lib/examples/instant_preview.lyx

   1 #LyX 2.3 created this file. For more info see http://www.lyx.org/
   2 \lyxformat 544
   3 \begin_document
   4 \begin_header
   5 \save_transient_properties true
   6 \origin /systemlyxdir/examples/
   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 false
  22 \language english
  23 \language_package default
  24 \inputencoding auto
  25 \fontencoding global
  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_osf false
  34 \font_sf_scale 100 100
  35 \font_tt_scale 100 100
  36 \use_microtype false
  37 \use_dash_ligatures false
  38 \graphics default
  39 \default_output_format pdf
  40 \output_sync 0
  41 \bibtex_command default
  42 \index_command default
  43 \paperfontsize default
  44 \spacing single
  45 \use_hyperref false
  46 \papersize default
  47 \use_geometry false
  48 \use_package amsmath 1
  49 \use_package amssymb 1
  50 \use_package cancel 1
  51 \use_package esint 1
  52 \use_package mathdots 1
  53 \use_package mathtools 1
  54 \use_package mhchem 1
  55 \use_package stackrel 1
  56 \use_package stmaryrd 1
  57 \use_package undertilde 1
  58 \cite_engine basic
  59 \cite_engine_type default
  60 \biblio_style plain
  61 \use_bibtopic false
  62 \use_indices false
  63 \paperorientation portrait
  64 \suppress_date false
  65 \justification true
  66 \use_refstyle 0
  67 \use_minted 0
  68 \index Index
  69 \shortcut idx
  70 \color #008000
  71 \end_index
  72 \secnumdepth 3
  73 \tocdepth 3
  74 \paragraph_separation indent
  75 \paragraph_indentation default
  76 \is_math_indent 0
  77 \math_numbering_side default
  78 \quotes_style english
  79 \dynamic_quotes 0
  80 \papercolumns 1
  81 \papersides 1
  82 \paperpagestyle default
  83 \tracking_changes false
  84 \output_changes false
  85 \html_math_output 0
  86 \html_css_as_file 0
  87 \html_be_strict true
  88 \end_header
  89
  90 \begin_body
  91
  92 \begin_layout Section
  93 Introduction
  94 \end_layout
  95
  96 \begin_layout Standard
  97 In order to properly typeset the document and have instant preview working,
  98  the following packages have to be installed:
  99 \end_layout
 100
 101 \begin_layout LyX-Code
 102 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf, etex
 103 \end_layout
 104
 105 \begin_layout Standard
 106 Due to the use of postscript specials in Section
 107 \begin_inset CommandInset ref
 108 LatexCommand ref
 109 reference "sec:PSTricks"
 110
 111 \end_inset
 112
 113 , only the Postscript or PDF (ps2pdf) output formats will correctly render
 114  the included images.
 115  However, the PDF (Xe\SpecialChar TeX
 116 ) output seems to also work, while trying to typeset
 117  the document with
 118 \family typewriter
 119 pdflatex
 120 \family default
 121  or
 122 \family typewriter
 123 pdflualatex
 124 \family default
 125  will generate errors.
 126 \end_layout
 127
 128 \begin_layout Section
 129 Diagrams by XY(-pic)
 130 \end_layout
 131
 132 \begin_layout Standard
 133 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
 134  examples, see
 135 \begin_inset Flex URL
 136 status collapsed
 137
 138 \begin_layout Plain Layout
 139
 140 https://www.ctan.org/tex-archive/macros/generic/diagrams/xypic/doc/xyguide.pdf
 141 \end_layout
 142
 143 \end_inset
 144
 145 .
 146 \end_layout
 147
 148 \begin_layout Description
 149 Braid
 150 \end_layout
 151
 152 \begin_layout Standard
 153 \begin_inset Preview
 154
 155 \begin_layout Standard
 156 \begin_inset ERT
 157 status collapsed
 158
 159 \begin_layout Plain Layout
 160
 161
 162 \backslash
 163 xy
 164 \end_layout
 165
 166 \begin_layout Plain Layout
 167
 168 (5,10)*{}; (-10,-10)*{} **
 169 \backslash
 170 crv{(6,-2)&(-12,4)}
 171 \end_layout
 172
 173 \begin_layout Plain Layout
 174
 175
 176 \backslash
 177 POS?(.25)*{
 178 \backslash
 179 hole}="x"
 180 \backslash
 181 POS?(.45)*{
 182 \backslash
 183 hole}="y"
 184 \backslash
 185 POS?(.6)*{
 186 \backslash
 187 hole}="z";
 188 \end_layout
 189
 190 \begin_layout Plain Layout
 191
 192 "y"+(0,-1); (2,-10)*{} **
 193 \backslash
 194 crv{}
 195 \backslash
 196 POS?(.2)*{
 197 \backslash
 198 hole}="M";
 199 \end_layout
 200
 201 \begin_layout Plain Layout
 202
 203 (-10,10)*{}; "z" **
 204 \backslash
 205 crv{(-9,0)};
 206 \end_layout
 207
 208 \begin_layout Plain Layout
 209
 210 "z"; "M" **
 211 \backslash
 212 crv{};
 213 \end_layout
 214
 215 \begin_layout Plain Layout
 216
 217 "M"; "x" **
 218 \backslash
 219 crv{(5,0)};
 220 \end_layout
 221
 222 \begin_layout Plain Layout
 223
 224 "x"; "y" **
 225 \backslash
 226 crv{(0,7) & (-5,6)};
 227 \end_layout
 228
 229 \begin_layout Plain Layout
 230
 231
 232 \backslash
 233 endxy
 234 \end_layout
 235
 236 \end_inset
 237
 238
 239 \end_layout
 240
 241 \end_inset
 242
 243
 244 \end_layout
 245
 246 \begin_layout Description
 247 Knots
 248 \end_layout
 249
 250 \begin_layout Standard
 251 \begin_inset Preview
 252
 253 \begin_layout Standard
 254 \begin_inset ERT
 255 status collapsed
 256
 257 \begin_layout Plain Layout
 258
 259
 260 \backslash
 261 xy
 262 \end_layout
 263
 264 \begin_layout Plain Layout
 265
 266 (6,9)*{}="1";
 267 \end_layout
