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.\" The BSD man macros can't handle " in arguments to font change macros,
.\" so use \(ts instead of ".
.tr \(ts"
.TH @G@EQN @MAN1EXT@ "@MDATE@" "Groff Version @VERSION@"
.SH NAME
@g@eqn \- format equations for troff
.SH SYNOPSIS
.B @g@eqn
[
.B \-rvCNR
]
[
.BI \-d cc
]
[
.BI \-T name
]
[
.BI \-M dir
]
[
.BI \-f F
]
[
.BI \-s n
]
[
.BI \-p n
]
[
.BI \-m n
]
[
.IR files \|.\|.\|.
]
.SH DESCRIPTION
This manual page describes the GNU version of
.BR eqn ,
which is part of the groff document formatting system.
.B eqn
compiles descriptions of equations embedded within
.B troff
input files into commands that are understood by
.BR troff .
Normally, it should be invoked using the
.B \-e
option of
.BR groff .
The syntax is quite compatible with Unix eqn.
The output of GNU eqn cannot be processed with Unix troff;
it must be processed with GNU troff.
If no files are given on the command line, the standard input
will be read.
A filename of
.B \-
will cause the standard input to be read.
.LP
.B eqn
searches for the file
.B eqnrc
using the path
.BR @MACROPATH@ .
If it exists, eqn will process it before the other input files.
The
.B \-R
option prevents this.
.LP
GNU eqn does not provide the functionality of neqn:
it does not support low-resolution, typewriter-like devices
(although it may work adequately for very simple input).
.SH OPTIONS
.TP
.B \-C
Recognize
.B .EQ
and
.B .EN
even when followed by a character other than space or newline.
.TP
.B \-N
Don't allow newlines within delimiters.
This option allows
.B eqn
to recover better from missing closing delimiters.
.TP
.B \-v
Print the version number.
.TP
.B \-r
Only one size reduction.
.TP
.BI \-m n
The minimum point-size is
.IR n .
eqn will not reduce the size of subscripts or superscripts to
a smaller size than
.IR n .
.TP
.BI \-T name
The output is for device
.IR name .
The only effect of this is to define a macro
.I name
with a value of
.BR 1 .
Typically
.B eqnrc
will use this to provide definitions appropriate for the output device.
The default output device is
.BR @DEVICE@ .
.TP
.BI \-M dir
Search
.I dir
for
.B eqnrc
before the default directories.
.TP
.B \-R
Don't load
.BR eqnrc .
.TP
.BI \-f F
This is equivalent to a
.BI gfont\  F
command.
.TP
.BI \-s n
This is equivalent to a
.BI gsize\  n
command.
This option is deprecated.
eqn will normally set equations at whatever the current point size
is when the equation is encountered.
.TP
.BI \-p n
This says that subscripts and superscripts should be
.I n
points smaller than the surrounding text.
This option is deprecated. 
Normally eqn makes sets subscripts and superscripts at 70% 
of the size of the surrounding text.
.SH USAGE
Only the differences between GNU eqn and Unix eqn are described here.
.LP
Most of the new features of GNU eqn
are based on \*(tx.
There are some references to the differences between \*(tx and GNU eqn below;
these may safely be ignored if you do not know \*(tx.
.SS Automatic spacing
.LP
.B eqn
gives each component of an equation a type, and adjusts the spacing
between components using that type.
Possible types are:
.TP \w'punctuation'u+2n
ordinary
an ordinary character such as 1 or
.IR x ;
.TP
operator
a large operator such as
.ds Su \s+5\(*S\s0
.if \n(.g .if !c\(*S .ds Su the summation operator
\*(Su;
.TP
binary
a binary operator such as +;
.TP
relation
a relation such as =;
.TP
opening
a opening bracket such as (;
.TP
closing
a closing bracket such as );
.TP
punctuation
a punctuation character such as ,;
.TP
inner
a subformula contained within brackets;
.TP
suppress
spacing that suppresses automatic spacing adjustment.
.LP
Components of an equation get a type in one of two ways.
.TP
.BI type\  t\ e
This yields an equation component that contains
.I e
but that has type
.IR t ,
where
.I t
is one of the types mentioned above.
For example,
.B times
is defined as
.RS
.IP
.B
type "binary" \e(mu
.RE
.IP
The name of the type doesn't have to be quoted, but quoting protects
from macro expansion.
