'\" et
.TH \%eqn 1 "16 October 2023" "groff 1.23.0"
.SH Name
\%eqn \- format mathematics (equations) for
.I groff
or MathML
.
.
.\" ====================================================================
.\" Legal Terms
.\" ====================================================================
.\"
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.\"
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.\" preserved on all copies.
.\"
.\" Permission is granted to copy and distribute modified versions of
.\" this manual under the conditions for verbatim copying, provided that
.\" the entire resulting derived work is distributed under the terms of
.\" a permission notice identical to this one.
.\"
.\" Permission is granted to copy and distribute translations of this
.\" manual into another language, under the above conditions for
.\" modified versions, except that this permission notice may be
.\" included in translations approved by the Free Software Foundation
.\" instead of in the original English.
.
.
.\" Save and disable compatibility mode (for, e.g., Solaris 10/11).
.do nr *groff_eqn_1_man_C \n[.cp]
.cp 0
.
.\" Define fallback for groff 1.23's MR macro if the system lacks it.
.nr do-fallback 0
.if !\n(.f           .nr do-fallback 1 \" mandoc
.if  \n(.g .if !d MR .nr do-fallback 1 \" older groff
.if !\n(.g           .nr do-fallback 1 \" non-groff *roff
.if \n[do-fallback]  \{\
.  de MR
.    ie \\n(.$=1 \
.      I \%\\$1
.    el \
.      IR \%\\$1 (\\$2)\\$3
.  .
.\}
.rr do-fallback
.
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.ie \n(.V<\n(.v \
.  ds tx T\h'-.1667m'\v'.224m'E\v'-.224m'\h'-.125m'X
.el \
.  ds tx TeX
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.
.\" ====================================================================
.SH Synopsis
.\" ====================================================================
.
.SY \%eqn
.RB [ \-CNrR ]
.RB [ \- d
.IR xy ]
.RB [ \-f
.IR F ]
.RB [ \-m
.IR n ]
.RB [ \-M
.IR dir ]
.RB [ \-p
.IR n ]
.RB [ \-s
.IR n ]
.RB [ \-T
.IR dev ]
.RI [ file\~ .\|.\|.]
.YS
.
.
.SY \%eqn
.B \-\-help
.YS
.
.
.SY \%eqn
.B \-v
.
.SY \%eqn
.B \-\-version
.YS
.
.
.\" ====================================================================
.SH Description
.\" ====================================================================
.
The GNU implementation of
.I eqn \" GNU
is part of the
.MR groff 7
document formatting system.
.
.I \%eqn
is a
.MR \%troff 1
preprocessor that translates expressions in its own language,
embedded in
.MR roff 7
input files,
into mathematical notation typeset by
.MR \%troff 1 .
.
It copies each
.IR file 's
contents to the standard output stream,
translating each
.I equation
between lines starting with
.B .EQ
and
.BR .EN ,
or within a pair of user-specified delimiters.
.
Normally,
.I \%eqn
is not executed directly by the user,
but invoked by specifying the
.B \-e
option to
.MR groff 1 .
.
While GNU
.IR eqn 's \" GNU
input syntax is highly compatible with AT&T
.IR eqn , \" AT&T
the output
.I \%eqn
produces cannot be processed by AT&T
.IR troff ; \" AT&T
GNU
.I troff \" GNU
(or a
.I troff \" generic
implementing relevant GNU extensions)
must be used.
.
If no
.I file
operands are given on the command line,
or if
.I file
is
.RB \[lq] \- \[rq],
.I \%eqn
reads the standard input stream.
.
.
.P
Unless the
.B \-R
option is used,
.I \%eqn
searches for the file
.I eqnrc
in the directories given with the
.B \-M
option first,
then in
.if !'no'no' .IR /usr/\:\%lib/\:\%groff/\:\%site\-tmac ,
.IR /usr/\:\%share/\:\%groff/\:\%site\-tmac ,
and finally in the standard macro directory
.IR /usr/\:\%share/\:\%groff/\:\%1.23.0/\:\%tmac .
.
If it exists and is readable,
.I \%eqn
processes it before any input files.
.
.
.P
This man page primarily discusses the differences between GNU
.I eqn \" GNU
and AT&T
.IR eqn .\" AT&T
.
Most of the new features of the GNU
.I eqn \" GNU
input language are based on \*[tx].
.
There are some references to the differences between \*[tx] and GNU
.I eqn \" GNU
below;
these may safely be ignored if you do not know \*[tx].
.
.
.P
Three points are worth special note. \" good, bad, and different
.
.
.IP \[bu] 2n
GNU
.I eqn \" GNU
emits Presentation MathML output when invoked with the
.RB \[lq] "\-T\~MathML" \[rq]
option.
.
.
.IP \[bu]
GNU
.I eqn \" GNU
does not support terminal devices well,
though it may suffice for simple inputs.
.
.
.IP \[bu]
GNU
.I eqn
sets the input token
.RB \[lq] .\|.\|.\& \[rq]
as an ellipsis on the text baseline,
not the three centered dots of AT&T
.IR eqn . \" AT&T
.
Set an ellipsis on the math axis with the GNU extension macro
.BR cdots .
.
.
.\" ====================================================================
.SS "Anatomy of an equation"
.\" ====================================================================
.
.I eqn
input consists of tokens.
.
Consider a form of Newton's second law of motion.
.
The input
.
.
.P
.RS
.EX
\&.EQ
F =
m a
\&.EN
.EE
.RE
.
.
.P
becomes
.EQ
F =
m a.
.EN
.
Each of
.BR F ,
.BR = ,
.BR m ,
and
.B a
is a token.
.
.
Spaces and newlines are interchangeable;
they separate tokens but do not break lines or produce space in
the output.
.
.
.P
The following input characters not only separate tokens,
but manage their grouping and spacing as well.
