eqn - format equations for troff or MathML


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


   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/1.22.3/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).


   It is possible to have whitespace between a command line option and its

   -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 encountered.

   -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:

          ordinary an ordinary character such as '1' or '

          operator     a large operator such as '';

          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 spacing
                       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 expansion.

   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 example,

                 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 the Fonts subsection.

   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 uses

                 <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 '+cq 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

                 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

   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 points.

                 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

                 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 operators.

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

                 The height of lowercase letters without ascenders such as

                 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

          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

          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 sup1.

          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 sup2.

          sub1   Subscripts are normally shifted down  by  at  least  this

          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

                 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 n-th 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 arguments.

   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 the BUGS section for translation limits specific to eqn.


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

   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 inefficient.


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


   Copyright  1989-2014 Free Software Foundation, Inc.

   Permission  is  granted  to make and distribute verbatim copies of this
   manual provided the copyright notice and  this  permission  notice  are
   preserved on all copies.

   Permission  is granted to copy and distribute modified versions of this
   manual under the conditions for verbatim  copying,  provided  that  the
   entire  resulting  derived  work  is  distributed  under the terms of a
   permission notice identical to this one.

   Permission is granted to  copy  and  distribute  translations  of  this
   manual  into  another language, under the above conditions for modified
   versions, except  that  this  permission  notice  may  be  included  in
   translations approved by the Free Software Foundation instead of in the
   original English.


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