RULE XVIII--SIGNS AND SYMBOLS OF GROUPING

Parentheses (round brackets)

• Left
  (

  	verbose	left-parenthesis

• Left Enlarged
  ,(

  	verbose	enlarged-left-parenthesis

• Right
  )

  	verbose	right-parenthesis

• Right Enlarged
  ,)

  	verbose	enlarged-right-parenthesis

Brackets (square brackets)

• Left
  @(

  	verbose	left-bracket

• Left Enlarged
  @,(

  	verbose	enlarged-left-bracket

• Right
  @)

  	verbose	right-bracket

• Right Enlarged
  @,)

  	verbose	enlarged-right-bracket

• Boldface Left
  _@(

  	verbose	bold left-bracket

• Boldface Right
  _@)

  	verbose	bold right-bracket

Braces (curly brackets)

• Left
  .(

  	verbose	left-brace

• Left Enlarged
  .,(

  	verbose	enlarged-left-brace

• Right
  .)

  	verbose	right-brace

• Right Enlarged
  .,)

  	verbose	enlarged-right-brace

Vertical Bar

• Single
  \

  	verbose	vertical-line

• Single Enlarged
  ,\

  	verbose	enlarged-vertical-line

• Double
  \\

  	verbose	double-vertical-line

• Double Enlarged
  ,\,\

  	verbose	enlarged-double-vertical-line

• Boldface Single
  _\

  	verbose	bold vertical-line

• Boldface Double
  _\_\

  	verbose	bold double-vertical-line

Angle Brackets (angular parentheses)

• Left
  ..(

  	verbose	left-angle-bracket

• Left Enlarged
  ..,(

  	verbose	enlarged-left-angle-bracket

• Right
  ..)

  	verbose	right-angle-bracket

• Right Enlarged
  ..,)

  	verbose	enlarged-right-angle-bracket

Barred Brackets

• Left
  @_(

  	verbose	left-barred-bracket

• Left Enlarged
  @_,(

  	verbose	enlarged-left-barred-bracket

• Right
  @_)

  	verbose	right-barred-bracket

• Right Enlarged
  @_,)

  	verbose	enlarged-right-barred-bracket

Barred Braces

• Left
  ._(

  	verbose	left-barred-brace

• Left Enlarged
  ._,(

  	verbose	enlarged-left-barred-brace

• Right
  ._)

  	verbose	right-barred-brace

• Right Enlarged
  ._,)

  	verbose	enlarged-right-barred-brace

Half Brackets

• Upper Left
  @^(

  	verbose	top-left-bracket

• Upper Left Enlarged
  @^,(

  	verbose	enlarged-top-left-bracket

• Upper Right
  @^)

  	verbose	top-right-bracket

• Upper Right Enlarged
  @^,)

  	verbose	enlarged-top-right-bracket

• Lower Left
  @;(

  	verbose	bottom-left-bracket

• Lower Left Enlarged
  @;,(

  	verbose	enlarged-bottom-left-bracket

• Lower Right
  @;)

  	verbose	bottom-right-bracket

• Lower Right Enlarged
  @;,)

  	verbose	enlarged-bottom-right-bracket

Transcriber's Grouping Symbols

• Left
  ,'

  verbose

  begin-transcriber-group

• Left Enlarged
  ,'(

  verbose

  enlarged-begin-transcriber-group

• Right
  ,'

  verbose

  end-transcriber-group

• Right Enlarged
  ,')

  verbose

  enlarged-end-transcriber-group

§120. Symbols of Grouping:

a. The grouping symbols listed above must be used everywhere in the transcription, whether for literary or mathematical purposes. The grouping symbols of English Braille must never be used except to enclose literary material on title pages. If a grouping sign occurs which is not listed above, then in the spirit of the Code, the transcriber must devise a symbol whose first component is ( for the opening grouping symbol and must use the same device but with last component ) for the closing symbol.

b. Although signs of grouping most commonly occur in pairs, this is not always so. If an opening grouping sign occurs without being followed later by the corresponding closing sign, or if the closing sign occurs without having been preceded by the corresponding opening sign, this situation must be preserved in the transcription.

§121. Horizontal Grouping Signs: When a horizontal grouping sign occurs over or under a mathematical expression, it must be regarded as a modifier. It is recommended that the horizontal grouping symbols be drawn. However, when they are to be represented in braille, the modified expression must be transcribed according to §86a. The left grouping symbol must be used when the modifier is directly over and the right grouping symbol when the modifier is directly under.

§122. Boldface Brackets: Boldface brackets are often used to designate the integer function.

§123. Half-Brackets: The upper half-brackets (left and right) are commonly used to represent the ceiling function. The lower half-brackets (left and right) are commonly used to represent the floor function. These signs are also used for miscellaneous purposes in many fields of mathematics and science.

§124. Vertical Bars:

a. Double boldface vertical bars are usually read as the norm of.

b. Single vertical bars are often read as the absolute value of, but are used for other purposes.

§125. Transcriber's Grouping Symbols: The regular transcriber's grouping symbols in the above list must be used to enclose any transcriber's note which has been inserted into the text (see §186b). These must not be used to enclose a list of transcriber's notes which appears at the beginning of a braille volume. The same rules which govern punctuation and contraction of expressions containing grouping symbols also govern transcriber's notes. For use of enlarged transcriber's grouping symbols see §184b.

§126. Use of Enlarged Grouping Symbols: When a system of mathematical expressions is arranged on two or more lines of ink print, and a sign of grouping is used to unify the system, the corresponding grouping symbol in the transcription must be indicated as enlarged by the use of dot 6 to indicate the enlargement. Among such systems of mathematical expressions are: systems of equations, determinants, and matrices. Each braille line which contains any part of the transcription of such a system must also contain the enlarged grouping symbol and these must be vertically aligned. If only the left or only the right member of a pair of grouping signs is present in ink print, only the corresponding grouping symbol must be represented in the transcription. However, when it is advisable for any reason to do so, for example, to save space by avoiding runovers, the enlarged grouping symbols may be drawn.

§127. Non-Use of Enlarged Grouping Symbols: Signs of grouping must not be indicated as enlarged in the transcription when the corresponding signs in ink print are made large such as for the purpose of covering a fraction, binomial coefficient or other material occupying a large amount of vertical space. No signs, except grouping signs, may ever be shown as being enlarged.

§128. Spacing with Symbols of Grouping:

a. Spaces may be required to be left after an opening enlarged grouping symbol or before a closing enlarged grouping symbol to preserve the vertical alignment of such symbols required in §126.

b. A space must be left between an opening and closing grouping symbol when there is a blank, not representing omission, between the corresponding signs in ink print.