Manual: geqn
eqn(1) General Commands Manual eqn(1)
Name
eqn - format mathematics (equations) for groff or MathML
Synopsis
eqn [-CNrR] [-d xy] [-f F] [-m n] [-M dir] [-p n] [-s n] [-T dev] [file ...]
eqn --help
eqn -v
eqn --version
Description
The GNU implementation of eqn is part of the groff(7) document formatting system. eqn is a troff(1) preprocessor
that translates expressions in its own language, embedded in roff(7) input files, into mathematical notation typeset
by troff(1). It copies each file's contents to the standard output stream, translating each equation between lines
starting with .EQ and .EN, or within a pair of user-specified delimiters. 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 “-”, eqn reads the
standard input stream.
Unless the -R option is used, eqn searches for the file eqnrc in the directories given with the -M option first, then
in /usr/share/groff/site-tmac, and finally in the standard macro directory /usr/share/groff/1.23.0/tmac. If it ex‐
ists and is readable, eqn processes it before any input files.
This man page primarily discusses the differences between GNU eqn and AT&T eqn. 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 support terminal devices well, though it may suffice for simple inputs.
• GNU eqn sets the input token “...” as an ellipsis on the text baseline, not the three centered dots of AT&T eqn.
Set an ellipsis on the math axis with the GNU extension macro cdots.
Anatomy of an equation
eqn input consists of tokens. Consider a form of Newton's second law of motion. The input
.EQ
F =
m a
.EN
becomes F=ma. Each of F, =, m, and a is a token. Spaces and newlines are interchangeable; they separate tokens but
do not break lines or produce space in the output.
The following input characters not only separate tokens, but manage their grouping and spacing as well.
{ } Braces perform grouping. Whereas “e sup a b” expresses “(e to the a) times b”, “e sup { a b }” means “e to
the (a times b)”. When immediately preceded by a “left” or “right” primitive, a brace loses its special mean‐
ing.
^ ~ are the half space and full space, respectively. Use them to tune the appearance of the output.
Tab and leader characters separate tokens as well as advancing the drawing position to the next tab stop, but are
seldom used in eqn input. When they occur, they must appear at the outermost lexical scope. This roughly means that
they can't appear within braces that are necessary to disambiguate the input; eqn will diagnose an error in this
event. (See subsection “Macros” below for additional token separation rules.)
Other tokens are primitives, macros, an argument to either of the foregoing, or components of an equation.
Primitives are fundamental keywords of the eqn language. They can configure an aspect of the preprocessor's state,
as when setting a “global” font selection or type size (gfont and gsize), or declaring or deleting macros (“define”
and undef); these are termed commands. Other primitives perform formatting operations on the tokens after them (as
with fat, over, sqrt, or up).
Equation components include mathematical variables, constants, numeric literals, and operators. eqn remaps some in‐
put character sequences to groff special character escape sequences for economy in equation entry and to ensure that
glyphs from an unstyled font are used; see groff_char(7).
+ \[pl] ' \[fm]
- \[mi] <= \[<=]
= \[eq] >= \[>=]
Macros permit primitives, components, and other macros to be collected and referred to by a single token. Predefined
macros make convenient the preparation of eqn input in a form resembling its spoken expression; for example, consider
cos, hat, inf, and lim.
Spacing and typeface
GNU eqn imputes types to the components of an equation, adjusting the spacing between them accordingly. Recognized
types are as follows; most affect spacing only, whereas the “letter” subtype of “ordinary” also assigns a style.
ordinary character such as “1”, “a”, or “!”
letter character to be italicized by default
digit n/a
operator large operator such as “Σ”
binary binary operator such as “+”
relation relational operator such as “=”
opening opening bracket such as “(”
closing closing bracket such as “)”
punctuation punctuation character such as “,”
inner sub-formula contained within brackets
suppress component to which automatic spacing is not applied
Two primitives apply types to equation components.
type t e
Apply type t to expression e.
chartype t text
Assign each character in (unquoted) text type t, persistently.
eqn sets up spacings and styles as if by the following commands.
