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 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 “-TMathML” 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.
Anatomyofanequationeqn 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 “esupab” expresses “(e to the a) times b”, “esup{ab}”
means “e to the (a times b)”. When immediately preceded by a “left” or “right” primitive, a brace
loses its special meaning.
^~ are the halfspace and fullspace, 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.
Spacingandtypeface
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.
typete
Apply type t to expression e.
chartypettext
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.
Primitiveseqn 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.
Newprimitives
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.
e1accente2
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.
bige 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'>
copyfileincludefile
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.
ifdefnameXanythingX
If name is defined as a primitive or macro, interpret anything.
nosplittext
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.
eopprime
As prime, but set the prime symbol as an operator on e. In the input “Aopprimesub1”, 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.
sdefinenameXanythingX
As “define”, but name is not recognized as a macro if called with arguments.
e1smallovere2
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.
spacen
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.
specialtroff-macroe
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 subscriptkern 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.
e1uaccente2
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.
undefname
Remove definition of macro or primitive name, making it undefined.
vcentere
Vertically center e about the mathaxis, 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 } !
Extendedprimitives
GNU eqn extends the syntax of some AT&T eqn primitives, introducing one deliberate incompatibility.
delimoneqn recognizes an “on” argument to the delim primitive specially, restoring any delimiters
previously disabled with “delimoff”. 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.
coln{ ... }ccoln{ ... }lcoln{ ... }rcoln{ ... }pilen{ ... }cpilen{ ... }lpilen{ ... }rpilen{ ... }
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.
setpn
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 parameterizedmacrocall:
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.
Predefinedmacros
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.
Fontseqn 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.
gbfontf
Select f as the bold font. This is a GNU extension.
gfontf
Select f as the italic font.
grfontf
Select f as the roman font. This is a GNU extension.
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