.
.
.TP
.B "{ }"
Braces perform grouping.
.
Whereas
.RB \[lq] "e sup a b" \[rq]
expresses
.ie n .RI \[lq]( e "\~to the\~" a )\~times\~ b \[rq],
.el \{\
.EQ
e sup a b ,
.EN
.\}
.RB \[lq] "e sup { a b }" \[rq]
means
.ie n .RI \[lq] e "\~to the\~(" a \~times\~ b )\[rq].
.el \{\
.EQ
e sup { a b } .
.EN
.\}
.
When immediately preceded by a
.RB \[lq] left \[rq]
or
.RB \[lq] right \[rq]
primitive,
a brace loses its special meaning.
.
.
.TP
.B "\[ha] \[ti]
are the
.I "half space"
and
.I "full space,"
respectively.
.
Use them to tune the appearance of the output.
.
.
.P
Tab and leader characters separate tokens as well as advancing the
drawing position to the next tab stop,
but are seldom used in
.I eqn
input.
.
When they occur,
they must appear at the outermost lexical scope.
.
This roughly means that they can't appear within braces that are
necessary to disambiguate the input;
.I \%eqn
will diagnose an error in this event.
.
(See subsection \[lq]Macros\[rq] below for additional token separation
rules.)
.
.
.P
Other tokens are primitives,
macros,
an argument to either of the foregoing,
or components of an equation.
.
.
.br
.ne 4v
.P
.I Primitives
are fundamental keywords of the
.I eqn
language.
.
They can configure an aspect of the preprocessor's state,
as when setting a \[lq]global\[rq] font selection or type size
.RB ( gfont
and
.BR gsize ),
or declaring or deleting macros
.RB \%(\[lq] define \[rq]
and
.BR undef );
these are termed
.I commands.
.
Other primitives perform formatting operations on the tokens after them
(as with
.BR fat ,
.BR over ,
.BR sqrt ,
or
.BR up ).
.
.
.P
Equation
.I components
include mathematical variables,
constants,
numeric literals,
and operators.
.
.I \%eqn
remaps some input character sequences to
.I groff
special character escape sequences for economy in equation entry and to
ensure that glyphs from an unstyled font are used;
see
.MR groff_char 7 .
.
.
.P
.RS
.TS
tab(@);
Lf(CR) Lf(CR) Lw(1i) Lf(CR) Lf(CR).
+@\[rs][pl]@\&@\[aq]@\[rs][fm]
-@\[rs][mi]@\&@<=@\[rs][<=]
\&=@\[rs][eq]@\&@>=@\[rs][>=]
.TE
.RE
.
.
.P
.I Macros
permit primitives,
components,
and other macros to be collected and referred to by a single token.
.
Predefined macros make convenient the preparation of
.I eqn
input in a form resembling its spoken expression;
for example,
consider
.BR cos ,
.BR hat ,
.BR inf ,
and
.BR lim .
.
.
.\" ====================================================================
.SS "Spacing and typeface"
.\" ====================================================================
.
GNU
.I eqn
imputes types to the components of an equation,
adjusting the spacing between them accordingly.
.
Recognized types are as follows;
most affect spacing only,
whereas the
.RB \%\[lq] letter \[rq]
subtype of
.RB \%\[lq] ordinary \[rq]
also assigns a style.
.
.
.RS 2n \" we need quite a bit of horizontal space for this table
.P
.TS
Lf(CR) Lx
Af(CR) Lx
Af(CR) Lx
Lf(CR) Lx.
ordinary	T{
character such as \[lq]1\[rq],
\[lq]a\[rq],
or
\[lq]!\&\[rq]
T}
letter	character to be italicized by default
digit	\f[I]n/a\f[]
operator	T{
large operator such as
.ds Su \[lq]\s+5\[*S]\s0\[rq]
.if \n(.g .if !c\[*S] .ds Su the summation operator
\*[Su]
.rm Su
T}
binary	binary operator such as \[lq]\[pl]\[rq]
relation	relational operator such as \[lq]=\[rq]
opening	opening bracket such as \[lq](\[rq]
closing	closing bracket such as \[lq])\[rq]
punctuation	punctuation character such as \[lq],\[rq]
inner	sub-formula contained within brackets
suppress	component to which automatic spacing is not applied
.TE
.RE
.
.
.P
Two primitives apply types to equation components.
.
.
.TP
.BI type\~ "t e"
Apply
.RI type\~ t
to
.RI expression\~ e .
.
.
.TP
.BI chartype\~ "t text"
Assign each character in (unquoted)
.I text
.RI type\~ t ,
persistently.
.
.
.P
.I \%eqn \" GNU
sets up spacings and styles as if by the following commands.
.
.P
.RS
.TS
tab(@);
Lf(CR)1 Lf(CR).
chartype \[dq]letter\[dq]@abcdefghiklmnopqrstuvwxyz
chartype \[dq]letter\[dq]@ABCDEFGHIKLMNOPQRSTUVWXYZ
chartype \[dq]letter\[dq]@\[rs][*a]\[rs][*b]\[rs][*g]\[rs][*d]\[rs][*e]\
\[rs][*z]
chartype \[dq]letter\[dq]@\[rs][*y]\[rs][*h]\[rs][*i]\[rs][*k]\[rs][*l]\
\[rs][*m]
chartype \[dq]letter\[dq]@\[rs][*n]\[rs][*c]\[rs][*o]\[rs][*p]\[rs][*r]\
\[rs][*s]
chartype \[dq]letter\[dq]@\[rs][*t]\[rs][*u]\[rs][*f]\[rs][*x]\[rs][*q]\
\[rs][*w]
chartype \[dq]binary\[dq]@*\[rs][pl]\[rs][mi]
chartype \[dq]relation\[dq]@<>\[rs][eq]\[rs][<=]\[rs][>=]
chartype \[dq]opening\[dq]@{([
chartype \[dq]closing\[dq]@})]
chartype \[dq]punctuation\[dq]@,;:.
chartype \[dq]suppress\[dq]@\[ha]\[ti]
.TE
.RE
.