chartype "letter" abcdefghiklmnopqrstuvwxyz
chartype "letter" ABCDEFGHIKLMNOPQRSTUVWXYZ
chartype "letter" \[*a]\[*b]\[*g]\[*d]\[*e]\[*z]
chartype "letter" \[*y]\[*h]\[*i]\[*k]\[*l]\[*m]
chartype "letter" \[*n]\[*c]\[*o]\[*p]\[*r]\[*s]
chartype "letter" \[*t]\[*u]\[*f]\[*x]\[*q]\[*w]
chartype "binary" *\[pl]\[mi]
chartype "relation" <>\[eq]\[<=]\[>=]
chartype "opening" {([
chartype "closing" })]
chartype "punctuation" ,;:.
chartype "suppress" ^~
eqn assigns all other ordinary and special roff characters, including numerals 0–9, the “ordinary” type. (The
“digit” type is not used, but is available for customization.) In keeping with common practice in mathematical type‐
setting, lowercase, but not uppercase, Greek letters are assigned the “letter” type to style them in italics. The
macros for producing ellipses, “...”, cdots, and ldots, use the “inner” type.
Primitives
eqn supports without alteration the AT&T eqn primitives above, back, bar, bold, define, down, fat, font, from, fwd,
gfont, gsize, italic, left, lineup, mark, matrix, ndefine, over, right, roman, size, sqrt, sub, sup, tdefine, to,
under, and up.
New primitives
The GNU extension primitives “type” and chartype are discussed in subsection “Spacing and typeface” above; “set” in
subsection “Customization” below; and grfont and gbfont in subsection “Fonts” below. In the following synopses, X
can be any character not appearing in the parameter thus bracketed.
e1 accent e2
Set e2 as an accent over e1. e2 is assumed to be at the appropriate height for a lowercase letter without an
ascender; eqn vertically shifts it depending on e1's height. For example, hat is defined as follows.
accent { "^" }
dotdot, dot, tilde, vec, and dyad are also defined using the accent primitive.
big e Enlarge the expression e; semantics like those of CSS “large” are intended. In troff output, the type size is
increased by 5 scaled points. MathML output emits the following.
copy file
include file
Interpolate the contents of file, omitting lines beginning with .EQ or .EN. If a relative path name, file is
sought relative to the current working directory.
ifdef name X anything X
If name is defined as a primitive or macro, interpret anything.
nosplit text
As "text", but since text is not quoted it is subject to macro expansion; it is not split up and the spacing
between characters not adjusted per subsection “Spacing and typeface” above.
e opprime
As prime, but set the prime symbol as an operator on e. In the input “A opprime sub 1”, the “1” is tucked un‐
der the prime as a subscript to the “A” (as is conventional in mathematical typesetting), whereas when prime
is used, the “1” is a subscript to the prime character. The precedence of opprime is the same as that of bar
and “under”, and higher than that of other primitives except accent and uaccent. In unquoted text, a neutral
apostrophe (') that is not the first character on the input line is treated like opprime.
sdefine name X anything X
As “define”, but name is not recognized as a macro if called with arguments.
e1 smallover e2
As over, but reduces the type size of e1 and e2, and puts less vertical space between e1 and e2 and the frac‐
tion bar. The over primitive corresponds to the TeX \over primitive in displayed equation styles; smallover
corresponds to \over in non-display (“inline”) styles.
space n
Set extra vertical spacing around the equation, replacing the default values, where n is an integer in hun‐
dredths of an em. If positive, n increases vertical spacing before the equation; if negative, it does so af‐
ter the equation. This primitive provides an interface to groff's \x escape sequence, but with the opposite
sign convention. It has no effect if the equation is part of a pic(1) picture.
special troff-macro e
Construct an object by calling troff-macro on e. The troff string 0s contains the eqn output for e, and the
registers 0w, 0h, 0d, 0skern, and 0skew the width, height, depth, subscript kern, and skew of e, respectively.
(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, returns the drawing position to the text baseline at the beginning of e, and
updates the foregoing registers to correspond to the new dimensions of the result.
