/ TeX 1995 July / TeX CD-ROM July 1995 (Disc 1)(Walnut Creek)(1995).ISO / macros / plain / contrib / samples / apjstyle.tex

< prev

next >

MacOS 8.1

Win98

DOS

browse contents

view JSON data

view as text

+--------+-------------------------+-------------------------+--------+--------+
|00000000| 25 0a 25 20 52 65 6d 6f | 76 69 6e 67 20 74 68 65 |%.% Remo|ving the|
|00000010| 20 60 20 25 20 27 20 66 | 72 6f 6d 20 74 68 65 20 | ` % ' f|rom the |
|00000020| 62 65 67 69 6e 6e 69 6e | 67 20 6f 66 20 74 68 65 |beginnin|g of the|
|00000030| 20 74 68 69 72 64 20 6c | 69 6e 65 20 6c 65 61 64 | third l|ine lead|
|00000040| 73 20 74 6f 20 61 20 31 | 2e 32 0a 25 20 6d 61 67 |s to a 1|.2.% mag|
|00000050| 6e 69 66 69 63 61 74 69 | 6f 6e 20 6f 66 20 74 68 |nificati|on of th|
|00000060| 65 20 6f 75 74 70 75 74 | 20 28 73 61 6d 65 20 6d |e output| (same m|
|00000070| 61 72 67 69 6e 73 20 6f | 66 20 63 6f 75 72 73 65 |argins o|f course|
|00000080| 29 2e 0a 25 20 5c 6d 61 | 67 6e 69 66 69 63 61 74 |)..% \ma|gnificat|
|00000090| 69 6f 6e 3d 31 32 30 30 | 0a 0a 5c 69 6e 70 75 74 |ion=1200|..\input|
|000000a0| 20 62 6f 62 6d 61 63 72 | 6f 20 20 20 25 20 54 68 | bobmacr|o   % Th|
|000000b0| 69 73 20 6c 6f 61 64 73 | 20 74 68 65 20 6d 61 63 |is loads| the mac|
|000000c0| 72 6f 66 69 6c 65 20 60 | 62 6f 62 6d 61 63 72 6f |rofile `|bobmacro|
|000000d0| 2e 74 65 78 27 20 77 68 | 69 63 68 20 63 6f 6e 74 |.tex' wh|ich cont|
|000000e0| 61 69 6e 73 0a 20 20 20 | 20 20 20 20 20 20 20 20 |ains.   |        |
|000000f0| 20 20 20 20 20 20 20 25 | 20 73 6f 6d 65 20 75 73 |       %| some us|
|00000100| 65 66 75 6c 20 64 65 66 | 69 6e 69 74 69 6f 6e 73 |eful def|initions|
|00000110| 2c 20 6c 69 6b 65 20 74 | 68 65 20 60 5c 74 69 74 |, like t|he `\tit|
|00000120| 6c 20 20 5c 65 6e 64 74 | 69 74 6c 27 0a 20 20 20 |l  \endt|itl'.   |
|00000130| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 25 |        |       %|
|00000140| 20 77 68 69 63 68 20 66 | 6f 6c 6c 6f 77 73 2e 20 | which f|ollows. |
|00000150| 60 20 25 20 27 20 74 65 | 6c 6c 73 20 74 65 78 20 |` % ' te|lls tex |
|00000160| 74 6f 20 69 67 6e 6f 72 | 65 20 74 68 65 20 72 65 |to ignor|e the re|
|00000170| 73 74 20 6f 66 20 0a 20 | 20 20 20 20 20 20 20 20 |st of . |        |
|00000180| 20 20 20 20 20 20 20 20 | 20 25 20 74 68 65 20 6c |        | % the l|
|00000190| 69 6e 65 2c 20 65 6e 61 | 62 6c 69 6e 67 20 6f 6e |ine, ena|bling on|
|000001a0| 65 20 74 6f 20 6d 61 6b | 65 20 63 6f 6d 6d 65 6e |e to mak|e commen|
|000001b0| 74 73 2e 20 49 66 20 74 | 68 65 20 66 69 6c 65 0a |ts. If t|he file.|
|000001c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000001d0| 20 20 25 20 79 6f 75 20 | 77 61 6e 74 20 74 6f 20 |  % you |want to |
|000001e0| 6c 6f 61 64 20 69 73 20 | 6e 6f 74 20 69 6e 20 79 |load is |not in y|
|000001f0| 6f 75 72 20 63 75 72 72 | 65 6e 74 20 64 69 72 65 |our curr|ent dire|
|00000200| 63 74 6f 72 79 2c 0a 20 | 20 20 20 20 20 20 20 20 |ctory,. |        |
|00000210| 20 20 20 20 20 20 20 20 | 20 25 20 75 73 65 3a 60 |        | % use:`|
|00000220| 5c 69 6e 70 75 74 20 74 | 65 78 24 73 75 62 3a 5b |\input t|ex$sub:[|
|00000230| 65 78 61 6d 70 6c 65 73 | 5d 62 6f 62 6d 61 63 72 |examples|]bobmacr|
|00000240| 6f 2e 74 65 78 27 20 66 | 6f 72 20 65 78 61 6d 70 |o.tex' f|or examp|
|00000250| 6c 65 2e 0a 0a 5c 74 69 | 74 6c 20 5c 63 65 6e 74 |le...\ti|tl \cent|
|00000260| 65 72 6c 69 6e 65 7b 45 | 58 41 4d 50 4c 45 20 4f |erline{E|XAMPLE O|
|00000270| 46 20 41 20 4d 41 4e 55 | 53 43 52 49 50 54 20 57 |F A MANU|SCRIPT W|
|00000280| 49 54 48 20 41 20 54 57 | 4f 2d 4c 49 4e 45 20 54 |ITH A TW|O-LINE T|
|00000290| 49 54 4c 45 7d 0a 20 20 | 20 20 20 20 5c 63 65 6e |ITLE}.  |    \cen|
|000002a0| 74 65 72 6c 69 6e 65 7b | 50 52 45 50 41 52 45 44 |terline{|PREPARED|
|000002b0| 20 46 4f 52 20 5c 54 65 | 58 24 5e 31 24 7d 20 5c | FOR \Te|X$^1$} \|
|000002c0| 65 6e 64 74 69 74 6c 0a | 0a 5c 63 65 6e 74 65 72 |endtitl.|.\center|
|000002d0| 6c 69 6e 65 7b 57 69 6c | 6c 69 61 6d 20 48 2e 20 |line{Wil|liam H. |
|000002e0| 50 72 65 73 73 5c 66 6f | 6f 74 6e 6f 74 65 5c 64 |Press\fo|otnote\d|
|000002f0| 61 67 7b 52 65 76 69 73 | 65 64 20 66 6f 72 20 5c |ag{Revis|ed for \|
|00000300| 54 65 58 38 32 0a 20 20 | 20 20 20 20 62 79 20 42 |TeX82.  |    by B|
|00000310| 6f 62 20 4a 61 6e 74 7a | 65 6e 7d 7d 0a 5c 63 65 |ob Jantz|en}}.\ce|
|00000320| 6e 74 65 72 6c 69 6e 65 | 7b 48 61 72 76 61 72 64 |nterline|{Harvard|
|00000330| 2d 53 6d 69 74 68 73 6f | 6e 69 61 6e 20 43 65 6e |-Smithso|nian Cen|
|00000340| 74 65 72 20 66 6f 72 20 | 41 73 74 72 6f 70 68 79 |ter for |Astrophy|
|00000350| 73 69 63 73 7d 0a 5c 52 | 65 63 65 69 76 65 64 20 |sics}.\R|eceived |
|00000360| 20 20 20 20 20 20 20 20 | 20 20 25 20 53 65 65 20 |        |  % See |
|00000370| 62 6f 62 6d 61 63 72 6f | 2e 74 65 78 0a 0a 5c 76 |bobmacro|.tex..\v|
|00000380| 66 69 6c 6c 20 20 20 20 | 25 20 54 68 69 73 20 65 |fill    |% This e|
|00000390| 78 70 61 6e 64 73 20 74 | 68 65 20 76 65 72 74 69 |xpands t|he verti|
|000003a0| 63 61 6c 20 73 70 61 63 | 65 20 68 65 72 65 20 74 |cal spac|e here t|
|000003b0| 6f 20 70 75 73 68 20 6d | 79 20 74 69 74 6c 65 20 |o push m|y title |
|000003c0| 66 6f 6f 74 6e 6f 74 65 | 0a 20 20 20 20 20 20 20 |footnote|.       |
|000003d0| 20 20 20 25 20 74 6f 20 | 74 68 65 20 62 6f 74 74 |   % to |the bott|
|000003e0| 6f 6d 20 6f 66 20 74 68 | 65 20 70 61 67 65 2e 20 |om of th|e page. |
|000003f0| 20 54 68 65 20 63 6f 6d | 6d 61 6e 64 20 60 5c 66 | The com|mand `\f|
|00000400| 6f 6f 74 6e 6f 74 65 27 | 20 73 71 75 65 65 7a 65 |ootnote'| squeeze|
|00000410| 73 20 69 6e 0a 20 20 20 | 20 20 20 20 20 20 20 25 |s in.   |       %|
|00000420| 20 61 66 74 65 72 20 74 | 68 61 74 20 74 68 6f 75 | after t|hat thou|
|00000430| 67 68 2e 0a 0a 24 5e 31 | 24 4e 6f 74 20 73 75 70 |gh...$^1|$Not sup|
|00000440| 70 6f 72 74 65 64 20 69 | 6e 20 70 61 72 74 20 62 |ported i|n part b|
|00000450| 79 20 61 6e 79 20 66 69 | 6e 64 69 6e 67 20 61 67 |y any fi|nding ag|
|00000460| 65 6e 63 79 20 6b 6e 6f | 77 6e 20 74 6f 0a 6d 61 |ency kno|wn to.ma|
|00000470| 6e 20 6f 72 20 62 65 61 | 73 74 2c 20 65 78 63 65 |n or bea|st, exce|
|00000480| 70 74 20 70 6f 73 73 69 | 62 6c 79 20 48 61 72 76 |pt possi|bly Harv|
|00000490| 61 72 64 20 55 6e 69 76 | 65 72 73 69 74 79 2c 20 |ard Univ|ersity, |
|000004a0| 6f 6e 65 20 6f 66 20 6f | 75 72 20 66 69 6e 65 73 |one of o|ur fines|
|000004b0| 74 0a 6f 6c 64 20 69 6e | 73 74 69 74 75 74 69 6f |t.old in|stitutio|
|000004c0| 6e 73 2e 0a 0a 5c 70 61 | 72 5c 65 6a 65 63 74 20 |ns...\pa|r\eject |
|000004d0| 20 20 25 20 4e 6f 72 6d | 61 6c 6c 79 20 61 6e 20 |  % Norm|ally an |
|000004e0| 65 78 70 6c 69 63 69 74 | 20 70 61 67 65 20 65 6e |explicit| page en|
|000004f0| 64 20 69 73 20 6d 61 72 | 6b 65 64 20 62 79 20 60 |d is mar|ked by `|
|00000500| 5c 70 61 72 5c 76 66 69 | 6c 6c 5c 65 6a 65 63 74 |\par\vfi|ll\eject|
|00000510| 27 0a 20 20 20 20 20 20 | 20 20 20 20 20 20 20 25 |'.      |       %|
|00000520| 20 77 68 69 63 68 20 65 | 6e 64 73 20 74 68 65 20 | which e|nds the |
|00000530| 6c 61 73 74 20 70 61 72 | 61 67 72 61 70 68 2c 20 |last par|agraph, |
|00000540| 66 69 6c 6c 73 20 75 70 | 20 74 68 65 20 72 65 6d |fills up| the rem|
|00000550| 61 69 6e 64 65 72 20 6f | 66 20 74 68 65 0a 20 20 |ainder o|f the.  |
|00000560| 20 20 20 20 20 20 20 20 | 20 20 20 25 20 70 61 67 |        |   % pag|
|00000570| 65 20 77 69 74 68 20 62 | 6c 61 6e 6b 20 73 70 61 |e with b|lank spa|
|00000580| 63 65 20 61 6e 64 20 65 | 6e 64 73 20 74 68 65 20 |ce and e|nds the |
|00000590| 70 61 67 65 2c 20 62 75 | 74 20 69 66 20 6d 6f 72 |page, bu|t if mor|