.
.P
.I \%eqn
assigns all other ordinary and special
.I roff
characters,
including numerals 0\[en]9,
the
.RB \%\[lq] ordinary \[rq]
type.
.
(The
.RB \[lq] digit \[rq]
type is not used,
but is available for customization.)
.\" XXX: How would you actually customize it, though?  There doesn't
.\" seem to be a means of replacing the font associated with a type.
.\" Is the "digit" type just cruft?
.
In keeping with common practice in mathematical typesetting,
lowercase,
but not uppercase,
Greek letters are assigned the
.RB \%\[lq] letter \[rq]
type to style them in italics.
.
The macros for producing ellipses,
.RB \[lq] .\|.\|. \[rq],
.BR cdots ,
and
.BR ldots ,
use the
.RB \%\[lq] inner \[rq]
type.
.
.
.\" ====================================================================
.SS Primitives
.\" ====================================================================
.
.I \%eqn
supports without alteration the AT&T
.I eqn \" AT&T
primitives
.BR above ,
.BR back ,
.BR bar ,
.BR bold ,
.BR \%define ,
.BR down ,
.BR fat ,
.BR font ,
.BR from ,
.BR fwd ,
.BR gfont ,
.BR gsize ,
.BR italic ,
.BR left ,
.BR lineup ,
.BR mark ,
.BR \%matrix ,
.BR \%ndefine ,
.BR over ,
.BR right ,
.BR roman ,
.BR size ,
.BR sqrt ,
.BR sub ,
.BR sup ,
.BR \%tdefine ,
.BR to ,
.BR \%under ,
and
.BR up .
.
.
.\" ====================================================================
.SS "New primitives"
.\" ====================================================================
.
The GNU extension primitives
.RB \[lq] type \[rq]
and
.B \%chartype
are discussed in subsection \[lq]Spacing and typeface\[rq] above;
.RB \[lq] set \[rq]
in subsection \[lq]Customization\[rq] below;
and
.B grfont
and
.B gbfont
in subsection \[lq]Fonts\[rq] below.
.
In the following synopses,
.I X
can be any character not appearing in the parameter thus bracketed.
.
.
.TP
.IB e1 \~accent\~ e2
Set
.I e2
as an accent over
.IR e1 .
.
.I e2
is assumed to be at the appropriate height for a lowercase letter
without an ascender;
.I \% eqn
vertically shifts it depending on
.IR e1 's
height.
.
For example,
.B hat
is defined as follows.
.
.
.RS
.IP
.EX
accent { "\[ha]" }
.EE
.RE
.
.
.IP
.BR dotdot ,
.BR dot ,
.BR tilde ,
.BR vec ,
and
.B dyad
are also defined using the
.B \%accent
primitive.
.
.
.TP
.BI big\~ e
Enlarge the expression
.IR e ;
semantics like those of CSS \[lq]large\[rq] are intended.
.
In
.I \%troff
output,
the type size is increased by\~5 scaled points.
.
MathML output emits the following.
.
.
.RS
.IP
.EX
<mstyle \%mathsize=\[aq]big\[aq]>
.EE
.RE
.
.
.TP
.BI copy\~ file
.TQ
.BI include\~ file
Interpolate the contents of
.IR file ,
omitting lines
beginning with
.B .EQ
or
.BR .EN .
.
If a relative path name,
.I file
is sought relative to the current working directory.
.
.
.TP
.BI ifdef\~ "name X anything X"
If
.I name
is defined as a primitive or macro,
interpret
.IR anything .
.
.
.TP
.BI nosplit\~ text
As
.RI \[dq] text \[dq],
but since
.I text
is not quoted it is subject to macro expansion;
it is not split up and the spacing between characters not adjusted per
subsection \[lq]Spacing and typeface\[rq] above.
.
.
.TP
.IB e\~ opprime
As
.BR prime ,
but set the prime symbol as an operator
.RI on\~ e .
.
In the input
.RB \[lq] "A opprime sub 1" \[rq],
the\~\[lq]1\[rq] is tucked under the prime as a subscript to
the\~\[lq]A\[rq]
(as is conventional in mathematical typesetting),
whereas when
.B prime
is used,
the\~\[lq]1\[rq] is a subscript to the prime character.
.
The precedence of
.B \%opprime
is the same as that of
.B bar
and
.RB \%\[lq] under \[rq],
and higher than that of other primitives except
.B \%accent
and
.BR uaccent .
.
In unquoted text,
a neutral apostrophe
.RB ( \[aq] )
that is not the first character on the input line is treated like
.BR \%opprime .
.
.
.TP
.BI sdefine\~ "name X anything X"
As
.RB \%\[lq] define \[rq],
but
.I name
is not recognized as a macro if called with arguments.
.
.
.TP
.IB e1 \~smallover\~ e2
As
.BR over ,
but reduces the type size of
.I e1
and
.IR e2 ,
and puts less vertical space between
.I e1
and
.I e2
and the fraction bar.
.
The
.B over
primitive corresponds to the \*[tx]
.B \[rs]over
primitive in displayed equation styles;
.B smallover
corresponds to
.B \[rs]over
in non-display (\[lq]inline\[rq]) styles.
.
.
.br
.ne 5v
.TP
.BI space\~ n
Set extra vertical spacing around the equation,
replacing the default values,
where
.IR n \~is
an integer in hundredths of an em.
.
If positive,
.IR n \~increases
vertical spacing before the equation;
if negative,
it does so after the equation.
.
