#LyX 2.3 created this file. For more info see http://www.lyx.org/
\lyxformat 544
\begin_document
\begin_header
\save_transient_properties true
\origin /systemlyxdir/examples/
\textclass article
\begin_preamble
\usepackage{etex}
\usepackage[all, knot]{xy}
\xyoption{arc} 
\usepackage{qtree}
\usepackage{tipa}
\usepackage{pstricks}
\usepackage{pst-plot}
\usepackage{rotating}
\usepackage{tikz}
\usetikzlibrary{scopes}
\end_preamble
\use_default_options false
\maintain_unincluded_children false
\language english
\language_package default
\inputencoding auto
\fontencoding global
\font_roman "lmodern" "default"
\font_sans "default" "default"
\font_typewriter "default" "default"
\font_math "auto" "auto"
\font_default_family default
\use_non_tex_fonts false
\font_sc false
\font_osf false
\font_sf_scale 100 100
\font_tt_scale 100 100
\use_microtype false
\use_dash_ligatures false
\graphics default
\default_output_format pdf
\output_sync 0
\bibtex_command default
\index_command default
\paperfontsize default
\spacing single
\use_hyperref false
\papersize default
\use_geometry false
\use_package amsmath 1
\use_package amssymb 1
\use_package cancel 1
\use_package esint 1
\use_package mathdots 1
\use_package mathtools 1
\use_package mhchem 1
\use_package stackrel 1
\use_package stmaryrd 1
\use_package undertilde 1
\cite_engine basic
\cite_engine_type default
\biblio_style plain
\use_bibtopic false
\use_indices false
\paperorientation portrait
\suppress_date false
\justification true
\use_refstyle 0
\use_minted 0
\index Index
\shortcut idx
\color #008000
\end_index
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
\paragraph_indentation default
\is_math_indent 0
\math_numbering_side default
\quotes_style english
\dynamic_quotes 0
\papercolumns 1
\papersides 1
\paperpagestyle default
\tracking_changes false
\output_changes false
\html_math_output 0
\html_css_as_file 0
\html_be_strict true
\end_header

\begin_body

\begin_layout Section
Introduction
\end_layout

\begin_layout Standard
In order to properly typeset the document and have instant preview working,
 the following packages have to be installed:
\end_layout

\begin_layout LyX-Code
xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf, etex
\end_layout

\begin_layout Standard
Due to the use of postscript specials in Section 
\begin_inset CommandInset ref
LatexCommand ref
reference "sec:PSTricks"

\end_inset

, only the Postscript or PDF (ps2pdf) output formats will correctly render
 the included images.
 However, the PDF (Xe\SpecialChar TeX
) output seems to also work, while trying to typeset
 the document with 
\family typewriter
pdflatex
\family default
 or 
\family typewriter
pdflualatex
\family default
 will generate errors.
\end_layout

\begin_layout Section
Diagrams by XY(-pic)
\end_layout

\begin_layout Standard
Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
 examples, see 
\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 Description
Braid
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
xy
\end_layout

\begin_layout Plain Layout

(5,10)*{}; (-10,-10)*{} **
\backslash
crv{(6,-2)&(-12,4)}
\end_layout

\begin_layout Plain Layout


\backslash
POS?(.25)*{
\backslash
hole}="x" 
\backslash
POS?(.45)*{
\backslash
hole}="y" 
\backslash
POS?(.6)*{
\backslash
hole}="z";
\end_layout

\begin_layout Plain Layout

"y"+(0,-1); (2,-10)*{} **
\backslash
crv{}
\backslash
POS?(.2)*{
\backslash
hole}="M";
\end_layout

\begin_layout Plain Layout

(-10,10)*{}; "z" **
\backslash
crv{(-9,0)};
\end_layout

\begin_layout Plain Layout

"z"; "M" **
\backslash
crv{};
\end_layout

\begin_layout Plain Layout

"M"; "x" **
\backslash
crv{(5,0)};
\end_layout

\begin_layout Plain Layout

"x"; "y" **
\backslash
crv{(0,7) & (-5,6)};
\end_layout

\begin_layout Plain Layout


\backslash
endxy 
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Description
Knots
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
xy
\end_layout

