.\"	$Id: eqn.7,v 1.38 2019/04/23 17:57:49 schwarze Exp $
.\"
.\" Copyright (c) 2011 Kristaps Dzonsons <kristaps@bsd.lv>
.\" Copyright (c) 2014 Ingo Schwarze <schwarze@openbsd.org>
.\"
.\" Permission to use, copy, modify, and distribute this software for any
.\" purpose with or without fee is hereby granted, provided that the above
.\" copyright notice and this permission notice appear in all copies.
.\"
.\" THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
.\" WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
.\" MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
.\" ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
.\" WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
.\" ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
.\" OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
.\"
.Dd $Mdocdate: April 23 2019 $
.Dt EQN 7
.Os
.Sh NAME
.Nm eqn
.Nd eqn language reference for mandoc
.Sh DESCRIPTION
The
.Nm eqn
language is an equation-formatting language.
It is used within
.Xr mdoc 7
and
.Xr man 7
.Ux
manual pages.
It describes the
.Em structure
of an equation, not its mathematical meaning.
This manual describes the
.Nm
language accepted by the
.Xr mandoc 1
utility, which corresponds to the Second Edition
.Nm
specification (see
.Sx SEE ALSO
for references).
.Pp
Equations within
.Xr mdoc 7
or
.Xr man 7
documents are enclosed by the standalone
.Sq \&.EQ
and
.Sq \&.EN
tags.
Equations are multi-line blocks consisting of formulas and control
statements.
.Sh EQUATION STRUCTURE
Each equation is bracketed by
.Sq \&.EQ
and
.Sq \&.EN
strings.
.Em Note :
these are not the same as
.Xr roff 7
macros, and may only be invoked as
.Sq \&.EQ .
.Pp
The equation grammar is as follows, where quoted strings are
case-sensitive literals in the input:
.Bd -literal -offset indent
eqn     : box | eqn box
box     : text
        | \(dq{\(dq eqn \(dq}\(dq
        | \(dqdefine\(dq text text
        | \(dqndefine\(dq text text
        | \(dqtdefine\(dq text text
        | \(dqgfont\(dq text
        | \(dqgsize\(dq text
        | \(dqset\(dq text text
        | \(dqundef\(dq text
        | \(dqsqrt\(dq box
        | box pos box
        | box mark
        | \(dqmatrix\(dq \(dq{\(dq [col \(dq{\(dq list \(dq}\(dq]* \(dq}\(dq
        | pile \(dq{\(dq list \(dq}\(dq
        | font box
        | \(dqsize\(dq text box
        | \(dqleft\(dq text eqn [\(dqright\(dq text]
col     : \(dqlcol\(dq | \(dqrcol\(dq | \(dqccol\(dq | \(dqcol\(dq
text    : [^space\e\(dq]+ | \e\(dq.*\e\(dq
pile    : \(dqlpile\(dq | \(dqcpile\(dq | \(dqrpile\(dq | \(dqpile\(dq
pos     : \(dqover\(dq | \(dqsup\(dq | \(dqsub\(dq | \(dqto\(dq | \(dqfrom\(dq
mark	: \(dqdot\(dq | \(dqdotdot\(dq | \(dqhat\(dq | \(dqtilde\(dq | \(dqvec\(dq
        | \(dqdyad\(dq | \(dqbar\(dq | \(dqunder\(dq
font    : \(dqroman\(dq | \(dqitalic\(dq | \(dqbold\(dq | \(dqfat\(dq
list    : eqn
        | list \(dqabove\(dq eqn
space   : [\e^~ \et]
.Ed
.Pp
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 \e(dq escape sequence.
.Pp
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.
.Pp
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
.Xr mandoc_char 7
can be used, too.
.Pp
The following control statements are available:
.Bl -tag -width Ds
.It Cm define
Replace all occurrences of a key with a value.
Its syntax is as follows:
.Pp
.D1 Cm define Ar key cvalc
.Pp
The first character of the value string,
.Ar c ,
is used as the delimiter for the value
.Ar val .
This allows for arbitrary enclosure of terms (not just quotes), such as
.Pp
.D1 Cm define Ar foo \(aqbar baz\(aq
.D1 Cm define Ar foo cbar bazc
.Pp
It is an error to have an empty
.Ar key
or
.Ar val .
Note that a quoted
.Ar key
causes errors in some
.Nm
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.
.Pp
Definitions can create arbitrary strings, for example, the following is
a legal construction.
.Bd -literal -offset indent
define foo \(aqdefine\(aq
foo bar \(aqbaz\(aq
.Ed
.Pp
Self-referencing definitions will raise an error.
The
.Cm ndefine
statement is a synonym for
.Cm define ,
while
.Cm tdefine
is discarded.
.It Cm gfont
Set the default font of subsequent output.
Its syntax is as follows:
.Pp
.D1 Cm gfont Ar font
.Pp
In mandoc, this value is discarded.
.It Cm gsize
Set the default size of subsequent output.
Its syntax is as follows:
.Pp
.D1 Cm gsize Oo +|\- Oc Ns Ar size
.Pp
The
.Ar size
value should be an integer.
If prepended by a sign,
the font size is changed relative to the current size.
.It Cm set
Set an equation mode.
In mandoc, both arguments are thrown away.
Its syntax is as follows:
.Pp
.D1 Cm set Ar key val
.Pp
The
.Ar key
and
.Ar val
are not expanded for replacements.
This statement is a GNU extension.
.It Cm undef
Unset a previously-defined key.
Its syntax is as follows:
.Pp
.D1 Cm define Ar key
.Pp
Once invoked, the definition for
.Ar key
is discarded.
The
.Ar key
is not expanded for replacements.
This statement is a GNU extension.
.El
.Pp
Operation keywords have the following semantics:
.Bl -tag -width Ds
.It Cm above
See
.Cm pile .
.It Cm bar
Draw a line over the preceding box.
.It Cm bold
Set the following box using bold font.
.It Cm ccol
Like
.Cm cpile ,
but for use in
.Cm matrix .
.It Cm cpile
Like
.Cm pile ,
but with slightly increased vertical spacing.
.It Cm dot
Set a single dot over the preceding box.
.It Cm dotdot
Set two dots (dieresis) over the preceding box.
.It Cm dyad
Set a dyad symbol (left-right arrow) over the preceding box.
.It Cm fat
A synonym for
.Cm bold .
.It Cm font
Set the second argument using the font specified by the first argument;
currently not recognized by the
.Xr mandoc 1
.Nm
parser.
.It Cm from
Set the following box below the preceding box,
using a slightly smaller font.
Used for sums, integrals, limits, and the like.
.It Cm hat
Set a hat (circumflex) over the preceding box.
.It Cm italic
Set the following box using italic font.
.It Cm lcol
Like
.Cm lpile ,
but for use in
.Cm matrix .
.It Cm left
Set the first argument as a big left delimiter before the second argument.
As an optional third argument,
.Cm right
can follow.
In that case, the fourth argument is set as a big right delimiter after
the second argument.
.It Cm lpile
Like
.Cm cpile ,
but subequations are left-justified.
.It Cm 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
.Cm pile
operators is that in a
.Cm matrix ,
corresponding subequations in all columns line up horizontally,
while each
.Cm pile
does vertical spacing independently.
.It Cm over
Set a fraction.
The preceding box is the numerator, the following box is the denominator.
.It Cm pile
Followed by a list of subequations enclosed in braces,
the subequations being separated by
.Cm above
keywords.
Sets the subequations one above the other, each of them centered.
Typically used to represent vectors in coordinate representation.
.It Cm rcol
Like
.Cm rpile ,
but for use in
.Cm matrix .
.It Cm right
See
.Cm left ;
.Cm right
cannot be used without
.Cm left .
To set a big right delimiter without a big left delimiter, the following
construction can be used:
.Pp
.D1 Cm left No \(dq\(dq Ar box Cm right Ar delimiter
.It Cm roman
Set the following box using the default font.
.It Cm rpile
Like
.Cm cpile ,
but subequations are right-justified.
.It Cm size
Set the second argument with the font size specified by the first
argument; currently ignored by
.Xr mandoc 1 .
By prepending a plus or minus sign to the first argument,
the font size can be selected relative to the current size.
.It Cm sqrt
Set the square root of the following box.
.It Cm sub
Set the following box as a subscript to the preceding box.
.It Cm sup
Set the following box as a superscript to the preceding box.
As a special case, if a
.Cm sup
clause immediately follows a
.Cm sub
clause as in
.Pp
.D1 Ar mainbox Cm sub Ar subbox Cm sup Ar supbox
.Pp
both are set with respect to the same
.Ar mainbox ,
that is,
.Ar supbox
is set above
.Ar subbox .
.It Cm tilde
Set a tilde over the preceding box.
.It Cm 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
.Cm to
clause immediately follows a
.Cm from
clause as in
.Pp
.D1 Ar mainbox Cm from Ar frombox Cm to Ar tobox
.Pp
both are set below and above the same
.Ar mainbox .
.It Cm under
Underline the preceding box.
.It Cm vec
Set a vector symbol (right arrow) over the preceding box.
.El
.Pp
The binary operations
.Cm from ,
.Cm to ,
.Cm sub ,
and
.Cm sup
group to the right, that is,
.Pp
.D1 Ar mainbox Cm sup Ar supbox Cm sub Ar subbox
.Pp
is the same as
.Pp
.D1 Ar mainbox Cm sup Brq Ar supbox Cm sub Ar subbox
.Pp
and different from
.Pp
.D1 Bro Ar mainbox Cm sup Ar supbox Brc Cm sub Ar subbox .
.Pp
By contrast,
.Cm over
groups to the left.
.Pp
In the following list, earlier operations bind more tightly than
later operations:
.Pp
.Bl -enum -compact
.It
.Cm dyad ,
.Cm vec ,
.Cm under ,
.Cm bar ,
.Cm tilde ,
.Cm hat ,
.Cm dot ,
.Cm dotdot
.It
.Cm fat ,
.Cm roman ,
.Cm italic ,
.Cm bold ,
.Cm size
.It
.Cm sub ,
.Cm sup
.It
.Cm sqrt
.It
.Cm over
.It
.Cm from ,
.Cm to
.El
.Sh COMPATIBILITY
This section documents the compatibility of mandoc
.Nm
and the troff
.Nm
implementation (including GNU troff).
.Pp
.Bl -dash -compact
.It
The text string
.Sq \e\(dq
is interpreted as a literal quote in troff.
In mandoc, this is interpreted as a comment.
.It
In troff, The circumflex and tilde white-space symbols map to
fixed-width spaces.
In mandoc, these characters are synonyms for the space character.
.It
The troff implementation of
.Nm
allows for equation alignment with the
.Cm mark
and
.Cm lineup
tokens.
mandoc discards these tokens.
The
.Cm back Ar n ,
.Cm fwd Ar n ,
.Cm up Ar n ,
and
.Cm down Ar n
commands are also ignored.
.El
.Sh SEE ALSO
.Xr mandoc 1 ,
.Xr man 7 ,
.Xr mandoc_char 7 ,
.Xr mdoc 7 ,
.Xr roff 7
.Rs
.%A Brian W. Kernighan
.%A Lorinda L. Cherry
.%T System for Typesetting Mathematics
.%J Communications of the ACM
.%V 18
.%P pp. 151\(en157
.%D March, 1975
.Re
.Rs
.%A Brian W. Kernighan
.%A Lorinda L. Cherry
.%T Typesetting Mathematics, User's Guide
.%D 1976
.Re
.Rs
.%A Brian W. Kernighan
.%A Lorinda L. Cherry
.%T Typesetting Mathematics, User's Guide (Second Edition)
.%D 1978
.Re
.Sh 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
.Xr mandoc 1
was added in 2011.
.Sh AUTHORS
This
.Nm
reference was written by
.An Kristaps Dzonsons Aq Mt kristaps@bsd.lv .