eqn man page on ElementaryOS

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EQN(1)									EQN(1)

NAME
eqn - format equations for troff or MathML

SYNOPSIS
eqn [-rvCNR] [-d xy] [-T name] [-M dir] [-f F] [-s n] [-p n] [-m n]
[files...]

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 is read.  A filename of - causes the standard input to be read.

eqn  searches  for  the file eqnrc in the directories given with the -M
option first, then in /usr/lib/groff/site-tmac,	/usr/share/groff/site-
tmac,	 and	finally	   in	 the	standard    macro    directory
/usr/share/groff/1.22.2/tmac.  If it exists, eqn	 processes  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
It is possible to have whitespace between a command line option and its
parameter.

-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.	 Also, the statement delim on' is not
handled specially.

-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 does not reduce the size of
subscripts or superscripts to a smaller size than n.

-Tname The output is for device name.  Normally,	 the  only  effect  of
this  is	to  define  a macro name with a value of 1; eqnrc uses
this to provide definitions appropriate for the  output  device.
However,	if  the	 specified  device  is “MathML”, the output is
MathML markup rather than	 troff	commands,  and	eqnrc  is  not
loaded at all.  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 normally sets	 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 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.

GNU  eqn	 emits	Presentation  MathML  output  when  invoked  with  the
-T MathML option.

GNU  eqn	 sets  the  input  token  "..."	 as three periods or low dots,
rather than the three centered dots of classic eqn.  To get three  cen‐
tered dots, write cdots or cdot cdot cdot.

Most  of	 the  new  features of the GNU eqn input language 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.

Controlling delimiters
If not in compatibility mode, eqn recognizes

delim on

to  restore  the	 delimiters which have been previously disabled with a
call to delim off'.  If delimiters haven't been	 specified,  the  call
has no effect.

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
big e  Enlarges the expression it modifies; intended to have  semantics
like  CSS large'.  In troff output, the point size is increased
by 5; in MathML output, the expression uses

<mstyle mathsize='big'>

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 }

(Note that vcenter is silently ignored when generating MathML.)

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 is moved down  accord‐
ing  to whether 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 is	 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  is	split up and the spacing between individual characters

nosplit text
This has the same effect as

"text"

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

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 is tucked under the prime as
a	 subscript  to the A (as is conventional in mathematical type‐
setting), whereas with prime the 1 is 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 charac‐
ter is 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 contains the out‐
put for e, and the number registers  0w,	0h,  0d,  0skern,  and
0skew contain the width, height, depth, subscript kern, and skew
of e.  (The subscript kern of an object says  how	 much  a  sub‐
script 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 outputs the desired result with its origin at  the  cur‐
rent  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 (the value
has no effect in MathML mode).  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
When eqn is generating troff markup, the	 appearance  of	 equations  is
controlled  by  a large number of parameters.  They have no effect when
generating MathML mode, which pushes typesetting and fine motions down‐
stream to a MathML rendering engine.  These parameters 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 doesn't 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.   This  parameter	is  not	 used  in MathML mode;

<mstyle mathvariant='double-struck'>

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

accent_width
When  bar	or under is applied to a single character, the
line is 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 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 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 shifts up the numerator by at least this
amount.

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

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

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

sup1   Normally  superscripts  are  shifted  up by at least this
amount.

sup2   Superscripts  within  superscripts	 or  upper  limits  or
numerators	 of  smallover	fractions are 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 are shifted up by at least this
amount.  This is usually less than sup2.

sub1   Subscripts are normally shifted down  by  at  least  this
amount.

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

sup_drop
The baseline of a superscript is no more than  this  much
amount  below  the	 top of the object on which the super‐
script is set.

sub_drop
The baseline of a subscript is 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 is 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 is 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 is 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 is at least this much below  the
bottom of the object on which the limit is set.

big_op_spacing5
This much vertical space is added above and below limits.

baseline_sep
The  baselines  of	 the rows in a pile or matrix are nor‐
mally 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 is shifted down by this much
from  the	axis.	In  most cases this should be equal to
axis_height.

column_sep
This much space is added between columns in a matrix.

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

draw_lines
If this is non-zero, lines are 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  is  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  is  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 behaves like define and
tdefine is ignored, otherwise tdefine behaves like define
and ndefine is 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, is replaced by the n-th argument if the  macro  is  called  with
arguments; if there are fewer than n arguments, it is replaced by noth‐
ing.  A word containing a left parenthesis where the part of  the  word
before  the  left parenthesis has been defined using the define command
is recognized as a macro call with arguments; characters following  the
left  parenthesis  up  to  a  matching right parenthesis are treated as
comma-separated arguments; commas inside nested parentheses do not ter‐
minate an argument.

sdefine name X anything X
This  is	like the define command, but name is not 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 are 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 causes a character to be set in italic type.  A type of digit
causes a character to be set in roman type.

FILES
/usr/share/groff/1.22.2/tmac/eqnrc
Initialization file.

MATHML MODE LIMITATIONS
MathML is designed on the assumption that  it  cannot  know  the	 exact
physical	 characteristics  of the media and devices on which it will be
rendered.  It does not support fine control of motions and sizes to the
same degree troff does.	Thus:

*      eqn parameters have no effect on the generated MathML.

*      The special, up, down, fwd, and back operations cannot be imple‐
mented, and yield a MathML <merror>' message instead.

*      The vcenter keyword is silently ignored,	as  centering  on  the
math axis is the MathML default.

*      Characters  that	eqn  over troff sets extra large – notably the
integral sign – may appear too small  and	 need  to  have	 their
<mstyle>' wrappers adjusted by hand.

As  in its troff mode, eqn in MathML mode leaves the .EQ and .EN delim‐
iters in place for displayed equations, but emits  no  explicit	delim‐
iters  around  inline  equations.   They can, however, be recognized as
strings that begin with <math>' and end	 with  </math>'  and  do  not
cross line boundaries.

See the BUGS section for translation limits specific to eqn.

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

In MathML mode, the mark and lineup features don't work.	 These	could,
in theory, be implemented with <maligngroup>' elements.

In  MathML  mode, each digit of a numeric literal gets a separate <mn>
</mn>' pair, and decimal points are tagged with <mo></mo>'.   This  is
allowed by the specification, but inefficient.

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

Groff Version 1.22.2	       07 February 2013				EQN(1)
`
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