N2590 - Additonal Mathematical and Letterlike Characters

Additional Mathematical and Letterlike
Characters
ISO/IEC JTC1/SC2/WG2 N2590
Date:
Source:Status:Action:August 23, 2003
The Unicode Consortium
Liaison contribution
For consideration by WG2 in preparing amendments to ISO/IEC 10646

SummaryThis a proposal for adding seven mathematical andletterlike characters that was considered and approved at a
recent Unicode Technical Committee meeting and is submitted as a liaison contribution. The text below is an
updated version of a proposal submitted to the UTC by the mathematical community.

Background
Unicode 3.2, but also Unicode 3.1 and to a lesser degree Unicode 4.0 added mathematical characters to
support the mathematical user community. The large number of character involved made these additions arather complex undertaking. During a recent review of the mathematical classification and mapping to the ISO
9573-13 entity sets for addition to Unicode Technical Report #25,Unicode support for Mathematics, several
characters were found missing. In some cases, these can more or less directly be encoded by combining
sequences, and where that was possible, they were removed from the request before completion of this
proposal. In reviewing existing character collections, some non-mathematicalletterlike characters werediscovered and are proposed here for addition.
One of the goals of MathML is complete support for the SGML entity sets from ISO 9573-13. Providing this
support allows existing SGML documents to be carried forward into MathML. The mapping of these entity
sets has three issues
1. some entities have no reasonable character to map to
2. some entities map to a character already mapped by a different entity form the same entity set
3. some entities map to a character already mapped by a different entity from another entity set
where characters are missing or were mistakenly unified, character additions are proposed in theList of
proposed characters. For the other types of issues thatarrise in mapping ISO 9573, a final recommendation has
not been made. However, the entities and characters in question are noted in
http://www.unicode.org/~asmus/Notes_on_mapping_ISO_9573.html.
A preponderance of existing mathematical literature is encoded inTeX format and related formats (LaTeX,etc.). TeX and its derivatives are macro languages that combine layout and glyph selection instructions directlywith an entity (macro) definition. This leads to particular concerns when trying to represent existing
mathematical texts in a model that is based on character encoding.
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N2590 - Additonal Mathematical and Letterlike Characters

List of proposed characters
SymbolName / CodeComments

COMBINING
LONG DOUBLESOLIDUSOVERLAY

This character is requested as part of the repertoire formathematical publications.

suggested code:

It should look like a doubled 0338. The STIX project has theuse of the following double slashed combinations attested:
double-slashed: italic A, italic E, italic F

0358
PERPENDICULAR This is requested for compatibility with ISO 9573-13 as well
as existing practice inTeX and LaTex. Today, two different
entities perp (perpendicular) and bot (bottom, i.e. up tack)suggested code:from the same ISO 9573-13 entity set (ISOTECH ) map to thesame existing character 22A5 UP TACK. The difference
27C2
between these two symbols is the way they are used: Perp, isan infix relation like <, and gets extra spacing, whilebot is an
ordinary variable. Unifying these two removes a distinctionthat must be expressed.
LaTeX has the following definition (and plainTeX the same
but less readable):\DeclareMathSymbol {\perp}{\mathrel}{symbols }{"3F}\DeclareMathSymbol {\bot}{\mathord}{symbols }{"3F}

which means that \perp and \bot will by default use thesame symbol, but with different white spacebehaviour. A"\mathrel " is an infix relation like <, and a\mathord is anormal letter like x, that gets no special spacing.
DOUBLE-STRUCK This is used by systems like Mathematica to unambiguously
SMALL PI
designate the value of pi ( = 3.14159265358979...), since theordinary Greek letter could also be used for unrelated
variables. This character completes the series of double-strucksuggested code:
Greek operators and special values found in the range
U+213D..U+213F
213C[The final glyph will be matched to the existing symbols]
MATHEMATICAL These dotless characters are primarily intended as a
ITALIC DOTLESS I compatibility character to map theISOAMS entities imath andjmath or TeX \imath and jmath . Most commonly, mappingthese entities to themathematical italic i or j andsuggested code
removing the dot when composing with math accents would
result in the intended display.
1D6A4
There are documents in which the undotted i and j are used
contrastively with the dotted versions. SeeAdditional
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N2590 - Additonal Mathematical and Letterlike Characters

information on imath and jmath symbols.
MATHEMATICAL Besides mathematical use, both dotless characters can be
ITALIC DOTLESS found in other fields, such as phonetic transcriptions, but notJnecessarily in their italic form.
suggested code:
1D6A5

The \imath and \jmath are by default always italic. Theirappearance in TeX (and in the ISO 9573-13 entity sets) issimilar to the shapes shown in the illustrations in this
proposal. It is suggested to not unify the\imath with theexisting U+0130 DOTLESS I because \imath is never used insituations where case mapping occurs.

