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EQN(1)									EQN(1)

delim $$

       eqn  - typeset mathematics

       eqn [ option ...	 ] [ file ...  ]

       Eqn  is	a troff(1) preprocessor for typesetting mathematics on a type‐
       setter.	Usage is almost always

	      eqn file ... | troff

       If no files are specified, eqn reads from the standard input.  Eqn pre‐
       pares  output  for  the	typesetter named in the -Tdest option (default
       -Tutf; see troff(1)).  When run with other  preprocessor	 filters,  eqn
       usually comes last.

       A line beginning with .EQ marks the start of an equation; the end of an
       equation is marked by a line beginning  with  .EN.   Neither  of	 these
       lines  is altered, so they may be defined in macro packages to get cen‐
       tering, numbering, etc.	It is also possible to set two	characters  as
       `delimiters';  text  between  delimiters is also eqn input.  Delimiters
       may be set to characters x and y with the option	 -dxy  or  (more  com‐
       monly)  with  delim  xy between .EQ and .EN.  Left and right delimiters
       may be identical.  (They are customarily taken to be $font L  "$$"  )$.
       Delimiters  are	turned	off by All text that is neither between delim‐
       iters nor between .EQ and .EN is passed through untouched.

       Tokens within eqn are separated by spaces, tabs, newlines, braces, dou‐
       ble  quotes,  tildes or circumflexes.  Braces {} are used for grouping;
       generally speaking, anywhere a single character like  could  appear,  a
       complicated construction enclosed in braces may be used instead.	 Tilde
       represents a full space in the output, circumflex half as much.

       Subscripts and superscripts are produced with the keywords sub and sup.
       Thus makes $x sub i$, produces $a sub i sup 2$, and gives $e sup {x sup
       2 + y sup 2}$.

       Over makes fractions: yields $a over b$.

       Sqrt produces square roots: results in $1 over sqrt {ax sup 2 +bx+c}$ .

       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

       Left  and  right	 brackets,  braces, etc., of the right height are made
       with left and right: produces $left [ x sup 2 +	y  sup	2  over	 alpha
       right  ]	 ~=~1$.	 The right clause is optional.	Legal characters after
       left and right are braces, brackets, bars, c  and  f  for  ceiling  and
       floor,  and  ""	for  nothing  at  all  (useful	for  a right-side-only

       Vertical piles of things are made with pile, lpile, cpile,  and	rpile:
       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.

       Matrices	 are made with matrix: produces $matrix { lcol { x sub i above
       y sub 2 } ccol { 1 above 2 } }$.	 In addition,  there  is  rcol	for  a
       right-justified column.

       Diacritical  marks  are	made with prime, dot, dotdot, hat, tilde, bar,
       under, vec, dyad, and under: is $x sub 0 sup prime = f(t)  bar  +  g(t)
       under$, and is $x vec = y dyad$.

       Sizes  and  fonts can be changed with prefix operators size n, size ±n,
       fat, roman, italic, bold, or font n.  Size and  fonts  can  be  changed
       globally	 in  a document by gsize n and gfont n, or by the command-line
       arguments -sn and -fn.

       Normally subscripts and superscripts are reduced by 3 point sizes  from
       the  previous  size;  this  may be changed by the command-line argument

       Successive display arguments can be lined up.  Place  mark  before  the
       desired	lineup	point in the first equation; place lineup at the place
       that is to line up vertically in subsequent equations.

       Shorthands may be defined or existing keywords redefined	 with  define:
       thing  replacement  defines  a  new  token  called  thing which will be
       replaced by replacement whenever it appears thereafter.	The may be any
       character that does not occur in

       Keywords	 like  (  sum  ),  ( int ), ( inf ), and shorthands like (>=),
       (->), and ( != ) are recognized.	 Greek letters are spelled out in  the
       desired case, as in or Mathematical words like are made Roman automati‐
       cally.  Troff(1) four-character escapes like (☜) can be used  anywhere.
       Strings	enclosed  in  double  quotes " " are passed through untouched;
       this permits keywords to be entered as text, and can be used to	commu‐
       nicate with troff when all else fails.

	      font descriptions for PostScript


       troff(1), tbl(1)
       J. F. Ossanna and B. W. Kernighan, ``Troff User's Manual''.
       B.  W.  Kernighan  and  L.  L. Cherry, ``Typesetting Mathematics—User's
       Guide'', Unix Research System Programmer's Manual, Tenth Edition,  Vol‐
       ume 2.

       To  embolden digits, parens, etc., it is necessary to quote them, as in
       delim off

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