\begin_layout Plain Layout

(6,9)*{}="1";
\end_layout

\begin_layout Plain Layout

(-8.5,-1)*{}="2";
\end_layout

\begin_layout Plain Layout

"1";"2" **
\backslash
crv{~*=<.5pt>{.} (0,30)}?(.75)*
\backslash
dir{>}+(-2,2)*{z};
\end_layout

\begin_layout Plain Layout

(-6.5,8)*{}="1";
\end_layout

\begin_layout Plain Layout

(-.5,-9)*{}="2";
\end_layout

\begin_layout Plain Layout

"1";"2" **
\backslash
crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
\backslash
dir{>}+(-2,-2)*{u};
\end_layout

\begin_layout Plain Layout

(-9.5,-3.35)*{}="1";
\end_layout

\begin_layout Plain Layout

(8.5,-3)*{}="2";
\end_layout

\begin_layout Plain Layout

"1";"2" **
\backslash
crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
\backslash
dir{>}+(-1,-3)*{x};
\end_layout

\begin_layout Plain Layout

(1,-10)*{}="1";
\end_layout

\begin_layout Plain Layout

(6.5,7.13)*{}="2";
\end_layout

\begin_layout Plain Layout

"1";"2" **
\backslash
crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
\backslash
dir{>}+(3,-1)*{y};
\end_layout

\begin_layout Plain Layout

(11,-1)*{}="1";
\end_layout

\begin_layout Plain Layout

(-4,8)*{}="2";
\end_layout

\begin_layout Plain Layout

"1";"2" **
\backslash
crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
\backslash
dir{>}+(1,2)*{w};
\end_layout

\begin_layout Plain Layout


\backslash
endxy
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Description
Circles
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
xy
\end_layout

\begin_layout Plain Layout

(0,0)*
\backslash
xycircle(14,8){++
\backslash
dir{<}};
\end_layout

\begin_layout Plain Layout

(0,0)*
\backslash
xycircle<10pt>{{.}};
\end_layout

\begin_layout Plain Layout

(0,0)*
\backslash
xycircle(5,2){:};
\end_layout

\begin_layout Plain Layout

(0,15)*
\backslash
xycircle(10,4){--};
\end_layout

\begin_layout Plain Layout


\backslash
endxy 
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Description
Cobordism
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
xy
\end_layout

