DATE: 1999-10-27

L2/99-346

DOC TYPE:	Expert contribution
TITLE:	Mathematical brace pieces
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	Mathematical brace pieces
2. Requester's name	Murray Sargent III
3. Requester type	Expert request.
4. Submission date	1999-10-27
5. Requester’s reference	Scientific and Technical Information Exchange (STIX)
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	25
3. Proposed category
4. Proposed level of implementation and rationale	Level 3; requires simple 2D display
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 plus a few symbols
6b. Font currently available?	Microsoft Symbol font plus some glyphs from M. Everson
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. Barbara Beeton, Murray Sargent III, Don Carroll, Frank da Cruz
2. Information on the user community?	Mathematical software
3a. The context of use for the proposed characters?	Used in publication of research mathematics and other hard sciences.
3b. Reference
4a. Proposed characters in current use?	Yes.
4b. Where?	Worldwide, by scientific and technical publishers, technical word processing programs
5a. Characters should be encoded entirely in BMP?	Yes.
5b. Rationale	Accurate publication of mathematical and scientific research on the Web is impossible without a comprehensive and accurate collection of symbols including various alphabetic variants in common use. Allocation in the BMP is in accordance with the Roadmap.
6. Should characters be kept in a continuous range?	Yes
7a. Can the characters be considered a presentation form of an existing character or character sequence?	No.
7b. Where?
7c. Reference
8a. Can any of the characters be considered to be similar (in appearance or function) to an existing character?	Yes
8b. Where?	The characters are used to create large forms of existing brackets, braces, parentheses, and integrals
8c. Reference
9a. Combining characters or use of composite sequences included?	Yes
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

The brace, bracket, parenthesis, and integral character pieces shown in the following table

æ ç è

ö ÷ ø

é ê ë

ù ú û

ó ô õ

ì í î ï

ü ý þ ï

(plus a few others given in the list below) appear in a number of existing character encodings. These encodings include TeX, PostScript, the Hewlett Packard Math8 character set, the Microsoft Symbol font, and DEC VT series terminals, clones and various emulation programs. They are used by technical word processing software to display arbitrarily large versions of (, ), [, ], {, }, å, and ò. Currently HP printers encode a set of such characters in the private-use zone. The top and bottom portions of the integral sign are already encoded at U+2320 and U+2321, respectively, since they occur in the DOS codepage 850. To be compatible with existing code sets and to aid in the printing and display of 2D mathematics, I propose that the following set of such characters be encoded (when the symbol exists in the PostScript symbol encoding vector, the PostScript name is also given; else the name from some other standard is given):

æ LEFT PARENTHESIS UPPER HOOK

® PostScript parenlefttp

ç LEFT PARENTHESIS EXTENSION

® PostScript parenleftex

® 007C | VERTICAL BAR

® 2758 | LIGHT VERTICAL BAR

® ï CURLY BRACE EXTENSION

® ÷ RIGHT BRACKET EXTENSION

® ÷ RIGHT CURLY BRACE EXTENSION

® ÷ LEFT BRACKET EXTENSION

® ÷ LEFT CURLY BRACE EXTENSION

® ôINTEGRAL EXTENSION

è LEFT PARENTHESIS LOWER HOOK

® PostScript parenleftbt

ö RIGHT PARENTHESIS UPPER HOOK

® PostScript parenrighttp

÷ RIGHT PARENTHESIS EXTENSION

® PostScript parenrightex

ø RIGHT PARENTHESIS LOWER HOOK

® PostScript parenrightbt

é LEFT BRACKET UPPER CORNER

® PostScript bracketlefttp

ê LEFT BRACKET EXTENSION

® PostScript bracketleftex

ë LEFT BRACKET LOWER CORNER

® PostScript bracketleftbt

ù RIGHT BRACKET UPPER CORNER

® PostScript bracketrighttp

ú RIGHT BRACKET EXTENSION

® PostScript bracketrightex

û RIGHT BRACKET LOWER CORNER

® PostScript bracketrightbt

ì LEFT CURLY BRACE UPPER HOOK

® PostScript bracelefttp

í LEFT CURLY BRACE MIDDLE PIECE

® PostScript braceleftmid

î LEFT CURLY BRACE LOWER HOOK

® PostScript braceleftbt

ï CURLY BRACE EXTENSION

® PostScript braceex (used for left and right)

ü RIGHT CURLY BRACE UPPER HOOK

® PostScript bracerighttp

ý RIGHT CURLY BRACE MIDDLE PIECE

® PostScript bracerightmid

þ RIGHT CURLY BRACE LOWER HOOK

® PostScript bracerightbt

ô INTEGRAL EXTENSION

® PostScript integralex

¾ HORIZONTAL LINE EXTENSION

® PostScript arrowhorizex

ì ^þ	UPPER-LEFT OR LOWER-RIGHT BRACE SECTION ® IBM SS250000
ü ^î	UPPER-RIGHT OR LOWERLEFT BRACE SECTION ® IBM SS240000

SUMMATION SYMBOL TOP

® DEC Tech 03/01, DG Math 01/08(2)

SUMMATION SYMBOL BOTTOM

® DEC Tech 03/02, DG Math 01/09(2)

Differently aligned vertical bars are needed to ensure that the built up symbols fit together correctly and all are in one or more existing standards.