RULE XIVMODIFIERS
Modification Indicators Directly Over
 First order<
 Second order<<
 Directly Under
 First order%
 Second order%%
 Multipurpose"
 Superposition@
 Termination]
 Arc
 Concave upward$a
 Concave downward$'
 Arrow
 Barbed at both ends$[33o
 Barbed at left$[33
 Barbed at left and dotted at right$[33*
 Barbed at right
 Contracted form$o
 Uncontracted form$33o
 Dotted at both ends$*33*
 Dotted at left (no barb)$*33
 Dotted at left and barbed at right$*33o
 Dotted at right (no barb)$33*
 Hollow dot at both ends$.*33.*
 Hollow dot at left (no barb)$.*33
 Hollow dot at left and barbed at right$.*33o
 Hollow dot at right and barbed at left$[33.*
 Hollow dot at right (no barb)$33.*
 Bar
 Horizontal (macron):
 Vertical\
 Caret (circumflex)_<
 Inverted_%
 Leftpointing;<
 Rightpointing;%
 Dot*
 Hollow dot.*
 Question Mark_8
 Tilde
 Extended@,:
 Simple@:
 Triangle (equilateral)$t
§85. Modifiers: A modifier is a superscript or subscript which occupies, respectively, a position directly over or directly under the sign to which it applies. The modifiers in the list at the beginning of this rule are those most commonly used, but other modifiers must be treated in the same manner.
§86. Modified Expressions:
a. The FiveStep Rule for Transcribing Modified Expressions: The components of a modified expression must appear in the following order:
i.
Multipurpose indicator "
ii. Expression
being modified.
iii.
Directlyover indicator < or
directlyunder indicator %
iv. Modifier.
v.Termination
indicator ]
These five components may never be separated from each other
by transition to another braille line. The termination indicator terminates
only the modified expression; it does not affect the level at which the
modified expression occurs.
(3)
"lim%x $o #0] f(x)
(the limit, as x approaches 0, of f of x)
verbose semantics 
limit Underscript
x rightarrow 0 EndScripts
f leftparenthesis x rightparenthesis 

(11)
"(a:_;,a+b:_;,b)<:]
(a with superscribed bar times boldface A plus b with
superscribed bar times boldface capitalized B, the whole expression with
superscribed bar)
verbose semantics 
ModifyingAbove Above
leftparenthesis
a overbar
Bold
Upper
A plus
b overbar
Bold
Upper
B rightparenthesis with bar


§87. Modifiers of Higher Order:
(2)
"x+y%:%%a .k #3%%%b .k #2]
(x plus y subscribed by a bar, which in turn is
subscribed by a=3, which is in turn subscribed by b equals 2)
verbose semantics 
ModifyingBelow
x plus y With bar
Underscript
a equals 3 UnderUnderscript
b equals 2 EndScripts


b. A modifier of order higher than the third must be treated in the manner suggested in a above.
(2)
".,s%n .k #1<,=]?1/2^n"# .k #1
(the Greek capitalized sigma with subscribed n equals
1 and superscribed infinity sign)
verbose semantics 
sigmasummation Underscript
n equals 1 Overscript
infinity EndScripts
StartFraction
1 Over
2 Superscript
n Baseline
EndFraction
equals 1 

(3)
"x+y%:%%a .k #3<:<<b .k #2]
(x plus y subscribed by a bar which is in turn
subscribed by a equals 3; superscribed by a bar which is in turn superscribed
by b equals 2)
verbose semantics 
ModifyingAbove
ModifyingBelow
x plus y With bar
with bar
Underscript
a equals 3 Overscript
b equals 2 EndScripts


(2)
(g;j"%a;j")
(the binomial coefficient with g sub j as the upper
sign and a sub j as the lower sign)
(2)
,a;"x<@:]+;"y<@:]
(A carries a subscript of x with superscribed tilde
plus y with superscribed tilde; the subscript level after the plus sign must be
restated before the multipurpose indicator)
§92. Plural Modified Expressions: (See §39).
A sign
belonging to a category lower on the list must be regarded as superposed on a
sign higher on the list, and the superposition transcribed accordingly. If two
signs belong to the same category, it is permissible to represent the
superposition in either order, provided that the same order is used consistently
throughout the entire transcription. The components of a sign compounded by
superposition must be joined by the superposition indicator and transcribed
unspaced, and without transition to another braille line. The termination
indicator must follow the second component. (For other examples, see
"Comparison Signs Compounded by Superposition" pages 140141, and
143.)
§94. Interior Modifiers with Signs of Shape: See §111.