There are two Nemeth translators built into MegaDots 2.3: MegaMath and Baby Nemeth. You can select either one. Use the style sheet Nemeth for MegaMath or Babynem for Baby Nemeth. MegaMath is more automatic, Baby Nemeth is much more manual.

MegaDots has several new features designed to assist you in producing a book in Nemeth Code. These features assist you in getting the correct translation and format. They are:

- Set the style sheet to
*Nemeth*. Go to the Style Sheet Selection screen in the Document Menu, and choose*Nemeth*. Selecting the NEMETH style sheet automatically sets the Braille Standard to*Math*, so that standard text and arithmetic problems can be properly translated with MegaDots. This changes the forward translation for numbers and punctuation. - These
*Nemeth*instructions are now available on-line in MegaDots to speed up finding the Nemeth Code information you need for data entry. Go to the Nemeth selection from the Help Menu (type F10 H N from the Editor).

Be aware that you will have to enter the mathematical sequences yourself. This means you need to know the basics of Nemeth Code in order to produce a book in Nemeth Code. If you want to avoid learning about Nemeth Code, wait for our full translator in early 1997.

To enter Nemeth sequences, enter the text in the way you feel comfortable (full keyboard or Perkins 6-key keyboard). Mark the Nemeth sequence in a block and press Control-T X. This sets the block to *exact translation*. This ensures that the entire block is not modified by the MegaDots translators at all. You can press F5 all you want, and the material marked as *exact translation* is unchanged.

The Nemeth sequences in this document are rendered in exact translation and are enclosed in braces. Do not type the braces. For example, the Nemeth for "y = 2sin x" is written as {

}. In Nemeth, the equal sign is space, dots 4-6, dots 1-3, space.
**y .k #2sin x**

To really learn Nemeth Code, you need a copy of *the Nemeth Braille Code for Mathematics and Science Notation*, which is available in both inkprint and braille copies from:

- American Printing House for the Blind
- 1839 Frankfort Avenue
- Louisville KY 40206
- 502-895-2405; or 800-223-1839
- Inkprint Copy Catalog No.: 7-8743
- Braille Copy Catalog No.: 5-8743

If you are producing chemistry material, there is a supplement called *Chemistry in Braille, 1991*, which is available in inkprint from:

- National Braille Association
- 3 Townline Circle
- Rochester, NY 14623
- (716) 427-8260

The Nemeth style sheet is a direct copy of the Textbook style sheet with some exceptions. The styles Exercise and Directions are modified according to the rules of Nemeth Code.

In Nemeth Code, directions start in cell 5, and run over to cell 3. In Nemeth code, exercises (called "non-spatial itemized material" in the code book) begin in cell 1 and run over to cell 3. Any subordinate items (levels 2 or above in MegaDots lingo) begin in cell 5 and run over to cell 3.

There are also two new styles in the Nemeth style sheet: Displayed mat. (displayed material) and Spatial mat. (spatial material).

Here is a list of math symbols with their Nemeth Code equivalent. It is based on how mathematical symbols are verbalized. If you do not know the names of the mathematical symbols you want to braille, this guide will not be of much use.

See also *start modified expression*, *modified expression*, *below*, and *terminate modified expression*; contrast with *superscript*. To modify the expression xxx to place yy above it, enter {

} (the dot 5 is the multipurpose indicator, showing a modified expression. The dots 1-2-6 shows that the following material is above. The dots 1-2-4-5-6 is the termination sign, showing that the modified expression is over.
**"xxx<yy]**

The first letter of the Hebrew alphabet, entered as {

}. Notice the ambiguity with a double capitalized word starting with the letter "a".
**,,a**

Greek letter a, entered as Alt-G a for lower case or Alt-G A for upper case. In braille, the lower case alpha is {`.a`

} and the upper case alpha is {`.,a`

}

You can show many different alphabets with Nemeth Code. Here is the list: English letter (Roman letter) {

}, German letter {**;**

}, Greek letter {**_**

}, Hebrew letter {**.**

}, and Russian letter {**,,**

}.
**@@**

The Nemeth Code book has these alphabets all printed out. This may be useful if you need a handy chart. If you know the names of the different letters, you can look things up in our main index. To write the Greek letter pi (a Greek p), just write {

} The order for indicators is: typefont indicator, alphabet indicator, capitalization indicator, followed by letter.
**.p**

Entered as {

}
**_&**

Entered in exact translation as: {

}, for example angle ABC is written as {**$[**

}.
**$[,a,b,c**

Units of measurement shown in inkprint as a capital A with a hollow dot above it, entered as {

}.
**@,a**

Entered in Exact Translation as: {

}. Just use an apostrophe outside of exact translation. See **'***MegaDots translation*.

Entered in Exact Translation as: {

}
**$'**

Entered in Exact Translation as: {

}
**$a**

Entered in Exact Translation as: {

}
**33**

Entered in Exact Translation as: {

}
**$[o**

Entered in Exact Translation as: {

}
**$[33o**

Entered in Exact Translation as: {

}
**$<[o**

Entered in Exact Translation as: {

}
**$<[33o**

Entered in Exact Translation as: {

}
**$%o**

Entered in Exact Translation as: {

}
**$%33o**

Entered in Exact Translation as: {

}
**$[33**

Entered in Exact Translation as: {

}
**$33o**

Entered in Exact Translation as: {

}
**$7o**

Entered in Exact Translation as: {

}
**$<o**

Entered in Exact Translation as: {

}
**$<33o**

The MegaDots translator can render simple, linear arithmetic problems into proper braille. The trick is representing the "times" symbol (which looks like an x) and the "divided by" symbol (which looks like a hyphen with dots above and below). To allow data entry, use \x (backslash x) for times, and \-: (backslash hyphen colon) for the divided by symbol (in a sense it is a hyphen jammed into a colon). Also use \? for an omission sign. To write "10 divided by 2 = ?? just enter `10\-:2=\?`

in the standard mode (not as exact translation). MegaDots will render this as {

} (divided by becomes dots 4-6 dots 3-4, the omission sign becomes a full cell). See also **#10./2 .k =***MegaDots translation*.

Spatial format of arithmetic problems is more difficult. Make extensive use of the blank character symbol (entered as Control-B). This symbol is an unbreakable space in the final braille. Use it to position equations so they line up in the braille output. See *spatial format*.

Entered in Exact Translation as: {

}
**@#**

Entered in Exact Translation as: {

}
**@a**

Entered in Exact Translation as: {

}
**_***

An inkprint diagonal line from the upper left to the lower right, entered as {

}.
**_***

Entered in Exact Translation as: {

}
**:@%:**

Entered in Exact Translation as: {

}
**:@+:**

Entered in Exact Translation as: {

}
**:@%.k**

Entered in Exact Translation as: {

}
**:@+.k**

Entered in Exact Translation as: {

}
**:@:@:**

Entered in Exact Translation as: {

}
**:.1**

Entered in Exact Translation as: {

}
**:_"k**

Entered in Exact Translation as: {

}
**:"k**

Entered in Exact Translation as: {

}
**:@%**

Entered in Exact Translation as: {

}
**:@+**

Looks like a backwards stretched c (or a sideways u with the opening to the left). Entered in Exact Translation as: {

}
**:_.1**

Entered in Exact Translation as: {

}
**:@:**

Entered in Exact Translation as: {

}
**@:@::**

Entered in Exact Translation as: {

}
**.1:**

Entered in Exact Translation as: {

}
**_"k:**

Entered in Exact Translation as: {

}
**.%:**

Entered in Exact Translation as: {

}
**"k:**

Entered in Exact Translation as: {

}
**@%:**

Entered in Exact Translation as: {

}
**@+:**

Entered in Exact Translation as: {

}
**_.1:**

Entered in Exact Translation as: {

}
**@::**

Entered in Exact Translation as: {

}
**.+:**

This symbol takes you back to the baseline from a subscript and superscript without needing a space. Entered in Exact Translation as: {

}. See also **"***subscript* and *superscript*.