LATIN SMALL
Many fonts contain dotless i and j glyphs, to be used to place
LETTER DOTLESS accents on i and j. In Unicode, placing an accent on a an i or jJcharacter removes the dot, therefore there is no need for acharacter to represent the dotless base character,unless it isused standalone. Just as dotlessi is used in Turkish as asuggested code:
standalone character, a dotless j is used in certain
orthographies and dictionaries.See Additional information on
0237
dotless j.
PER SIGN
suggested code:

This is a character used in print as an abbreviation for theword per, in expressions such as 'per day' or 'per month'. See
Additional information on the Per sign.

214C

Summary of proposed characters with suggested Unicode
properties
0237 SMALL LETTER DOTLESS J;Ll;0;L;;;;;N;;;;;
0358 COMBINING LONG DOUBLE SOLIDUS OVERLAY ;Mn;1;NSM;;;;;N;;;;;
27C2 PERPENDICULAR;Sm;0;L;;;;;N;;;;;
213C DOUBLE-STRUCK SMALL PI;Ll;0;L;;;;;N;;;;;214C PER SIGN;Ll;0;L;;;;;N;;;;;
1D6A4 MATHEMATICAL ITALIC DOTLESS I;Ll;0;L;<font> 0131;;;;N;;;;;
1D6A5 MATHEMATICAL ITALIC DOTLESS J;Ll;0;L;<font> 0237;;;;N;;;;;
Other properties can be assigned by comparison with existing characters in adjacent or neighboring positions.

Additional information on the imath and jmath symbols
Generally, \imath and \jmath in TeX are simply used as base forms to apply math accents to. However,Page 3

N2590 - Additonal Mathematical and Letterlike Charactersmathematical equations can have entire sub-expressions underneath a math accent, e.g. when a 'wide hat' isplaced on top of i+j. as in this example:$\widehat{\imath + \jmath} = \hat{\ imath} + \hat{\ jmath}.$In such a situation a renderer can no longer rely simply on the presence of an adjacent combining character tosubstitute the un-dotted glyph, and whether the dots should be removed in such a situation is not 100%
predictable. In TeX, this decision is left to the author, and some authors would want to use the dotted forms as
in $\widehat{\imath + \jmath}$. Authors are also known to have applied \imath and \jmath explicitly
without a dot. Here is one example of an electronically published journal article making use of unaccented
dotless i and j.
One can search for \imath and \jmath in the TeX source here
http/ejde.math.swt.edu/Volumes/2000/21/villa-tex. Or see the result in the pdf here:
http/ejde.math.swt.edu/Volumes/2000/21/villa.pdf
See especially the last line of Hypothesis 4.2 (b) on page 8 of thepdf which comes from this TeX source:$\imath \in {\bf I \/}$ ( resp. $\jmath\in{\bf J\/}$).

The article was published in Electronic Journal of Differential Equations, Vol.2000(2000), No. 21, pp. 1{17.
ISSN 1072-6691. URL http/ejde.math.swt.edu or http/ejde.math.unt.edu, or ftp ejde.math.swt.edu ftp
ejde.math.unt.edu (login ftp), which according to http/ejde.math.swt.edu/ is a fully refereed journal, witharticles indexed by Math Reviews etc.

Additional information on dotless j
According to people familiar with this writing system, dotless j is used in thelandsmålalfabet.
It is apparently also used for the transliteration in animportant early dictionary of the the Khakas language. A
relevant quote from a paper describing the method:
http/home.arcor.de/marcmarti/khakas/xakvoc/xakvoc_intro.htm:...Radloff employs two additional letters, a j without dot, and a j with comma-like dot. According
to his dictionary, these graphemes represent a y preceded by a soft t and by a soft d respectively;...
The other letter mentioned in the citation can be encoded as j + 0313
Unlike DOTLESS I as used in Turkish, there is no case relation fordotless j with a capital letter j with dot above.
In all other respects the Unicode character properties of the proposeddotless j should match those of theexisting DOTLESS I.