\begin_layout Plain Layout

(0,0)*
\backslash
ellipse(3,1){.};
\end_layout

\begin_layout Plain Layout

(0,0)*
\backslash
ellipse(3,1)__,=:a(-180){-};
\end_layout

\begin_layout Plain Layout

(-6,-8)*
\backslash
ellipse(3,1){.};
\end_layout

\begin_layout Plain Layout

(6,-8)*
\backslash
ellipse(3,1){.};
\end_layout

\begin_layout Plain Layout

(0,-8)*
\backslash
ellipse(3,1){.};
\end_layout

\begin_layout Plain Layout

(-6,-8)*
\backslash
ellipse(3,1)__,=:a(-180){-};
\end_layout

\begin_layout Plain Layout

(6,-8)*
\backslash
ellipse(3,1)__,=:a(-180){-};
\end_layout

\begin_layout Plain Layout

(0,-8)*
\backslash
ellipse(3,1)__,=:a(180){-};
\end_layout

\begin_layout Plain Layout

(-3,6)*
\backslash
ellipse(3,1){-};
\end_layout

\begin_layout Plain Layout

(3,6)*
\backslash
ellipse(3,1){-};
\end_layout

\begin_layout Plain Layout

(-3,12)*{}="1";
\end_layout

\begin_layout Plain Layout

(3,12)*{}="2";
\end_layout

\begin_layout Plain Layout

(-9,12)*{}="A2";
\end_layout

\begin_layout Plain Layout

(9,12)*{}="B2";
\end_layout

\begin_layout Plain Layout

"1";"2" **
\backslash
crv{(-3,7) & (3,7)};
\end_layout

\begin_layout Plain Layout

(-3,0)*{}="A";
\end_layout

\begin_layout Plain Layout

(3,0)*{}="B";
\end_layout

\begin_layout Plain Layout

(-3,1)*{}="A1";
\end_layout

\begin_layout Plain Layout

(3,1)*{}="B1";
\end_layout

\begin_layout Plain Layout

"A";"A1" **
\backslash
dir{-};
\end_layout

\begin_layout Plain Layout

"B";"B1" **
\backslash
dir{-};
\end_layout

\begin_layout Plain Layout

"B2";"B1" **
\backslash
crv{(8,7) & (3,5)};
\end_layout

\begin_layout Plain Layout

"A2";"A1" **
\backslash
crv{(-8,7) & (-3,5)};
\end_layout

\begin_layout Plain Layout

%REFLECT
\end_layout

\begin_layout Plain Layout

(3,-16)*{}="1";
\end_layout

\begin_layout Plain Layout

(9,-16)*{}="2";
\end_layout

\begin_layout Plain Layout

"1";"2" **
\backslash
crv{(3,-10) & (9,-10)};
\end_layout

\begin_layout Plain Layout

(-3,-16)*{}="1";
\end_layout

\begin_layout Plain Layout

(-9,-16)*{}="2";
\end_layout

\begin_layout Plain Layout

"1";"2" **
\backslash
crv{(-3,-10) & (-9,-10)};
\end_layout

\begin_layout Plain Layout

(-15,-16)*{}="A2";
\end_layout

\begin_layout Plain Layout

(15,-16)*{}="B2";
\end_layout

\begin_layout Plain Layout

(-3,0)*{}="A";
\end_layout

\begin_layout Plain Layout

(3,0)*{}="B";
\end_layout

\begin_layout Plain Layout

(-3,-1)*{}="A1";
\end_layout

\begin_layout Plain Layout

(3,-1)*{}="B1";
\end_layout

\begin_layout Plain Layout

"A";"A1" **
\backslash
dir{-};
\end_layout

\begin_layout Plain Layout

"B";"B1" **
\backslash
dir{-};
\end_layout

\begin_layout Plain Layout

"B2";"B1" **
\backslash
crv{(13,-6) & (2,-8)};
\end_layout

\begin_layout Plain Layout

"A2";"A1" **
\backslash
crv{(-13,-6) & (-2,-8)};
\end_layout

\begin_layout Plain Layout


\backslash
endxy
\end_layout

\end_inset


\end_layout

\end_inset

 
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
xy 0;/r.18pc/:
\end_layout

\begin_layout Plain Layout

(20,2)*{
\backslash
bullet}="RU"+(1,3)*{x^{
\backslash
ast}};
\end_layout

\begin_layout Plain Layout

(16,-3)*{
\backslash
bullet}="RD"+(2.5,2)*{x^{
\backslash
ast}};
\end_layout

\begin_layout Plain Layout

(-16,2)*{
\backslash
bullet}="LU"+(-1,2)*{x};
\end_layout

\begin_layout Plain Layout

(-20,-3)*{
\backslash
bullet}="LD"+(-1,2)*{x};
\end_layout

\begin_layout Plain Layout

"RU";"RD" **
\backslash
crv{(4,2) & (4,-1)}; ?(.1)*
\backslash
dir{<}; ?(.85)*
\backslash
dir{<};
\end_layout

