lib/examples/instant_preview.lyx

   1 #LyX 2.2 created this file. For more info see http://www.lyx.org/
   2 \lyxformat 503
   3 \begin_document
   4 \begin_header
   5 \origin /systemlyxdir/examples/
   6 \textclass article
   7 \begin_preamble
   8 \usepackage{etex}
   9 \usepackage[all, knot]{xy}
  10 \xyoption{arc}
  11 \usepackage{qtree}
  12 \usepackage{tipa}
  13 \usepackage{pstricks}
  14 \usepackage{pst-plot}
  15 \usepackage{rotating}
  16 \usepackage{tikz}
  17 \usetikzlibrary{scopes}
  18 \end_preamble
  19 \use_default_options false
  20 \maintain_unincluded_children false
  21 \language english
  22 \language_package default
  23 \inputencoding auto
  24 \fontencoding global
  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
  31 \font_sc false
  32 \font_osf false
  33 \font_sf_scale 100 100
  34 \font_tt_scale 100 100
  35 \graphics default
  36 \default_output_format pdf
  37 \output_sync 0
  38 \bibtex_command default
  39 \index_command default
  40 \paperfontsize default
  41 \spacing single
  42 \use_hyperref false
  43 \papersize default
  44 \use_geometry false
  45 \use_package amsmath 1
  46 \use_package amssymb 1
  47 \use_package cancel 0
  48 \use_package esint 1
  49 \use_package mathdots 1
  50 \use_package mathtools 0
  51 \use_package mhchem 1
  52 \use_package stackrel 0
  53 \use_package stmaryrd 0
  54 \use_package undertilde 0
  55 \cite_engine basic
  56 \cite_engine_type default
  57 \biblio_style plain
  58 \use_bibtopic false
  59 \use_indices false
  60 \paperorientation portrait
  61 \suppress_date false
  62 \justification true
  63 \use_refstyle 0
  64 \index Index
  65 \shortcut idx
  66 \color #008000
  67 \end_index
  68 \secnumdepth 3
  69 \tocdepth 3
  70 \paragraph_separation indent
  71 \paragraph_indentation default
  72 \quotes_language english
  73 \papercolumns 1
  74 \papersides 1
  75 \paperpagestyle default
  76 \tracking_changes false
  77 \output_changes false
  78 \html_math_output 0
  79 \html_css_as_file 0
  80 \html_be_strict true
  81 \end_header
  82
  83 \begin_body
  84
  85 \begin_layout Section
  86 Introduction
  87 \end_layout
  88
  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:
  92 \end_layout
  93
  94 \begin_layout LyX-Code
  95 xy, qtree, tipa, pstricks, pst-plot, rotating, tikz, pgf, etex
  96 \end_layout
  97
  98 \begin_layout Standard
  99 Due to the use of postscript specials in Section
 100 \begin_inset CommandInset ref
 101 LatexCommand ref
 102 reference "sec:PSTricks"
 103
 104 \end_inset
 105
 106 , only the Postscript or PDF (ps2pdf) output formats will correctly render
 107  the included images.
 108  However, the PDF (Xe\SpecialCharNoPassThru TeX
 109 ) output seems to also work, while trying to typeset
 110  the document with
 111 \family typewriter
 112 pdflatex
 113 \family default
 114  or
 115 \family typewriter
 116 pdflualatex
 117 \family default
 118  will generate errors.
 119 \end_layout
 120
 121 \begin_layout Section
 122 Diagrams by XY(-pic)
 123 \end_layout
 124
 125 \begin_layout Standard
 126 Few examples of diagrams were taken from Aaron Landa's archive of xy-pic
 127  examples, see
 128 \begin_inset Flex URL
 129 status collapsed
 130
 131 \begin_layout Plain Layout
 132
 133 http://www.math.columbia.edu/~lauda/xy/
 134 \end_layout
 135
 136 \end_inset
 137
 138 .
 139 \end_layout
 140
 141 \begin_layout Description
 142 Braid
 143 \end_layout
 144
 145 \begin_layout Standard
 146 \begin_inset Preview
 147
 148 \begin_layout Standard
 149 \begin_inset ERT
 150 status collapsed
 151
 152 \begin_layout Plain Layout
 153
 154
 155 \backslash
 156 xy
 157 \end_layout
 158
 159 \begin_layout Plain Layout
 160
 161 (5,10)*{}; (-10,-10)*{} **
 162 \backslash
 163 crv{(6,-2)&(-12,4)}
 164 \end_layout
 165
 166 \begin_layout Plain Layout
 167
 168
 169 \backslash
 170 POS?(.25)*{
 171 \backslash
 172 hole}="x"
 173 \backslash
 174 POS?(.45)*{
 175 \backslash
 176 hole}="y"
 177 \backslash
 178 POS?(.6)*{
 179 \backslash
 180 hole}="z";
 181 \end_layout
 182
 183 \begin_layout Plain Layout
 184
 185 "y"+(0,-1); (2,-10)*{} **
 186 \backslash
 187 crv{}
 188 \backslash
 189 POS?(.2)*{
 190 \backslash
 191 hole}="M";
 192 \end_layout
 193
 194 \begin_layout Plain Layout
 195
 196 (-10,10)*{}; "z" **
 197 \backslash
 198 crv{(-9,0)};
 199 \end_layout
 200
 201 \begin_layout Plain Layout
 202
 203 "z"; "M" **
 204 \backslash
 205 crv{};
 206 \end_layout
 207
 208 \begin_layout Plain Layout
 209
 210 "M"; "x" **
 211 \backslash
 212 crv{(5,0)};
 213 \end_layout
 214
 215 \begin_layout Plain Layout
 216
 217 "x"; "y" **
 218 \backslash
 219 crv{(0,7) & (-5,6)};
 220 \end_layout
 221
 222 \begin_layout Plain Layout
 223
 224
 225 \backslash
 226 endxy
 227 \end_layout
 228
 229 \end_inset
 230
 231
 232 \end_layout
 233
 234 \end_inset
 235
 236
 237 \end_layout
 238
 239 \begin_layout Description
 240 Knots
 241 \end_layout
 242
 243 \begin_layout Standard
 244 \begin_inset Preview
 245
 246 \begin_layout Standard
 247 \begin_inset ERT
 248 status collapsed
 249
 250 \begin_layout Plain Layout
 251
 252
 253 \backslash
 254 xy
 255 \end_layout
 256
 257 \begin_layout Plain Layout
 258
 259 (6,9)*{}="1";
 260 \end_layout
 261
 262 \begin_layout Plain Layout
 263
 264 (-8.5,-1)*{}="2";
 265 \end_layout
 266