|000005a0| 65 20 74 68 61 6e 20 6f | 6e 65 0a 20 20 20 20 20 |e than o|ne.     |
|000005b0| 20 20 20 20 20 20 20 20 | 25 20 60 5c 76 66 69 6c |        |% `\vfil|
|000005c0| 6c 27 20 6f 63 63 75 72 | 73 20 6f 6e 20 61 20 70 |l' occur|s on a p|
|000005d0| 61 67 65 2c 20 74 68 65 | 79 20 65 61 63 68 20 66 |age, the|y each f|
|000005e0| 69 6c 6c 20 75 70 20 74 | 68 65 69 72 20 73 68 61 |ill up t|heir sha|
|000005f0| 72 65 20 6f 66 0a 20 20 | 20 20 20 20 20 20 20 20 |re of.  |        |
|00000600| 20 20 20 25 20 74 68 65 | 20 72 65 6d 61 69 6e 69 |   % the| remaini|
|00000610| 6e 67 20 73 70 61 63 65 | 2c 20 73 6f 20 69 6e 20 |ng space|, so in |
|00000620| 74 68 69 73 20 65 78 61 | 6d 70 6c 65 2c 20 6f 75 |this exa|mple, ou|
|00000630| 72 20 74 69 74 6c 65 20 | 66 6f 6f 74 6e 6f 74 65 |r title |footnote|
|00000640| 0a 20 20 20 20 20 20 20 | 20 20 20 20 20 20 25 20 |.       |      % |
|00000650| 77 6f 75 6c 64 20 6e 6f | 74 20 62 65 20 70 75 73 |would no|t be pus|
|00000660| 68 65 64 20 74 6f 20 74 | 68 65 20 62 6f 74 74 6f |hed to t|he botto|
|00000670| 6d 20 6f 66 20 74 68 65 | 20 70 61 67 65 2e 0a 0a |m of the| page...|
|00000680| 5c 41 42 53 54 52 41 43 | 54 20 20 20 20 20 20 20 |\ABSTRAC|T       |
|00000690| 20 20 20 20 20 20 25 20 | 73 65 65 20 62 6f 62 6d |      % |see bobm|
|000006a0| 61 63 72 6f 2e 74 65 78 | 0a 57 65 20 68 65 72 65 |acro.tex|.We here|
|000006b0| 20 67 69 76 65 20 61 20 | 64 65 74 61 69 6c 65 64 | give a |detailed|
|000006c0| 20 65 78 61 6d 70 6c 65 | 20 6f 66 20 61 20 6d 61 | example| of a ma|
|000006d0| 6e 75 73 63 72 69 70 74 | 20 70 72 65 70 61 72 65 |nuscript| prepare|
|000006e0| 64 20 66 6f 72 20 73 75 | 62 6d 69 73 73 69 6f 6e |d for su|bmission|
|000006f0| 0a 74 6f 20 7b 5c 69 74 | 20 54 68 65 20 41 73 74 |.to {\it| The Ast|
|00000700| 72 6f 70 68 79 73 69 63 | 61 6c 20 4a 6f 75 72 6e |rophysic|al Journ|
|00000710| 61 6c 7d 20 75 73 69 6e | 67 20 74 68 65 20 5c 54 |al} usin|g the \T|
|00000720| 65 58 5c 20 6c 61 6e 67 | 75 61 67 65 20 61 6e 64 |eX\ lang|uage and|
|00000730| 20 61 20 73 74 61 6e 64 | 61 72 64 0a 66 69 6c 65 | a stand|ard.file|
|00000740| 20 63 6f 6e 74 61 69 6e | 69 6e 67 20 6d 61 63 72 | contain|ing macr|
|00000750| 6f 20 64 65 66 69 6e 69 | 74 69 6f 6e 73 2e 0a 5c |o defini|tions..\|
|00000760| 62 6c 61 6e 6b 6c 69 6e | 65 20 20 20 20 20 20 20 |blanklin|e       |
|00000770| 20 20 20 20 20 25 20 73 | 65 65 20 62 6f 62 6d 61 |     % s|ee bobma|
|00000780| 63 72 6f 2e 74 65 78 0a | 7b 5c 69 74 20 53 75 62 |cro.tex.|{\it Sub|
|00000790| 6a 65 63 74 20 68 65 61 | 64 69 6e 67 73 3a 7d 20 |ject hea|dings:} |
|000007a0| 73 74 61 72 73 3a 20 48 | 6f 6c 6c 79 77 6f 6f 64 |stars: H|ollywood|
|000007b0| 20 2d 2d 20 64 61 74 61 | 3a 20 69 72 72 65 70 72 | -- data|: irrepr|
|000007c0| 6f 64 75 63 69 62 6c 65 | 0a 0a 5c 70 61 72 5c 76 |oducible|..\par\v|
|000007d0| 66 69 6c 6c 5c 65 6a 65 | 63 74 0a 0a 5c 73 65 63 |fill\eje|ct..\sec|
|000007e0| 74 20 5c 63 65 6e 74 65 | 72 6c 69 6e 65 7b 49 2e |t \cente|rline{I.|
|000007f0| 20 49 4e 54 52 4f 44 55 | 43 54 49 4f 4e 7d 20 5c | INTRODU|CTION} \|
|00000800| 65 6e 64 73 65 63 74 20 | 20 20 25 20 73 65 65 20 |endsect |  % see |
|00000810| 62 6f 62 6d 61 63 72 6f | 2e 74 65 78 0a 0a 54 68 |bobmacro|.tex..Th|
|00000820| 69 73 20 69 73 20 74 68 | 65 20 69 6e 74 72 6f 64 |is is th|e introd|
|00000830| 75 63 74 69 6f 6e 2e 20 | 20 57 65 20 63 61 6e 20 |uction. | We can |
|00000840| 75 73 65 20 69 74 20 74 | 6f 20 74 72 79 20 6f 75 |use it t|o try ou|
|00000850| 74 20 61 20 66 65 77 20 | 62 65 6c 6c 73 20 61 6e |t a few |bells an|
|00000860| 64 0a 77 68 69 73 74 6c | 65 73 2e 20 20 46 69 72 |d.whistl|es.  Fir|
|00000870| 73 74 20 6e 6f 74 69 63 | 65 20 74 68 61 74 20 69 |st notic|e that i|
|00000880| 74 20 64 6f 65 73 6e 27 | 74 20 6d 61 6b 65 20 61 |t doesn'|t make a|
|00000890| 6e 79 20 64 69 66 66 65 | 72 65 6e 63 65 20 77 68 |ny diffe|rence wh|
|000008a0| 65 74 68 65 72 0a 49 20 | 69 6e 64 65 6e 74 20 74 |ether.I |indent t|
|000008b0| 68 65 20 70 61 72 61 67 | 72 61 67 68 2e 20 20 5c |he parag|ragh.  \|
|000008c0| 54 65 58 5c 20 64 6f 65 | 73 20 73 6f 20 61 6e 79 |TeX\ doe|s so any|
|000008d0| 77 61 79 2e 0a 0a 20 20 | 20 20 20 41 20 6e 65 77 |way...  |   A new|
|000008e0| 20 70 61 72 61 67 72 61 | 67 68 20 69 73 20 73 69 | paragra|gh is si|
|000008f0| 67 6e 61 6c 65 64 20 62 | 79 20 74 77 6f 20 72 65 |gnaled b|y two re|
|00000900| 74 75 72 6e 73 20 69 6e | 20 61 20 72 6f 77 2c 20 |turns in| a row, |
|00000910| 6f 72 20 62 79 20 61 6e | 0a 65 78 70 6c 69 63 69 |or by an|.explici|
|00000920| 74 20 6d 61 72 6b 69 6e | 67 20 73 75 63 68 20 61 |t markin|g such a|
|00000930| 73 20 6f 63 63 75 72 73 | 20 68 65 72 65 3a 5c 70 |s occurs| here:\p|
|00000940| 61 72 0a 20 20 20 20 20 | 53 6f 2c 20 74 68 69 73 |ar.     |So, this|
|00000950| 20 77 69 6c 6c 20 62 65 | 20 74 68 65 20 74 68 69 | will be| the thi|
|00000960| 72 64 20 70 61 72 61 67 | 72 61 67 68 2e 20 20 5c |rd parag|ragh.  \|
|00000970| 69 74 20 49 20 68 61 76 | 65 20 6a 75 73 74 20 63 |it I hav|e just c|
|00000980| 68 61 6e 67 65 64 0a 74 | 6f 20 69 74 61 6c 69 63 |hanged.t|o italic|
|00000990| 20 74 79 70 65 2e 20 20 | 5c 72 6d 20 4e 6f 77 20 | type.  |\rm Now |
|000009a0| 62 61 63 6b 20 74 6f 20 | 72 6f 6d 61 6e 2e 20 20 |back to |roman.  |
|000009b0| 5c 73 6c 20 4e 6f 77 20 | 74 6f 20 73 6c 61 6e 74 |\sl Now |to slant|
|000009c0| 65 64 20 72 6f 6d 61 6e | 2e 0a 5c 62 66 20 4e 6f |ed roman|..\bf No|
|000009d0| 77 20 74 6f 20 62 6f 6c | 64 66 61 63 65 2e 20 20 |w to bol|dface.  |
|000009e0| 5c 72 6d 20 49 66 20 49 | 20 77 61 6e 74 20 74 6f |\rm If I| want to|
|000009f0| 20 63 68 61 6e 67 65 20 | 6f 6e 6c 79 20 7b 5c 69 | change |only {\i|
|00000a00| 74 20 74 65 6d 70 6f 72 | 69 6c 79 7d 2c 0a 74 68 |t tempor|ily},.th|
|00000a10| 61 74 20 63 61 6e 20 62 | 65 20 64 6f 6e 65 20 74 |at can b|e done t|
|00000a20| 6f 6f 2e 20 20 55 6e 64 | 65 72 6c 69 6e 69 6e 67 |oo.  Und|erlining|
|00000a30| 2c 20 69 66 20 64 65 73 | 69 72 65 64 20 5c 74 65 |, if des|ired \te|
|00000a40| 78 74 75 6e 64 65 72 6c | 69 6e 65 7b 63 61 6e 20 |xtunderl|ine{can |
|00000a50| 62 65 20 64 6f 6e 65 0a | 6c 69 6b 65 20 74 68 69 |be done.|like thi|
|00000a60| 73 7d 2c 20 62 75 74 20 | 74 68 69 73 20 64 6f 65 |s}, but |this doe|
|00000a70| 73 6e 27 74 20 61 6c 77 | 61 79 73 20 77 6f 72 6b |sn't alw|ays work|
|00000a80| 2e 20 4c 61 74 65 72 20 | 6f 6e 20 79 6f 75 20 77 |. Later |on you w|
|00000a90| 69 6c 6c 20 75 6e 64 65 | 72 73 74 61 6e 64 0a 77 |ill unde|rstand.w|
|00000aa0| 68 79 2e 20 20 46 6f 72 | 20 74 68 6f 73 65 20 6f |hy.  For| those o|
|00000ab0| 66 20 79 6f 75 20 77 68 | 6f 20 61 63 74 75 61 6c |f you wh|o actual|
|00000ac0| 6c 79 20 70 72 65 66 65 | 72 20 74 79 70 65 77 72 |ly prefe|r typewr|
|00000ad0| 69 74 65 72 73 2c 20 7b | 5c 74 74 20 74 68 65 72 |iters, {|\tt ther|
|00000ae0| 65 20 69 73 20 65 76 65 | 6e 0a 61 20 77 61 79 20 |e is eve|n.a way |
|00000af0| 74 6f 20 64 6f 20 74 68 | 61 74 7d 2e 0a 0a 5c 73 |to do th|at}...\s|
|00000b00| 75 62 73 65 63 74 20 5c | 63 65 6e 74 65 72 6c 69 |ubsect \|centerli|
|00000b10| 6e 65 7b 61 2e 5c 71 71 | 75 61 64 20 53 75 62 73 |ne{a.\qq|uad Subs|
|00000b20| 65 63 74 69 6f 6e 20 48 | 65 61 64 69 6e 67 7d 20 |ection H|eading} |
|00000b30| 5c 65 6e 64 73 75 62 73 | 65 63 74 20 25 20 73 65 |\endsubs|ect % se|
|00000b40| 65 20 62 6f 62 6d 61 63 | 72 6f 2e 74 65 78 0a 0a |e bobmac|ro.tex..|
|00000b50| 20 20 20 20 20 20 54 68 | 69 73 20 69 73 20 61 20 |      Th|is is a |
|00000b60| 73 75 62 73 65 63 74 69 | 6f 6e 2e 20 49 74 20 68 |subsecti|on. It h|
|00000b70| 61 73 20 6e 6f 20 72 65 | 61 6c 20 70 75 72 70 6f |as no re|al purpo|