This primitive provides an interface to
.IR groff 's
.B \[rs]x
escape sequence,
but with the opposite sign convention.
.
It has no effect if the equation is part of a
.MR \%pic 1
picture.
.
.
.TP
.BI special\~ "troff-macro e"
Construct an object by calling
.I troff-macro
.RI on\~ e .
.
The
.I troff \" generic
string
.B 0s
contains the
.I eqn \" generic
output
.RI for\~ e ,
and the registers
.BR 0w ,
.BR 0h ,
.BR 0d ,
.BR 0skern ,
and
.B 0skew
the width,
height,
depth,
subscript kern,
and skew
.RI of\~ e ,
respectively.
.
(The
.I subscript kern
of an object indicates how much a subscript on that object should be
\[lq]tucked in\[rq],
or placed to the left relative to a non-subscripted glyph of the same
size.
.
The
.I skew
of an object is how far to the right of the center of the object an
accent over it should be placed.)
.
The macro must modify
.B 0s
so that it outputs the desired result,
returns the drawing position to the text baseline at the beginning of
.IR e ,
and updates the foregoing registers to correspond to the new dimensions
of the result.
.
.
.IP
Suppose you want a construct that \[lq]cancels\[rq] an expression by
drawing a diagonal line through it.
.
.
.br
.ne 11v
.RS
.IP
.EX
\&.de Ca
\&.  ds 0s \[rs]
\[rs]Z\[aq]\[rs]\[rs]*(0s\[aq]\[rs]
\[rs]v\[aq]\[rs]\[rs]n(0du\[aq]\[rs]
\[rs]D\[aq]l \[rs]\[rs]n(0wu \-\[rs]\[rs]n(0hu\-\[rs]\
\[rs]n(0du\[aq]\[rs]
\[rs]v\[aq]\[rs]\[rs]n(0hu\[aq]
\&..
\&.EQ
special Ca "x \[rs][mi] 3 \[rs][pl] x" \[ti] 3
\&.EN
.EE
.RE
.
.
.IP
We use the
.B \[rs][mi]
and
.B \[rs][pl]
special characters instead of + and \-
because they are part of the argument to a
.I \%troff
macro,
so
.I \%eqn
does not transform them to mathematical glyphs for us.
.
Here's a more complicated construct that draws a box around an
expression;
the bottom of the box rests on the text baseline.
.
We define the
.I eqn \" generic
macro
.B box
to wrap the call of the
.I \%troff
macro
.BR Bx .
.
.
.br
.ne 17v
.RS
.IP
.EX
\&.de Bx
\&.ds 0s \[rs]
\[rs]Z\[aq]\[rs]\[rs]h\[aq]1n\[aq]\[rs]\[rs]*[0s]\[aq]\[rs]
\[rs]v\[aq]\[rs]\[rs]n(0du+1n\[aq]\[rs]
\[rs]D\[aq]l \[rs]\[rs]n(0wu+2n 0\[aq]\[rs]
\[rs]D\[aq]l 0 \-\[rs]\[rs]n(0hu\-\[rs]\[rs]n(0du\-2n\[aq]\[rs]
\[rs]D\[aq]l \-\[rs]\[rs]n(0wu\-2n 0\[aq]\[rs]
\[rs]D\[aq]l 0 \[rs]\[rs]n(0hu+\[rs]\[rs]n(0du+2n\[aq]\[rs]
\[rs]h\[aq]\[rs]\[rs]n(0wu+2n\[aq]
\&.nr 0w +2n
\&.nr 0d +1n
\&.nr 0h +1n
\&..
\&.EQ
define box \[aq] special Bx $1 \[aq]
box(foo) \[ti] "bar"
\&.EN
.EE
.RE
.
.
.TP
.BI "split \[dq]" text \[dq]
As
.IR text ,
but since
.I text
is quoted,
it is not subject to macro expansion;
it is split up and the spacing between characters adjusted per
subsection \[lq]Spacing and typeface\[rq] above.
.
.
.TP
.IB e1 \~uaccent\~ e2
Set
.I e2
as an accent under
.IR e1 .
.
.I e2
is assumed to be at the appropriate height for a letter without a
descender;
.I \% eqn
vertically shifts it depending on whether
.I e1
has a descender.
.
.B utilde
is predefined using
.B uaccent
as a tilde accent below the baseline.
.
.
.TP
.BI undef\~ name
Remove definition of macro or primitive
.IR name ,
making it undefined.
.
.
.TP
.BI vcenter\~ e
Vertically center
.I e
about the
.IR "math axis" ,
a horizontal line upon which fraction bars and characters such as
\[lq]\[pl]\[rq] and \[lq]\[mi]\[rq] are aligned.
.
MathML already behaves this way,
so
.I \%eqn
ignores this primitive when producing that output format.
.
The built-in
.B sum
macro is defined as if by the following.
.
.RS
.IP
.EX
define sum ! { type "operator" vcenter size +5 \[rs](*S } !
.EE
.RE
.
.
.br
.ne 8v
.\" ====================================================================
.SS "Extended primitives"
.\" ====================================================================
.
GNU
.I eqn \" GNU
extends the syntax of some AT&T
.I eqn \" AT&T
primitives,
introducing one deliberate incompatibility.
.
.
.TP
.B "delim on"
.I \%eqn
recognizes an
.RB \[lq] on \[rq]
argument to the
.B \%delim
primitive specially,
restoring any delimiters previously disabled with
.RB \%\[lq] "delim off" \[rq].
.
If delimiters haven't been specified,
neither command has effect.
.
Few
.I eqn \" generic
documents are expected to use \[lq]o\[rq] and \[lq]n\[rq] as left and
right delimiters,
respectively.
.
If yours does,
consider swapping them,
or select others.
.
.
