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EQN(1)			    General Commands Manual			EQN(1)

NAME
eqn - format equations for troff

SYNOPSIS
eqn [ -rvCNR ] [	-dxy ] [ -Tname	] [ -Mdir ] [ -fF ] [ -sn ] [ -pn ]
[ -mn ] [ files... ]

It is possible to have whitespace between a command line	option and its
parameter.

DESCRIPTION
This manual page	describes the GNU version of eqn, which	is part	of the
groff document formatting system.  eqn compiles descriptions  of	 equa-
tions  embedded	within troff input files into commands that are	under-
stood by	troff.	Normally, it should be invoked using the -e option  of
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 in-
put will	be read.  A filename of	- will cause the standard input	to  be

eqn  searches  for  the file eqnrc in the directories given with	the -M
option first, then in /usr/share/tmac, /usr/share/tmac, and finally  in
the  standard  macro directory /usr/share/tmac.	If it exists, eqn will
process it before the other input files.	 The -R	option prevents	this.

GNU eqn does not	provide	the functionality of neqn: it does not support
low-resolution,	typewriter-like	 devices  (although  it	 may work ade-
quately for very	simple input).

OPTIONS
-dxy   Specify delimiters x and y for the left and right	 end,  respec-
tively,  of  in-line  equations.	 Any  delim  statements	in the
source file overrides this.

-C     Recognize	.EQ and	.EN even when followed by  a  character	 other
than space or newline.

-N     Don't  allow newlines within delimiters.	This option allows eqn
to recover better	from missing closing delimiters.

-v     Print the	version	number.

-r     Only one size reduction.

-mn    The minimum point-size is	n.  eqn	will not reduce	 the  size  of
subscripts or superscripts to a smaller size than	n.

-Tname The  output  is  for device name.	 The only effect of this is to
define a macro name with a value of 1.  Typically	eqnrc will use
this  to	provide	definitions appropriate	for the	output device.
The default output device	is ps.

-Mdir  Search dir for eqnrc before the default directories.

-fF    This is equivalent to a gfont F command.

-sn    This is equivalent to a gsize n command.	This option is	depre-
cated.   eqn will	normally set equations at whatever the current
point size is when the equation is encountered.

-pn    This says	that subscripts	and superscripts should	 be  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.

USAGE
Only the	differences between GNU	eqn and	Unix eqn are described here.

Most  of	 the new features of GNU eqn are based on TeX.	There are some
references to the differences between TeX and GNU eqn below; these  may
safely be ignored if you	do not know TeX.

Automatic spacing
eqn gives each component	of an equation a type, and adjusts the spacing
between components using	that type.  Possible types are:

ordinary	   an ordinary character such as 1' or	x';

operator	   a large operator such as <Sigma>';

binary	   a binary operator such as +';

relation	   a relation such as =';

opening	   a opening bracket such as (';

closing	   a closing bracket such as )';

punctuation  a punctuation character such	as ,';

inner	   a subformula	contained within brackets;

suppress	   spacing that	suppresses automatic  spacing  adjust-
ment.

Components of an	equation get a type in one of two ways.

type t e
This  yields  an equation	component that contains	e but that has
type t, where t is one of	the types mentioned above.  For	 exam-
ple, times is defined as

type "binary" \(mu

The name of the type doesn't have	to be quoted, but quoting pro-
tects from macro expansion.

chartype	t text
Unquoted groups of characters are	split up into individual char-
acters,  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	text from now on have type t.  For example,

chartype "punctuation" .,;:

would  make the characters .,;:'	have type punctuation whenever
they subsequently	appeared in an equation.  The type t can  also
be  letter  or  digit;  in these cases chartype changes the font
type of the characters.  See the Fonts subsection.

New primitives
e1 smallover e2
This is similar to over; smallover reduces the size  of  e1  and
e2;  it  also  puts less vertical	space between e1 or e2 and the
fraction bar.  The over primitive	corresponds to the  TeX	 \over
primitive	 in  display styles; smallover corresponds to \over in
non-display styles.

vcenter e
This vertically centers 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, sum is defined as

{ type "operator" vcenter size +5 \(*S }

e1 accent e2
This  sets  e2 as	an accent over e1.  e2 is assumed to be	at the
correct height for a lowercase letter; e2	will be	moved down ac-
cording if e1 is taller or shorter than a	lowercase letter.  For
example, hat is defined as

accent { "^" }

dotdot, dot, tilde, vec, and dyad	are also defined using the ac-
cent primitive.

e1 uaccent e2
This  sets e2 as an accent under e1.  e2 is assumed to be	at the
correct height for a character without a descender; e2  will  be
moved  down  if e1 has a descender.  utilde is pre-defined using
uaccent as a tilde accent	below the baseline.