|00000b80| 73 65 2c 20 62 75 74 20 | 49 20 73 75 70 70 6f 73 |se, but |I suppos|
|00000b90| 65 0a 49 20 63 6f 75 6c | 64 20 75 73 65 20 69 74 |e.I coul|d use it|
|00000ba0| 20 74 6f 20 65 78 70 6c | 61 69 6e 20 73 6f 6d 65 | to expl|ain some|
|00000bb0| 20 74 68 69 6e 67 73 2e | 20 4d 61 6e 79 20 66 65 | things.| Many fe|
|00000bc0| 61 74 75 72 65 73 20 6f | 66 20 5c 54 65 58 5c 20 |atures o|f \TeX\ |
|00000bd0| 63 61 6e 20 6f 6e 6c 79 | 0a 62 65 20 75 73 65 64 |can only|.be used|
|00000be0| 20 69 6e 20 60 60 6d 61 | 74 68 20 6d 6f 64 65 22 | in ``ma|th mode"|
|00000bf0| 2c 20 69 2e 65 2e 20 74 | 79 70 65 64 20 62 65 74 |, i.e. t|yped bet|
|00000c00| 77 65 65 6e 20 64 6f 6c | 6c 61 72 20 73 69 67 6e |ween dol|lar sign|
|00000c10| 73 2e 20 20 54 68 69 73 | 20 69 6e 63 6c 75 64 65 |s.  This| include|
|00000c20| 73 0a 63 6f 6d 65 20 63 | 6f 6d 6d 6f 6e 20 74 68 |s.come c|ommon th|
|00000c30| 69 6e 67 73 20 6c 69 6b | 65 20 73 75 70 65 72 73 |ings lik|e supers|
|00000c40| 63 72 69 70 74 73 3a 77 | 6f 72 64 24 5e 7b 73 75 |cripts:w|ord$^{su|
|00000c50| 70 65 72 77 6f 72 64 7d | 24 3b 0a 73 75 62 73 63 |perword}|$;.subsc|
|00000c60| 72 69 70 74 73 3a 20 24 | 77 6f 72 64 5f 7b 73 75 |ripts: $|word_{su|
|00000c70| 62 77 6f 72 64 7d 24 20 | 61 6c 6c 20 62 65 74 77 |bword}$ |all betw|
|00000c80| 65 65 6e 20 64 6f 6c 6c | 61 72 20 73 69 67 6e 73 |een doll|ar signs|
|00000c90| 2c 20 61 73 20 79 6f 75 | 20 73 65 65 2e 0a 42 75 |, as you| see..Bu|
|00000ca0| 74 20 64 6f 20 6e 6f 74 | 69 63 65 20 74 68 61 74 |t do not|ice that|
|00000cb0| 20 69 6e 20 6d 61 74 68 | 20 6d 6f 64 65 2c 20 5c | in math| mode, \|
|00000cc0| 54 65 58 5c 20 73 77 69 | 74 63 68 65 73 20 69 6e |TeX\ swi|tches in|
|00000cd0| 74 6f 20 69 74 61 6c 69 | 63 73 2e 20 20 49 66 20 |to itali|cs.  If |
|00000ce0| 79 6f 75 0a 64 6f 6e 27 | 74 20 77 61 6e 74 20 74 |you.don'|t want t|
|00000cf0| 68 69 73 2c 20 79 6f 75 | 20 68 61 76 65 20 74 6f |his, you| have to|
|00000d00| 20 74 79 70 65 20 77 6f | 72 64 24 5e 7b 5c 68 62 | type wo|rd$^{\hb|
|00000d10| 6f 78 7b 73 75 70 65 72 | 77 6f 72 64 7d 7d 24 2e |ox{super|word}}$.|
|00000d20| 0a 0a 5c 64 6f 75 62 6c | 65 73 70 61 63 65 0a 4d |..\doubl|espace.M|
|00000d30| 79 20 6e 65 78 74 20 70 | 61 72 61 67 72 61 67 68 |y next p|aragragh|
|00000d40| 20 6f 75 67 68 74 20 74 | 6f 20 63 6f 6d 65 20 6f | ought t|o come o|
|00000d50| 75 74 20 69 6e 20 64 6f | 75 62 6c 65 20 73 70 61 |ut in do|uble spa|
|00000d60| 63 65 2e 20 20 54 68 69 | 73 20 75 73 65 73 20 61 |ce.  Thi|s uses a|
|00000d70| 0a 63 6f 6d 6d 61 6e 64 | 20 74 68 61 74 20 69 73 |.command| that is|
|00000d80| 20 6e 6f 74 20 75 6e 69 | 76 65 72 73 61 6c 2c 20 | not uni|versal, |
|00000d90| 62 75 74 20 72 61 74 68 | 65 72 20 69 73 20 64 65 |but rath|er is de|
|00000da0| 66 69 6e 65 64 20 69 6e | 20 6d 79 20 6d 61 63 72 |fined in| my macr|
|00000db0| 6f 20 66 69 6c 65 0a 60 | 62 6f 62 6d 61 63 72 6f |o file.`|bobmacro|
|00000dc0| 2e 74 65 78 27 2c 20 74 | 68 65 20 6f 6e 65 20 69 |.tex', t|he one i|
|00000dd0| 6e 63 6c 75 64 65 64 20 | 62 79 20 74 68 65 20 63 |ncluded |by the c|
|00000de0| 6f 6d 6d 61 6e 64 20 20 | 60 60 24 5c 62 61 63 6b |ommand  |``$\back|
|00000df0| 73 6c 61 73 68 24 69 6e | 70 75 74 20 0a 62 6f 62 |slash$in|put .bob|
|00000e00| 6d 61 63 72 6f 22 20 61 | 74 20 74 68 65 20 62 65 |macro" a|t the be|
|00000e10| 67 69 6e 6e 69 6e 67 20 | 6f 66 20 74 68 69 73 20 |ginning |of this |
|00000e20| 69 6e 70 75 74 20 66 69 | 6c 65 2e 20 20 49 6e 63 |input fi|le.  Inc|
|00000e30| 69 64 65 6e 74 61 6c 6c | 79 2c 20 69 66 20 79 6f |identall|y, if yo|
|00000e40| 75 20 68 61 76 65 20 0a | 74 79 70 65 64 20 73 6f |u have .|typed so|
|00000e50| 6d 65 74 68 69 6e 67 20 | 69 6e 20 6c 6f 77 65 72 |mething |in lower|
|00000e60| 20 63 61 73 65 2c 20 6f | 72 20 6d 69 78 65 64 20 | case, o|r mixed |
|00000e70| 6c 6f 77 65 72 20 61 6e | 64 20 75 70 70 65 72 2c |lower an|d upper,|
|00000e80| 20 5c 75 70 70 65 72 63 | 61 73 65 7b 61 6e 64 20 | \upperc|ase{and |
|00000e90| 79 6f 75 0a 72 65 61 6c | 6c 79 20 69 6e 74 65 6e |you.real|ly inten|
|00000ea0| 64 65 64 20 69 74 20 74 | 6f 20 62 65 20 69 6e 20 |ded it t|o be in |
|00000eb0| 61 6c 6c 20 63 61 70 73 | 7d 2c 20 74 68 65 6e 20 |all caps|}, then |
|00000ec0| 79 6f 75 20 63 61 6e 20 | 63 6f 72 72 65 63 74 20 |you can |correct |
|00000ed0| 69 74 0a 65 61 73 69 6c | 79 20 61 73 20 73 68 6f |it.easil|y as sho|
|00000ee0| 77 6e 2e 20 20 53 69 6d | 69 6c 61 72 6c 79 20 5c |wn.  Sim|ilarly \|
|00000ef0| 6c 6f 77 65 72 63 61 73 | 65 7b 46 4f 52 20 53 4f |lowercas|e{FOR SO|
|00000f00| 4d 45 54 48 49 4e 47 20 | 54 59 50 45 44 20 49 4e |METHING |TYPED IN|
|00000f10| 20 41 4c 4c 20 43 41 50 | 53 7d 0a 77 68 69 63 68 | ALL CAP|S}.which|
|00000f20| 20 73 68 6f 75 6c 64 20 | 68 61 76 65 20 62 65 65 | should |have bee|
|00000f30| 6e 20 69 6e 20 6c 6f 77 | 65 72 63 61 73 65 2e 0a |n in low|ercase..|
|00000f40| 0a 5c 73 69 6e 67 6c 65 | 73 70 61 63 65 0a 5c 62 |.\single|space.\b|
|00000f50| 6c 61 6e 6b 6c 69 6e 65 | 0a 4e 6f 74 69 63 65 20 |lankline|.Notice |
|00000f60| 74 68 61 74 20 74 68 65 | 20 63 68 61 6e 67 65 20 |that the| change |
|00000f70| 74 6f 20 73 69 6e 67 6c | 65 73 70 61 63 65 20 63 |to singl|espace c|
|00000f80| 6f 6d 65 73 20 62 65 74 | 77 65 65 6e 20 74 77 6f |omes bet|ween two|
|00000f90| 20 70 61 72 61 67 72 61 | 70 68 73 2c 20 61 6e 64 | paragra|phs, and|
|00000fa0| 0a 74 68 61 74 20 69 74 | 20 77 6f 75 6c 64 20 68 |.that it| would h|
|00000fb0| 61 76 65 20 70 72 6f 64 | 75 63 65 64 20 6f 6e 6c |ave prod|uced onl|
|00000fc0| 79 20 61 20 73 69 6e 67 | 6c 65 20 73 70 61 63 65 |y a sing|le space|
|00000fd0| 20 62 65 74 77 65 65 6e | 20 74 68 65 6d 2e 20 20 | between| them.  |
|00000fe0| 54 6f 20 67 65 74 0a 74 | 68 65 20 64 6f 75 62 6c |To get.t|he doubl|
|00000ff0| 65 20 73 70 61 63 65 2c | 20 49 20 68 61 76 65 20 |e space,| I have |
|00001000| 74 6f 20 68 61 76 65 20 | 74 68 65 20 65 78 74 72 |to have |the extr|
|00001010| 61 20 60 60 62 6c 61 6e | 6b 6c 69 6e 65 22 2e 0a |a ``blan|kline"..|
|00001020| 54 68 69 73 20 69 73 20 | 74 68 65 20 66 69 6e 61 |This is |the fina|
|00001030| 6c 20 70 61 72 61 67 72 | 61 70 68 20 69 6e 20 74 |l paragr|aph in t|
|00001040| 68 65 20 73 75 62 73 65 | 63 74 69 6f 6e 2c 20 69 |he subse|ction, i|
|00001050| 6e 64 65 65 64 20 69 6e | 20 74 68 65 20 77 68 6f |ndeed in| the who|
|00001060| 6c 65 0a 69 6e 74 72 6f | 64 75 63 74 69 6f 6e 2e |le.intro|duction.|
|00001070| 20 20 41 73 20 62 65 66 | 69 74 73 20 61 6e 20 69 |  As bef|its an i|
|00001080| 6e 74 72 6f 64 75 63 74 | 69 6f 6e 2c 20 49 20 68 |ntroduct|ion, I h|
|00001090| 61 76 65 20 6e 6f 20 6d | 61 74 68 65 6d 61 74 69 |ave no m|athemati|
|000010a0| 63 73 20 69 6e 0a 74 68 | 65 20 69 6e 74 72 6f 64 |cs in.th|e introd|
|000010b0| 75 63 74 69 6f 6e 2c 20 | 61 6c 74 68 6f 75 67 68 |uction, |although|
|000010c0| 20 49 20 6d 69 67 68 74 | 20 68 61 76 65 20 28 69 | I might| have (i|
|000010d0| 6e 20 6c 69 6e 65 20 69 | 6e 20 74 68 65 20 74 65 |n line i|n the te|
|000010e0| 78 74 29 20 73 6f 6d 65 | 0a 24 5c 61 6c 70 68 61 |xt) some|.$\alpha|
|000010f0| 24 27 73 2c 20 24 5c 62 | 65 74 61 24 27 73 20 61 |$'s, $\b|eta$'s a|
|00001100| 6e 64 20 24 5c 67 61 6d | 6d 61 24 27 73 2c 20 0a |nd $\gam|ma$'s, .|
|00001110| 61 6e 64 20 61 20 24 5c | 6c 65 71 24 20 28 6e 6f |and a $\|leq$ (no|
|00001120| 74 65 20 75 73 65 20 6f | 66 20 6d 61 74 68 20 6d |te use o|f math m|
|00001130| 6f 64 65 29 3b 20 61 6e | 64 20 70 65 72 68 61 70 |ode); an|d perhap|
|00001140| 73 20 61 20 5c 24 20 5c | 20 6f 72 20 74 77 6f 20 |s a \$ \| or two |
|00001150| 28 5c 24 20 5c 24 29 2e | 0a 41 6c 73 6f 20 6e 6f |(\$ \$).|.Also no|
