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Name

eqn - format mathematics (equations) for groff or MathML

Synopsis

Description

The GNU implementation of eqn is part of the groff(7) document formatting system. eqn is a troff(1) preprocessor that translates expressions in its own language, embedded in roff(7) input files, into mathematical notation typeset by troff(1). It copies each file’s contents to the standard output stream, translating each equation between lines starting with .EQ and .EN, or within a pair of user-specified delimiters. 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 “-”, eqn reads the standard input stream.

Unless the -R option is used, eqn searches for the file eqnrc in the directories given with the -M option first, then in /usr/share/groff/ site-tmac, and finally in the standard macro directory /usr/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.

Anatomy of an equation
eqn input consists of tokens. Consider a form of Newton’s second law of motion. The input

.EQ
F =
m a
.EN

becomes

Each of F, =, m, and a is a token. Spaces and newlines are interchangeable; they separate tokens but do not break lines or produce space in the output.

The following input characters not only separate tokens, but manage their grouping and spacing as well.

Tab and leader characters separate tokens as well as advancing the drawing position to the next tab stop, but are seldom used in eqn input. When they occur, they must appear at the outermost lexical scope. This roughly means that they can’t appear within braces that are necessary to disambiguate the input; eqn will diagnose an error in this event. (See subsection “Macros” below for additional token separation rules.)

Other tokens are primitives, macros, an argument to either of the foregoing, or components of an equation.

Primitives are fundamental keywords of the eqn language. They can configure an aspect of the preprocessor’s state, as when setting a “global” font selection or type size (gfont and gsize), or declaring or deleting macros (“define” and undef); these are termed commands. Other primitives perform formatting operations on the tokens after them (as with fat, over, sqrt, or up).

Equation components include mathematical variables, constants, numeric literals, and operators. eqn remaps some input character sequences to groff special character escape sequences for economy in equation entry and to ensure that glyphs from an unstyled font are used; see groff_char(7).

Macros permit primitives, components, and other macros to be collected and referred to by a single token. Predefined macros make convenient the preparation of eqn input in a form resembling its spoken expression; for example, consider cos, hat, inf, and lim.

Spacing and typeface
GNU eqn imputes types to the components of an equation, adjusting the spacing between them accordingly. Recognized types are as follows; most affect spacing only, whereas the “letter” subtype of “ordinary” also assigns a style.

Two primitives apply types to equation components.
type t e

Apply type t to expression e.

chartype t text

Assign each character in (unquoted) text type t, persistently.

eqn sets up spacings and styles as if by the following commands.

eqn assigns all other ordinary and special roff characters, including numerals 0–9, the “ordinary” type. (The “digit” type is not used, but is available for customization.) In keeping with common practice in mathematical typesetting, lowercase, but not uppercase, Greek letters are assigned the “letter” type to style them in italics. The macros for producing ellipses, “...”, cdots, and ldots, use the “inner” type.

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
The GNU extension primitives “type” and chartype are discussed in subsection “Spacing and typeface” above; “set” in subsection “Customization” below; and grfont and gbfont in subsection “Fonts” below. In the following synopses, X can be any character not appearing in the parameter thus bracketed.
e1 accent e2

Set e2 as an accent over e1. e2 is assumed to be at the appropriate height for a lowercase letter without an ascender; eqn vertically shifts it depending on e1’s height. For example, hat is defined as follows.

accent { "^" }

dotdot, dot, tilde, vec, and dyad are also defined using the accent primitive.

<mstyle mathsize='big'>

copy file
include file

Interpolate the contents of file, omitting lines beginning with .EQ or .EN. If a relative path name, file is sought relative to the current working directory.

ifdef name X anything X

If name is defined as a primitive or macro, interpret anything.

nosplit text

As "text", but since text is not quoted it is subject to macro expansion; it is not split up and the spacing between characters not adjusted per subsection “Spacing and typeface” above.

e opprime

As prime, but set the prime symbol as an operator on e. In the input “A opprime sub 1”, the “1” is tucked under the prime as a subscript to the “A” (as is conventional in mathematical typesetting), whereas when prime is used, the “1” is a subscript to the prime character. The precedence of opprime is the same as that of bar and “under”, and higher than that of other primitives except accent and uaccent. In unquoted text, a neutral apostrophe (') that is not the first character on the input line is treated like opprime.

sdefine name X anything X

As “define”, but name is not recognized as a macro if called with arguments.

e1 smallover e2

As over, but reduces the type size of e1 and e2, and puts less vertical space between e1 and e2 and the fraction bar. The over primitive corresponds to the TeX \over primitive in displayed equation styles; smallover corresponds to \over in non-display (“inline”) styles.

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.

special troff-macro e

Construct an object by calling troff-macro 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.

