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[lyx.git] / lib / examples / Graphics_and_Insets / XY-Pic.lyx

#LyX 2.4 created this file. For more info see https://www.lyx.org/
\lyxformat 620
\begin_document
\begin_header
\save_transient_properties true
\origin /systemlyxdir/examples/Graphics_and_Insets/
\textclass scrartcl
\begin_preamble
% DO NOT ALTER THIS PREAMBLE!!!
%
% This preamble is designed to ensure that the file prints
% out as advertised. If you mess with this preamble,
% parts of this document may not print out as expected.  If you
% have problems LaTeXing this file, please contact 
% the documentation team
% email: lyx-docs@lists.lyx.org

\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
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  \pdfbookmark[1]{\contentsname}{}
  \myTOC }

% redefine the \LyX macro for PDF bookmarks
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  L\kern-.1667em\lower.25em\hbox{Y}\kern-.125emX\@}
  {LyX}}

% if pdflatex is used
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\ifpdf

% set fonts for nicer pdf view
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 {\usepackage{lmodern}}{}

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\options BCOR7.5mm
\use_default_options false
\maintain_unincluded_children no
\language english
\language_package default
\inputencoding utf8
\fontencoding auto
\font_roman "default" "default"
\font_sans "default" "default"
\font_typewriter "default" "default"
\font_math "auto" "auto"
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\use_non_tex_fonts false
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\paperfontsize 12
\spacing single
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\pdf_title "Using XY-pc in LyX"
\pdf_author "H. Peter Gumm"
\pdf_subject "LyX's XY-pic manual"
\pdf_keywords "LyX, documentation"
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\index Index
\shortcut idx
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\end_index
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\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 \SpecialChar LyX

\end_layout

\begin_layout Author
H.
 Peter Gumm
\end_layout

\begin_layout Abstract
With the recent versions of \SpecialChar LyX
 and with the 
\family typewriter
preview
\family default
-style installed in the \SpecialChar LaTeX
-System,
 the graph drawing package 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
Xy
\end_layout

\end_inset

-pic can be conveniently used inside \SpecialChar LyX
.
 Diagrams can be edited and displayed inside the main \SpecialChar 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 \SpecialChar 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 \SpecialChar LaTeX
.
 Unfortunately,
 its use in \SpecialChar LyX
 had long been restricted to the infamous \SpecialChar TeX
 code boxes,
 meaning that the \SpecialChar LyX
 editor could only display the \SpecialChar LaTeX
-source and not the finished diagram.
 The new 
\family typewriter
preview
\family default
-style of \SpecialChar LaTeX
 which is part of the AUC\SpecialChar TeX
 project
\begin_inset CommandInset citation
LatexCommand cite
key "AUCTeX"
literal "true"

\end_inset

,
 finally enables the editing and displaying of 
\family typewriter
xypic
\family default
-diagrams,
 constructed,
 displayed and interactively edited inside \SpecialChar 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%

\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 \SpecialChar LyX
,
 how diagrams can be created and edited.
 We have tested the following using \SpecialChar 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 \SpecialChar 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 \SpecialChar 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 \SpecialChar 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"
nolink "false"

\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 \SpecialChar 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"
literal "true"

\end_inset

 will not always function correctly inside \SpecialChar LyX
.
 
\end_layout

\begin_layout Section
Preparation
\end_layout

\begin_layout Standard
The following requires that the \SpecialChar LaTeX
-packages 
\family typewriter
xypic
\family default
 and 
\family typewriter
preview
\family default
 are installed in the \SpecialChar LaTeX
 system.
 They are available from CTAN,
 see at 
\begin_inset CommandInset citation
LatexCommand cite
key "instant-preview"
literal "true"

\end_inset

,
 resp.
 at 
\begin_inset CommandInset citation
LatexCommand cite
key "xypic"
literal "true"

\end_inset

.
 After freshly installing them,
 it may be necessary,
 to run 
\family sans
Tools\SpecialChar menuseparator
Reconfigure
\family default
 from the main \SpecialChar LyX
 menu.
 The steps to a first diagram output in \SpecialChar LyX
 are then:
\end_layout

\begin_layout Enumerate
Activate and test 
\family typewriter
preview
\end_layout

\begin_deeper
\begin_layout Enumerate
Open \SpecialChar 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 \SpecialChar LyX
-document and entering any math-formula,
 e.
\begin_inset space \thinspace{}
\end_inset

g.
\begin_inset space \space{}
\end_inset


\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 \SpecialChar 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"
literal "true"

\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 \SpecialChar 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 LyX-Code
\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.
\begin_inset space \space{}
\end_inset


