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eqn(1) General Commands Manual eqn(1)
eqn - format mathematics (equations) for groff or MathML
eqn [-CNrR] [-d xy] [-f global-italic-font] [-m minimum-type-
size] [-M eqnrc-directory] [-p super/subscript-size-
reduction] [-s global-type-size] [-T device] [file ...]
eqn --help
eqn -v
eqn --version
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 present, 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/
local/share/groff/site-tmac, and finally in the standard macro
directory /usr/local/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. Four points are worth 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.
• GNU eqn's delim command does not treat an “on” argument as a
pair of equation delimiters.
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.
Beyond their primary functions, the following input characters
separate tokens 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 (gifont and
gsize), or declaring or deleting macros (“define” and undef);
these are termed commands. Other primitives perform formatting
operations on the tokens around 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 used together as 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
We describe the GNU extension primitives “type” and chartype in
subsection “Spacing and typeface” above; “set” and “reset” in
subsection “Customization” below; and gbfont, gifont, and grfont
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. eqn assumes that e2 is at
the appropriate height for a lowercase letter without an
ascender, and shifts it vertically based on e1's height.
For example, eqn defines hat as follows.
accent { roman "^" }
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 reduce the type size of e1 and e2, and put
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, swap 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, uses the
formatter's \x escape sequence to increase the vertical
spacing between rows; eqn ignores it when producing
MathML. 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” and
“reset” primitives.
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.
reset p
restores the default value of parameter p.
Available parameters p 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 (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 (28).
half_space
configures the width of the space produced by the ^ token
(17).
full_space
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 GNU extension primitives grfont, gifont, and
gbfont. The defaults are the styles R, I, 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.
gifont f
Select f as the italic font. GNU eqn recognizes gfont as
a synonym for AT&T compatibility.
grfont f
Select f as the roman font.
--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 “gifont 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, allowing 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 super- and subscripts at most once
relative to the base type size.
-R Don't load eqnrc.
-s n is equivalent to “gsize n”. This option is deprecated.
-T dev Prepare output for the device dev. This option defines a
macro dev with the value 1; eqnrc thereby provides
definitions appropriate to the device. However, if dev is
“MathML”, eqn produces output in that language rather than
roff, and eqnrc is not loaded. The default device is ps.
/usr/local/share/groff/1.23.0/tmac/eqnrc
initializes the preprocessor for troff output. Any valid
eqn input is accepted.
MathML's design assumes 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.
• GNU eqn's rendering parameters (see section “Customziation”
above) 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.
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 “gifont PI” does not select groff's Palatino italic font
for the global italic face; you must use “gifont "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.
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.
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 affords an opportunity to use fractions,
radicals, and 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
“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) documents a variety of special character escape
sequences useful in mathematical typesetting. See subsections
“Logical symbols”, “Mathematical symbols”, and “Greek glyphs” in
particular.
groff(1), troff(1), pic(1), groff_font(5)
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 2024-06-14. (At
that time, the date of the most recent commit that was found in
the repository was 2024-06-10.) 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 improvements to the information in this COLOPHON
(which is not part of the original manual page), send a mail to
man-pages@man7.org
groff 1.23.0.1273-9d53-dirty 6 June 2024 eqn(1)
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