mirror of
https://git.lyx.org/repos/lyx.git
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3914 lines
63 KiB
Plaintext
3914 lines
63 KiB
Plaintext
#LyX 2.3 created this file. For more info see http://www.lyx.org/
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\lyxformat 544
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\begin_document
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\begin_header
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\save_transient_properties true
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\origin /systemlyxdir/examples/Graphics_and_Insets/
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\textclass scrartcl
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\begin_preamble
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% DO NOT ALTER THIS PREAMBLE!!!
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%
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% This preamble is designed to ensure that the file prints
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% out as advertised. If you mess with this preamble,
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% parts of this document may not print out as expected. If you
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% have problems LaTeXing this file, please contact
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% the documentation team
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% email: lyx-docs@lists.lyx.org
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\usepackage[all]{xy}
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% define new commands used in sec. 5.1
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\newcommand{\xyR}[1]{
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\xydef@\xymatrixrowsep@{#1}}
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\newcommand{\xyC}[1]{
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\xydef@\xymatrixcolsep@{#1}}
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\newdir{|>}{!/4.5pt/@{|}*:(1,-.2)@^{>}*:(1,+.2)@_{>}}
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% a pdf-bookmark for the TOC is added
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\let\myTOC\tableofcontents
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\renewcommand\tableofcontents{%
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\pdfbookmark[1]{\contentsname}{}
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\myTOC }
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% redefine the \LyX macro for PDF bookmarks
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\def\LyX{\texorpdfstring{%
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L\kern-.1667em\lower.25em\hbox{Y}\kern-.125emX\@}
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{LyX}}
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% if pdflatex is used
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\usepackage{ifpdf}
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\ifpdf
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% set fonts for nicer pdf view
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\IfFileExists{lmodern.sty}
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{\usepackage{lmodern}}{}
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\fi % end if pdflatex is used
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\end_preamble
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\options BCOR7.5mm
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\use_default_options false
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\maintain_unincluded_children false
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\language english
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\language_package default
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\inputencoding utf8
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\fontencoding global
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\font_roman "default" "default"
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\font_sans "default" "default"
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\font_typewriter "default" "default"
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\font_math "auto" "auto"
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\font_default_family default
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\use_non_tex_fonts false
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\font_sc false
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\font_osf false
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\font_sf_scale 100 100
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\font_tt_scale 100 100
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\use_microtype false
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\use_dash_ligatures false
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\graphics default
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\default_output_format default
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\output_sync 0
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\bibtex_command default
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\index_command default
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\paperfontsize 12
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\spacing single
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\use_hyperref true
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\pdf_title "Using XY-pc in LyX"
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\pdf_author "H. Peter Gumm"
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\pdf_subject "LyX's XY-pic manual"
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\pdf_keywords "LyX, documentation"
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\pdf_bookmarks true
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\pdf_bookmarksnumbered true
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\pdf_bookmarksopen true
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\pdf_bookmarksopenlevel 2
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\pdf_breaklinks false
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\pdf_pdfborder false
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\pdf_colorlinks true
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\pdf_backref false
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\pdf_pdfusetitle false
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\pdf_quoted_options "linkcolor=black, citecolor=black, urlcolor=blue, filecolor=blue,pdfpagelayout=OneColumn, pdfnewwindow=true,pdfstartview=XYZ, plainpages=false"
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\papersize a4paper
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\use_geometry false
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\use_package amsmath 1
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\use_package amssymb 1
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\use_package cancel 1
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\use_package esint 1
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\use_package mathdots 1
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\use_package mathtools 1
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\use_package mhchem 1
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\use_package stackrel 1
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\use_package stmaryrd 1
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\use_package undertilde 1
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\cite_engine basic
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\cite_engine_type default
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\biblio_style plain
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\use_bibtopic false
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\use_indices false
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\paperorientation portrait
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\suppress_date true
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\justification true
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\use_refstyle 0
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\use_minted 0
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\notefontcolor #0000ff
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\index Index
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\shortcut idx
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\color #008000
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\end_index
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\secnumdepth 3
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\tocdepth 3
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\paragraph_separation indent
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\paragraph_indentation default
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\is_math_indent 0
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\math_numbering_side default
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\quotes_style english
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\dynamic_quotes 0
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\papercolumns 1
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\papersides 2
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\paperpagestyle default
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\tracking_changes false
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\output_changes false
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\html_math_output 0
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\html_css_as_file 0
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\html_be_strict true
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\end_header
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\begin_body
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\begin_layout Title
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Using
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\begin_inset ERT
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status collapsed
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\begin_layout Plain Layout
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\backslash
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Xy
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\end_layout
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\end_inset
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-pic in \SpecialChar LyX
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\end_layout
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\begin_layout Author
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H.