|00001160| 74 65 20 74 68 61 74 20 | 69 6e 20 5c 53 20 49 49 |te that |in \S II|
|00001170| 2e 20 62 65 6c 6f 77 20 | 77 65 20 77 69 6c 6c 20 |. below |we will |
|00001180| 68 61 76 65 20 6d 6f 72 | 65 20 6d 61 74 68 2e 0a |have mor|e math..|
|00001190| 44 6f 6e 27 74 20 65 76 | 65 72 20 64 6f 20 74 68 |Don't ev|er do th|
|000011a0| 69 73 2c 20 62 75 74 20 | 61 63 74 75 61 6c 6c 79 |is, but |actually|
|000011b0| 20 49 20 63 61 6e 20 67 | 65 74 20 61 77 61 79 20 | I can g|et away |
|000011c0| 77 69 74 68 20 5c 61 6c | 70 68 61 5c 20 20 61 73 |with \al|pha\  as|
|000011d0| 20 77 65 6c 6c 20 61 73 | 0a 24 5c 61 6c 70 68 61 | well as|.$\alpha|
|000011e0| 24 2c 20 62 75 74 20 6f | 6e 6c 79 20 62 65 63 61 |$, but o|nly beca|
|000011f0| 75 73 65 20 49 20 68 61 | 76 65 20 61 20 66 61 6e |use I ha|ve a fan|
|00001200| 63 79 20 64 65 66 69 6e | 69 74 69 6f 6e 20 69 6e |cy defin|ition in|
|00001210| 20 6d 79 20 6d 61 63 72 | 6f 20 66 69 6c 65 2e 0a | my macr|o file..|
|00001220| 0a 5c 73 65 63 74 20 5c | 63 65 6e 74 65 72 6c 69 |.\sect \|centerli|
|00001230| 6e 65 7b 49 49 2e 20 4d | 41 54 48 45 4d 41 54 49 |ne{II. M|ATHEMATI|
|00001240| 43 53 7d 20 5c 65 6e 64 | 73 65 63 74 0a 0a 20 20 |CS} \end|sect..  |
|00001250| 20 20 20 57 65 6c 6c 2c | 20 6e 6f 77 20 77 65 20 |   Well,| now we |
|00001260| 63 6f 6d 65 20 74 6f 20 | 74 68 65 20 72 65 61 6c |come to |the real|
|00001270| 6c 79 20 66 75 6e 20 70 | 61 72 74 2c 20 6e 61 6d |ly fun p|art, nam|
|00001280| 65 6c 79 20 74 68 65 20 | 73 65 74 74 69 6e 67 20 |ely the |setting |
|00001290| 6f 66 0a 6d 61 74 68 65 | 6d 61 74 69 63 73 2e 20 |of.mathe|matics. |
|000012a0| 20 49 74 20 69 73 20 69 | 6e 63 72 65 64 69 62 6c | It is i|ncredibl|
|000012b0| 79 20 65 61 73 79 2e 20 | 20 4a 75 73 74 20 72 65 |y easy. | Just re|
|000012c0| 6d 65 6d 62 65 72 20 74 | 68 61 74 20 79 6f 75 20 |member t|hat you |
|000012d0| 61 72 65 20 65 69 74 68 | 65 72 0a 69 6e 20 68 6f |are eith|er.in ho|
|000012e0| 72 69 7a 6f 6e 74 61 6c | 20 6d 6f 64 65 20 28 66 |rizontal| mode (f|
|000012f0| 6f 72 20 74 79 70 69 6e | 67 20 74 65 78 74 20 6c |or typin|g text l|
|00001300| 69 6b 65 20 72 69 67 68 | 74 20 6e 6f 77 29 2c 20 |ike righ|t now), |
|00001310| 6f 72 20 28 62 65 74 77 | 65 65 6e 20 5c 24 20 27 |or (betw|een \$ '|
|00001320| 73 29 0a 69 6e 20 6d 61 | 74 68 20 6d 6f 64 65 20 |s).in ma|th mode |
|00001330| 28 66 6f 72 20 74 79 70 | 69 6e 67 20 69 6e 2d 6c |(for typ|ing in-l|
|00001340| 69 6e 65 20 66 6f 72 6d | 75 6c 61 65 0a 6c 69 6b |ine form|ulae.lik|
|00001350| 65 20 24 46 3d 28 5c 69 | 6e 74 20 66 28 78 29 20 |e $F=(\i|nt f(x) |
|00001360| 64 78 29 5e 7b 5c 78 69 | 7d 24 2c 20 6f 72 20 62 |dx)^{\xi|}$, or b|
|00001370| 65 74 77 65 65 6e 20 5c | 24 20 5c 24 20 27 73 29 |etween \|$ \$ 's)|
|00001380| 20 69 6e 20 6d 61 74 68 | 0a 64 69 73 70 6c 61 79 | in math|.display|
|00001390| 20 6d 6f 64 65 2c 20 77 | 68 69 63 68 20 70 72 6f | mode, w|hich pro|
|000013a0| 64 75 63 65 73 20 73 65 | 74 20 6f 66 66 20 65 71 |duces se|t off eq|
|000013b0| 75 61 74 69 6f 6e 73 20 | 6c 69 6b 65 20 24 24 20 |uations |like $$ |
|000013c0| 5c 50 68 69 20 3d 20 7b | 61 2b 62 20 5c 6f 76 65 |\Phi = {|a+b \ove|
|000013d0| 72 0a 63 2b 64 7d 2e 24 | 24 20 20 4e 6f 74 69 63 |r.c+d}.$|$  Notic|
|000013e0| 65 20 74 68 61 74 20 49 | 20 64 6f 6e 27 74 20 61 |e that I| don't a|
|000013f0| 63 74 75 61 6c 6c 79 20 | 73 65 74 20 6f 66 66 20 |ctually |set off |
|00001400| 74 68 65 20 65 71 75 61 | 74 69 6f 6e 20 69 6e 20 |the equa|tion in |
|00001410| 74 68 65 20 69 6e 70 75 | 74 0a 65 71 75 61 74 69 |the inpu|t.equati|
|00001420| 6f 6e 20 69 6e 20 74 68 | 65 20 69 6e 70 75 74 20 |on in th|e input |
|00001430| 66 69 6c 65 2c 20 61 6c | 74 68 6f 75 67 68 20 74 |file, al|though t|
|00001440| 68 65 72 65 20 69 73 20 | 6e 6f 74 68 69 6e 67 20 |here is |nothing |
|00001450| 77 72 6f 6e 67 20 77 69 | 74 68 20 64 6f 69 6e 67 |wrong wi|th doing|
|00001460| 20 73 6f 3a 0a 24 24 7b | 6e 75 6d 65 72 61 74 6f | so:.$${|numerato|
|00001470| 72 20 5c 6f 76 65 72 20 | 64 65 6e 6f 6d 69 6e 61 |r \over |denomina|
|00001480| 74 6f 72 7d 3d 65 61 73 | 79 24 24 0a 42 65 20 63 |tor}=eas|y$$.Be c|
|00001490| 61 72 65 66 75 6c 20 74 | 6f 20 75 73 65 20 61 20 |areful t|o use a |
|000014a0| 62 61 63 6b 73 6c 61 73 | 68 20 62 65 66 6f 72 65 |backslas|h before|
|000014b0| 20 73 69 6e 2c 20 63 6f | 73 2c 20 65 78 70 20 61 | sin, co|s, exp a|
|000014c0| 6e 64 20 73 69 6d 69 6c | 61 72 3a 0a 24 24 5c 73 |nd simil|ar:.$$\s|
|000014d0| 69 6e 20 28 78 29 20 5c | 71 71 75 61 64 20 61 6e |in (x) \|qquad an|
|000014e0| 64 20 5c 20 6e 6f 74 20 | 5c 71 71 75 61 64 20 73 |d \ not |\qquad s|
|000014f0| 69 6e 20 28 78 29 24 24 | 0a 28 77 68 65 72 65 20 |in (x)$$|.(where |
|00001500| 24 5c 62 61 63 6b 73 6c | 61 73 68 24 71 71 75 61 |$\backsl|ash$qqua|
|00001510| 64 20 69 73 2c 20 61 73 | 20 79 6f 75 20 63 61 6e |d is, as| you can|
|00001520| 20 73 65 65 2c 20 61 20 | 62 69 67 67 69 73 68 20 | see, a |biggish |
|00001530| 73 70 61 63 65 3b 20 61 | 6e 64 20 0a 62 61 63 6b |space; a|nd .back|
|00001540| 73 6c 61 73 68 2d 73 70 | 61 63 65 20 69 73 20 61 |slash-sp|ace is a|
|00001550| 20 73 6d 61 6c 6c 69 73 | 68 20 73 70 61 63 65 20 | smallis|h space |
|00001560| 2d 2d 20 69 6e 20 6d 61 | 74 68 20 6d 6f 64 65 20 |-- in ma|th mode |
|00001570| 61 6c 6c 20 70 6c 61 69 | 6e 20 73 70 61 63 65 73 |all plai|n spaces|
|00001580| 20 61 72 65 20 0a 69 67 | 6e 6f 72 65 64 21 29 2e | are .ig|nored!).|
|00001590| 0a 0a 45 71 75 61 74 69 | 6f 6e 20 6e 75 6d 62 65 |..Equati|on numbe|
|000015a0| 72 73 20 61 72 65 20 65 | 71 75 61 6c 6c 79 20 65 |rs are e|qually e|
|000015b0| 61 73 79 3a 20 6a 75 73 | 74 20 68 61 76 65 20 61 |asy: jus|t have a|
|000015c0| 6e 20 65 71 6e 6f 20 63 | 6f 6d 6d 61 6e 64 0a 62 |n eqno c|ommand.b|
|000015d0| 65 66 6f 72 65 20 74 68 | 65 20 63 6c 6f 73 69 6e |efore th|e closin|
|000015e0| 67 20 5c 24 20 5c 24 20 | 27 73 2c 0a 24 24 45 3d |g \$ \$ |'s,.$$E=|
|000015f0| 6d 63 5e 7b 32 7d 20 5c | 65 71 6e 6f 28 31 34 62 |mc^{2} \|eqno(14b|
|00001600| 29 24 24 2e 20 20 20 20 | 20 20 25 20 4e 6f 74 69 |)$$.    |  % Noti|
|00001610| 63 65 20 77 68 65 72 65 | 20 74 68 65 20 70 65 72 |ce where| the per|
|00001620| 69 6f 64 20 65 6e 64 73 | 20 75 70 2e 0a 20 20 20 |iod ends| up..   |
|00001630| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001640| 20 20 20 20 20 20 20 20 | 20 20 20 25 20 49 6e 73 |        |   % Ins|
|00001650| 74 65 61 64 20 60 5c 20 | 2e 27 20 73 68 6f 75 6c |tead `\ |.' shoul|
|00001660| 64 20 68 61 76 65 20 70 | 72 65 63 65 64 65 64 20 |d have p|receded |
|00001670| 60 5c 65 71 6e 6f 27 0a | 0a 4e 6f 77 20 66 6f 72 |`\eqno'.|.Now for|
|00001680| 20 73 6f 6d 65 20 66 61 | 6e 63 69 65 72 20 65 78 | some fa|ncier ex|
|00001690| 61 6d 70 6c 65 73 3a 0a | 0a 57 65 20 6d 69 67 68 |amples:.|.We migh|
|000016a0| 74 20 6e 65 65 64 20 73 | 75 6d 73 2c 0a 24 24 5c |t need s|ums,.$$\|
|000016b0| 73 75 6d 5f 7b 6e 3d 31 | 7d 5e 7b 6e 3d 5c 69 6e |sum_{n=1|}^{n=\in|
|000016c0| 66 74 79 7d 28 61 2b 62 | 29 21 20 3d 20 7b 5c 70 |fty}(a+b|)! = {\p|
|000016d0| 61 72 74 69 61 6c 20 66 | 20 5c 6f 76 65 72 20 5c |artial f| \over \|
|000016e0| 70 61 72 74 69 61 6c 20 | 78 7d 20 5c 65 71 6e 6f |partial |x} \eqno|
|000016f0| 28 31 35 29 24 24 0a 6f | 72 20 69 6e 74 65 67 72 |(15)$$.o|r integr|
|00001700| 61 6c 73 2c 0a 24 24 5c | 69 6e 74 5f 7b 30 7d 5e |als,.$$\|int_{0}^|
|00001710| 7b 31 7d 78 5e 7b 5c 61 | 6c 70 68 61 20 2d 31 7d |{1}x^{\a|lpha -1}|
|00001720| 28 31 2d 78 29 5e 7b 5c | 62 65 74 61 20 2d 20 31 |(1-x)^{\|beta - 1|
|00001730| 7d 20 64 78 24 24 0a 6f | 72 20 6d 61 74 72 69 63 |} dx$$.o|r matric|
