508 lines
13 KiB
Groff
508 lines
13 KiB
Groff
.\" $Id: eqn.7,v 1.39 2020/01/10 11:55:04 schwarze Exp $
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.\"
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.\" Copyright (c) 2011 Kristaps Dzonsons <kristaps@bsd.lv>
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.\" Copyright (c) 2014 Ingo Schwarze <schwarze@openbsd.org>
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.\"
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.\" Permission to use, copy, modify, and distribute this software for any
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.\" purpose with or without fee is hereby granted, provided that the above
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.\" copyright notice and this permission notice appear in all copies.
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.\"
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.\" THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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.\" WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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.\" MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
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.\" ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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.\" WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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.\" ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
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.\" OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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.\"
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.Dd $Mdocdate: January 10 2020 $
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.Dt EQN 7
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.Os
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.Sh NAME
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.Nm eqn
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.Nd eqn language reference for mandoc
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.Sh DESCRIPTION
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The
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.Nm eqn
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language is an equation-formatting language.
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It is used within
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.Xr mdoc 7
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and
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.Xr man 7
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.Ux
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manual pages.
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It describes the
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.Em structure
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of an equation, not its mathematical meaning.
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This manual describes the
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.Nm
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language accepted by the
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.Xr mandoc 1
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utility, which corresponds to the Second Edition
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.Nm
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specification (see
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.Sx SEE ALSO
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for references).
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.Pp
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An equation starts with an input line containing exactly the characters
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.Sq \&.EQ ,
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may contain multiple input lines, and ends with an input line
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containing exactly the characters
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.Sq \&.EN .
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Equivalently, an equation can be given in the middle of a single
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text input line by surrounding it with the equation delimiters
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defined with the
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.Cm delim
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statement.
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.Pp
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The equation grammar is as follows, where quoted strings are
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case-sensitive literals in the input:
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.Bd -literal -offset indent
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eqn : box | eqn box
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box : text
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| \(dq{\(dq eqn \(dq}\(dq
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| \(dqdefine\(dq text text
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| \(dqndefine\(dq text text
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| \(dqtdefine\(dq text text
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| \(dqgfont\(dq text
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| \(dqgsize\(dq text
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| \(dqset\(dq text text
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| \(dqundef\(dq text
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| \(dqsqrt\(dq box
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| box pos box
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| box mark
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| \(dqmatrix\(dq \(dq{\(dq [col \(dq{\(dq list \(dq}\(dq]* \(dq}\(dq
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| pile \(dq{\(dq list \(dq}\(dq
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| font box
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| \(dqsize\(dq text box
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| \(dqleft\(dq text eqn [\(dqright\(dq text]
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col : \(dqlcol\(dq | \(dqrcol\(dq | \(dqccol\(dq | \(dqcol\(dq
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text : [^space\e\(dq]+ | \e\(dq.*\e\(dq
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pile : \(dqlpile\(dq | \(dqcpile\(dq | \(dqrpile\(dq | \(dqpile\(dq
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pos : \(dqover\(dq | \(dqsup\(dq | \(dqsub\(dq | \(dqto\(dq | \(dqfrom\(dq
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mark : \(dqdot\(dq | \(dqdotdot\(dq | \(dqhat\(dq | \(dqtilde\(dq | \(dqvec\(dq
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| \(dqdyad\(dq | \(dqbar\(dq | \(dqunder\(dq
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font : \(dqroman\(dq | \(dqitalic\(dq | \(dqbold\(dq | \(dqfat\(dq
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list : eqn
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| list \(dqabove\(dq eqn
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space : [\e^~ \et]
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.Ed
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.Pp
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White-space consists of the space, tab, circumflex, and tilde
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characters.
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It is required to delimit tokens consisting of alphabetic characters
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and it is ignored at other places.
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Braces and quotes also delimit tokens.
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If within a quoted string, these space characters are retained.
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Quoted strings are also not scanned for keywords, glyph names,
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and expansion of definitions.