Suppose you want a construct that “cancels” an expression by drawing a diagonal line through it.
.de Ca
. ds 0s \
\Z'\\*(0s'\
\v'\\n(0du'\
\D'l \\n(0wu -\\n(0hu-\\n(0du'\
\v'\\n(0hu'
..
.EQ
special Ca "x \[mi] 3 \[pl] x" ~ 3
.EN
We use the \[mi] and \[pl] special characters instead of + and - because they are part of the argument to a
troff macro, so eqn does not transform them to mathematical glyphs for us. Here's a more complicated con‐
struct that draws a box around an expression; the bottom of the box rests on the text baseline. We define the
eqn macro box to wrap the call of the troff macro Bx.
.de Bx
.ds 0s \
\Z'\\h'1n'\\*[0s]'\
\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
..
.EQ
define box ' special Bx $1 '
box(foo) ~ "bar"
.EN
split "text"
As text, but since text is quoted, it is not subject to macro expansion; it is split up and the spacing be‐
tween characters adjusted per subsection “Spacing and typeface” above.
e1 uaccent e2
Set e2 as an accent under e1. e2 is assumed to be at the appropriate height for a letter without a descender;
eqn vertically shifts it depending on whether e1 has a descender. utilde is predefined using uaccent as a
tilde accent below the baseline.
undef name
Remove definition of macro or primitive name, making it undefined.
vcenter e
Vertically center e about the math axis, a horizontal line upon which fraction bars and characters such as “+”
and “−” are aligned. MathML already behaves this way, so eqn ignores this primitive when producing that out‐
put format. The built-in sum macro is defined as if by the following.
define sum ! { type "operator" vcenter size +5 \(*S } !
Extended primitives
GNU eqn extends the syntax of some AT&T eqn primitives, introducing one deliberate incompatibility.
delim on
eqn recognizes an “on” argument to the delim primitive specially, restoring any delimiters previously disabled
with “delim off”. If delimiters haven't been specified, neither command has effect. Few eqn documents are
expected to use “o” and “n” as left and right delimiters, respectively. If yours does, consider swapping
them, or select others.
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 es‐
cape sequence (the value has no effect in MathML mode). Negative values are accepted but have no effect. If
more than one n occurs in a matrix or pile, the largest is used.
Customization
When eqn generates troff input, the appearance of equations is controlled by a large number of parameters. They have
no effect when generating MathML, which delegates typesetting to a MathML rendering engine. Configure these parame‐
ters with the set primitive.
set p n
assigns parameter p the integer value n; n is interpreted in units of hundredths of an em unless otherwise
stated. For example,
set x_height 45
says that eqn should assume that the font's x-height is 0.45 ems.
Available parameters are as follows; defaults are shown in parentheses. We intend these descriptions to be
expository rather than rigorous.
minimum_size sets a floor for the type size (in scaled points) at which equations are set (5).
fat_offset The fat primitive emboldens an equation by overprinting two copies of the equation horizon‐
tally offset by this amount (4). In MathML mode, components to which fat_offset applies in‐
stead use the following.
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 (0).
accent_width When bar or under is applied to a single character, the line is this long (31). 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 (900).
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 (50).
null_delimiter_space
This much horizontal space is inserted on each side of a fraction (12).
script_space The width of subscripts and superscripts is increased by this amount (5).
thin_space This amount of space is automatically inserted after punctuation characters. It also config‐
ures the width of the space produced by the ^ token (17).
medium_space This amount of space is automatically inserted on either side of binary operators (22).
thick_space This amount of space is automatically inserted on either side of relations. It also config‐
ures the width of the space produced by the ~ token (28).
x_height The height of lowercase letters without ascenders such as “x” (45).
axis_height The height above the baseline of the center of characters such as “+” and “−” (26). 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 (4).
num1 The over primitive shifts up the numerator by at least this amount (70).
num2 The smallover primitive shifts up the numerator by at least this amount (36).
denom1 The over primitive shifts down the denominator by at least this amount (70).
denom2 The smallover primitive shifts down the denominator by at least this amount (36).
sup1 Normally superscripts are shifted up by at least this amount (42).
sup2 Superscripts within superscripts or upper limits or numerators of smallover fractions are
shifted up by at least this amount (37). Conventionally, this is less than sup1.
sup3 Superscripts within denominators or square roots or subscripts or lower limits are shifted up
by at least this amount (28). Conventionally, this is less than sup2.
sub1 Subscripts are normally shifted down by at least this amount (20).
sub2 When there is both a subscript and a superscript, the subscript is shifted down by at least
this amount (23).