Indicates the end of a superscript or subscript. Most inkprint signs share a common vertical reference; signs appearing above or below this baseline are interpreted as superscripts or subscripts. You go back to the baseline with a space, multipurpose indicator, or punctuation indicator. The multipurpose indicator is also used to start modified expressions. It is entered as {

}. To write "x cubed", enter {**"**

} (the space takes you back to the baseline. To write "x cubed plus 2 x squared" enter {**x^3**

} (since there is no space before the plus sign, you need the dot 5 multipurpose indicator to take you back to the baseline)
**x^3"+2x^2**

Looks like three dots, 2 above one dot. Entered in Exact Translation as: {

}
**@/**

Precedes material that will be printed directly under other material, entered as the directly-under indicator {

} within a modified expression. See also **%***start modified expression*, *above*, and *terminate modified expression*; contrast with *subscript*.

The second letter of the Hebrew alphabet, entered as {

}.
**,,b**

Greek letter b, entered as Alt-G b for lower case or Alt-G B for upper case. In braille, the lower case beta is {`.b`

} and the upper case beta is {`.,b`

}

A binomial is a mathematical expression shown as one quantity written above another quantity, enclosed within enlarged parenthesis. Use an open parenthesis, then the top element, then {

}, then the lower element, then a closed parenthesis.
**%**

Bold face is a typefont indicator. It is used for inkprint letters that are thicker and darker than normal. Enter as {

). For example, Enter a bold face capital x as: {**_**

}. The order for indicators is: typefont indicator, alphabet indicator, capitalization indicator, followed by letter.
**_;,x**

See note under *Chemistry*. A double horizontal bar connecting portions of a chemical structure. Enter as {`_7]`

}. For example, if the inkprint shows C=C, enter as {`,c_7],c`

}.

See note under *Chemistry*. A double vertical bar connecting portions of a chemical structure. Enter as {`__`

}. Be careful with spatial arrangments. Use Spacing same style and the control-B blank character to line things up in MegaDots.

See note under *Chemistry*. A single horizontal bar connecting portions of a chemical structure. Enter as {`_3]`

}. For example, if the inkprint shows H-O, enter as {`,h_3],o`

}.

See note under *Chemistry*. A vertical bar connecting portions of a chemical structure. Enter as {`_`

}. Be careful with spatial arrangments. Use Spacing same style and the control-B blank character to line things up in MegaDots.

See note under *Chemistry*. A triple horizontal bar connecting portions of a chemical structure. Enter as {`_=]`

}.

See note under *Chemistry*. A triple vertical bar connecting portions of a chemical structure. Enter as {`___`

}. Be careful with spatial arrangments. Use Spacing same style and the control-B blank character to line things up in MegaDots.

Symbol of enclosure that looks like this: {xxx}. They are also known as *curly brace*; open and close braces are entered with {

} and {**.(**

}.
**.)**

Looks like {xx. Entered in Exact Translation as: {

}
**.(**

Looks like {xx (only bigger). Entered in Exact Translation as: {

}
**.,(**

Looks like xx}. Entered in Exact Translation as: {

}
**.)**

Looks like xx} (only bigger). Entered in Exact Translation as: {

}
**.,)**

Looks like [xx]. Symbol of enclosure, also known as square bracket; open and close brackets are entered with {

} and {**@(**

}.
**@)**

Looks like [xx. Entered in Exact Translation as: {

}
**_@(**

Looks like xx]. Entered in Exact Translation as: {

}
**_@)**

Looks like [xx (only bigger). Entered in Exact Translation as: {

}
**@,(**

Looks like xx] (only bigger). Entered in Exact Translation as: {

}
**@,)**

Looks like <xx. Entered in Exact Translation as: {

}
**..(**

Looks like [xx. Entered in Exact Translation as: {

}
**@(**

Looks like xx>. Entered in Exact Translation as: {

}
**..)**

Looks like xx]. Entered in Exact Translation as: {

}
**@)**

Often a fraction is shown with different factors crossed off on both the numerator and the denominator. This is cancellation. To show that something is cancelled start with {

} and end with {**[**

}. For example, to show "xyz with y and z with individual slashes, enter {**]**

}.
**x[y][z]**

Capitalization is done the same in Nemeth Code as in standard braille. It is entered in Exact Translation as: {

}. If there are other symbols modifying a letter (German letter, etc.), the capitalization indicator goes next to the letter. The order for indicators is: typefont indicator, alphabet indicator, capitalization indicator, followed by letter. In a math expression, avoid using the double capitalization sign (two dot 6's). Instead use the single capitalization marker for each letter. Example: triangle ABC is written as {**,**

}
**$t ,a,b,c**

Entered in Exact Translation as: {

}
**,,**

Entered in Exact Translation as: {

}
**_<**

Entered in Exact Translation as: {

}
**".k<_<]**

Entered in Exact Translation as: {

}
**":<_<]**

Entered in Exact Translation as: {

}
**".k%_<]**

Entered in Exact Translation as: {

}
**":%_<]**

Entered in Exact Translation as: {

}
**_%**

Entered in Exact Translation as: {

}
**".k<_%]**

Entered in Exact Translation as: {

}
**;<**

Entered in Exact Translation as: {

}
**".k<;<]**

Entered in Exact Translation as: {

}
**;%**

Entered in Exact Translation as: {

}
**".k<;%]**

Entered in Exact Translation as: {

}
**@c**

Entered in Exact Translation as: {

}
**@>**

Chemistry is barely mentioned in the Nemeth Code Book. If you are producing chemistry material, there is a supplement called *Chemistry in Braille, 1991*, which is available from the National Braille Association. The address is at the top of this document under *Data Entry*.

Chi is a Greek letter. Entered as Alt-G c for lower case or Alt-G C for upper case. In braille, the lower case chi is {`.&`

} and the upper case chi is {`.,&`

}

Entered in Exact Translation as: {

}
**$c**

Entered in Exact Translation as: {

}
**_<**

Looks like xx}. Entered as {

}. See **.)***brace*.

Looks like xx]. Entered as {

}. See **@)***bracket*.

Entered as {

}. See **)***parenthesis*.

Entered in Exact Translation as: {

}. Just use a colon outside of exact translation. See **_3***MegaDots translation*.

Just use a comma outside of exact translation. If you have to use exact translation, you probably have a mathematical comma. See *comma, mathematical* and *MegaDots translation*.

A mathematical comma is used Entered in Exact Translation as: {

}. Just use a comma outside of exact translation. See **,***MegaDots translation*.

