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1.1 ! root 1: .so ../ADM/mac ! 2: .XX eqn 25 "Typesetting Mathematics \(em User's Guide" ! 3: .nr PI .2i ! 4: .nr PD .1v ! 5: .EQ ! 6: delim $$ ! 7: .EN ! 8: .TL ! 9: Typesetting Mathematics \(em User's Guide\(dg ! 10: .AU 2C-518 6021 ! 11: Brian W. Kernighan ! 12: Lorinda L. Cherry ! 13: .AI ! 14: .MH ! 15: .AB ! 16: .PP ! 17: This is the user's guide for ! 18: .IT eqn , ! 19: a system for typesetting ! 20: mathematics. ! 21: Mathematical expressions are described in a language ! 22: designed to be easy to use ! 23: by people who know neither mathematics nor typesetting. ! 24: Enough of the language to set in-line expressions like ! 25: $lim from {x-> pi /2} ( tan~x) sup{sin~2x}~=~1$ ! 26: or display equations like ! 27: .EQ I ! 28: G(z)~mark =~ e sup { ln ~ G(z) } ! 29: ~=~ exp left ( ! 30: sum from k>=1 {S sub k z sup k} over k right ) ! 31: ~=~ prod from k>=1 e sup {S sub k z sup k /k} ! 32: .EN ! 33: .EQ I ! 34: lineup = left ( 1 + S sub 1 z + ! 35: { S sub 1 sup 2 z sup 2 } over 2! + ".\^.\^." right ) ! 36: left ( 1+ { S sub 2 z sup 2 } over 2 ! 37: + { S sub 2 sup 2 z sup 4 } over { 2 sup 2 cdot 2! } ! 38: + ".\^.\^." right ) ".\^.\^." ! 39: .EN ! 40: .EQ I ! 41: lineup = sum from m>=0 left ( ! 42: sum from ! 43: pile { k sub 1 ,k sub 2 ",\^.\^.\^.\^," k sub m >=0 ! 44: above ! 45: k sub 1 +2k sub 2 + ".\^.\^." +mk sub m =m} ! 46: { S sub 1 sup {k sub 1} } over {1 sup k sub 1 k sub 1 ! } ~ ! 47: { S sub 2 sup {k sub 2} } over {2 sup k sub 2 k sub 2 ! } ~ ! 48: ".\^.\^." ! 49: { S sub m sup {k sub m} } over {m sup k sub m k sub m ! } ! 50: right ) z sup m ! 51: .EN ! 52: can be learned in an hour or so. ! 53: .PP ! 54: The language interfaces directly with ! 55: the formatting language ! 56: .IT troff , ! 57: so mathematical expressions can be embedded in the running ! 58: text ! 59: of a manuscript, ! 60: and the entire document produced in one process. ! 61: This user's guide is an example of its output. ! 62: .AE ! 63: .2C ! 64: .FS ! 65: \(dg This is a revised version of |reference(eqn cstr). ! 66: .FE ! 67: .NH ! 68: Introduction ! 69: .PP ! 70: .IT Eqn ! 71: is a ! 72: program and a language for typesetting mathematics. ! 73: The ! 74: .IT eqn ! 75: language was designed to be easy to use ! 76: by people who know neither mathematics ! 77: nor typesetting. ! 78: Thus ! 79: .IT eqn ! 80: knows relatively little about mathematics. ! 81: In particular, mathematical symbols like ! 82: +, \(mi, \(mu, parentheses, and so on have no special meanings. ! 83: .IT Eqn ! 84: is quite happy to set garbage (but it will look good). ! 85: .PP ! 86: .IT Eqn ! 87: is a preprocessor for the typesetter formatter ! 88: .IT troff , ! 89: so the normal mode of operation is to prepare ! 90: a document with both mathematics and ordinary text ! 91: interspersed, ! 92: and let ! 93: .IT eqn ! 94: set the mathematics while ! 95: .IT troff ! 96: does the body of the text. ! 97: .PP ! 98: To use ! 99: .IT eqn ! 100: on ! 101: .UX , ! 102: .P1 ! 103: eqn files | troff ! 104: .P2 ! 105: .PP ! 106: The design and implementation of ! 107: .I eqn ! 108: is discussed in |reference(kernighan cherry cacm). ! 109: .NH ! 110: Display Equations ! 111: .PP ! 112: To tell ! 113: .IT eqn ! 114: where a mathematical expression begins and ends, ! 115: one marks it with lines beginning ! 116: .CW .EQ ! 117: and ! 118: .CW .EN . ! 119: Thus ! 120: if you type the lines ! 121: .P1 ! 122: \&.EQ ! 123: x=y+z ! 124: \&.EN ! 125: .P2 ! 126: your output will look like ! 127: .EQ ! 128: x=y+z ! 129: .EN ! 130: The ! 131: .CW .EQ ! 132: and ! 133: .CW .EN ! 134: are copied through untouched; ! 135: they ! 136: are not otherwise processed ! 137: by ! 138: .IT eqn . ! 139: This means that you have to take care ! 140: of things like centering, numbering, and so on ! 141: yourself. ! 142: The most common way is to use a ! 143: .IT troff ! 144: macro package like ! 145: .CW -ms ! 146: or ! 147: .CW -mm , ! 148: which allow you to center, indent, left-justify, and number equations. ! 149: .PP ! 150: With the ! 151: .CW -ms ! 152: package, ! 153: equations are centered by default. ! 154: To left-justify an equation, use ! 155: .CW \&.EQ\ L ! 156: instead of ! 157: .CW .EQ . ! 158: To indent it, use ! 159: .CW .EQ\ I . ! 160: Any of these can be followed by an arbitrary `equation number' ! 161: which will be placed at the right margin. ! 162: For example, the input ! 163: .P1 ! 164: \&.EQ I (3.1a) ! 165: x = f(y/2) + y/2 ! 166: \&.EN ! 167: .P2 ! 168: produces the output ! 169: .EQ I (3.1a) ! 170: x = f(y/2) + y/2 ! 171: .EN ! 172: .PP ! 173: For stupid historical reasons, the ! 174: .CW -mm ! 175: macros package requires you to surround ! 176: .CW .EQ ! 177: and ! 178: .CW .EN ! 179: with a pair of totally unnecessary commands, ! 180: .CW .DS ! 181: and ! 182: .CW .DE : ! 183: .P1 ! 184: \&.DS \f2for \fP-mm\f2 only\fP ! 185: \&.EQ ! 186: \f2your equation\fP ! 187: \&.EN ! 188: \&.DE ! 189: .P2 ! 190: .PP ! 191: There is also a shorthand notation so ! 192: in-line expressions ! 193: like ! 194: $pi sub i sup 2$ ! 195: can be entered without ! 196: .CW .EQ ! 197: and ! 198: .CW .EN . ! 199: We will talk about it in section 9. ! 200: .NH ! 201: Input spaces ! 202: .PP ! 203: Spaces, tabs, and newlines within an expression are thrown away by ! 204: .IT eqn . ! 205: (Normal text is left absolutely alone.) ! 206: Thus ! 207: between ! 208: .CW .EQ ! 209: and ! 210: .CW .EN , ! 211: .P1 ! 212: x=y+z ! 213: .P2 ! 214: and ! 215: .P1 ! 216: x = y + z ! 217: .P2 ! 218: and ! 219: .P1 ! 220: x = y ! 221: + z ! 222: .P2 ! 223: and so on ! 224: all produce the same ! 225: output: ! 226: .EQ ! 227: x=y+z ! 228: .EN ! 229: You should use spaces and newlines freely to make your input equations ! 