logo for MegaDots Duxbury Systems, Inc. logo logo for MegaDots

Navigating the Nemeth Code Book

We know that many of the users of this Nemeth Code/braille math software are quite familiar with the Nemeth Code Book and its 25 rules. Others are not.

This is a guide for those that are familiar with the book. This guide looks at the software from the perspective of the 25 rules that make up "The Nemeth Braille Code for Mathematics", which is available in both inkprint and braille copies from:

Some Technical Issues

This manual assumes that you have purchased the MegaMath Translator, and are using the Nemeth style sheet. It further assumes that you know how to use the Control-I list as well as the various shortcuts of this software. If not, please refer to the main product documentation.

This guide is divided into 25 sections, one for each rule in the Nemeth code book. Most of these sections consist of one or more paragraphs of commentary followed by the list of items in the Control-I list which pertain to that rule.

Be aware that some of the items in the Control-I list are rarely used, since they are much more easily obtained by a data entry shortcut. For example, to enter a fraction, you would prefer to enter [x//y] rather than Control-I start frac x Control-I horizontal fraction bar y Control-I end fraction.

Things not found in this product

Rule 1: Braille Indicators

Though not really defined in the Nemeth Code Book, Braille Indicators are braille symbols which are not explicit signs in inkprint. Rather, their existence is implied by the font, position, or alphabet used in the inkprint. By and large, this collection is arbitrary from the standpoint of inkprint. It is also arbitrary from the standpoint of the Nemeth translation. If you are curious as to how to produce a braille symbol, look up the appropriate concept in the on-line documentation F10 H N.

Rule 2: Numeric Signs and Symbols

Numbers are handled properly in the Nemeth translation. In Nemeth code, some numbers get the numeric indicator (dots 3-4-5-6), and some do not. The basic rule is that the numeric indicator is dropped when there is no chance for confusion with punctuation. There is nothing you need to do in this area. The numeric indicator is used appropriately. If not, it is a bug and should be reported to Duxbury Systems.

The rules for enclosed lists are handled properly by the translator. No special data entry is need be used for enclosed lists (enclosed lists are things like ordered pairs, the number sign is not used if a construct follows the definition of an enclosed list).

The only change needed to data entry in some foreign usage, the comma is used for the decimal point, and the period (full stop) is used for the comma used to separate groups of digits. To make proper braille, enter these as is done in the United States. For example, if a number is written as 1.378,26 (one thousand three hundred and seventy eight point two six), change this to 1,378.26 for proper data entry.

Spatial arrangements for arithmetic is a separate issue. Press Alt-T <Enter> to select the Arithmetic style. Among other things, this suppresses the number sign.

Representation of Numerals to Non-Decimal Bases is not supported by the translator. You will need to produce these in exact translation.

Rule 3: Capitalization

Capitalization is properly handled by the translator. Try some experiments, such as "triangle ABC is used as a logo by the ABC company"

Rule 4: Alphabets

Use the Control-I list for Hebrew, German, Greek, or Russian letters. Another way to pick Greek letters is to type Alt-G followed by the appropriate letter.

The translator knows about the context when the English-letter indicator should be used. If not, it is a bug and should be reported to Duxbury Systems.

Rule 5: Type Forms

Here is a chart to show the data entry for different type forms:

There are other combinations as well: bold German, bold Greek, bold Russian, italic German, italic Greek, and italic Russian, script Greek, script Hebrew, script German, and script Russian.

To do these more exotic combinations, you need to know which Roman letter that is equivalent to the sign you want to produce. You need to enter that Roman letter after the appropriate Control-I command. For example, lets say you need to do a problem with both a regular alpha and an italic alpha. To enter the regular alpha, press Alt-G a. To enter the italic alpha, enter Control-I italic gr <down arrow> a.

Rule 6: Punctuation Signs and Symbols

Most common punctuation is found on the computer keyboard. Some, like the check mark or the cent mark is not. When in doubt, obtain these characters from the Control-I list.

There is a well known ambiguity in Nemeth code between numbers and punctuation. The translator puts in the punctuation indicator where it is appropriate. If not, it is a bug and should be reported to Duxbury Systems.

In addition, some items of punctuation are different in a literary and a math context. For example, comma has three forms: literary context, math context, and math context at a superscript or subscript level. The period is done differently if it is a decimal point.

The translator cannot handle European style digit grouping and decimal point. For example, 123,456.35 might be written as 123.456,35 in Europe. To produce proper Nemeth code, you need to change the data entry back to 123,456.35.

Rule 7: Reference Signs and Symbols

If you have a footnote. **** Need to check out footnotes with Aaron.

Rule 8: Abbreviations

Abbreviations are handled differently than other arbitray sequences in Nemeth code. These affect the use of the English letter sign (dots 5-6) and the use of literary punctuation. The translator puts in the English letter sign where it is appropriate. If not, it is a bug and should be reported to Duxbury Systems.

Rule 9: Contractions and Short Form Words

This software knows when to contract and when not to contract. If not, it is a bug and should be reported to Duxbury Systems.

Rule 10: Omissions

The general ommission symbol can be entered as ~? or as Control-I gen. Use this anytime there is an ommission (such as 4+?=9, in this case the ? is the ommission).

