1 #LyX 2.2 created this file. For more info see http://www.lyx.org/
5 \origin /systemlyxdir/examples/
9 \usepackage[all, knot]{xy}
17 \usetikzlibrary{scopes}
19 \use_default_options false
20 \maintain_unincluded_children false
22 \language_package default
25 \font_roman "lmodern" "default"
26 \font_sans "default" "default"
27 \font_typewriter "default" "default"
28 \font_math "auto" "auto"
29 \font_default_family default
30 \use_non_tex_fonts false
33 \font_sf_scale 100 100
34 \font_tt_scale 100 100
36 \default_output_format pdf
38 \bibtex_command default
39 \index_command default
40 \paperfontsize default
45 \use_package amsmath 1
46 \use_package amssymb 1
49 \use_package mathdots 1
50 \use_package mathtools 0
52 \use_package stackrel 0
53 \use_package stmaryrd 0
54 \use_package undertilde 0
56 \cite_engine_type default
60 \paperorientation portrait
70 \paragraph_separation indent
71 \paragraph_indentation default
72 \quotes_language english
75 \paperpagestyle default
76 \tracking_changes false
89 \begin_layout Standard
90 In order to properly typeset the document and have instant preview working,
91 the following packages have to be installed:
94 \begin_layout LyX-Code
95 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf, etex
98 \begin_layout Standard
99 Due to the use of postscript specials in Section
100 \begin_inset CommandInset ref
102 reference "sec:PSTricks"
106 , only the Postscript or PDF (ps2pdf) output formats will correctly render
108 However, the PDF (Xe\SpecialCharNoPassThru TeX
109 ) output seems to also work, while trying to typeset
118 will generate errors.
121 \begin_layout Section
125 \begin_layout Standard
126 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
128 \begin_inset Flex URL
131 \begin_layout Plain Layout
133 http://www.math.columbia.edu/~lauda/xy/
141 \begin_layout Description
145 \begin_layout Standard
148 \begin_layout Standard
152 \begin_layout Plain Layout
159 \begin_layout Plain Layout
161 (5,10)*{}; (-10,-10)*{} **
166 \begin_layout Plain Layout
183 \begin_layout Plain Layout
185 "y"+(0,-1); (2,-10)*{} **
194 \begin_layout Plain Layout
201 \begin_layout Plain Layout
208 \begin_layout Plain Layout
215 \begin_layout Plain Layout
222 \begin_layout Plain Layout
239 \begin_layout Description
243 \begin_layout Standard
246 \begin_layout Standard
250 \begin_layout Plain Layout
257 \begin_layout Plain Layout
262 \begin_layout Plain Layout
267 \begin_layout Plain Layout
271 crv{~*=<.5pt>{.} (0,30)}?(.75)*
276 \begin_layout Plain Layout
281 \begin_layout Plain Layout
286 \begin_layout Plain Layout
290 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
295 \begin_layout Plain Layout
300 \begin_layout Plain Layout
305 \begin_layout Plain Layout
309 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
314 \begin_layout Plain Layout
319 \begin_layout Plain Layout
324 \begin_layout Plain Layout
328 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
333 \begin_layout Plain Layout
338 \begin_layout Plain Layout
343 \begin_layout Plain Layout
347 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
352 \begin_layout Plain Layout
369 \begin_layout Description
373 \begin_layout Standard
376 \begin_layout Standard
380 \begin_layout Plain Layout
387 \begin_layout Plain Layout
396 \begin_layout Plain Layout
403 \begin_layout Plain Layout
410 \begin_layout Plain Layout
417 \begin_layout Plain Layout
434 \begin_layout Description
438 \begin_layout Standard
441 \begin_layout Standard
445 \begin_layout Plain Layout
452 \begin_layout Plain Layout
459 \begin_layout Plain Layout
463 ellipse(3,1)__,=:a(-180){-};
466 \begin_layout Plain Layout