|00001740| 65 73 2c 0a 24 24 20 20 | 41 3d 20 5c 70 6d 61 74 |es,.$$  |A= \pmat|
|00001750| 72 69 78 7b 31 26 30 26 | 30 5c 63 72 20 30 26 78 |rix{1&0&|0\cr 0&x|
|00001760| 2b 31 26 79 5c 63 72 20 | 30 26 30 26 31 5c 63 72 |+1&y\cr |0&0&1\cr|
|00001770| 7d 20 24 24 0a 6f 72 20 | 61 62 73 6f 6c 75 74 65 |} $$.or |absolute|
|00001780| 20 76 61 6c 75 65 20 62 | 61 72 73 20 28 6b 6e 6f | value b|ars (kno|
|00001790| 77 6e 20 61 73 20 60 60 | 76 65 72 74 69 63 61 6c |wn as ``|vertical|
|000017a0| 73 22 29 2c 0a 24 24 20 | 7c 78 7c 20 3d 20 5c 6c |s"),.$$ ||x| = \l|
|000017b0| 65 66 74 7c 7b 65 5e 7b | 2d 78 5e 32 7d 7d 5c 6f |eft|{e^{|-x^2}}\o|
|000017c0| 76 65 72 20 5c 73 69 6e | 20 28 78 29 20 2b 20 0a |ver \sin| (x) + .|
|000017d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000017e0| 30 2e 35 20 5c 63 6f 73 | 20 28 78 29 5c 72 69 67 |0.5 \cos| (x)\rig|
|000017f0| 68 74 7c 20 5c 71 75 61 | 64 2e 24 24 0a 4e 6f 74 |ht| \qua|d.$$.Not|
|00001800| 69 63 65 20 68 6f 77 20 | 49 20 63 61 6e 20 6a 75 |ice how |I can ju|
|00001810| 73 74 20 63 6f 6e 74 69 | 6e 75 65 20 74 79 70 69 |st conti|nue typi|
|00001820| 6e 67 20 74 68 65 20 66 | 6f 72 6d 75 6c 61 20 6f |ng the f|ormula o|
|00001830| 6e 20 61 73 20 6d 61 6e | 79 20 6c 69 6e 65 73 0a |n as man|y lines.|
|00001840| 61 73 20 69 74 20 68 61 | 70 70 65 6e 73 20 74 6f |as it ha|ppens to|
|00001850| 20 74 61 6b 65 2e 20 20 | 53 70 61 63 65 73 20 77 | take.  |Spaces w|
|00001860| 69 74 68 69 6e 20 5c 24 | 20 5c 24 20 27 73 20 6e |ithin \$| \$ 's n|
|00001870| 65 76 65 72 20 20 6d 61 | 74 74 65 72 2c 20 73 6f |ever  ma|tter, so|
|00001880| 20 49 20 63 61 6e 0a 69 | 6e 64 65 6e 74 20 73 75 | I can.i|ndent su|
|00001890| 62 73 65 71 75 65 6e 74 | 20 6c 69 6e 65 73 20 66 |bsequent| lines f|
|000018a0| 6f 72 20 72 65 61 64 69 | 62 69 6c 69 74 79 2e 0a |or readi|bility..|
|000018b0| 0a 4f 74 68 65 72 20 6c | 61 72 67 65 20 60 60 65 |.Other l|arge ``e|
|000018c0| 6e 63 6c 6f 73 65 72 73 | 22 20 61 72 65 20 73 69 |nclosers|" are si|
|000018d0| 6d 69 6c 61 72 3a 0a 24 | 24 20 5c 6c 65 66 74 28 |milar:.$|$ \left(|
|000018e0| 20 7b 61 2b 62 5c 6f 76 | 65 72 20 63 2b 64 7d 20 | {a+b\ov|er c+d} |
|000018f0| 5c 72 69 67 68 74 29 20 | 5c 71 71 75 61 64 20 5c |\right) |\qquad \|
|00001900| 6c 65 66 74 5b 20 7b 65 | 2b 66 20 5c 6f 76 65 72 |left[ {e|+f \over|
|00001910| 20 67 2b 68 7d 5c 72 69 | 67 68 74 5d 0a 20 20 20 | g+h}\ri|ght].   |
|00001920| 20 20 5c 71 71 75 61 64 | 20 5c 6c 65 66 74 5c 7b |  \qquad| \left\{|
|00001930| 20 7b 69 2b 6a 20 5c 6f | 76 65 72 20 6b 2b 6c 7d | {i+j \o|ver k+l}|
|00001940| 20 5c 72 69 67 68 74 5c | 7d 20 24 24 0a 28 42 72 | \right\|} $$.(Br|
|00001950| 61 63 65 73 20 61 72 65 | 20 73 70 65 63 69 61 6c |aces are| special|
|00001960| 20 73 69 6e 63 65 20 79 | 6f 75 20 61 72 65 6e 27 | since y|ou aren'|
|00001970| 74 20 61 6c 6c 6f 77 65 | 64 20 74 6f 20 74 79 70 |t allowe|d to typ|
|00001980| 65 20 74 68 65 20 61 63 | 74 75 61 6c 0a 63 68 61 |e the ac|tual.cha|
|00001990| 72 61 63 74 65 72 20 24 | 5c 7b 24 20 65 78 63 65 |racter $|\{$ exce|
|000019a0| 70 74 20 61 73 20 61 20 | 67 72 6f 75 70 20 64 65 |pt as a |group de|
|000019b0| 6c 69 6d 69 74 65 72 20 | 69 6e 20 74 68 65 20 69 |limiter |in the i|
|000019c0| 6e 70 75 74 20 66 69 6c | 65 2e 29 0a 0a 20 20 20 |nput fil|e.)..   |
|000019d0| 20 41 6c 69 67 6e 6d 65 | 6e 74 20 63 61 6e 20 62 | Alignme|nt can b|
|000019e0| 65 20 63 6f 6d 70 6c 69 | 63 61 74 65 64 2c 20 62 |e compli|cated, b|
|000019f0| 75 74 20 6d 6f 73 74 20 | 73 69 74 75 61 74 69 6f |ut most |situatio|
|00001a00| 6e 73 20 63 61 6e 20 62 | 65 20 68 61 6e 64 6c 65 |ns can b|e handle|
|00001a10| 64 0a 75 73 69 6e 67 20 | 74 68 65 20 65 71 61 6c |d.using |the eqal|
|00001a20| 69 67 6e 20 63 6f 6d 6d | 61 6e 64 2c 0a 24 24 5c |ign comm|and,.$$\|
|00001a30| 65 71 61 6c 69 67 6e 7b | 0a 20 20 20 20 20 20 61 |eqalign{|.      a|
|00001a40| 5f 31 2b 62 5f 31 77 2b | 63 5f 31 77 5e 32 20 26 |_1+b_1w+|c_1w^2 &|
|00001a50| 3d 20 20 5c 61 6c 70 68 | 61 20 2b 20 5c 62 65 74 |=  \alph|a + \bet|
|00001a60| 61 20 5c 63 72 0a 20 20 | 20 20 20 20 62 5f 32 78 |a \cr.  |    b_2x|
|00001a70| 2b 63 5f 32 78 5e 32 20 | 20 20 26 3d 20 30 2e 20 |+c_2x^2 |  &= 0. |
|00001a80| 20 5c 63 72 20 7d 20 5c | 65 71 6e 6f 28 33 30 29 | \cr } \|eqno(30)|
|00001a90| 24 24 0a 48 65 72 65 20 | 49 20 68 61 76 65 20 6c |$$.Here |I have l|
|00001aa0| 69 6e 65 64 20 75 70 20 | 74 68 65 20 61 6d 70 65 |ined up |the ampe|
|00001ab0| 72 73 61 6e 64 2d 65 71 | 75 61 6c 73 20 69 6e 20 |rsand-eq|uals in |
|00001ac0| 74 68 65 20 69 6e 70 75 | 74 20 66 69 6c 65 2c 20 |the inpu|t file, |
|00001ad0| 62 75 74 20 74 68 65 72 | 65 0a 69 73 20 6e 6f 20 |but ther|e.is no |
|00001ae0| 72 65 61 73 6f 6e 20 74 | 6f 20 64 6f 20 74 68 69 |reason t|o do thi|
|00001af0| 73 20 6f 74 68 65 72 20 | 74 68 61 6e 20 63 6c 61 |s other |than cla|
|00001b00| 72 69 74 79 2e 20 20 49 | 74 20 69 73 20 74 68 65 |rity.  I|t is the|
|00001b10| 20 61 6d 70 65 72 73 61 | 6e 64 20 77 68 69 63 68 | ampersa|nd which|
|00001b20| 0a 63 61 75 73 65 73 20 | 5c 54 65 58 5c 20 74 6f |.causes |\TeX\ to|
|00001b30| 20 6c 69 6e 65 20 74 68 | 69 6e 67 73 20 75 70 20 | line th|ings up |
|00001b40| 28 61 6c 6f 6e 67 20 77 | 69 74 68 2c 20 6f 66 20 |(along w|ith, of |
|00001b50| 63 6f 75 72 73 65 2c 20 | 74 68 65 20 65 71 61 6c |course, |the eqal|
|00001b60| 69 67 6e 20 63 6f 6d 6d | 61 6e 64 0a 69 74 73 65 |ign comm|and.itse|
|00001b70| 6c 66 29 2c 20 6e 6f 74 | 20 74 68 65 20 73 70 61 |lf), not| the spa|
|00001b80| 63 69 6e 67 20 6f 66 20 | 74 68 65 20 69 6e 70 75 |cing of |the inpu|
|00001b90| 74 20 66 69 6c 65 2e 0a | 41 6e 6f 74 68 65 72 20 |t file..|Another |
|00001ba0| 65 78 61 6d 70 6c 65 20 | 69 73 2c 0a 24 24 5c 65 |example |is,.$$\e|
|00001bb0| 71 61 6c 69 67 6e 6e 6f | 7b 0a 20 20 20 20 20 58 |qalignno|{.     X|
|00001bc0| 26 3d 61 2b 62 26 28 33 | 31 29 5c 63 72 0a 20 20 |&=a+b&(3|1)\cr.  |
|00001bd0| 20 20 20 59 2b 5a 2b 57 | 26 3d 63 26 28 33 32 29 |   Y+Z+W|&=c&(32)|
|00001be0| 5c 63 72 20 7d 24 24 0a | 69 2e 65 2e 2c 20 75 73 |\cr }$$.|i.e., us|
|00001bf0| 65 20 65 71 61 6c 69 67 | 6e 6e 6f 20 77 68 65 6e |e eqalig|nno when|
|00001c00| 20 79 6f 75 20 77 61 6e | 74 20 65 71 75 61 74 69 | you wan|t equati|
|00001c10| 6f 6e 20 6e 75 6d 62 65 | 72 73 20 6f 6e 20 65 61 |on numbe|rs on ea|
|00001c20| 63 68 20 6c 69 6e 65 2c | 20 61 6e 64 0a 24 24 5c |ch line,| and.$$\|
|00001c30| 65 71 61 6c 69 67 6e 6e | 6f 7b 0a 20 20 20 20 66 |eqalignn|o{.    f|
|00001c40| 28 78 29 26 3d 28 78 2d | 31 29 28 78 2b 31 29 5c |(x)&=(x-|1)(x+1)\|
|00001c50| 63 72 0a 20 20 20 26 3d | 78 5e 32 2d 31 26 28 33 |cr.   &=|x^2-1&(3|
|00001c60| 33 29 5c 63 72 7d 24 24 | 0a 77 68 69 63 68 20 73 |3)\cr}$$|.which s|
|00001c70| 68 6f 77 73 20 68 6f 77 | 20 61 20 6c 65 66 74 68 |hows how| a lefth|
|00001c80| 61 6e 64 20 73 69 64 65 | 20 61 6e 64 2f 6f 72 20 |and side| and/or |
|00001c90| 61 6e 20 65 71 75 61 74 | 69 6f 6e 20 6e 75 6d 62 |an equat|ion numb|
|00001ca0| 65 72 20 63 61 6e 20 62 | 65 20 61 62 73 65 6e 74 |er can b|e absent|
|00001cb0| 2e 0a 5c 62 6c 61 6e 6b | 6c 69 6e 65 5c 69 6e 64 |..\blank|line\ind|
|00001cc0| 65 6e 74 0a 20 20 20 20 | 20 54 68 69 73 20 69 73 |ent.    | This is|
|00001cd0| 20 61 73 20 67 6f 6f 64 | 20 61 20 70 6c 61 63 65 | as good| a place|
|00001ce0| 20 61 73 20 61 6e 79 20 | 74 6f 20 6c 69 73 74 20 | as any |to list |
|00001cf0| 61 6c 6c 20 74 68 65 20 | 73 70 65 63 69 61 6c 20 |all the |special |
|00001d00| 73 79 6d 62 6f 6c 73 0a | 28 74 68 61 74 20 49 20 |symbols.|(that I |
|00001d10| 6b 6e 6f 77 20 61 6e 64 | 20 63 6f 6e 73 69 64 65 |know and| conside|