 267 \begin_layout Plain Layout
 268
 269 "1";"2" **
 270 \backslash
 271 crv{~*=<.5pt>{.} (0,30)}?(.75)*
 272 \backslash
 273 dir{>}+(-2,2)*{z};
 274 \end_layout
 275
 276 \begin_layout Plain Layout
 277
 278 (-6.5,8)*{}="1";
 279 \end_layout
 280
 281 \begin_layout Plain Layout
 282
 283 (-.5,-9)*{}="2";
 284 \end_layout
 285
 286 \begin_layout Plain Layout
 287
 288 "1";"2" **
 289 \backslash
 290 crv{~*=<.5pt>{.} (-28.5,9.3)}?(.7)*
 291 \backslash
 292 dir{>}+(-2,-2)*{u};
 293 \end_layout
 294
 295 \begin_layout Plain Layout
 296
 297 (-9.5,-3.35)*{}="1";
 298 \end_layout
 299
 300 \begin_layout Plain Layout
 301
 302 (8.5,-3)*{}="2";
 303 \end_layout
 304
 305 \begin_layout Plain Layout
 306
 307 "1";"2" **
 308 \backslash
 309 crv{~*=<.5pt>{.} (-17.67,-24.19)}?(.7)*
 310 \backslash
 311 dir{>}+(-1,-3)*{x};
 312 \end_layout
 313
 314 \begin_layout Plain Layout
 315
 316 (1,-10)*{}="1";
 317 \end_layout
 318
 319 \begin_layout Plain Layout
 320
 321 (6.5,7.13)*{}="2";
 322 \end_layout
 323
 324 \begin_layout Plain Layout
 325
 326 "1";"2" **
 327 \backslash
 328 crv{~*=<.5pt>{.} (17.67,-24.19)}?(.7)*
 329 \backslash
 330 dir{>}+(3,-1)*{y};
 331 \end_layout
 332
 333 \begin_layout Plain Layout
 334
 335 (11,-1)*{}="1";
 336 \end_layout
 337
 338 \begin_layout Plain Layout
 339
 340 (-4,8)*{}="2";
 341 \end_layout
 342
 343 \begin_layout Plain Layout
 344
 345 "1";"2" **
 346 \backslash
 347 crv{~*=<.5pt>{.} (28.5,9.3)}?(.93)*
 348 \backslash
 349 dir{>}+(1,2)*{w};
 350 \end_layout
 351
 352 \begin_layout Plain Layout
 353
 354
 355 \backslash
 356 endxy
 357 \end_layout
 358
 359 \end_inset
 360
 361
 362 \end_layout
 363
 364 \end_inset
 365
 366
 367 \end_layout
 368
 369 \begin_layout Description
 370 Circles
 371 \end_layout
 372
 373 \begin_layout Standard
 374 \begin_inset Preview
 375
 376 \begin_layout Standard
 377 \begin_inset ERT
 378 status collapsed
 379
 380 \begin_layout Plain Layout
 381
 382
 383 \backslash
 384 xy
 385 \end_layout
 386
 387 \begin_layout Plain Layout
 388
 389 (0,0)*
 390 \backslash
 391 xycircle(14,8){++
 392 \backslash
 393 dir{<}};
 394 \end_layout
 395
 396 \begin_layout Plain Layout
 397
 398 (0,0)*
 399 \backslash
 400 xycircle<10pt>{{.}};
 401 \end_layout
 402
 403 \begin_layout Plain Layout
 404
 405 (0,0)*
 406 \backslash
 407 xycircle(5,2){:};
 408 \end_layout
 409
 410 \begin_layout Plain Layout
 411
 412 (0,15)*
 413 \backslash
 414 xycircle(10,4){--};
 415 \end_layout
 416
 417 \begin_layout Plain Layout
 418
 419
 420 \backslash
 421 endxy
 422 \end_layout
 423
 424 \end_inset
 425
 426
 427 \end_layout
 428
 429 \end_inset
 430
 431
 432 \end_layout
 433
 434 \begin_layout Description
 435 Cobordism
 436 \end_layout
 437
 438 \begin_layout Standard
 439 \begin_inset Preview
 440
 441 \begin_layout Standard
 442 \begin_inset ERT
 443 status collapsed
 444
 445 \begin_layout Plain Layout
 446
 447
 448 \backslash
 449 xy
 450 \end_layout
 451
 452 \begin_layout Plain Layout
 453
 454 (0,0)*
 455 \backslash
 456 ellipse(3,1){.};
 457 \end_layout
 458
 459 \begin_layout Plain Layout
 460
 461 (0,0)*
 462 \backslash
 463 ellipse(3,1)__,=:a(-180){-};
 464 \end_layout
 465
 466 \begin_layout Plain Layout
 467
 468 (-6,-8)*
 469 \backslash
 470 ellipse(3,1){.};
 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 (0,-8)*
 483 \backslash
 484 ellipse(3,1){.};
 485 \end_layout
 486
 487 \begin_layout Plain Layout
 488
 489 (-6,-8)*
 490 \backslash
 491 ellipse(3,1)__,=:a(-180){-};
 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 (0,-8)*
 504 \backslash
 505 ellipse(3,1)__,=:a(180){-};
 506 \end_layout
 507
 508 \begin_layout Plain Layout
 509
 510 (-3,6)*
 511 \backslash
 512 ellipse(3,1){-};
 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 (-3,12)*{}="1";
 525 \end_layout
 526
 527 \begin_layout Plain Layout
 528
 529 (3,12)*{}="2";
 530 \end_layout
 531
 532 \begin_layout Plain Layout
 533
 534 (-9,12)*{}="A2";
 535 \end_layout
 536
 537 \begin_layout Plain Layout
 538
 539 (9,12)*{}="B2";
 540 \end_layout
 541
 542 \begin_layout Plain Layout
 543
 544 "1";"2" **
 545 \backslash
 546 crv{(-3,7) & (3,7)};
 547 \end_layout
 548
 549 \begin_layout Plain Layout
 550
 551 (-3,0)*{}="A";
 552 \end_layout
 553
 554 \begin_layout Plain Layout
 555
 556 (3,0)*{}="B";
 557 \end_layout
 558
 559 \begin_layout Plain Layout
 560
 561 (-3,1)*{}="A1";
 562 \end_layout
 563
 564 \begin_layout Plain Layout
 565
 566 (3,1)*{}="B1";
 567 \end_layout
 568
 569 \begin_layout Plain Layout
 570
 571 "A";"A1" **
 572 \backslash
 573 dir{-};
 574 \end_layout
 575
 576 \begin_layout Plain Layout
 577
 578 "B";"B1" **
 579 \backslash
 580 dir{-};
 581 \end_layout
 582
 583 \begin_layout Plain Layout
 584
 585 "B2";"B1" **
 586 \backslash
 587 crv{(8,7) & (3,5)};
 588 \end_layout
 589
 590 \begin_layout Plain Layout
 591
 592 "A2";"A1" **
 593 \backslash
 594 crv{(-8,7) & (-3,5)};
 595 \end_layout
 596
 597 \begin_layout Plain Layout
 598
 599 %REFLECT
 600 \end_layout
 601
 602 \begin_layout Plain Layout
 603
 604 (3,-16)*{}="1";
 605 \end_layout
 606
 607 \begin_layout Plain Layout
 608
 609 (9,-16)*{}="2";
 610 \end_layout
 611
 612 \begin_layout Plain Layout
 613
 614 "1";"2" **
 615 \backslash
 616 crv{(3,-10) & (9,-10)};
 617 \end_layout
 618
 619 \begin_layout Plain Layout
 620
