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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] [file ...]

DESCRIPTION
This manual page describes the GNU version of eqn, which is part of the groff document for‐
matting 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 op‐
tion 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 di‐
rectory /usr/share/groff/1.22.4/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, type‐
writer-like devices (although it may work adequately for very simple input).

OPTIONS
Whitespace is permitted between a command-line option and its argument.

-dxy Specify delimiters x and y for the left and right end, respectively, of in-line equa‐
tions. 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 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 encountered.

-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 cen‐
tered 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 ref‐
erences 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 described in the table below.

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 a type 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 expan‐
sion.

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 ap‐
peared in an equation. The type t can also be letter or digit; in these cases char‐‐
type changes the font type of the characters. See subsection “Fonts” below.

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 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 posi‐
tion 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 re‐
sult 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 op‐‐
prime 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 out‐
puts 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 (the value has no effect in MathML mode). Negative val‐
ues 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 typeset‐
ting 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 defin‐
itive.

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 equa‐
tion 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 com‐
bined 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 com‐
bined 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 opera‐
tors.

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 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 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 ob‐
ject 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 ob‐
ject 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 ob‐
ject 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 Ap‐
pendix 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 nth 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 charac‐
ter 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 us‐
ing 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/1.22.4/tmac/eqnrc
Initialization file.

MATHML MODE LIMITATIONS
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 ap‐
pear 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 dis‐
played equations, but emits no explicit delimiters around inline equations. They can, how‐
ever, be recognized as strings that begin with ‘<math>’ and end with ‘</math>’ and do not
cross line boundaries.

See section “Bugs” below 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 imple‐
mented 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.

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

groff 1.22.4 23 March 2022 EQN(1)