lib/examples/Graphics_and_Insets/Instant_Preview.lyx

   1 #LyX 2.4 created this file. For more info see https://www.lyx.org/
   2 \lyxformat 612
   3 \begin_document
   4 \begin_header
   5 \save_transient_properties true
   6 \origin /systemlyxdir/examples/Graphics_and_Insets/
   7 \textclass article
   8 \begin_preamble
   9 \usepackage{etex}
  10 \usepackage[all, knot]{xy}
  11 \xyoption{arc}
  12 \usepackage{qtree}
  13 \usepackage{tipa}
  14 \usepackage{pstricks}
  15 \usepackage{pst-plot}
  16 \usepackage{rotating}
  17 \usepackage{tikz}
  18 \usetikzlibrary{scopes}
  19 \end_preamble
  20 \use_default_options false
  21 \maintain_unincluded_children no
  22 \language english
  23 \language_package default
  24 \inputencoding utf8
  25 \fontencoding auto
  26 \font_roman "lmodern" "default"
  27 \font_sans "default" "default"
  28 \font_typewriter "default" "default"
  29 \font_math "auto" "auto"
  30 \font_default_family default
  31 \use_non_tex_fonts false
  32 \font_sc false
  33 \font_roman_osf false
  34 \font_sans_osf false
  35 \font_typewriter_osf false
  36 \font_sf_scale 100 100
  37 \font_tt_scale 100 100
  38 \use_microtype false
  39 \use_dash_ligatures false
  40 \graphics default
  41 \default_output_format pdf
  42 \output_sync 0
  43 \bibtex_command default
  44 \index_command default
  45 \paperfontsize default
  46 \spacing single
  47 \use_hyperref false
  48 \papersize default
  49 \use_geometry false
  50 \use_package amsmath 1
  51 \use_package amssymb 1
  52 \use_package cancel 1
  53 \use_package esint 1
  54 \use_package mathdots 1
  55 \use_package mathtools 1
  56 \use_package mhchem 1
  57 \use_package stackrel 1
  58 \use_package stmaryrd 1
  59 \use_package undertilde 1
  60 \cite_engine basic
  61 \cite_engine_type default
  62 \biblio_style plain
  63 \use_bibtopic false
  64 \use_indices false
  65 \paperorientation portrait
  66 \suppress_date false
  67 \justification true
  68 \use_refstyle 0
  69 \use_minted 0
  70 \use_lineno 0
  71 \index Index
  72 \shortcut idx
  73 \color #008000
  74 \end_index
  75 \secnumdepth 3
  76 \tocdepth 3
  77 \paragraph_separation indent
  78 \paragraph_indentation default
  79 \is_math_indent 0
  80 \math_numbering_side default
  81 \quotes_style english
  82 \dynamic_quotes 0
  83 \papercolumns 1
  84 \papersides 1
  85 \paperpagestyle default
  86 \tablestyle default
  87 \tracking_changes false
  88 \output_changes false
  89 \change_bars false
  90 \postpone_fragile_content false
  91 \html_math_output 0
  92 \html_css_as_file 0
  93 \html_be_strict true
  94 \docbook_table_output 0
  95 \docbook_mathml_prefix 1
  96 \end_header
  97
  98 \begin_body
  99
 100 \begin_layout Section
 101 Introduction
 102 \end_layout
 103
 104 \begin_layout Standard
 105 In order to properly typeset the document and have instant preview working,
 106  the following packages have to be installed:
 107 \end_layout
 108
 109 \begin_layout LyX-Code
 110 xy,
 111  qtree,
 112  tipa,
 113  pstricks,
 114  pst-plot,
 115  rotating,
 116  tikz,
 117  pgf,
 118  etex
 119 \end_layout
 120
 121 \begin_layout Standard
 122 Due to the use of postscript specials in Section
 123 \begin_inset CommandInset ref
 124 LatexCommand ref
 125 reference "sec:PSTricks"
 126 nolink "false"
 127
 128 \end_inset
 129
 130 ,
 131  only the Postscript or PDF (ps2pdf) output formats will correctly render the included images.
 132  Starting with TeX Live 2021,
 133  you may need to add the flag
 134 \family typewriter
 135 -dALLOWPSTRANSPARENCY
 136 \family default
 137  to the
 138 \family typewriter
 139 ps2pdf
 140 \family default
 141  converter.
 142  The PDF (Xe\SpecialChar TeX
 143 ) output seems to also work,
 144  while trying to typeset the document with
 145 \family typewriter
 146 pdflatex
 147 \family default
 148  or
 149 \family typewriter
 150 pdflualatex
 151 \family default
 152  will generate errors.
 153 \end_layout
 154
 155 \begin_layout Section
 156 Diagrams by XY(-pic)
 157 \end_layout
 158
 159 \begin_layout Standard
 160 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic examples,
 161  see
 162 \begin_inset Flex URL
 163 status collapsed
 164
 165 \begin_layout Plain Layout
 166
 167 https://www.ctan.org/tex-archive/macros/generic/diagrams/xypic/doc/xyguide.pdf
 168 \end_layout
 169
 170 \end_inset
 171
 172 .