split "text"
This has the same	effect as simply

text

but text is not subject to macro expansion because it is quoted;
text will	be split up and	the spacing between individual charac-

nosplit text
This has the same	effect as

"text"

but because text is not quoted it	will be	subject	to  macro  ex-
pansion; text will not be	split up and the spacing between indi-
vidual characters	will not be adjusted.

e opprime
This is a	variant	of prime that acts as an operator  on  e.   It
produces	a  different result from prime in a case such as A op-
prime sub	1: with	opprime	the 1 will be tucked under  the	 prime
as  a  subscript	to  the	 A (as is conventional in mathematical
typesetting), whereas with prime the 1 will be  a	 subscript  to
the  prime  character.  The precedence of	opprime	is the same as
that of bar and under, which is higher than that	of  everything
except accent and	uaccent.  In unquoted text a ' that is not the
first character will be treated like opprime.

special text e
This constructs a	new object from	e using	a troff(1) macro named
text.   When the macro is	called,	the string 0s will contain the
output for e, and	the number registers 0w, 0h, 0d,  0skern,  and
0skew will contain the width, height, depth, subscript kern, and
skew of e.  (The subscript kern of an object  says  how  much  a
subscript	on that	object should be tucked	in; the	skew of	an ob-
ject says	how far	to the right of	the center of  the  object  an
accent over the object should be placed.)	 The macro must	modify
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.

For  example,  suppose  you wanted a construct that cancels' an
expression by drawing a diagonal line through it.

.EQ
define cancel 'special Ca'
.EN
.de Ca
.	ds 0s \
\Z'\\*(0s'\
\v'\\n(0du'\
\D'l \\n(0wu -\\n(0hu-\\n(0du'\
\v'\\n(0hu'
..

Then you could cancel an expression e with cancel	{ e }

Here's a more complicated	construct that draws a	box  round  an
expression:

.EQ
define box	'special Bx'
.EN
.de Bx
.	ds 0s \
\Z'\h'1n'\\*(0s'\
\Z'\
\v'\\n(0du+1n'\
\D'l \\n(0wu+2n 0'\
\D'l 0 -\\n(0hu-\\n(0du-2n'\
\D'l -\\n(0wu-2n 0'\
\D'l 0 \\n(0hu+\\n(0du+2n'\
'\
\h'\\n(0wu+2n'
.	nr 0w +2n
.	nr 0d +1n
.	nr 0h +1n
..

space n
A	 positive value	of the integer n (in hundredths	of an em) sets
the vertical spacing before the equation,	a negative value  sets
the  spacing  after  the equation, replacing the default values.
This primitive provides an interface to groff's \x  escape  (but
with opposite sign).

This keyword has no effect if the	equation is part of a pic pic-
ture.

Extended primitives
col n { ... }
ccol n {	... }
lcol n {	... }
rcol n {	... }
pile n {	... }
cpile n { ... }
lpile n { ... }
rpile n { ... }
The integer value	n (in hundredths of an em) increases the  ver-
tical  spacing  between rows, using groff's \x escape.  Negative
values are possible but have no effect.  If there	is more	than a
single value given in a matrix, the biggest one is used.

Customization
The  appearance of equations is controlled by a large number of parame-
ters.  These can	be set using the set command.

set p n
This sets	parameter p to value n;	n is an	integer.  For example,

set x_height 45

says that	eqn should assume an x height of 0.45 ems.

Possible parameters are as follows.  Values are in units of hun-
dredths  of  an  em unless otherwise stated.  These descriptions
are intended to be expository rather than	definitive.

minimum_size
eqn will not set anything at a  smaller  point-size  than
this.  The	value is in points.

fat_offset
The  fat  primitive emboldens an equation by overprinting
two copies	of the equation	horizontally  offset  by  this
amount.

over_hang
A	fraction  bar will be longer by	twice this amount than
the maximum of the	widths of the numerator	and  denomina-
tor;  in  other words, it will overhang the numerator and
denominator by at least this amount.

accent_width
When bar or under is applied to a single  character,  the
line  will	be this	long.  Normally, bar or	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.

delimiter_factor
Extensible	delimiters produced with the  left  and	 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 ex-
tends away	from the axis.

delimiter_shortfall
Extensible	delimiters produced with the  left  and	 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.

null_delimiter_space
This much horizontal space	is inserted on each side of  a
fraction.

script_space
The  width	of subscripts and superscripts is increased by
this amount.

thin_space
This amount of  space  is	automatically  inserted	 after
punctuation characters.

medium_space
This  amount of space is automatically inserted on	either
side of binary operators.

thick_space
This amount of space is automatically inserted on	either
side of relations.

x_height
The height	of lowercase letters without ascenders such as
x'.

