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EQN(1)									EQN(1)

NAME
       eqn - format equations for troff or MathML

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

DESCRIPTION
       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
       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/1.22.2/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  ade‐
       quately for very simple input).

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

       -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.

USAGE
       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:

	      ordinary	   an ordinary character such as `1' or `x';

	      operator	   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	   spacing that suppresses automatic  spacing  adjust‐
			   ment.

       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 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 `+' 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
	      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

		     text

	      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

		     "text"

	      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 opprime sub 1: with opprime the 1 is tucked under the prime as
	      a	 subscript  to the A (as is conventional in mathematical type‐
	      setting), 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.

		     .EQ
		     define cancel 'special Ca'
		     .EN
		     .de Ca
		     .	ds 0s \
		     \Z'\\*(0s'\
		     \v'\\n(0du'\
		     \D'l \\n(0wu -\\n(0hu-\\n(0du'\
		     \v'\\n(0hu'
		     ..

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

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

		     .EQ
		     define box 'special Bx'
		     .EN
		     .de Bx
		     .	ds 0s \
		     \Z'\h'1n'\\*(0s'\
		     \Z'\
		     \v'\\n(0du+1n'\
		     \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'\
		     '\
		     \h'\\n(0wu+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‐
	      ture.

   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.

   Customization
       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.

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

	      fat_offset
		     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'>

	      over_hang
		     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.

	      accent_width
		     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.

	      delimiter_factor
		     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.

	      delimiter_shortfall
		     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.

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

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

	      thin_space
		     This  amount  of  space  is  automatically inserted after
		     punctuation characters.

	      medium_space
		     This amount of space is automatically inserted on	either
		     side of binary operators.

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

	      x_height
		     The height of lowercase letters without ascenders such as
		     `x'.

	      axis_height
		     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.

	      default_rule_thickness
		     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 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
		     amount.

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

	      sup_drop
		     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.

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

	      big_op_spacing1
		     The  baseline  of	an  upper  limit is at least this much
		     above the top of the object on which the limit is set.

	      big_op_spacing2
		     The baseline of a lower limit is at least this much below
		     the bottom of the object on which the limit is set.

	      big_op_spacing3
		     The  bottom of an upper limit is at least this much above
		     the top of the object on which the limit is set.

	      big_op_spacing4
		     The top of a lower limit is at least this much below  the
		     bottom of the object on which the limit is set.

	      big_op_spacing5
		     This much vertical space is added above and below limits.

	      baseline_sep
		     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.

	      shift_down
		     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.

	      column_sep
		     This much space is added between columns in a matrix.

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

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

	      body_height
		     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.

	      body_depth
		     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
       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 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.

   Fonts
       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.

FILES
       /usr/share/groff/1.22.2/tmac/eqnrc
	      Initialization file.

MATHML MODE LIMITATIONS
       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 the BUGS section for translation limits specific to eqn.

BUGS
       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.

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

Groff Version 1.22.2	       07 February 2013				EQN(1)
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