Ubuntu Manpage: eqn - format equations for troff or MathML

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] [file ...]

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 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/1.22.4/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 adequately for very simple input).

OPTIONS

Whitespace is permitted between a command-line option and its argument.

-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. 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.

-R Don't load eqnrc.

-fF This is equivalent to a gfont F command.

-sn This is equivalent to a gsize n command. This option is deprecated. 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 centered 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 described in the table below.

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 a type 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 subsection “Fonts” below.

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

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 according 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 is adjusted.

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 characters is not 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 is tucked
under the prime as a subscript to the A (as is conventional in mathematical
typesetting), 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 character 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 output 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 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 outputs 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 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 (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 downstream 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 hundredths 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; instead, fat text uses

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 denominator 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 subscripts 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 superscript 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 normally 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 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, is replaced by
the nth argument if the macro is called with arguments; if there are fewer than
n arguments, it is 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 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 terminate 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/1.22.4/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 implemented, 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 delimiters  in  place  for
       displayed  equations, but emits no explicit delimiters 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 section “Bugs” below 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.