eqn

Name

eqn - format equations for groff or MathML

Synopsis

eqn [-CNrR] [-d xy] [-f F] [-m n] [-M dir] [-p n] [-s n] [-T name] [file ...]
eqn --help
eqn -v eqn --version

Description

The GNU implemenation of eqn is part of the groff(7) document formatting system. eqn is a troff(1) preprocessor that translates descriptions of equations embedded in roff(7) input files into the language understood by troff(1). It copies the contents of each file to the standard output stream, except that lines between .EQ and .EN (or “inline” within a pair of user-specified delimiters) are interpreted as equation descriptions. Normally, eqn is not executed directly by the user, but invoked by specifying the -e option to groff(1). While GNU eqn’s input syntax is highly compatible with AT&T eqn, the output eqn produces cannot be processed by AT&T troff; GNU troff (or a troff implementing relevant GNU extensions) must be used. If no file operands are given on the command line, or if file is “-”, the standard input stream is read.

Unless the -R option is given, eqn searches for the file eqnrc in the directories given with the -M option first, then in /usr/local/share/groff/ site-tmac, and finally in the standard macro directory /usr/local/share/ groff/1.23.0/tmac. If it exists and is readable, eqn processes it before any input files.

This man page primarily discusses the differences between GNU eqn and AT&T eqn. 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.

Three points are worth special note.

Automatic spacing

eqn imputes a type to each component of an equation, adjusting the spacing between them accordingly. Recognized types are as follows.

Two primitives apply types to equation components. Quote type names in eqn commands to prevent macro expansion from being attempted on their names.
type t e

Apply type t to expression e. For example, “times” is defined as if by the following.

define times ' type "binary" \(mu '

chartype t text

Each (unquoted) character in text is assigned type t, persistently. If t is “letter” or “digit”, chartype also assigns a typeface to each character in text. See subsection “Fonts” below. As an example, the default spacing for some punctuation characters is set up as if by the following eqn command.

chartype "punctuation" .,;:

Primitives

eqn supports without alteration the AT&T eqn primitives above, back, bar, bold, define, down, fat, font, from, fwd, gfont, gsize, italic, left, lineup, mark, matrix, ndefine, over, right, roman, size, sqrt, sub, sup, tdefine, to, under, and up.

New primitives

<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; it is also the vertical position used for fraction bars. For example, sum is defined as follows.

{ type "operator" vcenter size +5 \(*S }

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 follows.

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 predefined 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 neutral apostrophe (') that is not the first character on the input line is treated like opprime.

special text e

Construct an object by calling the troff macro text on e. The troff string 0s contains the eqn output for e, and the registers 0w, 0h, 0d, 0skern, and 0skew the width, height, depth, subscript kern, and skew of e, respectively. (The subscript kern of an object indicates how much a subscript on that object should be “tucked in”, or placed to the left relative to a non-subscripted glyph of the same size. The skew of an object is how far to the right of the center of the object an accent over it should be placed.) The macro must modify 0s so that it outputs the desired result, returns the drawing position to the text baseline at the beginning of e, and updates the foregoing registers to correspond to the new dimensions of the result.

For example, suppose you wanted a construct that “cancels” an expression by drawing a diagonal line through it.

.de Ca
. ds 0s \
\Z'\\*(0s'\
\v'\\n(0du'\
\D'l \\n(0wu -\\n(0hu-\\n(0du'\
\v'\\n(0hu'
..
.EQ
special Ca "x \[mi] 3 \[pl] x" ~ 3
.EN

We use the \[mi] and \[pl] special characters instead of + and - because they are part of the argument to a troff macro, so eqn does not transform them to mathematical glyphs for us. Here’s a more complicated construct that draws a box around an expression; the bottom of the box rests on the text baseline. We define the eqn macro box to wrap the call of the troff macro Bx.

.de Bx
.ds 0s \
\Z'\\h'1n'\\*[0s]'\
\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
..
.EQ
define box ' special Bx $1 '
box(foo) ~ "bar"
.EN

space n

Set extra vertical spacing around the equation, replacing the default values, where n is an integer in hundredths of an em. If positive, n increases vertical spacing before the equation; if negative, it does so after the equation. This primitive provides an interface to groff’s \x escape sequence, but with the opposite sign convention. It has no effect if the equation is part of a pic(1) picture.