\family typewriter
(.3)
\family default
.
 In \SpecialChar 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.
\begin_inset space \space{}
\end_inset


\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 \SpecialChar 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].
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="11" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top" width="0pt">
<column alignment="center" valignment="top">
<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 \SpecialChar 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:
\end_layout

\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="8" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="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" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Source code for \SpecialChar LyX

\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="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" 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" rightline="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" 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" rightline="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" 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" rightline="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" 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" rightline="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" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\family typewriter

\backslash
ar@^{>\SpecialChar ligaturebreak
>->\SpecialChar ligaturebreak
>}
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="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" 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" rightline="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" 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 \SpecialChar 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 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 \SpecialChar 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 
\family typewriter
@/
\family default

\begin_inset Formula $\ldots$
\end_inset


\family typewriter
/
\family default
 .
 The ellipsis stands for a \SpecialChar 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.
\begin_inset space \space{}
\end_inset


\family typewriter

\backslash
ar@/_1pc/
\family default
 for an arrow bending 
\family typewriter
1pc
\family default
 downwards,
 this cannot directly be done in \SpecialChar LyX
.
 It is necessary,
 to enclose the measure in a pair of braces,
 such as e.
\begin_inset space \thinspace{}
\end_inset

g.
\begin_inset space \space{}
\end_inset


\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 
\family typewriter
@(
\family default
\emph on
out
\emph default
,
\emph on
in
\family typewriter
\emph default
)
\family 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 \SpecialChar 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 horizontal rectangle is
\family typewriter
\series default
\shape default
\size default
\emph default
\bar default
\noun default
\color inherit

\begin_inset Newline newline
\end_inset


\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

\begin_inset Newline newline
\end_inset

This code can be placed in arbitrary cells of the xymatrix.
 
\end_layout

\begin_layout Section
Using \SpecialChar 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 \SpecialChar 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 \SpecialChar 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 \SpecialChar 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.
\begin_inset space \space{}
\end_inset


\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 \SpecialChar 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 \SpecialChar 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
,
 
\family typewriter
@(
\family default
\SpecialChar ldots
,\SpecialChar ldots

\family typewriter
)
\family default
 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 \SpecialChar 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 \SpecialChar 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 successfully 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 \SpecialChar 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 \SpecialChar 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,
 
\begin_inset CommandInset citation
LatexCommand cite
key "xypic manual"
literal "true"

\end_inset

,
 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
\begin_inset space ~
\end_inset

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,
 one cannot type 
\begin_inset Quotes eld
\end_inset


\family typewriter

\backslash
xymatrix@R=1pc
\family default

\begin_inset Quotes erd
\end_inset

 into a formula to get the desired matrix because the @-character is interpreted by \SpecialChar LyX
 as ending the 
\family typewriter

\backslash
xymatrix
\family default
 command.
 But there are two other ways of getting the desired matrix:
\end_layout

\begin_layout Itemize
One types e.g.
\begin_inset space \space{}
\end_inset


\family typewriter

\backslash
xymatrix@R=1pc
\family default
 as normal document text,
 then either highlight it and press 
\begin_inset Info
type  "shortcut"
arg   "math-mode"
\end_inset

 to get a formula,
 or copy it into an existing formula.
 You can now continue as normal.
\begin_inset Newline newline
\end_inset


\begin_inset Note Greyedout
status open

\begin_layout Plain Layout

\series bold
Note:

\series default
 This method only works for single spacing settings,
 so using
\begin_inset Newline newline
\end_inset


\family typewriter

\backslash
xymatrix@M=1pt
\family default
 is possible while 
\family typewriter

\backslash
xymatrix@M=1pt@C=1dd
\family default
 is not.
 The method also don't work if you use '!' to get a fixed grid with a defined dimension,
 e.g.
\begin_inset space \space{}
\end_inset


\family typewriter

\backslash
xymatrix@!R=3pt
\family default
 fails while
\family typewriter
 
\backslash
xymatrix@!R
\family default
 works.
\end_layout

\end_inset


\begin_inset Newline newline
\end_inset

For the following matrix,
 the command 
\family typewriter

\backslash
xymatrix@C=9pc
\family default
 was used:
\begin_inset Formula 
\[
\xymatrix@C=9pc{A\ar[r]\ar[d] & B\\
C\ar@{}[ur]|{\text{{horizontal stretch}}}
}
\]

\end_inset


\end_layout

\begin_layout Itemize
\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
\begin_inset Newline newline
\end_inset