230: readable and easy to edit. ! 231: In particular, very long lines are a bad idea, ! 232: since they are often hard to fix if you make a mistake. ! 233: .NH ! 234: Output spaces ! 235: .PP ! 236: To force extra spaces into the ! 237: .IT output, ! 238: use a tilde ! 239: .CW ~ '' `` ! 240: for each space you want: ! 241: .P1 ! 242: x~=~y~+~z ! 243: .P2 ! 244: gives ! 245: .EQ ! 246: x~=~y~+~z ! 247: .EN ! 248: You can also use a circumflex ! 249: .CW ^ '', `` ! 250: which gives a space half the width of a tilde. ! 251: It is mainly useful for fine-tuning. ! 252: .NH ! 253: Symbols, Special Names, Greek ! 254: .PP ! 255: .IT Eqn ! 256: knows some mathematical symbols, ! 257: some mathematical names, and the Greek alphabet. ! 258: For example, ! 259: .P1 ! 260: x=2 pi int sin ( omega t)dt ! 261: .P2 ! 262: produces ! 263: .EQ ! 264: x = 2 pi int sin ( omega t)dt ! 265: .EN ! 266: Here the spaces in the input are ! 267: necessary ! 268: to tell ! 269: .IT eqn ! 270: that ! 271: .CW int , ! 272: .CW pi , ! 273: .CW sin , ! 274: and ! 275: .CW omega ! 276: are separate entities that should get special treatment. ! 277: The ! 278: .CW sin , ! 279: digit 2, and parentheses are set in roman type instead of italic; ! 280: .CW pi ! 281: and ! 282: .CW omega ! 283: are made Greek; ! 284: and ! 285: .CW int ! 286: becomes the integral sign. ! 287: .PP ! 288: When in doubt, leave spaces around separate parts of the input. ! 289: A ! 290: common error is to type ! 291: .CW f(pi) ! 292: without leaving spaces on both sides of the ! 293: .CW pi . ! 294: As a result, ! 295: .IT eqn ! 296: does not recognize ! 297: .CW pi ! 298: as a special word, and you get ! 299: $f(pi)$ ! 300: instead of ! 301: $f( pi )$. ! 302: .PP ! 303: A list of ! 304: .IT eqn ! 305: names appears in section 24. ! 306: Knowledgeable users can also use ! 307: .IT troff ! 308: four-character names ! 309: for anything ! 310: .IT eqn ! 311: doesn't know about, ! 312: like ! 313: .CW \e(L1 ! 314: for the AT&T death-star \(L1. ! 315: .NH ! 316: Spaces, Again ! 317: .PP ! 318: The only way ! 319: .IT eqn ! 320: can deduce that some sequence ! 321: of letters might be special ! 322: is if that sequence is separated from the letters ! 323: on either side of it. ! 324: This can be done by surrounding a special word by spaces, ! 325: tabs, or newlines, ! 326: as we did in the previous section. ! 327: .PP ! 328: You can also make special words stand out by surrounding them ! 329: with tildes or circumflexes: ! 330: .P1 ! 331: x~=~2~pi~int~sin~(~omega~t~)~dt ! 332: .P2 ! 333: is much the same as the last example, ! 334: except that the tildes ! 335: not only ! 336: separate the magic words ! 337: like ! 338: .CW sin , ! 339: .CW omega , ! 340: and so on, ! 341: but also add extra spaces, ! 342: one space per tilde: ! 343: .EQ ! 344: x~=~2~pi~int~sin~(~omega~t~)~dt ! 345: .EN ! 346: .PP ! 347: Special words can also be separated by braces ! 348: .CW {} ! 349: and double quotes ! 350: .CW \&"" , ! 351: which have special meanings that we will ! 352: see soon. ! 353: ....... ! 354: .NH ! 355: Subscripts and Superscripts ! 356: .PP ! 357: Subscripts and superscripts are ! 358: obtained with the words ! 359: .CW sub ! 360: and ! 361: .CW sup . ! 362: .P1 ! 363: x sup 2 + y sub k ! 364: .P2 ! 365: gives ! 366: .EQ ! 367: x sup 2 + y sub k ! 368: .EN ! 369: .IT Eqn ! 370: takes care of all the size changes and vertical motions ! 371: needed to make the output look right. ! 372: The words ! 373: .CW sub ! 374: and ! 375: .CW sup ! 376: must be surrounded by spaces; ! 377: .CW "x sub2" ! 378: will give you ! 379: $x sub2$ instead of $x sub 2$. ! 380: Furthermore, don't forget to leave a space ! 381: (or a tilde, etc.)\& ! 382: to mark the end of a subscript or superscript. ! 383: A common error is to say ! 384: something like ! 385: .P1 ! 386: y = (x sup 2)+1 ! 387: .P2 ! 388: which causes ! 389: .EQ ! 390: y = (x sup 2)+1 ! 391: .EN ! 392: instead of ! 393: the intended ! 394: .EQ ! 395: y = (x sup 2 )+1 ! 396: .EN ! 397: .PP ! 398: Subscripted subscripts and superscripted superscripts ! 399: also work: ! 400: .P1 ! 401: x sub i sub 1 ! 402: .P2 ! 403: is ! 404: .EQ ! 405: x sub i sub 1 ! 406: .EN ! 407: A subscript and superscript on the same thing ! 408: are printed one above the other ! 409: if the subscript comes ! 410: .IT first : ! 411: .P1 ! 412: x sub i sup 2 ! 413: .P2 ! 414: is ! 415: .EQ ! 416: x sub i sup 2 ! 417: .EN ! 418: .PP ! 419: Other than this special case, ! 420: .CW sub ! 421: and ! 422: .CW sup ! 423: group to the right, so ! 424: .IT "x\ sup\ y\ sub\ z ! 425: means ! 426: $x sup {y sub z}$, not ${x sup y} sub z$. ! 427: .NH ! 428: Braces for Grouping ! 429: .PP ! 430: Normally, the end of a subscript or superscript is marked ! 431: simply by a blank (or tab or tilde, etc.) ! 432: What if the subscript or superscript is something that has to be typed ! 433: with blanks in it? ! 434: In that case, you can use the braces ! 435: { and } to mark the ! 436: beginning and end of the subscript or superscript: ! 437: .P1 ! 438: e sup {i omega t} ! 439: .P2 ! 440: is ! 441: .EQ ! 442: e sup {i omega t} ! 443: .EN ! 444: .sp ! 445: Rule: Braces can ! 446: always ! 447: be used to force ! 448: .IT eqn ! 449: to treat something as a unit, ! 450: or just to make your intent perfectly clear. ! 451: Thus: ! 452: .P1 ! 453: x sub {i sub 1} sup 2 ! 454: .P2 ! 455: is ! 456: .EQ ! 457: x sub {i sub 1} sup 2 ! 458: .EN ! 459: with braces, but ! 460: .P1 ! 461: x sub i sub 1 sup 2 ! 462: .P2 ! 463: is ! 464: .EQ ! 465: x sub i sub 1 sup 2 ! 466: .EN ! 467: which is rather different. ! 468: .PP ! 469: Braces can occur within braces: ! 470: .P1 ! 471: e sup {i pi sup {rho +1}} ! 472: .P2 ! 473: is ! 