473 \begin_layout Plain Layout
480 \begin_layout Plain Layout
487 \begin_layout Plain Layout
491 ellipse(3,1)__,=:a(-180){-};
494 \begin_layout Plain Layout
498 ellipse(3,1)__,=:a(-180){-};
501 \begin_layout Plain Layout
505 ellipse(3,1)__,=:a(180){-};
508 \begin_layout Plain Layout
515 \begin_layout Plain Layout
522 \begin_layout Plain Layout
527 \begin_layout Plain Layout
532 \begin_layout Plain Layout
537 \begin_layout Plain Layout
542 \begin_layout Plain Layout
549 \begin_layout Plain Layout
554 \begin_layout Plain Layout
559 \begin_layout Plain Layout
564 \begin_layout Plain Layout
569 \begin_layout Plain Layout
576 \begin_layout Plain Layout
583 \begin_layout Plain Layout
590 \begin_layout Plain Layout
594 crv{(-8,7) & (-3,5)};
597 \begin_layout Plain Layout
602 \begin_layout Plain Layout
607 \begin_layout Plain Layout
612 \begin_layout Plain Layout
616 crv{(3,-10) & (9,-10)};
619 \begin_layout Plain Layout
624 \begin_layout Plain Layout
629 \begin_layout Plain Layout
633 crv{(-3,-10) & (-9,-10)};
636 \begin_layout Plain Layout
641 \begin_layout Plain Layout
646 \begin_layout Plain Layout
651 \begin_layout Plain Layout
656 \begin_layout Plain Layout
661 \begin_layout Plain Layout
666 \begin_layout Plain Layout
673 \begin_layout Plain Layout
680 \begin_layout Plain Layout
684 crv{(13,-6) & (2,-8)};
687 \begin_layout Plain Layout
691 crv{(-13,-6) & (-2,-8)};
694 \begin_layout Plain Layout
711 \begin_layout Standard
715 \begin_layout Plain Layout
722 \begin_layout Plain Layout
726 bullet}="RU"+(1,3)*{x^{
731 \begin_layout Plain Layout
735 bullet}="RD"+(2.5,2)*{x^{
740 \begin_layout Plain Layout
744 bullet}="LU"+(-1,2)*{x};
747 \begin_layout Plain Layout
751 bullet}="LD"+(-1,2)*{x};
754 \begin_layout Plain Layout
758 crv{(4,2) & (4,-1)}; ?(.1)*
765 \begin_layout Plain Layout
769 crv{(-4,-2) & (-4,1)};
772 \begin_layout Plain Layout
781 \begin_layout Plain Layout
783 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
786 \begin_layout Plain Layout
790 crv{(7,-10) & (-7,-10)};
793 \begin_layout Plain Layout
797 bullet}="RDD"+(2.5,-1)*{x^{
802 \begin_layout Plain Layout
806 bullet}="LDD"+(-1,-3)*{x};
809 \begin_layout Plain Layout
813 bullet}="RUD"+(3.5,1)*{x^{
818 \begin_layout Plain Layout
825 \begin_layout Plain Layout
827 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
830 \begin_layout Plain Layout
837 \begin_layout Plain Layout
844 \begin_layout Plain Layout
851 \begin_layout Plain Layout
855 crv{(0,-17)}; ?(.57)*
860 \begin_layout Plain Layout
867 \begin_layout Plain Layout
874 \begin_layout Plain Layout
881 \begin_layout Plain Layout
885 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
890 \begin_layout Plain Layout
907 \begin_layout Description
911 \begin_layout Standard
914 \begin_layout Standard
918 \begin_layout Plain Layout
922 xy (-15,0)*{};(15,0)*{};
925 \begin_layout Plain Layout
932 \begin_layout Plain Layout
943 \begin_layout Plain Layout
945 (-10,12)*{}; (-10,-12)*{}; **
949 dir{<}+(-4,0)*{F(x)};
952 \begin_layout Plain Layout
957 \begin_layout Plain Layout
962 \begin_layout Plain Layout
967 \begin_layout Plain Layout
972 \begin_layout Plain Layout
977 \begin_layout Plain Layout
981 crv{(-4,-21)&(5,-15)};
984 \begin_layout Plain Layout
993 \begin_layout Plain Layout
1000 \begin_layout Plain Layout
1006 widetilde{F(i_x)}} ;
1009 \begin_layout Plain Layout
1018 \begin_layout Plain Layout
1025 \begin_layout Plain Layout
1030 \begin_layout Plain Layout
1035 \begin_layout Plain Layout
1039 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1042 \begin_layout Plain Layout
1047 \begin_layout Plain Layout
1052 \begin_layout Plain Layout
