# 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 implemenation of eqn is part of the groff(7) document
formatting system.  eqn is a troff(1) preprocessor that
translates descriptions of equations embedded in roff(7) input
files into the language understood by troff(1).  It copies the
contents of each file to the standard output stream, except that
lines between .EQ and .EN (or “inline” within a pair of user-
specified delimiters) are interpreted as equation descriptions.
Normally, eqn is not executed directly by the user, but invoked
by specifying the -e option to groff(1).  While GNU eqn's input
syntax is highly compatible with AT&T eqn, the output eqn
produces cannot be processed by AT&T troff; GNU troff (or a troff
implementing relevant GNU extensions) must be used.  If no file
operands are given on the command line, or if file is “-”, the

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/
1.23.0/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
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       an opening bracket such as “(”
closing       a closing bracket such as “)”
punctuation   a punctuation character such as “,”
inner         a sub-formula 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 example, 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
Each (unquoted) character in text is assigned type t.  The
type t can also be “letter” or “digit”; in these cases
chartype changes the font style of the characters.  See
subsection “Fonts” below.  For example,

chartype "punctuation" .,;:

assigns the “punctuation” type to each of the characters
in “.,;:” wherever they subsequently appear in an
equation.

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

<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 according 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

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

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 apostrophe (') 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
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 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
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
descriptions 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; fat text uses
<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 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 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 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 be 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 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 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
below 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
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 drivers.)

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, 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 driver)
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 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
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.


## 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 output driver 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 driver.  However, if the specified driver
is “MathML”, the output is MathML markup rather than troff
commands, and eqnrc is not loaded at all.  The default
output driver is ps.


## Files         top

       /usr/local/share/groff/1.23.0/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

•      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 “<mstyle>” wrappers adjusted by hand.

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), by Brian W.
Kernighan and Lorinda L. Cherry, 1978, AT&T Bell Laboratories
Computing Science Technical Report No. 17.

The TeXbook, by Donald E. Knuth, 1984, Addison-Wesley
Professional.

groff_char(7), particularly subsections “Logical symbols”,
“Mathematical symbols”, and “Greek glyphs”, documents a variety
of special character escapes useful in mathematical typesetting.

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/⟩.