474: .EQ ! 475: e sup {i pi sup {rho +1}} ! 476: .EN ! 477: The general rule is that anywhere you could use some single ! 478: thing like ! 479: .CW x , ! 480: you can use an arbitrarily complicated thing if you enclose ! 481: it in braces. ! 482: .IT Eqn ! 483: will look after all the details of positioning it and making ! 484: it the right size. ! 485: .PP ! 486: In all cases, make sure you have the ! 487: right number of braces. ! 488: Leaving one out or adding an extra will cause ! 489: .IT eqn ! 490: to complain bitterly. ! 491: .PP ! 492: Occasionally you will have to ! 493: print braces. ! 494: To do this, ! 495: enclose them in double quotes, ! 496: like ! 497: .CW \&"{" . ! 498: Quoting is discussed in more detail in section 15. ! 499: .NH ! 500: Shorthand for In-line Equations ! 501: .PP ! 502: With the ! 503: .CW -ms ! 504: and ! 505: .CW -mm ! 506: macro packages, ! 507: .CW .EQ ! 508: and ! 509: .CW .EN ! 510: imply a displayed equation. ! 511: But in most documents, ! 512: it is necessary to follow mathematical conventions ! 513: not just in display equations, ! 514: but also in the body of the text, ! 515: for example by making variable names like $x$ italic. ! 516: .PP ! 517: .IT Eqn ! 518: provides a shorthand for short in-line expressions. ! 519: You can define two characters to mark the left and right ends ! 520: of an in-line equation, and then type expressions right in the middle of text ! 521: lines. ! 522: To set both the left and right characters to dollar signs, for example, ! 523: add to the beginning of your document the three lines ! 524: .EQ ! 525: delim off ! 526: .EN ! 527: .P1 ! 528: \&.EQ ! 529: delim $$ ! 530: \&.EN ! 531: .P2 ! 532: Having done this, you can then say things like ! 533: .P1 ! 534: .fi ! 535: Let $alpha sub i$ be positive, ! 536: and let $beta$ be zero. ! 537: Then we can show that $alpha sub 1$ is $>=0$. ! 538: .P2 ! 539: .EQ ! 540: delim $$ ! 541: .EN ! 542: This works as ! 543: you might expect\(emspaces, newlines, and so on are significant ! 544: in the text, but not in the equation part itself. ! 545: Multiple equations can occur in a single input line. ! 546: .PP ! 547: Enough room is left before and after a line that contains ! 548: in-line expressions ! 549: that something tall like ! 550: $sum from i=1 to n x sub i$ ! 551: does not interfere with the lines surrounding it. ! 552: .PP ! 553: To turn off the delimiters, ! 554: .P1 ! 555: \&.EQ ! 556: delim off ! 557: \&.EN ! 558: .P2 ! 559: Warning: don't use braces, tildes, circumflexes, ! 560: or double quotes as delimiters\(emchaos will result. ! 561: .NH ! 562: Fractions ! 563: .PP ! 564: To make a fraction, ! 565: use the word ! 566: .CW over : ! 567: .P1 ! 568: a+b over 2c = 1 ! 569: .P2 ! 570: gives ! 571: .EQ ! 572: a+b over 2c = 1 ! 573: .EN ! 574: The line is made the right length and positioned automatically. ! 575: Braces can be used to make clear what goes over what: ! 576: .P1 ! 577: {alpha + beta} over {sin (x)} ! 578: .P2 ! 579: is ! 580: .EQ ! 581: {alpha + beta} over {sin (x)} ! 582: .EN ! 583: What happens when there is both an ! 584: .CW over ! 585: and a ! 586: .CW sup ! 587: in the same expression? ! 588: In such an apparently ambiguous case, ! 589: .IT eqn ! 590: does the ! 591: .CW sup ! 592: before the ! 593: .CW over , ! 594: so ! 595: .P1 ! 596: -b sup 2 over pi ! 597: .P2 ! 598: is ! 599: $-b sup 2 over pi$ ! 600: instead of ! 601: $-b sup {2 over pi}$. ! 602: The rules ! 603: that decide which operation is done first in cases like this ! 604: are summarized in section 24. ! 605: When in doubt, however, ! 606: use braces ! 607: to make clear what goes with what. ! 608: .NH ! 609: Square Roots ! 610: .PP ! 611: To draw a square root, use ! 612: .CW sqrt : ! 613: .P1 2 ! 614: sqrt a+b + 1 over sqrt {ax sup 2 +bx+c} ! 615: .P2 ! 616: is ! 617: .EQ ! 618: sqrt a+b + 1 over sqrt {ax sup 2 +bx+c} ! 619: .EN ! 620: Warning\(emsquare roots of tall quantities look bad, ! 621: because a root-sign ! 622: big enough to cover the quantity is ! 623: too dark and heavy: ! 624: .P1 ! 625: sqrt {a sup 2 over b sub 2} ! 626: .P2 ! 627: is ! 628: .EQ ! 629: sqrt {a sup 2 over b sub 2} ! 630: .EN ! 631: Big square roots are generally better written as something ! 632: to the power \(12: ! 633: .EQ ! 634: (a sup 2 /b sub 2 ) sup half ! 635: .EN ! 636: which is ! 637: .P1 ! 638: (a sup 2 /b sub 2 ) sup half ! 639: .P2 ! 640: .NH ! 641: Summation, Integral, Etc. ! 642: .PP ! 643: Summations, integrals, and similar constructions ! 644: are easy: ! 645: .P1 ! 646: sum from i=0 to {i= inf} x sup i ! 647: .P2 ! 648: produces ! 649: .EQ ! 650: sum from i=0 to {i= inf} x sup i ! 651: .EN ! 652: Notice that we used ! 653: braces to indicate where the upper ! 654: part ! 655: $i= inf$ ! 656: begins and ends. ! 657: No braces were necessary for the lower part $i=0$, ! 658: because it contained no blanks. ! 659: The braces will never hurt, ! 660: and if the ! 661: .CW from ! 662: and ! 663: .CW to ! 664: parts contain any blanks, you must use braces around them. ! 665: .PP ! 666: The ! 667: .CW from ! 668: and ! 669: .CW to ! 670: parts are both optional, ! 671: but if both are used, ! 672: they have to occur in that order. ! 673: .PP ! 674: Other useful characters can replace the ! 675: .CW sum ! 676: in our example: ! 677: .P1 ! 678: int prod union inter ! 679: .P2 ! 680: become, respectively, ! 681: .EQ ! 682: int ~~~~~~ prod ~~~~~~ union ~~~~~~ inter ! 683: .EN ! 684: Since the thing before the ! 685: .CW from ! 686: can be anything, ! 687: even something in braces, ! 688: .CW from\f2-\fPto ! 689: can often be used in unexpected ways: ! 690: .P1 ! 691: lim from {n \(mi> inf} x sub n =0 ! 692: .P2 ! 693: is ! 694: .EQ ! 695: lim from {n-> inf} x sub n =0 ! 