Rule 11: Cancellation

When writing a fraction, sometimes there is a cancellation of some of the common factors. To show that something is canceled, enter Control-I start <down arrow> <Enter>, the canceled text followed by Control-I end <Enter>.

Rule 12: Fractions

Fractions are easy to type in using a data entry shortcut. To enter 2 over 5, just type [2//5]. You can nest fractions, radicals, anything inside of fractions. In Nemeth code, a fraction that contains a fraction is called a complex fraction, and a fraction that contains a complex fraction is called a hypercomplex fraction. You do not need to worry about this terminology as you do your data entry. If you needed to write "the fraction two fifths, all divided by 3", just enter [[2//5]//3]. MegaDots does the rest.

To create a mixed number, place the integer right up to the fraction, for example "two plus one third" is entered as 2[1//3].

If the fraction is written like 1/3 (the one and the three are on the same vertical level), then just enter 1/3. Use [1//3] when a horizontal line separates the two parts of the fraction.

Rule 13: Superscripts and Subscripts

Superscripts and supscripts are easy to do in this software. To write x squared plus y squared, just enter :x^2+y^2. If you have an exponent that is over 1 character, enclose it in square brackets. For example x^[12] for x raised to the twelth power or y^[[1//3]] for y raised to the one third power.

It should be noted that Nemeth code itself does not draw any distinction between an exponent with one character or more than one character. It is the data entry shortcut that needs to know how long the exponent is.

Subscripts are entered with the underbar character. To enter x sub 3, enter x_3, to enter x sub 12, enter x_[12].

To enter e raised to the x squared power, enter: e^[x^2]. So all sorts of complex combinations are easy to enter. The example in the Nemeth code book (rule 13, paragraph 74 c ii (8) found on page 85 is entered as: x_[p_[a^m]].

The translator knows all the rules. It knows when to use a default numeric subscript and when not to. If there is an error, report it to Duxbury Systems.

While you can use do all the data entry with the Control-I list, it is much more work. This list is provided more to show the range of supported structures than a practical guide to data entry.

Rule 14: Modifiers

These are similar to subscripts and superscripts. To show that something is above something else, enter: [main]^^[on top] (if a segment is a single character, then that set of brackets can be dropped). To show that something is below something else, enter: [main]^^[below] (if a segment is a single character, then that set of brackets can be dropped). That is all there is to it.

While you can use do all the data entry with the Control-I list, it is much more work. This list is provided more to show the range of supported structures than a practical guide to data entry.

Rule 15: Radicals

Once again, we have a useful data entry shortcut. To show the square root of x plus y, enter: v[x+y]. The lower v next to the square bracket is designed to look like a square root in inkprint.

To enter a root, just enclose it in brackets. For example, the cube root of z is entered as: [3]v[z]. Notice that the brackets are all required. You cannot drop the brackets when they enclose a single character.

You can enter a square root of a square root (or any other combination). To enter the square root of the fraction 1 over the square root of 5, enter: v[[1//v[5]]].

While you can use do all the data entry with the Control-I list, it is much more work. This list is provided more to show the range of supported structures than a practical guide to data entry.

Rule 16: Shapes

There is no general shortcuts for the shapes. There are some shortcuts in the fastmath.meg file. You can enter more shortcuts into the fastmath.meg file if you need to.

Rule 17: Function Names

Here is the list of function names from the Nemeth code book. It is against the rules to use contractions in a function name. Contact Duxbury Systems if this ever happens.

In your data entry, make sure there is at least one space after each function name. Enter "sin x" not "sinx".

Rule 18: Signs and Symbols of Grouping

These are fairly straightforward. A few of these are found on the computer keyboard. Fortunately, these are the most common.

Be careful with the square brackets. Since these are used in many data entry shortcuts, you may have to preceed them with a backslash to mean a real bracket.

Rule 19: Signs and Symbols of Operation

To enter the plus or minus symbol, type in +-. To enter a plus followed by a minus, choose from the Control-I list. Or you can type \+\-.

Rule 20: Signs and Symbols of Comparison

Virtually all of these symbols need to be chosen from the Control-I list.

Rule 21: Arrows

Virtually all of these symbols need to be chosen from the Control-I list.

Rule 22: Miscellaneous Signs and Symbols

Virtually all of these symbols need to be chosen from the Control-I list.

Rule 23: Multipurpose Indicator

The multipurpose indicator is created automatically when appropriate for plus followed by minus, modified expressions, or going back to baseline. If the multipurpose indicator is used where it shouldn't or is missing, it is a bug, and should be reported to Duxbury Systems.

Rule 24: Spatial Arrangements

Lets start with the obvious. Spatial arrangements are tricky. The less obvious point is the software does not (as yet) have automated features to lay out complicated arithmetic problems. So you need to quite a bit of the formatting.

For arithmetic problems, use the Arithmetic style. This is found in the Alt-T group when you use the Nemeth style sheet. The arithmetic style does not wipe out multiple spaces, and it supresses the use of the number sign in front of numbers.

Use spaces and the hyphen to

To create properly formatted arithmetic problems means looking at the braille and adding spaces and dropped c's as needed. Try to make the "operation line" (the horizontal line) stick out by one cell on the left and the right. Look at the examples in the Nemeth code book to see what we are after.

Rule 25: Format

Many of the complex layouts shown in rule 25 are not supported by the software, or can be created only by carefully manipulating the data entry. This is clearly one area for improvement in the software.