.2C $gsize 9$.nr PS 9.nr VS 11p.NHIntroduction.PP``Mathematics is known in the trade as.uldifficult,or.ulpenalty, copybecause it is slower, more difficult,and more expensive to set in typethan any other kind of copy normallyoccurring in books and journals.''[1].PPOne difficulty with mathematical textis the multiplicity of characters,sizes, and fonts.An expression such as.EQlim from {x-> pi /2} ( tan~x) sup{sin~2x}~=~1.ENrequires an intimate mixture of roman, italic and greek letters, in three sizes,and a special character or two.(``Requires'' is perhaps the wrong word,but mathematics has its own typographical conventionswhich are quite different from thoseof ordinary text.)Typesetting such an expression by traditional methodsis still an essentially manual operation..PPA second difficulty is the two dimensional characterof mathematics,which the superscript and limits in the preceding exampleshowed in its simplest form.This is carried further by.EQa sub 0 + b sub 1 over  {a sub 1 + b sub 2 over    {a sub 2 + b sub 3 over      {a sub 3 + ... }}}.EN.spand still further by .EQdefine emx "{e sup mx}"define mab "{m sqrt ab}"define sa "{sqrt a}"define sb "{sqrt b}"int dx over {a emx - be sup -mx} ~=~left { lpile {     1 over {2 mab} ~log~ {sa emx - sb} over {sa emx + sb}   above     1 over mab ~ tanh sup -1 ( sa over sb emx )    above     -1 over mab ~ coth sup -1 ( sa over sb emx )}.ENThese examples also show line-drawing, built-up characters like braces and radicals,and a spectrum of positioning problems.(Section 6 showswhat a user has to type to produce theseon our system.)