\begin_layout Plain Layout

"LD";"LU" **
\backslash
crv{(-4,-2) & (-4,1)};
\end_layout

\begin_layout Plain Layout

?(.08)*
\backslash
dir{<}; ?(.85)*
\backslash
dir{<};
\end_layout

\begin_layout Plain Layout

(7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
\end_layout

\begin_layout Plain Layout

"x1"; "x2" **
\backslash
crv{(7,-10) & (-7,-10)};
\end_layout

\begin_layout Plain Layout

(16,-20)*{
\backslash
bullet}="RDD"+(2.5,-1)*{x^{
\backslash
ast}};
\end_layout

\begin_layout Plain Layout

(-20,-20)*{
\backslash
bullet}="LDD"+(-1,-3)*{x};
\end_layout

\begin_layout Plain Layout

(20,-12.5)*{
\backslash
bullet}="RUD"+(3.5,1)*{x^{
\backslash
ast}};
\end_layout

\begin_layout Plain Layout

(-16,-15)*{
\backslash
bullet}="LUD";
\end_layout

\begin_layout Plain Layout

(-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
\end_layout

\begin_layout Plain Layout

"RD"; "RDD" **
\backslash
dir{-};
\end_layout

\begin_layout Plain Layout

"LD"; "LDD" **
\backslash
dir{-};
\end_layout

\begin_layout Plain Layout

"A"; "LUD" **
\backslash
dir{.};
\end_layout

\begin_layout Plain Layout

"RDD"; "LDD" **
\backslash
crv{(0,-17)}; ?(.57)*
\backslash
dir{>};
\end_layout

\begin_layout Plain Layout

"RU"; "RUD" **
\backslash
dir{-};
\end_layout

\begin_layout Plain Layout

"LU"; "A" **
\backslash
dir{-};
\end_layout

\begin_layout Plain Layout

"B"; "RUD" **
\backslash
crv{(18,-14.15)};
\end_layout

\begin_layout Plain Layout

"B"; "LUD" **
\backslash
crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
\backslash
dir{<};
\end_layout

\begin_layout Plain Layout


\backslash
endxy
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Description
Strings
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
xy (-15,0)*{};(15,0)*{};
\end_layout

\begin_layout Plain Layout


\backslash
endxy
\end_layout

\begin_layout Plain Layout


\backslash
qquad = 
\backslash
qquad 
\backslash
xy
\end_layout

\begin_layout Plain Layout

(-10,12)*{}; (-10,-12)*{}; **
\backslash
dir{-}?(.5)*
\backslash
dir{<}+(-4,0)*{F(x)};
\end_layout

\begin_layout Plain Layout

(-2,12)*{}="1";
\end_layout

\begin_layout Plain Layout

(6,-7) *{}="2";
\end_layout

\begin_layout Plain Layout

(14,-7) *{}="3";
\end_layout

\begin_layout Plain Layout

(14,-13)*{}="3'";
\end_layout

\begin_layout Plain Layout

(18,0) *={}="";
\end_layout

\begin_layout Plain Layout

"1";"2" **
\backslash
crv{(-4,-21)&(5,-15)};
\end_layout

\begin_layout Plain Layout

?(.15)*
\backslash
dir{<}+(5,10)*{
\backslash
overline{F(x)}};
\end_layout

\begin_layout Plain Layout

"2";"3" **
\backslash
crv{(6,1)&(14,1)};
\end_layout

\begin_layout Plain Layout

?(0)*
\backslash
dir{<}+(4,8)*{
\backslash
widetilde{F(i_x)}} ;
\end_layout

\begin_layout Plain Layout

?(.95)*
\backslash
dir{<}+(5,-2)*{F(
\backslash
overline x)};
\end_layout

\begin_layout Plain Layout

"3";"3'" **
\backslash
dir{-};
\end_layout

\begin_layout Plain Layout

(-2,6)*{}="X1";
\end_layout

\begin_layout Plain Layout

(-10,6)*{}="X2";
\end_layout

\begin_layout Plain Layout

"X1";"X2" **
\backslash
crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
\end_layout

\begin_layout Plain Layout

(-2,-6)*{}="XA";
\end_layout

\begin_layout Plain Layout

(-10,-6)*{}="XB";
\end_layout

\begin_layout Plain Layout

"XA";"XB" **
\backslash
crv{~*=<2pt>{.}(-2,1)&(-10,1)};
\end_layout

\begin_layout Plain Layout


\backslash
endxy
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Description
Categories
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
xymatrix{
\end_layout

\begin_layout Plain Layout

(x 
\backslash
otimes 1) 
\backslash
otimes y
\end_layout

\begin_layout Plain Layout


\backslash
ar[rr]^{a_{x,1,y}}
\end_layout

\begin_layout Plain Layout


\backslash
ar[dr]_{r_x 
\backslash
otimes 1_y}
\end_layout

\begin_layout Plain Layout

&& x 
\backslash
otimes(1 
\backslash
otimes y)
\end_layout

\begin_layout Plain Layout


\backslash
ar[dl]^{1_x 
\backslash
otimes
\backslash
ell_y } 
\backslash

\backslash

\end_layout

\begin_layout Plain Layout

& x 
\backslash
otimes y }
\end_layout

\end_inset


\end_layout

\end_inset

 
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
xy
\end_layout

\begin_layout Plain Layout

(-9,0)*+{
\backslash
bullet}="1";
\end_layout

\begin_layout Plain Layout

(0,0)*+{
\backslash
bullet}="2";
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/^.9pc/ "1";"2"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.9pc/ "1";"2"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/^2pc/ "1";"2"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_2pc/ "1";"2"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
\end_layout

