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Nemeth Braille Code for Mathematics and Science
1972 Revision
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RULE XVIII--SIGNS AND SYMBOLS OF GROUPING

Parentheses (round brackets)
  • Left
    (
    Example as described in the content
    verbose
    left-parenthesis
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  • Left Enlarged
    ,(
    Example as described in the content
    verbose
    enlarged-left-parenthesis
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  • Right
    )
    Example as described in the content
    verbose
    right-parenthesis
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  • Right Enlarged
    ,)
    Example as described in the content
    verbose
    enlarged-right-parenthesis
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Brackets (square brackets)
  • Left
    @(
    Example as described in the content
    verbose
    left-bracket
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  • Left Enlarged
    @,(
    Example as described in the content
    verbose
    enlarged-left-bracket
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  • Right
    @)
    Example as described in the content
    verbose
    right-bracket
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  • Right Enlarged
    @,)
    Example as described in the content
    verbose
    enlarged-right-bracket
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  • Boldface Left
    _@(
    Example as described in the content
    verbose
    bold left-bracket
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  • Boldface Right
    _@)
    Example as described in the content
    verbose
    bold right-bracket
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Braces (curly brackets)
  • Left
    .(
    Example as described in the content
    verbose
    left-brace
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  • Left Enlarged
    .,(
    Example as described in the content
    verbose
    enlarged-left-brace
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  • Right
    .)
    Example as described in the content
    verbose
    right-brace
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  • Right Enlarged
    .,)
    Example as described in the content
    verbose
    enlarged-right-brace
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Vertical Bar
  • Single
    \
    Example as described in the content
    verbose
    vertical-line
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  • Single Enlarged
    ,\
    Example as described in the content
    verbose
    enlarged-vertical-line
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  • Double
    \\
    Example as described in the content
    verbose
    double-vertical-line
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  • Double Enlarged
    ,\,\
    Example as described in the content
    verbose
    enlarged-double-vertical-line
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  • Boldface Single
    _\
    Example as described in the content
    verbose
    bold vertical-line
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  • Boldface Double
    _\_\
    Example as described in the content
    verbose
    bold double-vertical-line
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Angle Brackets (angular parentheses)
  • Left
    ..(
    Example as described in the content
    verbose
    left-angle-bracket
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  • Left Enlarged
    ..,(
    Example as described in the content
    verbose
    enlarged-left-angle-bracket
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  • Right
    ..)
    Example as described in the content
    verbose
    right-angle-bracket
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  • Right Enlarged
    ..,)
    Example as described in the content
    verbose
    enlarged-right-angle-bracket
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Barred Brackets
  • Left
    @_(
    Example as described in the content
    verbose
    left-barred-bracket
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  • Left Enlarged
    @_,(
    Example as described in the content
    verbose
    enlarged-left-barred-bracket
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  • Right
    @_)
    Example as described in the content
    verbose
    right-barred-bracket
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  • Right Enlarged
    @_,)
    Example as described in the content
    verbose
    enlarged-right-barred-bracket
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Barred Braces
  • Left
    ._(
    Example as described in the content
    verbose
    left-barred-brace
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  • Left Enlarged
    ._,(
    Example as described in the content
    verbose
    enlarged-left-barred-brace
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  • Right
    ._)
    Example as described in the content
    verbose
    right-barred-brace
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  • Right Enlarged
    ._,)
    Example as described in the content
    verbose
    enlarged-right-barred-brace
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Half Brackets
  • Upper Left
    @^(
    Example as described in the content
    verbose
    top-left-bracket
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  • Upper Left Enlarged
    @^,(
    Example as described in the content
    verbose
    enlarged-top-left-bracket
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  • Upper Right
    @^)
    Example as described in the content
    verbose
    top-right-bracket
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  • Upper Right Enlarged
    @^,)
    Example as described in the content
    verbose
    enlarged-top-right-bracket
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  • Lower Left
    @;(
    Example as described in the content
    verbose
    bottom-left-bracket
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  • Lower Left Enlarged
    @;,(
    Example as described in the content
    verbose
    enlarged-bottom-left-bracket
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  • Lower Right
    @;)
    Example as described in the content
    verbose
    bottom-right-bracket
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  • Lower Right Enlarged
    @;,)
    Example as described in the content
    verbose
    enlarged-bottom-right-bracket
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Transcriber's Grouping Symbols
  • Left
    ,'
    verbose
    begin-transcriber-group
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  • Left Enlarged
    ,'(
    verbose
    enlarged-begin-transcriber-group
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  • Right
    ,'
    verbose
    end-transcriber-group
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  • Right Enlarged
    ,')
    verbose
    enlarged-end-transcriber-group
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§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.