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EQN(1)                               General Commands Manual                               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 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

eqn searches for the file eqnrc in the directories given with the -M option first, then in
/usr/lib/groff/site-tmac, /usr/share/groff/site-tmac, and finally in  the  standard  macro
directory  /usr/share/groff/1.22.3/tmac.   If it exists, eqn processes it before the other
input files.  The -R option prevents this.

GNU eqn does not provide the functionality of neqn: it does  not  support  low-resolution,
typewriter-like devices (although it may work adequately for very simple input).

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, 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.  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  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.

-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.

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

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

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 ‘+cq and ‘−’ are centered; also it is the  ver‐
tical 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

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.

FILES
/usr/share/groff/1.22.3/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

*      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 ‘’ 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 ‘$’ and end with ‘$’  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 ‘’ elements.

In MathML mode, each digit of a numeric literal gets a separate ‘’ pair, and dec‐
imal points are tagged with ‘’.  This is allowed by the specification, but  inef‐
ficient.

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

COPYING

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

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

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

Groff Version 1.22.3                     28 January 2016                                   EQN(1)


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