 621 (-3,-16)*{}="1";
 622 \end_layout
 623
 624 \begin_layout Plain Layout
 625
 626 (-9,-16)*{}="2";
 627 \end_layout
 628
 629 \begin_layout Plain Layout
 630
 631 "1";"2" **
 632 \backslash
 633 crv{(-3,-10) & (-9,-10)};
 634 \end_layout
 635
 636 \begin_layout Plain Layout
 637
 638 (-15,-16)*{}="A2";
 639 \end_layout
 640
 641 \begin_layout Plain Layout
 642
 643 (15,-16)*{}="B2";
 644 \end_layout
 645
 646 \begin_layout Plain Layout
 647
 648 (-3,0)*{}="A";
 649 \end_layout
 650
 651 \begin_layout Plain Layout
 652
 653 (3,0)*{}="B";
 654 \end_layout
 655
 656 \begin_layout Plain Layout
 657
 658 (-3,-1)*{}="A1";
 659 \end_layout
 660
 661 \begin_layout Plain Layout
 662
 663 (3,-1)*{}="B1";
 664 \end_layout
 665
 666 \begin_layout Plain Layout
 667
 668 "A";"A1" **
 669 \backslash
 670 dir{-};
 671 \end_layout
 672
 673 \begin_layout Plain Layout
 674
 675 "B";"B1" **
 676 \backslash
 677 dir{-};
 678 \end_layout
 679
 680 \begin_layout Plain Layout
 681
 682 "B2";"B1" **
 683 \backslash
 684 crv{(13,-6) & (2,-8)};
 685 \end_layout
 686
 687 \begin_layout Plain Layout
 688
 689 "A2";"A1" **
 690 \backslash
 691 crv{(-13,-6) & (-2,-8)};
 692 \end_layout
 693
 694 \begin_layout Plain Layout
 695
 696
 697 \backslash
 698 endxy
 699 \end_layout
 700
 701 \end_inset
 702
 703
 704 \end_layout
 705
 706 \end_inset
 707
 708
 709 \begin_inset Preview
 710
 711 \begin_layout Standard
 712 \begin_inset ERT
 713 status collapsed
 714
 715 \begin_layout Plain Layout
 716
 717
 718 \backslash
 719 xy 0;/r.18pc/:
 720 \end_layout
 721
 722 \begin_layout Plain Layout
 723
 724 (20,2)*{
 725 \backslash
 726 bullet}="RU"+(1,3)*{x^{
 727 \backslash
 728 ast}};
 729 \end_layout
 730
 731 \begin_layout Plain Layout
 732
 733 (16,-3)*{
 734 \backslash
 735 bullet}="RD"+(2.5,2)*{x^{
 736 \backslash
 737 ast}};
 738 \end_layout
 739
 740 \begin_layout Plain Layout
 741
 742 (-16,2)*{
 743 \backslash
 744 bullet}="LU"+(-1,2)*{x};
 745 \end_layout
 746
 747 \begin_layout Plain Layout
 748
 749 (-20,-3)*{
 750 \backslash
 751 bullet}="LD"+(-1,2)*{x};
 752 \end_layout
 753
 754 \begin_layout Plain Layout
 755
 756 "RU";"RD" **
 757 \backslash
 758 crv{(4,2) & (4,-1)}; ?(.1)*
 759 \backslash
 760 dir{<}; ?(.85)*
 761 \backslash
 762 dir{<};
 763 \end_layout
 764
 765 \begin_layout Plain Layout
 766
 767 "LD";"LU" **
 768 \backslash
 769 crv{(-4,-2) & (-4,1)};
 770 \end_layout
 771
 772 \begin_layout Plain Layout
 773
 774 ?(.08)*
 775 \backslash
 776 dir{<}; ?(.85)*
 777 \backslash
 778 dir{<};
 779 \end_layout
 780
 781 \begin_layout Plain Layout
 782
 783 (7.5,0)*{}="x1"; (-7.5,0)*{}="x2";
 784 \end_layout
 785
 786 \begin_layout Plain Layout
 787
 788 "x1"; "x2" **
 789 \backslash
 790 crv{(7,-10) & (-7,-10)};
 791 \end_layout
 792
 793 \begin_layout Plain Layout
 794
 795 (16,-20)*{
 796 \backslash
 797 bullet}="RDD"+(2.5,-1)*{x^{
 798 \backslash
 799 ast}};
 800 \end_layout
 801
 802 \begin_layout Plain Layout
 803
 804 (-20,-20)*{
 805 \backslash
 806 bullet}="LDD"+(-1,-3)*{x};
 807 \end_layout
 808
 809 \begin_layout Plain Layout
 810
 811 (20,-12.5)*{
 812 \backslash
 813 bullet}="RUD"+(3.5,1)*{x^{
 814 \backslash
 815 ast}};
 816 \end_layout
 817
 818 \begin_layout Plain Layout
 819
 820 (-16,-15)*{
 821 \backslash
 822 bullet}="LUD";
 823 \end_layout
 824
 825 \begin_layout Plain Layout
 826
 827 (-16,-2.5)*{}="A"; (16.1,-14.9)*{}="B";
 828 \end_layout
 829
 830 \begin_layout Plain Layout
 831
 832 "RD"; "RDD" **
 833 \backslash
 834 dir{-};
 835 \end_layout
 836
 837 \begin_layout Plain Layout
 838
 839 "LD"; "LDD" **
 840 \backslash
 841 dir{-};
 842 \end_layout
 843
 844 \begin_layout Plain Layout
 845
 846 "A"; "LUD" **
 847 \backslash
 848 dir{.};
 849 \end_layout
 850
 851 \begin_layout Plain Layout
 852
 853 "RDD"; "LDD" **
 854 \backslash
 855 crv{(0,-17)}; ?(.57)*
 856 \backslash
 857 dir{>};
 858 \end_layout
 859
 860 \begin_layout Plain Layout
 861
 862 "RU"; "RUD" **
 863 \backslash
 864 dir{-};
 865 \end_layout
 866
 867 \begin_layout Plain Layout
 868
 869 "LU"; "A" **
 870 \backslash
 871 dir{-};
 872 \end_layout
 873
 874 \begin_layout Plain Layout
 875
 876 "B"; "RUD" **
 877 \backslash
 878 crv{(18,-14.15)};
 879 \end_layout
 880
 881 \begin_layout Plain Layout
 882
 883 "B"; "LUD" **
 884 \backslash
 885 crv{~*=<4pt>{.}(0,-18)}; ?(.4)*
 886 \backslash
 887 dir{<};
 888 \end_layout
 889
 890 \begin_layout Plain Layout
 891
 892
 893 \backslash
 894 endxy
 895 \end_layout
 896
 897 \end_inset
 898
 899
 900 \end_layout
 901
 902 \end_inset
 903
 904
 905 \end_layout
 906
 907 \begin_layout Description
 908 Strings
 909 \end_layout
 910
 911 \begin_layout Standard
 912 \begin_inset Preview
 913
 914 \begin_layout Standard
 915 \begin_inset ERT
 916 status open
 917
 918 \begin_layout Plain Layout
 919
 920
 921 \backslash
 922 xy (-15,0)*{};(15,0)*{};
 923 \end_layout
 924
 925 \begin_layout Plain Layout
 926
 927
 928 \backslash
 929 endxy
 930 \end_layout
 931
 932 \begin_layout Plain Layout
 933
 934
 935 \backslash
 936 qquad =
 937 \backslash
 938 qquad
 939 \backslash
 940 xy
 941 \end_layout
 942
 943 \begin_layout Plain Layout
 944
 945 (-10,12)*{}; (-10,-12)*{}; **
 946 \backslash
 947 dir{-}?(.5)*
 948 \backslash
 949 dir{<}+(-4,0)*{F(x)};
 950 \end_layout
 951
 952 \begin_layout Plain Layout
 953
