eqn - format equations for troff or MathML

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EQN(1) EQN(1)

eqn - format equations for troff or MathML

eqn [-rvCNR] [-d xy] [-T name] [-M dir] [-f F] [-s n] [-p n] [-m n]

It is possible to have whitespace between a command line option and its

This manual page describes the GNU version of eqn, which is part of the
groff document formatting system. eqn compiles descriptions of equa‐
tions embedded within troff input files into commands that are under‐
stood 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/1.21/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 ade‐
quately for very simple input).

-dxy Specify delimiters x and y for the left and right end, respec‐
tively, 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 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 depre‐
cated. 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 cen‐
tered 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.

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 adjust‐

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 exam‐
ple, times is defined as

type "binary" \(mu

The name of the type doesn't have to be quoted, but quoting pro‐
tects from macro expansion.

chartype t text
Unquoted groups of characters are split up into individual char‐
acters, 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

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 accord‐
ing 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 charac‐
ters 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 charac‐
ter 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 out‐
put 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 sub‐
script 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 cur‐
rent 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 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 ver‐
tical 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 down‐
stream 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 hun‐
dredths 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

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 denomina‐
tor 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 sub‐
scripts 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 super‐
script 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 nor‐
mally 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 parame‐
ters 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 noth‐
ing. 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 ter‐
minate 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.

It is not advisable to use the hash character (#) as a delimiter for
in-line equations in eqn since tbl(1) uses a macro called .T#, causing
a clash.

/usr/share/groff/1.21/tmac/eqnrc 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 imple‐
mented, and yield a MathML `' 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
`' wrappers adjusted by hand.

As in its troff mode, eqn in MathML mode leaves the .EQ and .EN delim‐
iters in place for displayed equations, but emits no explicit delim‐
iters 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.

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 decimal points are tagged with `'. This is
allowed by the specification, but inefficient.

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

Groff Version 1.21 31 December 2010 EQN(1)