 268
 269 \begin_layout Plain Layout
 270
 271 (-8.5,-1)*{}="2";
 272 \end_layout
 273
 274 \begin_layout Plain Layout
 275
 276 "1";"2" **
 277 \backslash
 278 crv{~*=<.5pt>{.} (0,30)}?(.75)*
 279 \backslash
 280 dir{>}+(-2,2)*{z};
 281 \end_layout
 282
 283 \begin_layout Plain Layout
 284
 285 (-6.5,8)*{}="1";
 286 \end_layout
 287
 288 \begin_layout Plain Layout
 289
 290 (-.5,-9)*{}="2";
 291 \end_layout
 292
 293 \begin_layout Plain Layout
 294
 295 "1";"2" **
 296 \backslash
 297 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
 298 \backslash
 299 dir{>}+(-2,-2)*{u};
 300 \end_layout
 301
 302 \begin_layout Plain Layout
 303
 304 (-9.5,-3.35)*{}="1";
 305 \end_layout
 306
 307 \begin_layout Plain Layout
 308
 309 (8.5,-3)*{}="2";
 310 \end_layout
 311
 312 \begin_layout Plain Layout
 313
 314 "1";"2" **
 315 \backslash
 316 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
 317 \backslash
 318 dir{>}+(-1,-3)*{x};
 319 \end_layout
 320
 321 \begin_layout Plain Layout
 322
 323 (1,-10)*{}="1";
 324 \end_layout
 325
 326 \begin_layout Plain Layout
 327
 328 (6.5,7.13)*{}="2";
 329 \end_layout
 330
 331 \begin_layout Plain Layout
 332
 333 "1";"2" **
 334 \backslash
 335 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
 336 \backslash
 337 dir{>}+(3,-1)*{y};
 338 \end_layout
 339
 340 \begin_layout Plain Layout
 341
 342 (11,-1)*{}="1";
 343 \end_layout
 344
 345 \begin_layout Plain Layout
 346
 347 (-4,8)*{}="2";
 348 \end_layout
 349
 350 \begin_layout Plain Layout
 351
 352 "1";"2" **
 353 \backslash
 354 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
 355 \backslash
 356 dir{>}+(1,2)*{w};
 357 \end_layout
 358
 359 \begin_layout Plain Layout
 360
 361
 362 \backslash
 363 endxy
 364 \end_layout
 365
 366 \end_inset
 367
 368
 369 \end_layout
 370
 371 \end_inset
 372
 373
 374 \end_layout
 375
 376 \begin_layout Description
 377 Circles
 378 \end_layout
 379
 380 \begin_layout Standard
 381 \begin_inset Preview
 382
 383 \begin_layout Standard
 384 \begin_inset ERT
 385 status collapsed
 386
 387 \begin_layout Plain Layout
 388
 389
 390 \backslash
 391 xy
 392 \end_layout
 393
 394 \begin_layout Plain Layout
 395
 396 (0,0)*
 397 \backslash
 398 xycircle(14,8){++
 399 \backslash
 400 dir{<}};
 401 \end_layout
 402
 403 \begin_layout Plain Layout
 404
 405 (0,0)*
 406 \backslash
 407 xycircle<10pt>{{.}};
 408 \end_layout
 409
 410 \begin_layout Plain Layout
 411
 412 (0,0)*
 413 \backslash
 414 xycircle(5,2){:};
 415 \end_layout
 416
 417 \begin_layout Plain Layout
 418
 419 (0,15)*
 420 \backslash
 421 xycircle(10,4){--};
 422 \end_layout
 423
 424 \begin_layout Plain Layout
 425
 426
 427 \backslash
 428 endxy
 429 \end_layout
 430
 431 \end_inset
 432
 433
 434 \end_layout
 435
 436 \end_inset
 437
 438
 439 \end_layout
 440
 441 \begin_layout Description
 442 Cobordism
 443 \end_layout
 444
 445 \begin_layout Standard
 446 \begin_inset Preview
 447
 448 \begin_layout Standard
 449 \begin_inset ERT
 450 status collapsed
 451
 452 \begin_layout Plain Layout
 453
 454
 455 \backslash
 456 xy
 457 \end_layout
 458
 459 \begin_layout Plain Layout
 460
 461 (0,0)*
 462 \backslash
 463 ellipse(3,1){.};
 464 \end_layout
 465
 466 \begin_layout Plain Layout
 467
 468 (0,0)*
 469 \backslash
 470 ellipse(3,1)__,=:a(-180){-};
 471 \end_layout
 472
 473 \begin_layout Plain Layout
 474
 475 (-6,-8)*
 476 \backslash
 477 ellipse(3,1){.};
 478 \end_layout
 479
 480 \begin_layout Plain Layout
 481
 482 (6,-8)*
 483 \backslash
 484 ellipse(3,1){.};
 485 \end_layout
 486
 487 \begin_layout Plain Layout
 488
 489 (0,-8)*
 490 \backslash
 491 ellipse(3,1){.};
 492 \end_layout
 493
 494 \begin_layout Plain Layout
 495
 496 (-6,-8)*
 497 \backslash
 498 ellipse(3,1)__,=:a(-180){-};
 499 \end_layout
 500
 501 \begin_layout Plain Layout
 502
 503 (6,-8)*
 504 \backslash
 505 ellipse(3,1)__,=:a(-180){-};
 506 \end_layout
 507
 508 \begin_layout Plain Layout
 509
 510 (0,-8)*
 511 \backslash
 512 ellipse(3,1)__,=:a(180){-};
 513 \end_layout
 514
 515 \begin_layout Plain Layout
 516
 517 (-3,6)*
 518 \backslash
 519 ellipse(3,1){-};
 520 \end_layout
 521
 522 \begin_layout Plain Layout
 523
 524 (3,6)*
 525 \backslash
 526 ellipse(3,1){-};
 527 \end_layout
 528
 529 \begin_layout Plain Layout
 530
 531 (-3,12)*{}="1";
 532 \end_layout
 533
 534 \begin_layout Plain Layout
 535
 536 (3,12)*{}="2";
 537 \end_layout
 538
 539 \begin_layout Plain Layout
 540
 541 (-9,12)*{}="A2";
 542 \end_layout
 543
 544 \begin_layout Plain Layout
 545
 546 (9,12)*{}="B2";
 547 \end_layout
 548
 549 \begin_layout Plain Layout
 550
 551 "1";"2" **
 552 \backslash
 553 crv{(-3,7) & (3,7)};
 554 \end_layout
 555
 556 \begin_layout Plain Layout
 557
 558 (-3,0)*{}="A";
 559 \end_layout
 560
 561 \begin_layout Plain Layout
 562
 563 (3,0)*{}="B";
 564 \end_layout
 565
 566 \begin_layout Plain Layout
 567
 568 (-3,1)*{}="A1";
 569 \end_layout
 570
 571 \begin_layout Plain Layout
 572
 573 (3,1)*{}="B1";
 574 \end_layout
 575
 576 \begin_layout Plain Layout
 577
 578 "A";"A1" **
 579 \backslash
 580 dir{-};
 581 \end_layout
 582
 583 \begin_layout Plain Layout
 584
 585 "B";"B1" **
