Status of this Document
This section describes the status of this document at the time
of its publication. Other documents may supersede this document. A
list of current W3C publications and the latest revision of this
technical report can be found in the W3C technical reports index at
http://www.w3.org/TR/.
This document has been reviewed by W3C Members, by software
developers, and by other W3C groups and interested parties, and is
endorsed by the Director as a W3C Recommendation. It is a stable
document and may be used as reference material or cited from another
document. W3C's role in making the Recommendation is to draw attention
to the specification and to promote its widespread deployment. This
enhances the functionality and interoperability of the Web.
This document was produced by the
W3C Math Working Group
as a Recommendation and as part of the W3C
Math Activity.
The goals of the W3C Math Working Group are discussed in the
W3C Math WG Charter.
The authors of this document are W3C Math Working Group members.
Comments should be sent to the
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see also instructions).
When sending an e-mail comment on the XML Entity Definitions for Characters, please
put the text “XML-Entities” in the subject line, preferably like this:
“[XML-Entities] …summary of comment ”.
This document was produced by a group operating under the
5 February 2004 W3C Patent Policy.
W3C maintains a
public list of any patent disclosures made in connection with
the deliverables of the group; that page also includes instructions
for disclosing a patent. An individual who has actual knowledge of
a patent which the individual believes contains
Essential Claim(s)
must disclose the information in accordance with
section 6 of the W3C Patent Policy.
Appendix B Changes details the changes since earlier versions of this document.
1 Introduction
Notation and symbols have proved very important for human communication,
especially in scientific documents. Mathematics has
grown in part because its notation continually changes toward being succinct
and suggestive. There have been many new signs
developed for use in mathematical notation, and
mathematicians have not held back from making use of many symbols
originally introduced elsewhere. The result is that
science in general, and particularly mathematics, makes use of
a very large collection of symbols. It is
difficult to write science fluently if these characters are not
available for use. It is difficult to read science if
corresponding glyphs are not available for presentation on specific
display devices. In the majority of cases it is preferable to store
characters directly as Unicode character data or as XML numeric
character references.
However, in some environments it is more
convenient to use the ASCII input mechanism provided by XML entity
references. Many entity names are in common use, and this
specification aims to provide standard mappings to Unicode for each of
these names. It introduces no names that have not already been used in
earlier specifications. Note that these names are short mnemonic names
designed for input methods such as XML entity references, not the longer formal names
that form part of the Unicode standard.
Specifically, the entity names in the sets
starting with the letters "iso" were first standardized in SGML ([SGML]) and updated in [ISO9573-13-1991].
The W3C Math Working Group has been
invited to take over the maintenance and development of these sets by the
original standards committee (ISO/IECJTC1 SC34). The sets with names
starting "mml" were first standardized in
MathML [MathML2] and those starting
with "xhtml" were first standardized in HTML [HTML4].
This document is the result of years of employing entity names on the Web. There were
always a few named entities used for special characters in HTML, but a flood of new
names came with the symbols of mathematics. This means that this document can be
viewed as an extension and final revision of Chapter 6 of the MathML 2.0
[MathML2] recommendation. Now it presents a completed listing harmonizing
the known uses of character entity names throughout the XML world and Unicode.
Since there are so many character entity names, and the files specifying them
are resources that may be subject to frequent lookup, a template catalog file has also been
provided. Users are strongly encouraged to design their implementations so that
relevant entity name tables are cached locally, since it is not expected that
the listings provided with this specification will need changing for some long time.
2 Sets of names
This specification defines mappings to Unicode of many sets of names
that have been defined by earlier specifications.
We first present two tables listing all the sets combined, first in
Unicode order and then in alphabetic order:
Then there come tables
documenting each of the entity sets. Each set has a link to the DTD
entity declaration for the corresponding entity set, and also a link
to an XSLT2 stylesheet that will implement a reverse mapping from
characters to entity names (this is, of course, only possible for entity names
that map to a single Unicode code point).
In addition to the stylesheets and entity files corresponding
to each individual entity set, a combined
stylesheet is provided, as well as two combined entity sets, each
in two formats. First as a small file that
references the individual entity sets listed above, and then as a
larger file that directly contains a definition of each entity,
with the definitions sorted in order of entity names, with
duplicates removed. The first set, w3centities includes
all the entity sets defined in this specification. the second,
htmlmathml, is a slightly smaller set just comprising the
entity sets included in HTML and MathML. These are the entities
most likely to work (due to cached DTD or built in entity support)
if used in a web context.