696: .EN ! 697: .PP ! 698: Notice the difference between ! 699: .CW from\f2-\fPto ! 700: and ! 701: .CW sub\f2-\fPsup : ! 702: .P1 ! 703: int from a to b ~~~ int sub a sup b ! 704: .P2 ! 705: is ! 706: .EQ ! 707: int from a to b ~~~ int sub a sup b ! 708: .EN ! 709: .NH ! 710: Size and Font Changes ! 711: .PP ! 712: By default, equations are set in ! 713: the current point size (this text is 10-point type), ! 714: with standard mathematical conventions ! 715: to determine what characters are in roman and what in italic. ! 716: Although ! 717: .IT eqn ! 718: makes a valiant attempt to use ! 719: aesthetically pleasing sizes and fonts, ! 720: it is not perfect. ! 721: To change sizes and fonts, use ! 722: .CW size ! 723: .IT n ! 724: and ! 725: .CW roman , ! 726: .CW italic , ! 727: .CW bold ! 728: and ! 729: .CW fat . ! 730: Like ! 731: .CW sub ! 732: and ! 733: .CW sup , ! 734: size ! 735: and font changes affect only the thing that follows ! 736: them, and revert to the normal situation ! 737: at the end of it. Thus ! 738: .P1 ! 739: bold x y ! 740: .P2 ! 741: is ! 742: .EQ ! 743: bold x y ! 744: .EN ! 745: and ! 746: .P1 ! 747: size 12 bold x = y + ! 748: size 12 {alpha + beta} ! 749: .P2 ! 750: gives ! 751: .EQ ! 752: size 12 bold x = y + ! 753: size 12 {alpha + beta} ! 754: .EN ! 755: As always, you can use braces if you want to affect something ! 756: more complicated than a single letter. ! 757: For example, you can change the size of an entire equation by ! 758: .P1 ! 759: size 8 { ... } ! 760: .P2 ! 761: You can also change the size ! 762: by ! 763: a given amount; ! 764: for example, you can say ! 765: .CW size\ +2 ! 766: to make the size two points bigger, ! 767: or ! 768: .CW size\ -3 ! 769: to make it three points smaller. ! 770: This has the advantage that you don't have ! 771: to know what the current size is. ! 772: .PP ! 773: If you are using fonts other than roman, italic and bold, ! 774: you can say ! 775: .CW font ! 776: .IT X ! 777: where ! 778: .IT X ! 779: is a ! 780: .IT troff ! 781: name or number for the font, ! 782: one or two characters long. ! 783: Since ! 784: .IT eqn ! 785: is tuned for roman, italic and bold, ! 786: other fonts may not give quite as good an appearance. ! 787: .PP ! 788: The ! 789: .CW fat ! 790: operation takes the current font and widens it by overstriking: ! 791: .CW fat\ grad ! 792: is ! 793: $fat grad$ and ! 794: .CW fat ! 795: .CW "{x sub i} ! 796: is ! 797: $fat {x sub i}$. ! 798: .PP ! 799: If an entire document is to be in a non-standard size ! 800: or font, it is a severe nuisance ! 801: to have to write out a size and font change for each ! 802: equation. ! 803: Accordingly, you can set a ``global'' size or font ! 804: which thereafter affects all equations. ! 805: At the beginning of any equation, you might say, for instance, ! 806: .P1 ! 807: \&.EQ ! 808: gsize 16 ! 809: gfont R ! 810: \&... ! 811: \&.EN ! 812: .P2 ! 813: to set the size to 16 and the font to roman thereafter. ! 814: In place of R, you can use any of the ! 815: .IT troff ! 816: font names. ! 817: The size after ! 818: .CW gsize ! 819: can be a relative change with ! 820: .CW + ! 821: or ! 822: .CW - . ! 823: .PP ! 824: Generally, ! 825: .CW gsize ! 826: and ! 827: .CW gfont ! 828: will appear at the beginning of a document ! 829: but they can also appear ! 830: throughout a document: the global font and size ! 831: can be changed as often as needed.\(dd ! 832: .FS ! 833: \l'1i' ! 834: .br ! 835: \(ddIn a footnote like this one, in which we have a ! 836: few random ! 837: expressions like $x sub i$ and $pi sup 2$, ! 838: .IT eqn ! 839: handles the size change automatically. ! 840: .FE ! 841: .PP ! 842: Since ! 843: .IT eqn ! 844: manages most size changes automatically, ! 845: .CW gsize ! 846: is rarely necessary. ! 847: .NH ! 848: Diacritical Marks ! 849: .PP ! 850: To get diacritical marks on top of letters, ! 851: there are several words: ! 852: .P1 ! 853: .ta 1i ! 854: .vs +3 ! 855: x dot $x dot$ ! 856: x dotdot $x dotdot$ ! 857: x hat $x hat$ ! 858: x tilde $x tilde$ ! 859: x vec $x vec$ ! 860: x dyad $x dyad$ ! 861: x bar $x bar$ ! 862: x under $x under$ ! 863: x utilde $x utilde$ ! 864: .vs -3 ! 865: .P2 ! 866: The diacritical mark is placed at the right height. ! 867: The ! 868: .CW bar ! 869: and ! 870: .CW under ! 871: are made the right length for the entire construct, ! 872: as in $x+y+z bar$; ! 873: other marks are centered. ! 874: .PP ! 875: Sometimes ! 876: .IT eqn ! 877: guesses wrong on the height for bars. ! 878: As an interim fix, the words ! 879: .CW highbar ! 880: and ! 881: .CW lowbar ! 882: are synonymous with ! 883: .CW bar, ! 884: but force the bar to be either high ! 885: (as with $X bar$) ! 886: or low (as with $x bar$) regardless of the apparent height of the object. ! 887: This is useful for constructions like ! 888: ${x sub 1} lowbar$, which is ! 889: .CW "{x sub 1} lowbar" . ! 890: ....... ! 891: .NH ! 892: Quoted Text ! 893: .PP ! 894: Any input entirely within quotes ! 895: .CW \&"\f2...\fP" ! 896: is not subject to any of the normal font changes and spacing ! 897: adjustments. ! 898: This provides a way to do your own spacing and adjusting if needed: ! 899: .P1 ! 900: italic "sin(x)" + sin (x) ! 901: .P2 ! 902: is ! 903: .EQ ! 904: italic "sin(x)" + sin (x) ! 905: .EN ! 906: .PP ! 907: Quotes are also used to get braces and other ! 908: .IT eqn ! 909: keywords printed: ! 910: .P1 ! 911: "{ size alpha }" ! 912: .P2 ! 913: is ! 914: .EQ ! 915: "{ size alpha }" ! 916: .EN ! 917: and ! 918: .P1 ! 919: roman "{ size alpha }" ! 920: .P2 ! 921: is ! 922: .EQ ! 923: roman "{ size alpha }" ! 924: .EN ! 925: .PP ! 926: The construction ! 927: .CW \&"" ! 928: is often used as a place-holder ! 929: when grammatically ! 