mirror of
https://git.lyx.org/repos/lyx.git
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1621 lines
18 KiB
Plaintext
1621 lines
18 KiB
Plaintext
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#LyX 2.0.0svn created this file. For more info see http://www.lyx.org/
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\lyxformat 381
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\begin_document
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\begin_header
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\textclass article
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\begin_preamble
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\usepackage[all, knot]{xy}
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\xyoption{arc}
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\usepackage{qtree}
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\usepackage{tipa}
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\end_preamble
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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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\inputencoding auto
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\fontencoding global
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\font_roman lmodern
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\font_sans default
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\font_typewriter default
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\font_default_family default
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\use_xetex false
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\font_sc false
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\font_osf false
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\font_sf_scale 100
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\font_tt_scale 100
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\graphics default
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\default_output_format default
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\bibtex_command default
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\index_command default
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\paperfontsize default
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\spacing single
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\use_hyperref false
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\papersize default
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\use_geometry false
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\use_amsmath 1
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\use_esint 1
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\use_mhchem 1
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\cite_engine basic
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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 false
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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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\quotes_language english
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\papercolumns 1
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\papersides 1
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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_be_strict true
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\end_header
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\begin_body
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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 following packages are needed to be installed at your computer in order
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to typeset the document properly and have instant preview working:
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\end_layout
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\begin_layout LyX-Code
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xy.sty, qtree.sty, tipa.sty
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\end_layout
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\begin_layout Section
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Diagrams from by XY(-pic)
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\end_layout
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\begin_layout Standard
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Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
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examples, see
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\begin_inset Flex URL
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status collapsed
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\begin_layout Plain Layout
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http://www.math.columbia.edu/~lauda/xy/
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\end_layout
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\end_inset
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.
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\end_layout
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\begin_layout Description
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Braid
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\end_layout
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\begin_layout Standard
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\begin_inset Preview
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\begin_layout Standard
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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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\begin_layout Plain Layout
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(5,10)*{}; (-10,-10)*{} **
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\backslash
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crv{(6,-2)&(-12,4)}
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\end_layout
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\begin_layout Plain Layout
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\backslash
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POS?(.25)*{
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\backslash
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hole}="x"
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\backslash
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POS?(.45)*{
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\backslash
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hole}="y"
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\backslash
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POS?(.6)*{
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\backslash
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hole}="z";
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\end_layout
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\begin_layout Plain Layout
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"y"+(0,-1); (2,-10)*{} **
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\backslash
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crv{}
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\backslash
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POS?(.2)*{
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\backslash
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hole}="M";
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\end_layout
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\begin_layout Plain Layout
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(-10,10)*{}; "z" **
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\backslash
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crv{(-9,0)};
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\end_layout
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\begin_layout Plain Layout
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"z"; "M" **
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\backslash
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crv{};
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\end_layout
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\begin_layout Plain Layout
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"M"; "x" **
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\backslash
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crv{(5,0)};
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\end_layout
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\begin_layout Plain Layout
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"x"; "y" **
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\backslash
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crv{(0,7) & (-5,6)};
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\end_layout
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\begin_layout Plain Layout
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\backslash
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endxy
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Description
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Knots
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\end_layout
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\begin_layout Standard
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\begin_inset Preview
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\begin_layout Standard
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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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\begin_layout Plain Layout
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(6,9)*{}="1";
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\end_layout
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\begin_layout Plain Layout
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(-8.5,-1)*{}="2";
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\end_layout
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\begin_layout Plain Layout
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"1";"2" **
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\backslash
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crv{~*=<.5pt>{.} (0,30)}?(.75)*
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\backslash
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dir{>}+(-2,2)*{z};
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\end_layout
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\begin_layout Plain Layout
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(-6.5,8)*{}="1";
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\end_layout
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\begin_layout Plain Layout
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(-.5,-9)*{}="2";
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\end_layout
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\begin_layout Plain Layout
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"1";"2" **
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\backslash
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crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
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\backslash
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dir{>}+(-2,-2)*{u};
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\end_layout
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\begin_layout Plain Layout
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(-9.5,-3.35)*{}="1";
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\end_layout
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\begin_layout Plain Layout