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 (38).
sub_drop The baseline of a subscript is at least this much below the bottom of the object on which the
subscript is set (5).
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 (11).
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 (17).
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 (20).
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 (60).
big_op_spacing5 This much vertical space is added above and below limits (10).
baseline_sep The baselines of the rows in a pile or matrix are normally this far apart (140). Usually
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 (26). Usually equal to axis_height.
column_sep This much space is added between columns in a matrix (100).
matrix_side_sep This much space is added at each side of a matrix (17).
draw_lines If non-zero, eqn draws lines using the troff \D escape sequence, rather than the \l escape
sequence and the \[ru] special character. The eqnrc file sets the default: 1 on ps, html,
and the X11 devices, otherwise 0.
body_height is the presumed height of an equation above the text baseline; eqn adds any excess as extra
pre-vertical line spacing with troff's \x escape sequence (85).
body_depth is the presumed depth of an equation below the text baseline; eqn adds any excess as extra
post-vertical line spacing with troff's \x escape sequence (35).
nroff If non-zero, then ndefine behaves like define and tdefine is ignored, otherwise tdefine be‐
haves like define and ndefine is ignored. The eqnrc file sets the default: 1 on ascii,
latin1, utf8, and cp1047 devices, otherwise 0.
Macros
In GNU eqn, macros can take arguments. A word defined by any of the define, ndefine, or tdefine primitives followed
immediately by a left parenthesis is treated as a parameterized macro call: subsequent tokens up to a matching right
parenthesis are treated as comma-separated arguments. In this context only, commas and parentheses also serve as to‐
ken separators. A macro argument is not terminated by a comma inside parentheses nested within it. In a macro defi‐
nition, $n, where n is between 1 and 9 inclusive, is replaced by the nth argument; if there are fewer than n argu‐
ments, it is replaced by nothing.
Predefined macros
GNU eqn supports the predefined macros offered by AT&T eqn: and, approx, arc, cos, cosh, del, det, dot, dotdot, dyad,
exp, for, grad, half, hat, if, inter, Im, inf, int, lim, ln, log, max, min, nothing, partial, prime, prod, Re, sin,
sinh, sum, tan, tanh, tilde, times, union, vec, ==, !=, +=, ->, <-, <<, >>, and “...”. The lowercase classical Greek
letters are available as alpha, beta, chi, delta, epsilon, eta, gamma, iota, kappa, lambda, mu, nu, omega, omicron,
phi, pi, psi, rho, sigma, tau, theta, upsilon, xi, and zeta. Spell them with an initial capital letter (Alpha) or in
full capitals (ALPHA) to obtain uppercase forms.
GNU eqn further defines the macros cdot, cdots, and utilde (all discussed above), dollar, which sets a dollar sign,
and ldots, which sets an ellipsis on the text baseline.
Fonts
eqn uses up to three typefaces to set an equation: italic (oblique), roman (upright), and bold. Assign each a groff
typeface with the primitives gfont, grfont, and gbfont. The defaults are the styles I, R, and B (applied to the cur‐
rent font family). The chartype primitive (see above) sets a character's type, which determines the face used to set
it. The “letter” type is set in italics; others are set in roman. Use the bold primitive to select an (upright)
bold style.
gbfont f
Select f as the bold font. This is a GNU extension.
gfont f
Select f as the italic font.
grfont f
Select f as the roman font. This is a GNU extension.
Options
--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.