.TP
.BI chartype\  t\ text
Unquoted groups of characters are split up into individual characters,
and the type of each character is looked up;
this changes the type that is stored for each character;
it says that the characters in
.I text
from now on have type
.IR t .
For example,
.RS
.IP
.B
chartype "punctuation" .,;:
.RE
.IP
would make the characters
.B .,;:
have type punctuation
whenever they subsequently appeared in an equation.
The type
.I t
can also be
.B letter
or
.BR digit ;
in these cases
.B chartype
changes the font type of the characters.
See the Fonts subsection.
.SS New primitives
.TP
.IB e1\  smallover\  e2
This is similar to
.BR over ;
.B smallover
reduces the size of
.I e1
and
.IR e2 ;
it also puts less vertical space between
.I e1
or
.I e2
and the fraction bar.
The
.B over
primitive corresponds to the \*(tx
.B \eover
primitive in display styles;
.B smallover
corresponds to
.B \eover
in non-display styles.
.TP
.BI vcenter\  e
This vertically centers
.I e
about the math axis.
The math axis is the vertical position about which characters
such as + and - are centered; also it is the vertical position
used for the bar of fractions.
For example,
.B sum
is defined as
.RS
.IP
.B
{ type "operator" vcenter size +5 \e(*S }
.RE
.TP
.IB e1\  accent\  e2
This sets
.I e2
as an accent over
.IR e1 .
.I e2
is assumed to be at the correct height for a lowercase letter;
.I e2
will be moved down according if
.I e1
is taller or shorter than a lowercase letter.
For example,
.B hat
is defined as
.RS
.IP
.B
accent { "^" }
.RE
.IP
.BR dotdot ,
.BR dot ,
.BR tilde ,
.B vec
and
.B dyad
are also defined using the
.B accent
primitive.
.TP
.IB e1\  uaccent\  e2
This sets
.I e2
as an accent under
.IR e1 .
.I e2
is assumed to be at the correct height for a character without a descender;
.I e2
will be moved down if
.I e1
has a descender.
.B utilde
is pre-defined using
.B uaccent
as a tilde accent below the baseline.
.TP
.BI split\ \(ts text \(ts
This has the same effect as simply
.RS
.IP
.I text
.RE
.IP
but
.I text
is not subject to macro expansion because it is quoted;
.I text
will be split up and the spacing between individual characters
will be adjusted.
.TP
.BI nosplit\  text
This has the same effect as
.RS
.IP
.BI \(ts text \(ts
.RE
.IP
but because
.I text
is not quoted it will be subject to macro expansion;
.I text
will not be split up
and the spacing between individual characters will not be adjusted.
.TP
.IB e\  opprime
This is a variant of
.B prime
that acts as an operator on
.IR e .
It produces a different result from
.B prime
in a case such as
.BR A\ opprime\ sub\ 1 :
with
.B opprime
the
.B 1
will be tucked under the prime as a subscript to the
.B A
(as is conventional in mathematical typesetting),
whereas with
.B prime
the
.B 1
will be a subscript to the prime character.
The precedence of
.B opprime
is the same as that of
.B bar
and
.BR under ,
which is higher than that of everything except
.B accent
and
.BR uaccent .
In unquoted text a
.B '
that is not the first character will be treated like
.BR opprime .
.TP
.BI special\  text\ e
This constructs a new object from
.I e
using a
.BR @g@troff  (@MAN1EXT@)
macro named
.IR text .
When the macro is called,
the string
.B 0s
will contain the output for
.IR e ,
and the number registers
.BR 0w ,
.BR 0h ,
.BR 0d ,
.BR 0skern
and
.BR 0skew
will contain the width, height, depth, subscript kern, and skew of
.IR e .
(The
.I "subscript kern"
of an object says how much a subscript on that object should be tucked in;
the
.I skew
of an object says how far to the right of the center of the object an
accent over the object should be placed.)
The macro must modify
.B 0s
so that it will output the desired result with its origin at the current
point, and increase the current horizontal position by the width
of the object.
The number registers must also be modified so that they correspond to the
result.
.RS
.LP
For example, suppose you wanted a construct that `cancels' an expression
by drawing a diagonal line through it.
.IP
.nf
.ft B
.ne 6+\n(.Vu
\&.EQ
define cancel 'special Ca'
\&.EN
\&.de Ca
\&.ds 0s \eZ'\e\e*(0s'\ev'\e\en(0du'\eD'l \e\en(0wu -\e\en(0hu-\e\en(0du'\ev'\e\en(0hu'
\&..