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(8.5,-3)*{}="2";
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\end_layout
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\begin_layout Plain Layout
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"1";"2" **
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\backslash
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crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
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\backslash
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dir{>}+(-1,-3)*{x};
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\end_layout
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\begin_layout Plain Layout
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(1,-10)*{}="1";
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\end_layout
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\begin_layout Plain Layout
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(6.5,7.13)*{}="2";
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\end_layout
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\begin_layout Plain Layout
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"1";"2" **
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\backslash
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crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
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\backslash
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dir{>}+(3,-1)*{y};
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\end_layout
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\begin_layout Plain Layout
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(11,-1)*{}="1";
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\end_layout
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\begin_layout Plain Layout
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(-4,8)*{}="2";
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\end_layout
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\begin_layout Plain Layout
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"1";"2" **
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\backslash
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crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
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\backslash
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dir{>}+(1,2)*{w};
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\end_layout
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\begin_layout Plain Layout
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\backslash
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endxy
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Description
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|
Circles
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\end_layout
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||
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|
\begin_layout Standard
|
||
|
\begin_inset Preview
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|
\begin_layout Standard
|
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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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\begin_layout Plain Layout
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(0,0)*
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\backslash
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xycircle(14,8){++
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\backslash
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dir{<}};
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\end_layout
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\begin_layout Plain Layout
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(0,0)*
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\backslash
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xycircle<10pt>{{.}};
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\end_layout
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\begin_layout Plain Layout
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(0,0)*
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\backslash
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xycircle(5,2){:};
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\end_layout
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\begin_layout Plain Layout
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(0,15)*
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\backslash
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xycircle(10,4){--};
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\end_layout
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\begin_layout Plain Layout
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\backslash
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endxy
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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||
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||
|
\begin_layout Description
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||
|
Cobordism
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|
\end_layout
|
||
|
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||
|
\begin_layout Standard
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||
|
\begin_inset Preview
|
||
|
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||
|
\begin_layout Standard
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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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\begin_layout Plain Layout
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(0,0)*
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\backslash
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ellipse(3,1){.};
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\end_layout
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\begin_layout Plain Layout
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(0,0)*
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\backslash
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ellipse(3,1)__,=:a(-180){-};
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\end_layout
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\begin_layout Plain Layout
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(-6,-8)*
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\backslash
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ellipse(3,1){.};
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\end_layout
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\begin_layout Plain Layout
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(6,-8)*
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\backslash
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ellipse(3,1){.};
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\end_layout
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\begin_layout Plain Layout
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(0,-8)*
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\backslash
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ellipse(3,1){.};
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\end_layout
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\begin_layout Plain Layout
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(-6,-8)*
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\backslash
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ellipse(3,1)__,=:a(-180){-};
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\end_layout
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\begin_layout Plain Layout
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(6,-8)*
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\backslash
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ellipse(3,1)__,=:a(-180){-};
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\end_layout
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||
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||
|
\begin_layout Plain Layout
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||
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(0,-8)*
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\backslash
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ellipse(3,1)__,=:a(180){-};
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\end_layout
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||
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||
|
\begin_layout Plain Layout
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||
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(-3,6)*
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\backslash
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ellipse(3,1){-};
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||
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\end_layout
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||
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||
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\begin_layout Plain Layout
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(3,6)*
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\backslash
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ellipse(3,1){-};
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||
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\end_layout
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||
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||
|
\begin_layout Plain Layout
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|
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||
|
(-3,12)*{}="1";
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||
|
\end_layout
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||
|
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||
|
\begin_layout Plain Layout
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||
|
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||
|
(3,12)*{}="2";
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||
|
\end_layout
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||
|
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||
|
\begin_layout Plain Layout
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||
|
(-9,12)*{}="A2";
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||
|
\end_layout
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||
|
|
||
|
\begin_layout Plain Layout
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||
|
|
||
|
(9,12)*{}="B2";
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||
|
\end_layout
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||
|
|
||
|
\begin_layout Plain Layout
|
||
|
|
||
|
"1";"2" **
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||
|
\backslash
|
||
|
crv{(-3,7) & (3,7)};
|
||
|
\end_layout
|
||
|
|
||
|
\begin_layout Plain Layout
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||
|
|
||
|
(-3,0)*{}="A";
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||
|
\end_layout
|
||
|
|
||
|
\begin_layout Plain Layout
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||
|
|
||
|
(3,0)*{}="B";
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||
|
\end_layout
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||
|
|
||
|
\begin_layout Plain Layout
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||
|
|
||
|
(-3,1)*{}="A1";
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||
|
\end_layout
|
||
|
|
||
|
\begin_layout Plain Layout
|
||
|
|
||
|
(3,1)*{}="B1";
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||
|
\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
|
||
|
|
||
|
\end_body
|
||
|
\end_document
|