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Peter Gumm
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\end_layout
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\begin_layout Abstract
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With the recent versions of \SpecialChar LyX
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and with the
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\family typewriter
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preview
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\family default
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-style installed in the \SpecialChar LaTeX
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-System, the graph drawing package
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\begin_inset ERT
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status collapsed
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\begin_layout Plain Layout
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\backslash
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Xy
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\end_layout
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\end_inset
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-pic can be conveniently used inside \SpecialChar LyX
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.
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Diagrams can be edited and displayed inside the main \SpecialChar LyX
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editing window.
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Here, we shall describe how to use the
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\family typewriter
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\backslash
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xymatrix
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\family default
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command from
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\family typewriter
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xypic
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\family default
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inside \SpecialChar LyX
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in order to draw, to edit and to preview diagrams as typically
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used in category theory, algebra, and related fields.
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\end_layout
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\begin_layout Abstract
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\begin_inset CommandInset toc
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LatexCommand tableofcontents
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\end_inset
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\end_layout
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\begin_layout Section
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Introduction
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\end_layout
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\begin_layout Standard
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The
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\family typewriter
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xypic
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\family default
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-package has long served as a convenient tool for easily constructing graphs
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and diagrams in \SpecialChar LaTeX
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.
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Unfortunately, its use in \SpecialChar LyX
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had long been restricted to the infamous \SpecialChar TeX
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code
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boxes, meaning that the \SpecialChar LyX
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editor could only display the \SpecialChar LaTeX
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-source and not
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the finished diagram.
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The new
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\family typewriter
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preview
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\family default
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-style of \SpecialChar LaTeX
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which is part of the AUC\SpecialChar TeX
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project
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\begin_inset CommandInset citation
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LatexCommand cite
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key "AUCTeX"
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literal "true"
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\end_inset
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, finally enables the editing and displaying of
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\family typewriter
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xypic
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\family default
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-diagrams, constructed, displayed and interactively edited inside \SpecialChar LyX
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.
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\end_layout
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\begin_layout Standard
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\begin_inset VSpace defskip
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\end_inset
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\end_layout
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\begin_layout Standard
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\align center
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\begin_inset Graphics
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filename xyfigure.png
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width 75col%
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\end_inset
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\end_layout
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\begin_layout Standard
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\begin_inset VSpace defskip
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\end_inset
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\end_layout
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\begin_layout Standard
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In this note, we describe how
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\begin_inset ERT
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status collapsed
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\begin_layout Plain Layout
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\backslash
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Xy
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\end_layout
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\end_inset
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-pic can be used from inside \SpecialChar LyX
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, how diagrams can be created and edited.
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We have tested the following using \SpecialChar LyX
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versions 1.3.7 up to 1.6, running under
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Windows
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\begin_inset space \thinspace{}
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\end_inset
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XP and under Windows Vista.
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\end_layout
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\begin_layout Standard
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There are two modes of operations: For a start, and for some first tests,
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it may be easiest to first enter the
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\begin_inset ERT
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status collapsed
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\begin_layout Plain Layout
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\backslash
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Xy
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\end_layout
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\end_inset
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-pic code inside the \SpecialChar LyX
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-window, select it all and convert it to a graphical
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representation by pressing
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\family sans
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Ctrl-m
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\family default
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or
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\family sans
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Ctrl-M
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\family default
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.
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If you use
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\begin_inset ERT
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status collapsed
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\begin_layout Plain Layout
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\backslash
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Xy
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\end_layout
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\end_inset
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-pic more frequently, or if you want to modify your initial figure, you
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will want to assemble and modify your figures using \SpecialChar LyX
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's math editor.