930: .IT eqn ! 931: needs something, but you don't actually want anything in your output. ! 932: For example, to make ! 933: $"" sup 2 roman He$, ! 934: you can't just type ! 935: .CW "sup 2 roman He ! 936: because a ! 937: .CW sup ! 938: has to be a superscript ! 939: .IT on ! 940: something. ! 941: Thus you must say ! 942: .P1 ! 943: "" sup 2 roman He ! 944: .P2 ! 945: .PP ! 946: To get a literal quote ! 947: use ! 948: .CW \&"\e"" . ! 949: If delimiters are set with ! 950: .CW delim , ! 951: you can include them in a quoted string too. ! 952: .IT Troff ! 953: special-character names like ! 954: .CW \e(bs ! 955: can appear unquoted, but all other ! 956: .IT troff ! 957: constructions ! 958: should ! 959: always ! 960: be quoted. ! 961: .NH ! 962: Lining up Equations ! 963: .PP ! 964: Sometimes it's necessary to line up a series of equations ! 965: at some horizontal position, often at an equals sign. ! 966: This is done with two operations called ! 967: .CW mark ! 968: and ! 969: .CW lineup . ! 970: .PP ! 971: The word ! 972: .CW mark ! 973: may appear once at any place in an equation. ! 974: It remembers the horizontal position where it appeared. ! 975: Successive equations can contain one occurrence of the word ! 976: .CW lineup . ! 977: The place where ! 978: .CW lineup ! 979: appears is made to line up ! 980: with the place marked by the previous ! 981: .CW mark ! 982: if possible. ! 983: Thus, for example, ! 984: you can say ! 985: .P1 ! 986: \&.EQ I ! 987: x+y mark = z ! 988: \&.EN ! 989: \&.EQ I ! 990: x lineup = 1 ! 991: \&.EN ! 992: .P2 ! 993: to produce ! 994: .EQ I ! 995: x+y mark = z ! 996: .EN ! 997: .EQ I ! 998: x lineup = 1 ! 999: .EN ! 1000: For reasons too complicated to talk about, ! 1001: when you use ! 1002: .IT eqn ! 1003: and ! 1004: .CW -ms , ! 1005: use either ! 1006: .CW .EQ\ I ! 1007: or ! 1008: .CW .EQ\ L ; ! 1009: .CW mark ! 1010: and ! 1011: .CW lineup ! 1012: don't work with centered equations. ! 1013: Also bear in mind that ! 1014: .CW mark ! 1015: doesn't look ahead; ! 1016: .P1 ! 1017: x mark =1 ! 1018: \&... ! 1019: x+y lineup =z ! 1020: .P2 ! 1021: will not work if there isn't room ! 1022: for the ! 1023: .CW x+y ! 1024: part after the ! 1025: .CW mark ! 1026: remembers where the ! 1027: .CW x ! 1028: is. ! 1029: If you use ! 1030: .CW .EQ ! 1031: .CW I , ! 1032: that may suffice; ! 1033: if not, use tildes to move the first equation to the right. ! 1034: .NH ! 1035: Big Brackets, Etc. ! 1036: .PP ! 1037: To get big brackets, ! 1038: braces, parentheses, and bars ! 1039: around things, use the ! 1040: .CW left ! 1041: and ! 1042: .CW right ! 1043: commands: ! 1044: .P1 ! 1045: left { a over b + 1 right } ! 1046: ~=~ left ( c over d right ) ! 1047: + left [ e right ] ! 1048: .P2 ! 1049: is ! 1050: .EQ ! 1051: left { a over b + 1 right } ~=~ left ( c over d right ) + left [ e right ] ! 1052: .EN ! 1053: The resulting brackets are made big enough to cover whatever they enclose. ! 1054: Other characters can be used besides these, ! 1055: but are not likely to look very good. ! 1056: The ! 1057: .CW floor ! 1058: and ! 1059: .CW ceiling ! 1060: characters are exceptions: ! 1061: .P1 .2i ! 1062: left floor x over y right floor <= ! 1063: left ceiling a over b right ceiling ! 1064: .P2 ! 1065: produces ! 1066: .EQ ! 1067: left floor x over y right floor ! 1068: <= left ceiling a over b right ceiling ! 1069: .EN ! 1070: .PP ! 1071: Several warnings about brackets are in order. ! 1072: First, braces are typically bigger than brackets and parentheses, ! 1073: because they are made up of three, five, seven, etc., pieces, ! 1074: while brackets can be made up of two, three, etc. ! 1075: Second, big left and right parentheses often look poor, ! 1076: because the character set is poorly designed. ! 1077: .PP ! 1078: The ! 1079: .CW right ! 1080: part may be omitted: ! 1081: a ``left something'' need not have a ! 1082: corresponding ! 1083: ``right ! 1084: something''. ! 1085: If the ! 1086: .CW right ! 1087: part is omitted, ! 1088: put braces around the thing you want the left bracket ! 1089: to encompass. ! 1090: Otherwise, the resulting brackets may be too large. ! 1091: .PP ! 1092: If you want to omit the ! 1093: .CW left ! 1094: part, things are more complicated, ! 1095: because technically you can't have a ! 1096: .CW right ! 1097: without a corresponding ! 1098: .CW left . ! 1099: Instead you have to say ! 1100: .P1 ! 1101: left "" ... right ) ! 1102: .P2 ! 1103: for example. ! 1104: The ! 1105: .CW ! 1106: left "" ! 1107: .R ! 1108: means a ``left nothing''. ! 1109: This satisfies the rules without hurting your output. ! 1110: .NH ! 1111: Piles ! 1112: .PP ! 1113: There is a general facility for making vertical piles ! 1114: of things; it comes in several flavors. ! 1115: For example: ! 1116: .P1 ! 1117: A ~=~ left [ ! 1118: pile { a above b above c } ! 1119: ~~ pile { x above y above z } ! 1120: right ] ! 1121: .P2 ! 1122: will make ! 1123: .EQ ! 1124: A ~=~ left [ ! 1125: pile { a above b above c } ~~ pile { x above y above z } ! 1126: right ] ! 1127: .EN ! 1128: The elements of the pile (there can be as many as you want) ! 1129: are centered one above another, at the right height for ! 1130: most purposes. ! 1131: The keyword ! 1132: .CW above ! 1133: is used to separate the pieces; ! 1134: braces are used around the entire list. ! 1135: The elements of a pile can be as complicated as needed, even containing more piles. ! 1136: .PP ! 1137: Three other forms of pile exist: ! 1138: .CW lpile ! 1139: makes a pile with the elements left-justified; ! 1140: .CW rpile ! 1141: makes a right-justified pile; ! 1142: and ! 1143: .CW cpile ! 1144: makes a centered pile, just like ! 1145: .CW pile. ! 1146: The vertical spacing between the pieces ! 