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1.1       root        1: .\"    @(#)e1  6.1 (Berkeley) 5/22/86
                      2: .\"
                      3: .2C $gsize 9$
                      4: .nr PS 9
                      5: .nr VS 11p
                      6: .NH
                      7: Introduction
                      8: .PP
                      9: ``Mathematics is known in the trade as
                     10: .ul
                     11: difficult,
                     12: or
                     13: .ul
                     14: penalty, copy
                     15: because it is slower, more difficult,
                     16: and more expensive to set in type
                     17: than any other kind of copy normally
                     18: occurring in books and journals.''
                     19: [1]
                     20: .PP
                     21: One difficulty with mathematical text
                     22: is the multiplicity of characters,
                     23: sizes, and fonts.
                     24: An expression such as
                     25: .EQ
                     26: lim from {x-> pi /2} ( tan~x) sup{sin~2x}~=~1
                     27: .EN
                     28: requires an intimate mixture of roman, italic and greek letters, in three sizes,
                     29: and a special character or two.
                     30: (``Requires'' is perhaps the wrong word,
                     31: but mathematics has its own typographical conventions
                     32: which are quite different from those
                     33: of ordinary text.)
                     34: Typesetting such an expression by traditional methods
                     35: is still an essentially manual operation.
                     36: .PP
                     37: A second difficulty is the two dimensional character
                     38: of mathematics,
                     39: which the superscript and limits in the preceding example
                     40: showed in its simplest form.
                     41: This is carried further by
                     42: .EQ
                     43: a sub 0 + b sub 1 over
                     44:   {a sub 1 + b sub 2 over
                     45:     {a sub 2 + b sub 3 over
                     46:       {a sub 3 + ... }}}
                     47: .EN
                     48: .sp
                     49: and still further by 
                     50: .EQ
                     51: define emx "{e sup mx}"
                     52: define mab "{m sqrt ab}"
                     53: define sa "{sqrt a}"
                     54: define sb "{sqrt b}"
                     55: int dx over {a emx - be sup -mx} ~=~
                     56: left { lpile {
                     57:      1 over {2 mab} ~log~ {sa emx - sb} over {sa emx + sb}
                     58:    above
                     59:      1 over mab ~ tanh sup -1 ( sa over sb emx ) 
                     60:    above
                     61:      -1 over mab ~ coth sup -1 ( sa over sb emx )
                     62: }
                     63: .EN
                     64: These examples also show line-drawing, built-up characters like braces and radicals,
                     65: and a spectrum of positioning problems.
                     66: (Section 6 shows
                     67: what a user has to type to produce these
                     68: on our system.)

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