1056 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1059 \begin_layout Plain Layout
1076 \begin_layout Description
1080 \begin_layout Standard
1081 \begin_inset Preview
1083 \begin_layout Standard
1087 \begin_layout Plain Layout
1094 \begin_layout Plain Layout
1103 \begin_layout Plain Layout
1110 \begin_layout Plain Layout
1119 \begin_layout Plain Layout
1128 \begin_layout Plain Layout
1143 \begin_layout Plain Layout
1158 \begin_inset Preview
1160 \begin_layout Standard
1164 \begin_layout Plain Layout
1171 \begin_layout Plain Layout
1178 \begin_layout Plain Layout
1185 \begin_layout Plain Layout
1189 ar@/^.9pc/ "1";"2"};
1192 \begin_layout Plain Layout
1196 ar@/_.9pc/ "1";"2"};
1199 \begin_layout Plain Layout
1206 \begin_layout Plain Layout
1213 \begin_layout Plain Layout
1217 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1220 \begin_layout Plain Layout
1224 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1227 \begin_layout Plain Layout
1231 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1234 \begin_layout Plain Layout
1241 \begin_layout Plain Layout
1248 \begin_layout Plain Layout
1255 \begin_layout Plain Layout
1262 \begin_layout Plain Layout
1269 \begin_layout Plain Layout
1276 \begin_layout Plain Layout
1283 \begin_layout Plain Layout
1287 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1290 \begin_layout Plain Layout
1294 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1297 \begin_layout Plain Layout
1314 \begin_layout Description
1318 \begin_layout Standard
1319 \begin_inset Preview
1321 \begin_layout Standard
1325 \begin_layout Plain Layout
1330 Natural transformation between functors.
1333 \begin_layout Plain Layout
1340 \begin_layout Plain Layout
1347 \begin_layout Plain Layout
1354 \begin_layout Plain Layout
1358 ar@/^.25pc/ "a";"b"};
1361 \begin_layout Plain Layout
1365 ar@/_.25pc/"a";"c"};
1368 \begin_layout Plain Layout
1372 ar@/_.15pc/ "b";"c"};
1375 \begin_layout Plain Layout
1380 \begin_layout Plain Layout
1387 \begin_layout Plain Layout
1394 \begin_layout Plain Layout
1401 \begin_layout Plain Layout
1405 ar@/^.25pc/ "ta";"tb"};
1408 \begin_layout Plain Layout
1412 ar@/_.25pc/ "ta";"tc"};
1415 \begin_layout Plain Layout
1419 ar@/_.15pc/ "tb";"tc"};
1422 \begin_layout Plain Layout
1427 \begin_layout Plain Layout
1434 \begin_layout Plain Layout
1441 \begin_layout Plain Layout
1448 \begin_layout Plain Layout
1452 ar@/^.25pc/@{.>} "ba";"bb"};
1455 \begin_layout Plain Layout
1459 ar@/_.25pc/ "ba";"bc"};
1462 \begin_layout Plain Layout
1466 ar@/_.15pc/ "bb";"bc"};
1469 \begin_layout Plain Layout
1474 \begin_layout Plain Layout
1478 ar@/_.15pc/ "ta";"ba"};
1481 \begin_layout Plain Layout
1485 ar@/_.15pc/ "tb";"bb"};
1488 \begin_layout Plain Layout
1492 ar@/_.15pc/ "tc";"bc"};
1495 \begin_layout Plain Layout
1497 %START ARROWS AND LABELS
1500 \begin_layout Plain Layout
1505 \begin_layout Plain Layout
1510 \begin_layout Plain Layout
1514 ar@/^.35pc/^F "DF";"CF"};
1517 \begin_layout Plain Layout
1522 \begin_layout Plain Layout
1527 \begin_layout Plain Layout
1531 ar@/_.35pc/_G "DF";"CF"};
1534 \begin_layout Plain Layout
1539 \begin_layout Plain Layout
1544 \begin_layout Plain Layout
1553 \begin_layout Plain Layout
1558 \begin_layout Plain Layout
1563 \begin_layout Plain Layout
1580 \begin_layout Section
1584 \begin_layout Standard
1585 \begin_inset Preview
1587 \begin_layout Standard
1591 \begin_layout Plain Layout
1595 textipa{Ekspl@"neIS@n}
1608 \begin_layout Section
1612 \begin_layout Standard
1613 \begin_inset Preview
1615 \begin_layout Standard
1619 \begin_layout Plain Layout
1623 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1634 \begin_inset Preview