.ft
.fi
.LP
Then you could cancel an expression
.I e
with
.BI cancel\ {\  e\  }
.LP
Here's a more complicated construct that draws a box round an expression:
.IP
.nf
.ft B
.ne 11+\n(.Vu
\&.EQ
define box 'special Bx'
\&.EN
\&.de Bx
\&.ds 0s \eZ'\eh'1n'\e\e*(0s'\e
\eZ'\ev'\e\en(0du+1n'\eD'l \e\en(0wu+2n 0'\eD'l 0 -\e\en(0hu-\e\en(0du-2n'\e
\eD'l -\e\en(0wu-2n 0'\eD'l 0 \e\en(0hu+\e\en(0du+2n''\eh'\e\en(0wu+2n'
\&.nr 0w +2n
\&.nr 0d +1n
\&.nr 0h +1n
\&..
.ft
.fi
.RE
.SS Customization
The appearance of equations is controlled by
a large number of parameters. These can be set using
the
.B set
command.
.TP
.BI set\  p\ n
This sets parameter
.I p
to value
.I n ;
.I n
is an integer.
For example,
.RS
.IP
.B
set x_height 45
.RE
.IP
says that
.B eqn
should assume an x height of 0.45 ems.
.RS
.LP
Possible parameters are as follows.
Values are in units of hundredths of an em unless otherwise stated.
These descriptions are intended to be expository rather than
definitive.
.TP \w'\fBdefault_rule_thickness'u+2n
.B minimum_size
.B eqn
will not set anything at a smaller point-size than this.
The value is in points.
.TP
.B fat_offset
The
.B fat
primitive emboldens an equation
by overprinting two copies of the equation
horizontally offset by this amount.
.TP
.B over_hang
A fraction bar will be longer by twice this amount than
the maximum of the widths of the numerator and denominator;
in other words, it will overhang the numerator and
denominator by at least this amount.
.TP
.B accent_width
When
.B bar
or
.B under
is applied to a single character,
the line will be this long.
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 will 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.
.TP
.B delimiter_shortfall
Extensible delimiters produced with the
.B left
and
.B right
primitives will 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.
.TP
.B null_delimiter_space
This much horizontal space is inserted
on each side of a fraction.
.TP
.B script_space
The width of subscripts and superscripts is increased by this amount.
.TP
.B thin_space
This amount of space is automatically inserted after punctuation
characters.
.TP
.B medium_space
This amount of space is automatically inserted on either side
of binary operators.
.TP
.B thick_space
This amount of space is automatically inserted on either side of
relations.
.TP
.B x_height
The height of lowercase letters without ascenders such as x.
.TP
.B axis_height
The height above the baseline of the center of characters
such as \(pl and \(mi.
It is important that this value is correct for the font
you are using.
.TP
.B default_rule_thickness
This should set to the thickness of the
.B \e(ru
character, or the thickness of horizontal lines produced with the
.B \eD
escape sequence.
.TP
.B num1
The
.B over
command will shift up the numerator by at least this amount.
.TP
.B num2
The
.B smallover
command will shift up the numerator by at least this amount.
.TP
.B denom1
The
.B over
command will shift down the denominator by at least this amount.
.TP
.B denom2
The
.B smallover
command will shift down the denominator by at least this amount.
.TP
.B sup1
Normally superscripts will be shifted up by at least this amount.
.TP
.B sup2
Superscripts within superscripts or upper limits
or numerators of
.B smallover
fractions
will be shifted up by at least this amount.
This is usually less than sup1.
.TP
.B sup3
Superscripts within denominators or square roots
or subscripts or lower limits will be shifted up by at least
this amount.
This is usually less than sup2.
.TP
.B sub1
Subscripts will normally be shifted down by at least this amount.
.TP
.B sub2
When there is both a subscript and a superscript, the subscript
will be shifted down by at least this amount.
.TP
.B sup_drop
The baseline of a superscript will be no more
than this much amount below the top of the object on
which the superscript is set.
.TP
.B sub_drop
The baseline of a subscript will be at least this much below
the bottom of the object on which the subscript is set.
.TP
.B big_op_spacing1
The baseline of an upper limit will be at least this
much above the top of the object on which the limit is set.