.TP
.BI col\~ n\~\c
.BR {\~ .\|.\|.\& \~}
.TQ
.BI ccol\~ n\~\c
.BR {\~ .\|.\|.\& \~}
.TQ
.BI lcol\~ n\~\c
.BR {\~ .\|.\|.\& \~}
.TQ
.BI rcol\~ n\~\c
.BR {\~ .\|.\|.\& \~}
.TQ
.BI pile\~ n\~\c
.BR {\~ .\|.\|.\& \~}
.TQ
.BI cpile\~ n\~\c
.BR {\~ .\|.\|.\& \~}
.TQ
.BI lpile\~ n\~\c
.BR {\~ .\|.\|.\& \~}
.TQ
.BI rpile\~ n\~\c
.BR {\~ .\|.\|.\& \~}
The integer
.RI value\~ n
(in hundredths of an em)
increases the vertical spacing between rows,
using
.IR groff 's
.B \[rs]x
escape sequence
(the value has no effect in MathML mode).
.
Negative values are accepted but have no effect.
.
If more than one
.I n
occurs in a matrix or pile,
the largest is used.
.
.
.\" ====================================================================
.SS Customization
.\" ====================================================================
.
When
.I \%eqn
generates
.I \%troff
input,
the appearance of equations is controlled by a large number of
parameters.
.
They have no effect when generating MathML,
which delegates typesetting to a MathML rendering engine.
.
Configure these parameters with the
.B set
primitive.
.
.
.TP
.BI set\~ "p n"
assigns
.RI parameter\~ p
the integer
.RI value\~ n ;
.IR n \~is
interpreted in units of hundredths of an em unless otherwise stated.
.
For example,
.
.
.RS
.IP
.EX
set x_height 45
.EE
.RE
.
.
.IP
says that
.I \%eqn
should assume that the font's x-height is 0.45\~ems.
.
.
.RS
.P
Available parameters are as follows;
defaults are shown in parentheses.
.
We intend these descriptions to be expository rather than rigorous.
.
.
.TP 17n
.B minimum_size
sets a floor for the type size
(in scaled points)
at which equations are set
.RB ( 5 ).
.
.
.TP
.B fat_offset
The
.B fat
primitive emboldens an equation by overprinting two copies of the
equation horizontally offset by this amount
.RB ( 4 ).
.
In MathML mode,
components to which
.B \%fat_offset
applies instead use the following.
.
.RS
.RS
.EX
<mstyle mathvariant=\[aq]double\-struck\[aq]>
.EE
.RE
.RE
.
.
.TP
.B over_hang
A fraction bar is longer by twice this amount than
the maximum of the widths of the numerator and denominator;
in other words,
it overhangs the numerator and denominator by at least this amount
.RB ( 0 ).
.
.
.TP
.B accent_width
When
.B bar
or
.B \%under
is applied to a single character,
the line is this long
.RB ( 31 ).
.
Normally,
.B bar
or
.B \%under
produces a line whose length is the width of the object to which it
applies;
in the case of a single character,
this tends to produce a line that looks too long.
.
.
.TP
.B delimiter_factor
Extensible delimiters produced with the
.B left
and
.B right
primitives have a combined height and depth of at least this many
thousandths of twice the maximum amount by which the sub-equation that
the delimiters enclose extends away from the axis
.RB ( 900 ).
.
.
.TP
.B delimiter_shortfall
Extensible delimiters produced with the
.B left
and
.B right
primitives have a combined height and depth not less than the
difference of twice the maximum amount by which the sub-equation that
the delimiters enclose extends away from the axis and this amount
.RB ( 50 ).
.
.
.TP
.B null_delimiter_space
This much horizontal space is inserted on each side of a fraction
.RB ( 12 ).
.
.
.TP
.B script_space
The width of subscripts and superscripts is increased by this amount
.RB ( 5 ).
.
.
.TP
.B thin_space
This amount of space is automatically inserted after punctuation
characters.
.
It also configures the width of the space produced by the
.B \[ha]
token
.RB ( 17 ).
.
.
.TP
.B medium_space
This amount of space is automatically inserted on either side of
binary operators
.RB ( 22 ).
.
.
.TP
.B thick_space
This amount of space is automatically inserted on either side of
relations.
.
It also configures the width of the space produced by the
.B \[ti]
token
.RB ( 28 ).
.
.
.TP
.B x_height
The height of lowercase letters without ascenders such as \[lq]x\[rq]
.RB ( 45 ).
.
.
.TP
.B axis_height
The height above the baseline of the center of characters such as
\[lq]\[pl]\[rq] and \[lq]\[mi]\[rq]
.RB ( 26 ).
.
It is important that this value is correct for the font
you are using.
.
.
.TP
.B default_rule_thickness
This should be set to the thickness of the
.B \[rs][ru]
character,
or the thickness of horizontal lines produced with the
.B \[rs]D
escape sequence
.RB ( 4 ).
.
.
.TP
.B num1
The
.B over
primitive shifts up the numerator by at least this amount
.RB ( 70 ).
.
.
.TP
.B num2
The
.B smallover
primitive shifts up the numerator by at least this amount
.RB ( 36 ).
.
.
.TP
.B denom1
The
.B over
primitive shifts down the denominator by at least this amount
.RB ( 70 ).
.
.
.TP
.B denom2
The
.B smallover
primitive shifts down the denominator by at least this amount
.RB ( 36 ).
.
.
.TP
.B sup1
Normally superscripts are shifted up by at least this amount
.RB ( 42 ).
.
.
.TP
.B sup2
Superscripts within superscripts or upper limits
or numerators of
.B smallover
fractions are shifted up by at least this amount
.RB ( 37 ).
.
Conventionally,
this is less than
.BR sup1 .
.
.
.TP
.B sup3
Superscripts within denominators or square roots
or subscripts or lower limits are shifted up by at least
this amount
.RB ( 28 ).