 586 \backslash
 587 dir{-};
 588 \end_layout
 589
 590 \begin_layout Plain Layout
 591
 592 "B2";"B1" **
 593 \backslash
 594 crv{(8,7) & (3,5)};
 595 \end_layout
 596
 597 \begin_layout Plain Layout
 598
 599 "A2";"A1" **
 600 \backslash
 601 crv{(-8,7) & (-3,5)};
 602 \end_layout
 603
 604 \begin_layout Plain Layout
 605
 606 %REFLECT
 607 \end_layout
 608
 609 \begin_layout Plain Layout
 610
 611 (3,-16)*{}="1";
 612 \end_layout
 613
 614 \begin_layout Plain Layout
 615
 616 (9,-16)*{}="2";
 617 \end_layout
 618
 619 \begin_layout Plain Layout
 620
 621 "1";"2" **
 622 \backslash
 623 crv{(3,-10) & (9,-10)};
 624 \end_layout
 625
 626 \begin_layout Plain Layout
 627
 628 (-3,-16)*{}="1";
 629 \end_layout
 630
 631 \begin_layout Plain Layout
 632
 633 (-9,-16)*{}="2";
 634 \end_layout
 635
 636 \begin_layout Plain Layout
 637
 638 "1";"2" **
 639 \backslash
 640 crv{(-3,-10) & (-9,-10)};
 641 \end_layout
 642
 643 \begin_layout Plain Layout
 644
 645 (-15,-16)*{}="A2";
 646 \end_layout
 647
 648 \begin_layout Plain Layout
 649
 650 (15,-16)*{}="B2";
 651 \end_layout
 652
 653 \begin_layout Plain Layout
 654
 655 (-3,0)*{}="A";
 656 \end_layout
 657
 658 \begin_layout Plain Layout
 659
 660 (3,0)*{}="B";
 661 \end_layout
 662
 663 \begin_layout Plain Layout
 664
 665 (-3,-1)*{}="A1";
 666 \end_layout
 667
 668 \begin_layout Plain Layout
 669
 670 (3,-1)*{}="B1";
 671 \end_layout
 672
 673 \begin_layout Plain Layout
 674
 675 "A";"A1" **
 676 \backslash
 677 dir{-};
 678 \end_layout
 679
 680 \begin_layout Plain Layout
 681
 682 "B";"B1" **
 683 \backslash
 684 dir{-};
 685 \end_layout
 686
 687 \begin_layout Plain Layout
 688
 689 "B2";"B1" **
 690 \backslash
 691 crv{(13,-6) & (2,-8)};
 692 \end_layout
 693
 694 \begin_layout Plain Layout
 695
 696 "A2";"A1" **
 697 \backslash
 698 crv{(-13,-6) & (-2,-8)};
 699 \end_layout
 700
 701 \begin_layout Plain Layout
 702
 703
 704 \backslash
 705 endxy
 706 \end_layout
 707
 708 \end_inset
 709
 710
 711 \end_layout
 712
 713 \end_inset
 714
 715
 716 \begin_inset Preview
 717
 718 \begin_layout Standard
 719 \begin_inset ERT
 720 status collapsed
 721
 722 \begin_layout Plain Layout
 723
 724
 725 \backslash
 726 xy 0;/r.18pc/:
 727 \end_layout
 728
 729 \begin_layout Plain Layout
 730
 731 (20,2)*{
 732 \backslash
 733 bullet}="RU"+(1,3)*{x^{
 734 \backslash
 735 ast}};
 736 \end_layout
 737
 738 \begin_layout Plain Layout
 739
 740 (16,-3)*{
 741 \backslash
 742 bullet}="RD"+(2.5,2)*{x^{
 743 \backslash
 744 ast}};
 745 \end_layout
 746
 747 \begin_layout Plain Layout
 748
 749 (-16,2)*{
 750 \backslash
 751 bullet}="LU"+(-1,2)*{x};
 752 \end_layout
 753
 754 \begin_layout Plain Layout
 755
 756 (-20,-3)*{
 757 \backslash
 758 bullet}="LD"+(-1,2)*{x};
 759 \end_layout
 760
 761 \begin_layout Plain Layout
 762
 763 "RU";"RD" **
 764 \backslash
 765 crv{(4,2) & (4,-1)}; ?(.1)*
 766 \backslash
 767 dir{<}; ?(.85)*
 768 \backslash
 769 dir{<};
 770 \end_layout
 771
 772 \begin_layout Plain Layout
 773
 774 "LD";"LU" **
 775 \backslash
 776 crv{(-4,-2) & (-4,1)};
 777 \end_layout
 778
 779 \begin_layout Plain Layout
 780
 781 ?(.08)*
 782 \backslash
 783 dir{<}; ?(.85)*
 784 \backslash
 785 dir{<};
 786 \end_layout
 787
 788 \begin_layout Plain Layout
 789
 790 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
 791 \end_layout
 792
 793 \begin_layout Plain Layout
 794
 795 "x1"; "x2" **
 796 \backslash
 797 crv{(7,-10) & (-7,-10)};
 798 \end_layout
 799
 800 \begin_layout Plain Layout
 801
 802 (16,-20)*{
 803 \backslash
 804 bullet}="RDD"+(2.5,-1)*{x^{
 805 \backslash
 806 ast}};
 807 \end_layout
 808
 809 \begin_layout Plain Layout
 810
 811 (-20,-20)*{
 812 \backslash
 813 bullet}="LDD"+(-1,-3)*{x};
 814 \end_layout
 815
 816 \begin_layout Plain Layout
 817
 818 (20,-12.5)*{
 819 \backslash
 820 bullet}="RUD"+(3.5,1)*{x^{
 821 \backslash
 822 ast}};
 823 \end_layout
 824
 825 \begin_layout Plain Layout
 826
 827 (-16,-15)*{
 828 \backslash
 829 bullet}="LUD";
 830 \end_layout
 831
 832 \begin_layout Plain Layout
 833
 834 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
 835 \end_layout
 836
 837 \begin_layout Plain Layout
 838
 839 "RD"; "RDD" **
 840 \backslash
 841 dir{-};
 842 \end_layout
 843
 844 \begin_layout Plain Layout
 845
 846 "LD"; "LDD" **
 847 \backslash
 848 dir{-};
 849 \end_layout
 850
 851 \begin_layout Plain Layout
 852
 853 "A"; "LUD" **
 854 \backslash
 855 dir{.};
 856 \end_layout
 857
 858 \begin_layout Plain Layout
 859
 860 "RDD"; "LDD" **
 861 \backslash
 862 crv{(0,-17)}; ?(.57)*
 863 \backslash
 864 dir{>};
 865 \end_layout
 866
 867 \begin_layout Plain Layout
 868
 869 "RU"; "RUD" **
 870 \backslash
 871 dir{-};
 872 \end_layout
 873
 874 \begin_layout Plain Layout
 875
 876 "LU"; "A" **
 877 \backslash
 878 dir{-};
 879 \end_layout
 880
 881 \begin_layout Plain Layout
 882
 883 "B"; "RUD" **
 884 \backslash
 885 crv{(18,-14.15)};
 886 \end_layout
 887
 888 \begin_layout Plain Layout
 889
 890 "B"; "LUD" **
 891 \backslash
 892 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
 893 \backslash
 894 dir{<};
 895 \end_layout
 896
 897 \begin_layout Plain Layout
 898
 899