Entered in Exact Translation as: {

}
**[**

A fraction of a fraction. Show the start, middle and end of a complex fraction with {

}, {**,?**

}, and {**,/**

}.
**,#**

Entered in Exact Translation as: {

}
**,#**

Entered in Exact Translation as: {

}
**,?**

Entered in Exact Translation as: {

}
**,/**

Looks like a stretched letter c (or a sideways u wi the opening to the right). Entered in Exact Translation as: {

}
**_"k**

Looks like a stretched backwards letter c (or a sideways u with the opening to the left). Entered in Exact Translation as: {

}
**_.1**

Looks like a centered x. Entered in Exact Translation as: {

}
**@***

Entered in Exact Translation as: {

}
**@$**

Entered in Exact Translation as: {

}
**@h**

Entered in Exact Translation as: {

}
**@.l**

Entered in Exact Translation as: {

}
**@,r**

The symbol which looks like a number sign. Entered in Exact Translation as: {

}
**.#**

An index of radical value of three, shown in inkprint as an elevated 3 followed by the inkprint radical sign, entered as {

}. See also **<3>***terminate cube root*.

A superscript of 3, entered as any character followed by {

}. Compare with **^3***superscript* and *squared*.

Entered in Exact Translation as: {

}
**_]**

Entered in Exact Translation as: {

}
**__]**

Entered in Exact Translation as: {

}
**--**

Entered in Exact Translation as: {

}
**----**

If you have a number outside of exact translation (i.e. an isolated number or part of an arithmetic problem), you do not have to worry about numbers or decimal points. The translator will handle it appropriately. See *MegaDots translation*. If a number occurs inside of exact translation, use the numeric indicator if the number comes after a space, new paragraph, or a punctuation. See *numeric indicator*. A decimal point in Exact Translation as: {

}
**.**

A hollow dot in the superscript position. You can enter this inside or outside of exact translation. Inside of exact translation, write 90 degrees as entered as {

}. Outside of exact translation, just type 90 Alt-plus sign d (Alt-plus sign d selects a degree sign from the punctuation menu.
**#90^.***

Entered in Exact Translation as: {

}
**".k<.*]**

Looks like an upside down triangle. Entered in Exact Translation as: {

}
**.$**

Looks like a bold upside down triangle. Entered in Exact Translation as: {

}
**_.$**

Greek letter d, entered as Alt-G d for lower case or Alt-G D for upper case. In braille, the lower case delta is {`.d`

} and the upper case delta is {`.,d`

}

Entered in Exact Translation as: {

}
**_/**

See *numeral* and *numeric indicator*.

Entered in Exact Translation as: {

}. To modify the expression xxx to place yy above it, enter {**<**

} (the dot 5 is the multipurpose indicator, showing a modified expression. The dots 1-2-6 shows that the following material is above. The dots 1-2-4-5-6 is the termination sign, showing that the modified expression is over. See also **"xxx<yy]***start modified expression*, *modified expression*, *below*, and *terminate modified expression*; contrast with *superscript*.

Entered in Exact Translation as: {

}. Precedes material that will be printed directly under other material, entered as the directly-under indicator {**%**

} within a modified expression. To modify the expression xxx to place yy below it, enter {**%**

} (the dot 5 is the multipurpose indicator, showing a modified expression. The dots 1-4-6 shows that the following material is below. The dots 1-2-4-5-6 is the termination sign, showing that the modified expression is over. See also **"xxx%yy]***start modified expression* and *terminate modified expression*; contrast with *subscript*.

Looks like a double quote symbol. Entered in Exact Translation as: {

}
**,'**

The symbol looks like a hyphen with a dots above and a dot below. It is the symbol used in arithmetic to show division, enter in Exact Translation as: {

}. Outside of exact translation, enter as backslash hyphen colon. \-: See also **./***arithmetic*.

See *divided by*.

Entered in Exact Translation as: {

}
**@s**

A centered dot which often represents multiplication, entered as {

}.
*****

Entered in Exact Translation as: {

}
*****

Entered in Exact Translation as: {

}
**".k%*<*]**

Entered in Exact Translation as: {

}
**".k<*]**

Entered in Exact Translation as: {

}
**":%*]**

Entered in Exact Translation as: {

}
**"@:%*]**

Two angled strokes, entered as {

}. See also **''***prime*.

Two wavy horizontal lines stacked vertically, entered as {

}. Often means **@:@:***approximately equal to*. Compare with *tilde*.

These are beyond the scope of this guide. If you are producing chemistry material, there is a supplement called *Chemistry in Braille, 1991*, which is available from the National Braille Association. The address is at the top of this document under *Data Entry*.

Entered in Exact Translation as: {

}
**@e**

Entered in Exact Translation as: {

}
**$e**

Entered in Exact Translation as: {

}
**'''**

Looks like zero with a slash through it. Entered in Exact Translation as: {

}
**@_0**

Follows the denominator material and implies a return to the vertical position before the fraction. Entered as {

} when preceded by start fraction indicator and fraction line. See also **#***complex* and *hypercomplex*.

Entered in Exact Translation as: {

}. The order for indicators is: typefont indicator, alphabet indicator, capitalization indicator, followed by letter.
**_;**

Entered in Exact Translation as: {

}. The order for indicators is: typefont indicator, alphabet indicator, capitalization indicator, followed by letter.
**_;,**

Letters are the same as Nemeth Code as in standard braille. In standard braille, dots 5-6 is called the *letter sign*. The letter sign is used to show that something is uncontracted. For example, "letter sign b" means just a b, not the word "but". In Nemeth Code, dots 5-6 plays a similar role, but goes by the name of the *English Letter Sign*. The English letter sign is used in places where you need a letter sign in regular braille. Also use it when letters are shown in a different typefont. For example **AX** (AX in boldface) is {

} (dots 4-5-6 for boldface, then the English letter sign, then the capitalization sign, then the letter). The order for indicators is: typefont indicator, alphabet indicator, capitalization indicator, followed by letter.
**_;,a_;,x**

The rules for the use and non-use of the English letter sign are actually quite complex. See the Nemeth Code book for the full story.

Greek letter e, entered as Alt-G e for lower case or Alt-G E for upper case. In braille, the lower case elsolon is {`.e`

} and the upper case epsilon is {`.,e`

}

Entered in Exact Translation as: {

}. As with all symbols of comparison, leave a space on either side of it. But leave out the space near a grouping symbol (parenthesis, braces or brackets), or any punctuation which applies to the sign of comparison. See also ** .k ***arithmetic*.