Additional information on the Per sign
The character is listed on p175 of The United States Government Printing Office Style Manual 2000
http://www.access.gpo.gov/styleman/2000/pdf/chap10.pdf, where it is listed between the number sign and thepercent sign. It can also be found in the Cambridge Encyclopedia of Language, p. 190, which reproduces a list
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N2590 - Additonal Mathematical and Letterlike Characterstaken from a 1916 book (L. A. Legros & J. C. Grant, /Typographical Printing-Surfaces/ (London:Longmans,
Green 1916)), giving "the ordinary fount of 275 characters" which has "Commercial Signs" in a row@ [per] lb / £ $ % + - × ÷ =In that listing it is definitelyupper case, in the sense that it extends from the top of the l and b to below thebaseline.
Modern use in print can be found a.o. in a modern printed edition of 17th- to 19th century handwritten English
letters (Miller,Kerby A., Arnold Schrier, Bruce D. Boling, & David N. Doyle. 2002. Irish immigrants in theland of Canaan letters and memoirs from colonial and revolutionary America, 1675-1815.Oxford, Oxford
UP) where it is used to abbreviateper in 'per day' or 'per week'.
While the origin of this character may have been a handwritten contraction, its use in print can be considered
well established.

More on the origin
The per sign can also be found along with other symbols used in the OED at
http://dictionary.oed.com/public/help/Advanced/symbols.htm#mod1letter. (Not all these symbols are currently
part of Unicode.)
It is probably the sign indicated by the editors ofThe Papers of George Washington at
http://gwpapers.virginia.edu/search/index.html:
The ampersand has been retained and the thorn transcribed as t"h."The symbol for per ($PR) is used when it appears in the manuscript.
Unfortunately this ($PR) does not appear in any of the transcription or facsimile examples on the website. But
at http://www.roma.unisa.edu.au/07305/symbols.htm#Percentpart of an Italian manuscript of 1684 is shownin which an early form of the percent sign is preceded by what seems to be this same per sign. The graphic canbe seen more clearly at http://www.roma.unisa.edu.au/07305/Symbolsfolder/S406.JPG. The suspected originof the glyph for the per sign the p with a bar through its descender which was the standard medieval character
for "per".
See http://www.rootsweb.com/~chevaud/abbrev.htmfor a version with a single loop, seemingly a calligraphic
development of the version found athttp://www.lib.umich.edu/eebo/docs/dox/instruct.htmlcalled "&abper".
See also both http://www.hum.ku.dk/ami/handbook/chapter4.html(and search on "persarum") andhttp://helmer.hit.uib.no/mufi/proposal/range9-v2.html(and search on "&pbardes").

Relation to the barred P
The difference between medieval and more modern glyphs is great and ap with a bar though the descender
has also been used to indicate a fricative labial or anf-sound in some phonetic and transliteration traditions.
For example f or p with bar above the character or below the descender is generally used today intransliterating Hebrew. Accordingly it might be best to code two symbols, ap with a bar through thedescender (with corresponding uppercase) to indicate the both medievalper sign and modern phonetic usage
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N2590 - Additonal Mathematical and Letterlike Charactersof barred p and a separate character per sign for the more modern swirly descendant of the medievalper sign.
This suggestion has been raised before; here are some pointers to the mail archives of relevant discussions:
There is a mention of barred-p by Robert LloydWheelock at, though he visualizes p with a bar
http://www.unicode.org/mail-arch/unicode-ml/y2002-m09/0019.html
through the bowl, not the descender. An answer by Jim Allan is at
http://www.unicode.org/mail-arch/unicode-ml/y2002-m09/0039.htmland has links to a number of fonts withbarred characters. though only Junicode He privately reported having seen p with a bar through the stem
listed in Hebrew transliteration tables, and perhaps elsewhere. Of the fonts he cites, only theJunicode fonts
available at http://www.engl.virginia.edu/OE/junicode/junicode.htmlhas a p with a bar though the descender— which he takes to be the medieval per sign— as well as the upper case, a P with a bar through the stem.

Acknowledgements
Jim Allan unearthed the likely history of the per symbol and relates it to the barred p. LukasPietsch traced
modern printed use of the per symbol. AlistairVining traced it to a listing from a book from 1916. Barbara
Beeton requested the double slash overlay and located the attestations of their occurrence in the literature aspart of the STIX project. David Carlisle, one of the editors of MathML, submitted the request forjmath andlocated the additional information about their use, as well as the request for perpendicular.