1636 \begin_layout Standard
1640 \begin_layout Plain Layout
1663 \begin_layout Section
1665 \begin_inset CommandInset label
1674 \begin_layout Standard
1675 Some simple graphing examples.
1678 \begin_layout Subsection
1682 \begin_layout Standard
1683 \begin_inset Preview
1685 \begin_layout Standard
1689 \begin_layout Plain Layout
1693 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1696 \begin_layout Plain Layout
1700 psaxes{->}(0,0)(0,-3)(10,3)
1703 \begin_layout Plain Layout
1707 uput[-90](10,0){$x$}
1709 uput[0](0,3){$f(x)$}
1712 \begin_layout Plain Layout
1716 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1719 \begin_layout Plain Layout
1736 \begin_layout Subsection
1737 Inline data plotting
1740 \begin_layout Standard
1742 \begin_inset Preview
1744 \begin_layout Standard
1749 \begin_layout Plain Layout
1753 begin{pspicture*}(-1.5,-1.5)(11,5)
1756 \begin_layout Plain Layout
1760 psaxes{->}(0,0)(0,0)(10,5)
1763 \begin_layout Plain Layout
1767 psset{linewidth=2.5pt}
1770 \begin_layout Plain Layout
1774 rput(5.0,-1.0){Speed [MPH]}
1777 \begin_layout Plain Layout
1783 begin{rotate}{90}Cost [Dollars]
1788 \begin_layout Plain Layout
1794 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1797 \begin_layout Plain Layout
1801 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1806 \begin_layout Plain Layout
1823 \begin_layout Subsection
1827 \begin_layout Standard
1828 \begin_inset Preview
1830 \begin_layout Standard
1834 \begin_layout Plain Layout
1838 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1841 \begin_layout Plain Layout
1845 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1849 \begin_layout Plain Layout
1864 \begin_inset space \hfill{}
1868 \begin_inset Preview
1870 \begin_layout Standard
1874 \begin_layout Plain Layout
1878 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1881 \begin_layout Plain Layout
1885 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1886 mul cos 100 t mul sin}
1889 \begin_layout Plain Layout
1904 \begin_inset space \hfill{}
1908 \begin_inset Preview
1910 \begin_layout Standard
1914 \begin_layout Plain Layout
1918 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1921 \begin_layout Plain Layout
1925 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1926 mul cos 200 t mul sin}
1929 \begin_layout Plain Layout
1944 \begin_inset space \hfill{}
1948 \begin_inset Preview
1950 \begin_layout Standard
1954 \begin_layout Plain Layout
1958 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1961 \begin_layout Plain Layout
1965 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1966 mul cos 200 t mul sin}
1969 \begin_layout Plain Layout
1986 \begin_layout Section
1990 \begin_layout Standard
1991 \begin_inset Flex URL
1994 \begin_layout Plain Layout
1996 http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
2004 \begin_layout Standard
2005 \begin_inset Preview
2007 \begin_layout Standard
2011 \begin_layout Plain Layout
2017 iangle{35} % Angle of the inclined plane
2020 \begin_layout Plain Layout
2029 \begin_layout Plain Layout
2035 arcr{0.5cm} % Radius of the arc used to indicate angles
2038 \begin_layout Plain Layout
2042 \begin_layout Plain Layout
2049 \begin_layout Plain Layout
2051 force/.style={>=latex,draw=blue,fill=blue},
2054 \begin_layout Plain Layout
2056 axis/.style={densely dashed,gray,font=
2061 \begin_layout Plain Layout
2063 M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2066 \begin_layout Plain Layout
2068 m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2071 \begin_layout Plain Layout
