DESCRIPTION
The eqn language is an equationformatting 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 multiline 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 casesensitive 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]
Whitespace 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 (centerdot), nothing (zerowidth space), approx (approximately equals), prime (prime), half (onehalf), partial (partial differential), inf (infinity), >> (much greater), << (much less), > (left arrow), < (right arrow), + (plusminus), != (not equal), == (equivalence), <= (lessthanequal), and >= (morethanequal). 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'
Selfreferencing 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 previouslydefined 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 (leftright 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 leftjustified.
 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 rightjustified.
 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 whitespace symbols map to fixedwidth 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.