An equals sign below a sign of comparison, entered by placing {

} after a sign of comparison.
**.k**

An equals sign above a sign of comparison. Entered as placing {

} before a sign of comparison.
**.k**

Entered in Exact Translation as: {

}
**.k@+:**

Entered in Exact Translation as: {

}
**.k@%:**

Entered in Exact Translation as: {

}
**.k@%.k**

Entered in Exact Translation as: {

}
**.k@+.k**

Entered in Exact Translation as: {

}
**.k@:@:**

Entered in Exact Translation as: {

}
**.k.1**

Entered in Exact Translation as: {

}
**.k_"k**

Entered in Exact Translation as: {

}
**.k"k**

Entered in Exact Translation as: {

}
**.k@%**

Entered in Exact Translation as: {

}
**.k@+**

Entered in Exact Translation as: {

}
**.k_.1**

Entered in Exact Translation as: {

}
**.k@:**

An equals sign below a sign of comparison, entered by placing {

} after a sign of comparison.
**.k**

Entered in Exact Translation as: {

}
**@:@:.k**

Entered in Exact Translation as: {

}
**.1.k**

Entered in Exact Translation as: {

}
**_"k.k**

Entered in Exact Translation as: {

}
**.%.k**

Entered in Exact Translation as: {

}
**@%.k**

Entered in Exact Translation as: {

}
**@+.k**

Entered in Exact Translation as: {

}
**_.1.k**

Entered in Exact Translation as: {

}
**@:.k**

Entered in Exact Translation as: {

}
**.+.k**

Entered in Exact Translation as: {

}
**_.k**

Entered in Exact Translation as: {

}
**@<,<**

Eta is a Greek letter. It is entered as Alt-G h for lower case or Alt-G H for upper case. In braille, the lower case eta is {`.:`

} and the upper case eta is {`.,:`

}.

Entered in Exact Translation as: {

}. Just use an exclamation mark outside of exact translation. See **_6***MegaDots translation*. If the exclamation follows a number or is used in a mathematical context, it might be a factorial. See *factorial*.

Looks like a backwards uppercase e. Entered in Exact Translation as: {

}
**@=**

An exponent is the power that something is raised to. It is written as a superscript. For example, x with an exponent of 5 is written as x with a superscript of 5. In Nemeth Code, use dots 4-5 to show a superscript. To come back from the baseline, use either a space or a dot 5. To write "x to the exponent of 5", enter {

}. To write "x squared plus y squared", enter {**x^5**

}. See also **x^2"+y^2***superscript* and *baseline*.

Looks like an exclamation mark. Entered in Exact Translation as: {

}. For example "6 factorial" is entered {**&**

}
**#6&**

Entered in Exact Translation as: {

}. Just use an single quote outside of exact translation. See **'***MegaDots translation*.

Looks like an upside down uppercase A. Entered in Exact Translation as: {

}
**@&**

Looks like a backwards uppercase E followed by a vertical line. Entered in Exact Translation as: {

}
**@=\**

Looks like a backwards uppercase E. Entered in Exact Translation as: {

}
**@=**

Entered in Exact Translation as: {

}
**#**

To write the fraction 1/5, enter as {

} (in other words, write the fraction in exact translation the way that is natural using the ASCII keyboard, use the "th" sign to start a fraction, the "st" sign for the fraction bar, and the "ble" sign to end the fraction.
**?1/5#**

Because of the ambiguity involved, you cannot use contractions inside a fraction. So if you need to inclose the word "distance" in the fraction, you need to write the word in grade one.

Indicates end of numerator material and beginning of denominator material. Shown in inkprint as a horizontal line slightly longer than the longest sign in numerator or denominator. Entered as {

} when preceded by start fraction indicator and followed by end fraction indicator. See also **/***complex* and *hypercomplex*.

Examples of function names are "sin" and "cos". Do not contract a function name. Always leave a space after a function name.

Greek letter g, entered as Alt-G g for lower case or Alt-G G for upper case. In braille, the lower case gamma is {`.g`

} and the upper case gamma is {`.,g`

}.

Entered in Exact Translation as: {

}. The order for indicators is: typefont indicator, alphabet indicator, capitalization indicator, followed by letter.
**_**

Entered in Exact Translation as: {

}. The order for indicators is: typefont indicator, alphabet indicator, capitalization indicator, followed by letter.
**_,**

Looks like upside down triangle. Entered in Exact Translation as: {

}
**.$**

Entered in Exact Translation as: {

}. As with all symbols of comparison, leave a space on either side of it. But leave out the space near a grouping symbol (parenthesis, braces or brackets), or any punctuation which applies to the sign of comparison.
**.1**

Entered in Exact Translation as: {

}
**.1".k""k**

Entered in Exact Translation as: {

}
**.1""k**

Entered in Exact Translation as: {

}
**.1@.1]**

Entered in Exact Translation as: {

}. The order for indicators is: typefont indicator, alphabet indicator, capitalization indicator, followed by letter.
**.**

Entered in Exact Translation as: {

}. The order for indicators is: typefont indicator, alphabet indicator, capitalization indicator, followed by letter.
**.,**

Entered in Exact Translation as: {

}
**@;(**

Entered in Exact Translation as: {

}
**@;)**

Entered in Exact Translation as: {

}
**@^(**

Entered in Exact Translation as: {

}
**@^)**

Entered in Exact Translation as: {

}. The order for indicators is: typefont indicator, alphabet indicator, capitalization indicator, followed by letter.
**,,**

Entered in Exact Translation as: {

}
**,,a**

Entered in Exact Translation as: {

}
**,,b**

A centered small circle, entered as {

}. Also see **.****degree*.

Entered in Exact Translation as: {

}
**.***

Entered in Exact Translation as: {

}
**:**

A horizontal bar below a sign of comparison, entered by placing {

} after a sign of comparison.
**:**

A horizontal bar above a sign of comparison. Entered as {

} before a sign of comparison.
**:**

A Chemistry symbol. Entered in Exact Translation as: {

}
**_7]**

A Chemistry symbol. Entered in Exact Translation as: {

}
**_3]**

A Chemistry symbol. Entered in Exact Translation as: {

}
**_g]**

A Chemistry symbol. Entered in Exact Translation as: {

}
**_=]**

A fraction of a fraction of a fraction. See *complex fraction*. Entered as {

}, {**,,?**

}, and {**,,/**

}.
**,,#**

Entered in Exact Translation as: {

}
**,,?**

Entered in Exact Translation as: {

}
**,,/**

Entered in Exact Translation as: {

}
**-**

Looks like 3 horizontal lines (equal sign with extra horizontal stroke). Entered in Exact Translation as: {

}
**_l**

Looks like 3 horizontal lines (equal sign with extra horizontal stroke). Entered in Exact Translation as: {

}
**_l**

Entered in Exact Translation as: {

}. Just use two single quotes outside of exact translation. See **''***MegaDots translation*.

Looks like a stretched letter c (or a sideways u wi the opening to the right). Entered in Exact Translation as: {

}
**_"k**

Precedes the value defining which mathematical root is being extracted from a radical. Shown in inkprint as an elevated value followed by the inkprint radical sign, entered as {

}. See **<***cube root* and *terminate radical*.

Looks like a sideways number 8. Entered in Exact Translation as: {

}
**,=**

A radical inside a radical, entered by {

} placed before one of the following: {**.**

}, {**>**

}, or {**]**

}.
**<**

An infinite sum represented by a tall, thin, stylized *S*; entered by {

}. To write "the integral from 0 to 1 of x squared dx" enter {**!**

}
**!;0^1 x^2 dx**

Entered in Exact Translation as: {

}
**!@$c]**

Entered in Exact Translation as: {

}
**!@,=]**

Entered in Exact Translation as: {

}
**!@$r]**

Entered in Exact Translation as: {

}
**!@$4]**

Entered in Exact Translation as: {

}
**!!**

Entered in Exact Translation as: {

}
**"!%:]**

Entered in Exact Translation as: {

}
**!!!**

Entered in Exact Translation as: {

}
**"!<:]**

Looks like a large upside down u. Entered in Exact Translation as: {

}
**.%**

Greek letter i, entered as Alt-G i for lower case or Alt-G I for upper case. In braille, the lower case iota is {`.i`

} and the upper case iota is {`.,i`

}.