 900 \backslash
 901 endxy
 902 \end_layout
 903
 904 \end_inset
 905
 906
 907 \end_layout
 908
 909 \end_inset
 910
 911
 912 \end_layout
 913
 914 \begin_layout Description
 915 Strings
 916 \end_layout
 917
 918 \begin_layout Standard
 919 \begin_inset Preview
 920
 921 \begin_layout Standard
 922 \begin_inset ERT
 923 status open
 924
 925 \begin_layout Plain Layout
 926
 927
 928 \backslash
 929 xy (-15,0)*{};(15,0)*{};
 930 \end_layout
 931
 932 \begin_layout Plain Layout
 933
 934
 935 \backslash
 936 endxy
 937 \end_layout
 938
 939 \begin_layout Plain Layout
 940
 941
 942 \backslash
 943 qquad =
 944 \backslash
 945 qquad
 946 \backslash
 947 xy
 948 \end_layout
 949
 950 \begin_layout Plain Layout
 951
 952 (-10,12)*{}; (-10,-12)*{}; **
 953 \backslash
 954 dir{-}?(.5)*
 955 \backslash
 956 dir{<}+(-4,0)*{F(x)};
 957 \end_layout
 958
 959 \begin_layout Plain Layout
 960
 961 (-2,12)*{}="1";
 962 \end_layout
 963
 964 \begin_layout Plain Layout
 965
 966 (6,-7) *{}="2";
 967 \end_layout
 968
 969 \begin_layout Plain Layout
 970
 971 (14,-7) *{}="3";
 972 \end_layout
 973
 974 \begin_layout Plain Layout
 975
 976 (14,-13)*{}="3'";
 977 \end_layout
 978
 979 \begin_layout Plain Layout
 980
 981 (18,0) *={}="";
 982 \end_layout
 983
 984 \begin_layout Plain Layout
 985
 986 "1";"2" **
 987 \backslash
 988 crv{(-4,-21)&(5,-15)};
 989 \end_layout
 990
 991 \begin_layout Plain Layout
 992
 993 ?(.15)*
 994 \backslash
 995 dir{<}+(5,10)*{
 996 \backslash
 997 overline{F(x)}};
 998 \end_layout
 999
1000 \begin_layout Plain Layout
1001
1002 "2";"3" **
1003 \backslash
1004 crv{(6,1)&(14,1)};
1005 \end_layout
1006
1007 \begin_layout Plain Layout
1008
1009 ?(0)*
1010 \backslash
1011 dir{<}+(4,8)*{
1012 \backslash
1013 widetilde{F(i_x)}} ;
1014 \end_layout
1015
1016 \begin_layout Plain Layout
1017
1018 ?(.95)*
1019 \backslash
1020 dir{<}+(5,-2)*{F(
1021 \backslash
1022 overline x)};
1023 \end_layout
1024
1025 \begin_layout Plain Layout
1026
1027 "3";"3'" **
1028 \backslash
1029 dir{-};
1030 \end_layout
1031
1032 \begin_layout Plain Layout
1033
1034 (-2,6)*{}="X1";
1035 \end_layout
1036
1037 \begin_layout Plain Layout
1038
1039 (-10,6)*{}="X2";
1040 \end_layout
1041
1042 \begin_layout Plain Layout
1043
1044 "X1";"X2" **
1045 \backslash
1046 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1047 \end_layout
1048
1049 \begin_layout Plain Layout
1050
1051 (-2,-6)*{}="XA";
1052 \end_layout
1053
1054 \begin_layout Plain Layout
1055
1056 (-10,-6)*{}="XB";
1057 \end_layout
1058
1059 \begin_layout Plain Layout
1060
1061 "XA";"XB" **
1062 \backslash
1063 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1064 \end_layout
1065
1066 \begin_layout Plain Layout
1067
1068
1069 \backslash
1070 endxy
1071 \end_layout
1072
1073 \end_inset
1074
1075
1076 \end_layout
1077
1078 \end_inset
1079
1080
1081 \end_layout
1082
1083 \begin_layout Description
1084 Categories
1085 \end_layout
1086
1087 \begin_layout Standard
1088 \begin_inset Preview
1089
1090 \begin_layout Standard
1091 \begin_inset ERT
1092 status collapsed
1093
1094 \begin_layout Plain Layout
1095
1096
1097 \backslash
1098 xymatrix{
1099 \end_layout
1100
1101 \begin_layout Plain Layout
1102
1103 (x
1104 \backslash
1105 otimes 1)
1106 \backslash
1107 otimes y
1108 \end_layout
1109
1110 \begin_layout Plain Layout
1111
1112
1113 \backslash
1114 ar[rr]^{a_{x,1,y}}
1115 \end_layout
1116
1117 \begin_layout Plain Layout
1118
1119
1120 \backslash
1121 ar[dr]_{r_x
1122 \backslash
1123 otimes 1_y}
1124 \end_layout
1125
1126 \begin_layout Plain Layout
1127
1128 && x
1129 \backslash
1130 otimes(1
1131 \backslash
1132 otimes y)
1133 \end_layout
1134
1135 \begin_layout Plain Layout
1136
1137
1138 \backslash
1139 ar[dl]^{1_x
1140 \backslash
1141 otimes
1142 \backslash
1143 ell_y }
1144 \backslash
1145
1146 \backslash
1147
1148 \end_layout
1149
1150 \begin_layout Plain Layout
1151
1152 & x
1153 \backslash
1154 otimes y }
1155 \end_layout
1156
1157 \end_inset
1158
1159
1160 \end_layout
1161
1162 \end_inset
1163
1164
1165 \begin_inset Preview
1166
1167 \begin_layout Standard
1168 \begin_inset ERT
1169 status collapsed
1170
1171 \begin_layout Plain Layout
1172
1173
1174 \backslash
1175 xy
1176 \end_layout
1177
1178 \begin_layout Plain Layout
1179
1180 (-9,0)*+{
1181 \backslash
1182 bullet}="1";
1183 \end_layout
1184
1185 \begin_layout Plain Layout
1186
1187 (0,0)*+{
1188 \backslash
1189 bullet}="2";
1190 \end_layout
1191
1192 \begin_layout Plain Layout
1193
1194 {
1195 \backslash
1196 ar@/^.9pc/ "1";"2"};
1197 \end_layout
1198
1199 \begin_layout Plain Layout
1200
1201 {
1202 \backslash
1203 ar@/_.9pc/ "1";"2"};
1204 \end_layout
1205
1206 \begin_layout Plain Layout
1207
1208 {
1209 \backslash
1210 ar@/^2pc/ "1";"2"};
1211 \end_layout
1212
1213 \begin_layout Plain Layout
1214
1215 {
1216 \backslash
1217 ar@/_2pc/ "1";"2"};
1218 \end_layout
1219
1220 \begin_layout Plain Layout
1221
1222 {
1223 \backslash
1224 ar@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1225 \end_layout
1226
1227 \begin_layout Plain Layout
1228
1229 {
1230 \backslash
1231 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1232 \end_layout
1233
1234 \begin_layout Plain Layout