 173 \end_layout
 174
 175 \begin_layout Description
 176 Braid
 177 \end_layout
 178
 179 \begin_layout Standard
 180 \begin_inset Preview
 181
 182 \begin_layout Standard
 183 \begin_inset ERT
 184 status collapsed
 185
 186 \begin_layout Plain Layout
 187
 188
 189 \backslash
 190 xy
 191 \end_layout
 192
 193 \begin_layout Plain Layout
 194
 195 (5,10)*{};
 196  (-10,-10)*{} **
 197 \backslash
 198 crv{(6,-2)&(-12,4)}
 199 \end_layout
 200
 201 \begin_layout Plain Layout
 202
 203
 204 \backslash
 205 POS?(.25)*{
 206 \backslash
 207 hole}="x"
 208 \backslash
 209 POS?(.45)*{
 210 \backslash
 211 hole}="y"
 212 \backslash
 213 POS?(.6)*{
 214 \backslash
 215 hole}="z";
 216 \end_layout
 217
 218 \begin_layout Plain Layout
 219
 220 "y"+(0,-1);
 221  (2,-10)*{} **
 222 \backslash
 223 crv{}
 224 \backslash
 225 POS?(.2)*{
 226 \backslash
 227 hole}="M";
 228 \end_layout
 229
 230 \begin_layout Plain Layout
 231
 232 (-10,10)*{};
 233  "z" **
 234 \backslash
 235 crv{(-9,0)};
 236 \end_layout
 237
 238 \begin_layout Plain Layout
 239
 240 "z";
 241  "M" **
 242 \backslash
 243 crv{};
 244 \end_layout
 245
 246 \begin_layout Plain Layout
 247
 248 "M";
 249  "x" **
 250 \backslash
 251 crv{(5,0)};
 252 \end_layout
 253
 254 \begin_layout Plain Layout
 255
 256 "x";
 257  "y" **
 258 \backslash
 259 crv{(0,7) & (-5,6)};
 260 \end_layout
 261
 262 \begin_layout Plain Layout
 263
 264
 265 \backslash
 266 endxy
 267 \end_layout
 268
 269 \end_inset
 270
 271
 272 \end_layout
 273
 274 \end_inset
 275
 276
 277 \end_layout
 278
 279 \begin_layout Description
 280 Knots
 281 \end_layout
 282
 283 \begin_layout Standard
 284 \begin_inset Preview
 285
 286 \begin_layout Standard
 287 \begin_inset ERT
 288 status collapsed
 289
 290 \begin_layout Plain Layout
 291
 292
 293 \backslash
 294 xy
 295 \end_layout
 296
 297 \begin_layout Plain Layout
 298
 299 (6,9)*{}="1";
 300 \end_layout
 301
 302 \begin_layout Plain Layout
 303
 304 (-8.5,-1)*{}="2";
 305 \end_layout
 306
 307 \begin_layout Plain Layout
 308
 309 "1";"2" **
 310 \backslash
 311 crv{~*=<.5pt>{.} (0,30)}?(.75)*
 312 \backslash
 313 dir{>}+(-2,2)*{z};
 314 \end_layout
 315
 316 \begin_layout Plain Layout
 317
 318 (-6.5,8)*{}="1";
 319 \end_layout
 320
 321 \begin_layout Plain Layout
 322
 323 (-.5,-9)*{}="2";
 324 \end_layout
 325
 326 \begin_layout Plain Layout
 327
 328 "1";"2" **
 329 \backslash
 330 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
 331 \backslash
 332 dir{>}+(-2,-2)*{u};
 333 \end_layout
 334
 335 \begin_layout Plain Layout
 336
 337 (-9.5,-3.35)*{}="1";
 338 \end_layout
 339
 340 \begin_layout Plain Layout
 341
 342 (8.5,-3)*{}="2";
 343 \end_layout
 344
 345 \begin_layout Plain Layout
 346
 347 "1";"2" **
 348 \backslash
 349 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
 350 \backslash
 351 dir{>}+(-1,-3)*{x};
 352 \end_layout
 353
 354 \begin_layout Plain Layout
 355
 356 (1,-10)*{}="1";
 357 \end_layout
 358
 359 \begin_layout Plain Layout
 360
 361 (6.5,7.13)*{}="2";
 362 \end_layout
 363
 364 \begin_layout Plain Layout
 365
 366 "1";"2" **
 367 \backslash
 368 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
 369 \backslash
 370 dir{>}+(3,-1)*{y};
 371 \end_layout
 372
 373 \begin_layout Plain Layout
 374
 375 (11,-1)*{}="1";
 376 \end_layout
 377
 378 \begin_layout Plain Layout
 379
 380 (-4,8)*{}="2";
 381 \end_layout
 382
 383 \begin_layout Plain Layout
 384
 385 "1";"2" **
 386 \backslash
 387 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
 388 \backslash
 389 dir{>}+(1,2)*{w};
 390 \end_layout
 391
 392 \begin_layout Plain Layout
 393
 394
 395 \backslash
 396 endxy
 397 \end_layout
 398
 399 \end_inset
 400
 401
 402 \end_layout
 403
 404 \end_inset
 405
 406
 407 \end_layout
 408
 409 \begin_layout Description
 410 Circles
 411 \end_layout
 412
 413 \begin_layout Standard
 414 \begin_inset Preview
 415
 416 \begin_layout Standard
 417 \begin_inset ERT
 418 status collapsed
 419
 420 \begin_layout Plain Layout
 421
 422
 423 \backslash
 424 xy
 425 \end_layout
 426
 427 \begin_layout Plain Layout
 428
 429 (0,0)*
 430 \backslash
 431 xycircle(14,8){++
 432 \backslash
 433 dir{<}};
 434 \end_layout
 435
 436 \begin_layout Plain Layout
 437
 438 (0,0)*
 439 \backslash
 440 xycircle<10pt>{{.}};
 441 \end_layout
 442
 443 \begin_layout Plain Layout
 444
 445 (0,0)*
 446 \backslash
 447 xycircle(5,2){:};
 448 \end_layout
 449
 450 \begin_layout Plain Layout
 451
 452 (0,15)*
 453 \backslash
 454 xycircle(10,4){--};
 455 \end_layout
 456
 457 \begin_layout Plain Layout
 458
 459
 460 \backslash
 461 endxy
 462 \end_layout
 463
 464 \end_inset
 465
 466
 467 \end_layout
 468
 469 \end_inset
 470
 471
 472 \end_layout
 473
 474 \begin_layout Description
 475 Cobordism
 476 \end_layout
 477
 478 \begin_layout Standard
 479 \begin_inset Preview
 480
 481 \begin_layout Standard
 482 \begin_inset ERT
 483 status collapsed
 484
 485 \begin_layout Plain Layout
 486
 487
 488 \backslash
 489 xy
 490 \end_layout
 491
 492 \begin_layout Plain Layout
 493
 494 (0,0)*
 495 \backslash
 496 ellipse(3,1){.};
 497 \end_layout
 498
 499 \begin_layout Plain Layout
 500
 501 (0,0)*
 502 \backslash
 503 ellipse(3,1)__,=:a(-180){-};
 504 \end_layout
 505
 506 \begin_layout Plain Layout
 507
 508 (-6,-8)*
 509 \backslash
 510 ellipse(3,1){.};
 511 \end_layout
 512
 513 \begin_layout Plain Layout
 514
 515 (6,-8)*
 516 \backslash
 517 ellipse(3,1){.};