axis_height
The height	above the baseline of the center of characters
such  as +' and -'.  It is important that this value is
correct for the font you are using.

default_rule_thickness
This should set to	the thickness of the  \(ru  character,
or	the thickness of horizontal lines produced with	the \D
escape sequence.

num1   The over command will shift up the	numerator by at	 least
this amount.

num2   The  smallover  command will shift	up the numerator by at
least this	amount.

denom1 The over command will shift down the  denominator	by  at
least this	amount.

denom2 The  smallover command will shift down the	denominator by
at	least this amount.

sup1   Normally superscripts will	be shifted up by at least this
amount.

sup2   Superscripts  within  superscripts	or upper limits	or nu-
merators of smallover fractions will be shifted up	by  at
least this	amount.	 This is usually less than sup1.

sup3   Superscripts  within denominators or square roots or sub-
scripts or	lower limits will be shifted up	 by  at	 least
this amount.  This	is usually less	than sup2.

sub1   Subscripts	will normally be shifted down by at least this
amount.

sub2   When there	is both	a subscript  and  a  superscript,  the
subscript will be shifted down by at least	this amount.

sup_drop
The  baseline  of a superscript will be no	more than this
much amount below the top of the object on	which the  su-
perscript is set.

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.

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.

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.

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.

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.

big_op_spacing5
This  much	 vertical  space will be added above and below
limits.

baseline_sep
The baselines of the rows in a pile or matrix  will  nor-
mally  be	this  far apart.  In most cases	this should be
equal to the sum of num1 and denom1.

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	axis_height.

column_sep
This  much	 space	will be	added between columns in a ma-
trix.

matrix_side_sep
This much space will be added at each side	of a matrix.

draw_lines
If	this is	non-zero, lines	will be	drawn using the	\D es-
cape  sequence,  rather  than with	the \l escape sequence
and the \(ru character.

body_height
The amount	by which the height of	the  equation  exceeds
this  will	 be  added as extra space before the line con-
taining the equation (using \x).  The  default  value  is
85.

body_depth
The  amount  by  which  the depth of the equation exceeds
this will be added	as extra space after the line contain-
ing the equation (using \x).  The default value is	35.

nroff  If	this is	non-zero, then ndefine will behave like	define
and tdefine will be ignored, otherwise tdefine  will  be-
have  like	 define	 and ndefine will be ignored.  The de-
fault value is 0 (This is typically changed to 1  by  the
eqnrc  file  for  the ascii, latin1, utf8,	and cp1047 de-
vices.)

A	more precise description of the	role of	many of	these  parame-
ters can be found	in Appendix H of The TeXbook.

Macros
Macros  can  take  arguments.  In a macro body, \$n where	n is between 1
and 9, will be replaced by the n-th argument if	the  macro  is	called
with  arguments;	 if  there  are	fewer than n arguments,	it will	be re-
placed by nothing.  A word containing a left parenthesis	where the part
of  the word before the left parenthesis	has been defined using the de-
fine command will be recognized as a macro call with arguments; charac-
ters  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.

sdefine name X anything X
This is like the define command, but name	will not be recognized
if called	with arguments.

include "file"
copy "file"
Include the contents of file (include and	 copy  are  synonyms).
Lines of file beginning with .EQ or .EN will be ignored.

ifdef name X anything X
If  name	has  been defined by define (or	has been automatically
defined because name is the  output  device)  process  anything;
otherwise	ignore anything.  X can	be any character not appearing
in anything.

undef name
Remove definition	of name, making	it undefined.

Besides the macros  mentioned  above,  the  following  definitions  are
available:  Alpha,  Beta,  ..., Omega (this is the same as ALPHA, BETA,
..., OMEGA), ldots (three dots on the base line), and dollar.

Fonts
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 gfont
command changes the font	that is	used as	the italic font.   By  default
this  is	I.  The	font that is used as the roman font can	be changed us-
ing the new grfont command.

grfont f
Set the roman font to f.

The italic primitive uses the current italic font set by	gfont; the ro-
man primitive uses the current roman font set by	grfont.	 There is also
a new gbfont command, which changes the font used by  the  bold	primi-
tive.  If you only use the roman, italic	and bold primitives to changes
fonts within an equation, you can change	all the	 fonts	used  by  your
equations just by using gfont, grfont and gbfont	commands.

You  can	control	which characters are treated as	letters	(and therefore
set in italics) by using	the chartype command described above.  A  type
of  letter  will	cause a	character to be	set in italic type.  A type of
digit will cause	a character to be set in roman type.

FILES
/usr/share/tmac/eqnrc  Initialization file.

BUGS
Inline equations	will be	set at the point size that is current  at  the
beginning of the	input line.

`