Provided by: groff-base_1.22.4-10_amd64 bug


       eqn - format equations for troff or MathML


       eqn [-rvCNR] [-d xy] [-T name] [-M dir] [-f F] [-s n] [-p n] [-m n] [file ...]


       This  manual  page  describes  the GNU version of eqn, which is part of the groff document
       formatting system.  eqn compiles descriptions of equations  embedded  within  troff  input
       files  into  commands  that are understood by troff.  Normally, it should be invoked using
       the -e option of groff.  The syntax is quite compatible with Unix eqn.  The output of  GNU
       eqn cannot be processed with Unix troff; it must be processed with GNU troff.  If no files
       are given on the command line, the standard input is read.  A filename  of  -  causes  the
       standard input to be read.

       eqn searches for the file eqnrc in the directories given with the -M option first, then in
       /usr/lib/groff/site-tmac, /usr/share/groff/site-tmac, and finally in  the  standard  macro
       directory  /usr/share/groff/1.22.4/tmac.   If it exists, eqn processes it before the other
       input files.  The -R option prevents this.

       GNU eqn does not provide the functionality of neqn: it does  not  support  low-resolution,
       typewriter-like devices (although it may work adequately for very simple input).


       Whitespace is permitted between a command-line option and its argument.

       -dxy   Specify  delimiters  x  and  y for the left and right end, respectively, of in-line
              equations.  Any delim statements in the source file overrides this.

       -C     Recognize .EQ and .EN even when  followed  by  a  character  other  than  space  or
              newline.  Also, the statement ‘delim on’ is not handled specially.

       -N     Don't  allow  newlines within delimiters.  This option allows eqn to recover better
              from missing closing delimiters.

       -v     Print the version number.

       -r     Only one size reduction.

       -mn    The minimum point-size is n.  eqn  does  not  reduce  the  size  of  subscripts  or
              superscripts to a smaller size than n.

       -Tname The  output  is  for device name.  Normally, the only effect of this is to define a
              macro name with a value of 1; eqnrc uses this to  provide  definitions  appropriate
              for the output device.  However, if the specified device is “MathML”, the output is
              MathML markup rather than troff commands, and eqnrc is  not  loaded  at  all.   The
              default output device is ps.

       -Mdir  Search dir for eqnrc before the default directories.

       -R     Don't load eqnrc.

       -fF    This is equivalent to a gfont F command.

       -sn    This  is equivalent to a gsize n command.  This option is deprecated.  eqn normally
              sets equations at  whatever  the  current  point  size  is  when  the  equation  is

       -pn    This  says  that  subscripts  and  superscripts should be n points smaller than the
              surrounding text.  This option is deprecated.  Normally  eqn  sets  subscripts  and
              superscripts at 70% of the size of the surrounding text.


       Only the differences between GNU eqn and Unix eqn are described here.

       GNU eqn emits Presentation MathML output when invoked with the -T MathML option.

       GNU  eqn  sets  the input token "..."  as three periods or low dots, rather than the three
       centered dots of classic eqn.  To get three centered dots, write cdots or cdot cdot cdot.

       Most of the new features of the GNU eqn input language are based on TeX.  There  are  some
       references  to  the differences between TeX and GNU eqn below; these may safely be ignored
       if you do not know TeX.

   Controlling delimiters
       If not in compatibility mode, eqn recognizes

              delim on

       to restore the delimiters which have been previously disabled with a call to ‘delim  off’.
       If delimiters haven't been specified, the call has no effect.

   Automatic spacing
       eqn gives each component of an equation a type, and adjusts the spacing between components
       using that type.  Possible types are described in the table below.

       ordinary      an ordinary character such as ‘1’ or ‘xoperator      a large operator such as ‘Σ’
       binary        a binary operator such as ‘+’
       relation      a relation such as ‘=’
       opening       a opening bracket such as ‘(’
       closing       a closing bracket such as ‘)’
       punctuation   a punctuation character such as ‘,’
       inner         a subformula contained within brackets
       suppress      a type that suppresses automatic spacing adjustment

       Components of an equation get a type in one of two ways.

       type t e
              This yields an equation component that contains e but that has type t, where  t  is
              one of the types mentioned above.  For example, times is defined as

                     type "binary" \(mu

              The  name  of  the  type doesn't have to be quoted, but quoting protects from macro

       chartype t text
              Unquoted groups of characters are split up into individual characters, and the type
              of  each  character  is  looked  up;  this changes the type that is stored for each
              character; it says that the characters in text  from  now  on  have  type  t.   For

                     chartype "punctuation" .,;:

              would  make  the characters ‘.,;:’ have type punctuation whenever they subsequently
              appeared in an equation.  The type t can also be letter or digit;  in  these  cases
              chartype changes the font type of the characters.  See subsection “Fonts” below.

