Updated: 2021/Apr/14

EQN(1)                      General Commands Manual                     EQN(1)

NAME
eqn - format equations for troff

SYNOPSIS
eqn [ -rvCNR ] [ -dxy ] [ -Tname ] [ -Mdir ] [ -fF ] [ -sn ] [ -pn ] [ -mn ]
[ 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 will be read.  A filename of - will cause the

eqn searches for the file eqnrc in the directories given with the -M
option first, then in /usr/share/tmac, /usr/share/tmac, and finally in
the standard macro directory /usr/share/tmac.  If it exists, eqn will
process 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

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 newline.

-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 will not reduce the size of
subscripts or superscripts to a smaller size than n.

-Tname The output is for device name.  The only effect of this is to
define a macro name with a value of 1.  Typically eqnrc will use
this to provide definitions appropriate for the output device.
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 will normally set 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 makes 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.

Most of the new features of GNU eqn 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 <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   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 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
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 }

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 will be moved down
according if 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 will be
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 will be split up and the spacing between individual

nosplit text
This has the same effect as

"text"

but because text is not quoted it will be subject to macro
expansion; text will not be split up and the spacing between
individual characters will not be 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 will be tucked under the
prime as a subscript to the A (as is conventional in
mathematical typesetting), whereas with prime the 1 will be 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 will be 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 will contain the
output for e, and the number registers 0w, 0h, 0d, 0skern, and
0skew will 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 will output 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 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
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.
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
The appearance of equations is controlled by a large number of
parameters.  These 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 will not 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.

over_hang
A fraction bar will be longer by twice this amount than
the maximum of the widths of the numerator and
denominator; in other words, it will overhang the
numerator and denominator by at least this amount.

accent_width
When bar or under is applied to a single character, the
line will be 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 will 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 will 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 will shift up the numerator by at least
this amount.

num2   The smallover command will shift up the numerator by at
least this amount.

denom1 The over command will shift down the denominator by at
least this amount.

denom2 The smallover command will shift down the denominator by
at least this amount.

sup1   Normally superscripts will be shifted up by at least this
amount.

sup2   Superscripts within superscripts or upper limits or
numerators of smallover fractions will be 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 will be shifted up by at least
this amount.  This is usually less than sup2.

sub1   Subscripts will normally be shifted down by at least this
amount.

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

sup_drop
The baseline of a superscript will be 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 will be 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 will be 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 will be 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 will be 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 will be at least this much below
the bottom of the object on which the limit is set.

big_op_spacing5
This much vertical space will be added above and below
limits.

baseline_sep
The baselines of the rows in a pile or matrix will
normally be 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 will be shifted down by this
much from the axis.  In most cases this should be equal
to axis_height.

column_sep
This much space will be added between columns in a
matrix.

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

draw_lines
If this is non-zero, lines will be 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 will be 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 will be 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 will behave like define
and tdefine will be ignored, otherwise tdefine will
behave like define and ndefine will be 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, will be replaced by the n-th argument if the macro is called
with arguments; if there are fewer than n arguments, it will be
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 will be recognized as a macro call with arguments;
characters following the left parenthesis up to a matching right
parenthesis will be 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 will not be 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 will be 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 will cause a character to be set in italic type.  A type of
digit will cause a character to be set in roman type.

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

BUGS
Inline equations will be set at the point size that is current at the
beginning of the input line.

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