EQN(7) Miscellaneous Information Manual EQN(7)

eqn — eqn language reference for mandoc

The eqn language is an equation-formatting language. It is used within mdoc(7) and man(7) UNIX manual pages. It describes the of an equation, not its mathematical meaning. This manual describes the eqn language accepted by the mandoc(1) utility, which corresponds to the Second Edition eqn specification (see SEE ALSO for references).

An equation starts with an input line containing exactly the characters ‘.EQ’, may contain multiple input lines, and ends with an input line containing exactly the characters ‘.EN’. Equivalently, an equation can be given in the middle of a single text input line by surrounding it with the equation delimiters defined with the delim statement.

The equation grammar is as follows, where quoted strings are case-sensitive literals in the input:

eqn     : box | eqn box
box     : text
        | "{" eqn "}"
        | "define" text text
        | "ndefine" text text
        | "tdefine" text text
        | "gfont" text
        | "gsize" text
        | "set" text text
        | "undef" text
        | "sqrt" box
        | box pos box
        | box mark
        | "matrix" "{" [col "{" list "}"]* "}"
        | pile "{" list "}"
        | font box
        | "size" text box
        | "left" text eqn ["right" text]
col     : "lcol" | "rcol" | "ccol" | "col"
text    : [^space\"]+ | \".*\"
pile    : "lpile" | "cpile" | "rpile" | "pile"
pos     : "over" | "sup" | "sub" | "to" | "from"
mark	: "dot" | "dotdot" | "hat" | "tilde" | "vec"
        | "dyad" | "bar" | "under"
font    : "roman" | "italic" | "bold" | "fat"
list    : eqn
        | list "above" eqn
space   : [\^~ \t]

White-space consists of the space, tab, circumflex, and tilde characters. It is required to delimit tokens consisting of alphabetic characters and it is ignored at other places. Braces and quotes also delimit tokens. If within a quoted string, these space characters are retained. Quoted strings are also not scanned for keywords, glyph names, and expansion of definitions. To print a literal quote character, it can be prepended with a backslash or expressed with the \(dq escape sequence.

Subequations can be enclosed in braces to pass them as arguments to operation keywords, overriding standard operation precedence. Braces can be nested. To set a brace verbatim, it needs to be enclosed in quotes.

The following text terms are translated into a rendered glyph, if available: alpha, beta, chi, delta, epsilon, eta, gamma, iota, kappa, lambda, mu, nu, omega, omicron, phi, pi, psi, rho, sigma, tau, theta, upsilon, xi, zeta, DELTA, GAMMA, LAMBDA, OMEGA, PHI, PI, PSI, SIGMA, THETA, UPSILON, XI, inter (intersection), union (union), prod (product), int (integral), sum (summation), grad (gradient), del (vector differential), times (multiply), cdot (center-dot), nothing (zero-width space), approx (approximately equals), prime (prime), half (one-half), partial (partial differential), inf (infinity), >> (much greater), << (much less), <- (left arrow), -> (right arrow), +- (plus-minus), != (not equal), == (equivalence), <= (less-than-equal), and >= (more-than-equal). The character escape sequences documented in mandoc_char(7) can be used, too.

The following control statements are available:

Replace all occurrences of a key with a value. Its syntax is as follows:

define key cvalc

The first character of the value string, c, is used as the delimiter for the value val. This allows for arbitrary enclosure of terms (not just quotes), such as

define foo 'bar baz'
define foo cbar bazc

It is an error to have an empty key or val. Note that a quoted key causes errors in some eqn implementations and should not be considered portable. It is not expanded for replacements. Definitions may refer to other definitions; these are evaluated recursively when text replacement occurs and not when the definition is created.

Definitions can create arbitrary strings, for example, the following is a legal construction.

define foo 'define'
foo bar 'baz'

Self-referencing definitions will raise an error. The ndefine statement is a synonym for define, while tdefine is discarded.

This statement takes a string argument consisting of two bytes, to be used as the opening and closing delimiters for equations in the middle of text input lines. Conventionally, the dollar sign is used for both delimiters, as follows: 
.EQ
delim $$
.EN
An equation like $sin pi = 0$ can now be entered
in the middle of a text input line.

The special statement delim off temporarily disables previously declared delimiters and delim on reenables them.

Set the default font of subsequent output. Its syntax is as follows:

gfont font

In mandoc, this value is discarded.

