L2/00-412

DATE: 2000-11-08

DOC TYPE:	Expert contribution
TITLE:	Special mathematical operators used in plain-text mathematical expressions
SOURCE:	Murray Sargent III
PROJECT:
STATUS:	Proposal
ACTION ID:	FYI
DUE DATE:	--
DISTRIBUTION:	Worldwide
MEDIUM:	Paper and html
NO. OF PAGES:	4

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A. Administrative
1. Title	Special mathematical operators used in computational algebra
2. Requester's name	Murray Sargent III
3. Requester type	Expert request.
4. Submission date	07-11-2000
5. Requester’s reference
6a. Completion	Complete proposal
6b. More information to be provided?	If requested

B. Technical -- General
1a. New script? Name?	No.
1b. Addition of characters to existing block? Name?	Miscellaneous technical
2. Number of characters	5
3. Proposed category
4. Proposed level of implementation and rationale	Level 1
5a. Character names included in proposal?	Yes.
5b. Character names in accordance with guidelines?	Yes.
5c. Character shapes reviewable?
6a. Who will provide computerized font?	Microsoft Symbol font
6b. Font currently available?	Microsoft Symbol font
6c. Font format?	TrueType
7a. Are references (to other character sets, dictionaries, descriptive texts, etc.) provided?	Yes.
7b. Are published examples (such as samples from newspapers, magazines, or other sources) of use of proposed characters attached?	No
8. Does the proposal address other aspects of character data processing?	No

C. Technical -- Justification
1. Contact with the user community?	Yes. TeX and PS Technical Word Processor
2. Information on the user community?	Mathematical software
3a. The context of use for the proposed characters?	Used in plain-text encoding of mathematics
3b. Reference	See references at end of this proposal
4a. Proposed characters in current use?	Yes.
4b. Where?	PS Technical Word Processor.
5a. Characters should be encoded entirely in BMP?	Yes.
5b. Rationale	Small number of characters
6. Should characters be kept in a continuous range?	Preferably (easier to parse)
7a. Can the characters be considered a presentation form of an existing character or character sequence?	No, although existing characters like ^ and _ are overloaded to have the same semantics
7b. Where?	TeX
7c. Reference
8a. Can any of the characters be considered to be similar (in appearance or function) to an existing character?	Yes
8b. Where?
8c. Reference
9a. Combining characters or use of composite sequences included?	No
9b. List of composite sequences and their corresponding glyph images provided?	na
10. Characters with any special properties such as control function, etc. included?	No

D. SC2/WG2 Administrative

To be completed by SC2/WG2

1. Relevant SC 2/WG 2 document numbers:

2. Status (list of meeting number and corresponding action or disposition)

3. Additional contact to user communities, liaison organizations etc.

4. Assigned category and assigned priority/time frame

Other Comments

Three additional operators allow most mathematical expressions to be encoded in a simple plain-text format. The first two of these characters are similar in spirit to the Unicode FRACTION SLASH (2044), in that they are used to request built-up display. Hence I recommend that they follow 2044.

These characters are:

SUPERSCRIPT OPERATOR

× (up arrow ® 2191)

_¯ SUBSCRIPT OPERATOR

× (down arrow ® 2193)

L LITERAL OPERATOR

× (circled Latin capital letter L ® 24C1)

{ MATHEMATICS ON (symbol in dashed box)

} MATHEMATICS OFF (symbol in dashed box)

The simplest example of subscript/superscript operator usage is to replace T_EX’s math use of ^ and _, respectively, which currently have to be “escaped” to be displayed. The glyphs are created by a superscripted bold up arrow and a subscripted bold down arrow, respectively. As in T_EX, the subscript and superscript operators allow nested subscripts and superscripts. In combination with other Unicode characters, these “operator” characters allow most common mathematical expressions to be represented without overloading the use of display characters like ^. An appropriate rendering algorithm can use them to produce built-up mathematical text.

The literal operator is used to reduce an operator character like the FRACTION SLASH and the subscript/superscript operators to be displayed as an ordinary character, instead of in built-up form.

The math-on/math-off symbols are analogous to the left-to-right U+200E and right-to-left U+200F bidirectional marks.

For further discussion, please see my articles “Unicode Plain-Text Encoding of Mathematics” in the Proceedings of the Unicode Implementers’ Workshop 6, Santa Clara, CA (Sept. 8-9, 1994) and “Unicode, Rich Text, and Mathematics”, in the Proceedings of the Seventh International Unicode Conference, San Jose, CA (Sept. 14-15, 1995)