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\end_layout
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\begin_layout Standard
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Once the cursor is moved over a diagram, this is displayed as an array of
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nodes and arrow-commands.
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These can be changed interactively.
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When the cursor leaves the editing area, the diagram reappears.
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\end_layout
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\begin_layout Standard
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In the first two sections of this documentation, we explain how to use \SpecialChar LyX
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in the first mentioned mode and we introduce all
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\begin_inset ERT
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status collapsed
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\begin_layout Plain Layout
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\backslash
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Xy
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\end_layout
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\end_inset
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-pic features that might be of use for drawing commutative diagrams, graphs
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or automata.
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Section
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "sec:math-editor"
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\end_inset
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explains how to use the
|
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\begin_inset ERT
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status collapsed
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\begin_layout Plain Layout
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\backslash
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Xy
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\end_layout
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\end_inset
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|
-pic commands inside a math-editing area.
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\end_layout
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|
\begin_layout Standard
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It is not our intention to write another introduction to
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\begin_inset ERT
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status collapsed
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|
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|
\begin_layout Plain Layout
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|
|
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\backslash
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Xy
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\end_layout
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\end_inset
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|
-pic, rather our motivation is to give an introduction how the most important
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commands work inside \SpecialChar LyX
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, since the keystrokes as explained in the
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\begin_inset ERT
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status collapsed
|
|
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\begin_layout Plain Layout
|
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|
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\backslash
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Xy
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\end_layout
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\end_inset
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|
-pic manual
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\begin_inset CommandInset citation
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LatexCommand cite
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key "xypic manual"
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literal "true"
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\end_inset
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will not always function correctly inside \SpecialChar LyX
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.
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\end_layout
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\begin_layout Section
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|
Preparation
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\end_layout
|
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|
\begin_layout Standard
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The following requires that the \SpecialChar LaTeX
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-packages
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\family typewriter
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xypic
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\family default
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and
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\family typewriter
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preview
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\family default
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are installed in the \SpecialChar LaTeX
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system.
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They are available from CTAN, see at
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\begin_inset CommandInset citation
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|
LatexCommand cite
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key "instant-preview"
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literal "true"
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\end_inset
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|
, resp.
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at
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\begin_inset CommandInset citation
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LatexCommand cite
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key "xypic"
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literal "true"
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\end_inset
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|
.
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After freshly installing them, it may be necessary, to run
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\family sans
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Tools\SpecialChar menuseparator
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Reconfigure
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\family default
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from the main \SpecialChar LyX
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menu.
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The steps to a first diagram output in \SpecialChar LyX
|
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are then:
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\end_layout
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|
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|
\begin_layout Enumerate
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|
Activate and test
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\family typewriter
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preview
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\end_layout
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|
\begin_deeper
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\begin_layout Enumerate
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Open \SpecialChar LyX
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, choose
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\family sans
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Tools\SpecialChar menuseparator
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Preferences\SpecialChar menuseparator
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Look and Feel\SpecialChar menuseparator
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Display
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\family default
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|
and turn
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\emph on
|
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Instant Preview
|
|
\emph default
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on.
|
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\end_layout
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|
|
|
\begin_layout Enumerate
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|
In
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\family sans
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|
Document\SpecialChar menuseparator
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Settings\SpecialChar menuseparator
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|
Math
|
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\begin_inset space ~
|
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\end_inset
|
|
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|
Options
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\family default
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|
, uncheck
|
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\emph on
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|
Use AMS Math package automatically
|
|
\emph default
|
|
and check
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|
\emph on
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|
Use AMS Math package
|
|
\emph default
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|
.
|
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\end_layout
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|
|
|
\begin_layout Enumerate
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|
Test, if
|
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\family typewriter
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instant-preview
|
|
\family default
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|
works by opening a \SpecialChar LyX
|
|
-document and entering any math-formula, e.
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\begin_inset space \thinspace{}
|
|
\end_inset
|
|
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|
g.
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|
\begin_inset space \space{}
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|
\end_inset
|
|
|
|
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|
\begin_inset Formula $a+b=c$
|
|
\end_inset
|
|
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|
.
|
|
|
|
\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 horizonta
|
|
l 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 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 \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 automatica
|
|
lly 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/xytutori
|
|
al.html
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_body
|
|
\end_document
|