Looks like a slash followed by three dots: 1 dot above 2 dots. Entered in Exact Translation as: {

}
**/,***

Italics is a typefont indicator. It is used for inkprint letters that are placed on a slant. Enter a italics capital x as {

}. The order for indicators is: typefont indicator, alphabet indicator, capitalization indicator, followed by letter.
**.;,x**

Greek letter k, entered as Alt-G k for lower case or Alt-G K for upper case. In braille, the lower case kappa is {`.k`

} and the upper case kappa is {`.,k`

}.

Obsolete Greek letter entered as {

}.
**.q**

Greek letter l, entered as Alt-G l for lower case or Alt-G L for upper case. In braille, the lower case lambda is {`.l`

} and the upper case lambda is {`.,l`

}.

Entered in Exact Translation as: {

}
**@.l**

Entered in Exact Translation as: {

}
**.1@.1]**

Entered in Exact Translation as: {

}
**[**

Entered in Exact Translation as: {

}
**"k.k**

Entered in Exact Translation as: {

}. As with all symbols of comparison, leave a space on either side of it. But leave out the space near a grouping symbol (parenthesis, braces or brackets), or any punctuation which applies to the sign of comparison.
**"k**

Entered in Exact Translation as: {

}
**"k".k".1**

Entered in Exact Translation as: {

}
**"k".1**

Entered in Exact Translation as: {

}
**"k@"k]**

Letters are the same as Nemeth Code as in standard braille. In standard braille, dots 5-6 is called the *letter sign*. The letter sign is used to show that something is uncontracted. For example, "letter sign b" means just a b, not the word "but". In Nemeth Code, dots 5-6 plays a similar role, but goes by the name of the *English Letter Sign*. The English letter sign is used in places where you need a letter sign in regular braille. Also use it when letters are shown in a different typefont. For example **AX** (AX in boldface) is {

} (dots 4-5-6 for boldface, then the English letter sign, then the capitalization sign, then the letter). The order for indicators is: typefont indicator, alphabet indicator, capitalization indicator, followed by letter.
**_;,a_;,x**

The rules for the use and non-use of the English letter sign are actually quite complex. See the Nemeth Code book for the full story.

Linear format means you are writing out the mathematics as a single stream. Contrast with *spatial format* which tries to give a sense of the inkprint layout of fractions or arithmetic problems. Linear format is easy to do in MegaDots. Convert the mathematics into a verbal stream. Then apply the symbols in that order.

Entered in Exact Translation as: {

}
**@%**

Entered in Exact Translation as: {

}
**@+**

Written as lim or limit with an underbar. Entered in Exact Translation as: {

} or {**%lim**

}
**%limit**

Entered in Exact Translation as: {

}
**:**

With MegaDots, all Nemeth sequences need to be entered in exact translation. You can enter the sequences in the inkprint mode, then mark the sequences in a block, and then enter Control-T X. Or you may prefer to first type Control-X to start a block, then enter the sequence, and then enter Control-T X. MegaDots allows both approaches.

When the *Translation Standard* in your document is set to *M* for *Math (Nemeth)*, then MegaDots properly handles numbers, punctuation, and parenthesis that are outside of the exact translation. In addition, the regular translator knows how to handle simple arithmetic problems. See *arithmetic*.

Entered in Exact Translation as: {

}
**@e**

Entered in Exact Translation as: {

}
**@5**

Entered in Exact Translation as: {

}. See also **-***arithmetic*.

Entered in Exact Translation as: {

}
**-+**

Entered in Exact Translation as: {

}
**_-**

Entered in Exact Translation as: {

}
**_-"_+**

Entered in Exact Translation as: {

}
**_-"+**

Entered in Exact Translation as: {

}
**-"_+**

Entered in Exact Translation as: {

}
**-"+**

Entered in Exact Translation as: {

}. Just use an single quote outside of exact translation. See **'***MegaDots translation*.

A modified expression is a math symbol with something above it or below it (or both) To write a modified expression (with something above and below), start with a dot 5, followed by the modified symbol, followed by the "sh" sign, followed by the stuff below, followed by the "ar" sign, followed by the stuff above followed by the "er" sign. The dot 5 tells the reader that the expression is being modified, the "sh" is the "directly under", the "ar" is the "directly over", and the "er" is the termination to show that the whole expression is finished. The "er" sign is also used to terminate a square root. See *modified expression, start*, *modified expression, terminate*, *directly over* and *directly under*.

To write "the summation from n equals 1 to 50 of the fraction 1 over 2 to the nth power end fraction" enter as follows: {

} (the {**".,s%n .k #1>#50] ?1/2^n"#**

} is the summation sign).
**.,s**

Entered in Exact Translation as: {

}
**"**

Entered in Exact Translation as: {

}
**]**

Greek letter m, entered as Alt-G m for lower case or Alt-G M for upper case. In braille, the lower case mu is {`.m`

} and the upper case mu is {`.,m`

}.

If the symbol looks like a centered x or cross, enter in Exact Translation as: {

}. Outside of exact translation, enter as backslash x. See **@****arithmetic*.

If the symbol looks like a centered dot, enter in Exact Translation as: {

}.
*****

Entered in Exact Translation as: {

}. Used in to contexts: to take you back to the baseline or to start a modified expression. See **"***baseline* and *modified expression*.

Looks like upside down triangle. Entered in Exact Translation as: {

}
**.$**

Entered in Exact Translation as: {

}
**/$l**

Entered in Exact Translation as: {

}
**/$p**

Greek letter n, entered as Alt-G n for lower case or Alt-G N for upper case. In braille, the lower case nu is {`.n`

} and the upper case nu is {`.,n`

}.

Numbers are done as *Nemeth numbers*, or dropped a-j. The numeric indicator {

} is used after a space or the beginning of a new line, or after a punctuation mark.
**#**

The complete rules for the use and non-use of the numeric indicator are actually quite complex. They boil down to this: the same symbols are used for digits as punctuation. In places where numbers might be confused with punctuation, use a numeric indicator.

While MegaDots does not have a full Nemeth translator, it does know how to translate numbers in Nemeth Code. See *MegaDots translation*. If the number is isolated or part of an arithmetic problem, you can leave it outside of exact translation. If numbers are not written inside of exact translation, then MegaDots uses the rules built into the *Math* braille standard to render them into braille. While not perfect, this does a satisfactory job. For example, if "2+2 = 4" appears in the text, just leave it alone. MegaDots will properly translate this into {

}. See **#2+2 .k #4***arithmetic*.