ISO/IEC JTC 1/SC 2/WG 2
PROPOSAL SUMMARY FORM TO ACCOMPANY SUBMISSIONSFOR ADDITIONS TO THE REPERTOIRE OF ISO/IEC 10646(Form number: N2352-F (Original 1994-10-14; Revised 1995-01, 1995-04, 1996-04, 1996-08, 1999-03, 2001-05, 2001-09)

A. Administrative
1. Title:____ Additional Mathematical and Letterlike Characters__ ______

2. Requester's name: _____Unicode Consortium_________________________________
3. Requester type (Member body/Liaison/Individual contribution): __Liaison___4. Submission date:_______________
5. Requester's reference (if applicable): _L2 03/194, L2 03/201, L2 03/136R__
6. (Choose one of the following:)
This is a complete proposal:_____yes_______or, More information will be provided later:_______________

B. Technical - General
1. (Choose one of the following:)
a. This proposal is for a new script (set of characters):_____________
Proposed name of script: _________________________________________________
b. The proposal is for addition of character(s ) to an existing block: _yes_
Name of the existing block: _________several______________________________
2. Number of characters in proposal:_______7______
3. Proposed category (see section II, Character Categories):_____various__

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N2590 - Additonal Mathematical and Letterlike Characters
4. Proposed Level of Implementation (1, 2 or 3)(see clause 14, ISO/IEC 10646-1: 2000):______1_and_3__
Is a rationale provided for the choice?
_____no_______
If Yes, reference: _______________________________________________________
5. Is a repertoire including character names provided?
_____yes______
a. If YES, are the names in accordance with the'character naming guidelines in Annex L of ISO/IEC 10646-1: 2000? _yes___b. Are the character shapes attached in a legible form suitable for review?
__yes_
6. Who will provide the appropriate computerized font (ordered preference:
True Type, or PostScript format) for publishing the standard?
__Unicode_________________________________________________________________
If available now, identify source(s) for the font (include address,e-mail, ftp-site, etc.) and indicate the tools used:______________________________________________________________________________________________________________________________________________________________________________________________________________________________
7. References:a. Are references (to other character sets, dictionaries, descriptive
texts etc.) provided?
___yes________
b. Are published examples of use (such as samples from newspapers,
magazines, or other sources) of proposed characters attached? __yes_____
8. Special encoding issues:
Does the proposal address other aspects of character data processing(if applicable) such as input, presentation, sorting, searching, indexing,
transliteration etc. (if yes please enclose information)?
__where applicable_______________________________________________________

9. Additional Information:
See the other sections of this document.

C. Technical - Justification
1. Has this proposal for addition of character(s ) been submitted before? _no_If YES explain ___________________________________________________________
2. Has contact been made to members of the user community (for example:
National Body, user groups of the script or characters,other experts, etc.)?
_____yes______
If YES, with whom? __ mathml working group, STIX, other experts____________
If YES, available relevant documents: ___see other sections_____________
3. Information on the user community for the proposed characters(for example: size, demographics, information technology use, or
publishing use) is included?
____yes_______
Reference: __________see other sections__________________________________
4. The context of use for the proposed characters (type of use;common or rare)____varies____Reference: ______________________________________________________________
5. Are the proposed characters in current use by the user community? __yes___If YES, where? Reference: ____________see other sections ________________
6. After giving due considerations to the principles in Principles andProcedures document (a WG 2 standing document) must the proposedcharacters be entirely in the BMP?
_not entirely_
If YES, is a rationale provided?
_from context_
If YES, reference: _____________see other sections_______________________
7. Should the proposed characters be kept together in a contiguous range(rather than being scattered)?
_isolated_____
8. Can any of the proposed characters be considered a presentation form of an
existing character or character sequence?
_____yes______
If YES, is a rationale for its inclusion provided?
_____yes______
If YES, reference: _____________see other sections_______________________
9. Can any of the proposed characters be encoded using a composed character

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N2590 - Additonal Mathematical and Letterlike Characterssequence of either existing characters or other proposed characters? _No__If YES, is a rationale for its inclusion provided?
______________
If YES, reference: ______________________________________________________
10. Can any of the proposed character(s ) be considered to be similar (inappearance or function) to an existing character?
____yes_______
If YES, is a rationale for its inclusion provided?
____yes_______
If YES, reference: ____________see other sections________________________
11. Does the proposal include use of combining characters and/or use ofcomposite sequences (see clauses 4.12 and 4.14
in ISO/IEC 10646-1: 2000)?
___Yes_______
If YES, is a rationale for such use provided?
____no________
If YES, reference: _____________________________________________________Is a list of composite sequences and their corresponding glyph images(graphic symbols) provided?
______________
If YES, reference: ______________________________________________________
12. Does the proposal contain characters with any special properties such as
control function or similar semantics?
______none____If YES, describe in detail (include attachment if necessary) _____________
13. Does the proposal contain any Ideographic compatibility character(s )? _N_
If YES, is the equivalent corresponding unified ideographic character(s )identified?
____________
If YES, reference: ______________________________________________________

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