Modifiers- Part II

1. A modifier and its related expression must always be placed on the same level of writing. When a modifier affects both an expression on the baseline of writing and its superscript or subscript, the baseline indicator must be used after the superscript or subscript and before the directly-over or the directly-under indicator to indicate the level where the expression as a whole appears. However, it is not necessary to indicate a return to the baseline after numeric subscript indicator.

   Note: The contracted form of transcription must not be used when a horizontal bar extends above a superscript or subscript.

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2. When a letter modified either by the five-step rule or by the contracted form of transcription is followed by a numeric subscript, the subscript indicatores required.
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3. When an expression carrying a superscript or subscript is immediately followed, without a space, by a modified expression written on the baseline of writing, the baseline indicator must be used to terminate the effect of the level indicator, except when the expression follows a numeric subscript not requiring the subscript indicator. If the modified expression the baseline requires application of the five-step rule, both baseline indicator and the multipurpose indicator must be used.
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4. When a modified expression occurs in a superscript or subscript, the appropriate level indicator must be placed before the multipurpose indicator. If the modified expression occurs in the middle or the end of the superscript or subscript, the appropriate level indicator must be repeated before the multipurpose indicator to show continuation of the same level of writing. It is not necessary to repeat the level indicator when the contracted form of transcription is used and the multipurpose indicator is absent.
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1. An arrow must be treated as a modifier when it occurs directly over or directly under a symbol other than a sign of comparison. An arrow which occurs above or below a sign of comparison must be treated as part of a sign of comparison compounded vertically. When a right-pointing arrow in regular type with a full barb and single shaft of ordinary length is used as a modifier above or below a mathematical expression, the arrow must be transcribed in its contracted form. However, if such a right-pointing arrow is itself modified, or is part of a compound modifier, its contracted form must not be used. All other arrows require all their appropriate symbols.
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2. When identical arrows are used above vectors in boldface type throughout the text, they must be omitted from the braille transcription unless the author specifically refers to them as a notational device. If the arrows are to be omitted in braille, a transcriber's note must be included explaining that the arrows are present in print.

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   (OP is in boldface type, arrow omitted, T.N. required)

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   (OP is in ordinary type; arrow shown; T.N. not required)

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   (Both arrows must be shown since they are not of uniform construction. T.N. not required)

1. In print the recurrence of one or more digits in a decimal numeral may be indicated by one dot over each recurring digit. However, in braille only one dot is used as a modifier. The dot is placed after the last modified digit in the recurring sequence.
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2. When one or more dots occur over or under a single mathematical expression, the symbol for the dot must be used as many times as necessary to conform with the print text.
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   Horizontal Grouping Signs as Modifiers:

   A horizontal grouping sign over or under a mathematical expression must be treated as a modifier. It is recommended that such grouping signs be drawn.

   However, horizontal grouping signs may also be represented by braille symbols, in which case the entire modified expression must be transcribed in accordance with the five-step rule. The opening sign of grouping must be used when the modifier is above, and the closing sign of grouping when the modifier is below.

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   Modified Signs of Comparison:

   A modified sign of comparison consists of a simple sign of comparison, such as the equals sign or the tilde, modified by a caret, dot, triangle, question mark, vertical bar, or any symbol except another sign of comparison. Such a combination must be transcribed in accordance with the five-step rule for modified expressions. However, when a simple sign of comparison occurs above or below another simple sign of comparison, the combination must be transcribed as a sign of comparison compounded vertically, and the five-step rule must not be used.

   A modified sign of comparison may also consist of a horizontal bar modified by a dot under it or by a caret directly over or under it. However, if the horizontal bar is modified by a dot over it, the combination is a sign of operation.

   The following list contains the modified signs of comparison most commonly used. Unlisted modified comparison signs must be transcribed in accordance with the same principles.

   Equals Sign	Caret Over Caret Under (is projective to) Inverted Caret Over Left-pointing Caret Over Right-pointing Caret Over Dot Over (is approximately) Dot Over and Dot Under Two Dots Over and Two Dots Under Hollow Dot Over (is equals to) Equilateral Triangle Over Qustion Mark Over Vertical Bar Over
   Simple Tilde	Dot Under Dot Over
   Horizontal Bar	Caret Over Caret Under (is perspective to) Dot Under

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