 954 (-2,12)*{}="1";
 955 \end_layout
 956
 957 \begin_layout Plain Layout
 958
 959 (6,-7) *{}="2";
 960 \end_layout
 961
 962 \begin_layout Plain Layout
 963
 964 (14,-7) *{}="3";
 965 \end_layout
 966
 967 \begin_layout Plain Layout
 968
 969 (14,-13)*{}="3'";
 970 \end_layout
 971
 972 \begin_layout Plain Layout
 973
 974 (18,0) *={}="";
 975 \end_layout
 976
 977 \begin_layout Plain Layout
 978
 979 "1";"2" **
 980 \backslash
 981 crv{(-4,-21)&(5,-15)};
 982 \end_layout
 983
 984 \begin_layout Plain Layout
 985
 986 ?(.15)*
 987 \backslash
 988 dir{<}+(5,10)*{
 989 \backslash
 990 overline{F(x)}};
 991 \end_layout
 992
 993 \begin_layout Plain Layout
 994
 995 "2";"3" **
 996 \backslash
 997 crv{(6,1)&(14,1)};
 998 \end_layout
 999
1000 \begin_layout Plain Layout
1001
1002 ?(0)*
1003 \backslash
1004 dir{<}+(4,8)*{
1005 \backslash
1006 widetilde{F(i_x)}} ;
1007 \end_layout
1008
1009 \begin_layout Plain Layout
1010
1011 ?(.95)*
1012 \backslash
1013 dir{<}+(5,-2)*{F(
1014 \backslash
1015 overline x)};
1016 \end_layout
1017
1018 \begin_layout Plain Layout
1019
1020 "3";"3'" **
1021 \backslash
1022 dir{-};
1023 \end_layout
1024
1025 \begin_layout Plain Layout
1026
1027 (-2,6)*{}="X1";
1028 \end_layout
1029
1030 \begin_layout Plain Layout
1031
1032 (-10,6)*{}="X2";
1033 \end_layout
1034
1035 \begin_layout Plain Layout
1036
1037 "X1";"X2" **
1038 \backslash
1039 crv{~*=<2pt>{.}(-2,-1)&(-10,-1)};
1040 \end_layout
1041
1042 \begin_layout Plain Layout
1043
1044 (-2,-6)*{}="XA";
1045 \end_layout
1046
1047 \begin_layout Plain Layout
1048
1049 (-10,-6)*{}="XB";
1050 \end_layout
1051
1052 \begin_layout Plain Layout
1053
1054 "XA";"XB" **
1055 \backslash
1056 crv{~*=<2pt>{.}(-2,1)&(-10,1)};
1057 \end_layout
1058
1059 \begin_layout Plain Layout
1060
1061
1062 \backslash
1063 endxy
1064 \end_layout
1065
1066 \end_inset
1067
1068
1069 \end_layout
1070
1071 \end_inset
1072
1073
1074 \end_layout
1075
1076 \begin_layout Description
1077 Categories
1078 \end_layout
1079
1080 \begin_layout Standard
1081 \begin_inset Preview
1082
1083 \begin_layout Standard
1084 \begin_inset ERT
1085 status collapsed
1086
1087 \begin_layout Plain Layout
1088
1089
1090 \backslash
1091 xymatrix{
1092 \end_layout
1093
1094 \begin_layout Plain Layout
1095
1096 (x
1097 \backslash
1098 otimes 1)
1099 \backslash
1100 otimes y
1101 \end_layout
1102
1103 \begin_layout Plain Layout
1104
1105
1106 \backslash
1107 ar[rr]^{a_{x,1,y}}
1108 \end_layout
1109
1110 \begin_layout Plain Layout
1111
1112
1113 \backslash
1114 ar[dr]_{r_x
1115 \backslash
1116 otimes 1_y}
1117 \end_layout
1118
1119 \begin_layout Plain Layout
1120
1121 && x
1122 \backslash
1123 otimes(1
1124 \backslash
1125 otimes y)
1126 \end_layout
1127
1128 \begin_layout Plain Layout
1129
1130
1131 \backslash
1132 ar[dl]^{1_x
1133 \backslash
1134 otimes
1135 \backslash
1136 ell_y }
1137 \backslash
1138
1139 \backslash
1140
1141 \end_layout
1142
1143 \begin_layout Plain Layout
1144
1145 & x
1146 \backslash
1147 otimes y }
1148 \end_layout
1149
1150 \end_inset
1151
1152
1153 \end_layout
1154
1155 \end_inset
1156
1157
1158 \begin_inset Preview
1159
1160 \begin_layout Standard
1161 \begin_inset ERT
1162 status collapsed
1163
1164 \begin_layout Plain Layout
1165
1166
1167 \backslash
1168 xy
1169 \end_layout
1170
1171 \begin_layout Plain Layout
1172
1173 (-9,0)*+{
1174 \backslash
1175 bullet}="1";
1176 \end_layout
1177
1178 \begin_layout Plain Layout
1179
1180 (0,0)*+{
1181 \backslash
1182 bullet}="2";
1183 \end_layout
1184
1185 \begin_layout Plain Layout
1186
1187 {
1188 \backslash
1189 ar@/^.9pc/ "1";"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@/^2pc/ "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@{=>} (-4.5,1.5)*{};(-4.5,-1.5)*{}} ;
1218 \end_layout
1219
1220 \begin_layout Plain Layout
1221
1222 {
1223 \backslash
1224 ar@{=>} (-4.5,7.25)*{};(-4.5,4.75)*{}} ;
1225 \end_layout
1226
1227 \begin_layout Plain Layout
1228
1229 {
1230 \backslash
1231 ar@{=>} (-4.5,-4.75)*{};(-4.5,-7.25)*{}} ;
1232 \end_layout
1233
1234 \begin_layout Plain Layout
1235
1236 (0,0)*+{
1237 \backslash
1238 bullet}="1";
1239 \end_layout
1240
1241 \begin_layout Plain Layout
1242
1243 (9,0)*+{
1244 \backslash
1245 bullet}="2";
1246 \end_layout
1247
1248 \begin_layout Plain Layout
1249
1250 (18,0)*+{
1251 \backslash
1252 bullet}="3";
1253 \end_layout
1254
1255 \begin_layout Plain Layout
1256
1257 {
1258 \backslash
1259 ar "1";"2"};
1260 \end_layout
1261
1262 \begin_layout Plain Layout
1263
1264 {
1265 \backslash
1266 ar "2";"3"};
1267 \end_layout
1268
1269 \begin_layout Plain Layout
1270
1271 {
1272 \backslash
1273 ar@/^1pc/ "1";"2"};
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@{=>} (4.5,3)*{};(4.5,.75)*{}} ;
1288 \end_layout
1289
1290 \begin_layout Plain Layout
1291
1292 {
1293 \backslash
1294 ar@{=>} (4.5,-.75)*{};(4.5,-3)*{}} ;
1295 \end_layout
1296
1297 \begin_layout Plain Layout
1298
1299
1300 \backslash
1301 endxy
1302 \end_layout
1303
1304 \end_inset
1305
1306
1307 \end_layout
1308
1309 \end_inset
1310
1311
1312 \end_layout
1313
1314 \begin_layout Description
1315 Transformations
1316 \end_layout
1317
1318 \begin_layout Standard
1319 \begin_inset Preview
1320
1321 \begin_layout Standard
1322 \begin_inset ERT
1323 status collapsed
1324
1325 \begin_layout Plain Layout
1326
1327
1328 \backslash
1329 xy %FIG.19.
