delim $$

     eqn  -  typeset mathematics

     eqn [ file ] ...

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

          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

     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

     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.

     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)

     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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