EQN(1) General Commands Manual 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/1.22.3/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.

-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 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 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 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

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 ‘+cq 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

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 charac‐

ters 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 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 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;

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 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/1.22.3/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 ‘

* 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

‘

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 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 ‘

In MathML mode, each digit of a numeric literal gets a separate ‘

allowed by the specification, but inefficient.

### SEE ALSO

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

COPYING

Copyright © 1989-2014 Free Software Foundation, Inc.

Permission is granted to make and distribute verbatim copies of this

manual provided the copyright notice and this permission notice are

preserved on all copies.

Permission is granted to copy and distribute modified versions of this

manual under the conditions for verbatim copying, provided that the

entire resulting derived work is distributed under the terms of a per‐

mission notice identical to this one.

Permission is granted to copy and distribute translations of this man‐

ual into another language, under the above conditions for modified ver‐

sions, except that this permission notice may be included in transla‐

tions approved by the Free Software Foundation instead of in the origi‐

nal English.

Groff Version 1.22.3 28 January 2016 EQN(1)