# eqn(1) — Linux manual page

eqn(1)                     General Commands Manual                    eqn(1)


## Name         top

       eqn - format equations for groff or MathML


## Synopsis         top

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

eqn --help

eqn -v
eqn --version


## Description         top

       The GNU version of eqn is part of the groff(7) document formatting
system.  eqn compiles descriptions of equations embedded in roff(7)
input files into commands that are understood by troff(1).  Normally,
it should be invoked using the -e option of groff(1).  Its syntax is
compatible with AT&T eqn, its output cannot be processed with AT&T
troff; it must be processed with GNU troff.  If no file operands are
given on the command line, or if file is “-”, the standard input

Unless the -R option is given, eqn searches for the file eqnrc in the
directories given with the -M option first, then in /usr/local/lib/
groff/site-tmac, /usr/local/share/groff/site-tmac, and finally in the
standard macro directory /usr/local/share/groff/1.22.4/tmac.  If it
exists, eqn processes it before the other input files.

Only the differences between GNU eqn and AT&T eqn are described in
this document.  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.

Three points are worth special note.

•      GNU eqn emits Presentation MathML output when invoked with the
“-T MathML” option.

•      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).

•      GNU eqn sets the input token “...” as three periods or low
dots, rather than the three centered dots of AT&T eqn.  To get
three centered dots, write cdots or “cdot cdot cdot”.

Controlling delimiters
If not in compatibility mode, eqn recognizes
delim on
as a command 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 spac‐
ing 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 without 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 ex‐
ample, times is defined as follows.

type "binary" \(mu

The name of the type doesn't have to be quoted, but quoting it
protects it 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 ex‐
ample,

chartype "punctuation" .,;:

would make the characters “.,;:” have type punctuation when‐
ever 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 subsection “Fonts” be‐
low.

New primitives
big e  Enlarges the expression it modifies; intended to have seman‐
tics like CSS “large”.  In troff output, the point size is in‐
creased by 5; in MathML output, the expression uses

<mstyle mathsize='big'>

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; it is also the vertical position used
for fraction bars.  For example, sum is defined as follows.

{ type "operator" vcenter size +5 \(*S }

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 ac‐
cording to whether e1 is taller or shorter than a lowercase
letter.  For example, hat is defined as follows.

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

nosplit text
This has the same effect as

"text"

but because text is not quoted it is subject to macro expan‐
sion; text is not split up and the spacing between individual

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
typesetting), 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 neutral apos‐
trophe (') that is not the first character on the input line
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 indicates how
much a subscript on that object should be “tucked in”, or
placed to the left relative to a non-subscripted glyph of the
same size.  The skew of an object is how far to the right of
the center of the object an accent over it 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'
..

You could then cancel an expression e with “cancel { e }”.

Here's a more complicated construct that draws a box around 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 de‐
fault 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 pos‐
sible 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 typesetting 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, where 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 descrip‐
tions are intended to be expository rather than definitive.

minimum_size
eqn won'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; in‐

<mstyle mathvariant='double-struck'>

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 denomi‐
nator 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 ex‐
tends 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 ex‐
tends 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 ei‐
ther side of binary operators.

thick_space
This amount of space is automatically inserted on ei‐
ther 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 charac‐
ters 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] charac‐
ter, 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 nu‐
merators 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 super‐
script 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 be‐
low 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 lim‐
its.

baseline_sep
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.

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 es‐
cape 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 param‐
eters 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 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 fol‐
lowing the left parenthesis up to a matching right parenthesis are
treated as comma-separated arguments.  Commas inside nested parenthe‐
ses 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 character not appear‐
ing 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 baseline), 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 AT&T eqn
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 there‐
fore 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.


## Options         top

       --help displays a usage message, while -v and --version show version
information; all exit afterward.

-C     Recognize .EQ and .EN even when followed by a character other
than space or newline, and do not handle the “delim on”
statement specially.

-d xy  Specify delimiters x and y for the left and right ends,
respectively, of inline equations.  Any delim statements in
the source file override this.

-f F   This is equivalent to a “gfont F” command.

-m n   Set the minimum point size to n.  eqn will not reduce the size
of subscripts or superscripts to a smaller size than n.

-M dir Search dir for eqnrc before the default directories.

-N     Don't allow newlines within delimiters.  This option allows
eqn to recover better from missing closing delimiters.

-p n   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.

-r     Only one size reduction.

-s n   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.

-T name
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.


## Files         top

       /usr/local/share/groff/1.22.4/tmac/eqnrc
Initialization file.


## MathML Mode Limitations         top

       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 sets extra large in troff mode—notably the
integral sign—may appear too small and need to have their

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 section “Bugs” below for translation limits specific to eqn.


## Bugs         top

       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 “<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.


       “Typesetting Mathematics—User's Guide” (2nd edition); Computing
Science Technical Report #17; Brian W. Kernighan, Lorinda L. Cherry;
AT&T Bell Laboratories; 1978.

The TeXbook; Donald E. Knuth; Addison-Wesley Professional; 1984.

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


## COLOPHON         top

       This page is part of the groff (GNU troff) project.  Information
about the project can be found at
⟨http://www.gnu.org/software/groff/⟩.  If you have a bug report for
this manual page, see ⟨http://www.gnu.org/software/groff/⟩.  This
page was obtained from the project's upstream Git repository
⟨https://git.savannah.gnu.org/git/groff.git⟩ on 2020-11-01.  (At that
time, the date of the most recent commit that was found in the repos‐
itory was 2020-11-01.)  If you discover any rendering problems in
this HTML version of the page, or you believe there is a better or
more up-to-date source for the page, or you have corrections or im‐
provements to the information in this COLOPHON (which is not part of
the original manual page), send a mail to man-pages@man7.org

groff 1.22.4.610-f543-dirty    28 October 2020                        eqn(1)