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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...]

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 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/1.20.1/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
-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 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.

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 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/1.20.1/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  $' and end with $' 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.

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