   New primitives
       big e  Enlarges  the  expression it modifies; intended to have semantics like CSS ‘large’.
              In troff output, the point size is increased by 5; in MathML output, the expression

                     <mstyle mathsize='big'>

       e1 smallover e2
              This is similar to over; smallover reduces the size of e1 and e2; it also puts less
              vertical space between  e1  or  e2  and  the  fraction  bar.   The  over  primitive
              corresponds  to the TeX \over primitive in display styles; smallover corresponds to
              \over in non-display styles.

       vcenter e
              This vertically centers e about the math axis.   The  math  axis  is  the  vertical
              position  about  which  characters such as ‘+’ and ‘−’ are centered; also it is the
              vertical position used for the bar of fractions.  For example, sum is defined as

                     { type "operator" vcenter size +5 \(*S }

              (Note that vcenter is silently ignored when generating MathML.)

       e1 accent e2
              This sets e2 as an accent over e1.  e2 is assumed to be at the correct height for a
              lowercase  letter;  e2  is  moved down according to whether e1 is taller or shorter
              than a lowercase letter.  For example, hat is defined as

                     accent { "^" }

              dotdot, dot, tilde, vec, and dyad are also defined using the accent primitive.

       e1 uaccent e2
              This sets e2 as an accent under e1.  e2 is assumed to be at the correct height  for
              a character without a descender; e2 is moved down if e1 has a descender.  utilde is
              pre-defined using uaccent as a tilde accent below the baseline.

       split "text"
              This has the same effect as simply


              but text is not subject to macro expansion because it is quoted; text is  split  up
              and the spacing between individual characters is adjusted.

       nosplit text
              This has the same effect as


              but  because text is not quoted it is subject to macro expansion; text is not split
              up and the spacing between individual characters is not adjusted.

       e opprime
              This is a variant of prime that acts as an operator on e.  It produces a  different
              result  from  prime in a case such as A opprime sub 1: with opprime the 1 is tucked
              under the prime as a subscript  to  the  A  (as  is  conventional  in  mathematical
              typesetting),  whereas with prime the 1 is a subscript to the prime character.  The
              precedence of opprime is the same as that of bar and under, which  is  higher  than
              that of everything except accent and uaccent.  In unquoted text a ' that is not the
              first character is treated like opprime.

       special text e
              This constructs a new object from e using a troff(1) macro named  text.   When  the
              macro  is called, the string 0s contains the output for e, and the number registers
              0w, 0h, 0d, 0skern, and 0skew contain the width, height, depth, subscript kern, and
              skew  of  e.   (The  subscript  kern of an object says how much a subscript on that
              object should be tucked in; the skew of an object says how far to the right of  the
              center  of  the object an accent over the object should be placed.)  The macro must
              modify 0s so that it outputs the desired result with  its  origin  at  the  current
              point,  and  increase  the  current horizontal position by the width of the object.
              The number registers must also be modified so that they correspond to the result.

              For example, suppose you wanted a construct that ‘cancels’ an expression by drawing
              a diagonal line through it.

                     define cancel 'special Ca'
                     .de Ca
                     .  ds 0s \
                     \D'l \\n(0wu -\\n(0hu-\\n(0du'\

              Then you could cancel an expression e with cancel { e }

              Here's a more complicated construct that draws a box round an expression:

                     define box 'special Bx'
                     .de Bx
                     .  ds 0s \
                     \D'l \\n(0wu+2n 0'\
                     \D'l 0 -\\n(0hu-\\n(0du-2n'\
                     \D'l -\\n(0wu-2n 0'\
                     \D'l 0 \\n(0hu+\\n(0du+2n'\
                     .  nr 0w +2n
                     .  nr 0d +1n
                     .  nr 0h +1n

       space n
              A  positive  value  of  the  integer  n  (in hundredths of an em) sets the vertical
              spacing before the equation, a negative value sets the spacing after the  equation,
              replacing  the  default values.  This primitive provides an interface to groff's \x
              escape (but with opposite sign).

              This keyword has no effect if the equation is part of a pic picture.

