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
/opt/homebrew/etc/groff/site-tmac, and finally in the standard macro
directory /opt/homebrew/Cellar/groff/1.23.0_1/share/groff/1.23.0/tmac.
If it exists 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 = m a. 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 meaning.
^ ~ 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 input 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 typesetting, 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.
<mstyle mathsize='big'>
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 under 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 fraction 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 hundredths of an em.
If positive, n increases vertical spacing before the equation;
if negative, it does so after 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 construct 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 between 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 output 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 escape 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 parameters 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
horizontally offset by this amount (4). In
MathML mode, components to which fat_offset
applies instead use the following.
<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 (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
configures 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
configures 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
behaves 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
token separators. A macro argument is not terminated by a comma inside
parentheses nested within it. In a macro definition, $n, where n is
between 1 and 9 inclusive, is replaced by the nth argument; if there
are fewer than n arguments, 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 current 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 delimiters.
-p n Set sub- and superscripts n points smaller than the surrounding
text. This option is deprecated. eqn normally 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
/opt/homebrew/Cellar/groff/1.23.0_1/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 “<merror>” message instead.
• 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 “<mstyle>”
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
“<math>”, end with “</math>”, 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 identifiers. 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 immediately 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 “<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.
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 token ~.
.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 parameter 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 5 July 2023 eqn(1)