.
Conventionally,
this is less than
.BR sup2 .
.
.
.TP
.B sub1
Subscripts are normally shifted down by at least this amount
.RB ( 20 ).
.
.
.TP
.B sub2
When there is both a subscript and a superscript,
the subscript is shifted down by at least this amount
.RB ( 23 ).
.
.
.TP
.B sup_drop
The baseline of a superscript is no more than this much below the top of
the object on which the superscript is set
.RB ( 38 ).
.
.
.TP
.B sub_drop
The baseline of a subscript is at least this much below the bottom of
the object on which the subscript is set
.RB ( 5 ).
.
.
.TP
.B big_op_spacing1
The baseline of an upper limit is at least this much above the top of
the object on which the limit is set
.RB ( 11 ).
.
.
.TP
.B big_op_spacing2
The baseline of a lower limit is at least this much below the bottom
of the object on which the limit is set
.RB ( 17 ).
.
.
.TP
.B big_op_spacing3
The bottom of an upper limit is at least this much above the top of
the object on which the limit is set
.RB ( 20 ).
.
.
.TP
.B big_op_spacing4
The top of a lower limit is at least this much below the bottom of the
object on which the limit is set
.RB ( 60 ).
.
.
.TP
.B big_op_spacing5
This much vertical space is added above and below limits
.RB ( 10 ).
.
.
.TP
.B baseline_sep
The baselines of the rows in a pile or matrix are normally this far
apart
.RB ( 140 ).
.
Usually equal to the sum of
.B num1
and
.BR denom1 .
.
.
.TP
.B shift_down
The midpoint between the top baseline and the bottom baseline in a
matrix or pile is shifted down by this much from the axis
.RB ( 26 ).
.
Usually equal to
.BR axis_height .
.
.
.TP
.B column_sep
This much space is added between columns in a matrix
.RB ( 100 ).
.
.
.TP
.B matrix_side_sep
This much space is added at each side of a matrix
.RB ( 17 ).
.
.
.br
.ne 4v
.TP
.B draw_lines
If non-zero,
.I \%eqn
draws lines using the
.I troff \" generic
.B \[rs]D
escape sequence,
rather than the
.B \[rs]l
escape sequence and the
.B \[rs][ru]
special character.
.
The
.I eqnrc
file sets the default:
.BR 1 \~on
.BR ps ,
.BR html ,
and the X11 devices,
.RB otherwise\~ 0 .
.
.
.TP
.B body_height
is the presumed height of an equation above the text baseline;
.I \%eqn
adds any excess as extra pre-vertical line spacing with
.IR troff 's\" generic
.B \[rs]x
escape sequence
.RB ( 85 ).
.
.
.TP
.B body_depth
is the presumed depth of an equation below the text baseline;
.I \%eqn
adds any excess as extra post-vertical line spacing with
.IR troff 's\" generic
.B \[rs]x
escape sequence
.RB ( 35 ).
.
.
.TP
.B nroff
If non-zero,
then
.B \%ndefine
behaves like
.B \%define
and
.B \%tdefine
is ignored,
otherwise
.B \%tdefine
behaves like
.B \%define
and
.B \%ndefine
is ignored.
.
The
.I eqnrc
file sets the default:
.BR 1 \~on
.BR ascii ,
.BR latin1 ,
.BR utf8 ,
and
.B cp1047
devices,
.RB otherwise\~ 0 .
.RE
.
.
.\" ====================================================================
.SS Macros
.\" ====================================================================
.
In GNU
.IR eqn , \" GNU
macros can take arguments.
.
A word defined by any of the
.BR \%define ,
.BR \%ndefine ,
or
.B \%tdefine
primitives followed immediately by a left parenthesis is treated as a
.I "parameterized macro call:"
subsequent tokens up to a matching right parenthesis are treated as
comma-separated arguments.
.
In this context only,
commas and parentheses also serve as token separators.
.
A macro argument is not terminated by a comma inside parentheses nested
within it.
.
In a macro definition,
.BI $ n\c
,
where
.I n
is between 1 and\~9 inclusive,
is replaced by the
.IR n th
argument;
if there are fewer than
.IR n \~arguments,
it is replaced by nothing.
.
.
.\" ====================================================================
.SS "Predefined macros"
.\" ====================================================================
.
GNU
.I eqn \" GNU
supports the predefined macros offered by AT&T
.IR eqn : \" AT&T
.BR and ,
.BR \%approx ,
.BR arc ,
.BR cos ,
.BR cosh ,
.BR del ,
.BR det ,
.BR dot ,
.BR \%dotdot ,
.BR dyad ,
.BR exp ,
.BR for ,
.BR grad ,
.BR half ,
.BR hat ,
.BR if ,
.BR \%inter ,
.BR Im ,
.BR inf ,
.BR int ,
.BR lim ,
.BR ln ,
.BR log ,
.BR max ,
.BR min ,
.BR \%nothing ,
.BR \%partial ,
.BR prime ,
.BR prod ,
.BR Re ,
.BR sin ,
.BR sinh ,
.BR sum ,
.BR tan ,
.BR tanh ,
.BR tilde ,
.BR times ,
.BR union ,
.BR vec ,
.BR == ,
.BR != ,
.BR += ,
.BR \-> ,
.BR <\- ,
.BR << ,
.BR >> ,
and
.RB \[lq] .\|.\|. \[rq].
.
The lowercase classical Greek letters are available as
.BR \%alpha ,
.BR beta ,
.BR chi ,
.BR delta ,
.BR \%epsilon ,
.BR eta ,
.BR gamma ,
.BR iota ,
.BR kappa ,
.BR lambda ,
.BR mu ,
.BR nu ,
.BR omega ,
.BR \%omicron ,
.BR phi ,
.BR pi ,
.BR psi ,
.BR rho ,
.BR sigma ,
.BR tau ,
.BR theta ,
.BR \%upsilon ,
.BR xi ,
and
.BR zeta .