-d xy Specify delimiters x for left and y for right ends of equations not bracketed by .EQ/.EN. x and y need not be
distinct. Any “delim xy” statements in the source file override this option.
-f F is equivalent to “gfont F”.
-m n is equivalent to “set minimum_size n”.
-M dir Search dir for eqnrc before those listed in section “Description” above.
-N Prohibit newlines within delimiters. This option allows eqn to recover better from missing closing delim‐
iters.
-p n Set sub- and superscripts n points smaller than the surrounding text. This option is deprecated. eqn nor‐
mally sets sub- and superscripts at 70% of the type size of the surrounding text.
-r Reduce the type size of subscripts at most once relative to the base type size for the equation.
-R Don't load eqnrc.
-s n is equivalent to “gsize n”. This option is deprecated.
-T dev Prepare output for the device dev. In most cases, the effect of this is to define a macro dev with a value
of 1; eqnrc uses this to provide definitions appropriate for the device. However, if the specified driver is
“MathML”, the output is MathML markup rather than troff input, and eqnrc is not loaded at all. The default
output device is ps.
Files
/usr/share/groff/1.23.0/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 control of motions and sizes to the same degree troff does.
• eqn customization parameters have no effect on generated MathML.
• The special, up, down, fwd, and back primitives cannot be implemented, and yield a MathML “” message in‐
stead.
• The vcenter primitive 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 “” wrappers adjusted by hand.
As in its troff mode, eqn in MathML mode leaves the .EQ and .EN tokens in place, but emits nothing corresponding to
delim delimiters. They can, however, be recognized as character sequences that begin with “”, and do not cross line boundaries.
Caveats
Tokens must be double-quoted in eqn input if they are not to be recognized as names of macros or primitives, or if
they are to be interpreted by troff. In particular, short ones, like “pi” and “PI”, can collide with troff identi‐
fiers. For instance, the eqn command “gfont PI” does not select groff's Palatino italic font for the global italic
face; you must use “gfont "PI"” instead.
Delimited equations are set at the type size current at the beginning of the input line, not necessarily that immedi‐
ately preceding the opening delimiter.
Unlike TeX, eqn does not inherently distinguish displayed and inline equation styles; see the smallover primitive
above. However, macro packages frequently define EQ and EN macros such that the equation within is displayed. These
macros may accept arguments permitting the equation to be labeled or captioned; see the package's documentation.
Bugs
eqn abuses terminology—its “equations” can be inequalities, bare expressions, or unintelligible gibberish. But
there's no changing it now.
In nroff mode, lowercase Greek letters are rendered in roman instead of italic style.
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.
Examples
We first illustrate eqn usage with a trigonometric identity.
.EQ
sin ( alpha + beta ) = sin alpha cos beta + cos alpha sin beta
.EN
It can be convenient to set up delimiters if mathematical content will appear frequently in running text.
.EQ
delim $$
.EN
Having cached a table of logarithms,
the property $ln ( x y ) = ln x + ln y$ sped calculations.
The quadratic formula illustrates use of fractions and radicals, and affords an opportunity to use the full space to‐
ken ~.
.EQ
x = { - b ~ \[+-] ~ sqrt { b sup 2 - 4 a c } } over { 2 a }
.EN
Alternatively, we could define the plus-minus sign as a binary operator. Automatic spacing puts 0.06 em less space
on either side of the plus-minus than ~ does, this being the difference between the widths of the medium_space para‐
meter used by binary operators and that of the full space. Independently, we can define a macro “frac” for setting
fractions.
.EQ
chartype "binary" \[+-]
define frac ! { $1 } over { $2 } !
x = frac(- b \[+-] sqrt { b sup 2 - 4 a c }, 2 a)
.EN
See also
“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. Appendix G discusses many of the parameters from
section “Customization” above in greater detail.
groff_char(7), particularly subsections “Logical symbols”, “Mathematical symbols”, and “Greek glyphs”, documents a
variety of special character escape sequences useful in mathematical typesetting.
groff(1), troff(1), pic(1), groff_font(5)
groff 1.23.0 2 December 2025 eqn(1)