# FreeBSD 11.0 - man page for eqn (freebsd section 1)

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
equations embedded within troff input files into commands that are understood 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

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, respectively, 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 deprecated.  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.  Nor-
mally 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 >';

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 example,
times is defined as

type "binary" \(mu

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

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 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 accord-
ing 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 characters

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

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 mathematical type-
setting), 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 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 oppo-
site sign).

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

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 vertical 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 parameters.  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 hundredths 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 denominator; 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 subscripts 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 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 equa-
tion (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 equa-
tion (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 parameters 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 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 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 Version 1.19.2						   23 March 2013							    EQN(1)`