Extended primitives

eqn recognizes an “on” argument to the delim primitive specially, restoring any delimiters previously disabled with “delim off”. If delimiters haven’t been specified, neither command has effect.
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 sequence (the value has no effect in MathML mode). Negative values are possible but have no effect. If more than one n occurs in a matrix, the largest is used.

Customization

When eqn generates troff input, 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 primitive.
set p n

This sets parameter p to value n, where 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 won’t set anything at a smaller type 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; fat text uses

<mstyle mathvariant='double-struck'>

instead.

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 be set to the thickness of the \[ru] character, or the thickness of horizontal lines produced with the \D escape sequence.

denom1

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

denom2

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

sup_drop

The baseline of a superscript is no more than this much 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.

Appendix H of The TeXbook discusses many of these parameters in greater detail.

Macros

In GNU eqn, 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 primitive 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. In the following synopses, X can be any character not appearing in the parameter thus bracketed.
sdefine name X anything X

This is like the define primitive, but name is not recognized if called with arguments.

include file
copy file

Interpolate the contents of file. Lines in 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 driver) process anything; otherwise ignore anything.

undef name

Remove definition of name, making it undefined.

Predefined macros

GNU eqn supports the predefined macros offered by AT&T eqn: and, approx, arc, cos, cosh, del, det, dot, dotdot, dyad, exp, for, grad, half, hat, if, inter, Im, inf, int, lim, ln, log, max, min, nothing, partial, prime, prod, Re, sin, sinh, sum, tan, tanh, tilde, times, union, vec, ==, !=, +=, ->, <-, <<, >>, and “...”. The lowercase classical Greek letters are available as alpha, beta, chi, delta, epsilon, eta, gamma, iota, kappa, lambda, mu, nu, omega, omicron, phi, pi, psi, rho, sigma, tau, theta, upsilon, xi, and zeta. Obtain their uppercase forms by spelling these names with an initial capital letter or in full capitals, as in Alpha or ALPHA.

GNU eqn further defines the macros cdot, cdots, and utilde (all discussed above), dollar, which sets a dollar sign, and ldots, which sets three dots on the baseline.

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 AT&T eqn gfont primitive 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. GNU eqn offers a gbfont primitive, which changes the font used by the bold primitive. If you use only the roman, italic and bold primitives to change fonts within an equation, then gfont, grfont and gbfont suffice to configure all the typefaces used by your equations.

You can control which characters are treated as letters (and therefore set in italics) by using the chartype primitive 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.

Options

--help displays a usage message, while -v and --version show version information; all exit afterward.

-M dir

Search dir for eqnrc before those listed in section “Description” above.

-T name

Prepare output for the device name. In most cases, the effect of this is to define a macro name with a value of 1; eqnrc uses this to provide definitions appropriate for the device. However, if the specified driver is “MathML”, the output is MathML markup rather than troff input, and eqnrc is not loaded at all. The default output device is ps.

Files

/usr/local/share/groff/1.23.0/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:

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.

Bugs

Words must be quoted anywhere they occur in eqn input if they are not to be recognized as names of macros or primitives, or if they are to be interpreted by troff. These names, particularly short ones like “pi” and “PI”, can collide with troff identifiers. For instance, the eqn command

gfont PI

does not select groff’s Palatino italic font for the “global” equation face; you must use

gfont "PI"

instead.

Inline equations are set at the type 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.

See also

“Typesetting Mathematics—User’s Guide” (2nd edition), by Brian W. Kernighan and Lorinda L. Cherry, 1978, AT&T Bell Laboratories Computing Science Technical Report No. 17.

The TeXbook, by Donald E. Knuth, 1984, Addison-Wesley Professional.

groff_char(7), particularly subsections “Logical symbols”, “Mathematical symbols”, and “Greek glyphs”, documents a variety of special character escape sequences useful in mathematical typesetting.

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