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**PROGRAM:**

**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/1.22.3/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 adequately for very simple input).

**OPTIONS**

It is possible to have whitespace between a command line option and its parameter.

**-d**

__xy__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.

**-m**

__n__The minimum point-size is

__n__.

**eqn**does not reduce the size of subscripts or

superscripts to a smaller size than

__n__.

**-T**

__name__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**.

**-M**

__dir__Search

__dir__for

**eqnrc**before the default directories.

**-R**Don't load

**eqnrc**.

**-f**

__F__This is equivalent to a

**gfont**

__F__command.

**-s**

__n__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.

**-p**

__n__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

<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 ‘+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 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

<mstyle mathvariant='double-struck'>

**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.

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