EQN(7)

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:

1.  dyad, vec, under, bar, tilde, hat, dot, dotdot
2.  fat, roman, italic, bold, size
3.  sub, sup
4.  sqrt
5.  over
6.  from, to

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, Lorinda L. Cherry, System for Typesetting Mathematics, Communications of the ACM, 18, 151–157, March, 1975. Brian W. Kernighan, Lorinda L. Cherry, Typesetting Mathematics, User's Guide, 1976. Brian W. Kernighan, 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>.