EQN(1)                      General Commands Manual                     EQN(1)

       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 equa-
       tions embedded within troff input files into commands that  are  under-
       stood  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 in-
       put 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 in-
       put 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  ade-
       quately 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, respec-
              tively, 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  depre-
              cated.   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 cen-
       tered 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 'x'
       operator      a large operator such as '<Sigma>'
       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 exam-
              ple, times is defined as

                     type "binary" \(mu

              The name of the type doesn't have to be quoted, but quoting pro-
              tects from macro expansion.

       chartype t text
              Unquoted groups of characters are split up into individual char-
              acters, 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 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 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 '+' 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 accord-
              ing 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 ac-
              cent 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  charac-
              ters 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 op-
              prime sub 1:  with  opprime the 1 is tucked under the prime as a
              subscript to the A (as is conventional in mathematical  typeset-
              ting),  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 charac-
              ter 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 out-
              put  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 sub-
              script 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 cur-
              rent 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 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 ver-
              tical 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 down-
       stream 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 hun-
              dredths 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;  in-
                     stead, 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 denomina-
                     tor 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 ex-
                     tends 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 nu-
                     merators 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 sub-
                     scripts 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  super-
                     script 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  nor-
                     mally 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 parame-
              ters 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 ar-
       guments; if there are fewer than n arguments, it is replaced  by  noth-
       ing.   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 ter-
       minate 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  us-
       ing the new grfont command.

       grfont f
              Set the roman font to f.

       The italic primitive uses the current italic font set by gfont; the ro-
       man primitive uses the current roman font set by grfont.  There is also
       a  new  gbfont  command, which changes the font used by the bold primi-
       tive.  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 imple-
              mented, 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  delim-
       iters  in  place  for displayed equations, but emits no explicit delim-
       iters 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  be-
       ginning 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

groff 1.22.4                     21 March 2020                          EQN(1)
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