From: Asmus Freytag <asmusf_at_ix.netcom.com>

Date: Thu, 12 Jul 2012 10:23:36 -0700

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Date: Thu, 12 Jul 2012 10:23:36 -0700

Here's my *updated* summary of the annotations that we've been
discussing so far:

U+003A COLON

* also used to denote division or scale, for that usage 2236 :
RATIO is preferred in mathematical use

U+00B7 MIDDLE DOT

* also used as raised decimal point or to denote multiplication,
for the latter usage 22C5 · DOT OPERATOR is preferred

U+2052 COMMERCIAL MINUS SIGN

x 00F7 division sign

U+22C5 DOT OPERATOR

* Used in preference to 00B7 · to denote multiplication

U+2236 RATIO

* Used in preference to 003A : to denote division or scale in
mathematical use

U+00F7 DIVISION SIGN

= obelus

* also used as an alternate, more visually distinct 2212 - MINUS
SIGN or 2011 – EN DASH in some contexts

* historically used as a punctuation mark to denote questionable
passages in manuscripts

x 070B syriac harklean obelus

x 2212 minus sign

x 2052 commercial minus sign

x 2236 ratio

(the reference to en-dash is based on the Italian usage cited in
the Wikipedia article for Obelus)

The discussion of these symbols in the relevant chapters of the
standard could also be improved.

On page 200, the subsection "Other Punctuation" should be
augmented by this sub-sub-section

/Obelus/ Originally a punctuation mark to denote questionable
passages in manuscripts, U+00F7 DIVISION SIGN is now most commonly
used as a symbol indicating division. However, even modern use is
not limited to that meaning. The character can be found as
indicating a range (similar to the /en-dash/) or as a form of
/minus sign/. The former use is attested for Russian, Polish and
Italian and latter use is still widespread in Scandinavian
countries in some contexts, but may occur elsewhere as well. (see
also "Commercial Minus").

[for background documentation for the above passage see:
http://www.unicode.org/mail-arch/unicode-ml/y2012-m07/0134.html]

On page 203 after "Scandinavia" add "(see also Obelus)".

On page 202 of chapter 6 add under "Other..."

Several punctuation marks, such as COLON, MIDDLE DOT and SOLIDUS
closely resemble mathematical operators, such as U+2236 RATIO,
U+22xx DOT OPERATOR and U+22xx DIVISION SLASH. The latter are the
preferred characters, but the former, being more easily typed, are
often substituted.

On page 511 of chapter 15 add in "Semantics" after "context".

"For some common mathematical symbols there are also local
variations in usage. For example, U+00D7 DIVISION SIGN, besides
having a long history of use as punctuation mark, is also used in
certain cases to indicate negative numbers in several European
countries."

It might be worth mentioning U+00D7 MULTIPLICATION SIGN in chapter
15.5, because it's arguably a mathematical operator, even though
not encoded in the standard blocks of operators.

/Mathematical Operators In other Blocks/

A small number of mathematical operators and related characters in
common use have been encoded in other blocks. These include U+002B
PLUS SIGN, U+00D7 MULTIPLICATION SIGN and U+00F7 DIVISION SIGN, as
well as 003C GREATER THAN, 003D EQUALS SIGN and 003E LESS THAN.
The /factorial operator / is unified with U+0021 EXCLAMATION MARK

In Chapter 15.5, add this table after /Unifications/ on page 512

Table 15-xxx

Mathematical Operators Disunified from Punctuation

002D - HYPHEN-MINUS

2212 − MINUS SIGN

003F / SOLIDUS or /slash/

2215 ∕ DIVISION SLASH

005C \ REVERSE SOLIDUS or /backslash/

2216 ∖ SET MINUS

002A * ASTERISK

2217 ∗ ASTERISK OPERATOR

25E6 ◦ WHITE BULLET

2218 ∘ RING OPERATOR

2022 • BULLET

2219 ∙ BULLET OPERATOR

007C | VERTICAL BAR

2223 ∣ DIVIDES

2016 ‖ DOUBLE VERTICAL BAR

2225 ∥ PARALLEL TO

003A : COLON

2236 ∶ RATIO

007E ~ TILDE

22C3 ∼ TILDE OPERATOR

00B7 · MIDDLE DOT

22C5 ⋅ DOT OPERATOR

[My mailer makes huge gaps between paragraphs - where mathematical
fonts are used - the intent is to have three columns, CODE, GLYPH,
NAME and each table row containing two rows of text (i.e. the pair
of characters).]

/Disunifications/ A number of mathematical operators

have been disunified form related or similar punctuation

characters (see table 15-xx). In addition to allowing the

encode of specifically mathematical semantics, there are

some display differences. Math operators render

on the math centerline, and the angle or length

of the operator version of certain slashes or bars

may be different from their punctuation counterpart.

For certain pairs, such COLON and RATIO, there's a

difference in spacing, with RATIO spaced as a relational

operator that includes spaces on both sides, while colon

as a punctuation mark does not have such spaces.

The same applies to MIDDLE DOT vs. DOT OPERATOR,

among others. This allows MIDDLE DOT to be uses

as /raised decimal point/ in distinction to DOT OPERATOR

signifying multiplication.

For mathematical use, the use of the mathematical

operator is preferred.

Where there are no rendering differences, such as for

U+0021 ! EXCLAMATION MARK and /factorial/ or U+002E FULL STOP

and /decimal point/ only one character has been encoded.

A./

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