Set the default size of subsequent output. Its syntax is as follows:

gsize [+|-]size

The size value should be an integer. If prepended by a sign, the font size is changed relative to the current size.

Set an equation mode. In mandoc, both arguments are thrown away. Its syntax is as follows:

set key val

The key and val are not expanded for replacements. This statement is a GNU extension.

Unset a previously-defined key. Its syntax is as follows:

define key

Once invoked, the definition for key is discarded. The key is not expanded for replacements. This statement is a GNU extension.

Operation keywords have the following semantics:

See pile.
Draw a line over the preceding box.
Set the following box using bold font.
Like cpile, but for use in matrix.
Like pile, but with slightly increased vertical spacing.
Set a single dot over the preceding box.
Set two dots (dieresis) over the preceding box.
Set a dyad symbol (left-right arrow) over the preceding box.
A synonym for bold.
Set the second argument using the font specified by the first argument; currently not recognized by the mandoc(1) eqn parser.
Set the following box below the preceding box, using a slightly smaller font. Used for sums, integrals, limits, and the like.
Set a hat (circumflex) over the preceding box.
Set the following box using italic font.
Like lpile, but for use in matrix.
Set the first argument as a big left delimiter before the second argument. As an optional third argument, right can follow. In that case, the fourth argument is set as a big right delimiter after the second argument.
Like cpile, but subequations are left-justified.
Followed by a list of columns enclosed in braces. All columns need to have the same number of subequations. The columns are set as a matrix. The difference compared to multiple subsequent pile operators is that in a matrix, corresponding subequations in all columns line up horizontally, while each pile does vertical spacing independently.
Set a fraction. The preceding box is the numerator, the following box is the denominator.
Followed by a list of subequations enclosed in braces, the subequations being separated by above keywords. Sets the subequations one above the other, each of them centered. Typically used to represent vectors in coordinate representation.
Like rpile, but for use in matrix.
See left; right cannot be used without left. To set a big right delimiter without a big left delimiter, the following construction can be used:

left "" box right delimiter
Set the following box using the default font.
Like cpile, but subequations are right-justified.
Set the second argument with the font size specified by the first argument; currently ignored by mandoc(1). By prepending a plus or minus sign to the first argument, the font size can be selected relative to the current size.
Set the square root of the following box.
Set the following box as a subscript to the preceding box.
Set the following box as a superscript to the preceding box. As a special case, if a sup clause immediately follows a sub clause as in

mainbox sub subbox sup supbox

both are set with respect to the same mainbox, that is, supbox is set above subbox.

Set a tilde over the preceding box.
Set the following box above the preceding box, using a slightly smaller font. Used for sums and integrals and the like. As a special case, if a to clause immediately follows a from clause as in

mainbox from frombox to tobox

both are set below and above the same mainbox.

Underline the preceding box.
Set a vector symbol (right arrow) over the preceding box.

The binary operations from, to, sub, and sup group to the right, that is,

mainbox sup supbox sub subbox

is the same as

mainbox sup {supbox sub subbox}

and different from

{mainbox sup supbox} sub subbox
.

By contrast, over groups to the left.

In the following list, earlier operations bind more tightly than later operations:

  1. , vec, under, bar, tilde, hat, dot, dotdot
  2. , roman, italic, bold, size
  3. , sup
  6. , to

This section documents the compatibility of mandoc eqn and the troff eqn implementation (including GNU troff).

mandoc(1), man(7), mandoc_char(7), mdoc(7), roff(7)

Brian W. Kernighan and Lorinda L. Cherry, System for Typesetting Mathematics, Communications of the ACM, 18, pp. 151–157, March, 1975.

Brian W. Kernighan and Lorinda L. Cherry, Typesetting Mathematics, User's Guide, 1976.

Brian W. Kernighan and Lorinda L. Cherry, Typesetting Mathematics, User's Guide (Second Edition), 1978.

The eqn utility, a preprocessor for troff, was originally written by Brian W. Kernighan and Lorinda L. Cherry in 1975. The GNU reimplementation of eqn, part of the GNU troff package, was released in 1989 by James Clark. The eqn component of mandoc(1) was added in 2011.

This eqn reference was written by Kristaps Dzonsons <kristaps@bsd.lv>.

January 10, 2020 macOS 15.0