   Extended primitives
       col n { ... }
       ccol n { ... }
       lcol n { ... }
       rcol n { ... }
       pile n { ... }
       cpile n { ... }
       lpile n { ... }
       rpile n { ... }
              The integer value n (in hundredths of an em) increases the vertical spacing between
              rows,  using  groff's \x escape (the value has no effect in MathML mode).  Negative
              values are possible but have no effect.  If there is more than a single value given
              in a matrix, the biggest one is used.

       When  eqn is generating troff markup, the appearance of equations is controlled by a large
       number of parameters.  They have no effect  when  generating  MathML  mode,  which  pushes
       typesetting  and  fine  motions downstream to a MathML rendering engine.  These parameters
       can be set using the set command.

       set p n
              This sets parameter p to value n; n is an integer.  For example,

                     set x_height 45

              says that eqn should assume an x height of 0.45 ems.

              Possible parameters are as follows.  Values are in units of  hundredths  of  an  em
              unless  otherwise  stated.  These descriptions are intended to be expository rather
              than definitive.

                     eqn doesn't set anything at a smaller point-size than this.  The value is in

                     The  fat  primitive  emboldens an equation by overprinting two copies of the
                     equation horizontally offset by this amount.  This parameter is not used  in
                     MathML mode; instead, fat text uses

                            <mstyle mathvariant='double-struck'>

                     A fraction bar is longer by twice this amount than the maximum of the widths
                     of the numerator and denominator; in other words, it overhangs the numerator
                     and denominator by at least this amount.

                     When  bar  or under is applied to a single character, the line is this long.
                     Normally, bar or under produces a line whose length  is  the  width  of  the
                     object to which it applies; in the case of a single character, this tends to
                     produce a line that looks too long.

                     Extensible delimiters produced with the left and  right  primitives  have  a
                     combined  height  and  depth  of at least this many thousandths of twice the
                     maximum amount by which the sub-equation that the delimiters enclose extends
                     away from the axis.

                     Extensible  delimiters  produced  with  the left and right primitives have a
                     combined height and depth not less than the difference of twice the  maximum
                     amount  by  which  the sub-equation that the delimiters enclose extends away
                     from the axis and this amount.

                     This much horizontal space is inserted on each side of a fraction.

                     The width of subscripts and superscripts is increased by this amount.

                     This amount of space is automatically inserted after punctuation characters.

                     This amount of space is automatically inserted  on  either  side  of  binary

                     This amount of space is automatically inserted on either side of relations.

                     The height of lowercase letters without ascenders such as ‘x’.

                     The  height  above  the baseline of the center of characters such as ‘+’ and
                     ‘−’.  It is important that this value is correct for the font you are using.

                     This should set to the thickness of the \(ru character, or the thickness  of
                     horizontal lines produced with the \D escape sequence.

              num1   The over command shifts up the numerator by at least this amount.

              num2   The smallover command shifts up the numerator by at least this amount.

              denom1 The over command shifts down the denominator by at least this amount.

              denom2 The smallover command shifts down the denominator by at least this amount.

              sup1   Normally superscripts are shifted up by at least this amount.

              sup2   Superscripts  within superscripts or upper limits or numerators of smallover
                     fractions are shifted up by at least this amount.  This is usually less than

              sup3   Superscripts  within  denominators  or  square  roots or subscripts or lower
                     limits are shifted up by at least this amount.  This is  usually  less  than

              sub1   Subscripts are normally shifted down by at least this amount.

              sub2   When  there  is both a subscript and a superscript, the subscript is shifted
                     down by at least this amount.

                     The baseline of a superscript is no more than this much amount below the top
                     of the object on which the superscript is set.

                     The  baseline  of  a subscript is at least this much below the bottom of the
                     object on which the subscript is set.

                     The baseline of an upper limit is at least this much above the  top  of  the
                     object on which the limit is set.

                     The  baseline of a lower limit is at least this much below the bottom of the
                     object on which the limit is set.

                     The bottom of an upper limit is at least this much  above  the  top  of  the
                     object on which the limit is set.

                     The  top  of  a  lower  limit  is at least this much below the bottom of the
                     object on which the limit is set.

                     This much vertical space is added above and below limits.

                     The baselines of the rows in a pile or matrix are normally this  far  apart.
                     In most cases this should be equal to the sum of num1 and denom1.

                     The midpoint between the top baseline and the bottom baseline in a matrix or
                     pile is shifted down by this much from the axis.  In most cases this  should
                     be equal to axis_height.

                     This much space is added between columns in a matrix.

                     This much space is added at each side of a matrix.