|00001d20| 72 20 75 73 65 66 75 6c | 20 61 74 20 74 68 69 73 |r useful| at this|
|00001d30| 20 74 69 6d 65 2c 20 62 | 75 74 20 63 68 65 63 6b | time, b|ut check|
|00001d40| 0a 74 68 65 20 7b 5c 54 | 65 58 7d 62 6f 6f 6b 20 |.the {\T|eX}book |
|00001d50| 66 6f 72 20 74 68 65 20 | 72 65 73 74 29 20 61 6e |for the |rest) an|
|00001d60| 64 20 74 68 65 20 63 6f | 6d 6d 61 6e 64 73 20 0a |d the co|mmands .|
|00001d70| 66 6f 72 20 74 68 65 6d | 2e 20 20 42 65 20 73 75 |for them|.  Be su|
|00001d80| 72 65 20 74 6f 20 72 65 | 6d 65 6d 62 65 72 20 74 |re to re|member t|
|00001d90| 68 61 74 20 6d 6f 73 74 | 20 73 70 65 63 69 61 6c |hat most| special|
|00001da0| 20 73 79 6d 62 6f 6c 73 | 20 6f 6e 6c 79 20 77 6f | symbols| only wo|
|00001db0| 72 6b 0a 69 6e 20 6d 61 | 74 68 20 6d 6f 64 65 2c |rk.in ma|th mode,|
|00001dc0| 20 62 65 74 77 65 65 6e | 20 5c 24 20 27 73 21 0a | between| \$ 's!.|
|00001dd0| 0a 5c 68 61 6c 69 67 6e | 7b 20 5c 6c 66 74 7b 24 |.\halign|{ \lft{$|
|00001de0| 5c 62 61 63 6b 73 6c 61 | 73 68 24 23 7d 5c 71 75 |\backsla|sh$#}\qu|
|00001df0| 61 64 20 26 20 5c 6c 66 | 74 7b 24 23 24 7d 5c 71 |ad & \lf|t{$#$}\q|
|00001e00| 71 75 61 64 0a 20 20 20 | 20 20 20 20 20 20 26 20 |quad.   |      & |
|00001e10| 5c 6c 66 74 7b 24 5c 62 | 61 63 6b 73 6c 61 73 68 |\lft{$\b|ackslash|
|00001e20| 20 24 23 7d 5c 71 75 61 | 64 20 26 20 5c 6c 66 74 | $#}\qua|d & \lft|
|00001e30| 7b 24 23 24 7d 5c 71 71 | 75 61 64 0a 20 20 20 20 |{$#$}\qq|uad.    |
|00001e40| 20 20 20 20 20 26 20 5c | 6c 66 74 7b 24 5c 62 61 |     & \|lft{$\ba|
|00001e50| 63 6b 73 6c 61 73 68 20 | 24 23 7d 5c 71 75 61 64 |ckslash |$#}\quad|
|00001e60| 20 26 20 5c 6c 66 74 7b | 24 23 24 7d 5c 71 71 75 | & \lft{|$#$}\qqu|
|00001e70| 61 64 0a 20 20 20 20 20 | 20 20 20 20 26 20 5c 6c |ad.     |    & \l|
|00001e80| 66 74 7b 24 5c 62 61 63 | 6b 73 6c 61 73 68 20 24 |ft{$\bac|kslash $|
|00001e90| 23 7d 5c 71 75 61 64 20 | 26 20 5c 6c 66 74 7b 24 |#}\quad |& \lft{$|
|00001ea0| 23 24 7d 5c 71 71 75 61 | 64 20 5c 63 72 0a 61 6c |#$}\qqua|d \cr.al|
|00001eb0| 70 68 61 26 5c 61 6c 70 | 68 61 26 62 65 74 61 26 |pha&\alp|ha&beta&|
|00001ec0| 5c 62 65 74 61 26 67 61 | 6d 6d 61 26 5c 67 61 6d |\beta&ga|mma&\gam|
|00001ed0| 6d 61 26 64 65 6c 74 61 | 26 5c 64 65 6c 74 61 5c |ma&delta|&\delta\|
|00001ee0| 63 72 0a 65 70 73 69 6c | 6f 6e 26 5c 65 70 73 69 |cr.epsil|on&\epsi|
|00001ef0| 6c 6f 6e 26 7a 65 74 61 | 26 5c 7a 65 74 61 26 65 |lon&zeta|&\zeta&e|
|00001f00| 74 61 26 5c 65 74 61 26 | 74 68 65 74 61 26 5c 74 |ta&\eta&|theta&\t|
|00001f10| 68 65 74 61 5c 63 72 0a | 69 6f 74 61 26 5c 69 6f |heta\cr.|iota&\io|
|00001f20| 74 61 26 6b 61 70 70 61 | 26 5c 6b 61 70 70 61 26 |ta&kappa|&\kappa&|
|00001f30| 6c 61 6d 62 64 61 26 5c | 6c 61 6d 62 64 61 26 6d |lambda&\|lambda&m|
|00001f40| 75 26 5c 6d 75 5c 63 72 | 0a 6e 75 26 5c 6e 75 26 |u&\mu\cr|.nu&\nu&|
|00001f50| 78 69 26 5c 78 69 26 3f | 26 6f 26 70 69 26 5c 70 |xi&\xi&?|&o&pi&\p|
|00001f60| 69 5c 63 72 0a 72 68 6f | 26 5c 72 68 6f 26 73 69 |i\cr.rho|&\rho&si|
|00001f70| 67 6d 61 26 5c 73 69 67 | 6d 61 26 74 61 75 26 5c |gma&\sig|ma&tau&\|
|00001f80| 74 61 75 26 75 70 73 69 | 6c 6f 6e 26 5c 75 70 73 |tau&upsi|lon&\ups|
|00001f90| 69 6c 6f 6e 5c 63 72 0a | 70 68 69 26 5c 70 68 69 |ilon\cr.|phi&\phi|
|00001fa0| 26 63 68 69 26 5c 63 68 | 69 26 70 73 69 26 5c 70 |&chi&\ch|i&psi&\p|
|00001fb0| 73 69 26 6f 6d 65 67 61 | 26 5c 6f 6d 65 67 61 5c |si&omega|&\omega\|
|00001fc0| 63 72 0a 76 61 72 65 70 | 73 69 6c 6f 6e 26 5c 76 |cr.varep|silon&\v|
|00001fd0| 61 72 65 70 73 69 6c 6f | 6e 26 76 61 72 74 68 65 |arepsilo|n&varthe|
|00001fe0| 74 61 26 5c 76 61 72 74 | 68 65 74 61 26 76 61 72 |ta&\vart|heta&var|
|00001ff0| 70 69 26 5c 76 61 72 70 | 69 26 76 61 72 72 68 6f |pi&\varp|i&varrho|
|00002000| 26 5c 76 61 72 72 68 6f | 5c 63 72 0a 76 61 72 73 |&\varrho|\cr.vars|
|00002010| 69 67 6d 61 26 5c 76 61 | 72 73 69 67 6d 61 26 76 |igma&\va|rsigma&v|
|00002020| 61 72 70 68 69 26 5c 76 | 61 72 70 68 69 26 7b 7d |arphi&\v|arphi&{}|
|00002030| 26 7b 7d 26 65 6c 6c 26 | 5c 65 6c 6c 5c 63 72 0a |&{}&ell&|\ell\cr.|
|00002040| 47 61 6d 6d 61 26 5c 47 | 61 6d 6d 61 26 44 65 6c |Gamma&\G|amma&Del|
|00002050| 74 61 26 5c 44 65 6c 74 | 61 26 54 68 65 74 61 26 |ta&\Delt|a&Theta&|
|00002060| 5c 54 68 65 74 61 26 4c | 61 6d 62 64 61 26 5c 4c |\Theta&L|ambda&\L|
|00002070| 61 6d 62 64 61 5c 63 72 | 0a 58 69 26 5c 58 69 26 |ambda\cr|.Xi&\Xi&|
|00002080| 50 69 26 5c 50 69 26 53 | 69 67 6d 61 26 5c 53 69 |Pi&\Pi&S|igma&\Si|
|00002090| 67 6d 61 26 55 70 73 69 | 6c 6f 6e 26 5c 55 70 73 |gma&Upsi|lon&\Ups|
|000020a0| 69 6c 6f 6e 5c 63 72 0a | 50 68 69 26 5c 50 68 69 |ilon\cr.|Phi&\Phi|
|000020b0| 26 50 73 69 26 5c 50 73 | 69 26 4f 6d 65 67 61 26 |&Psi&\Ps|i&Omega&|
|000020c0| 5c 4f 6d 65 67 61 26 63 | 64 6f 74 73 26 5c 63 64 |\Omega&c|dots&\cd|
|000020d0| 6f 74 73 5c 63 72 0a 47 | 61 6d 6d 61 69 74 26 5c |ots\cr.G|ammait&\|
|000020e0| 47 61 6d 6d 61 69 74 26 | 44 65 6c 74 61 69 74 26 |Gammait&|Deltait&|
|000020f0| 5c 44 65 6c 74 61 69 74 | 26 54 68 65 74 61 69 74 |\Deltait|&Thetait|
|00002100| 26 5c 54 68 65 74 61 69 | 74 26 4c 61 6d 62 64 61 |&\Thetai|t&Lambda|
|00002110| 69 74 26 5c 4c 61 6d 62 | 64 61 69 74 5c 63 72 0a |it&\Lamb|dait\cr.|
|00002120| 58 69 69 74 26 5c 58 69 | 69 74 26 50 69 69 74 26 |Xiit&\Xi|it&Piit&|
|00002130| 5c 50 69 69 74 26 53 69 | 67 6d 61 69 74 26 5c 53 |\Piit&Si|gmait&\S|
|00002140| 69 67 6d 61 69 74 26 55 | 70 73 69 6c 6f 6e 69 74 |igmait&U|psilonit|
|00002150| 26 5c 55 70 73 69 6c 6f | 6e 69 74 5c 63 72 0a 50 |&\Upsilo|nit\cr.P|
|00002160| 68 69 69 74 26 5c 50 68 | 69 69 74 26 50 73 69 69 |hiit&\Ph|iit&Psii|
|00002170| 74 26 5c 50 73 69 69 74 | 26 4f 6d 65 67 61 69 74 |t&\Psiit|&Omegait|
|00002180| 26 5c 4f 6d 65 67 61 69 | 74 26 6c 64 6f 74 73 26 |&\Omegai|t&ldots&|
|00002190| 5c 6c 64 6f 74 73 5c 63 | 72 0a 41 73 63 72 26 5c |\ldots\c|r.Ascr&\|
|000021a0| 41 73 63 72 26 42 73 63 | 72 26 5c 42 73 63 72 26 |Ascr&Bsc|r&\Bscr&|
|000021b0| 2e 2e 2e 65 74 63 2e 2e | 2e 26 7b 7d 26 5a 73 63 |...etc..|.&{}&Zsc|
|000021c0| 72 26 5c 5a 73 63 72 5c | 63 72 0a 70 6d 26 5c 70 |r&\Zscr\|cr.pm&\p|
|000021d0| 6d 26 6d 70 26 5c 6d 70 | 26 74 69 6d 65 73 26 5c |m&mp&\mp|&times&\|
|000021e0| 74 69 6d 65 73 26 64 69 | 76 26 5c 64 69 76 5c 63 |times&di|v&\div\c|
|000021f0| 72 0a 62 61 63 6b 73 6c | 61 73 68 26 5c 62 61 63 |r.backsl|ash&\bac|
|00002200| 6b 73 6c 61 73 68 26 63 | 64 6f 74 26 5c 63 64 6f |kslash&c|dot&\cdo|
|00002210| 74 26 6f 70 6c 75 73 26 | 5c 6f 70 6c 75 73 26 6f |t&oplus&|\oplus&o|
|00002220| 6d 69 6e 75 73 26 5c 6f | 6d 69 6e 75 73 5c 63 72 |minus&\o|minus\cr|
|00002230| 0a 6f 74 69 6d 65 73 26 | 5c 6f 74 69 6d 65 73 26 |.otimes&|\otimes&|
|00002240| 6f 73 6c 61 73 68 26 5c | 6f 73 6c 61 73 68 26 6f |oslash&\|oslash&o|
|00002250| 64 6f 74 26 5c 6f 64 6f | 74 26 61 73 74 26 5c 61 |dot&\odo|t&ast&\a|
|00002260| 73 74 5c 63 72 0a 63 69 | 72 63 26 5c 63 69 72 63 |st\cr.ci|rc&\circ|
|00002270| 26 62 75 6c 6c 65 74 26 | 5c 62 75 6c 6c 65 74 26 |&bullet&|\bullet&|
|00002280| 75 70 61 72 72 6f 77 26 | 5c 75 70 61 72 72 6f 77 |uparrow&|\uparrow|
|00002290| 26 64 6f 77 6e 61 72 72 | 6f 77 26 5c 64 6f 77 6e |&downarr|ow&\down|
|000022a0| 61 72 72 6f 77 5c 63 72 | 0a 76 65 72 74 26 5c 76 |arrow\cr|.vert&\v|
|000022b0| 65 72 74 26 7c 26 5c 7c | 26 6c 6c 26 5c 6c 6c 26 |ert&|&\||&ll&\ll&|
|000022c0| 67 67 26 5c 67 67 5c 63 | 72 0a 73 69 6d 65 71 26 |gg&\gg\c|r.simeq&|
|000022d0| 5c 73 69 6d 65 71 26 61 | 70 70 72 6f 78 26 5c 61 |\simeq&a|pprox&\a|
|000022e0| 70 70 72 6f 78 26 6c 61 | 6e 67 6c 65 26 5c 6c 61 |pprox&la|ngle&\la|
|000022f0| 6e 67 6c 65 26 72 61 6e | 67 6c 65 26 5c 72 61 6e |ngle&ran|gle&\ran|