2073 plane/.style={draw=black,fill=blue!10},
2076 \begin_layout Plain Layout
2078 string/.style={draw=red, thick},
2081 \begin_layout Plain Layout
2083 pulley/.style={thick},
2086 \begin_layout Plain Layout
2091 \begin_layout Plain Layout
2095 \begin_layout Plain Layout
2099 matrix[column sep=1cm] {
2102 \begin_layout Plain Layout
2107 \begin_layout Plain Layout
2111 draw[plane] (0,-1) coordinate (base)
2114 \begin_layout Plain Layout
2116 -- coordinate[pos=0.5] (mid) ++(
2118 iangle:3) coordinate (top)
2121 \begin_layout Plain Layout
2126 \begin_layout Plain Layout
2130 path (mid) node[M,rotate=
2132 iangle,yshift=0.25cm] (M) {};
2135 \begin_layout Plain Layout
2139 draw[pulley] (top) -- ++(
2141 iangle:0.25) circle (0.25cm)
2144 \begin_layout Plain Layout
2148 iangle:0.5) coordinate (pulley);
2151 \begin_layout Plain Layout
2155 draw[string] (M.east) -- ++(
2157 iangle:1.5cm) arc (90+
2162 \begin_layout Plain Layout
2164 -- ++(0,-1) node[m] {};
2167 \begin_layout Plain Layout
2171 \begin_layout Plain Layout
2184 \begin_layout Plain Layout
2197 \begin_layout Plain Layout
2202 \begin_layout Plain Layout
2206 \begin_layout Plain Layout
2211 \begin_layout Plain Layout
2213 %% Free body diagram of M
2216 \begin_layout Plain Layout
2220 begin{scope}[rotate=
2225 \begin_layout Plain Layout
2229 node[M,transform shape] (M) {};
2232 \begin_layout Plain Layout
2234 % Draw axes and help lines
2237 \begin_layout Plain Layout
2241 \begin_layout Plain Layout
2246 \begin_layout Plain Layout
2250 draw (0,-1) -- (0,2) node[right] {$+y$};
2253 \begin_layout Plain Layout
2257 draw (M) -- ++(2,0) node[right] {$+x$};
2260 \begin_layout Plain Layout
2263 The code is a bit awkward.
2266 \begin_layout Plain Layout
2270 \begin_layout Plain Layout
2274 draw[solid,shorten >=0.5pt] (
2283 \begin_layout Plain Layout
2296 \begin_layout Plain Layout
2311 \begin_layout Plain Layout
2316 \begin_layout Plain Layout
2320 \begin_layout Plain Layout
2325 \begin_layout Plain Layout
2330 \begin_layout Plain Layout
2332 % Assuming that Mg = 1.
2333 The normal force will therefore be cos(alpha)
2336 \begin_layout Plain Layout
2340 draw (M.center) -- ++(0,{cos(
2342 iangle)}) node[above right] {$N$};
2345 \begin_layout Plain Layout
2349 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2352 \begin_layout Plain Layout
2356 draw (M.east) -- ++(1,0) node[above] {$T$};
2359 \begin_layout Plain Layout
2364 \begin_layout Plain Layout
2368 \begin_layout Plain Layout
2375 \begin_layout Plain Layout
2377 % Draw gravity force.
2378 The code is put outside the rotated
2381 \begin_layout Plain Layout
2383 % scope for simplicity.
2384 No need to do any angle calculations.
2388 \begin_layout Plain Layout
2392 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2395 \begin_layout Plain Layout
2400 \begin_layout Plain Layout
2404 \begin_layout Plain Layout
2409 \begin_layout Plain Layout
2414 \begin_layout Plain Layout
2416 % Free body diagram of m
2419 \begin_layout Plain Layout
2426 \begin_layout Plain Layout
2430 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2433 \begin_layout Plain Layout
2438 \begin_layout Plain Layout
2442 draw (m.north) -- ++(0,1) node[above] {$T'$};
2445 \begin_layout Plain Layout
2449 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2452 \begin_layout Plain Layout
2457 \begin_layout Plain Layout
2461 \begin_layout Plain Layout
2470 \begin_layout Plain Layout
2475 \begin_layout Plain Layout
2482 \begin_layout Plain Layout