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       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/1.22.2/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
       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 `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

       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 `+' 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