\begin_layout Plain Layout

(0,0)*+{
\backslash
bullet}="1";
\end_layout

\begin_layout Plain Layout

(9,0)*+{
\backslash
bullet}="2";
\end_layout

\begin_layout Plain Layout

(18,0)*+{
\backslash
bullet}="3";
\end_layout

\begin_layout Plain Layout

{
\backslash
ar "1";"2"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar "2";"3"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/^1pc/ "1";"2"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_1pc/ "1";"2"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
\end_layout

\begin_layout Plain Layout


\backslash
endxy 
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Description
Transformations
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
xy %FIG.19.
 Natural transformation between functors.
\end_layout

\begin_layout Plain Layout

(-26,-2)*+{
\backslash
bullet}="a";
\end_layout

\begin_layout Plain Layout

(-12,3)*+{
\backslash
bullet}="b";
\end_layout

\begin_layout Plain Layout

(-16,-5)*+{
\backslash
bullet}="c";
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/^.25pc/ "a";"b"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.25pc/"a";"c"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.15pc/ "b";"c"};
\end_layout

\begin_layout Plain Layout

%START TOP
\end_layout

\begin_layout Plain Layout

(12,10)*+{
\backslash
bullet}="ta";
\end_layout

\begin_layout Plain Layout

(26,15)*+{
\backslash
bullet}="tb";
\end_layout

\begin_layout Plain Layout

(22,8)*+{
\backslash
bullet}="tc";
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/^.25pc/ "ta";"tb"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.25pc/ "ta";"tc"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.15pc/ "tb";"tc"};
\end_layout

\begin_layout Plain Layout

%START bottom
\end_layout

\begin_layout Plain Layout

(12,-10)*+{
\backslash
bullet}="ba";
\end_layout

\begin_layout Plain Layout

(26,-5)*+{
\backslash
bullet}="bb";
\end_layout

\begin_layout Plain Layout

(22,-12)*+{
\backslash
bullet}="bc";
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/^.25pc/@{.>} "ba";"bb"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.25pc/ "ba";"bc"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.15pc/ "bb";"bc"};
\end_layout

\begin_layout Plain Layout

%START CONNECT
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.15pc/ "ta";"ba"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.15pc/ "tb";"bb"};
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.15pc/ "tc";"bc"};
\end_layout

\begin_layout Plain Layout

%START ARROWS AND LABELS
\end_layout

\begin_layout Plain Layout

(-12,6)*{}="DF";
\end_layout

\begin_layout Plain Layout

(6,10)*{}="CF";
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/^.35pc/^F "DF";"CF"};
\end_layout

\begin_layout Plain Layout

(-12,-6)*{}="DF";
\end_layout

\begin_layout Plain Layout

(6,-10)*{}="CF";
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@/_.35pc/_G "DF";"CF"};
\end_layout

\begin_layout Plain Layout

(-2,5)*{}="DF";
\end_layout

\begin_layout Plain Layout

(-2,-5)*{}="CF";
\end_layout

\begin_layout Plain Layout

{
\backslash
ar@{=>}^{
\backslash
alpha} "DF";"CF"};
\end_layout

\begin_layout Plain Layout

(29,3)*{D};
\end_layout

\begin_layout Plain Layout

(-23,3)*{C};
\end_layout

\begin_layout Plain Layout


\backslash
endxy 
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Section
IPA
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
textipa{Ekspl@"neIS@n}
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Section
QTree
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ] 
\end_layout

\end_inset


\end_layout

\end_inset


\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
Tree [.$
\backslash
sigma$ $
\backslash
mu$ $
\backslash
mu$ ]
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Section
PSTricks
\begin_inset CommandInset label
LatexCommand label
name "sec:PSTricks"

\end_inset


\end_layout

\begin_layout Standard
Some simple graphing examples.
\end_layout

\begin_layout Subsection
Function plotting
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{pspicture*}(-1,-3.5)(10.5,3.5)
\end_layout

\begin_layout Plain Layout


\backslash
psaxes{->}(0,0)(0,-3)(10,3)
\end_layout

\begin_layout Plain Layout


\backslash
uput[-90](10,0){$x$}
\backslash
uput[0](0,3){$f(x)$}
\end_layout

\begin_layout Plain Layout


\backslash
psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
\end_layout

\begin_layout Plain Layout


\backslash
end{pspicture*}
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Inline data plotting
\end_layout

