EQN(1)                                                     EQN(1)

              delim $$

          eqn  - typeset mathematics

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

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

               eqn file ... | troff

          If no files are specified, eqn reads from the standard
          input.  Eqn prepares 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 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 L "$$" )$.  Delimiters are turned off by `delim
          off'.  All text that is neither between delimiters nor
          between .EQ and .EN is passed through untouched.

          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

          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 $e sup {x sup 2 + y sup 2}$.

          Over makes fractions: `a over b' yields $a over b$.

          Sqrt produces 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

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     EQN(1)                                                     EQN(1)

          i$ is made with `lim from {n -> inf} sum from 0 to n x sub

          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-

          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 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 -pn.

          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

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     EQN(1)                                                     EQN(1)

          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.

          /sys/lib/troff/font/devutf  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, Volume 2.

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

     Page 3                       Plan 9             (printed 4/18/24)