- w3centities W3C entities collection; referencing all entity sets listed above
- w3centities-f the same set of entity definitions, expanded into a single file, with duplicates removed
- htmlmathml
htmlmathml collection; referencing the entity sets used in HTML or MathML
- htmlmathml-f the expanded set of HTML and MathML entity definitions
3 Unicode Character Ranges for Scientific Documents
Certain characters are of particular relevance to scientific document production. The following
tables display Unicode ranges containing the characters that are most used in mathematics.
Note that each of the tables linked from this section contains 256 images and may take a
while to load if the images have not been cached locally.
- 000 C0 Controls and Basic Latin, C1 Controls and Latin-1 Supplement
- 001 Latin Extended-A, Latin Extended-B
- 002 IPA Extensions, Spacing Modifier Letters
- 003 Combining Diacritical Marks, Greek and Coptic
- 004 Cyrillic
- 020 General Punctuation, Superscripts and Subscripts, Currency Symbols, Combining Diacritical Marks for Symbols
- 021 Letterlike Symbols, Number Forms, Arrows
- 022 Mathematical Operators
- 023 Miscellaneous Technical
- 024 Control Pictures, Optical Character Recognition, Enclosed Alphanumerics
- 025 Box Drawing, Block Elements, Geometric Shapes
- 026 Miscellaneous Symbols
- 027 Dingbats, Miscellaneous Mathematical Symbols-A, Supplemental Arrows-A
- 029 Supplemental Arrows-B, Miscellaneous Mathematical Symbols-B
- 02A Supplemental Mathematical Operators
- 02B Miscellaneous Symbols and Arrows
- 0FB Alphabetic Presentation Forms, Arabic Presentation Forms-A
- 0FE Variation Selectors, Vertical Forms, Combining Half Marks, CJK Compatibility Forms, Small Form Variants, Arabic Presentation Forms-B
- 1D4 Mathematical Alphanumeric Symbols
- 1D5 Mathematical Alphanumeric Symbols (continued)
- 1D6 Mathematical Alphanumeric Symbols (continued)
- 1D7 Mathematical Alphanumeric Symbols (continued)
4 Mathematical Alphanumeric Characters
Many of the entities defined by this specification relate to the
mathematical alphanumeric characters contained in the letter-like
symbols block of Unicode Plane 0, or in the Mathematical Alphanumeric Symbols
block in Unicode Plane 1. The following tables list all these symbols,
highlighting those that are not in Plane 1, and giving entity names
where appropriate.
5 Entities for Negated and Variant Characters
Each of the entity definitions in a majority of the specification expands
to a single Unicode character. The definitions that expand to a sequence of
two or more characters are outlined in this section.
5.1 Negated Mathematical Characters
In addition to the Unicode Characters so far listed, one may use the
combining characters U+0338 (/),
U+20D2 (|) and
U+20E5 (\) to produce
negated or canceled forms of
characters. A combining character
should be placed immediately after its "base" character, with no
intervening markup or space, just as is the case for combining accents.
In principle, the negation characters may be applied to any Unicode
character, although fonts designed for mathematics typically have some
negated glyphs ready composed. A MathML renderer should be able to use
these pre-composed glyphs in these cases. A compound character code
either represents a UCS character that is already available, as in the
case of U+003D U+0338 which amounts to
U+2260, or it does not, as is the
case for U+2202 U+0338. The common cases of
negations, of the latter type,
that have been identified are listed in the tables.
Note that it is the policy of the W3C and of Unicode that if a single
character is already defined for what can be achieved with a combining
character, that character must be used instead of the decomposed form.
It is also intended that no new single characters representing what
can be done by with existing compositions will be introduced.
For further information on these matters see
the Unicode Standard Annex 15, Unicode Normalization Forms
[Unicode15], especially
the discussion of Normalization Form C.
5.2 Variant
Mathematical Characters
Unicode attempts to avoid having several character codes for simple
font variants. For a code point to be assigned there should be
more than a nuance in glyphs to be recorded. To record
variants worth noting there is a special character in
Unicode 3.2, U+FE00 (VARIATION SELECTOR-1), which
acts as a postfix modifier. However the legally allowed
combinations with this variation selector are restricted to a
list recorded as part of Unicode. The VARIATION SELECTOR-1
character may only be applied to the characters listed here.
The resulting combination is not regarded by Unicode as a separate
character, but a variation on the base character. Unicode aware systems
may render the combination as the base if the available fonts do not
support the variant glyph shape.