1147: is somewhat larger for ! 1148: .CW l , ! 1149: .CW r , ! 1150: and ! 1151: .CW cpiles ! 1152: than it is for ordinary piles. ! 1153: .P1 .1i ! 1154: roman sign (x)~=~ ! 1155: left { ! 1156: lpile {1 above 0 above -1} ! 1157: ~~ lpile ! 1158: {if~x>0 above if~x=0 above if~x<0} ! 1159: .P2 ! 1160: makes ! 1161: .EQ ! 1162: roman sign (x)~=~ ! 1163: left { ! 1164: lpile {1 above 0 above -1} ! 1165: ~~ lpile ! 1166: {if~x>0 above if~x=0 above if~x<0} ! 1167: .EN ! 1168: Notice the left brace ! 1169: without a matching right one. ! 1170: .PP ! 1171: It is possible to change the default vertical separation ! 1172: between elements of a pile, ! 1173: by adding a number immediately after the word ! 1174: .CW lpile , ! 1175: etc. The number is in units of 1/100's of an em ! 1176: (an em is about the width of the letter `m'); ! 1177: .CW "lpile 33 ! 1178: makes the spacing 1/3 of an em. ! 1179: .NH ! 1180: Matrices ! 1181: .PP ! 1182: It is also possible to make matrices. ! 1183: For example, to make ! 1184: a neat array like ! 1185: .EQ ! 1186: matrix { ! 1187: ccol { x sub i above y sub i } ! 1188: ccol { x sup 2 above y sup 2 } ! 1189: } ! 1190: .EN ! 1191: you have to type ! 1192: .P1 ! 1193: matrix { ! 1194: ccol { x sub i above y sub i } ! 1195: ccol { x sup 2 above y sup 2 } ! 1196: } ! 1197: .P2 ! 1198: This produces a matrix with ! 1199: two centered columns. ! 1200: The elements of the columns are then listed just as for a pile, ! 1201: each element separated by the word ! 1202: .CW above. ! 1203: You can also use ! 1204: .CW lcol ! 1205: or ! 1206: .CW rcol ! 1207: to left or right adjust columns. ! 1208: Each column can be separately adjusted, ! 1209: and there can be as many columns as you like. ! 1210: .PP ! 1211: The words ! 1212: .CW pile ! 1213: and ! 1214: .CW col , ! 1215: .CW lpile ! 1216: and ! 1217: .CW lcol , ! 1218: etc., are synonyms. ! 1219: .PP ! 1220: The reason for using a matrix instead of two adjacent piles, by the way, ! 1221: is that if the elements of the piles don't all have the same height, ! 1222: they won't line up properly. ! 1223: A matrix forces them to line up, ! 1224: because it looks at the entire structure before deciding what ! 1225: spacing to use. ! 1226: .PP ! 1227: A word of warning about matrices\(emeach column must have the same number of elements in it. ! 1228: The world will end if you get this wrong. ! 1229: .NH ! 1230: Local Motions ! 1231: .EQ ! 1232: delim $$ ! 1233: .EN ! 1234: .PP ! 1235: Although ! 1236: .IT eqn ! 1237: tries to print things at the right place, ! 1238: it isn't perfect, and occasionally you will need to tune ! 1239: the output to make it just right. ! 1240: Small extra horizontal spaces can be obtained with ! 1241: tilde and circumflex. ! 1242: You can also say ! 1243: .CW back ! 1244: .IT n ! 1245: and ! 1246: .CW fwd ! 1247: .IT n ! 1248: to move small amounts horizontally. ! 1249: .IT n ! 1250: is how far to move in 1/100's of an em. ! 1251: Thus ! 1252: .CW back ! 1253: .CW 50 ! 1254: moves back about half the width of an m. ! 1255: For example, ! 1256: .CW << ! 1257: produces ! 1258: $<<$, while ! 1259: .CW "< back 50 < ! 1260: produces $< back 50 <$. ! 1261: .PP ! 1262: Similarly you can move things up or down with ! 1263: .CW up ! 1264: .IT n ! 1265: and ! 1266: .CW down ! 1267: .IT n . ! 1268: .P1 ! 1269: x sub down 20 i sup up 20 j ! 1270: .P2 ! 1271: produces $x sub down 20 i sup up 20 j$ instead of the usual $x sub i sup j$. ! 1272: .PP ! 1273: As with ! 1274: .CW sub ! 1275: or ! 1276: .CW sup , ! 1277: the local motions affect the next thing in the input, ! 1278: and this can be something arbitrarily complicated if it is enclosed ! 1279: in braces. ! 1280: .NH ! 1281: Definitions ! 1282: .PP ! 1283: .IT Eqn ! 1284: provides a facility so you can give ! 1285: a frequently-used string of characters a name, ! 1286: and thereafter just type the name instead of the ! 1287: whole string. ! 1288: For example, if the sequence ! 1289: .P1 ! 1290: x sub i + y sub i ! 1291: .P2 ! 1292: appears repeatedly throughout a paper, ! 1293: you can save re-typing it each time by defining it like this: ! 1294: .P1 2 ! 1295: define xy 'x sub i + y sub i' ! 1296: .P2 ! 1297: This makes ! 1298: .CW xy ! 1299: a shorthand for whatever characters occur between the single quotes ! 1300: in the definition. ! 1301: You can use any character instead of quote to mark the ends of the definition, ! 1302: so long as it doesn't appear inside the definition. ! 1303: .PP ! 1304: Now you can use ! 1305: .CW xy ! 1306: like this: ! 1307: .P1 ! 1308: \&.EQ ! 1309: f(x) = xy ... ! 1310: \&.EN ! 1311: .P2 ! 1312: and so on. ! 1313: Each occurrence of ! 1314: .CW xy ! 1315: will expand into what it was defined as. ! 1316: Be careful to leave spaces or their equivalent ! 1317: around the name ! 1318: when you actually use it, so ! 1319: .IT eqn ! 1320: will be able to identify it as special. ! 1321: .PP ! 1322: There are several things to watch out for. ! 1323: First, although definitions can use previous definitions, ! 1324: as in ! 1325: .P1 ! 1326: \&.EQ ! 1327: define xi ' x sub i ' ! 1328: define xi1 ' xi sub 1 ' ! 1329: \&.EN ! 1330: .P2 ! 1331: .ul ! 1332: Don't define something in terms of itself! ! 1333: A favorite error is to say ! 1334: .P1 ! 1335: define X ' roman X ' ! 1336: .P2 ! 1337: This is a guaranteed disaster, ! 1338: since ! 1339: .CW X ! 1340: is ! 1341: now defined in terms of itself. ! 1342: If you say ! 1343: .P1 ! 1344: define X ' roman "X" ' ! 1345: .P2 ! 1346: however, the quotes ! 1347: protect the second ! 1348: .CW X , ! 1349: and everything works fine. ! 1350: .PP ! 1351: .IT Eqn ! 1352: keywords can be redefined. ! 1353: You can make ! 1354: .CW / ! 1355: mean ! 1356: .CW over ! 