1330  Natural transformation between functors.
1331 \end_layout
1332
1333 \begin_layout Plain Layout
1334
1335 (-26,-2)*+{
1336 \backslash
1337 bullet}="a";
1338 \end_layout
1339
1340 \begin_layout Plain Layout
1341
1342 (-12,3)*+{
1343 \backslash
1344 bullet}="b";
1345 \end_layout
1346
1347 \begin_layout Plain Layout
1348
1349 (-16,-5)*+{
1350 \backslash
1351 bullet}="c";
1352 \end_layout
1353
1354 \begin_layout Plain Layout
1355
1356 {
1357 \backslash
1358 ar@/^.25pc/ "a";"b"};
1359 \end_layout
1360
1361 \begin_layout Plain Layout
1362
1363 {
1364 \backslash
1365 ar@/_.25pc/"a";"c"};
1366 \end_layout
1367
1368 \begin_layout Plain Layout
1369
1370 {
1371 \backslash
1372 ar@/_.15pc/ "b";"c"};
1373 \end_layout
1374
1375 \begin_layout Plain Layout
1376
1377 %START TOP
1378 \end_layout
1379
1380 \begin_layout Plain Layout
1381
1382 (12,10)*+{
1383 \backslash
1384 bullet}="ta";
1385 \end_layout
1386
1387 \begin_layout Plain Layout
1388
1389 (26,15)*+{
1390 \backslash
1391 bullet}="tb";
1392 \end_layout
1393
1394 \begin_layout Plain Layout
1395
1396 (22,8)*+{
1397 \backslash
1398 bullet}="tc";
1399 \end_layout
1400
1401 \begin_layout Plain Layout
1402
1403 {
1404 \backslash
1405 ar@/^.25pc/ "ta";"tb"};
1406 \end_layout
1407
1408 \begin_layout Plain Layout
1409
1410 {
1411 \backslash
1412 ar@/_.25pc/ "ta";"tc"};
1413 \end_layout
1414
1415 \begin_layout Plain Layout
1416
1417 {
1418 \backslash
1419 ar@/_.15pc/ "tb";"tc"};
1420 \end_layout
1421
1422 \begin_layout Plain Layout
1423
1424 %START bottom
1425 \end_layout
1426
1427 \begin_layout Plain Layout
1428
1429 (12,-10)*+{
1430 \backslash
1431 bullet}="ba";
1432 \end_layout
1433
1434 \begin_layout Plain Layout
1435
1436 (26,-5)*+{
1437 \backslash
1438 bullet}="bb";
1439 \end_layout
1440
1441 \begin_layout Plain Layout
1442
1443 (22,-12)*+{
1444 \backslash
1445 bullet}="bc";
1446 \end_layout
1447
1448 \begin_layout Plain Layout
1449
1450 {
1451 \backslash
1452 ar@/^.25pc/@{.>} "ba";"bb"};
1453 \end_layout
1454
1455 \begin_layout Plain Layout
1456
1457 {
1458 \backslash
1459 ar@/_.25pc/ "ba";"bc"};
1460 \end_layout
1461
1462 \begin_layout Plain Layout
1463
1464 {
1465 \backslash
1466 ar@/_.15pc/ "bb";"bc"};
1467 \end_layout
1468
1469 \begin_layout Plain Layout
1470
1471 %START CONNECT
1472 \end_layout
1473
1474 \begin_layout Plain Layout
1475
1476 {
1477 \backslash
1478 ar@/_.15pc/ "ta";"ba"};
1479 \end_layout
1480
1481 \begin_layout Plain Layout
1482
1483 {
1484 \backslash
1485 ar@/_.15pc/ "tb";"bb"};
1486 \end_layout
1487
1488 \begin_layout Plain Layout
1489
1490 {
1491 \backslash
1492 ar@/_.15pc/ "tc";"bc"};
1493 \end_layout
1494
1495 \begin_layout Plain Layout
1496
1497 %START ARROWS AND LABELS
1498 \end_layout
1499
1500 \begin_layout Plain Layout
1501
1502 (-12,6)*{}="DF";
1503 \end_layout
1504
1505 \begin_layout Plain Layout
1506
1507 (6,10)*{}="CF";
1508 \end_layout
1509
1510 \begin_layout Plain Layout
1511
1512 {
1513 \backslash
1514 ar@/^.35pc/^F "DF";"CF"};
1515 \end_layout
1516
1517 \begin_layout Plain Layout
1518
1519 (-12,-6)*{}="DF";
1520 \end_layout
1521
1522 \begin_layout Plain Layout
1523
1524 (6,-10)*{}="CF";
1525 \end_layout
1526
1527 \begin_layout Plain Layout
1528
1529 {
1530 \backslash
1531 ar@/_.35pc/_G "DF";"CF"};
1532 \end_layout
1533
1534 \begin_layout Plain Layout
1535
1536 (-2,5)*{}="DF";
1537 \end_layout
1538
1539 \begin_layout Plain Layout
1540
1541 (-2,-5)*{}="CF";
1542 \end_layout
1543
1544 \begin_layout Plain Layout
1545
1546 {
1547 \backslash
1548 ar@{=>}^{
1549 \backslash
1550 alpha} "DF";"CF"};
1551 \end_layout
1552
1553 \begin_layout Plain Layout
1554
1555 (29,3)*{D};
1556 \end_layout
1557
1558 \begin_layout Plain Layout
1559
1560 (-23,3)*{C};
1561 \end_layout
1562
1563 \begin_layout Plain Layout
1564
1565
1566 \backslash
1567 endxy
1568 \end_layout
1569
1570 \end_inset
1571
1572
1573 \end_layout
1574
1575 \end_inset
1576
1577
1578 \end_layout
1579
1580 \begin_layout Section
1581 IPA
1582 \end_layout
1583
1584 \begin_layout Standard
1585 \begin_inset Preview
1586
1587 \begin_layout Standard
1588 \begin_inset ERT
1589 status collapsed
1590
1591 \begin_layout Plain Layout
1592
1593
1594 \backslash
1595 textipa{Ekspl@"neIS@n}
1596 \end_layout
1597
1598 \end_inset
1599
1600
1601 \end_layout
1602
1603 \end_inset
1604
1605
1606 \end_layout
1607
1608 \begin_layout Section
1609 QTree
1610 \end_layout
1611
1612 \begin_layout Standard
1613 \begin_inset Preview
1614
1615 \begin_layout Standard
1616 \begin_inset ERT
1617 status collapsed
1618
1619 \begin_layout Plain Layout
1620
1621
1622 \backslash
1623 Tree[.S [.N This ] [.V is ] [.NP [.Det a ] [.N test ] ] ]
1624 \end_layout
1625
1626 \end_inset
1627
1628
1629 \end_layout
1630
1631 \end_inset
1632
1633
1634 \begin_inset Preview
1635
1636 \begin_layout Standard
1637 \begin_inset ERT
1638 status collapsed
1639
1640 \begin_layout Plain Layout
1641
1642
1643 \backslash
1644 Tree [.$
1645 \backslash
1646 sigma$ $
1647 \backslash
1648 mu$ $
1649 \backslash
1650 mu$ ]
1651 \end_layout
1652
1653 \end_inset
1654
1655
1656 \end_layout
1657
1658 \end_inset
1659
1660
1661 \end_layout
1662
1663 \begin_layout Section