.
Spell them with an initial capital letter
.RB \%( Alpha )
or in full capitals
.RB \%( ALPHA )
to obtain uppercase forms.
.
.
.P
GNU
.I eqn \" GNU
further defines the macros
.BR cdot ,
.BR cdots ,
and
.B utilde
(all discussed above),
.BR \%dollar ,
which sets a dollar sign,
and
.BR ldots ,
which sets an ellipsis on the text baseline.
.
.
.\" ====================================================================
.SS Fonts
.\" ====================================================================
.
.I \%eqn
uses up to three typefaces to set an equation:
italic (oblique),
roman (upright),
and bold.
.
Assign each a
.I groff
typeface with the primitives
.BR gfont ,
.BR \%grfont ,
and
.B \%gbfont.
.
The defaults are the styles
.BR I ,
.BR R ,
and
.B B
(applied to the current font family).
.
The
.B \%chartype
primitive
(see above)
sets a character's type,
which determines the face used to set it.
.
The
.RB \%\[lq] letter \[rq]
type is set in italics;
others are set in roman.
.
Use the
.B bold
primitive to select an (upright) bold style.
.
.
.TP
.BI gbfont\~ f
.RI Select\~ f
as the bold font.
.
This is a GNU extension.
.
.
.TP
.BI gfont\~ f
.RI Select\~ f
as the italic font.
.
.
.TP
.BI grfont\~ f
.RI Select\~ f
as the roman font.
.
This is a GNU extension.
.
.
.br
.ne 4v
.\" ====================================================================
.SH Options
.\" ====================================================================
.
.B \-\-help
displays a usage message,
while
.B \-v
and
.B \-\-version
show version information;
all exit afterward.
.
.
.TP
.B \-C
Recognize
.B .EQ
and
.B .EN
even when followed by a character other than space or newline.
.
.
.TP
.BI \-d\~ xy
Specify delimiters
.I x
for left
.RI and\~ y
for right ends
of equations not bracketed by
.BR .EQ / .EN .
.
.I x
and
.I y
need not be distinct.
.
Any
.RB \%\[lq] delim
.IR xy \[rq]
statements in the source file override this option.
.
.
.TP
.BI \-f\~ F
is equivalent to
.RB \[lq] gfont
.IR F \[rq].
.
.
.TP
.BI \-m\~ n
is equivalent to
.RB \[lq] "set \%minimum_size"
.IR n \[rq].
.
.
.TP
.BI \-M\~ dir
Search
.I dir
for
.I eqnrc
before those listed in section \[lq]Description\[rq] above.
.
.
.TP
.B \-N
Prohibit newlines within delimiters.
.
This option allows
.I \%eqn
to recover better from missing closing delimiters.
.
.
.TP
.BI \-p\~ n
Set sub- and superscripts
.IR n \~points
smaller than the surrounding text.
.
This option is deprecated.
.
.I \%eqn
normally sets sub- and superscripts at 70% of the type size of the
surrounding text.
.
.
.TP
.B \-r
Reduce the type size of subscripts at most once relative to the base
type size for the equation.
.
.
.TP
.B \-R
Don't load
.IR eqnrc .
.
.
.TP
.BI \-s\~ n
is equivalent to
.RB \[lq] gsize
.IR n \[rq].
.
This option is deprecated.
.
.
.TP
.BI \-T\~ dev
Prepare output for the device
.IR dev .
.
In most cases,
the effect of this is to define a macro
.I dev
with a value
.RB of\~ 1 ;
.I eqnrc
uses this to provide definitions appropriate for the device.
.
However,
if the specified driver is \[lq]MathML\[rq],
the output is MathML markup rather than
.I \%troff
input,
and
.I eqnrc
is not loaded at all.
.
The default output device is
.BR \%ps .
.
.
.\" ====================================================================
.SH Files
.\" ====================================================================
.
.TP
.I /usr/\:\%share/\:\%groff/\:\%1.23.0/\:\%tmac/\:\%eqnrc
Initialization file.
.
.
.\" ====================================================================
.SH "MathML mode limitations"
.\" ====================================================================
.
MathML is designed on the assumption that it cannot know the exact
physical characteristics of the media and devices on which it will
be rendered.
.
It does not support control of motions and sizes to the same
degree
.I \%troff
does.
.
.
.IP \[bu] 2n
.I \%eqn
customization parameters have no effect on generated MathML.
.
.
.IP \[bu]
The
.BR \%special ,
.BR up ,
.BR down ,
.BR fwd ,
and
.B back
primitives cannot be implemented,
and yield a MathML \%\[lq]<merror>\[rq] message instead.
.
.
.IP \[bu]
The
.B vcenter
primitive is silently ignored,
as centering on the math axis is the MathML default.
.
.
.IP \[bu]
Characters that
.I \%eqn
sets extra large in
.I troff \" mode
mode\[em]notably the integral sign\[em]may appear too small and need to
have their \[lq]<mstyle>\[rq] wrappers adjusted by hand.
.
.
.P
As in its
.I troff \" mode
mode,
.I \%eqn
in MathML mode leaves the
.B .EQ
and
.B .EN
tokens in place,
but emits nothing corresponding to
.B \%delim
delimiters.
.
They can,
however,
be recognized as character sequences that begin with \[lq]<math>\[rq],
end with \[lq]</math>\[rq],
and do not cross line boundaries.
.
.
.\" ====================================================================
.SH Caveats
.\" ====================================================================
.
Tokens must be double-quoted in
.I eqn \" generic
input if they are not to be recognized as names of macros or primitives,
or if they are to be interpreted by
.IR troff . \" generic
.