1235
1236 {
1237 \backslash
1238 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1239 \end_layout
1240
1241 \begin_layout Plain Layout
1242
1243 (0,0)*+{
1244 \backslash
1245 bullet}="1";
1246 \end_layout
1247
1248 \begin_layout Plain Layout
1249
1250 (9,0)*+{
1251 \backslash
1252 bullet}="2";
1253 \end_layout
1254
1255 \begin_layout Plain Layout
1256
1257 (18,0)*+{
1258 \backslash
1259 bullet}="3";
1260 \end_layout
1261
1262 \begin_layout Plain Layout
1263
1264 {
1265 \backslash
1266 ar "1";"2"};
1267 \end_layout
1268
1269 \begin_layout Plain Layout
1270
1271 {
1272 \backslash
1273 ar "2";"3"};
1274 \end_layout
1275
1276 \begin_layout Plain Layout
1277
1278 {
1279 \backslash
1280 ar@/^1pc/ "1";"2"};
1281 \end_layout
1282
1283 \begin_layout Plain Layout
1284
1285 {
1286 \backslash
1287 ar@/_1pc/ "1";"2"};
1288 \end_layout
1289
1290 \begin_layout Plain Layout
1291
1292 {
1293 \backslash
1294 ar@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1295 \end_layout
1296
1297 \begin_layout Plain Layout
1298
1299 {
1300 \backslash
1301 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1302 \end_layout
1303
1304 \begin_layout Plain Layout
1305
1306
1307 \backslash
1308 endxy
1309 \end_layout
1310
1311 \end_inset
1312
1313
1314 \end_layout
1315
1316 \end_inset
1317
1318
1319 \end_layout
1320
1321 \begin_layout Description
1322 Transformations
1323 \end_layout
1324
1325 \begin_layout Standard
1326 \begin_inset Preview
1327
1328 \begin_layout Standard
1329 \begin_inset ERT
1330 status collapsed
1331
1332 \begin_layout Plain Layout
1333
1334
1335 \backslash
1336 xy %FIG.19.
1337  Natural transformation between functors.
1338 \end_layout
1339
1340 \begin_layout Plain Layout
1341
1342 (-26,-2)*+{
1343 \backslash
1344 bullet}="a";
1345 \end_layout
1346
1347 \begin_layout Plain Layout
1348
1349 (-12,3)*+{
1350 \backslash
1351 bullet}="b";
1352 \end_layout
1353
1354 \begin_layout Plain Layout
1355
1356 (-16,-5)*+{
1357 \backslash
1358 bullet}="c";
1359 \end_layout
1360
1361 \begin_layout Plain Layout
1362
1363 {
1364 \backslash
1365 ar@/^.25pc/ "a";"b"};
1366 \end_layout
1367
1368 \begin_layout Plain Layout
1369
1370 {
1371 \backslash
1372 ar@/_.25pc/"a";"c"};
1373 \end_layout
1374
1375 \begin_layout Plain Layout
1376
1377 {
1378 \backslash
1379 ar@/_.15pc/ "b";"c"};
1380 \end_layout
1381
1382 \begin_layout Plain Layout
1383
1384 %START TOP
1385 \end_layout
1386
1387 \begin_layout Plain Layout
1388
1389 (12,10)*+{
1390 \backslash
1391 bullet}="ta";
1392 \end_layout
1393
1394 \begin_layout Plain Layout
1395
1396 (26,15)*+{
1397 \backslash
1398 bullet}="tb";
1399 \end_layout
1400
1401 \begin_layout Plain Layout
1402
1403 (22,8)*+{
1404 \backslash
1405 bullet}="tc";
1406 \end_layout
1407
1408 \begin_layout Plain Layout
1409
1410 {
1411 \backslash
1412 ar@/^.25pc/ "ta";"tb"};
1413 \end_layout
1414
1415 \begin_layout Plain Layout
1416
1417 {
1418 \backslash
1419 ar@/_.25pc/ "ta";"tc"};
1420 \end_layout
1421
1422 \begin_layout Plain Layout
1423
1424 {
1425 \backslash
1426 ar@/_.15pc/ "tb";"tc"};
1427 \end_layout
1428
1429 \begin_layout Plain Layout
1430
1431 %START bottom
1432 \end_layout
1433
1434 \begin_layout Plain Layout
1435
1436 (12,-10)*+{
1437 \backslash
1438 bullet}="ba";
1439 \end_layout
1440
1441 \begin_layout Plain Layout
1442
1443 (26,-5)*+{
1444 \backslash
1445 bullet}="bb";
1446 \end_layout
1447
1448 \begin_layout Plain Layout
1449
1450 (22,-12)*+{
1451 \backslash
1452 bullet}="bc";
1453 \end_layout
1454
1455 \begin_layout Plain Layout
1456
1457 {
1458 \backslash
1459 ar@/^.25pc/@{.>} "ba";"bb"};
1460 \end_layout
1461
1462 \begin_layout Plain Layout
1463
1464 {
1465 \backslash
1466 ar@/_.25pc/ "ba";"bc"};
1467 \end_layout
1468
1469 \begin_layout Plain Layout
1470
1471 {
1472 \backslash
1473 ar@/_.15pc/ "bb";"bc"};
1474 \end_layout
1475
1476 \begin_layout Plain Layout
1477
1478 %START CONNECT
1479 \end_layout
1480
1481 \begin_layout Plain Layout
1482
1483 {
1484 \backslash
1485 ar@/_.15pc/ "ta";"ba"};
1486 \end_layout
1487
1488 \begin_layout Plain Layout
1489
1490 {
1491 \backslash
1492 ar@/_.15pc/ "tb";"bb"};
1493 \end_layout
1494
1495 \begin_layout Plain Layout
1496
1497 {
1498 \backslash
1499 ar@/_.15pc/ "tc";"bc"};
1500 \end_layout
1501
1502 \begin_layout Plain Layout
1503
1504 %START ARROWS AND LABELS
1505 \end_layout
1506
1507 \begin_layout Plain Layout
1508
1509 (-12,6)*{}="DF";
1510 \end_layout
1511
1512 \begin_layout Plain Layout
1513
1514 (6,10)*{}="CF";
1515 \end_layout
1516
1517 \begin_layout Plain Layout
1518
1519 {
1520 \backslash
1521 ar@/^.35pc/^F "DF";"CF"};
1522 \end_layout
1523
1524 \begin_layout Plain Layout
1525
1526 (-12,-6)*{}="DF";
1527 \end_layout
1528
1529 \begin_layout Plain Layout
1530
1531 (6,-10)*{}="CF";
1532 \end_layout
1533
1534 \begin_layout Plain Layout
1535
1536 {
1537 \backslash
1538 ar@/_.35pc/_G "DF";"CF"};
1539 \end_layout
1540
1541 \begin_layout Plain Layout
1542
1543 (-2,5)*{}="DF";
1544 \end_layout
1545
1546 \begin_layout Plain Layout
1547
1548 (-2,-5)*{}="CF";
1549 \end_layout
1550
1551 \begin_layout Plain Layout
1552
1553 {
1554 \backslash
1555 ar@{=>}^{
1556 \backslash
1557 alpha} "DF";"CF"};