If the number is part of something more complex, enter it in exact translation. For example, to enter x cubed, type {

}. Remember to use the numeric indicator if the number is right after a space or punctuation.
**x^3**

If you have a number outside of exact translation (i.e. an isolated number or part of an arithmetic problem), you do not have to worry about the numeric indicator. The translator will use it appropriately. If a number occurs inside of exact translation, use the numeric indicator if the number comes after a space, new paragraph, or a punctuation. Entered in Exact Translation as: {

}
**.#**

If you have a number outside of exact translation (i.e. an isolated number or part of an arithmetic problem), you do not have to worry about numbers. The translator will handle it appropriately. See *MegaDots translation*. If a number occurs inside of exact translation, use the numeric indicator if the number comes after a space, new paragraph, or a punctuation. See *numeric indicator*. Entered in Exact Translation as: {

}
**0**

If you have a number outside of exact translation (i.e. an isolated number or part of an arithmetic problem), you do not have to worry about numbers. The translator will handle it appropriately. See *MegaDots translation*. If a number occurs inside of exact translation, use the numeric indicator if the number comes after a space, new paragraph, or a punctuation. See *numeric indicator*. Entered in Exact Translation as: {

}
**1**

If you have a number outside of exact translation (i.e. an isolated number or part of an arithmetic problem), you do not have to worry about numbers. The translator will handle it appropriately. See *MegaDots translation*. If a number occurs inside of exact translation, use the numeric indicator if the number comes after a space, new paragraph, or a punctuation. See *numeric indicator*. Entered in Exact Translation as: {

}
**2**

If you have a number outside of exact translation (i.e. an isolated number or part of an arithmetic problem), you do not have to worry about numbers. The translator will handle it appropriately. See *MegaDots translation*. If a number occurs inside of exact translation, use the numeric indicator if the number comes after a space, new paragraph, or a punctuation. See *numeric indicator*. Entered in Exact Translation as: {

}
**3**

If you have a number outside of exact translation (i.e. an isolated number or part of an arithmetic problem), you do not have to worry about numbers. The translator will handle it appropriately. See *MegaDots translation*. If a number occurs inside of exact translation, use the numeric indicator if the number comes after a space, new paragraph, or a punctuation. See *numeric indicator*. Entered in Exact Translation as: {

}
**4**

If you have a number outside of exact translation (i.e. an isolated number or part of an arithmetic problem), you do not have to worry about numbers. The translator will handle it appropriately. See *MegaDots translation*. If a number occurs inside of exact translation, use the numeric indicator if the number comes after a space, new paragraph, or a punctuation. See *numeric indicator*. Entered in Exact Translation as: {

}
**5**

If you have a number outside of exact translation (i.e. an isolated number or part of an arithmetic problem), you do not have to worry about numbers. The translator will handle it appropriately. See *MegaDots translation*. If a number occurs inside of exact translation, use the numeric indicator if the number comes after a space, new paragraph, or a punctuation. See *numeric indicator*. Entered in Exact Translation as: {

}
**6**

If you have a number outside of exact translation (i.e. an isolated number or part of an arithmetic problem), you do not have to worry about numbers. The translator will handle it appropriately. See *MegaDots translation*. If a number occurs inside of exact translation, use the numeric indicator if the number comes after a space, new paragraph, or a punctuation. See *numeric indicator*. Entered in Exact Translation as: {

}
**7**

If you have a number outside of exact translation (i.e. an isolated number or part of an arithmetic problem), you do not have to worry about numbers. The translator will handle it appropriately. See *MegaDots translation*. If a number occurs inside of exact translation, use the numeric indicator if the number comes after a space, new paragraph, or a punctuation. See *numeric indicator*. Entered in Exact Translation as: {

}
**8**

If you have a number outside of exact translation (i.e. an isolated number or part of an arithmetic problem), you do not have to worry about numbers. The translator will handle it appropriately. See *MegaDots translation*. If a number occurs inside of exact translation, use the numeric indicator if the number comes after a space, new paragraph, or a punctuation. See *numeric indicator*. Entered in Exact Translation as: {

}
**9**

Entered in Exact Translation as: {

}
**_#**

A Chemistry symbol. Entered in Exact Translation as: {

}
**_//**

A Chemistry symbol. Entered in Exact Translation as: {

}
**_****

A Chemistry symbol. Entered in Exact Translation as: {

}
**_/**

A Chemistry symbol. Entered in Exact Translation as: {

}
**_***

A Greek letter. It is entered as Alt-G w for lower case or Alt-G W for upper case. In braille, the lower case omega is {`.w`

} and the upper case omega is {`.,w`

}.

Greek letter o, entered as Alt-G o for lower case or Alt-G O for upper case. In braille, the lower case omicron is {`.o`

} and the upper case omicron is {`.,o`

}.

Often represented in inkprint as a question mark. Entered as {

} in exact translation. Outside of exact translation, enter as backslash question mark. See **=***MegaDots translation*.

Looks like {xx. Entered as {

}. See **.(***brace*.

Looks like [xx. Entered as {

}. See **@(***bracket*.

Entered as {

}. See **(***parenthesis*.

Entered in Exact Translation as: {

}
**?**

Entered in Exact Translation as: {

}
**$e**

A horizontal bar placed over a character, entered by placing {

} after a character. For example, x with overbar is entered by {**:**

}. To put an overbar over more than one character, use a modified expression. For example "xyz with overbar" is entered as {**x:**

} see also **"xyz:]***modified expression* and *terminate overbar expression*.

An inkprint sign like an uppercase P with two parallel vertical strokes, entered as {

}.
**@,p**

Two parallel vertical lines, entered as {

}.
**$l**

Open and close parenthesis are entered with {

} and {**(**

}.
**)**

Entered in Exact Translation as: {

}
**,(**

Entered in Exact Translation as: {

}
**,)**

Entered in Exact Translation as: {

}
**@d**

Entered in Exact Translation as: {

}
**@0**

Entered in Exact Translation as: {

}. Just use a period outside of exact translation. See **_4***MegaDots translation*.

Inkprint sign like upside down uppercase T, entered as {

}.
**$p**

A Greek letter. It is entered as Alt-G f for lower case or Alt-G F for upper case. In braille, the lower case phi is {`.f`

} and the upper case phi is {`.,f`

}. There is an alternate form of phi which is entered in Exact Translation as: {

}.
**.@f**

Greek letter p, entered as Alt-G p for lower case or Alt-G P for upper case. In braille, the lower case pi is {`.p`

} and the upper case omicron is {`.,p`

}. Pi often represents the quantity 3.14159...

Entered in Exact Translation as: {

}. See also **+***arithmetic*.

Entered in Exact Translation as: {

}
**+-**

Entered in Exact Translation as: {

}
**_+**

Entered in Exact Translation as: {

}
**_+"_-**

Entered in Exact Translation as: {

}
**_+"-**

Entered in Exact Translation as: {

}
**+"_-**

Entered in Exact Translation as: {

}
**+"-**

The decimal point, entered as {

}.
**.**

Entered in Exact Translation as: {

}
**.#**

An inkprint symbol used to represent English currency, entered as {

}.
**@l**

An angled stroke; often used to represent minutes or feet, entered as {

}. See also **'***double prime*.

Entered in Exact Translation as: {

}
**''**

Entered in Exact Translation as: {

}
**'''**

An inkprint symbol consisting of an enlarged capital pi, entered as {

}. Some symbols, such as the **.,p***product sign* have math symbols above and below them. In Nemeth Code terminology, the product sign is *modified* by having something *directly-over* and something *directly-under*.

