Man page 1 : eqn

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 `\c x '; .
• operator
      a large operator such as \*(Su; .
• binary
      a binary operator such as `(pl'; .
• 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\~\c ebut that has type\~\c t , where tis 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 textfrom now on have type\~\c t . For example, .

chartype "punctuation" .,;: .

would make the characters `.,;:' have type punctuation whenever they subsequently appeared in an equation. The type\~\c tcan also be

letter or

R digit ; in these cases

chartype changes the font type of the characters. See the

Fonts subsection. .

• 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'>

.

• .IB e1  smallover  e2
      This is similar to

R over ;

smallover reduces the size of e1and e2 ; it also puts less vertical space between e1or e2and the fraction bar. The

over primitive corresponds to the \*(tx

\over primitive in display styles;

smallover corresponds to

\over in non-display styles. .

• vcenter  e
      This vertically centers eabout the math axis. The math axis is the vertical position about which characters such as `(pl' and `(mi' 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.) .

• .IB e1  accent  e2
      This sets e2as an accent over e1 . e2is assumed to be at the correct height for a lowercase letter; e2is moved down according to whether e1is taller or shorter than a lowercase letter. For example,

hat is defined as .

accent { "^" } .

R dotdot ,

R dot ,

R tilde ,

R vec , and

dyad are also defined using the

accent primitive. .

• .IB e1  uaccent  e2
      This sets e2as an accent under e1 . e2is assumed to be at the correct height for a character without a descender; e2is moved down if e1has a descender.

utilde is pre-defined using

uaccent as a tilde accent below the baseline. .

• split (ts text (ts
      This has the same effect as simply .

text.

but textis not subject to macro expansion because it is quoted; textis split up and the spacing between individual characters is adjusted. .

• nosplit  text
      This has the same effect as .

(ts text (ts .

but because textis not quoted it is subject to macro expansion; textis not split up and the spacing between individual characters is not adjusted. .

• .IB e  opprime
      This is a variant of

prime that acts as an operator on\~\c e . It produces a different result from

prime in a case such as

R A opprime sub 1 : with

opprime the\~\c

1 is tucked under the prime as a subscript to the\~\c

A (as is conventional in mathematical typesetting), whereas with

prime the\~\c

1 is a subscript to the prime character. The precedence of

opprime is the same as that of

bar and

R under , which is higher than that of everything except

accent and

R uaccent . In unquoted text a\~\c

' that is not the first character is treated like

R opprime . .

• special  text e
      This constructs a new object from\~\c eusing a

R troff (1) macro named text . When the macro is called, the string

0s contains the output for\~\c e , and the number registers

R 0w ,

R 0h ,

R 0d ,

R 0skern , and

R 0skew contain the width, height, depth, subscript kern, and skew of\~\c e . (The "subscript kern"of an object says how much a subscript on that object should be tucked in; the skewof 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. .

define cancel 'special Ca'

.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\~\c ewith cancel {  e  } .

Here's a more complicated construct that draws a box round an expression: .

define box 'special Bx'

.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\~\c 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

R groff 's

\x escape (but with opposite sign). .

This keyword has no effect if the equation is part of a

pic picture. .

• col  n  {  . . .  }
      
  ccol  n  {  . . .  }
  lcol  n  {  . . .  }
  rcol  n  {  . . .  }
  pile  n  {  . . .  }
  cpile  n  {  . . .  }
  lpile  n  {  . . .  }
  rpile  n  {  . . .  } The integer value\~\c n(in hundredths of an em) increases the vertical spacing between rows, using

R 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. .

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\~\c pto value\~\c n ; n\~\cis 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. . .ie t \ . TP +2n . TP

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 `(pl' and `(mi'. 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

R 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

R 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

R \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

R \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

R ascii ,

R latin1 ,

R utf8 , and

cp1047 devices.) .

A more precise description of the role of many of these parameters can be found in Appendix\~H of "The \*(txbook" . .

Macros can take arguments. In a macro body, $ n where nis between 1 and\~9, is replaced by the n-th argument if the macro is called with arguments; if there are fewer than n\~\carguments, 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 nameis not recognized if called with arguments. .

• include (ts file (ts
      
  copy (ts file (ts Include the contents of file ( include and

copy are synonyms). Lines of filebeginning with

.EQ or

.EN are ignored. .

• ifdef  name X anything X
      If namehas been defined by

define (or has been automatically defined because nameis the output device) process anything ; otherwise ignore anything . Xcan 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:

R Alpha ,

R Beta , . . .,

Omega (this is the same as

R ALPHA ,

R BETA , . . .,

R OMEGA ),

ldots (three dots on the base line), and

R dollar . .

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\~\c

R 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\~\c f . .

The

italic primitive uses the current italic font set by

R gfont ; the

roman primitive uses the current roman font set by

R grfont . There is also a new

gbfont command, which changes the font used by the

bold primitive. If you only use the

R roman ,

italic and

bold primitives to changes fonts within an equation, you can change all the fonts used by your equations just by using

R 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. . .