In particular,
short ones,
like
.RB \[lq] pi \[rq]
and
.RB \[lq] PI \[rq],
can collide with
.I troff \" generic
identifiers.
.
For instance,
the
.I eqn \" generic
command
.RB \%\[lq]\^ "gfont PI" \^\[rq]
does not select
.IR groff 's
Palatino italic font for the global italic face;
you must use
.RB \%\[lq]\^ "gfont \[dq]PI\[dq]" \^\[rq]
instead.
.
.
.P
Delimited equations are set at the type size current at the beginning of
the input line,
not necessarily that immediately preceding the opening delimiter.
.
.
.P
Unlike \*[tx],
.I eqn \" generic
does not inherently distinguish displayed and inline equation styles;
see the
.B smallover
primitive above.
.
However,
macro packages frequently define
.B EQ
and
.B EN
macros such that the equation within is displayed.
.
These macros may accept arguments permitting the equation to be labeled
or captioned;
see the package's documentation.
.
.
.\" ====================================================================
.SH Bugs
.\" ====================================================================
.
.I eqn \" generic
abuses terminology\[em]its
\[lq]equations\[rq]
can be inequalities,
bare expressions,
or unintelligible gibberish.
.
But there's no changing it now.
.
.
.P
In
.I nroff \" mode
mode,
lowercase Greek letters are rendered in roman instead of italic style.
.
.
.P
In MathML mode,
the
.B mark
and
.B lineup
features don't work.
.
These could,
in theory,
be implemented with \%\[lq]<maligngroup>\[rq] elements.
.
.
.P
In MathML mode,
each digit of a numeric literal gets a separate \[lq]<mn>\:</mn>\[rq]
pair,
and decimal points are tagged with \[lq]<mo>\:</mo>\[rq].
.
This is allowed by the specification,
but inefficient.
.
.
.\" ====================================================================
.SH Examples
.\" ====================================================================
.
We first illustrate
.I \%eqn
usage with a trigonometric identity.
.
.
.RS
.P
.EX
\&.EQ
sin ( alpha + beta ) = sin alpha cos beta + cos alpha sin beta
\&.EN
.EE
.if t \{\
.
.
.P
.RS
.EQ
sin ( alpha + beta ) = sin alpha cos beta + cos alpha sin beta
.EN
.RE
.\}
.RE
.
.
.P
It can be convenient to set up delimiters if mathematical content will
appear frequently in running text.
.
.
.RS
.P
.EX
\&.EQ
delim $$
\&.EN
.
Having cached a table of logarithms,
the property $ln ( x y ) = ln x + ln y$ sped calculations.
.EE
.if t \{\
.
.
.P
.RS
.EQ
delim $$
.EN
.
Having cached a table of logarithms,
the property $ln ( x y ) = ln x + ln y$ sped calculations.
.
.\" We _must_ shut delimiters back off when serially processing man
.\" pages, or subsequent documents cannot safely use those characters.
.EQ
delim off
.EN
.RE
.\}
.RE
.
.
.P
The quadratic formula illustrates use of fractions and radicals,
and affords an opportunity to use the full space token
.BR \[ti] .
.
.
.RS
.P
.EX
\&.EQ
x = { \- b \[ti] \[rs][+\-] \[ti] sqrt { b sup 2 \- 4 a c } } \
over { 2 a }
\&.EN
.EE
.if t \{\
.
.
.P
.RS
.EQ
x = { - b ~ \[+-] ~ sqrt { b sup 2 - 4 a c } } over { 2 a }
.EN
.RE
.\}
.RE
.
.
.P
Alternatively,
we could define the plus-minus sign as a binary operator.
.
Automatic spacing puts 0.06\~em less space on either side of the
plus-minus than \[ti] does,
this being the difference between the widths of the
.B medium_space
parameter used by binary operators and that of the full space.
.
Independently,
we can define a macro \[lq]frac\[rq] for setting fractions.
.
.
.RS
.P
.EX
\&.EQ
chartype "binary" \[rs][+\-]
define frac ! { $1 } over { $2 } !
x = frac(\- b \[rs][+\-] sqrt { b sup 2 \- 4 a c }, 2 a)
\&.EN
.EE
.if t \{\
.
.
.P
.RS
.EQ
chartype "binary" \[+-]
define frac ! { $1 } over { $2 } !
x = frac(- b \[+-] sqrt { b sup 2 - 4 a c }, 2 a)
.EN
.RE
.\}
.RE
.
.
.\" ====================================================================
.SH "See also"
.\" ====================================================================
.
\[lq]Typesetting Mathematics\[em]User's Guide\[rq]
(2nd edition),
by Brian W.\& Kernighan
and Lorinda L.\& Cherry,
1978,
AT&T Bell Laboratories Computing Science Technical Report No.\& 17.
.
.
.P
.IR The\~\*[tx]book ,
by Donald E.\& Knuth,
1984,
Addison-Wesley Professional.
.
Appendix\~G
discusses many of the parameters from section \[lq]Customization\[rq]
above in greater detail.
.
.
.P
.MR groff_char 7 ,
particularly subsections \[lq]Logical symbols\[rq],
\[lq]Mathematical symbols\[rq],
and \[lq]Greek glyphs\[rq],
documents a variety of special character escape sequences useful in
mathematical typesetting.
.
.
.P
.MR groff 1 ,
.MR \%troff 1 ,
.MR \%pic 1 ,
.MR groff_font 5
.
.
.\" Clean up.
.rm tx
.
.\" Restore compatibility mode (for, e.g., Solaris 10/11).
.cp \n[*groff_eqn_1_man_C]
.do rr *groff_eqn_1_man_C
.
.
.\" Local Variables:
.\" fill-column: 72
.\" mode: nroff
.\" tab-width: 12
.\" End:
.\" vim: set filetype=groff tabstop=12 textwidth=72: