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] [files...]

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/1.22.2/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 adequately 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, 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:

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 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
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 n-th
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/1.22.2/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  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 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.