 518 \end_layout
 519
 520 \begin_layout Plain Layout
 521
 522 (0,-8)*
 523 \backslash
 524 ellipse(3,1){.};
 525 \end_layout
 526
 527 \begin_layout Plain Layout
 528
 529 (-6,-8)*
 530 \backslash
 531 ellipse(3,1)__,=:a(-180){-};
 532 \end_layout
 533
 534 \begin_layout Plain Layout
 535
 536 (6,-8)*
 537 \backslash
 538 ellipse(3,1)__,=:a(-180){-};
 539 \end_layout
 540
 541 \begin_layout Plain Layout
 542
 543 (0,-8)*
 544 \backslash
 545 ellipse(3,1)__,=:a(180){-};
 546 \end_layout
 547
 548 \begin_layout Plain Layout
 549
 550 (-3,6)*
 551 \backslash
 552 ellipse(3,1){-};
 553 \end_layout
 554
 555 \begin_layout Plain Layout
 556
 557 (3,6)*
 558 \backslash
 559 ellipse(3,1){-};
 560 \end_layout
 561
 562 \begin_layout Plain Layout
 563
 564 (-3,12)*{}="1";
 565 \end_layout
 566
 567 \begin_layout Plain Layout
 568
 569 (3,12)*{}="2";
 570 \end_layout
 571
 572 \begin_layout Plain Layout
 573
 574 (-9,12)*{}="A2";
 575 \end_layout
 576
 577 \begin_layout Plain Layout
 578
 579 (9,12)*{}="B2";
 580 \end_layout
 581
 582 \begin_layout Plain Layout
 583
 584 "1";"2" **
 585 \backslash
 586 crv{(-3,7) & (3,7)};
 587 \end_layout
 588
 589 \begin_layout Plain Layout
 590
 591 (-3,0)*{}="A";
 592 \end_layout
 593
 594 \begin_layout Plain Layout
 595
 596 (3,0)*{}="B";
 597 \end_layout
 598
 599 \begin_layout Plain Layout
 600
 601 (-3,1)*{}="A1";
 602 \end_layout
 603
 604 \begin_layout Plain Layout
 605
 606 (3,1)*{}="B1";
 607 \end_layout
 608
 609 \begin_layout Plain Layout
 610
 611 "A";"A1" **
 612 \backslash
 613 dir{-};
 614 \end_layout
 615
 616 \begin_layout Plain Layout
 617
 618 "B";"B1" **
 619 \backslash
 620 dir{-};
 621 \end_layout
 622
 623 \begin_layout Plain Layout
 624
 625 "B2";"B1" **
 626 \backslash
 627 crv{(8,7) & (3,5)};
 628 \end_layout
 629
 630 \begin_layout Plain Layout
 631
 632 "A2";"A1" **
 633 \backslash
 634 crv{(-8,7) & (-3,5)};
 635 \end_layout
 636
 637 \begin_layout Plain Layout
 638
 639 %REFLECT
 640 \end_layout
 641
 642 \begin_layout Plain Layout
 643
 644 (3,-16)*{}="1";
 645 \end_layout
 646
 647 \begin_layout Plain Layout
 648
 649 (9,-16)*{}="2";
 650 \end_layout
 651
 652 \begin_layout Plain Layout
 653
 654 "1";"2" **
 655 \backslash
 656 crv{(3,-10) & (9,-10)};
 657 \end_layout
 658
 659 \begin_layout Plain Layout
 660
 661 (-3,-16)*{}="1";
 662 \end_layout
 663
 664 \begin_layout Plain Layout
 665
 666 (-9,-16)*{}="2";
 667 \end_layout
 668
 669 \begin_layout Plain Layout
 670
 671 "1";"2" **
 672 \backslash
 673 crv{(-3,-10) & (-9,-10)};
 674 \end_layout
 675
 676 \begin_layout Plain Layout
 677
 678 (-15,-16)*{}="A2";
 679 \end_layout
 680
 681 \begin_layout Plain Layout
 682
 683 (15,-16)*{}="B2";
 684 \end_layout
 685
 686 \begin_layout Plain Layout
 687
 688 (-3,0)*{}="A";
 689 \end_layout
 690
 691 \begin_layout Plain Layout
 692
 693 (3,0)*{}="B";
 694 \end_layout
 695
 696 \begin_layout Plain Layout
 697
 698 (-3,-1)*{}="A1";
 699 \end_layout
 700
 701 \begin_layout Plain Layout
 702
 703 (3,-1)*{}="B1";
 704 \end_layout
 705
 706 \begin_layout Plain Layout
 707
 708 "A";"A1" **
 709 \backslash
 710 dir{-};
 711 \end_layout
 712
 713 \begin_layout Plain Layout
 714
 715 "B";"B1" **
 716 \backslash
 717 dir{-};
 718 \end_layout
 719
 720 \begin_layout Plain Layout
 721
 722 "B2";"B1" **
 723 \backslash
 724 crv{(13,-6) & (2,-8)};
 725 \end_layout
 726
 727 \begin_layout Plain Layout
 728
 729 "A2";"A1" **
 730 \backslash
 731 crv{(-13,-6) & (-2,-8)};
 732 \end_layout
 733
 734 \begin_layout Plain Layout
 735
 736
 737 \backslash
 738 endxy
 739 \end_layout
 740
 741 \end_inset
 742
 743
 744 \end_layout
 745
 746 \end_inset
 747
 748
 749 \begin_inset Preview
 750
 751 \begin_layout Standard
 752 \begin_inset ERT
 753 status collapsed
 754
 755 \begin_layout Plain Layout
 756
 757
 758 \backslash
 759 xy 0;/r.18pc/:
 760 \end_layout
 761
 762 \begin_layout Plain Layout
 763
 764 (20,2)*{
 765 \backslash
 766 bullet}="RU"+(1,3)*{x^{
 767 \backslash
 768 ast}};
 769 \end_layout
 770
 771 \begin_layout Plain Layout
 772
 773 (16,-3)*{
 774 \backslash
 775 bullet}="RD"+(2.5,2)*{x^{
 776 \backslash
 777 ast}};
 778 \end_layout
 779
 780 \begin_layout Plain Layout
 781
 782 (-16,2)*{
 783 \backslash
 784 bullet}="LU"+(-1,2)*{x};
 785 \end_layout
 786
 787 \begin_layout Plain Layout
 788
 789 (-20,-3)*{
 790 \backslash
 791 bullet}="LD"+(-1,2)*{x};
 792 \end_layout
 793
 794 \begin_layout Plain Layout
 795
 796 "RU";"RD" **
 797 \backslash
 798 crv{(4,2) & (4,-1)};
 799  ?(.1)*
 800 \backslash
 801 dir{<};
 802  ?(.85)*
 803 \backslash
 804 dir{<};
 805 \end_layout
 806
 807 \begin_layout Plain Layout
 808
 809 "LD";"LU" **
 810 \backslash
 811 crv{(-4,-2) & (-4,1)};
 812 \end_layout
 813
 814 \begin_layout Plain Layout
 815
 816 ?(.08)*
 817 \backslash
 818 dir{<};
 819  ?(.85)*
 820 \backslash
 821 dir{<};
 822 \end_layout
 823
 824 \begin_layout Plain Layout
 825
 826 (7.5,0)*{}="x1";
 827  (-7.5,0)*{}="x2";
 828 \end_layout
 829
 830 \begin_layout Plain Layout
 831
 832 "x1";
 833  "x2" **
 834 \backslash
 835 crv{(7,-10) & (-7,-10)};
 836 \end_layout
 837
 838 \begin_layout Plain Layout
 839
 840 (16,-20)*{
 841 \backslash
 842 bullet}="RDD"+(2.5,-1)*{x^{
 843 \backslash
 844 ast}};
 845 \end_layout
 846
 847 \begin_layout Plain Layout
 848
 849 (-20,-20)*{
 850 \backslash
 851 bullet}="LDD"+(-1,-3)*{x};
 852 \end_layout
 853
 854 \begin_layout Plain Layout
 855
 856 (20,-12.5)*{