\family typewriter

\backslash
xymatrixrowsep@
\family default
 and 
\family typewriter

\backslash
xymatrixcolsep@
\family default
.
 So one can add the following macro to the preamble (
\family sans
Layout\SpecialChar menuseparator
Document\SpecialChar menuseparator
Preamble
\family default
):
\end_layout

\begin_deeper
\begin_layout LyX-Code

\backslash
newcommand{
\backslash
xyR}[1]{%
\end_layout

\begin_layout LyX-Code

\backslash
xydef@
\backslash
xymatrixrowsep@{#1}}
\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 formula before 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 automatically supplied by \SpecialChar LyX
.
 Inside the braces enter the dimensions.
\begin_inset Newline newline
\end_inset


\begin_inset Note Greyedout
status open

\begin_layout Plain Layout

\series bold
Note:

\series default
 these commands affect all following 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
Xy
\end_layout

\end_inset

-matrices.
 Therefore don't forget to reset the values to default after the usage of 
\family typewriter

\backslash
xyR
\family default
 etc.
\end_layout

\end_inset


\begin_inset Newline newline
\end_inset

The default is 
\family typewriter
2pc
\family default
.
 Here you see a diagram which is squashed vertically and stretched horizontally with 
\family typewriter

\backslash
xyR{.5pc}
\backslash
xyC{9pc}
\family default
:
\begin_inset Formula 
\[
\xyR{.5pc}\xyC{9pc}\xymatrix{A\ar[r]\ar[d] & B\\
C\ar@{}[ur]|{\text{{horizontal stretch}}}
}
\]

\end_inset


\begin_inset Formula $\xyR{2pc}\xyC{2pc}$
\end_inset


\begin_inset Note Note
status collapsed

\begin_layout Plain Layout
reset to default
\end_layout

\end_inset


\end_layout

\end_deeper
\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 \SpecialChar 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.
\begin_inset space \space{}
\end_inset


\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
Xy
\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 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
Xy
\end_layout

\end_inset

-package.
 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"
literal "true"

\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"
literal "true"

\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
Instant_Preview.lyx
\family default
 example shipped with \SpecialChar 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
\SpecialChar TeX

\begin_inset space ~
\end_inset

Code
\family default
 and 
\family typewriter
Instant preview
\family default
 insets.
\end_layout

\begin_layout Standard
\begin_inset Newpage newpage
\end_inset


\end_layout

\begin_layout Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
key "xypic manual"
literal "true"

\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
.
\begin_inset Newline newline
\end_inset


\begin_inset Flex URL
status collapsed

\begin_layout Plain Layout

https://www.ctan.org/tex-archive/macros/generic/diagrams/xypic/doc/xyguide.pdf
\end_layout

\end_inset


\end_layout

\begin_layout Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
key "xypic reference"
literal "true"

\end_inset

Kristoffer H.
 Rose and Ross Moore:
 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
Xy
\end_layout

\end_inset


\emph on
-pic Reference Manual
\emph default
.
\begin_inset Newline newline
\end_inset


\begin_inset Flex URL
status collapsed

\begin_layout Plain Layout

https://www.ctan.org/tex-archive/macros/generic/diagrams/xypic/doc/xyrefer.pdf
\end_layout

\end_inset


\end_layout

\begin_layout Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
key "xypic"
literal "true"

\end_inset

Homepage of the package 
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
Xy
\end_layout

\end_inset


\emph on
-pic
\emph default
:
 
\begin_inset Flex URL
status collapsed

\begin_layout Plain Layout

https://www.ctan.org/pkg/xypic
\end_layout

\end_inset


\end_layout

\begin_layout Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
key "instant-preview"
literal "true"

\end_inset

Homepage of preview-latex:
\begin_inset Newline newline
\end_inset


\begin_inset Flex URL
status collapsed

\begin_layout Plain Layout

https://www.gnu.org/software/auctex/preview-latex.html
\end_layout

\end_inset


\end_layout

\begin_layout Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
key "AUCTeX"
literal "true"

\end_inset

Homepage of AUC\SpecialChar TeX
:
 
\begin_inset Flex URL
status collapsed

\begin_layout Plain Layout

https://www.gnu.org/software/auctex/
\end_layout

\end_inset


\end_layout

\begin_layout Bibliography
\begin_inset CommandInset bibitem
LatexCommand bibitem
key "Lauda"
literal "true"

\end_inset

Aaron 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 Newline newline
\end_inset


\begin_inset Flex URL
status collapsed

\begin_layout Plain Layout

https://web.archive.org/web/20080222044349/https://www.dpmms.cam.ac.uk/~al366/xytutorial.html
\end_layout

\end_inset


\end_layout

\end_body
\end_document