| 1 | .2C $gsize 9$ |
| 2 | .nr PS 9 |
| 3 | .nr VS 11p |
| 4 | .NH |
| 5 | Introduction |
| 6 | .PP |
| 7 | ``Mathematics is known in the trade as |
| 8 | .ul |
| 9 | difficult, |
| 10 | or |
| 11 | .ul |
| 12 | penalty, copy |
| 13 | because it is slower, more difficult, |
| 14 | and more expensive to set in type |
| 15 | than any other kind of copy normally |
| 16 | occurring in books and journals.'' |
| 17 | [1] |
| 18 | .PP |
| 19 | One difficulty with mathematical text |
| 20 | is the multiplicity of characters, |
| 21 | sizes, and fonts. |
| 22 | An expression such as |
| 23 | .EQ |
| 24 | lim from {x-> pi /2} ( tan~x) sup{sin~2x}~=~1 |
| 25 | .EN |
| 26 | requires an intimate mixture of roman, italic and greek letters, in three sizes, |
| 27 | and a special character or two. |
| 28 | (``Requires'' is perhaps the wrong word, |
| 29 | but mathematics has its own typographical conventions |
| 30 | which are quite different from those |
| 31 | of ordinary text.) |
| 32 | Typesetting such an expression by traditional methods |
| 33 | is still an essentially manual operation. |
| 34 | .PP |
| 35 | A second difficulty is the two dimensional character |
| 36 | of mathematics, |
| 37 | which the superscript and limits in the preceding example |
| 38 | showed in its simplest form. |
| 39 | This is carried further by |
| 40 | .EQ |
| 41 | a sub 0 + b sub 1 over |
| 42 | {a sub 1 + b sub 2 over |
| 43 | {a sub 2 + b sub 3 over |
| 44 | {a sub 3 + ... }}} |
| 45 | .EN |
| 46 | .sp |
| 47 | and still further by |
| 48 | .EQ |
| 49 | define emx "{e sup mx}" |
| 50 | define mab "{m sqrt ab}" |
| 51 | define sa "{sqrt a}" |
| 52 | define sb "{sqrt b}" |
| 53 | int dx over {a emx - be sup -mx} ~=~ |
| 54 | left { lpile { |
| 55 | 1 over {2 mab} ~log~ {sa emx - sb} over {sa emx + sb} |
| 56 | above |
| 57 | 1 over mab ~ tanh sup -1 ( sa over sb emx ) |
| 58 | above |
| 59 | -1 over mab ~ coth sup -1 ( sa over sb emx ) |
| 60 | } |
| 61 | .EN |
| 62 | These examples also show line-drawing, built-up characters like braces and radicals, |
| 63 | and a spectrum of positioning problems. |
| 64 | (Section 6 shows |
| 65 | what a user has to type to produce these |
| 66 | on our system.) |