 857 \backslash
 858 bullet}="RUD"+(3.5,1)*{x^{
 859 \backslash
 860 ast}};
 861 \end_layout
 862
 863 \begin_layout Plain Layout
 864
 865 (-16,-15)*{
 866 \backslash
 867 bullet}="LUD";
 868 \end_layout
 869
 870 \begin_layout Plain Layout
 871
 872 (-16,-2.5)*{}="A";
 873  (16.1,-14.9)*{}="B";
 874 \end_layout
 875
 876 \begin_layout Plain Layout
 877
 878 "RD";
 879  "RDD" **
 880 \backslash
 881 dir{-};
 882 \end_layout
 883
 884 \begin_layout Plain Layout
 885
 886 "LD";
 887  "LDD" **
 888 \backslash
 889 dir{-};
 890 \end_layout
 891
 892 \begin_layout Plain Layout
 893
 894 "A";
 895  "LUD" **
 896 \backslash
 897 dir{.};
 898 \end_layout
 899
 900 \begin_layout Plain Layout
 901
 902 "RDD";
 903  "LDD" **
 904 \backslash
 905 crv{(0,-17)};
 906  ?(.57)*
 907 \backslash
 908 dir{>};
 909 \end_layout
 910
 911 \begin_layout Plain Layout
 912
 913 "RU";
 914  "RUD" **
 915 \backslash
 916 dir{-};
 917 \end_layout
 918
 919 \begin_layout Plain Layout
 920
 921 "LU";
 922  "A" **
 923 \backslash
 924 dir{-};
 925 \end_layout
 926
 927 \begin_layout Plain Layout
 928
 929 "B";
 930  "RUD" **
 931 \backslash
 932 crv{(18,-14.15)};
 933 \end_layout
 934
 935 \begin_layout Plain Layout
 936
 937 "B";
 938  "LUD" **
 939 \backslash
 940 crv{~*=<4pt>{.}(0,-18)};
 941  ?(.4)*
 942 \backslash
 943 dir{<};
 944 \end_layout
 945
 946 \begin_layout Plain Layout
 947
 948
 949 \backslash
 950 endxy
 951 \end_layout
 952
 953 \end_inset
 954
 955
 956 \end_layout
 957
 958 \end_inset
 959
 960
 961 \end_layout
 962
 963 \begin_layout Description
 964 Strings
 965 \end_layout
 966
 967 \begin_layout Standard
 968 \begin_inset Preview
 969
 970 \begin_layout Standard
 971 \begin_inset ERT
 972 status open
 973
 974 \begin_layout Plain Layout
 975
 976
 977 \backslash
 978 xy (-15,0)*{};(15,0)*{};
 979 \end_layout
 980
 981 \begin_layout Plain Layout
 982
 983
 984 \backslash
 985 endxy
 986 \end_layout
 987
 988 \begin_layout Plain Layout
 989
 990
 991 \backslash
 992 qquad =
 993 \backslash
 994 qquad
 995 \backslash
 996 xy
 997 \end_layout
 998
 999 \begin_layout Plain Layout
1000
1001 (-10,12)*{};
1002  (-10,-12)*{};
1003  **
1004 \backslash
1005 dir{-}?(.5)*
1006 \backslash
1007 dir{<}+(-4,0)*{F(x)};
1008 \end_layout
1009
1010 \begin_layout Plain Layout
1011
1012 (-2,12)*{}="1";
1013 \end_layout
1014
1015 \begin_layout Plain Layout
1016
1017 (6,-7) *{}="2";
1018 \end_layout
1019
1020 \begin_layout Plain Layout
1021
1022 (14,-7) *{}="3";
1023 \end_layout
1024
1025 \begin_layout Plain Layout
1026
1027 (14,-13)*{}="3'";
1028 \end_layout
1029
1030 \begin_layout Plain Layout
1031
1032 (18,0) *={}="";
1033 \end_layout
1034
1035 \begin_layout Plain Layout
1036
1037 "1";"2" **
1038 \backslash
1039 crv{(-4,-21)&(5,-15)};
1040 \end_layout
1041
1042 \begin_layout Plain Layout
1043
1044 ?(.15)*
1045 \backslash
1046 dir{<}+(5,10)*{
1047 \backslash
1048 overline{F(x)}};
1049 \end_layout
1050
1051 \begin_layout Plain Layout
1052
1053 "2";"3" **
1054 \backslash
1055 crv{(6,1)&(14,1)};
1056 \end_layout
1057
1058 \begin_layout Plain Layout
1059
1060 ?(0)*
1061 \backslash
1062 dir{<}+(4,8)*{
1063 \backslash
1064 widetilde{F(i_x)}} ;
1065 \end_layout
1066
1067 \begin_layout Plain Layout
1068
1069 ?(.95)*
1070 \backslash
1071 dir{<}+(5,-2)*{F(
1072 \backslash
1073 overline x)};
1074 \end_layout
1075
1076 \begin_layout Plain Layout
1077
1078 "3";"3'" **
1079 \backslash
1080 dir{-};
1081 \end_layout
1082
1083 \begin_layout Plain Layout
1084
1085 (-2,6)*{}="X1";
1086 \end_layout
1087
1088 \begin_layout Plain Layout
1089
1090 (-10,6)*{}="X2";
1091 \end_layout
1092
1093 \begin_layout Plain Layout
1094
1095 "X1";"X2" **
1096 \backslash
1097 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1098 \end_layout
1099
1100 \begin_layout Plain Layout
1101
1102 (-2,-6)*{}="XA";
1103 \end_layout
1104
1105 \begin_layout Plain Layout
1106
1107 (-10,-6)*{}="XB";
1108 \end_layout
1109
1110 \begin_layout Plain Layout
1111
1112 "XA";"XB" **
1113 \backslash
1114 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1115 \end_layout
1116
1117 \begin_layout Plain Layout
1118
1119
1120 \backslash
1121 endxy
1122 \end_layout
1123
1124 \end_inset
1125
1126
1127 \end_layout
1128
1129 \end_inset
1130
1131
1132 \end_layout
1133
1134 \begin_layout Description
1135 Categories
1136 \end_layout
1137
1138 \begin_layout Standard
1139 \begin_inset Preview
1140
1141 \begin_layout Standard
1142 \begin_inset ERT
1143 status collapsed
1144
1145 \begin_layout Plain Layout
1146
1147
1148 \backslash
1149 xymatrix{
1150 \end_layout
1151
1152 \begin_layout Plain Layout
1153
1154 (x
1155 \backslash
1156 otimes 1)
1157 \backslash
1158 otimes y
1159 \end_layout
1160
1161 \begin_layout Plain Layout
1162
1163
1164 \backslash
1165 ar[rr]^{a_{x,1,y}}
1166 \end_layout
1167
1168 \begin_layout Plain Layout
1169
1170
1171 \backslash
1172 ar[dr]_{r_x
1173 \backslash
1174 otimes 1_y}
1175 \end_layout
1176
1177 \begin_layout Plain Layout
1178
1179 && x
1180 \backslash
1181 otimes(1
1182 \backslash
1183 otimes y)
1184 \end_layout
1185
1186 \begin_layout Plain Layout
1187
1188
1189 \backslash
1190 ar[dl]^{1_x
1191 \backslash
1192 otimes
1193 \backslash
1194 ell_y }
1195 \backslash
1196
1197 \backslash
1198
1199 \end_layout
1200
1201 \begin_layout Plain Layout
1202
1203 & x
1204 \backslash
1205 otimes y }
1206 \end_layout
1207
1208 \end_inset
1209
1210
1211 \end_layout
1212
1213 \end_inset
1214
1215
1216 \begin_inset Preview
