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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...]

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

DESCRIPTION
       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/1.21/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).

OPTIONS
       -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  new-
	      line.

       -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  super-
	      scripts 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  encoun-
	      tered.

       -pn    This says that subscripts and superscripts should be n points smaller than the sur-
	      rounding text.  This option is deprecated.  Normally eqn sets subscripts and super-
	      scripts 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 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.

   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 `>';

	      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 char-
	      acter; 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  corre-
	      sponds 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 posi-
	      tion about which characters such as `+' and `-' are centered; also it is the verti-
	      cal 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

		     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 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  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 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.

		     .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 spac-
	      ing 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.

   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 type-
       setting 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.

	      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 denominator 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 subscripts or lower lim-
		     its 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 superscript 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 normally 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 parameters 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  argu-
       ments,  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  recog-
       nized  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 argu-
	      ments.

       include "file"
       copy "file"
	      Include the contents of file (include and copy are synonyms).  Lines of file begin-
	      ning 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  primi-
       tives to changes fonts within an equation, you can change all the fonts used by your equa-
       tions 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.

INTERACTION WITH TBL
       It is not advisable to use the hash character (#) as a delimiter for in-line equations  in
       eqn since tbl(1) uses a macro called .T#, causing a clash.

FILES
       /usr/share/groff/1.21/tmac/eqnrc  Initialization file.

MATHML MODE LIMITATIONS
       MathML  is  designed on the assumption that it cannot know the exact physical characteris-
       tics of the media and devices on which it will be rendered.  It does not support fine con-
       trol 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.

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 dec-
       imal points are tagged with `<mo></mo>'.  This is allowed by the specification, but  inef-
       ficient.

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

Groff Version 1.21			 31 December 2010				   EQN(1)
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