SC2/WG2 N2086

L2/99-195

DATE: 1999-09-02

DOC TYPE:	Expert contribution
TITLE:	Proposal to encode mathematical alphanumeric symbols
SOURCE:	Murray Sargent III, Barbara Beeton
PROJECT:
STATUS:	Proposal
ACTION ID:	FYI
DUE DATE:	--
DISTRIBUTION:	Worldwide
MEDIUM:	Paper and html
NO. OF PAGES:	5

A. Administrative
1. Title	Proposal to encode mathematical alphanumeric symbols
2. Requester's name	Murray Sargent III, Barbara Beeton
3. Requester type	Expert request.
4. Submission date	1999-9-9
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?	No.
2. Number of characters	991 new alphanumeric symbols
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?	None needed (they already exist)
6b. Font currently available?	None needed (standard fonts are adequate)
6c. Font format?	na
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?	Not attached, but available.
8. Does the proposal address other aspects of character data processing?	No

C. Technical -- Justification
1. Contact with the user community?	Yes. Patrick Ion, Barbara Beeton, Murray Sargent III, MathML W3C Math Working Group
2. Information on the user community?	Professional mathematicians, physicists, astronomers, engineers, and other scientific and technical researchers.
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 and other users of mathematics
5a. Characters should be encoded entirely in BMP?	No, entirely in plane 1.
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.
6. Should characters be kept in a continuous range?	Yes in order to fit in one 1024-character surrogate block
7a. Can the characters be considered a presentation form of an existing character or character sequence?	No. A given alphabetic symbol has different semantics when its style is changed and should not be found by the same plain-text search string.
7b. Where?
7c. Reference
8a. Can any of the characters be considered to be similar (in appearance or function) to an existing character?	Some letterlike symbols look similar to corresponding characters in some alphabets, e.g., some capital script letters. These are left as holes in the proposed code assignments
8b. Where?	Letterlike symbols
8c. Reference
9a. Combining characters or use of composite sequences included?	No
9b. List of composite sequences and their corresponding glyph images provided?	No
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

Mathematics has need for a number of Latin and Greek alphabets that on first thought appear to be font variations of one another, e.g., normal, bold, italic and script H. However in any given document, these characters have distinct mathematical semantics. For example, a normal H represents a different variable from a bold H, etc. If one drops these distinctions in plain text, one gets gibberish. Instead of the well-known Hamiltonian formula

H = òdt(eE² + mH²),

you’d get the integral equation (!)

H = òdt(eE² + mH²).

Accordingly, the STIX project requests adding normal, bold, italic, script, etc., Latin and Greek alphabets. Straight encoding leads to 991 characters and loses some useful common information, such as all variants of H might not be trivially recognizable as H’s. But it does allow plain text to retain the proper character semantics and it allows simple (nonrich) search methods to work.

The alphabetic symbols encountered in mathematics are given in the following table (exclusions for 25 Letterlike Symbols already encoded are not subtracted from the counts in this table, but are listed in a subsequent table):

Math style	Characters	Count	Proposed Name Prefix
bold	a-z, A-Z, 0-9, a-w, A-Ω (Greek)	120	MATH BOLD
italic	a-z, A-Z, a-w, A-Ω (Greek)	110	MATH ITALIC
bold italic	a-z, A-Z, a-w, A-Ω (Greek)	110	MATH BOLD ITALIC
script (calligraphic)	a-z, A-Z	52	MATH SCRIPT
bold script (calligraphic)	a-z, A-Z	52	MATH SCRIPT BOLD
fraktur	a-z, A-Z	52	MATH FRAKTUR
bold fraktur	a-z, A-Z	52	MATH BOLD FRAKTUR
open-face	a-z, A-Z, 0-9	62	MATH OPEN-FACE
sans-serif	a-z, A-Z, 0-9	62	MATH SANS
sans-serif bold	a-z, A-Z, 0-9, a-w, A-Ω (Greek)	120	MATH SANS BOLD
sans-serif italic	a-z, A-Z	52	MATH SANS ITALIC
sans-serif bold italic	a-z, A-Z, a-w, A-Ω (Greek)	110	MATH SANS BOLD ITALIC
monospace	a-z, A-Z, 0-9	62	MATH MONOSPACE

Note that which normal, script, fraktur, open-face, sans-serif, or monospace fonts are used is beyond the scope of plain-text. The upper-case Greek letters A-Ω are defined by the Unicode Greek character range U+0391 through U+03A9 plus the nabla Ñ (U+2207). a-w are defined by the Unicode Greek character range U+03B1 through U+03C9 plus the partial differential sign ¶ (U+2202) and the six glyph variants of e, q, κ, f, ρ, and π, given by (new BMP code that resembles U+220A), U+03D1, U+03F0, U+03D5, U+3C1, U+03F1, and U+03D6 (since both glyphs for each of these can appear in the same document with different semantics). The upper-case position U+03A2 corresponding to the final sigma ς is used for the upper-case Θ variant, which looks like the usual Θ except that the “H” in the middle is replaced by a “-”. This gives 25+1 upper-case Greek characters and 25+7 lowercase characters. In addition, corresponding characters in the BMP are used for upright serifed characters when they occur in mathematical expressions.