|00002300| 67 6c 65 5c 63 72 0a 73 | 75 6d 26 5c 73 75 6d 26 |gle\cr.s|um&\sum&|
|00002310| 69 6e 74 26 5c 69 6e 74 | 26 6f 69 6e 74 26 5c 6f |int&\int|&oint&\o|
|00002320| 69 6e 74 26 70 72 6f 64 | 26 5c 70 72 6f 64 5c 63 |int&prod|&\prod\c|
|00002330| 72 0a 69 6e 66 74 79 26 | 5c 69 6e 66 74 79 26 70 |r.infty&|\infty&p|
|00002340| 72 69 6d 65 26 5c 70 72 | 69 6d 65 26 70 61 72 74 |rime&\pr|ime&part|
|00002350| 69 61 6c 26 5c 70 61 72 | 74 69 61 6c 26 6e 61 62 |ial&\par|tial&nab|
|00002360| 6c 61 26 5c 6e 61 62 6c | 61 5c 63 72 0a 53 26 5c |la&\nabl|a\cr.S&\|
|00002370| 68 62 6f 78 7b 5c 53 7d | 26 64 61 67 67 65 72 26 |hbox{\S}|&dagger&|
|00002380| 5c 64 61 67 67 65 72 26 | 64 64 61 67 67 65 72 26 |\dagger&|ddagger&|
|00002390| 5c 64 64 61 67 67 65 72 | 26 50 26 5c 68 62 6f 78 |\ddagger|&P&\hbox|
|000023a0| 7b 5c 50 7d 5c 63 72 0a | 5c 24 26 5c 24 26 73 69 |{\P}\cr.|\$&\$&si|
|000023b0| 6d 26 5c 73 69 6d 26 6c | 65 66 74 61 72 72 6f 77 |m&\sim&l|eftarrow|
|000023c0| 26 5c 6c 65 66 74 61 72 | 72 6f 77 26 72 69 67 68 |&\leftar|row&righ|
|000023d0| 74 61 72 72 6f 77 26 5c | 72 69 67 68 74 61 72 72 |tarrow&\|rightarr|
|000023e0| 6f 77 5c 63 72 0a 65 71 | 75 69 76 26 5c 65 71 75 |ow\cr.eq|uiv&\equ|
|000023f0| 69 76 26 6c 65 71 26 5c | 6c 65 71 26 67 65 71 26 |iv&leq&\|leq&geq&|
|00002400| 5c 67 65 71 26 24 5c 23 | 24 26 5c 23 5c 63 72 0a |\geq&$\#|$&\#\cr.|
|00002410| 66 6f 72 61 6c 6c 26 5c | 66 6f 72 61 6c 6c 26 65 |forall&\|forall&e|
|00002420| 78 69 73 74 73 26 5c 65 | 78 69 73 74 73 26 5c 25 |xists&\e|xists&\%|
|00002430| 26 5c 25 26 20 5c 26 20 | 26 20 5c 26 20 5c 63 72 |&\%& \& |& \& \cr|
|00002440| 0a 68 65 61 72 74 73 75 | 69 74 26 5c 68 65 61 72 |.heartsu|it&\hear|
|00002450| 74 73 75 69 74 26 52 65 | 26 5c 52 65 26 62 6f 74 |tsuit&Re|&\Re&bot|
|00002460| 26 5c 62 6f 74 26 66 6c | 61 74 26 5c 66 6c 61 74 |&\bot&fl|at&\flat|
|00002470| 5c 63 72 0a 65 6d 70 74 | 79 73 65 74 26 5c 65 6d |\cr.empt|yset&\em|
|00002480| 70 74 79 73 65 74 26 63 | 75 70 26 5c 63 75 70 26 |ptyset&c|up&\cup&|
|00002490| 73 74 61 72 26 5c 73 74 | 61 72 26 2e 2e 2e 65 74 |star&\st|ar&...et|
|000024a0| 63 2e 2e 2e 26 7b 7d 5c | 63 72 7d 0a 0a 0a 5c 62 |c...&{}\|cr}...\b|
|000024b0| 6c 61 6e 6b 6c 69 6e 65 | 5c 69 6e 64 65 6e 74 0a |lankline|\indent.|
|000024c0| 20 20 20 20 20 4f 66 20 | 63 6f 75 72 73 65 2c 20 |     Of |course, |
|000024d0| 74 68 65 20 73 79 6d 62 | 6f 6c 73 20 3f 2c 2f 2c |the symb|ols ?,/,|
|000024e0| 2b 2c 21 2c 3d 2c 60 2c | 27 2c 22 2c 61 6e 64 20 |+,!,=,`,|',",and |
|000024f0| 60 60 20 63 61 6e 20 62 | 65 0a 74 79 70 65 64 20 |`` can b|e.typed |
|00002500| 64 69 72 65 63 74 6c 79 | 20 66 72 6f 6d 20 74 68 |directly| from th|
|00002510| 65 20 6b 65 79 62 6f 61 | 72 64 20 61 73 20 69 6e |e keyboa|rd as in|
|00002520| 64 69 63 61 74 65 64 20 | 28 65 78 63 65 70 74 20 |dicated |(except |
|00002530| 74 68 61 74 20 60 60 20 | 69 73 0a 61 63 74 75 61 |that `` |is.actua|
|00002540| 6c 6c 79 20 74 77 6f 20 | 73 65 71 75 65 6e 74 69 |lly two |sequenti|
|00002550| 61 6c 20 73 69 6e 67 6c | 65 20 61 63 63 65 6e 74 |al singl|e accent|
|00002560| 20 67 72 61 76 65 73 29 | 2c 20 62 75 74 20 24 3c | graves)|, but $<|
|00002570| 24 20 61 6e 64 20 24 3e | 24 20 6d 75 73 74 0a 62 |$ and $>|$ must.b|
|00002580| 65 20 69 6e 20 6d 61 74 | 68 20 6d 6f 64 65 20 6f |e in mat|h mode o|
|00002590| 72 20 79 6f 75 20 77 69 | 6c 6c 20 67 65 74 20 3c |r you wi|ll get <|
|000025a0| 20 61 6e 64 20 3e 20 72 | 65 73 70 65 63 74 69 76 | and > r|espectiv|
|000025b0| 65 6c 79 2e 0a 41 6c 73 | 6f 20 6e 6f 74 65 3a 20 |ely..Als|o note: |
|000025c0| 2d 2c 20 2d 2d 2c 20 2d | 2d 2d 2c 0a 66 66 2c 20 |-, --, -|--,.ff, |
|000025d0| 66 69 2c 20 66 6c 2c 20 | 66 66 69 2c 20 66 66 6c |fi, fl, |ffi, ffl|
|000025e0| 2c 20 5c 73 73 20 2c 20 | 5c 61 65 20 2c 20 5c 41 |, \ss , |\ae , \A|
|000025f0| 45 20 2c 20 5c 6f 65 20 | 2c 20 5c 4f 45 20 2c 20 |E , \oe |, \OE , |
|00002600| 5c 6f 20 2c 20 5c 4f 20 | 2c 20 5c 61 61 20 2c 20 |\o , \O |, \aa , |
|00002610| 5c 41 41 2e 0a 54 68 65 | 72 65 20 61 72 65 20 6d |\AA..The|re are m|
|00002620| 6f 72 65 20 6f 66 20 74 | 68 65 73 65 20 69 6e 20 |ore of t|hese in |
|00002630| 74 68 65 20 7b 5c 54 65 | 58 7d 62 6f 6f 6b 2e 0a |the {\Te|X}book..|
|00002640| 49 20 63 61 6e 27 74 20 | 66 69 6e 64 20 61 6e 79 |I can't |find any|
|00002650| 74 68 69 6e 67 20 66 6f | 72 20 74 68 65 20 73 65 |thing fo|r the se|
|00002660| 6d 69 64 69 72 65 63 74 | 20 70 72 6f 64 75 63 74 |midirect| product|
|00002670| 2e 20 20 53 68 75 63 6b | 73 2e 0a 0a 57 68 65 77 |.  Shuck|s...Whew|
|00002680| 2c 20 74 68 61 74 20 77 | 61 73 20 61 20 6c 6f 74 |, that w|as a lot|
|00002690| 20 6f 66 20 73 79 6d 62 | 6f 6c 20 74 79 70 69 6e | of symb|ol typin|
|000026a0| 67 2e 5c 66 6f 6f 74 6e | 6f 74 65 2a 7b 0a 57 65 |g.\footn|ote*{.We|
|000026b0| 20 68 61 76 65 20 62 65 | 65 6e 20 75 73 69 6e 67 | have be|en using|
|000026c0| 20 50 4c 41 49 4e 20 5c | 54 65 58 5c 20 61 6e 64 | PLAIN \|TeX\ and|
|000026d0| 20 61 20 63 6f 75 70 6c | 65 20 6f 66 20 6d 61 63 | a coupl|e of mac|
|000026e0| 72 6f 73 20 66 72 6f 6d | 0a 74 68 65 20 66 69 6c |ros from|.the fil|
|000026f0| 65 20 62 6f 62 6d 61 63 | 72 6f 2e 74 65 78 20 77 |e bobmac|ro.tex w|
|00002700| 68 69 63 68 20 63 6f 6e | 74 61 69 6e 73 20 74 68 |hich con|tains th|
|00002710| 65 20 64 65 66 69 6e 69 | 74 69 6f 6e 73 20 6f 66 |e defini|tions of|
|00002720| 20 61 20 66 65 77 0a 75 | 73 65 66 75 6c 20 63 6f | a few.u|seful co|
|00002730| 6d 6d 61 6e 64 73 2e 20 | 4e 6f 74 69 63 65 20 74 |mmands. |Notice t|
|00002740| 68 61 74 20 74 68 65 20 | 60 24 5c 62 61 63 6b 73 |hat the |`$\backs|
|00002750| 6c 61 73 68 24 66 6f 6f | 74 6e 6f 74 65 27 20 6d |lash$foo|tnote' m|
|00002760| 61 63 72 6f 20 70 72 6f | 76 69 64 65 64 20 62 79 |acro pro|vided by|
|00002770| 0a 70 6c 61 69 6e 2e 74 | 65 78 20 69 73 20 6e 6f |.plain.t|ex is no|
|00002780| 74 20 76 65 72 79 20 73 | 61 74 69 73 66 61 63 74 |t very s|atisfact|
|00002790| 6f 72 79 2e 20 53 65 65 | 20 70 61 67 65 20 34 31 |ory. See| page 41|
|000027a0| 36 20 6f 66 20 74 68 65 | 20 7b 5c 54 65 58 7d 62 |6 of the| {\TeX}b|
|000027b0| 6f 6f 6b 2e 7d 0a 0a 5c | 52 45 46 45 52 45 4e 43 |ook.}..\|REFERENC|
|000027c0| 45 53 0a 5c 72 65 66 20 | 41 61 72 64 76 61 72 6b |ES.\ref |Aardvark|
|000027d0| 2c 20 4a 2e 4d 2e 20 61 | 6e 64 20 42 6c 61 74 68 |, J.M. a|nd Blath|
|000027e0| 65 72 2c 20 52 2e 50 2e | 20 31 39 38 32 2c 20 7b |er, R.P.| 1982, {|
|000027f0| 5c 69 74 20 50 72 6f 63 | 2e 20 52 6f 79 2e 20 53 |\it Proc|. Roy. S|
|00002800| 6f 63 2e 0a 4d 61 64 61 | 67 61 73 63 61 72 7d 2c |oc..Mada|gascar},|
|00002810| 20 7b 5c 62 66 20 32 33 | 34 7d 2c 20 34 39 32 2e | {\bf 23|4}, 492.|
|00002820| 20 20 28 41 6c 73 6f 20 | 74 72 61 6e 73 6c 61 74 |  (Also |translat|
|00002830| 65 64 20 69 6e 20 7b 5c | 69 74 20 53 6f 76 2e 20 |ed in {\|it Sov. |
|00002840| 50 68 79 73 2e 20 55 73 | 70 65 6b 68 69 7d 2c 0a |Phys. Us|pekhi},.|
|00002850| 7b 5c 62 66 20 33 34 7d | 2c 20 38 37 39 2e 0a 5c |{\bf 34}|, 879..\|
|00002860| 72 65 66 20 4e 75 6c 6c | 2c 20 4e 2e 4e 2e 20 61 |ref Null|, N.N. a|
|00002870| 6e 64 20 4e 6f 6e 65 2c | 20 4e 2e 20 31 39 37 32 |nd None,| N. 1972|
|00002880| 2c 20 7b 5c 69 74 20 41 | 70 2e 20 4a 2e 7d 2c 20 |, {\it A|p. J.}, |
|00002890| 7b 5c 62 66 20 31 38 36 | 7d 2c 20 32 34 2e 0a 0a |{\bf 186|}, 24...|
|000028a0| 25 20 54 68 65 20 61 6d | 70 65 72 73 61 6e 64 20 |% The am|persand |
|000028b0| 63 61 6e 20 62 65 20 75 | 73 65 64 20 74 6f 20 6d |can be u|sed to m|
|000028c0| 61 6b 65 20 63 6f 6d 6d | 65 6e 74 73 20 77 68 69 |ake comm|ents whi|