1217
1218 \begin_layout Standard
1219 \begin_inset ERT
1220 status collapsed
1221
1222 \begin_layout Plain Layout
1223
1224
1225 \backslash
1226 xy
1227 \end_layout
1228
1229 \begin_layout Plain Layout
1230
1231 (-9,0)*+{
1232 \backslash
1233 bullet}="1";
1234 \end_layout
1235
1236 \begin_layout Plain Layout
1237
1238 (0,0)*+{
1239 \backslash
1240 bullet}="2";
1241 \end_layout
1242
1243 \begin_layout Plain Layout
1244
1245 {
1246 \backslash
1247 ar@/^.9pc/ "1";"2"};
1248 \end_layout
1249
1250 \begin_layout Plain Layout
1251
1252 {
1253 \backslash
1254 ar@/_.9pc/ "1";"2"};
1255 \end_layout
1256
1257 \begin_layout Plain Layout
1258
1259 {
1260 \backslash
1261 ar@/^2pc/ "1";"2"};
1262 \end_layout
1263
1264 \begin_layout Plain Layout
1265
1266 {
1267 \backslash
1268 ar@/_2pc/ "1";"2"};
1269 \end_layout
1270
1271 \begin_layout Plain Layout
1272
1273 {
1274 \backslash
1275 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1276 \end_layout
1277
1278 \begin_layout Plain Layout
1279
1280 {
1281 \backslash
1282 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1283 \end_layout
1284
1285 \begin_layout Plain Layout
1286
1287 {
1288 \backslash
1289 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1290 \end_layout
1291
1292 \begin_layout Plain Layout
1293
1294 (0,0)*+{
1295 \backslash
1296 bullet}="1";
1297 \end_layout
1298
1299 \begin_layout Plain Layout
1300
1301 (9,0)*+{
1302 \backslash
1303 bullet}="2";
1304 \end_layout
1305
1306 \begin_layout Plain Layout
1307
1308 (18,0)*+{
1309 \backslash
1310 bullet}="3";
1311 \end_layout
1312
1313 \begin_layout Plain Layout
1314
1315 {
1316 \backslash
1317 ar "1";"2"};
1318 \end_layout
1319
1320 \begin_layout Plain Layout
1321
1322 {
1323 \backslash
1324 ar "2";"3"};
1325 \end_layout
1326
1327 \begin_layout Plain Layout
1328
1329 {
1330 \backslash
1331 ar@/^1pc/ "1";"2"};
1332 \end_layout
1333
1334 \begin_layout Plain Layout
1335
1336 {
1337 \backslash
1338 ar@/_1pc/ "1";"2"};
1339 \end_layout
1340
1341 \begin_layout Plain Layout
1342
1343 {
1344 \backslash
1345 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1346 \end_layout
1347
1348 \begin_layout Plain Layout
1349
1350 {
1351 \backslash
1352 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1353 \end_layout
1354
1355 \begin_layout Plain Layout
1356
1357
1358 \backslash
1359 endxy
1360 \end_layout
1361
1362 \end_inset
1363
1364
1365 \end_layout
1366
1367 \end_inset
1368
1369
1370 \end_layout
1371
1372 \begin_layout Description
1373 Transformations
1374 \end_layout
1375
1376 \begin_layout Standard
1377 \begin_inset Preview
1378
1379 \begin_layout Standard
1380 \begin_inset ERT
1381 status collapsed
1382
1383 \begin_layout Plain Layout
1384
1385
1386 \backslash
1387 xy %FIG.19.
1388  Natural transformation between functors.
1389 \end_layout
1390
1391 \begin_layout Plain Layout
1392
1393 (-26,-2)*+{
1394 \backslash
1395 bullet}="a";
1396 \end_layout
1397
1398 \begin_layout Plain Layout
1399
1400 (-12,3)*+{
1401 \backslash
1402 bullet}="b";
1403 \end_layout
1404
1405 \begin_layout Plain Layout
1406
1407 (-16,-5)*+{
1408 \backslash
1409 bullet}="c";
1410 \end_layout
1411
1412 \begin_layout Plain Layout
1413
1414 {
1415 \backslash
1416 ar@/^.25pc/ "a";"b"};
1417 \end_layout
1418
1419 \begin_layout Plain Layout
1420
1421 {
1422 \backslash
1423 ar@/_.25pc/"a";"c"};
1424 \end_layout
1425
1426 \begin_layout Plain Layout
1427
1428 {
1429 \backslash
1430 ar@/_.15pc/ "b";"c"};
1431 \end_layout
1432
1433 \begin_layout Plain Layout
1434
1435 %START TOP
1436 \end_layout
1437
1438 \begin_layout Plain Layout
1439
1440 (12,10)*+{
1441 \backslash
1442 bullet}="ta";
1443 \end_layout
1444
1445 \begin_layout Plain Layout
1446
1447 (26,15)*+{
1448 \backslash
1449 bullet}="tb";
1450 \end_layout
1451
1452 \begin_layout Plain Layout
1453
1454 (22,8)*+{
1455 \backslash
1456 bullet}="tc";
1457 \end_layout
1458
1459 \begin_layout Plain Layout
1460
1461 {
1462 \backslash
1463 ar@/^.25pc/ "ta";"tb"};
1464 \end_layout
1465
1466 \begin_layout Plain Layout
1467
1468 {
1469 \backslash
1470 ar@/_.25pc/ "ta";"tc"};
1471 \end_layout
1472
1473 \begin_layout Plain Layout
1474
1475 {
1476 \backslash
1477 ar@/_.15pc/ "tb";"tc"};
1478 \end_layout
1479
1480 \begin_layout Plain Layout
1481
1482 %START bottom
1483 \end_layout
1484
1485 \begin_layout Plain Layout
1486
1487 (12,-10)*+{
1488 \backslash
1489 bullet}="ba";
1490 \end_layout
1491
1492 \begin_layout Plain Layout
1493
1494 (26,-5)*+{
1495 \backslash
1496 bullet}="bb";
1497 \end_layout
1498
1499 \begin_layout Plain Layout
1500
1501 (22,-12)*+{
1502 \backslash
1503 bullet}="bc";
1504 \end_layout
1505
1506 \begin_layout Plain Layout
1507
1508 {
1509 \backslash
1510 ar@/^.25pc/@{.>} "ba";"bb"};
1511 \end_layout
1512
1513 \begin_layout Plain Layout
1514
1515 {
1516 \backslash
1517 ar@/_.25pc/ "ba";"bc"};
1518 \end_layout
1519
1520 \begin_layout Plain Layout
1521
1522 {
1523 \backslash
1524 ar@/_.15pc/ "bb";"bc"};
1525 \end_layout
1526
1527 \begin_layout Plain Layout
1528
1529 %START CONNECT
1530 \end_layout
1531
1532 \begin_layout Plain Layout
1533
1534 {
1535 \backslash
1536 ar@/_.15pc/ "ta";"ba"};
1537 \end_layout
1538
1539 \begin_layout Plain Layout
1540
1541 {
1542 \backslash
1543 ar@/_.15pc/ "tb";"bb"};
1544 \end_layout
1545
1546 \begin_layout Plain Layout
1547
1548 {
1549 \backslash
1550 ar@/_.15pc/ "tc";"bc"};
1551 \end_layout
1552
1553 \begin_layout Plain Layout
1554
1555 %START ARROWS AND LABELS
1556 \end_layout
