>>->>}
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula \xymatrix{\ \ar@{^{<}-_{>}}[r] & \ }
+
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+
+\backslash
+ar@{^<-_>}
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula \xymatrix{\ \ar@2{--}[r] & \ }
+
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+
+\family typewriter
+
+\backslash
+ar@2{--}
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\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.
+ You might want to look on
+\family typewriter
+inset_preview.lyx
+\family default
+ example shipped with LyX, which demonstrates how to use more advanced
+\begin_inset ERT
+status collapsed
+
+\begin_layout Plain Layout
+
+
+\backslash
+Xy
+\end_layout
+
+\end_inset
+
+-commands via
+\family typewriter
+ERT
+\family default
+ and
+\family typewriter
+Instant preview
+\family default
+ insets.
+ 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
+\labelwidthstring References
+\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
+\labelwidthstring References
+\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
+\labelwidthstring References
+\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
+\labelwidthstring References
+\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
+\labelwidthstring References
+\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.math.columbia.edu/~lauda/xy/
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Bibliography
+\labelwidthstring References
+\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
projects / lyx.git / blobdiff