David's Note: The title of this chapter is a German word that seems to encompass superscripts, subscripts, roots, and powers. There does not seem to be a similar word in English. So I will use EXPONENT in all caps as the Umbrella term. As used in this chapter, we include subscripts, square roots, and Roots to other powers. See the examples to see how much mathematical teritorry that is covered in this chapter.
chart
% square root
/ right (normal) superscript
* right (normal) subscript
/ or #/ left superscript
* or #* left subscript
. Indicator sign for Generic upper markings
_ Indicator for Generic lower markings
: Closing sign for simple EXPONENT
. Complex EXPONENT indicator
" Second complex EXPONENT indicator
.: or ": closing characters for complex EXPONENTS
=: closing sign for the whole EXPONENTS structure
In the inkprint the meaning of a symbol is understood by the elevation (high or low) of a subsequent character. An example of this are subscripts and superscripts. Some symbols (like the square root sign) may be drawn to show how far their impact reaches.
In Braille you cannot physically show an up or down position. That is not possible. Likewise, no braille can overlap another braille cell. That's why the braille script uses the same techniques as used for writing math linearly.
An EXPONENT is indicated by Braille signs, which the Show high or low position or the mathematical Symbol. This is followed by the actual expression. The impact of the EXPONENT indicator will be valid until there is another symbol to change or cancel it.
In braille, there is a distinction between simple and complex EXPONENTS a distinction made between different EXPONENTS. Complex EXPONENTS can contain certain elements that are not allowed in a simple EXPONENT.
A simple EXPONENT is indicated by the proper braille indicator. There must be no spaces and no additional EXPONENT included. The effect of the EXPONENT is ended by one of the following elements:
In all other cases, the end of the scope terminated with the character :. When the end of an EXPONENT does not have a closing sign, you get shorter - and therefore mostly clearer - Expressions. In case of doubt, it is always better to use the Closing sign.
In order avoid a complex EXPONENT, you can replace spaces with the cohesion dot :. This technique is especially useful for short EXPONENTS. This is especiall useful with operation characters, such as a plus sign in an exponent.
When an EXPONENT contains further EXPONENTS, spaces or Break lines, it must be "made complex". This is done by putting the complex EXPONENT sign . before the Sign for the EXPONENT in question. The scope of the EXPONENT becomes mandatory by a complex closing sign .: ended.
complex EXPONENTs can also be nested. The Outer EXPONENT is using . as a complex indicator, the first inner EXPONENT with the alternative complex sign " indicator. At each additional nesting level alternate the two complex signs. The respective associated closing sign highlights the effect of complex EXPONENT sign on. If all EXPONENTS end in the same place, the final closing sign =: should be used with the sequence of closing characters.
In the inkprint the subscript or superscript are one of several symbols of mathematical significance, this becomes in Braille mathematics writing as "upper" or "lower" indicators. Exponents are not typographically from different superscripts and therefore are shown with the same braille sign.
Superscripts to the right of the main symbol are also displayed in the Braille display. written immediately to the right of this symbol. These are labeled with the upper / or lower * braille indicator. If necessary, this character becomes combined with a complex EXPONENT indicator. If a symbol has several right subscripts and superscripts, then they are written one after the other. Each addition has a single indicator. A possibly existing exponent comes at the end.
Simple markings are an integral part of the main symbols and are usually preceded by subscript or superscript (see "8.1 Simple Marks").
To indicate a subscript or superscript left of a main charater are two forms of indicator sign to use. The short forms / and * are preferred, if it is not confusing. The long forms #/and #* are used where there is a likelihood of confusion with subscripts or superscipts on the previous symbol, for example immediately after one variable. After a space, equality or operation sign or an opening parenthesis this confusing cannot happen and the short forms are to be used.
If an subscript or superscript consists only of an integer, this can without the number sign using the lowered notation for numbers for the subscript or superscript. For negative numbers the minus sign without cohesion dot @ between inserted into the subscript or superscript character and the number. Should the positive property of the number to be emphasized by a plus sign, on the other hand, the standard notation must be used to mean and the plus sign through the cohesion dot @ from the subscript or superscript character.
After the number in lowered notation, there is no need to show the end of a simple EXPONENT in braille.
Square roots (without index 2) are used with the Symbol for roots (possibly with a complex EXPONENT sign combined) indicator. The EXPONENT ending indicator functions the same as the inkprint ending location of the Root line.
Numbers that indicate that this is a third, fourth, or other roots are shown as left superscripts before use of the Root symbol.