1557
1558 \begin_layout Plain Layout
1559
1560 (-12,6)*{}="DF";
1561 \end_layout
1562
1563 \begin_layout Plain Layout
1564
1565 (6,10)*{}="CF";
1566 \end_layout
1567
1568 \begin_layout Plain Layout
1569
1570 {
1571 \backslash
1572 ar@/^.35pc/^F "DF";"CF"};
1573 \end_layout
1574
1575 \begin_layout Plain Layout
1576
1577 (-12,-6)*{}="DF";
1578 \end_layout
1579
1580 \begin_layout Plain Layout
1581
1582 (6,-10)*{}="CF";
1583 \end_layout
1584
1585 \begin_layout Plain Layout
1586
1587 {
1588 \backslash
1589 ar@/_.35pc/_G "DF";"CF"};
1590 \end_layout
1591
1592 \begin_layout Plain Layout
1593
1594 (-2,5)*{}="DF";
1595 \end_layout
1596
1597 \begin_layout Plain Layout
1598
1599 (-2,-5)*{}="CF";
1600 \end_layout
1601
1602 \begin_layout Plain Layout
1603
1604 {
1605 \backslash
1606 ar@{=>}^{
1607 \backslash
1608 alpha} "DF";"CF"};
1609 \end_layout
1610
1611 \begin_layout Plain Layout
1612
1613 (29,3)*{D};
1614 \end_layout
1615
1616 \begin_layout Plain Layout
1617
1618 (-23,3)*{C};
1619 \end_layout
1620
1621 \begin_layout Plain Layout
1622
1623
1624 \backslash
1625 endxy
1626 \end_layout
1627
1628 \end_inset
1629
1630
1631 \end_layout
1632
1633 \end_inset
1634
1635
1636 \end_layout
1637
1638 \begin_layout Section
1639 IPA
1640 \end_layout
1641
1642 \begin_layout Standard
1643 \begin_inset Preview
1644
1645 \begin_layout Standard
1646 \begin_inset ERT
1647 status collapsed
1648
1649 \begin_layout Plain Layout
1650
1651
1652 \backslash
1653 textipa{Ekspl@"neIS@n}
1654 \end_layout
1655
1656 \end_inset
1657
1658
1659 \end_layout
1660
1661 \end_inset
1662
1663
1664 \end_layout
1665
1666 \begin_layout Section
1667 QTree
1668 \end_layout
1669
1670 \begin_layout Standard
1671 \begin_inset Preview
1672
1673 \begin_layout Standard
1674 \begin_inset ERT
1675 status collapsed
1676
1677 \begin_layout Plain Layout
1678
1679
1680 \backslash
1681 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1682 \end_layout
1683
1684 \end_inset
1685
1686
1687 \end_layout
1688
1689 \end_inset
1690
1691
1692 \begin_inset Preview
1693
1694 \begin_layout Standard
1695 \begin_inset ERT
1696 status collapsed
1697
1698 \begin_layout Plain Layout
1699
1700
1701 \backslash
1702 Tree [.$
1703 \backslash
1704 sigma$ $
1705 \backslash
1706 mu$ $
1707 \backslash
1708 mu$ ]
1709 \end_layout
1710
1711 \end_inset
1712
1713
1714 \end_layout
1715
1716 \end_inset
1717
1718
1719 \end_layout
1720
1721 \begin_layout Section
1722 PSTricks
1723 \begin_inset CommandInset label
1724 LatexCommand label
1725 name "sec:PSTricks"
1726
1727 \end_inset
1728
1729
1730 \end_layout
1731
1732 \begin_layout Standard
1733 Some simple graphing examples.
1734 \end_layout
1735
1736 \begin_layout Subsection
1737 Function plotting
1738 \end_layout
1739
1740 \begin_layout Standard
1741 \begin_inset Preview
1742
1743 \begin_layout Standard
1744 \begin_inset ERT
1745 status open
1746
1747 \begin_layout Plain Layout
1748
1749
1750 \backslash
1751 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1752 \end_layout
1753
1754 \begin_layout Plain Layout
1755
1756
1757 \backslash
1758 psaxes{->}(0,0)(0,-3)(10,3)
1759 \end_layout
1760
1761 \begin_layout Plain Layout
1762
1763
1764 \backslash
1765 uput[-90](10,0){$x$}
1766 \backslash
1767 uput[0](0,3){$f(x)$}
1768 \end_layout
1769
1770 \begin_layout Plain Layout
1771
1772
1773 \backslash
1774 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1775 \end_layout
1776
1777 \begin_layout Plain Layout
1778
1779
1780 \backslash
1781 end{pspicture*}
1782 \end_layout
1783
1784 \end_inset
1785
1786
1787 \end_layout
1788
1789 \end_inset
1790
1791
1792 \end_layout
1793
1794 \begin_layout Subsection
1795 Inline data plotting
1796 \end_layout
1797
1798 \begin_layout Standard
1799 \align center
1800 \begin_inset Preview
1801
1802 \begin_layout Standard
1803 \align center
1804 \begin_inset ERT
1805 status open
1806
1807 \begin_layout Plain Layout
1808
1809
1810 \backslash
1811 begin{pspicture*}(-1.5,-1.5)(11,5)
1812 \end_layout
1813
1814 \begin_layout Plain Layout
1815
1816
1817 \backslash
1818 psaxes{->}(0,0)(0,0)(10,5)
1819 \end_layout
1820
1821 \begin_layout Plain Layout
1822
1823
1824 \backslash
1825 psset{linewidth=2.5pt}
1826 \end_layout
1827
1828 \begin_layout Plain Layout
1829
1830
1831 \backslash
1832 rput(5.0,-1.0){Speed [MPH]}
1833 \end_layout
1834
1835 \begin_layout Plain Layout
1836
1837
1838 \backslash
1839 rput(-1.0,1.0){
1840 \backslash
1841 begin{rotate}{90}Cost [Dollars]
1842 \backslash
1843 end{rotate}}
1844 \end_layout
1845
1846 \begin_layout Plain Layout
1847
1848
1849 \backslash
1850 savedata{
1851 \backslash
1852 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1853 \end_layout
1854
1855 \begin_layout Plain Layout
1856
1857
1858 \backslash
1859 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1860 \backslash
1861 mydata}
1862 \end_layout
1863
1864 \begin_layout Plain Layout
1865
1866
1867 \backslash
1868 end{pspicture*}
1869 \end_layout
1870
1871 \end_inset
1872
1873
1874 \end_layout
1875
1876 \end_inset
1877
1878
1879 \end_layout
1880
1881 \begin_layout Subsection
1882 Lissajous curves
1883 \end_layout
1884
1885 \begin_layout Standard
1886 \begin_inset Preview
1887
1888 \begin_layout Standard
1889 \begin_inset ERT
1890 status open
1891
1892 \begin_layout Plain Layout
1893
1894
1895 \backslash
1896 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1897 \end_layout
1898
1899 \begin_layout Plain Layout
1900
1901
1902 \backslash