Proposed Encoding Approach

Outright encoding stores the alphabets in plane 1 for a total of 991 characters as currently entered. No accented characters are included. Accented mathematical symbols are always represented by combining character sequences. These characters fit into 1024 code positions (addressable using one high-surrogate value) by using the following scheme (one column is one hexadecade):

Character group	Total number	Layout	# of Columns
13 Latin alphabets	676	42 full columns + 4 chars	42+ columns
5 Greek alphabets	290	18 full columns + 2 chars	18+ columns
5 sets of digits	50	3 full columns + 2. End at end of 1024-char block	3+ columns
Exclusions (below)	25
3 groups – 25 exclus.	991		64 columns

This is a total of 64 columns, which is a block of 1024 (one surrogate block). The suggested block is D400…D7FF on plane 1. Please see proposed explicit code assignments at the end of this document.

An alternative approach to separate encoding of each style of alphanumeric mathematical alphabet was given serious consideration (see L2/99-188). That consisted of encoding a math style variant tag for each significant difference in alphabets. However, while technically feasible for the representation of the required mathematical alphabets, the encoding of such math style variant tags raised unanswerable questions regarding what would happen if they were applied outside their intended mathematical domain--for example, to accented Latin letters, or even to other scripts such as Han characters. This approach was also too close to the introduction of explicit stylistic markup into the character encoding – something regarding which there is general consensus in the character encoding committees that such a step would be undesireable.

Block Title

The proposed block title name is “Mathematical Alphabets”.

Proposed ISO Naming Conventions

The character names are those used for the corresponding characters in the BMP with the proposed prefixes given in the table above, but simplified as in the Letterlike Symbols block. For example, the character H in the Hamiltonian formula above has the proposed name “MATH SCRIPT CAPITAL H”. The code position for this particular character is marked as reserved, since the character already exists in the Letterlike-Symbols block with the name “SCRIPT CAPITAL H”. This and other such reserved code positions are listed in the next section.

Exclusions

The code positions for the following characters should be left <reserved> (unassigned), since these characters already appear in the Letterlike-Symbols block:

Math character	Letterlike Symbol character	Code
MATH OPEN-FACE CAPITAL C	DOUBLE-STRUCK CAPITAL C	2102
MATH SCRIPT SMALL G	SCRIPT SMALL G	210A
MATH SCRIPT CAPITAL H	SCRIPT CAPITAL H	210B
MATH FRAKTUR CAPITAL H	BLACK-LETTER CAPITAL H	210C
MATH OPEN-FACE CAPITAL H	DOUBLE-STRUCK CAPITAL H	210D
MATH ITALIC SMALL H	PLANCK CONSTANT	210E
MATH SCRIPT CAPITAL I	SCRIPT CAPITAL I	2110
MATH FRAKTUR CAPITAL I	BLACK-LETTER CAPITAL I	2111
MATH SCRIPT CAPITAL L	SCRIPT CAPITAL L	2112
MATH SCRIPT SMALL L	SCRIPT SMALL L	2113
MATH OPEN-FACE CAPITAL N	DOUBLE-STRUCK CAPITAL N	2115
MATH OPEN-FACE CAPITAL P	DOUBLE-STRUCK CAPITAL P	2119
MATH OPEN-FACE CAPITAL Q	DOUBLE-STRUCK CAPITAL Q	211A
MATH SCRIPT CAPITAL R	SCRIPT CAPITAL R	211B
MATH FRAKTUR CAPITAL R	BLACK-LETTER CAPITAL R	211C
MATH OPEN-FACE CAPITAL R	DOUBLE-STRUCK CAPITAL R	211D
MATH OPEN-FACE CAPITAL Z	DOUBLE-STRUCK CAPITAL Z	2124
MATH FRAKTUR CAPITAL Z	BLACK-LETTER CAPITAL Z	2128
MATH SCRIPT CAPITAL B	SCRIPT CAPITAL B	212C
MATH FRAKTUR CAPITAL C	BLACK-LETTER CAPITAL C	212D
MATH SCRIPT SMALL E	SCRIPT SMALL E	212F
MATH SCRIPT CAPITAL E	SCRIPT CAPITAL E	2130
MATH SCRIPT CAPITAL F	SCRIPT CAPITAL F	2131
MATH SCRIPT CAPITAL M	SCRIPT CAPITAL M	2133
MATH SCRIPT SMALL O	SCRIPT SMALL O	2134

Discussion

Rendering mathematics requires a fairly sophisticated 2D layout engine. Compared to the complexity needed in this engine, handling surrogate pairs is straightforward. Furthermore it is anticipated that handling surrogate pairs will be easy, partly because they will be handled by computer operating systems thanks to the strong business case for supporting East Asian characters in plane 2.

Proposed Code Assignments in Plane 1

The proposed code assignments will be given in Unicode layout format shortly. A layout in the form of ISO/IEC 10646-2 can be provided to the editor.