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 ;

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.

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 \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 }

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 will be moved down according if 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 will be 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 will be split up and the spacing between individual characters will be adjusted.

nosplit text

This has the same effect as

text

but because text is not quoted it will be subject to macro expansion; text will not be split up and the spacing between individual characters will not be 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 will be tucked under the prime as a subscript to the A (as is conventional in mathematical typesetting), whereas with prime the 1 will be 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 will be 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 will contain the output for e, and the number registers 0w, 0h, 0d, 0skern and 0skew will 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 will output 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
..

The appearance of equations is controlled by a large number of parameters. These 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 will not 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.

over_hang

A fraction bar will be longer by twice this amount than the maximum of the widths of the numerator and denominator; in other words, it will overhang the numerator and denominator by at least this amount.

accent_width

When bar or under is applied to a single character, the line will be 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 will 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 will 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 will shift up the numerator by at least this amount.

num2

The smallover command will shift up the numerator by at least this amount.

denom1

The over command will shift down the denominator by at least this amount.

denom2

The smallover command will shift down the denominator by at least this amount.

sup1

Normally superscripts will be shifted up by at least this amount.

sup2

Superscripts within superscripts or upper limits or numerators of smallover fractions will be 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 will be shifted up by at least this amount. This is usually less than sup2.

sub1

Subscripts will normally be shifted down by at least this amount.

sub2

When there is both a subscript and a superscript, the subscript will be shifted down by at least this amount.

sup_drop

The baseline of a superscript will be 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 will be 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 will be 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 will be 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 will be 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 will be at least this much below the bottom of the object on which the limit is set.

big_op_spacing5

This much vertical space will be added above and below limits.

baseline_sep

The baselines of the rows in a pile or matrix will normally be 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 will be shifted down by this much from the axis. In most cases this should be equal to axis_height.

column_sep

This much space will be added between columns in a matrix.

matrix_side_sep

This much space will be added at each side of a matrix.

draw_lines

If this is non-zero, lines will be 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 will be 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 will be 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 will behave like define and tdefine will be ignored, otherwise tdefine will behave like define and ndefine will be 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 book.

Macros can take arguments. In a macro body, $n where n is between 1 and 9, will be replaced by the n-th argument if the macro is called with arguments; if there are fewer than n arguments, it will be 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 will be recognized as a macro call with arguments; characters following the left parenthesis up to a matching right parenthesis will be 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 will not be recognized if called with arguments.

include file

Include the contents of file. Lines of file beginning with .EQ or .EN will be 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.

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 will cause a character to be set in italic type. A type of digit will cause a character to be set in roman type.