1664 PSTricks
1665 \begin_inset CommandInset label
1666 LatexCommand label
1667 name "sec:PSTricks"
1668
1669 \end_inset
1670
1671
1672 \end_layout
1673
1674 \begin_layout Standard
1675 Some simple graphing examples.
1676 \end_layout
1677
1678 \begin_layout Subsection
1679 Function plotting
1680 \end_layout
1681
1682 \begin_layout Standard
1683 \begin_inset Preview
1684
1685 \begin_layout Standard
1686 \begin_inset ERT
1687 status open
1688
1689 \begin_layout Plain Layout
1690
1691
1692 \backslash
1693 begin{pspicture*}(-1,-3.5)(10.5,3.5)
1694 \end_layout
1695
1696 \begin_layout Plain Layout
1697
1698
1699 \backslash
1700 psaxes{->}(0,0)(0,-3)(10,3)
1701 \end_layout
1702
1703 \begin_layout Plain Layout
1704
1705
1706 \backslash
1707 uput[-90](10,0){$x$}
1708 \backslash
1709 uput[0](0,3){$f(x)$}
1710 \end_layout
1711
1712 \begin_layout Plain Layout
1713
1714
1715 \backslash
1716 psplot[linecolor=red,linewidth=1pt]{0.1}{10}{ x ln }
1717 \end_layout
1718
1719 \begin_layout Plain Layout
1720
1721
1722 \backslash
1723 end{pspicture*}
1724 \end_layout
1725
1726 \end_inset
1727
1728
1729 \end_layout
1730
1731 \end_inset
1732
1733
1734 \end_layout
1735
1736 \begin_layout Subsection
1737 Inline data plotting
1738 \end_layout
1739
1740 \begin_layout Standard
1741 \align center
1742 \begin_inset Preview
1743
1744 \begin_layout Standard
1745 \align center
1746 \begin_inset ERT
1747 status open
1748
1749 \begin_layout Plain Layout
1750
1751
1752 \backslash
1753 begin{pspicture*}(-1.5,-1.5)(11,5)
1754 \end_layout
1755
1756 \begin_layout Plain Layout
1757
1758
1759 \backslash
1760 psaxes{->}(0,0)(0,0)(10,5)
1761 \end_layout
1762
1763 \begin_layout Plain Layout
1764
1765
1766 \backslash
1767 psset{linewidth=2.5pt}
1768 \end_layout
1769
1770 \begin_layout Plain Layout
1771
1772
1773 \backslash
1774 rput(5.0,-1.0){Speed [MPH]}
1775 \end_layout
1776
1777 \begin_layout Plain Layout
1778
1779
1780 \backslash
1781 rput(-1.0,1.0){
1782 \backslash
1783 begin{rotate}{90}Cost [Dollars]
1784 \backslash
1785 end{rotate}}
1786 \end_layout
1787
1788 \begin_layout Plain Layout
1789
1790
1791 \backslash
1792 savedata{
1793 \backslash
1794 mydata}[{{0,0},{1.3,0.32},{5.5,1.1},{6.5,1.15},{8.1,1.28},{10,4}}]
1795 \end_layout
1796
1797 \begin_layout Plain Layout
1798
1799
1800 \backslash
1801 dataplot[plotstyle=curve,showpoints=true,dotstyle=triangle,linecolor=blue]{
1802 \backslash
1803 mydata}
1804 \end_layout
1805
1806 \begin_layout Plain Layout
1807
1808
1809 \backslash
1810 end{pspicture*}
1811 \end_layout
1812
1813 \end_inset
1814
1815
1816 \end_layout
1817
1818 \end_inset
1819
1820
1821 \end_layout
1822
1823 \begin_layout Subsection
1824 Lissajous curves
1825 \end_layout
1826
1827 \begin_layout Standard
1828 \begin_inset Preview
1829
1830 \begin_layout Standard
1831 \begin_inset ERT
1832 status open
1833
1834 \begin_layout Plain Layout
1835
1836
1837 \backslash
1838 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1839 \end_layout
1840
1841 \begin_layout Plain Layout
1842
1843
1844 \backslash
1845 parametricplot[plotstyle=line,plotpoints=50,linecolor=red]{0}{8}{50 t mul
1846  cos 100 t mul sin}
1847 \end_layout
1848
1849 \begin_layout Plain Layout
1850
1851
1852 \backslash
1853 end{pspicture*}
1854 \end_layout
1855
1856 \end_inset
1857
1858
1859 \end_layout
1860
1861 \end_inset
1862
1863
1864 \begin_inset space \hfill{}
1865 \end_inset
1866
1867
1868 \begin_inset Preview
1869
1870 \begin_layout Standard
1871 \begin_inset ERT
1872 status open
1873
1874 \begin_layout Plain Layout
1875
1876
1877 \backslash
1878 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1879 \end_layout
1880
1881 \begin_layout Plain Layout
1882
1883
1884 \backslash
1885 parametricplot[plotstyle=line,plotpoints=100,linecolor=red]{0}{8}{150 t
1886  mul cos 100 t mul sin}
1887 \end_layout
1888
1889 \begin_layout Plain Layout
1890
1891
1892 \backslash
1893 end{pspicture*}
1894 \end_layout
1895
1896 \end_inset
1897
1898
1899 \end_layout
1900
1901 \end_inset
1902
1903
1904 \begin_inset space \hfill{}
1905 \end_inset
1906
1907
1908 \begin_inset Preview
1909
1910 \begin_layout Standard
1911 \begin_inset ERT
1912 status open
1913
1914 \begin_layout Plain Layout
1915
1916
1917 \backslash
1918 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1919 \end_layout
1920
1921 \begin_layout Plain Layout
1922
1923
1924 \backslash
1925 parametricplot[plotstyle=line,plotpoints=150,linecolor=red]{0}{8}{150 t
1926  mul cos 200 t mul sin}
1927 \end_layout
1928
1929 \begin_layout Plain Layout
1930
1931
1932 \backslash
1933 end{pspicture*}
1934 \end_layout
1935
1936 \end_inset
1937
1938
1939 \end_layout
1940
1941 \end_inset
1942
1943
1944 \begin_inset space \hfill{}
1945 \end_inset
1946
1947
1948 \begin_inset Preview
1949
1950 \begin_layout Standard
1951 \begin_inset ERT
1952 status open
1953
1954 \begin_layout Plain Layout
1955
1956
1957 \backslash
1958 begin{pspicture*}(-1.1,-1.1)(1.1,1.1)
1959 \end_layout
1960
1961 \begin_layout Plain Layout
1962
1963
1964 \backslash
1965 parametricplot[plotstyle=line,plotpoints=200,linecolor=red]{0}{8}{250 t
1966  mul cos 200 t mul sin}
1967 \end_layout
1968