|000028d0| 63 68 20 77 69 6c 6c 20 | 62 65 20 69 67 6e 6f 72 |ch will |be ignor|
|000028e0| 65 64 20 62 79 20 5c 54 | 65 58 2e 0a 25 20 54 68 |ed by \T|eX..% Th|
|000028f0| 69 73 20 72 65 6d 61 72 | 6b 20 77 69 6c 6c 20 6e |is remar|k will n|
|00002900| 65 76 65 72 20 61 70 70 | 65 61 72 20 69 6e 20 79 |ever app|ear in y|
|00002910| 6f 75 72 20 5c 54 65 58 | 5c 20 6f 75 74 70 75 74 |our \TeX|\ output|
|00002920| 2e 0a 25 20 49 66 20 79 | 6f 75 20 77 61 6e 74 20 |..% If y|ou want |
|00002930| 62 69 67 67 65 72 20 70 | 72 69 6e 74 2c 20 74 72 |bigger p|rint, tr|
|00002940| 79 20 70 75 74 74 69 6e | 67 20 5c 6d 61 67 6e 69 |y puttin|g \magni|
|00002950| 66 69 63 61 74 69 6f 6e | 3d 31 32 30 30 20 61 74 |fication|=1200 at|
|00002960| 20 74 68 65 20 62 65 67 | 69 6e 6e 69 6e 67 2e 0a | the beg|inning..|
|00002970| 25 20 54 68 69 73 20 6d | 61 67 6e 69 66 69 65 73 |% This m|agnifies|
|00002980| 20 74 68 65 20 66 6f 6e | 74 73 20 62 79 20 61 20 | the fon|ts by a |
|00002990| 66 61 63 74 6f 72 20 6f | 66 20 31 2e 32 2e 0a 25 |factor o|f 1.2..%|
|000029a0| 20 41 6e 64 20 61 6c 73 | 6f 20 5c 6f 6e 65 61 6e | And als|o \onean|
|000029b0| 64 61 68 61 6c 66 73 70 | 61 63 65 20 61 66 74 65 |dahalfsp|ace afte|
|000029c0| 72 20 74 68 61 74 20 69 | 66 20 79 6f 75 20 77 61 |r that i|f you wa|
|000029d0| 6e 74 20 61 20 6c 69 74 | 74 6c 65 20 6d 6f 72 65 |nt a lit|tle more|
|000029e0| 20 73 70 61 63 65 0a 25 | 20 20 20 20 62 65 74 77 | space.%|    betw|
|000029f0| 65 65 6e 20 6c 69 6e 65 | 73 2e 20 20 4f 72 20 65 |een line|s.  Or e|
|00002a00| 76 65 6e 20 5c 64 6f 75 | 62 6c 65 73 70 61 63 65 |ven \dou|blespace|
|00002a10| 2e 0a 0a 5c 73 65 63 74 | 20 41 50 50 45 4e 44 49 |...\sect| APPENDI|
|00002a20| 58 5c 65 6e 64 73 65 63 | 74 0a 0a 46 6f 72 20 74 |X\endsec|t..For t|
|00002a30| 68 6f 73 65 20 70 65 6f | 70 6c 65 20 77 68 6f 20 |hose peo|ple who |
|00002a40| 69 6e 73 69 73 74 20 6f | 6e 20 64 6f 69 6e 67 20 |insist o|n doing |
|00002a50| 61 20 6c 6f 74 20 6f 66 | 20 69 6e 64 65 78 20 6a |a lot of| index j|
|00002a60| 75 67 67 6c 69 6e 67 2c | 20 74 68 65 20 63 6f 6d |uggling,| the com|
|00002a70| 6d 61 6e 64 0a 60 60 24 | 5c 62 61 63 6b 73 6c 61 |mand.``$|\backsla|
|00002a80| 73 68 24 6e 75 6c 6c 22 | 20 77 68 69 63 68 20 73 |sh$null"| which s|
|00002a90| 74 61 6e 64 73 20 66 6f | 72 20 61 6e 20 65 6d 70 |tands fo|r an emp|
|00002aa0| 74 79 20 62 6f 78 20 28 | 6e 61 6d 65 6c 79 20 0a |ty box (|namely .|
|00002ab0| 24 5c 62 61 63 6b 73 6c | 61 73 68 24 68 62 6f 78 |$\backsl|ash$hbox|
|00002ac0| 24 5c 7b 5c 7d 24 29 20 | 69 73 20 76 65 72 79 20 |$\{\}$) |is very |
|00002ad0| 75 73 65 66 75 6c 20 62 | 65 63 61 75 73 65 20 69 |useful b|ecause i|
|00002ae0| 74 20 65 6e 64 73 20 74 | 68 65 20 70 72 65 76 69 |t ends t|he previ|
|00002af0| 6f 75 73 20 73 79 6d 62 | 6f 6c 20 61 6e 64 0a 61 |ous symb|ol and.a|
|00002b00| 6e 79 20 73 75 62 73 63 | 72 69 70 74 73 20 6f 72 |ny subsc|ripts or|
|00002b10| 20 73 75 70 65 72 73 63 | 72 69 70 74 73 20 77 68 | supersc|ripts wh|
|00002b20| 69 63 68 20 66 6f 6c 6c | 6f 77 20 74 68 65 6e 20 |ich foll|ow then |
|00002b30| 61 72 65 20 70 6c 61 63 | 65 64 20 61 74 20 74 68 |are plac|ed at th|
|00002b40| 65 20 6e 6f 72 6d 61 6c | 0a 6c 65 76 65 6c 73 20 |e normal|.levels |
|00002b50| 69 6e 73 74 65 61 64 20 | 6f 66 20 63 6c 69 6d 62 |instead |of climb|
|00002b60| 69 6e 67 20 75 70 20 6f | 72 20 64 6f 77 6e 20 69 |ing up o|r down i|
|00002b70| 66 20 74 68 65 20 70 72 | 65 76 69 6f 75 73 20 73 |f the pr|evious s|
|00002b80| 79 6d 62 6f 6c 20 73 74 | 69 63 6b 73 20 75 70 20 |ymbol st|icks up |
|00002b90| 6f 72 20 64 6f 77 6e 0a | 74 6f 6f 20 66 61 72 2e |or down.|too far.|
|00002ba0| 20 20 49 74 20 61 6c 73 | 6f 20 61 6c 6c 6f 77 73 |  It als|o allows|
|00002bb0| 20 61 6c 69 67 6e 6d 65 | 6e 74 20 6f 66 20 75 70 | alignme|nt of up|
|00002bc0| 20 61 6e 64 20 64 6f 77 | 6e 20 69 6e 64 69 63 65 | and dow|n indice|
|00002bd0| 73 20 6e 65 63 65 73 73 | 61 72 79 20 66 6f 72 0a |s necess|ary for.|
|00002be0| 72 61 69 73 69 6e 67 20 | 61 6e 64 20 6c 6f 77 65 |raising |and lowe|
|00002bf0| 72 69 6e 67 20 69 6e 64 | 69 63 65 73 20 77 69 74 |ring ind|ices wit|
|00002c00| 68 20 61 20 6d 65 74 72 | 69 63 0a 24 24 5c 65 71 |h a metr|ic.$$\eq|
|00002c10| 61 6c 69 67 6e 7b 20 20 | 26 5c 47 61 6d 6d 61 5e |align{  |&\Gamma^|
|00002c20| 7b 5c 61 6c 70 68 61 7d | 5c 6e 75 6c 6c 5f 7b 5c |{\alpha}|\null_{\|
|00002c30| 62 65 74 61 5c 67 61 6d | 6d 61 7d 5c 71 75 61 64 |beta\gam|ma}\quad|
|00002c40| 20 5c 68 62 6f 78 7b 69 | 6e 73 74 65 61 64 20 6f | \hbox{i|nstead o|
|00002c50| 66 7d 0a 20 20 20 20 5c | 71 75 61 64 20 5c 47 61 |f}.    \|quad \Ga|
|00002c60| 6d 6d 61 5e 7b 5c 61 6c | 70 68 61 7d 5f 7b 5c 62 |mma^{\al|pha}_{\b|
|00002c70| 65 74 61 5c 67 61 6d 6d | 61 7d 5c 63 72 0a 20 20 |eta\gamm|a}\cr.  |
|00002c80| 20 26 5c 75 6e 64 65 72 | 73 69 6d 7b 5c 74 69 6c | &\under|sim{\til|
|00002c90| 64 65 7b 52 7d 7d 5c 6e | 75 6c 6c 5e 7b 5c 61 6c |de{R}}\n|ull^{\al|
|00002ca0| 70 68 61 7d 5c 6e 75 6c | 6c 5f 7b 5c 62 65 74 61 |pha}\nul|l_{\beta|
|00002cb0| 5c 67 61 6d 6d 61 7d 5c | 6e 75 6c 6c 5e 7b 5c 64 |\gamma}\|null^{\d|
|00002cc0| 65 6c 74 61 7d 0a 20 20 | 20 5c 71 75 61 64 20 5c |elta}.  | \quad \|
|00002cd0| 68 62 6f 78 7b 69 6e 73 | 74 65 61 64 20 6f 66 7d |hbox{ins|tead of}|
|00002ce0| 5c 71 75 61 64 20 5c 75 | 6e 64 65 72 73 69 6d 7b |\quad \u|ndersim{|
|00002cf0| 5c 74 69 6c 64 65 20 52 | 7d 5e 7b 5c 61 6c 70 68 |\tilde R|}^{\alph|
|00002d00| 61 7d 5f 7b 5c 62 65 74 | 61 5c 67 61 6d 6d 61 7d |a}_{\bet|a\gamma}|
|00002d10| 5c 6e 75 6c 6c 0a 20 20 | 20 20 5e 7b 5c 64 65 6c |\null.  |  ^{\del|
|00002d20| 74 61 7d 5c 71 75 61 64 | 2e 5c 63 72 7d 24 24 0a |ta}\quad|.\cr}$$.|
|00002d30| 49 66 20 74 68 65 72 65 | 20 68 61 64 20 6e 6f 74 |If there| had not|
|00002d40| 20 62 65 65 6e 20 61 20 | 24 5c 62 61 63 6b 73 6c | been a |$\backsl|
|00002d50| 61 73 68 24 6e 75 6c 6c | 20 69 6e 20 74 68 65 20 |ash$null| in the |
|00002d60| 6c 61 73 74 20 73 79 6d | 62 6f 6c 20 61 20 60 60 |last sym|bol a ``|
|00002d70| 64 6f 75 62 6c 65 20 0a | 73 75 62 73 63 72 69 70 |double .|subscrip|
|00002d80| 74 22 20 65 72 72 6f 72 | 20 77 6f 75 6c 64 20 68 |t" error| would h|
|00002d90| 61 76 65 20 72 65 73 75 | 6c 74 65 64 20 73 6f 20 |ave resu|lted so |
|00002da0| 74 68 69 73 20 63 6f 6d | 6d 61 6e 64 20 61 6c 6c |this com|mand all|
|00002db0| 6f 77 73 20 79 6f 75 20 | 74 6f 20 67 65 74 20 61 |ows you |to get a|
|00002dc0| 72 6f 75 6e 64 0a 74 68 | 65 20 60 60 6e 6f 20 64 |round.th|e ``no d|
|00002dd0| 6f 75 62 6c 65 20 73 75 | 62 73 63 72 69 70 74 22 |ouble su|bscript"|
|00002de0| 20 72 75 6c 65 2e 20 20 | 49 66 20 61 20 73 75 62 | rule.  |If a sub|
|00002df0| 73 63 72 69 70 74 20 73 | 68 6f 75 64 20 6e 6f 74 |script s|houd not|
|00002e00| 20 62 65 20 73 68 72 75 | 6e 6b 20 69 6e 20 73 69 | be shru|nk in si|
|00002e10| 7a 65 2c 0a 24 5c 62 61 | 63 6b 73 6c 61 73 68 24 |ze,.$\ba|ckslash$|
|00002e20| 68 62 6f 78 20 63 61 6e | 20 62 65 20 75 73 65 64 |hbox can| be used|
|00002e30| 20 74 6f 20 70 72 65 76 | 65 6e 74 20 74 68 65 20 | to prev|ent the |
|00002e40| 73 68 72 69 6e 6b 69 6e | 67 0a 24 24 5c 6e 61 62 |shrinkin|g.$$\nab|
|00002e50| 6c 61 5f 7b 5c 68 62 6f | 78 7b 24 65 5f 61 24 7d |la_{\hbo|x{$e_a$}|
|00002e60| 7d 5c 74 68 69 6e 73 70 | 61 63 65 20 65 5f 62 3d |}\thinsp|ace e_b=|
|00002e70| 5c 47 61 6d 6d 61 5e 63 | 5c 6e 75 6c 6c 5f 7b 61 |\Gamma^c|\null_{a|
|00002e80| 62 7d 65 5f 63 5c 71 75 | 61 64 2e 24 24 0a 0a 5c |b}e_c\qu|ad.$$..\|
|00002e90| 62 79 65 0a 0a 0a       |                         |bye...  |        |
+--------+-------------------------+-------------------------+--------+--------+