\begin_layout Standard
\align center
\begin_inset Preview

\begin_layout Standard
\align center
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{pspicture*}(-1.5,-1.5)(11,5)
\end_layout

\begin_layout Plain Layout


\backslash
psaxes{->}(0,0)(0,0)(10,5)
\end_layout

\begin_layout Plain Layout


\backslash
psset{linewidth=2.5pt}
\end_layout

\begin_layout Plain Layout


\backslash
rput(5.0,-1.0){Speed [MPH]}
\end_layout

\begin_layout Plain Layout


\backslash
rput(-1.0,1.0){
\backslash
begin{rotate}{90}Cost [Dollars]
\backslash
end{rotate}}
\end_layout

\begin_layout Plain Layout


\backslash
savedata{
\backslash
mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
\end_layout

\begin_layout Plain Layout


\backslash
dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
\backslash
mydata} 
\end_layout

\begin_layout Plain Layout


\backslash
end{pspicture*}
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsection
Lissajous curves
\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
\end_layout

\begin_layout Plain Layout


\backslash
parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
 cos 100 t mul sin}
\end_layout

\begin_layout Plain Layout


\backslash
end{pspicture*}
\end_layout

\end_inset


\end_layout

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
\end_layout

\begin_layout Plain Layout


\backslash
parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
 mul cos 100 t mul sin}
\end_layout

\begin_layout Plain Layout


\backslash
end{pspicture*}
\end_layout

\end_inset


\end_layout

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
\end_layout

\begin_layout Plain Layout


\backslash
parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
 mul cos 200 t mul sin}
\end_layout

\begin_layout Plain Layout


\backslash
end{pspicture*}
\end_layout

\end_inset


\end_layout

\end_inset


\begin_inset space \hfill{}
\end_inset


\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status open

\begin_layout Plain Layout


\backslash
begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
\end_layout

\begin_layout Plain Layout


\backslash
parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
 mul cos 200 t mul sin}
\end_layout

\begin_layout Plain Layout


\backslash
end{pspicture*}
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Section
TikZ
\end_layout

\begin_layout Standard
\begin_inset Flex URL
status collapsed

\begin_layout Plain Layout

http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
\end_layout

\end_inset


\end_layout

\begin_layout Standard
\begin_inset Preview

\begin_layout Standard
\begin_inset ERT
status collapsed

\begin_layout Plain Layout


\backslash
def
\backslash
iangle{35} % Angle of the inclined plane
\end_layout

\begin_layout Plain Layout


\backslash
def
\backslash
down{-90}
\end_layout

\begin_layout Plain Layout


\backslash
def
\backslash
arcr{0.5cm} % Radius of the arc used to indicate angles
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout


\backslash
begin{tikzpicture}[
\end_layout

\begin_layout Plain Layout

    force/.style={>=latex,draw=blue,fill=blue},
\end_layout

\begin_layout Plain Layout

    axis/.style={densely dashed,gray,font=
\backslash
small},
\end_layout

\begin_layout Plain Layout

    M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
\end_layout

\begin_layout Plain Layout

    m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
\end_layout

\begin_layout Plain Layout

    plane/.style={draw=black,fill=blue!10},
\end_layout

\begin_layout Plain Layout

    string/.style={draw=red, thick},
\end_layout

\begin_layout Plain Layout

    pulley/.style={thick},
\end_layout

\begin_layout Plain Layout

]
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout


\backslash
matrix[column sep=1cm] {
\end_layout

\begin_layout Plain Layout

    %% Sketch
\end_layout

\begin_layout Plain Layout

    
\backslash
draw[plane] (0,-1) coordinate (base)
\end_layout

\begin_layout Plain Layout

                     -- coordinate[pos=0.5] (mid) ++(
\backslash
iangle:3) coordinate (top)
\end_layout

\begin_layout Plain Layout

                     |- (base) -- cycle;
\end_layout

\begin_layout Plain Layout

    
\backslash
path (mid) node[M,rotate=
\backslash
iangle,yshift=0.25cm] (M) {};
\end_layout

\begin_layout Plain Layout

    
\backslash
draw[pulley] (top) -- ++(
\backslash
iangle:0.25) circle (0.25cm)
\end_layout