1969 \begin_layout Plain Layout
1970
1971
1972 \backslash
1973 end{pspicture*}
1974 \end_layout
1975
1976 \end_inset
1977
1978
1979 \end_layout
1980
1981 \end_inset
1982
1983
1984 \end_layout
1985
1986 \begin_layout Section
1987 TikZ
1988 \end_layout
1989
1990 \begin_layout Standard
1991 \begin_inset Flex URL
1992 status collapsed
1993
1994 \begin_layout Plain Layout
1995
1996 http://www.texample.net/media/tikz/examples/TEX/free-body-diagrams.tex
1997 \end_layout
1998
1999 \end_inset
2000
2001
2002 \end_layout
2003
2004 \begin_layout Standard
2005 \begin_inset Preview
2006
2007 \begin_layout Standard
2008 \begin_inset ERT
2009 status collapsed
2010
2011 \begin_layout Plain Layout
2012
2013
2014 \backslash
2015 def
2016 \backslash
2017 iangle{35} % Angle of the inclined plane
2018 \end_layout
2019
2020 \begin_layout Plain Layout
2021
2022
2023 \backslash
2024 def
2025 \backslash
2026 down{-90}
2027 \end_layout
2028
2029 \begin_layout Plain Layout
2030
2031
2032 \backslash
2033 def
2034 \backslash
2035 arcr{0.5cm} % Radius of the arc used to indicate angles
2036 \end_layout
2037
2038 \begin_layout Plain Layout
2039
2040 \end_layout
2041
2042 \begin_layout Plain Layout
2043
2044
2045 \backslash
2046 begin{tikzpicture}[
2047 \end_layout
2048
2049 \begin_layout Plain Layout
2050
2051     force/.style={>=latex,draw=blue,fill=blue},
2052 \end_layout
2053
2054 \begin_layout Plain Layout
2055
2056     axis/.style={densely dashed,gray,font=
2057 \backslash
2058 small},
2059 \end_layout
2060
2061 \begin_layout Plain Layout
2062
2063     M/.style={rectangle,draw,fill=lightgray,minimum size=0.5cm,thin},
2064 \end_layout
2065
2066 \begin_layout Plain Layout
2067
2068     m/.style={rectangle,draw=black,fill=lightgray,minimum size=0.3cm,thin},
2069 \end_layout
2070
2071 \begin_layout Plain Layout
2072
2073     plane/.style={draw=black,fill=blue!10},
2074 \end_layout
2075
2076 \begin_layout Plain Layout
2077
2078     string/.style={draw=red, thick},
2079 \end_layout
2080
2081 \begin_layout Plain Layout
2082
2083     pulley/.style={thick},
2084 \end_layout
2085
2086 \begin_layout Plain Layout
2087
2088 ]
2089 \end_layout
2090
2091 \begin_layout Plain Layout
2092
2093 \end_layout
2094
2095 \begin_layout Plain Layout
2096
2097
2098 \backslash
2099 matrix[column sep=1cm] {
2100 \end_layout
2101
2102 \begin_layout Plain Layout
2103
2104     %% Sketch
2105 \end_layout
2106
2107 \begin_layout Plain Layout
2108
2109
2110 \backslash
2111 draw[plane] (0,-1) coordinate (base)
2112 \end_layout
2113
2114 \begin_layout Plain Layout
2115
2116                      -- coordinate[pos=0.5] (mid) ++(
2117 \backslash
2118 iangle:3) coordinate (top)
2119 \end_layout
2120
2121 \begin_layout Plain Layout
2122
2123                      |- (base) -- cycle;
2124 \end_layout
2125
2126 \begin_layout Plain Layout
2127
2128
2129 \backslash
2130 path (mid) node[M,rotate=
2131 \backslash
2132 iangle,yshift=0.25cm] (M) {};
2133 \end_layout
2134
2135 \begin_layout Plain Layout
2136
2137
2138 \backslash
2139 draw[pulley] (top) -- ++(
2140 \backslash
2141 iangle:0.25) circle (0.25cm)
2142 \end_layout
2143
2144 \begin_layout Plain Layout
2145
2146                    ++ (90-
2147 \backslash
2148 iangle:0.5) coordinate (pulley);
2149 \end_layout
2150
2151 \begin_layout Plain Layout
2152
2153
2154 \backslash
2155 draw[string] (M.east) -- ++(
2156 \backslash
2157 iangle:1.5cm) arc (90+
2158 \backslash
2159 iangle:0:0.25)
2160 \end_layout
2161
2162 \begin_layout Plain Layout
2163
2164                   -- ++(0,-1) node[m] {};
2165 \end_layout
2166
2167 \begin_layout Plain Layout
2168
2169 \end_layout
2170
2171 \begin_layout Plain Layout
2172
2173
2174 \backslash
2175 draw[->] (base)++(
2176 \backslash
2177 arcr,0) arc (0:
2178 \backslash
2179 iangle:
2180 \backslash
2181 arcr);
2182 \end_layout
2183
2184 \begin_layout Plain Layout
2185
2186
2187 \backslash
2188 path (base)++(
2189 \backslash
2190 iangle*0.5:
2191 \backslash
2192 arcr+5pt) node {$
2193 \backslash
2194 alpha$};
2195 \end_layout
2196
2197 \begin_layout Plain Layout
2198
2199     %%
2200 \end_layout
2201
2202 \begin_layout Plain Layout
2203
2204 \end_layout
2205
2206 \begin_layout Plain Layout
2207
2208 &
2209 \end_layout
2210
2211 \begin_layout Plain Layout
2212
2213     %% Free body diagram of M
2214 \end_layout
2215
2216 \begin_layout Plain Layout
2217
2218
2219 \backslash
2220 begin{scope}[rotate=
2221 \backslash
2222 iangle]
2223 \end_layout
2224
2225 \begin_layout Plain Layout
2226
2227
2228 \backslash
2229 node[M,transform shape] (M) {};
2230 \end_layout
2231
2232 \begin_layout Plain Layout
2233
2234         % Draw axes and help lines
2235 \end_layout
2236
2237 \begin_layout Plain Layout
2238
2239 \end_layout
2240
2241 \begin_layout Plain Layout
2242
2243         {[axis,->]
2244 \end_layout
2245
2246 \begin_layout Plain Layout
2247
2248
2249 \backslash
2250 draw (0,-1) -- (0,2) node[right] {$+y$};
2251 \end_layout
2252
2253 \begin_layout Plain Layout
2254
2255
2256 \backslash
2257 draw (M) -- ++(2,0) node[right] {$+x$};
2258 \end_layout
2259
2260 \begin_layout Plain Layout
2261
2262             % Indicate angle.