.TP
.B big_op_spacing2
The baseline of a lower limit will be at least this
much below the bottom of the object on which the limit is set.
.TP
.B big_op_spacing3
The bottom of an upper limit will be at least this much above the
top of the object on which the limit is set.
.TP
.B big_op_spacing4
The top of a lower limit will be at least this much below
the bottom of the object on which the limit is set.
.TP
.B big_op_spacing5
This much vertical space will be added above and below limits.
.TP
.B baseline_sep
The baselines of the rows in a pile or matrix will normally be
this far apart.
In most cases this should be 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 will be shifted down by this much from the axis.
In most cases this should be equal to
.BR axis_height .
.TP
.B column_sep
This much space will be added between columns in a matrix.
.TP
.B matrix_side_sep
This much space will be added at each side of a matrix.
.TP
.B draw_lines
If this is non-zero, lines will be drawn using the
.B \eD
escape sequence, rather than with the
.B \el
escape sequence and the
.B \e(ru
character.
.TP
.B body_height
The amount by which the height of the equation exceeds this
will be added as extra space before the line containing the equation
(using
.BR \ex .)
The default value is 85.
.TP
.B body_depth
The amount by which the depth of the equation exceeds this
will be added as extra space after the line containing the equation
(using
.BR \ex .)
The default value is 35.
.TP
.B nroff
If this is non-zero,
then
.B ndefine
will behave like
.B define
and
.B tdefine
will be ignored,
otherwise
.B tdefine
will behave like
.B define
and
.B ndefine
will be ignored.
The default value is 0
(This is typically changed to 1 by the
.B eqnrc
file for the
.B ascii
and
.B latin1
devices.)
.LP
A more precise description of the role of many of these
parameters can be found in Appendix H of
.IR The\ \*(txbook .
.RE
.SS Macros
Macros can take arguments.
In a macro body,
.BI $ n
where
.I n
is between 1 and 9,
will be replaced by the
.IR n-th
argument if the macro is called with arguments;
if there are fewer than
.I n
arguments, it will be replaced by nothing.
A word containing a left parenthesis where the part of the word
before the left parenthesis has been defined using the
.B define
command
will be recognized as a macro call with arguments;
characters following the left parenthesis
up to a matching right parenthesis will be treated as comma-separated
arguments;
commas inside nested parentheses do not terminate an argument.
.TP
.BI sdefine\  name\ X\ anything\ X
This is like the
.B define
command, but
.I name
will not be recognized if called with arguments.
.TP
.BI include\ \(ts file \(ts
Include the contents of
.IR file .
Lines of
.I file
beginning with
.B .EQ
or
.B .EN
will be ignored.
.TP
.BI ifdef\  name\ X\ anything\ X
If
.I name
has been defined by
.B define
(or has been automatically defined because
.I name
is the output device)
process
.IR anything ;
otherwise ignore
.IR anything .
.I X
can be any character not appearing in
.IR anything .
.SS Fonts
.B eqn
normally uses at least two fonts to set an equation:
an italic font for letters,
and a roman font for everything else.
The existing
.B gfont
command
changes the font that is used as the italic font.
By default this is
.BR I .
The font that is used as the roman font can be changed
using the new
.B grfont
command.
.TP
.BI grfont\  f
Set the roman font to
.IR f .
.LP
The
.B italic
primitive uses the current italic font set by
.BR gfont ;
the
.B roman
primitive uses the current roman font set by
.BR grfont .
There is also a new
.B gbfont
command, which changes the font used by the
.B bold
primitive.
If you only use the
.BR roman ,
.B italic
and
.B bold
primitives to changes fonts within an equation,
you can change all the fonts used by your equations
just by using
.BR gfont ,
.B grfont
and
.B gbfont
commands.
.LP
You can control which characters are treated as letters
(and therefore set in italics) by using the
.B chartype
command described above.
A type of
.B letter
will cause a character to be set in italic type.
A type of
.B digit
will cause a character to be set in roman type.
.SH FILES
.Tp \w'\fB@MACRODIR@/eqnrc'u+2n
.B @MACRODIR@/eqnrc
Initialization file.
.SH BUGS
Inline equations will be set at the point size that is current at the
beginning of the input line.
.SH "SEE ALSO"
.BR groff (@MAN1EXT@),
.BR @g@troff (@MAN1EXT@),
.BR groff_font (@MAN5EXT@),
.I The\ \*(txbook