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To print a literal quote character, it can be prepended with a
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backslash or expressed with the \e(dq escape sequence.
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.Pp
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Subequations can be enclosed in braces to pass them as arguments
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to operation keywords, overriding standard operation precedence.
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Braces can be nested.
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To set a brace verbatim, it needs to be enclosed in quotes.
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.Pp
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The following text terms are translated into a rendered glyph, if
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available: alpha, beta, chi, delta, epsilon, eta, gamma, iota, kappa,
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lambda, mu, nu, omega, omicron, phi, pi, psi, rho, sigma, tau, theta,
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upsilon, xi, zeta, DELTA, GAMMA, LAMBDA, OMEGA, PHI, PI, PSI, SIGMA,
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THETA, UPSILON, XI, inter (intersection), union (union), prod (product),
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int (integral), sum (summation), grad (gradient), del (vector
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differential), times (multiply), cdot (center-dot), nothing (zero-width
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space), approx (approximately equals), prime (prime), half (one-half),
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partial (partial differential), inf (infinity), >> (much greater), <<
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(much less), <\- (left arrow), \-> (right arrow), +\- (plus-minus), !=
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(not equal), == (equivalence), <= (less-than-equal), and >=
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(more-than-equal).
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The character escape sequences documented in
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.Xr mandoc_char 7
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can be used, too.
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.Pp
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The following control statements are available:
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.Bl -tag -width Ds
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.It Cm define
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Replace all occurrences of a key with a value.
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Its syntax is as follows:
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.Pp
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.D1 Cm define Ar key cvalc
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.Pp
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The first character of the value string,
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.Ar c ,
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is used as the delimiter for the value
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.Ar val .
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This allows for arbitrary enclosure of terms (not just quotes), such as
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.Pp
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.D1 Cm define Ar foo \(aqbar baz\(aq
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.D1 Cm define Ar foo cbar bazc
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.Pp
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It is an error to have an empty
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.Ar key
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or
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.Ar val .
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Note that a quoted
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.Ar key
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causes errors in some
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.Nm
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implementations and should not be considered portable.
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It is not expanded for replacements.
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Definitions may refer to other definitions; these are evaluated
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recursively when text replacement occurs and not when the definition is
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created.
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.Pp
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Definitions can create arbitrary strings, for example, the following is
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a legal construction.
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.Bd -literal -offset indent
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define foo \(aqdefine\(aq
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foo bar \(aqbaz\(aq
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.Ed
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.Pp
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Self-referencing definitions will raise an error.
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The
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.Cm ndefine
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statement is a synonym for
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.Cm define ,
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while
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.Cm tdefine
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is discarded.
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.It Cm delim
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This statement takes a string argument consisting of two bytes,
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to be used as the opening and closing delimiters for equations
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in the middle of text input lines.
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Conventionally, the dollar sign is used for both delimiters,
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as follows:
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.Bd -literal -offset indent
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\&.EQ
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delim $$
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\&.EN
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An equation like $sin pi = 0$ can now be entered
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in the middle of a text input line.
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.Ed
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.Pp
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The special statement
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.Cm delim off
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temporarily disables previously declared delimiters and
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.Cm delim on
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reenables them.
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.It Cm gfont
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Set the default font of subsequent output.
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Its syntax is as follows:
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.Pp
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.D1 Cm gfont Ar font
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.Pp
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In mandoc, this value is discarded.
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.It Cm gsize
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Set the default size of subsequent output.
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Its syntax is as follows:
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.Pp
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.D1 Cm gsize Oo +|\- Oc Ns Ar size
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.Pp
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The
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.Ar size
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value should be an integer.
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If prepended by a sign,
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the font size is changed relative to the current size.
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.It Cm set
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Set an equation mode.
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In mandoc, both arguments are thrown away.
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Its syntax is as follows:
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.Pp
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.D1 Cm set Ar key val
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.Pp
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The
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.Ar key
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and
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.Ar val
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are not expanded for replacements.
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This statement is a GNU extension.
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.It Cm undef
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Unset a previously-defined key.
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Its syntax is as follows:
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.Pp
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.D1 Cm define Ar key
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.Pp
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Once invoked, the definition for
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.Ar key
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is discarded.
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The
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.Ar key
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is not expanded for replacements.
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This statement is a GNU extension.
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.El
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.Pp
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Operation keywords have the following semantics:
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.Bl -tag -width Ds
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.It Cm above
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See
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.Cm pile .
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.It Cm bar
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Draw a line over the preceding box.
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.It Cm bold
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Set the following box using bold font.
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.It Cm ccol
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Like
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.Cm cpile ,
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but for use in
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.Cm matrix .
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.It Cm cpile
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Like
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.Cm pile ,
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but with slightly increased vertical spacing.
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.It Cm dot
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Set a single dot over the preceding box.
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.It Cm dotdot
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Set two dots (dieresis) over the preceding box.
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.It Cm dyad
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Set a dyad symbol (left-right arrow) over the preceding box.
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.It Cm fat
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A synonym for
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.Cm bold .
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.It Cm font
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Set the second argument using the font specified by the first argument;
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currently not recognized by the
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.Xr mandoc 1
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.Nm
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parser.
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.It Cm from
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Set the following box below the preceding box,
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using a slightly smaller font.
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Used for sums, integrals, limits, and the like.
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.It Cm hat
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Set a hat (circumflex) over the preceding box.
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.It Cm italic
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Set the following box using italic font.
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.It Cm lcol
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Like
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.Cm lpile ,
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but for use in
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.Cm matrix .
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.It Cm left
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Set the first argument as a big left delimiter before the second argument.
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As an optional third argument,
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.Cm right
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can follow.
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In that case, the fourth argument is set as a big right delimiter after
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the second argument.
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.It Cm lpile
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Like
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.Cm cpile ,
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but subequations are left-justified.
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.It Cm matrix
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Followed by a list of columns enclosed in braces.
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All columns need to have the same number of subequations.
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The columns are set as a matrix.
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The difference compared to multiple subsequent
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.Cm pile
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operators is that in a
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.Cm matrix ,
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corresponding subequations in all columns line up horizontally,
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while each
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.Cm pile
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does vertical spacing independently.
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.It Cm over
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Set a fraction.
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The preceding box is the numerator, the following box is the denominator.
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.It Cm pile
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Followed by a list of subequations enclosed in braces,
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the subequations being separated by
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.Cm above
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keywords.
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Sets the subequations one above the other, each of them centered.
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Typically used to represent vectors in coordinate representation.
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.It Cm rcol
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Like
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.Cm rpile ,
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but for use in
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.Cm matrix .
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.It Cm right
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See
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.Cm left ;
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.Cm right
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cannot be used without
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.Cm left .
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To set a big right delimiter without a big left delimiter, the following
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construction can be used:
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.Pp
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.D1 Cm left No \(dq\(dq Ar box Cm right Ar delimiter
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.It Cm roman
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Set the following box using the default font.
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.It Cm rpile
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Like
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.Cm cpile ,
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but subequations are right-justified.
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.It Cm size
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Set the second argument with the font size specified by the first
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argument; currently ignored by
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.Xr mandoc 1 .
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By prepending a plus or minus sign to the first argument,
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the font size can be selected relative to the current size.
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.It Cm sqrt
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Set the square root of the following box.
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.It Cm sub
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Set the following box as a subscript to the preceding box.
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.It Cm sup
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Set the following box as a superscript to the preceding box.
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As a special case, if a
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.Cm sup
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clause immediately follows a
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.Cm sub
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clause as in
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.Pp
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.D1 Ar mainbox Cm sub Ar subbox Cm sup Ar supbox
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.Pp
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both are set with respect to the same
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.Ar mainbox ,
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that is,
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.Ar supbox
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is set above
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.Ar subbox .
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.It Cm tilde
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Set a tilde over the preceding box.
