mirror of
https://git.lyx.org/repos/lyx.git
synced 2025-01-11 03:03:06 +00:00
a15303b938
Especially after the change to use semantic linefeeds (7b23c76b
),
the diffs are large and it's hard to figure out what diff is the
result of the linefeed change and which diff is the result of an
edit.
By updating the docs, it will make the edits easier to understand
from the diff.
This commit used the LyX binary to write the new .lyx files since
lyx2lyx does not apply semantic linefeeds.
I used the following command:
./development/tools/updatedocs.py [path to 'lyx' binary]
A few documents were not updated (e.g., the command sequence used
failed because a dialog about a missing dependency was shown).
I did not update Additional.lyx for any language since it is
undergoing changes. I also didn't change anything in doc/fr since JP
is working on some of those. I also didn't change doc/ru since it
appears Yuriy already updated those.
2553 lines
30 KiB
Plaintext
2553 lines
30 KiB
Plaintext
#LyX 2.4 created this file. For more info see https://www.lyx.org/
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\lyxformat 612
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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 article
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\begin_preamble
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\usepackage{etex}
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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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\usepackage{pstricks}
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\usepackage{pst-plot}
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\usepackage{rotating}
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\usepackage{tikz}
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\usetikzlibrary{scopes}
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\end_preamble
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\use_default_options false
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\maintain_unincluded_children no
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\language english
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\language_package default
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\inputencoding utf8
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\fontencoding auto
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\font_roman "lmodern" "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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\font_sans_osf false
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\font_tt_scale 100 100
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\default_output_format pdf
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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 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_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 false
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\justification true
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\use_refstyle 0
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\use_minted 0
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\use_lineno 0
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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 1
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\paperpagestyle default
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\tablestyle default
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\tracking_changes false
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\output_changes false
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\change_bars false
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\postpone_fragile_content false
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\html_math_output 0
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\html_be_strict true
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\docbook_table_output 0
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\docbook_mathml_prefix 1
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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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In order to properly typeset the document and have instant preview working,
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the following packages have to be installed:
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\end_layout
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\begin_layout LyX-Code
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xy,
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qtree,
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tipa,
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pstricks,
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pst-plot,
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rotating,
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tikz,
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pgf,
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etex
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\end_layout
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\begin_layout Standard
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Due to the use of postscript specials in Section
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "sec:PSTricks"
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nolink "false"
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\end_inset
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,
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only the Postscript or PDF (ps2pdf) output formats will correctly render the included images.
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Starting with TeX Live 2021,
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you may need to add the flag
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\family typewriter
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-dALLOWPSTRANSPARENCY
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\family default
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to the
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\family typewriter
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ps2pdf
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\family default
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converter.
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The PDF (Xe\SpecialChar TeX
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) output seems to also work,
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while trying to typeset the document with
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\family typewriter
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pdflatex
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\family default
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or
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\family typewriter
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pdflualatex
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\family default
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will generate errors.
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\end_layout
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\begin_layout Section
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Diagrams 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 examples,
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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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https://www.ctan.org/tex-archive/macros/generic/diagrams/xypic/doc/xyguide.pdf
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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)*{};
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(-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);
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(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)*{};
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"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";
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"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";
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"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";
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"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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(-6.5,8)*{}="1";
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(-.5,-9)*{}="2";
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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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(-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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\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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(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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\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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\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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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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\begin_layout Plain Layout
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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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\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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\end_layout
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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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\end_layout
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\begin_layout Plain Layout
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(-3,12)*{}="1";
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\end_layout
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\begin_layout Plain Layout
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(3,12)*{}="2";
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\end_layout
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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
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"1";"2" **
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\backslash
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crv{(-3,7) & (3,7)};
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\end_layout
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\begin_layout Plain Layout
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(-3,0)*{}="A";
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\end_layout
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\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
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\begin_layout Plain Layout
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(3,1)*{}="B1";
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\end_layout
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\begin_layout Plain Layout
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"A";"A1" **
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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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"B";"B1" **
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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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"B2";"B1" **
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\backslash
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crv{(8,7) & (3,5)};
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\end_layout
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\begin_layout Plain Layout
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"A2";"A1" **
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\backslash
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crv{(-8,7) & (-3,5)};
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\end_layout
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\begin_layout Plain Layout
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%REFLECT
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\end_layout
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\begin_layout Plain Layout
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(3,-16)*{}="1";
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\end_layout
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\begin_layout Plain Layout
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(9,-16)*{}="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{(3,-10) & (9,-10)};
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\end_layout
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\begin_layout Plain Layout
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(-3,-16)*{}="1";
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\end_layout
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\begin_layout Plain Layout
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(-9,-16)*{}="2";
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\end_layout
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\begin_layout Plain Layout
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|
"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
|