Suppose you want 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

split "text"

As text, but since text is quoted, it is not subject to macro expansion; it is split up and the spacing between characters adjusted per subsection “Spacing and typeface” above.

e1 uaccent e2

Set e2 as an accent under e1. e2 is assumed to be at the appropriate height for a letter without a descender; eqn vertically shifts it depending on whether e1 has a descender. utilde is predefined using uaccent as a tilde accent below the baseline.

undef name

Remove definition of macro or primitive name, making it undefined.

vcenter e

Vertically center e about the math axis, a horizontal line upon which fraction bars and characters such as “+” and “−” are aligned. MathML already behaves this way, so eqn ignores this primitive when producing that output format. The built-in sum macro is defined as if by the following.

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

Extended primitives
GNU eqn extends the syntax of some AT&T eqn primitives, introducing one deliberate incompatibility.
delim on

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. Few eqn documents are expected to use “o” and “n” as left and right delimiters, respectively. If yours does, consider swapping them, or select others.

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 accepted but have no effect. If more than one n occurs in a matrix or pile, 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, which delegates typesetting to a MathML rendering engine. Configure these parameters with the set primitive.
set p n

assigns parameter p the integer value n; n is interpreted in units of hundredths of an em unless otherwise stated. For example,

set x_height 45

says that eqn should assume that the font’s x-height is 0.45 ems.

Available parameters are as follows; defaults are shown in parentheses. We intend these descriptions to be expository rather than rigorous.

<mstyle mathvariant='double-struck'>

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 (50).

null_delimiter_space

This much horizontal space is inserted on each side of a fraction (12).

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 (4).

Macros
In GNU eqn, macros can take arguments. A word defined by any of the define, ndefine, or tdefine primitives followed immediately by a left parenthesis is treated as a parameterized macro call: subsequent tokens up to a matching right parenthesis are treated as comma-separated arguments. In this context only, commas and parentheses also serve as token separators. A macro argument is not terminated by a comma inside parentheses nested within it. In a macro definition, $n, where n is between 1 and 9 inclusive, is replaced by the nth argument; if there are fewer than n arguments, it is replaced by nothing.

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. Spell them with an initial capital letter (Alpha) or in full capitals (ALPHA) to obtain uppercase forms.

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

Fonts
eqn uses up to three typefaces to set an equation: italic (oblique), roman (upright), and bold. Assign each a groff typeface with the primitives gfont, grfont, and gbfont. The defaults are the styles I, R, and B (applied to the current font family). The chartype primitive (see above) sets a character’s type, which determines the face used to set it. The “letter” type is set in italics; others are set in roman. Use the bold primitive to select an (upright) bold style.
gbfont f

Select f as the bold font. This is a GNU extension.

gfont f

Select f as the italic font.

grfont f

Select f as the roman font. This is a GNU extension.

Options

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

Files

/usr/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 control of motions and sizes to the same degree troff does.

As in its troff mode, eqn in MathML mode leaves the .EQ and .EN tokens in place, but emits nothing corresponding to delim delimiters. They can, however, be recognized as character sequences that begin with “<math>”, end with “</math>”, and do not cross line boundaries.

Caveats

Tokens must be double-quoted 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. In particular, 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 italic face; you must use “gfont "PI"” instead.

Delimited equations are set at the type size current at the beginning of the input line, not necessarily that immediately preceding the opening delimiter.

Unlike TeX, eqn does not inherently distinguish displayed and inline equation styles; see the smallover primitive above. However, macro packages frequently define EQ and EN macros such that the equation within is displayed. These macros may accept arguments permitting the equation to be labeled or captioned; see the package’s documentation.

Bugs

eqn abuses terminology—its “equations” can be inequalities, bare expressions, or unintelligible gibberish. But there’s no changing it now.

In nroff mode, lowercase Greek letters are rendered in roman instead of italic style.

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.

Examples

We first illustrate eqn usage with a trigonometric identity.

.EQ
sin ( alpha + beta ) = sin alpha cos beta + cos alpha sin beta
.EN

It can be convenient to set up delimiters if mathematical content will appear frequently in running text.

.EQ
delim $$
.EN
Having cached a table of logarithms,
the property $ln ( x y ) = ln x + ln y$ sped calculations.

The quadratic formula illustrates use of fractions and radicals, and affords an opportunity to use the full space token ~.

.EQ
x = { - b ~ \[+-] ~ sqrt { b sup 2 - 4 a c } } over { 2 a }
.EN

Alternatively, we could define the plus-minus sign as a binary operator. Automatic spacing puts 0.06 em less space on either side of the plus-minus than ~ does, this being the difference between the widths of the medium_space parameter used by binary operators and that of the full space. Independently, we can define a macro “frac” for setting fractions.

.EQ
chartype "binary" \[+-]
define frac ! { $1 } over { $2 } !
x = frac(- b \[+-] sqrt { b sup 2 - 4 a c }, 2 a)
.EN

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. Appendix G discusses many of the parameters from section “Customization” above in greater detail.

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)