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     EQN(1)                                                     EQN(1)

              delim $$

     NAME
          eqn, neqn, checkeq - typeset mathematics

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

          neqn [ option ... ] [ file ... ]

          checkeq [ file ... ]

     DESCRIPTION
          Eqn is a troff(1) preprocessor for typesetting mathematics
          on a phototypesetter, neqn on terminals.  Usage is almost
          always

               eqn file ... | troff
               neqn file ... | nroff

          If no files are specified, these programs read from the
          standard input.  Eqn prepares output for the typesetter
          named in the -Tdest option (Mergenthaler Linotron 202
          default, 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 centering, 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
          commonly) with delim xy between .EQ and .EN.  Left and right
          delimiters may be identical.  (They are customarily taken to
          be $font CW "$$" )$.  Delimiters are turned off by `delim
          off'.  All text that is neither between delimiters nor
          between .EQ and .EN is passed through untouched.

          Checkeq reports missing or unbalanced delimiters and .EQ/.EN
          pairs.

          Tokens within eqn are separated by spaces, tabs, newlines,
          braces, double quotes, tildes or circumflexes.  Braces {}
          are used for grouping; generally speaking, anywhere a single
          character like `x' could appear, a complicated construction
          enclosed in braces may be used instead.  Tilde `~' repre-
          sents a full space in the output, circumflex `^' half as
          much.

          WARNING to users of the on-line manual.  Unless your termi-
          nal understands half-spacing, the examples below will be

     EQN(1)                                                     EQN(1)

          nearly unreadable.  To get a well printed copy execute man
          -t eqn | lp.

          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' yields $a over b$.

          sqrt makes square roots: `1 over sqrt {ax sup 2 +bx+c}'
          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 `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.  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 bracket).

          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 ele-
          ments in a pile.  lpile left-justifies, pile and cpile cen-
          ter, with different vertical spacing, and rpile right justi-
          fies.

          Matrices are made with matrix: `matrix { lcol { x sub i
          above y sub 2 } ccol { 1 above 2 } }' 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: `x sub 0 sup prime
          = f(t) bar + g(t) under' is $x sub 0 sup prime = f(t) bar +
          g(t) under$, and `x vec = y dyad' is $x vec = y dyad$.

          Sizes and font 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 -pn.

     EQN(1)                                                     EQN(1)

          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 subse-
          quent equations.

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

          Keywords like `sum' ( sum ) `int' ( int ) `inf' ( inf ) and
          shorthands like `>=' (>=) `->' (->), and `!=' ( != ) are
          recognized.  Greek letters are spelled out in the desired
          case, as in `alpha' or `GAMMA'.  Mathematical words like
          `sin', `cos', `log' are made Roman automatically.  Troff(1)
          four-character escapes like `\(lh' () 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 communicate with troff when all else fails.

     SEE ALSO
          troff(1), tbl(1), ms(6), eqnchar(6), doctype(1)
          B. W. Kernighan and L. L. Cherry, `Typesetting Mathematics-
          User's Guide', this manual, Volume 2
          J. F. Ossanna and B. W. Kernighan, `NROFF/TROFF User's Man-
          ual', ibid.

     BUGS
          To embolden digits, parens, etc., it is necessary to quote
          them, as in `bold "12.3"'.  delim off