1903 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul cos 100 t mul sin}
1904 \end_layout
1905
1906 \begin_layout Plain Layout
1907
1908
1909 \backslash
1910 end{pspicture*}
1911 \end_layout
1912
1913 \end_inset
1914
1915
1916 \end_layout
1917
1918 \end_inset
1919
1920
1921 \begin_inset space \hfill{}
1922 \end_inset
1923
1924
1925 \begin_inset Preview
1926
1927 \begin_layout Standard
1928 \begin_inset ERT
1929 status open
1930
1931 \begin_layout Plain Layout
1932
1933
1934 \backslash
1935 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1936 \end_layout
1937
1938 \begin_layout Plain Layout
1939
1940
1941 \backslash
1942 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t mul cos 100 t mul sin}
1943 \end_layout
1944
1945 \begin_layout Plain Layout
1946
1947
1948 \backslash
1949 end{pspicture*}
1950 \end_layout
1951
1952 \end_inset
1953
1954
1955 \end_layout
1956
1957 \end_inset
1958
1959
1960 \begin_inset space \hfill{}
1961 \end_inset
1962
1963
1964 \begin_inset Preview
1965
1966 \begin_layout Standard
1967 \begin_inset ERT
1968 status open
1969
1970 \begin_layout Plain Layout
1971
1972
1973 \backslash
1974 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1975 \end_layout
1976
1977 \begin_layout Plain Layout
1978
1979
1980 \backslash
1981 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t mul cos 200 t mul sin}
1982 \end_layout
1983
1984 \begin_layout Plain Layout
1985
1986
1987 \backslash
1988 end{pspicture*}
1989 \end_layout
1990
1991 \end_inset
1992
1993
1994 \end_layout
1995
1996 \end_inset
1997
1998
1999 \begin_inset space \hfill{}
2000 \end_inset
2001
2002
2003 \begin_inset Preview
2004
2005 \begin_layout Standard
2006 \begin_inset ERT
2007 status open
2008
2009 \begin_layout Plain Layout
2010
2011
2012 \backslash
2013 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
2014 \end_layout
2015
2016 \begin_layout Plain Layout
2017
2018
2019 \backslash
2020 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t mul cos 200 t mul sin}
2021 \end_layout
2022
2023 \begin_layout Plain Layout
2024
2025
2026 \backslash
2027 end{pspicture*}
2028 \end_layout
2029
2030 \end_inset
2031
2032
2033 \end_layout
2034
2035 \end_inset
2036
2037
2038 \end_layout
2039
2040 \begin_layout Section
2041 TikZ
2042 \end_layout
2043
2044 \begin_layout Standard
2045 \begin_inset Flex URL
2046 status collapsed
2047
2048 \begin_layout Plain Layout
2049
2050 http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
2051 \end_layout
2052
2053 \end_inset
2054
2055
2056 \end_layout
2057
2058 \begin_layout Standard
2059 \begin_inset Preview
2060
2061 \begin_layout Standard
2062 \begin_inset ERT
2063 status collapsed
2064
2065 \begin_layout Plain Layout
2066
2067
2068 \backslash
2069 def
2070 \backslash
2071 iangle{35} % Angle of the inclined plane
2072 \end_layout
2073
2074 \begin_layout Plain Layout
2075
2076
2077 \backslash
2078 def
2079 \backslash
2080 down{-90}
2081 \end_layout
2082
2083 \begin_layout Plain Layout
2084
2085
2086 \backslash
2087 def
2088 \backslash
2089 arcr{0.5cm} % Radius of the arc used to indicate angles
2090 \end_layout
2091
2092 \begin_layout Plain Layout
2093
2094 \end_layout
2095
2096 \begin_layout Plain Layout
2097
2098
2099 \backslash
2100 begin{tikzpicture}[
2101 \end_layout
2102
2103 \begin_layout Plain Layout
2104
2105     force/.style={>=latex,draw=blue,fill=blue},
2106 \end_layout
2107
2108 \begin_layout Plain Layout
2109
2110     axis/.style={densely dashed,gray,font=
2111 \backslash
2112 small},
2113 \end_layout
2114
2115 \begin_layout Plain Layout
2116
2117     M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2118 \end_layout
2119
2120 \begin_layout Plain Layout
2121
2122     m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2123 \end_layout
2124
2125 \begin_layout Plain Layout
2126
2127     plane/.style={draw=black,fill=blue!10},
2128 \end_layout
2129
2130 \begin_layout Plain Layout
2131
2132     string/.style={draw=red,
2133  thick},
2134 \end_layout
2135
2136 \begin_layout Plain Layout
2137
2138     pulley/.style={thick},
2139 \end_layout
2140
2141 \begin_layout Plain Layout
2142
2143 ]
2144 \end_layout
2145
2146 \begin_layout Plain Layout
2147
2148 \end_layout
2149
2150 \begin_layout Plain Layout
2151
2152
2153 \backslash
2154 matrix[column sep=1cm] {
2155 \end_layout
2156
2157 \begin_layout Plain Layout
2158
2159     %% Sketch
2160 \end_layout
2161
2162 \begin_layout Plain Layout
2163
2164
2165 \backslash
2166 draw[plane] (0,-1) coordinate (base)
2167 \end_layout
2168
2169 \begin_layout Plain Layout
2170
2171                      -- coordinate[pos=0.5] (mid) ++(
2172 \backslash
2173 iangle:3) coordinate (top)
2174 \end_layout
2175
2176 \begin_layout Plain Layout
2177
2178                      |- (base) -- cycle;
2179 \end_layout
2180
2181 \begin_layout Plain Layout
2182
2183
2184 \backslash
2185 path (mid) node[M,rotate=
2186 \backslash
2187 iangle,yshift=0.25cm] (M) {};
2188 \end_layout
2189
2190 \begin_layout Plain Layout
2191
2192
2193 \backslash
2194 draw[pulley] (top) -- ++(
2195 \backslash
2196 iangle:0.25) circle (0.25cm)
2197 \end_layout
2198
2199 \begin_layout Plain Layout
2200
2201                    ++ (90-
2202 \backslash
2203 iangle:0.5) coordinate (pulley);
2204 \end_layout
2205
2206 \begin_layout Plain Layout
2207
2208
2209 \backslash
2210 draw[string] (M.east) -- ++(
2211 \backslash
2212 iangle:1.5cm) arc (90+
2213 \backslash
2214 iangle:0:0.25)
2215 \end_layout
2216
2217 \begin_layout Plain Layout
