Undone Things: German and Russian Math

German Fractions

Numerical fractions: such as #bg36 for 27/36. You can includes mixed numbers, but you cannot include a negative number. This has been done.

In general, German uses dropped b to start, "space dots 1256 space" for the slash, and dots 56 to end a fraction. Elements can be dropped as needed:

• "French-style" (just a fraction line; no start and ending marks): use without any signs that generate spaces (no plus or minus or similar signs)
• "Nemeth-style" (no spaces around the fraction line): use without any signs that generate spaces; can be used when there are negative numbers or if there is material before or after the fraction without a space.
• "Nemeth-style with spaces" use spaces around the fraction line; use when there is a sign that generates a space.
• It is possible to replace a generated space with dot 4, to use a simplier format. Do not use in complex fractions)
• In really complex fractions (both use "Nemeth-style with spaces"), place a full cell before the final dots 56 to show that the entire fraction is over.

Russian Fractions

Very similar to German fractions. Almost all use the start and end fraction; the fraction bar is shown by space dots 1256 (no space after dots 1256).

Testing Results

There are 10 fraction examples on page 67 (69 in the pdf) of the Russian manual. These are in two files gfrac.dxp and rfrac.dxp (both in g:\ge) so one can test both the German math and the Russian math of these examples.

When we started today, 7 of these examples did not meet the definition of "simplified fraction". After adding the unary minus as a piece of the definition, we now have four which do not meet this definition. The ones that still fail are #2, #4, #6, and #9.

I have fixed the Russian variation so that all of the fractions work for all four fraction attributes as long as they are recognized as being "simplified fraction"

So at this point, I invite you to enhance the definition of "simplified fraction" so that these four will now meet the definition. Feel free to do so by either offering them as "simplified fractions" for both German and Russian; or for Russian only as is your taste in equations.

We need to lean towards complex fractions when the fraction is an exponent (see p 77 of the Russian book)

Formatting

We need to use dot 4 as a continuation indicator.

Number Issues (chapter 2 examples)

1. Example 2.1.2 B02: Done: end exponent is : end fraction is ; (if at same place, drop the :)
2. Example 2.1.2 B03: Done: letter e raised to numeric (with a decimal place) power needs a number sign and upper numbers
3. Example 2.1.3 B02: When there is a period followed by 2 digits, it is not a number separator, it is a decimal point
4. Example 2.1.3 B06: Done: Fr. 3.50 In this example we need the dots 456 currency indicator
5. Example 2.1.4 B01+: Done: For overbar for a repeating decimal, treat as if it was inkprint parenthesis
6. Example 2.1.5 B02: Done: hard space becomes a dot 3 number separator in a multi-digit number
7. Example 2.1.5 B04: Done: (in the literary code) repeat the number sign after a hyphen
8. Example 2.1.6 B07: In some contexts, use a number sign and then a lower number to indicate an exercise number (might only be for lower grades)
9. Example 2.1.6 B08: 3.5.11 should be #3e11 -- I do not understand at all!
10. Example 2.1.6 B09: 24.12.2010 should be #24ab#bjaj -- very compact way of showing a date -- I do not understand at all!
11. Example 2.2 B03: Done: Be careful! Roman numerals need to be in math mode!

Letter Issues (chapter 3 examples)

1. Example 3.2 B06: If there is a letter right after a fraction, use the letter sign (dot 6)
2. Example 3.3 B06: Done: For signs with a space (plus, minus, etc.) replace the space with a dot 4 in fractions, superscript, subscript, etc.
3. Example 3.4 B03: how to we get the dot 5 between the two digit 6's?
4. Example 3.4 B04+: Done a bit on vectors now
5. Example 3.5 B02: Done: This example needs the use the support of the Blackboard emphasis characters.
6. Example 3.5 B02: This example uses the dot 4 as a continuation indicator. We are not supporting this yet.
7. ?? Perhaps other issues.

Operator Issues (chapter 5 examples)

1. We need a better handle on the space before a hyphen/minus sign: space with a real minus sign; no space with unary hyphen; no space with both numeric.
2. When colon is used as an operator (to mean division, use space dropped c instead of dot 6 dropped c.