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.It Cm to
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Set the following box above the preceding box,
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using a slightly smaller font.
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Used for sums and integrals and the like.
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As a special case, if a
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.Cm to
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clause immediately follows a
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.Cm from
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clause as in
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.Pp
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.D1 Ar mainbox Cm from Ar frombox Cm to Ar tobox
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.Pp
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both are set below and above the same
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.Ar mainbox .
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.It Cm under
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Underline the preceding box.
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.It Cm vec
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Set a vector symbol (right arrow) over the preceding box.
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.El
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.Pp
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The binary operations
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.Cm from ,
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.Cm to ,
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.Cm sub ,
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and
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.Cm sup
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group to the right, that is,
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.Pp
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.D1 Ar mainbox Cm sup Ar supbox Cm sub Ar subbox
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.Pp
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is the same as
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.Pp
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.D1 Ar mainbox Cm sup Brq Ar supbox Cm sub Ar subbox
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.Pp
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and different from
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.Pp
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.D1 Bro Ar mainbox Cm sup Ar supbox Brc Cm sub Ar subbox .
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.Pp
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By contrast,
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.Cm over
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groups to the left.
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.Pp
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In the following list, earlier operations bind more tightly than
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later operations:
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.Pp
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.Bl -enum -compact
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.It
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.Cm dyad ,
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.Cm vec ,
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.Cm under ,
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.Cm bar ,
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.Cm tilde ,
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.Cm hat ,
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.Cm dot ,
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.Cm dotdot
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.It
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.Cm fat ,
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.Cm roman ,
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.Cm italic ,
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.Cm bold ,
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.Cm size
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.It
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.Cm sub ,
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.Cm sup
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.It
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.Cm sqrt
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.It
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.Cm over
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.It
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.Cm from ,
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.Cm to
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.El
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.Sh COMPATIBILITY
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This section documents the compatibility of mandoc
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.Nm
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and the troff
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.Nm
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implementation (including GNU troff).
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.Pp
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.Bl -dash -compact
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.It
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The text string
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.Sq \e\(dq
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is interpreted as a literal quote in troff.
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In mandoc, this is interpreted as a comment.
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.It
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In troff, The circumflex and tilde white-space symbols map to
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fixed-width spaces.
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In mandoc, these characters are synonyms for the space character.
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.It
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The troff implementation of
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.Nm
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allows for equation alignment with the
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.Cm mark
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and
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.Cm lineup
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tokens.
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mandoc discards these tokens.
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The
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.Cm back Ar n ,
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.Cm fwd Ar n ,
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.Cm up Ar n ,
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and
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.Cm down Ar n
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commands are also ignored.
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.El
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.Sh SEE ALSO
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.Xr mandoc 1 ,
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.Xr man 7 ,
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.Xr mandoc_char 7 ,
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.Xr mdoc 7 ,
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.Xr roff 7
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.Rs
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.%A Brian W. Kernighan
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.%A Lorinda L. Cherry
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.%T System for Typesetting Mathematics
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.%J Communications of the ACM
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.%V 18
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.%P pp. 151\(en157
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.%D March, 1975
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.Re
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.Rs
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.%A Brian W. Kernighan
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.%A Lorinda L. Cherry
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.%T Typesetting Mathematics, User's Guide
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.%D 1976
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.Re
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.Rs
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.%A Brian W. Kernighan
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.%A Lorinda L. Cherry
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.%T Typesetting Mathematics, User's Guide (Second Edition)
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.%D 1978
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.Re
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.Sh HISTORY
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The eqn utility, a preprocessor for troff, was originally written by
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Brian W. Kernighan and Lorinda L. Cherry in 1975.
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The GNU reimplementation of eqn, part of the GNU troff package, was
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released in 1989 by James Clark.
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The eqn component of
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.Xr mandoc 1
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was added in 2011.
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.Sh AUTHORS
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This
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.Nm
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reference was written by
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.An Kristaps Dzonsons Aq Mt kristaps@bsd.lv .
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