2218
2219                   -- ++(0,-1) node[m] {};
2220 \end_layout
2221
2222 \begin_layout Plain Layout
2223
2224 \end_layout
2225
2226 \begin_layout Plain Layout
2227
2228
2229 \backslash
2230 draw[->] (base)++(
2231 \backslash
2232 arcr,0) arc (0:
2233 \backslash
2234 iangle:
2235 \backslash
2236 arcr);
2237 \end_layout
2238
2239 \begin_layout Plain Layout
2240
2241
2242 \backslash
2243 path (base)++(
2244 \backslash
2245 iangle*0.5:
2246 \backslash
2247 arcr+5pt) node {$
2248 \backslash
2249 alpha$};
2250 \end_layout
2251
2252 \begin_layout Plain Layout
2253
2254     %%
2255 \end_layout
2256
2257 \begin_layout Plain Layout
2258
2259 \end_layout
2260
2261 \begin_layout Plain Layout
2262
2263 &
2264 \end_layout
2265
2266 \begin_layout Plain Layout
2267
2268     %% Free body diagram of M
2269 \end_layout
2270
2271 \begin_layout Plain Layout
2272
2273
2274 \backslash
2275 begin{scope}[rotate=
2276 \backslash
2277 iangle]
2278 \end_layout
2279
2280 \begin_layout Plain Layout
2281
2282
2283 \backslash
2284 node[M,transform shape] (M) {};
2285 \end_layout
2286
2287 \begin_layout Plain Layout
2288
2289         % Draw axes and help lines
2290 \end_layout
2291
2292 \begin_layout Plain Layout
2293
2294 \end_layout
2295
2296 \begin_layout Plain Layout
2297
2298         {[axis,->]
2299 \end_layout
2300
2301 \begin_layout Plain Layout
2302
2303
2304 \backslash
2305 draw (0,-1) -- (0,2) node[right] {$+y$};
2306 \end_layout
2307
2308 \begin_layout Plain Layout
2309
2310
2311 \backslash
2312 draw (M) -- ++(2,0) node[right] {$+x$};
2313 \end_layout
2314
2315 \begin_layout Plain Layout
2316
2317             % Indicate angle.
2318  The code is a bit awkward.
2319 \end_layout
2320
2321 \begin_layout Plain Layout
2322
2323 \end_layout
2324
2325 \begin_layout Plain Layout
2326
2327
2328 \backslash
2329 draw[solid,shorten >=0.5pt] (
2330 \backslash
2331 down-
2332 \backslash
2333 iangle:
2334 \backslash
2335 arcr)
2336 \end_layout
2337
2338 \begin_layout Plain Layout
2339
2340                 arc(
2341 \backslash
2342 down-
2343 \backslash
2344 iangle:
2345 \backslash
2346 down:
2347 \backslash
2348 arcr);
2349 \end_layout
2350
2351 \begin_layout Plain Layout
2352
2353
2354 \backslash
2355 node at (
2356 \backslash
2357 down-0.5*
2358 \backslash
2359 iangle:1.3*
2360 \backslash
2361 arcr) {$
2362 \backslash
2363 alpha$};
2364 \end_layout
2365
2366 \begin_layout Plain Layout
2367
2368         }
2369 \end_layout
2370
2371 \begin_layout Plain Layout
2372
2373 \end_layout
2374
2375 \begin_layout Plain Layout
2376
2377         % Forces
2378 \end_layout
2379
2380 \begin_layout Plain Layout
2381
2382         {[force,->]
2383 \end_layout
2384
2385 \begin_layout Plain Layout
2386
2387             % Assuming that Mg = 1.
2388  The normal force will therefore be cos(alpha)
2389 \end_layout
2390
2391 \begin_layout Plain Layout
2392
2393
2394 \backslash
2395 draw (M.center) -- ++(0,{cos(
2396 \backslash
2397 iangle)}) node[above right] {$N$};
2398 \end_layout
2399
2400 \begin_layout Plain Layout
2401
2402
2403 \backslash
2404 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2405 \end_layout
2406
2407 \begin_layout Plain Layout
2408
2409
2410 \backslash
2411 draw (M.east) -- ++(1,0) node[above] {$T$};
2412 \end_layout
2413
2414 \begin_layout Plain Layout
2415
2416         }
2417 \end_layout
2418
2419 \begin_layout Plain Layout
2420
2421 \end_layout
2422
2423 \begin_layout Plain Layout
2424
2425
2426 \backslash
2427 end{scope}
2428 \end_layout
2429
2430 \begin_layout Plain Layout
2431
2432     % Draw gravity force.
2433  The code is put outside the rotated
2434 \end_layout
2435
2436 \begin_layout Plain Layout
2437
2438     % scope for simplicity.
2439  No need to do any angle calculations.
2440
2441 \end_layout
2442
2443 \begin_layout Plain Layout
2444
2445
2446 \backslash
2447 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2448 \end_layout
2449
2450 \begin_layout Plain Layout
2451
2452     %%
2453 \end_layout
2454
2455 \begin_layout Plain Layout
2456
2457 \end_layout
2458
2459 \begin_layout Plain Layout
2460
2461 &
2462 \end_layout
2463
2464 \begin_layout Plain Layout
2465
2466     %%%
2467 \end_layout
2468
2469 \begin_layout Plain Layout
2470
2471     % Free body diagram of m
2472 \end_layout
2473
2474 \begin_layout Plain Layout
2475
2476
2477 \backslash
2478 node[m] (m) {};
2479 \end_layout
2480
2481 \begin_layout Plain Layout
2482
2483
2484 \backslash
2485 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2486 \end_layout
2487
2488 \begin_layout Plain Layout
2489
2490     {[force,->]
2491 \end_layout
2492
2493 \begin_layout Plain Layout
2494
2495
2496 \backslash
2497 draw (m.north) -- ++(0,1) node[above] {$T'$};
2498 \end_layout
2499
2500 \begin_layout Plain Layout
2501
2502
2503 \backslash
2504 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2505 \end_layout
2506
2507 \begin_layout Plain Layout
2508
2509     }
2510 \end_layout
2511
2512 \begin_layout Plain Layout
2513
2514 \end_layout
2515
2516 \begin_layout Plain Layout
2517
2518
2519 \backslash
2520
2521 \backslash
2522
2523 \end_layout
2524
2525 \begin_layout Plain Layout
2526
2527 };
2528 \end_layout
2529
2530 \begin_layout Plain Layout
2531
2532
2533 \backslash
2534 end{tikzpicture}
2535 \end_layout
2536
2537 \begin_layout Plain Layout
2538
2539 \end_layout
2540
2541 \end_inset
2542
2543
2544 \end_layout
2545
2546 \end_inset
2547
2548
2549 \end_layout
2550
2551 \end_body
2552 \end_document