\begin_layout Plain Layout

                   ++ (90-
\backslash
iangle:0.5) coordinate (pulley);
\end_layout

\begin_layout Plain Layout

    
\backslash
draw[string] (M.east) -- ++(
\backslash
iangle:1.5cm) arc (90+
\backslash
iangle:0:0.25)
\end_layout

\begin_layout Plain Layout

                  -- ++(0,-1) node[m] {};
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout

    
\backslash
draw[->] (base)++(
\backslash
arcr,0) arc (0:
\backslash
iangle:
\backslash
arcr);
\end_layout

\begin_layout Plain Layout

    
\backslash
path (base)++(
\backslash
iangle*0.5:
\backslash
arcr+5pt) node {$
\backslash
alpha$};
\end_layout

\begin_layout Plain Layout

    %%
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout

&
\end_layout

\begin_layout Plain Layout

    %% Free body diagram of M
\end_layout

\begin_layout Plain Layout

    
\backslash
begin{scope}[rotate=
\backslash
iangle]
\end_layout

\begin_layout Plain Layout

        
\backslash
node[M,transform shape] (M) {};
\end_layout

\begin_layout Plain Layout

        % Draw axes and help lines
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout

        {[axis,->]
\end_layout

\begin_layout Plain Layout

            
\backslash
draw (0,-1) -- (0,2) node[right] {$+y$};
\end_layout

\begin_layout Plain Layout

            
\backslash
draw (M) -- ++(2,0) node[right] {$+x$};
\end_layout

\begin_layout Plain Layout

            % Indicate angle.
 The code is a bit awkward.
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout

            
\backslash
draw[solid,shorten >=0.5pt] (
\backslash
down-
\backslash
iangle:
\backslash
arcr)
\end_layout

\begin_layout Plain Layout

                arc(
\backslash
down-
\backslash
iangle:
\backslash
down:
\backslash
arcr);
\end_layout

\begin_layout Plain Layout

            
\backslash
node at (
\backslash
down-0.5*
\backslash
iangle:1.3*
\backslash
arcr) {$
\backslash
alpha$};
\end_layout

\begin_layout Plain Layout

        }
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout

        % Forces
\end_layout

\begin_layout Plain Layout

        {[force,->]
\end_layout

\begin_layout Plain Layout

            % Assuming that Mg = 1.
 The normal force will therefore be cos(alpha)
\end_layout

\begin_layout Plain Layout

            
\backslash
draw (M.center) -- ++(0,{cos(
\backslash
iangle)}) node[above right] {$N$};
\end_layout

\begin_layout Plain Layout

            
\backslash
draw (M.west) -- ++(-1,0) node[left] {$f_R$};
\end_layout

\begin_layout Plain Layout

            
\backslash
draw (M.east) -- ++(1,0) node[above] {$T$};
\end_layout

\begin_layout Plain Layout

        }
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout

    
\backslash
end{scope}
\end_layout

\begin_layout Plain Layout

    % Draw gravity force.
 The code is put outside the rotated
\end_layout

\begin_layout Plain Layout

    % scope for simplicity.
 No need to do any angle calculations.
 
\end_layout

\begin_layout Plain Layout

    
\backslash
draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
\end_layout

\begin_layout Plain Layout

    %%
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout

&
\end_layout

\begin_layout Plain Layout

    %%%
\end_layout

\begin_layout Plain Layout

    % Free body diagram of m
\end_layout

\begin_layout Plain Layout

    
\backslash
node[m] (m) {};
\end_layout

\begin_layout Plain Layout

    
\backslash
draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
\end_layout

\begin_layout Plain Layout

    {[force,->]
\end_layout

\begin_layout Plain Layout

        
\backslash
draw (m.north) -- ++(0,1) node[above] {$T'$};
\end_layout

\begin_layout Plain Layout

        
\backslash
draw (m.south) -- ++(0,-1) node[right] {$mg$};
\end_layout

\begin_layout Plain Layout

    }
\end_layout

\begin_layout Plain Layout

\end_layout

\begin_layout Plain Layout


\backslash

\backslash

\end_layout

\begin_layout Plain Layout

};
\end_layout

\begin_layout Plain Layout


\backslash
end{tikzpicture}
\end_layout

\begin_layout Plain Layout

\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\end_body
\end_document