                     If  this  is  non-zero, lines are drawn using the \D escape sequence, rather
                     than with the \l escape sequence and the \(ru character.

                     The amount by which the height of the equation  exceeds  this  is  added  as
                     extra space before the line containing the equation (using \x).  The default
                     value is 85.

                     The amount by which the depth of the equation exceeds this is added as extra
                     space  after the line containing the equation (using \x).  The default value
                     is 35.

              nroff  If this is non-zero,  then  ndefine  behaves  like  define  and  tdefine  is
                     ignored,  otherwise tdefine behaves like define and ndefine is ignored.  The
                     default value is 0 (This is typically changed to 1 by the eqnrc file for the
                     ascii, latin1, utf8, and cp1047 devices.)

              A  more precise description of the role of many of these parameters can be found in
              Appendix H of The TeXbook.

       Macros can take arguments.  In a macro body, $n where n is between 1 and 9, is replaced by
       the  nth  argument  if  the  macro  is  called  with  arguments;  if  there are fewer than
       n arguments, it is replaced by nothing.  A word containing a left  parenthesis  where  the
       part  of the word before the left parenthesis has been defined using the define command is
       recognized as a macro call with arguments; characters following the left parenthesis up to
       a  matching  right  parenthesis  are  treated  as comma-separated arguments; commas inside
       nested parentheses do not terminate an argument.

       sdefine name X anything X
              This is like the define  command,  but  name  is  not  recognized  if  called  with

       include "file"
       copy "file"
              Include  the  contents  of  file  (include  and  copy are synonyms).  Lines of file
              beginning with .EQ or .EN are ignored.

       ifdef name X anything X
              If name has been defined by define (or has been automatically defined because  name
              is  the  output  device) process anything; otherwise ignore anything.  X can be any
              character not appearing in anything.

       undef name
              Remove definition of name, making it undefined.

       Besides the macros mentioned above, the following definitions are available: Alpha,  Beta,
       ...,  Omega  (this  is the same as ALPHA, BETA, ..., OMEGA), ldots (three dots on the base
       line), and dollar.

       eqn normally uses at least two fonts to set an equation: an italic font for letters, and a
       roman  font for everything else.  The existing gfont command changes the font that is used
       as the italic font.  By default this is I.  The font that is used as the roman font can be
       changed using the new grfont command.

       grfont f
              Set the roman font to f.

       The  italic  primitive uses the current italic font set by gfont; the roman primitive uses
       the current roman font set by grfont.  There is also a new gbfont command,  which  changes
       the  font  used  by  the  bold  primitive.   If  you  only  use the roman, italic and bold
       primitives to changes fonts within an equation, you can change all the fonts used by  your
       equations just by using gfont, grfont and gbfont commands.

       You  can control which characters are treated as letters (and therefore set in italics) by
       using the chartype command described above.  A type of letter causes a character to be set
       in italic type.  A type of digit causes a character to be set in roman type.


              Initialization file.


       MathML   is   designed   on  the  assumption  that  it  cannot  know  the  exact  physical
       characteristics of the media and devices on which  it  will  be  rendered.   It  does  not
       support fine control of motions and sizes to the same degree troff does.  Thus:

       *      eqn parameters have no effect on the generated MathML.

       *      The  special, up, down, fwd, and back operations cannot be implemented, and yield a
              MathML ‘<merror>’ message instead.

       *      The vcenter keyword is silently ignored, as centering  on  the  math  axis  is  the
              MathML default.

       *      Characters  that  eqn over troff sets extra large – notably the integral sign – may
              appear too small and need to have their ‘<mstyle>’ wrappers adjusted by hand.

       As in its troff mode, eqn in MathML mode leaves the .EQ and .EN delimiters  in  place  for
       displayed  equations, but emits no explicit delimiters around inline equations.  They can,
       however, be recognized as strings that begin with ‘<math>’ and end with ‘</math>’  and  do
       not cross line boundaries.

       See section “Bugs” below for translation limits specific to eqn.


       Inline  equations  are set at the point size that is current at the beginning of the input

       In MathML mode, the mark and lineup features don't  work.   These  could,  in  theory,  be
       implemented with ‘<maligngroup>’ elements.

       In  MathML  mode,  each  digit  of a numeric literal gets a separate ‘<mn></mn>’ pair, and
       decimal points are tagged with ‘<mo></mo>’.  This is allowed  by  the  specification,  but


       groff(1), troff(1), pic(1), groff_font(5), The TeXbook