1357: by saying ! 1358: .P1 ! 1359: define / ' over ' ! 1360: .P2 ! 1361: or redefine ! 1362: .CW over ! 1363: as ! 1364: .CW / ! 1365: with ! 1366: .P1 ! 1367: define over ' / ' ! 1368: .P2 ! 1369: .PP ! 1370: .EQ ! 1371: delim off ! 1372: .EN ! 1373: It is possible to create a parameterized definition, which will ! 1374: expand into something different each time it is used. ! 1375: If a definition contains occurrences of ! 1376: .CW $1 , ! 1377: .CW $2 , ! 1378: etc., as in ! 1379: .P1 ! 1380: define f 'font $1 {"$2"}' ! 1381: .P2 ! 1382: then subsequent uses of that name that are followed by a parenthesized ! 1383: list of values will have the values substituted for the ! 1384: .CW $\f2n\fP\f1's:\fP ! 1385: .P1 ! 1386: f(CW, a phrase) ! 1387: .P2 ! 1388: will print ! 1389: .CW "a phrase ! 1390: in the constant-width font ! 1391: .CW CW . ! 1392: .PP ! 1393: You can test whether something is defined with ! 1394: .CW ifdef : ! 1395: .P1 ! 1396: ifdef f / \f2anything at all\fP / ! 1397: .P2 ! 1398: is replaced by ! 1399: .IT "anything at all ! 1400: if ! 1401: .CW f ! 1402: is defined. ! 1403: .NH ! 1404: File Inclusion ! 1405: .PP ! 1406: You can include a file of ! 1407: .IT eqn ! 1408: input as part of an equation by the construction ! 1409: .P1 ! 1410: include "\f2filename\fP" ! 1411: .P2 ! 1412: For historical reasons, ! 1413: .CW copy ! 1414: is a synonym for ! 1415: .CW include . ! 1416: .NH ! 1417: A Large Example ! 1418: .PP ! 1419: Here is the complete source for the three display equations ! 1420: in the abstract of this guide. ! 1421: .br ! 1422: .ps -3 ! 1423: .vs -3 ! 1424: .P1 0 ! 1425: \&.EQ I ! 1426: G(z)~mark =~ e sup { ln ~ G(z) } ! 1427: ~=~ exp left ( ! 1428: sum from k>=1 {S sub k z sup k} over k right ) ! 1429: ~=~ prod from k>=1 e sup {S sub k z sup k /k} ! 1430: \&.EN ! 1431: \&.EQ I ! 1432: lineup = left ( 1 + S sub 1 z + ! 1433: { S sub 1 sup 2 z sup 2 } over 2! + .\^.\^. right ) ! 1434: left ( 1+ { S sub 2 z sup 2 } over 2 ! 1435: + { S sub 2 sup 2 z sup 4 } over { 2 sup 2 cdot 2! } ! 1436: + .\^.\^. right ) .\^.\^. ! 1437: \&.EN ! 1438: \&.EQ I ! 1439: lineup = sum from m>=0 left ( ! 1440: sum from ! 1441: pile { k sub 1 ,k sub 2 ,\^.\^.\^.\^, k sub m >=0 ! 1442: above ! 1443: k sub 1 +2k sub 2 + .\^.\^. +mk sub m =m} ! 1444: { S sub 1 sup {k sub 1} } over {1 sup k sub 1 k sub 1 ! } ~ ! 1445: { S sub 2 sup {k sub 2} } over {2 sup k sub 2 k sub 2 ! } ~ ! 1446: \&.\^.\^. ! 1447: { S sub m sup {k sub m} } over {m sup k sub m k sub m ! } ! 1448: right ) z sup m ! 1449: \&.EN ! 1450: .P2 ! 1451: .ps +3 ! 1452: .vs +3 ! 1453: ...... ! 1454: .NH ! 1455: Keywords, Precedences, Etc. ! 1456: .PP ! 1457: Here are the keywords of ! 1458: .IT eqn ! 1459: in order of decreasing precedence: ! 1460: .P1 .1i ! 1461: dyad vec under utilde bar tilde ! 1462: hat dot dotdot ! 1463: left right ! 1464: fwd back down up ! 1465: fat roman italic bold size ! 1466: sub sup ! 1467: sqrt over ! 1468: from to ! 1469: .P2 ! 1470: These operations group to the left: ! 1471: .P1 .1i ! 1472: over sqrt left right ! 1473: .P2 ! 1474: All others group to the right. ! 1475: .PP ! 1476: Digits, parentheses, brackets, punctuation marks, and these mathematical words ! 1477: are converted ! 1478: to Roman font when encountered: ! 1479: .P1 .1i ! 1480: sin cos tan sinh cosh tanh arc ! 1481: max min lim log ln exp ! 1482: Re Im and if for det ! 1483: .P2 ! 1484: These character sequences are recognized and translated as shown. ! 1485: .EQ ! 1486: delim $$ ! 1487: .EN ! 1488: .P1 ! 1489: >= $>=$ nothing $nothing$ ! 1490: <= $<=$ cdot $cdot$ ! 1491: == $==$ times $times$ ! 1492: != $!=$ del $del$ ! 1493: +- $+-$ grad $grad$ ! 1494: -> $->$ \&... $"..."$ ! 1495: <- $<-$ ,..., $",...,"$ ! 1496: << $<<$ sum $sum$ ! 1497: .sp 3p ! 1498: >> $>>$ int $int$ ! 1499: inf $inf$ prod $prod$ ! 1500: partial $partial$ union $union$ ! 1501: half $half$ inter $inter$ ! 1502: prime $prime$ dollar $dollar$ ! 1503: approx $approx$ ! 1504: .P2 ! 1505: .PP ! 1506: To obtain Greek letters, ! 1507: simply spell them out in whatever case you want: ! 1508: .P1 ! 1509: .ta .7i 1.4i 2.1i ! 1510: DELTA $DELTA$ iota $iota$ ! 1511: GAMMA $GAMMA$ kappa $kappa$ ! 1512: LAMBDA $LAMBDA$ lambda $lambda$ ! 1513: OMEGA $OMEGA$ mu $mu$ ! 1514: PHI $PHI$ nu $nu$ ! 1515: PI $PI$ omega $omega$ ! 1516: PSI $PSI$ omicron $omicron$ ! 1517: SIGMA $SIGMA$ phi $phi$ ! 1518: THETA $THETA$ pi $pi$ ! 1519: UPSILON $UPSILON$ psi $psi$ ! 1520: XI $XI$ rho $rho$ ! 1521: alpha $alpha$ sigma $sigma$ ! 1522: beta $beta$ tau $tau$ ! 1523: chi $chi$ theta $theta$ ! 1524: delta $delta$ upsilon $upsilon$ ! 1525: epsilon $epsilon$ xi $xi$ ! 1526: eta $eta$ zeta $zeta$ ! 1527: gamma $gamma$ ! 1528: .P2 ! 1529: .IT Eqn ! 1530: really ought to know the whole Greek alphabet, ! 1531: but the missing upper-case characters are identical to Roman ones. ! 1532: .PP ! 1533: These are all the words known to ! 1534: .IT eqn , ! 1535: except for characters with names. ! 1536: .P1 ! 1537: above fat lcol size ! 1538: back font left space ! 1539: bar from lineup sqrt ! 1540: bold fwd lowbar sub ! 1541: ccol gfont lpile sum ! 1542: col gsize mark sup ! 1543: copy hat matrix tilde ! 1544: cpile highbar over to ! 1545: define ifdef pile under ! 1546: delim include prod union ! 1547: dot int rcol up ! 1548: dotdot integral right utilde ! 1549: down inter roman vec ! 1550: dyad italic rpile ! 1551: .P2 ! 1552: .NH ! 1553: Troubleshooting ! 1554: .PP ! 1555: If you make a mistake in an equation, ! 1556: like leaving out a brace (very common) ! 1557: or having one too many (very common) ! 1558: or having a ! 1559: .CW sup ! 1560: with nothing before it (common), ! 1561: .IT eqn ! 1562: will tell you with the message ! 1563: .P1 2 ! 1564: syntax error near line \f2n\fP, file \f2f\fP, ! 