1558 \end_layout
1559
1560 \begin_layout Plain Layout
1561
1562 (29,3)*{D};
1563 \end_layout
1564
1565 \begin_layout Plain Layout
1566
1567 (-23,3)*{C};
1568 \end_layout
1569
1570 \begin_layout Plain Layout
1571
1572
1573 \backslash
1574 endxy
1575 \end_layout
1576
1577 \end_inset
1578
1579
1580 \end_layout
1581
1582 \end_inset
1583
1584
1585 \end_layout
1586
1587 \begin_layout Section
1588 IPA
1589 \end_layout
1590
1591 \begin_layout Standard
1592 \begin_inset Preview
1593
1594 \begin_layout Standard
1595 \begin_inset ERT
1596 status collapsed
1597
1598 \begin_layout Plain Layout
1599
1600
1601 \backslash
1602 textipa{Ekspl@"neIS@n}
1603 \end_layout
1604
1605 \end_inset
1606
1607
1608 \end_layout
1609
1610 \end_inset
1611
1612
1613 \end_layout
1614
1615 \begin_layout Section
1616 QTree
1617 \end_layout
1618
1619 \begin_layout Standard
1620 \begin_inset Preview
1621
1622 \begin_layout Standard
1623 \begin_inset ERT
1624 status collapsed
1625
1626 \begin_layout Plain Layout
1627
1628
1629 \backslash
1630 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1631 \end_layout
1632
1633 \end_inset
1634
1635
1636 \end_layout
1637
1638 \end_inset
1639
1640
1641 \begin_inset Preview
1642
1643 \begin_layout Standard
1644 \begin_inset ERT
1645 status collapsed
1646
1647 \begin_layout Plain Layout
1648
1649
1650 \backslash
1651 Tree [.$
1652 \backslash
1653 sigma$ $
1654 \backslash
1655 mu$ $
1656 \backslash
1657 mu$ ]
1658 \end_layout
1659
1660 \end_inset
1661
1662
1663 \end_layout
1664
1665 \end_inset
1666
1667
1668 \end_layout
1669
1670 \begin_layout Section
1671 PSTricks
1672 \begin_inset CommandInset label
1673 LatexCommand label
1674 name "sec:PSTricks"
1675
1676 \end_inset
1677
1678
1679 \end_layout
1680
1681 \begin_layout Standard
1682 Some simple graphing examples.
1683 \end_layout
1684
1685 \begin_layout Subsection
1686 Function plotting
1687 \end_layout
1688
1689 \begin_layout Standard
1690 \begin_inset Preview
1691
1692 \begin_layout Standard
1693 \begin_inset ERT
1694 status open
1695
1696 \begin_layout Plain Layout
1697
1698
1699 \backslash
1700 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1701 \end_layout
1702
1703 \begin_layout Plain Layout
1704
1705
1706 \backslash
1707 psaxes{->}(0,0)(0,-3)(10,3)
1708 \end_layout
1709
1710 \begin_layout Plain Layout
1711
1712
1713 \backslash
1714 uput[-90](10,0){$x$}
1715 \backslash
1716 uput[0](0,3){$f(x)$}
1717 \end_layout
1718
1719 \begin_layout Plain Layout
1720
1721
1722 \backslash
1723 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1724 \end_layout
1725
1726 \begin_layout Plain Layout
1727
1728
1729 \backslash
1730 end{pspicture*}
1731 \end_layout
1732
1733 \end_inset
1734
1735
1736 \end_layout
1737
1738 \end_inset
1739
1740
1741 \end_layout
1742
1743 \begin_layout Subsection
1744 Inline data plotting
1745 \end_layout
1746
1747 \begin_layout Standard
1748 \align center
1749 \begin_inset Preview
1750
1751 \begin_layout Standard
1752 \align center
1753 \begin_inset ERT
1754 status open
1755
1756 \begin_layout Plain Layout
1757
1758
1759 \backslash
1760 begin{pspicture*}(-1.5,-1.5)(11,5)
1761 \end_layout
1762
1763 \begin_layout Plain Layout
1764
1765
1766 \backslash
1767 psaxes{->}(0,0)(0,0)(10,5)
1768 \end_layout
1769
1770 \begin_layout Plain Layout
1771
1772
1773 \backslash
1774 psset{linewidth=2.5pt}
1775 \end_layout
1776
1777 \begin_layout Plain Layout
1778
1779
1780 \backslash
1781 rput(5.0,-1.0){Speed [MPH]}
1782 \end_layout
1783
1784 \begin_layout Plain Layout
1785
1786
1787 \backslash
1788 rput(-1.0,1.0){
1789 \backslash
1790 begin{rotate}{90}Cost [Dollars]
1791 \backslash
1792 end{rotate}}
1793 \end_layout
1794
1795 \begin_layout Plain Layout
1796
1797
1798 \backslash
1799 savedata{
1800 \backslash
1801 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1802 \end_layout
1803
1804 \begin_layout Plain Layout
1805
1806
1807 \backslash
1808 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1809 \backslash
1810 mydata}
1811 \end_layout
1812
1813 \begin_layout Plain Layout
1814
1815
1816 \backslash
1817 end{pspicture*}
1818 \end_layout
1819
1820 \end_inset
1821
1822
1823 \end_layout
1824
1825 \end_inset
1826
1827
1828 \end_layout
1829
1830 \begin_layout Subsection
1831 Lissajous curves
1832 \end_layout
1833
1834 \begin_layout Standard
1835 \begin_inset Preview
1836
1837 \begin_layout Standard
1838 \begin_inset ERT
1839 status open
1840
1841 \begin_layout Plain Layout
1842
1843
1844 \backslash
1845 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1846 \end_layout
1847
1848 \begin_layout Plain Layout
1849
1850
1851 \backslash
1852 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1853  cos 100 t mul sin}
1854 \end_layout
1855
1856 \begin_layout Plain Layout
1857
1858
1859 \backslash
1860 end{pspicture*}
1861 \end_layout
1862
1863 \end_inset
1864
1865
1866 \end_layout
1867
1868 \end_inset
1869
1870
1871 \begin_inset space \hfill{}
1872 \end_inset
1873
1874
1875 \begin_inset Preview
1876
1877 \begin_layout Standard
1878 \begin_inset ERT
1879 status open
1880
1881 \begin_layout Plain Layout
1882
1883
1884 \backslash
1885 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1886 \end_layout
1887
