# FreeBSD Manual Pages

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/local/lib/groff/site-tmac,   /usr/lo-
cal/share/groff/site-tmac,  and finally in the standard macro directory
/usr/local/share/groff/1.18.1/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 adjustment.

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
..

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	 exam-
ple,

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	 equa-
tion 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 denominator;
in other words, it will overhang the nu-
merator 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 maxi-
mum amount  by  which  the  sub-equation
that the delimiters enclose extends 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	opera-
tors.

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 cor-
rect for the font	you are	using.

default_rule_thickness  This should set to the thickness of  the
\(ru character, or the thickness of hor-
izontal lines produced with the  \D  es-
cape sequence.

num1		      The  over	 command will shift up the nu-
merator 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 de-
nominator	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  up-
per  limits  or  numerators 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 subscripts or lower lim-
its 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 su-
perscript, 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  superscript
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 ob-
ject 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 normally 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 matrix.

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  escape  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  containing
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  containing
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	behave
like define and ndefine will be ignored.
The default value	is 0  (This  is	 typi-
cally 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"
Include  the contents of file.  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.

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/local/share/groff/1.18.1/tmac/eqnrc
Initialization file.

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

`