1565: context is >>> \f2something\fP <<< ! 1566: .P2 ! 1567: where ! 1568: .IT n ! 1569: is approximately the line ! 1570: where the trouble occurred, ! 1571: .IT f ! 1572: is the name ! 1573: of the input file, and ! 1574: .IT something ! 1575: is a guess about what input was in error. ! 1576: The line number and context is approximate\(emlook nearby as well. ! 1577: There are also self-explanatory messages that arise if you leave out a quote ! 1578: or try to run ! 1579: .IT eqn ! 1580: on a non-existent file. ! 1581: .PP ! 1582: If you want to check a document before actually printing it, ! 1583: .P1 ! 1584: eqn files >/dev/null ! 1585: .P2 ! 1586: will ! 1587: throw away the output but print the messages. ! 1588: .PP ! 1589: If you use something like dollar signs as delimiters, ! 1590: it is easy to leave one out. ! 1591: This causes very strange troubles. ! 1592: The program ! 1593: .CW checkeq ! 1594: checks for misplaced or missing delimiters ! 1595: and similar troubles. ! 1596: .PP ! 1597: In-line equations can only be so big ! 1598: because of an internal limit in ! 1599: .IT troff . ! 1600: If you get the message ! 1601: ``word overflow,'' ! 1602: you have exceeded this limit. ! 1603: If you print the equation as a displayed equation ! 1604: this message will usually go away. ! 1605: The message ! 1606: ``line overflow'' ! 1607: indicates you have exceeded a different, bigger internal limit. ! 1608: The only cure for this is to break the equation into two separate ones. ! 1609: .PP ! 1610: On a related topic, ! 1611: .IT eqn ! 1612: does not break equations by itself\(emyou must split long equations up across multiple lines ! 1613: by yourself, ! 1614: marking each by a separate ! 1615: .CW .EQ ! 1616: \&...\& ! 1617: .CW .EN ! 1618: sequence. ! 1619: .NH ! 1620: Use on UNIX ! 1621: .PP ! 1622: To print a document that contains mathematics, ! 1623: .P1 ! 1624: eqn files | troff ! 1625: .P2 ! 1626: If ! 1627: there are any ! 1628: .IT troff ! 1629: options, they go after the ! 1630: .IT troff ! 1631: part of the command. For example, ! 1632: .P1 ! 1633: eqn files | troff -ms ! 1634: .P2 ! 1635: .IT Eqn ! 1636: assumes the output is aimed at a Postscript device. ! 1637: If you are using some other typesetter or printer, ! 1638: you have to tell ! 1639: .IT eqn ! 1640: with the same ! 1641: .CW -T ! 1642: argument that you use with ! 1643: .IT troff : ! 1644: .P1 ! 1645: eqn -Taps files | troff -Taps ... ! 1646: .P2 ! 1647: .IT Eqn ! 1648: also uses the environment variable ! 1649: .CW TYPESETTER ; ! 1650: the default is ! 1651: .CW post , ! 1652: as it is for ! 1653: .IT troff . ! 1654: .PP ! 1655: .IT Eqn ! 1656: can be used with the ! 1657: .IT tbl ! 1658: program ! 1659: for setting tables that contain mathematics. ! 1660: Use ! 1661: .IT tbl ! 1662: before ! 1663: .IT eqn , ! 1664: like this: ! 1665: .P1 ! 1666: tbl files | eqn | troff ! 1667: .P2 ! 1668: .PP ! 1669: When ! 1670: .IT eqn ! 1671: is used with ! 1672: .IT pic ! 1673: or ! 1674: .IT grap , ! 1675: the additional vertical space ! 1676: that ! 1677: .IT eqn ! 1678: adds to a line to keep it from colliding ! 1679: with adjacent lines will conflict with ! 1680: .IT pic ! 1681: and ! 1682: .IT grap ! 1683: spacing. ! 1684: The phrase ! 1685: .CW "space 0 ! 1686: at the beginning of an equation will turn off the extra space. ! 1687: .SH ! 1688: Acknowledgements ! 1689: .PP ! 1690: We are deeply indebted to the late J. F. Ossanna, ! 1691: the author of ! 1692: .IT troff , ! 1693: for his willingness to extend ! 1694: .IT troff ! 1695: to make our task easier, ! 1696: and for his ! 1697: continuous assistance during the development ! 1698: and evolution ! 1699: of ! 1700: .IT eqn . ! 1701: We are also grateful to A. V. Aho ! 1702: for advice on language design, ! 1703: to S. C. Johnson for assistance with ! 1704: the ! 1705: .IT yacc ! 1706: compiler-compiler, ! 1707: and to all the ! 1708: .IT eqn ! 1709: users ! 1710: who have made helpful suggestions and criticisms. ! 1711: .SH ! 1712: References ! 1713: .LP ! 1714: |reference_placement ! 1715: .SH ! 1716: Appendix 1. Tuning \fIeqn\fP Output ! 1717: .PP ! 1718: There are numerous values that can be adjusted to tune the output ! 1719: of ! 1720: .IT eqn ! 1721: for a particular output device. ! 1722: In general, it is necessary to have access to the source code ! 1723: to do this tuning. ! 1724: .PP ! 1725: Some values can be set without access to the source. ! 1726: The names shown below (together with their default values) control the positioning ! 1727: of diacritical marks and special characters. ! 1728: They can be defined with any string value, ! 1729: as in ! 1730: .P1 0 ! 1731: define vec_def " \ev'-.5m'\es-3\e(->\es0\ev'.5m' ! 1732: .P2 ! 1733: .1C ! 1734: .KF bottom ! 1735: .nr dP 1 ! 1736: .nr dV 2p ! 1737: .SP ! 1738: .P1 20n ! 1739: vec_def \ev'-.5m'\es-3\e(->\es0\ev'.5m' ! 1740: dyad_def \ev'-.5m'\es-3\ez\e(<-\e|\e(->\es0\ev'.5m' ! 1741: hat_def \ev'-.05m'\es+1^\es0\ev'.05m' ! 1742: tilde_def \ev'-.05m'\es+1~\es0\ev'.05m' ! 1743: dot_def \ev'-.67m'.\ev'.67m' ! 1744: dotdot_def \ev'-.67m'..\ev'.67m' ! 1745: utilde_def \ev'1.0m'\es+2~\es-2\ev'-1.0m' ! 1746: sum_def \e|\ev'.3m'\es+5\e(*S\es-5\ev'-.3m'\e| ! 1747: union_def \e|\ev'.3m'\es+5\e(cu\es-5\ev'-.3m'\e| ! 1748: inter_def \e|\ev'.3m'\es+5\e(ca\es-5\ev'-.3m'\e| ! 1749: prod_def \e|\ev'.3m'\es+5\e(*P\es-5\ev'-.3m'\e| ! 1750: int_def \ev'.1m'\es+4\e(is\es-4\ev'-.1m' ! 1751: Subbase 0.2 ! 1752: Supbase 0.4 ! 1753: .P2 ! 1754: .KE ! 1755: .2C ! 1756: The amount by which a subscript is shifted down ! 1757: and a superscript shifted up are controlled by ! 1758: .CW Subbase ! 1759: and ! 1760: .CW Supbase .
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