1888 \begin_layout Plain Layout
1889
1890
1891 \backslash
1892 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1893  mul cos 100 t mul sin}
1894 \end_layout
1895
1896 \begin_layout Plain Layout
1897
1898
1899 \backslash
1900 end{pspicture*}
1901 \end_layout
1902
1903 \end_inset
1904
1905
1906 \end_layout
1907
1908 \end_inset
1909
1910
1911 \begin_inset space \hfill{}
1912 \end_inset
1913
1914
1915 \begin_inset Preview
1916
1917 \begin_layout Standard
1918 \begin_inset ERT
1919 status open
1920
1921 \begin_layout Plain Layout
1922
1923
1924 \backslash
1925 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1926 \end_layout
1927
1928 \begin_layout Plain Layout
1929
1930
1931 \backslash
1932 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1933  mul cos 200 t mul sin}
1934 \end_layout
1935
1936 \begin_layout Plain Layout
1937
1938
1939 \backslash
1940 end{pspicture*}
1941 \end_layout
1942
1943 \end_inset
1944
1945
1946 \end_layout
1947
1948 \end_inset
1949
1950
1951 \begin_inset space \hfill{}
1952 \end_inset
1953
1954
1955 \begin_inset Preview
1956
1957 \begin_layout Standard
1958 \begin_inset ERT
1959 status open
1960
1961 \begin_layout Plain Layout
1962
1963
1964 \backslash
1965 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1966 \end_layout
1967
1968 \begin_layout Plain Layout
1969
1970
1971 \backslash
1972 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1973  mul cos 200 t mul sin}
1974 \end_layout
1975
1976 \begin_layout Plain Layout
1977
1978
1979 \backslash
1980 end{pspicture*}
1981 \end_layout
1982
1983 \end_inset
1984
1985
1986 \end_layout
1987
1988 \end_inset
1989
1990
1991 \end_layout
1992
1993 \begin_layout Section
1994 TikZ
1995 \end_layout
1996
1997 \begin_layout Standard
1998 \begin_inset Flex URL
1999 status collapsed
2000
2001 \begin_layout Plain Layout
2002
2003 http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
2004 \end_layout
2005
2006 \end_inset
2007
2008
2009 \end_layout
2010
2011 \begin_layout Standard
2012 \begin_inset Preview
2013
2014 \begin_layout Standard
2015 \begin_inset ERT
2016 status collapsed
2017
2018 \begin_layout Plain Layout
2019
2020
2021 \backslash
2022 def
2023 \backslash
2024 iangle{35} % Angle of the inclined plane
2025 \end_layout
2026
2027 \begin_layout Plain Layout
2028
2029
2030 \backslash
2031 def
2032 \backslash
2033 down{-90}
2034 \end_layout
2035
2036 \begin_layout Plain Layout
2037
2038
2039 \backslash
2040 def
2041 \backslash
2042 arcr{0.5cm} % Radius of the arc used to indicate angles
2043 \end_layout
2044
2045 \begin_layout Plain Layout
2046
2047 \end_layout
2048
2049 \begin_layout Plain Layout
2050
2051
2052 \backslash
2053 begin{tikzpicture}[
2054 \end_layout
2055
2056 \begin_layout Plain Layout
2057
2058     force/.style={>=latex,draw=blue,fill=blue},
2059 \end_layout
2060
2061 \begin_layout Plain Layout
2062
2063     axis/.style={densely dashed,gray,font=
2064 \backslash
2065 small},
2066 \end_layout
2067
2068 \begin_layout Plain Layout
2069
2070     M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2071 \end_layout
2072
2073 \begin_layout Plain Layout
2074
2075     m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2076 \end_layout
2077
2078 \begin_layout Plain Layout
2079
2080     plane/.style={draw=black,fill=blue!10},
2081 \end_layout
2082
2083 \begin_layout Plain Layout
2084
2085     string/.style={draw=red, thick},
2086 \end_layout
2087
2088 \begin_layout Plain Layout
2089
2090     pulley/.style={thick},
2091 \end_layout
2092
2093 \begin_layout Plain Layout
2094
2095 ]
2096 \end_layout
2097
2098 \begin_layout Plain Layout
2099
2100 \end_layout
2101
2102 \begin_layout Plain Layout
2103
2104
2105 \backslash
2106 matrix[column sep=1cm] {
2107 \end_layout
2108
2109 \begin_layout Plain Layout
2110
2111     %% Sketch
2112 \end_layout
2113
2114 \begin_layout Plain Layout
2115
2116
2117 \backslash
2118 draw[plane] (0,-1) coordinate (base)
2119 \end_layout
2120
2121 \begin_layout Plain Layout
2122
2123                      -- coordinate[pos=0.5] (mid) ++(
2124 \backslash
2125 iangle:3) coordinate (top)
2126 \end_layout
2127
2128 \begin_layout Plain Layout
2129
2130                      |- (base) -- cycle;
2131 \end_layout
2132
2133 \begin_layout Plain Layout
2134
2135
2136 \backslash
2137 path (mid) node[M,rotate=
2138 \backslash
2139 iangle,yshift=0.25cm] (M) {};
2140 \end_layout
2141
2142 \begin_layout Plain Layout
2143
2144
2145 \backslash
2146 draw[pulley] (top) -- ++(
2147 \backslash
2148 iangle:0.25) circle (0.25cm)
2149 \end_layout
2150
2151 \begin_layout Plain Layout
2152
2153                    ++ (90-
2154 \backslash
2155 iangle:0.5) coordinate (pulley);
2156 \end_layout
2157
2158 \begin_layout Plain Layout
2159
2160
2161 \backslash
2162 draw[string] (M.east) -- ++(
2163 \backslash
2164 iangle:1.5cm) arc (90+
2165 \backslash
2166 iangle:0:0.25)
2167 \end_layout
2168
2169 \begin_layout Plain Layout
2170
2171                   -- ++(0,-1) node[m] {};
2172 \end_layout
2173
2174 \begin_layout Plain Layout
2175
2176 \end_layout
2177
2178 \begin_layout Plain Layout
2179
2180
2181 \backslash
2182 draw[->] (base)++(
2183 \backslash
2184 arcr,0) arc (0:
2185 \backslash
2186 iangle:
2187 \backslash
2188 arcr);
2189 \end_layout
2190
2191 \begin_layout Plain Layout
2192
2193
2194 \backslash
2195 path (base)++(
2196 \backslash
2197 iangle*0.5:
2198 \backslash
2199 arcr+5pt) node {$
2200 \backslash
2201 alpha$};
2202 \end_layout
2203
2204 \begin_layout Plain Layout
2205
2206     %%
2207 \end_layout
2208
2209 \begin_layout Plain Layout
2210
2211 \end_layout
2212
2213 \begin_layout Plain Layout
2214
2215 &
2216 \end_layout
2217
2218 \begin_layout Plain Layout
2219
2220     %% Free body diagram of M
2221 \end_layout
2222
2223 \begin_layout Plain Layout
2224
2225
2226 \backslash
2227 begin{scope}[rotate=
2228 \backslash
2229 iangle]
2230 \end_layout
2231
2232 \begin_layout Plain Layout
2233
2234
2235 \backslash
2236 node[M,transform shape] (M) {};
2237 \end_layout
2238
2239 \begin_layout Plain Layout
2240
2241         % Draw axes and help lines
2242 \end_layout
2243
2244 \begin_layout Plain Layout
2245
2246 \end_layout
2247
2248 \begin_layout Plain Layout
2249
2250         {[axis,->]
2251 \end_layout
2252
2253 \begin_layout Plain Layout
2254
2255
2256 \backslash
2257 draw (0,-1) -- (0,2) node[right] {$+y$};
2258 \end_layout
2259
2260 \begin_layout Plain Layout
2261
2262
2263 \backslash
2264 draw (M) -- ++(2,0) node[right] {$+x$};
2265 \end_layout
2266
2267 \begin_layout Plain Layout
2268
2269             % Indicate angle.
2270  The code is a bit awkward.
2271 \end_layout
2272
2273 \begin_layout Plain Layout
2274
2275 \end_layout
2276
2277 \begin_layout Plain Layout
2278
2279
2280 \backslash
2281 draw[solid,shorten >=0.5pt] (
2282 \backslash
2283 down-
2284 \backslash
2285 iangle:
2286 \backslash
2287 arcr)
2288 \end_layout
2289
2290 \begin_layout Plain Layout
2291
2292                 arc(
2293 \backslash
2294 down-
2295 \backslash
2296 iangle:
2297 \backslash
2298 down:
2299 \backslash
2300 arcr);
2301 \end_layout
2302
2303 \begin_layout Plain Layout
2304
2305
2306 \backslash
2307 node at (
2308 \backslash
2309 down-0.5*
2310 \backslash
2311 iangle:1.3*
2312 \backslash
2313 arcr) {$
2314 \backslash
2315 alpha$};
2316 \end_layout
2317
2318 \begin_layout Plain Layout
2319
2320         }
2321 \end_layout
2322
2323 \begin_layout Plain Layout
2324
2325 \end_layout
2326
2327 \begin_layout Plain Layout
2328
2329         % Forces
2330 \end_layout
2331
2332 \begin_layout Plain Layout
2333
2334         {[force,->]
2335 \end_layout
2336
2337 \begin_layout Plain Layout
2338
2339             % Assuming that Mg = 1.
2340  The normal force will therefore be cos(alpha)
2341 \end_layout
2342
2343 \begin_layout Plain Layout
2344
2345
2346 \backslash
2347 draw (M.center) -- ++(0,{cos(
2348 \backslash
2349 iangle)}) node[above right] {$N$};
2350 \end_layout
2351
2352 \begin_layout Plain Layout
2353
2354
2355 \backslash
2356 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2357 \end_layout
2358
2359 \begin_layout Plain Layout
2360
2361
2362 \backslash
2363 draw (M.east) -- ++(1,0) node[above] {$T$};
2364 \end_layout
2365
2366 \begin_layout Plain Layout
2367
2368         }
2369 \end_layout
2370
2371 \begin_layout Plain Layout
2372
2373 \end_layout
2374
2375 \begin_layout Plain Layout
2376
2377
2378 \backslash
2379 end{scope}
2380 \end_layout
2381
2382 \begin_layout Plain Layout
2383
2384     % Draw gravity force.
2385  The code is put outside the rotated
2386 \end_layout
2387
2388 \begin_layout Plain Layout
2389
2390     % scope for simplicity.
2391  No need to do any angle calculations.
2392
2393 \end_layout
2394
2395 \begin_layout Plain Layout
2396
2397
2398 \backslash
2399 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2400 \end_layout
2401
2402 \begin_layout Plain Layout
2403
2404     %%
2405 \end_layout
2406
2407 \begin_layout Plain Layout
2408
2409 \end_layout
2410
2411 \begin_layout Plain Layout
2412
2413 &
2414 \end_layout
2415
2416 \begin_layout Plain Layout
2417
2418     %%%
2419 \end_layout
2420
2421 \begin_layout Plain Layout
2422
2423     % Free body diagram of m
2424 \end_layout
2425
2426 \begin_layout Plain Layout
2427
2428
2429 \backslash
2430 node[m] (m) {};
2431 \end_layout
2432
2433 \begin_layout Plain Layout
2434
2435
2436 \backslash
2437 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2438 \end_layout
2439
2440 \begin_layout Plain Layout
2441
2442     {[force,->]
2443 \end_layout
2444
2445 \begin_layout Plain Layout
2446
2447
2448 \backslash
2449 draw (m.north) -- ++(0,1) node[above] {$T'$};
2450 \end_layout
2451
2452 \begin_layout Plain Layout
2453
2454
2455 \backslash
2456 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2457 \end_layout
2458
2459 \begin_layout Plain Layout
2460
2461     }
2462 \end_layout
2463
2464 \begin_layout Plain Layout
2465
2466 \end_layout
2467
2468 \begin_layout Plain Layout
2469
2470
2471 \backslash
2472
2473 \backslash
2474
2475 \end_layout
2476
2477 \begin_layout Plain Layout
2478
2479 };
2480 \end_layout
2481
2482 \begin_layout Plain Layout
2483
2484
2485 \backslash
2486 end{tikzpicture}
2487 \end_layout
2488
2489 \begin_layout Plain Layout
2490
2491 \end_layout
2492
2493 \end_inset
2494
2495
2496 \end_layout
2497
2498 \end_inset
2499
2500
2501 \end_layout
2502
2503 \end_body
2504 \end_document