To write a modified expression, start with a dot 5, followed by the modified symbol, followed by the "sh" sign, followed by the stuff below, followed by the "ar" sign, followed by the stuff above followed by the "er" sign. The dot 5 tells the reader that the expression is being modified, the "sh" is the "directly under", the "ar" is the "directly over", and the "er" is the termination to show that the whole expression is finished. The "er" sign is also used to terminate a square root.

To write "the product from n equals 2 to 10 of the fraction 1 over 2 to the nth power end fraction" enter as follows: {

} (the {**".,p%n .k #2>#10] ?1/2^n"#**

} is the product sign).
**.,p**

Entered in Exact Translation as: {

}
**.-**

Entered in Exact Translation as: {

}
**;2**

A Greek letter. It is entered as Alt-G y for lower case or Alt-G Y for upper case. In braille, the lower case psi is {`.y`

} and the upper case psi is {`.,y`

}.

The braille for punctuation is the same as in standard grade two braille. The major problem is that the same symbols are used for digits. The digit 1 could be confused with comma, the digit 2 could be confused with semi-colon, the digit 3 could be confused with colon, the digit 4 could be confused with period, the digit 6 could be confused with exclamation, and the digit 8 could be confused with question mark. To remove ambiguity, the punctuation indicator (dots 4-5-6) {

} is used before punctuation to show that it is indeed a punctuation mark.
**_**

Parenthesis is done differently in Nemeth. Use the "of" sign for open parenthesis, and the "with" sign for close parenthesis.

If punctuation are not written inside of exact translation, then MegaDots uses the rules built into the *Math* braille standard to render them into braille. While not perfect, this does a satisfactory job. For example, if a period after a sentence does not get a punctuation indicator, but a period after a number does get one. The MegaDots translator also gets parenthesis right. See *MegaDots translation*.

Entered in Exact Translation as: {

}. Just use a question mark outside of exact translation. See **_8***MegaDots translation*. If the question mark shows a missing answer, this is an omission sign. See *omission sign*.

Entered in Exact Translation as: {

}
**".k<_8]**

Entered in Exact Translation as: {

}. Just use a quote outside of exact translation. See **_0***MegaDots translation*.

Entered in Exact Translation as: {

}. Just use a quote outside of exact translation. See **_0'***MegaDots translation*.

Entered in Exact Translation as: {

}. Just use a quote outside of exact translation. See **_8***MegaDots translation*.

Entered in Exact Translation as: {

}. Just use a quote outside of exact translation. See **_,8***MegaDots translation*.

An inkprint mathematical symbol that shows a mathematical root. See *square root of*, *terminate square root*, *cube root of*, *terminate cube root*, *index of radical*, *of*, and *terminate radical*.

Entered in Exact Translation as: {

}
**.**

Entered in Exact Translation as: {

}
**..**

Entered in Exact Translation as: {

}
**...**

Entered in Exact Translation as: {

}
**]**

Entered in Exact Translation as: {

}
**"1**

Entered in Exact Translation as: {

}
**$r**

Entered in Exact Translation as: {

}
**@]**

Looks like a backwards stretched c (or a sideways u with the opening to the left). Entered in Exact Translation as: {

}
**_.1**

Greek letter r, entered as Alt-G r for lower case or Alt-G R for upper case. In braille, the lower case rho is {`.r`

} and the upper case rho is {`.,r`

}.

Entered in Exact Translation as: {

}
**$o**

See *English Letter sign*.

Entered in Exact Translation as: {

}. The order for indicators is: typefont indicator, alphabet indicator, capitalization indicator, followed by letter.
**@@**

An obsolete Greek letter, entered as {

}.
**.c**

Sanserif is a typefont indicator. The sanserif indicator is {

}. Enter a sanserif capital x as: {**,.**

}. The order for indicators is: typefont indicator, alphabet indicator, capitalization indicator, followed by letter.
**,.;,x**

Entered in Exact Translation as: {

}. The order for indicators is: typefont indicator, alphabet indicator, capitalization indicator, followed by letter.
**@;**

Entered in Exact Translation as: {

}. The order for indicators is: typefont indicator, alphabet indicator, capitalization indicator, followed by letter.
**@;,**

Entered in Exact Translation as: {

}. Just use an two single quote outside of exact translation. See **''***MegaDots translation*.

Entered in Exact Translation as: {

}
**@,s**

Entered in Exact Translation as: {

}
**@,s@,s**

Entered in Exact Translation as: {

}. Just use a semicolon outside of exact translation. See **_2***MegaDots translation*.

Entered in Exact Translation as: {

}
**$**

Greek letter s, entered as Alt-G s for lower case or Alt-G S for upper case. In braille, the lower case sigma is {`.s`

} and the upper case sigma is {`.,s`

}. There is an alternative form of sigma which is entered in Exact Translation as: {

}.
**.@s**

Looks like three dots, 2 above one dot. Entered in Exact Translation as: {

}
**@/**

An inkprint diagonal line from the lower left to the upper right, entered as {

}.
**_/**

Entered in Exact Translation as: {

}
**"k@"k]**

Spatial format uses the layout to show the rough layout of fractions or arithemetic problems. Contrast with *linear format*. Spatial arrangements are difficult to do in MegaDots. You need to know exactly what you are aiming for. You can set the style for Left flush, and then type in arithmetic problems roughly how they look in inkprint. Do not use spaces. Instead, type Control-B. This is a MegaDots command called "the blank character". It is an unyielding space.

When you translate into braille, insert or delete these blank characters until the columns are aligned (by digits, decimal points, or by commas), space the symbol of operation away from the number. Use a row of hyphens for the horizontal bar. The horizontal bar should be longer by one character in each direction than the other material. See the Nemeth Code Book for examples of spatial arrangements.

Entered in Exact Translation as: {

}
**$4**

Square roots are easy. Use the "ar" sign to start a square root, and the "er" sign to end a square root. To write the square root of 16, enter {

} To write the square root of 16, enter {**>#16]**

} To write the "square root of x squared plus y squared" enter {**>#16]**

} (Notice that you need to come back to the baseline before ending the square root.)
**>x^2"+y^2"]**

Because of the ambiguity involved, you cannot use contractions inside a square root. So if you need to inclose the word "area" in the square root symbol, you need to write the word in grade one.

Entered in Exact Translation as: {

}
**]**

Entered in Exact Translation as: {

}
**$_4**

A superscript of 2, entered as any character followed by {

}. Compare with **^2***superscript* and *cubed*.

Entered in Exact Translation as: {

}
**$s**

Precedes the numerator of a fraction. Material up to the *fraction line* is the numerator, shown above the fraction line; numerator and denominator are centered horizontally relative to the fraction line. Entered as {

} followed by fraction line and end fraction indicator. See also **?***fraction line*, *end fraction*, *complex*, and *hypercomplex*.

Indicates the beginning of some material which has other signs printed above and/or below it, entered as {

}. See also **"***above*, *below*, *terminate overbar expression*, *terminate underbar expression*, and *terminate modified expression*.

A subscript is something just below the baseline. To write the formula for water (H 2 O), the 2 is a subscript. In Nemeth Code, use dots 5-6 to show a subscript. To come back from the baseline, use either a space or a dot 5. We would expect to write the formula for water as {

}, but it would be wrong. If a subscript is entirely a number does not need the subscript mark or the dot 5 after it. The correct Nemeth Code is {**,h;2",o**

}. The reader, seeing a number placed against the letter knows that there is a subscript. See also **,h2,o***baseline*.

