    delim $$

    NAME
         eqn  -  typeset mathematics

    SYNOPSIS
         eqn [ file ] ...

    DESCRIPTION
         Eqn  is a troff(I) preprocessor for typesetting mathematics
         on the Graphics Systems phototypesetter.   Usage  is  almost
         always

              eqn file ... | troff

         If  no  files are specified, eqn reads from the standard in-
         put.  A line beginning with ``.EQ'' marks the  start  of  an
         equation;  the end of an equation is marked by a line begin-
         ning with ``.EN''.  Neither of these lines is altered or de-
         fined by eqn, so you can define them yourself to get center-
         ing, numbering, etc.  All other lines are  treated  as  com-
         ments, and passed through untouched.

         Spaces,  tabs,  newlines,  braces,  double quotes, tilde and
         circumflex are the only delimiters.  Braces ``{}'' are  used
         for  grouping.   Use  tildes ``~'' to get extra spaces in an
         equation.

         Subscripts and superscripts are produced with  the  keywords
         sub  and  sup.   Thus x sub i makes $x sub i$, a sub i sup 2
         produces $a sub i sup 2$, and e sup {x sup 2 + y sup 2}
         gives  $e sup {x sup 2 + y sup 2}$.  Fractions are made with
         over. a over b is $a over b$ and 1 over sqrt {ax sup 2
         +bx+c}  is  $1  over  sqrt  {ax  sup 2 +bx+c}$ .  sqrt makes
         square roots.

         The keywords from and to introduce lower and upper limits on
         arbitrary  things: $lim from {n-> inf} sum from 0 to n x sub
         i$ is made with lim from {n-> inf} sum from 0 to n x sub i.
         Left  and  right brackets, braces, etc., of the right height
         are made with left and right: left [ x sup 2 + y sup 2 over
         alpha right ] ~=~1 produces $left [ x sup 2 + y sup 2 over
         alpha right ] ~=~1$.  The right clause is optional.

         Vertical piles of things are made with pile, lpile, cpile,
         and  rpile: pile {a above b above c} produces $pile {a above
         b above c}$.  There can be an arbitrary number  of  elements
         in  a  pile.   lpile  left-justifies, pile and cpile center,
         with different vertical spacing, and rpile right  justifies.

         Diacritical marks are made with dot, dotdot, hat, bar: x dot
         = f(t) bar is $x dot = f(t) bar$.  Default sizes  and  fonts
         can be changed with size n and various of roman, italic, and
         bold.

         Keywords like sum ( sum ) int ( int ) inf ( inf ) and short-
         hands  like  >=  (>=)  ->  (->),  != ( != ), are recognized.
         Spell out Greek letters in the desired case,  as  in  alpha,
         GAMMA.  Mathematical words like sin, cos, log are made Roman
         automatically.  Troff(I) four-character escapes  like  \(ci
         (O) can be used anywhere.  Strings enclosed in double quotes

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    EQN(I)                       2/22/74                       EQN(I)

         "..."  are passed through untouched.

    SEE ALSO
         A System for Typesetting Mathematics (Computer Science Tech-
         nical Report #17, Bell Laboratories, 1974.)
         TROFF Users' Manual (internal memorandum)
         TROFF Made Trivial (internal memorandum)
         troff(I), neqn(I)

    BUGS
         Undoubtedly.   Watch  out  for  small or large point sizes -
         it's tuned too well for size 10.  Be cautious  if  inserting
         horizontal or vertical motions, and of backslashes in gener-
         al.  delim off

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