## NAME

`eqn`

—
eqn language reference for
mandoc

## DESCRIPTION

The `eqn`

language is an equation-formatting
language. It is used within
mdoc(7) and man(7) UNIX manual pages. It
describes the
*structure*
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).

Equations within mdoc(7) or man(7) documents are enclosed by the standalone ‘.EQ’ and ‘.EN’ tags. Equations are multi-line blocks consisting of formulas and control statements.

## EQUATION STRUCTURE

Each equation is bracketed by ‘.EQ’ and
‘.EN’ strings.
*Note*:
these are not the same as
roff(7) macros, and may only be invoked as ‘.EQ’.

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:

`define`

- 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. `gfont`

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

`font`In mandoc, this value is discarded.

`gsize`

- 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`

- 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. `undef`

- 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:

`above`

- See
`pile`

. `bar`

- Draw a line over the preceding box.
`bold`

- Set the following box using bold font.
`ccol`

- Like
`cpile`

, but for use in`matrix`

. `cpile`

- Like
`pile`

, but with slightly increased vertical spacing. `dot`

- Set a single dot over the preceding box.
`dotdot`

- Set two dots (dieresis) over the preceding box.
`dyad`

- Set a dyad symbol (left-right arrow) over the preceding box.
`fat`

- A synonym for
`bold`

. `font`

- Set the second argument using the font specified by the first argument;
currently not recognized by the
mandoc(1)
`eqn`

parser. `from`

- Set the following box below the preceding box, using a slightly smaller font. Used for sums, integrals, limits, and the like.
`hat`

- Set a hat (circumflex) over the preceding box.
`italic`

- Set the following box using italic font.
`lcol`

- Like
`lpile`

, but for use in`matrix`

. `left`

- 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. `lpile`

- Like
`cpile`

, but subequations are left-justified. `matrix`

- 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. `over`

- Set a fraction. The preceding box is the numerator, the following box is the denominator.
`pile`

- 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. `rcol`

- Like
`rpile`

, but for use in`matrix`

. `right`

- 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` `roman`

- Set the following box using the default font.
`rpile`

- Like
`cpile`

, but subequations are right-justified. `size`

- 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.
`sqrt`

- Set the square root of the following box.
`sub`

- Set the following box as a subscript to the preceding box.
`sup`

- 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`. `tilde`

- Set a tilde over the preceding box.
`to`

- 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`. `under`

- Underline the preceding box.
`vec`

- 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:

## COMPATIBILITY

This section documents the compatibility of mandoc
`eqn`

and the troff `eqn`

implementation (including GNU troff).

- The text string ‘\"’ is interpreted as a literal quote in troff. In mandoc, this is interpreted as a comment.
- In troff, The circumflex and tilde white-space symbols map to fixed-width spaces. In mandoc, these characters are synonyms for the space character.
- The troff implementation of
`eqn`

allows for equation alignment with the`mark`

and`lineup`

tokens. mandoc discards these tokens. The`back`

`n`,`fwd`

`n`,`up`

`n`, and`down`

`n`commands are also ignored.

## SEE ALSO

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,
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.

## HISTORY

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.

## AUTHORS

This `eqn`

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