# eqn

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
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/1.18.1.1/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
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 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.

-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 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 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 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
characters will be adjusted.

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
..

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"
Include the contents of file.  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.

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/groff/1.18.1.1/tmac/eqnrc
Initialization file.

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

Groff Version 1.18.1.1          05 October 2001                         EQN(1)`