Begins a subscript of a subscript, an expression which is written below the subscript level, entered as {

}. For example, to write "q sub x sub a baseline plus 1" (the a is a subscript to x, the x is a subscript to q) enter {**;;**

}
**q;x;;a"+1**

Entered in Exact Translation as: {

}
**;;**

Entered in Exact Translation as: {

}
**;;;**

Entered in Exact Translation as: {

}
**;;^**

Begins a superscript of a subscript, an expression which is written above the subscript level, entered as {

}.
**;^**

Entered in Exact Translation as: {

}
**;^**

Entered in Exact Translation as: {

}
**;^;**

Entered in Exact Translation as: {

}
**;^^**

Looks like a stretched letter c (or a sideways u wi the opening to the right). Entered in Exact Translation as: {

}
**_"k**

An inkprint symbol consisting of a capital sigma, entered as {

}. Some symbols, such as the **.,s***summation sign* have math symbols above and below them. In Nemeth Code terminology, the summation sign is *modified* by having something *directly-over* and something *directly-under*.

To write a modified expression, start with a dot 5, followed by the modified symbol, followed by the "sh" sign, followed by the stuff below, followed by the "ar" sign, followed by the stuff above followed by the "er" sign. The dot 5 tells the reader that the expression is being modified, the "sh" is the "directly under", the "ar" is the "directly over", and the "er" is the termination to show that the whole expression is finished. The "er" sign is also used to terminate a square root.

To write "the summation from n equals 1 to 50 of the fraction 1 over 2 to the nth power end fraction" enter as follows: {

} (the {**".,s%n .k #1>#50] ?1/2^n"#**

} is the summation sign).
**.,s**

To show that two symbols are superimposed, first enter the first symbol, then {

} then the second symbol, then the termination symbol {**@**

}. For example, an integral sign with a superimposed rectangle is {**]**

}.
**!@$r]**

A superscript is something just above the baseline. To write "x squared", the 2 is a superscript. In Nemeth Code, use dots 4-5 to show a superscript. To come back from the baseline, use either a space or a dot 5. To write "x squared", enter {

}. To write "x squared plus y squared", enter {**x^2**

}. See also **x^2"+y^2***baseline*.

Begins a subscript of a superscript, an expression which is written below the superscript level, entered as {

}.
**^;**

Entered in Exact Translation as: {

}
**^;**

Entered in Exact Translation as: {

}
**^;;**

Entered in Exact Translation as: {

}
**^;^**

Begins a superscript of a superscript, an expression which is written above the superscript level, entered as {

}.
**^^**

Entered in Exact Translation as: {

}
**^^**

Entered in Exact Translation as: {

}
**^^;**

Entered in Exact Translation as: {

}
**^^^**

Greek letter t, entered as Alt-G t for lower case or Alt-G T for upper case. In braille, the lower case tau is {`.t`

} and the upper case tau is {`.,t`

}.

The end of a cube root, entered as ] preceded by {

}. See also **<3>***cube root of*.

The end of a modified expression, entered as the {

} termination indicator.
**]**

Entered in Exact Translation as: {

}
**<:]**

Entered in Exact Translation as: {

}
**%:]**

The end of a modified expression that has a horizontal bar over it. Entered as {

} that is preceded by a {**<:]**

}. Also see **"***start modified expression*.

The end of a radical, entered as {]} preceded by {

}, which in turn is preceded by {**>**

}. See also **<***index of radical*, and *of*.

The end of a square root, entered as {

} preceded by {**]**

}. See also **>***square root of*.

The end of a modified expression that has a horizontal bar under it. Entered as {

} that is preceded by a {**%:]**

}. Also see **"***start modified expression*.

Looks like a backwards uppercase e. Entered in Exact Translation as: {

}
**@=**

Looks like a backwards uppercase e followed by a vertical bar. Entered in Exact Translation as: {

}
**@=\**

Looks like a backwards uppercase e followed by a vertical bar. Entered in Exact Translation as: {

}
**@=\**

Looks like three dots, one above two dots. Entered in Exact Translation as: {

}
**,***

A Greek letter. It is entered as Alt-G j for lower case or Alt-G J for upper case. In braille, the lower case theta is {`.?`

} and the upper case theta is {`.,?`

}.

A wavy horizontal line, slightly longer than a dash, entered as {

}. Often used to mean similar; may modify a sign of comparison.
**@:**

Entered in Exact Translation as: {

}
**@:"@:**

Entered in Exact Translation as: {

}
**@:@:**

Entered in Exact Translation as: {

}
**@,:**

If the symbol looks like a centered x or cross, enter in Exact Translation as: {

}. Outside of exact translation, enter as backslash x. See **@****arithmetic*.

If the symbol looks like a centered dot, enter in Exact Translation as: {

}.
*****

Entered in Exact Translation as: {

}
**$t**

Entered in Exact Translation as: {

}
**".k<$t]**

Entered in Exact Translation as: {

}
**".k%**<**]**

You can show several different typefonts in Nemeth code. See *bold*, *italics*, *sanserif*, and *script*.

See *terminate underbar expression*.

Looks like a large uppercase u. Entered in Exact Translation as: {

}
**.+**

Looks like an upside down uppercase a. Entered in Exact Translation as: {

}
**@&**

Often represented in inkprint as a question mark.Entered as the general omission sign, entered as {

}.
**=**

Precedes an entire capitalized word. Uppercase lock is ended with a space, number, or punctuation. Entered as {

}. See **,,***capitalization*.

Written as lim or limit with an overbar. Entered in Exact Translation as: {

} or {**<lim**

}.
**<limit**

Greek letter u, entered as Alt-G u for lower case or Alt-G U for upper case. In braille, the lower case upsilon is {`.u`

} and the upper case upsilon is {`.,u`

}.

Entered in Exact Translation as: {

}
**_=**

Obsolete Greek letter, entered as {

}.
**.v**

Entered in Exact Translation as: {

}
**\**

Entered in Exact Translation as: {

}
**\"\**

Entered in Exact Translation as: {

}
**".k<\]**

Entered in Exact Translation as: {

}
**_\**

Entered in Exact Translation as: {

}
**\\**

Entered in Exact Translation as: {

}
**_\_\**

Entered in Exact Translation as: {

}
**,,\,,\**

Entered in Exact Translation as: {

}
**,\,\**

Entered in Exact Translation as: {

}
**\\"\\**

Entered in Exact Translation as: {

}
**,,\**

Entered in Exact Translation as: {

}
**,\**

Entered in Exact Translation as: {

}
**\\\**

A Chemistry symbol. Entered in Exact Translation as: {

}
**\**

A Chemistry symbol. Entered in Exact Translation as: {

}
**\\**

A Chemistry symbol. Entered in Exact Translation as: {

}
**\\\**

Greek letter x, entered as Alt-G x for lower case or Alt-G X for upper case. In braille, the lower case xi is {`.x`

} and the upper case xi is {`.,x`

}.

Greek letter z, entered as Alt-G z for lower case or Alt-G Z for upper case. In braille, the lower case zeta is {`.z`

} and the upper case zeta is {`.,z`

}.