2263  The code is a bit awkward.
2264 \end_layout
2265
2266 \begin_layout Plain Layout
2267
2268 \end_layout
2269
2270 \begin_layout Plain Layout
2271
2272
2273 \backslash
2274 draw[solid,shorten >=0.5pt] (
2275 \backslash
2276 down-
2277 \backslash
2278 iangle:
2279 \backslash
2280 arcr)
2281 \end_layout
2282
2283 \begin_layout Plain Layout
2284
2285                 arc(
2286 \backslash
2287 down-
2288 \backslash
2289 iangle:
2290 \backslash
2291 down:
2292 \backslash
2293 arcr);
2294 \end_layout
2295
2296 \begin_layout Plain Layout
2297
2298
2299 \backslash
2300 node at (
2301 \backslash
2302 down-0.5*
2303 \backslash
2304 iangle:1.3*
2305 \backslash
2306 arcr) {$
2307 \backslash
2308 alpha$};
2309 \end_layout
2310
2311 \begin_layout Plain Layout
2312
2313         }
2314 \end_layout
2315
2316 \begin_layout Plain Layout
2317
2318 \end_layout
2319
2320 \begin_layout Plain Layout
2321
2322         % Forces
2323 \end_layout
2324
2325 \begin_layout Plain Layout
2326
2327         {[force,->]
2328 \end_layout
2329
2330 \begin_layout Plain Layout
2331
2332             % Assuming that Mg = 1.
2333  The normal force will therefore be cos(alpha)
2334 \end_layout
2335
2336 \begin_layout Plain Layout
2337
2338
2339 \backslash
2340 draw (M.center) -- ++(0,{cos(
2341 \backslash
2342 iangle)}) node[above right] {$N$};
2343 \end_layout
2344
2345 \begin_layout Plain Layout
2346
2347
2348 \backslash
2349 draw (M.west) -- ++(-1,0) node[left] {$f_R$};
2350 \end_layout
2351
2352 \begin_layout Plain Layout
2353
2354
2355 \backslash
2356 draw (M.east) -- ++(1,0) node[above] {$T$};
2357 \end_layout
2358
2359 \begin_layout Plain Layout
2360
2361         }
2362 \end_layout
2363
2364 \begin_layout Plain Layout
2365
2366 \end_layout
2367
2368 \begin_layout Plain Layout
2369
2370
2371 \backslash
2372 end{scope}
2373 \end_layout
2374
2375 \begin_layout Plain Layout
2376
2377     % Draw gravity force.
2378  The code is put outside the rotated
2379 \end_layout
2380
2381 \begin_layout Plain Layout
2382
2383     % scope for simplicity.
2384  No need to do any angle calculations.
2385
2386 \end_layout
2387
2388 \begin_layout Plain Layout
2389
2390
2391 \backslash
2392 draw[force,->] (M.center) -- ++(0,-1) node[below] {$Mg$};
2393 \end_layout
2394
2395 \begin_layout Plain Layout
2396
2397     %%
2398 \end_layout
2399
2400 \begin_layout Plain Layout
2401
2402 \end_layout
2403
2404 \begin_layout Plain Layout
2405
2406 &
2407 \end_layout
2408
2409 \begin_layout Plain Layout
2410
2411     %%%
2412 \end_layout
2413
2414 \begin_layout Plain Layout
2415
2416     % Free body diagram of m
2417 \end_layout
2418
2419 \begin_layout Plain Layout
2420
2421
2422 \backslash
2423 node[m] (m) {};
2424 \end_layout
2425
2426 \begin_layout Plain Layout
2427
2428
2429 \backslash
2430 draw[axis,->] (m) -- ++(0,-2) node[left] {$+$};
2431 \end_layout
2432
2433 \begin_layout Plain Layout
2434
2435     {[force,->]
2436 \end_layout
2437
2438 \begin_layout Plain Layout
2439
2440
2441 \backslash
2442 draw (m.north) -- ++(0,1) node[above] {$T'$};
2443 \end_layout
2444
2445 \begin_layout Plain Layout
2446
2447
2448 \backslash
2449 draw (m.south) -- ++(0,-1) node[right] {$mg$};
2450 \end_layout
2451
2452 \begin_layout Plain Layout
2453
2454     }
2455 \end_layout
2456
2457 \begin_layout Plain Layout
2458
2459 \end_layout
2460
2461 \begin_layout Plain Layout
2462
2463
2464 \backslash
2465
2466 \backslash
2467
2468 \end_layout
2469
2470 \begin_layout Plain Layout
2471
2472 };
2473 \end_layout
2474
2475 \begin_layout Plain Layout
2476
2477
2478 \backslash
2479 end{tikzpicture}
2480 \end_layout
2481
2482 \begin_layout Plain Layout
2483
2484 \end_layout
2485
2486 \end_inset
2487
2488
2489 \end_layout
2490
2491 \end_inset
2492
2493
2494 \end_layout
2495
2496 \end_body
2497 \end_document