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EQN(1)									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
input will be read.  A filename of - will cause the standard  input  to

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 Σ';

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
according	 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
accent 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
expansion;  text	will  not  be split up and the spacing between
individual 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 opprime sub 1: with opprime the 1 will	be  tucked  under  the
prime  as a subscript to the A (as is conventional in mathemati‐
cal 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	every‐
thing  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
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
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
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 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
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 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
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 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
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 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
behave  like  define  and	ndefine	 will be ignored.  The
default value is 0 (This is typically changed to 1 by the
eqnrc  file  for  the  ascii,  latin1,  utf8,  and cp1047
devices.)

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
replaced by nothing.  A word containing a left  parenthesis  where  the
part of the word before the left parenthesis has been defined using the
define command will be recognized as a macro call with arguments; char‐
acters  following the left parenthesis up to a matching right parenthe‐
sis 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
using the new grfont command.

grfont f
Set the roman font to f.

The italic primitive uses the current italic font  set  by  gfont;  the
roman  primitive	 uses  the current roman font set by grfont.  There is
also a new gbfont command, which changes the  font  used	 by  the  bold
primitive.   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.

groff(1), troff(1), pic(1), groff_font(5), The TeXbook

Groff Version 1.19.2		20 October 2005				EQN(1)
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