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<h1><a name="chars" id="chars"></a>6 Characters, Entities and Fonts
</h1>
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<div class="minitoc">
Overview: <a href="overview-d.html">Mathematical Markup Language (MathML) Version 2.0 (Second Edition)</a><br>
Previous: 5 <a href="chapter5-d.html">Combining Presentation and Content Markup</a><br>
Next: 7 <a href="chapter7-d.html">The MathML Interface</a><br><br>6 <a href="chapter6-d.html">Characters, Entities and Fonts</a><br> 6.1 <a href="chapter6-d.html#chars.intro">Introduction</a><br> 6.2 <a href="chapter6-d.html#chars.mathmlchars">MathML Characters</a><br> 6.2.1 <a href="chapter6-d.html#chars.unicodechars">Unicode Character Data</a><br> 6.2.2 <a href="chapter6-d.html#chars.mglyph">Special Characters Not in Unicode</a><br> 6.2.3 <a href="chapter6-d.html#chars.BMP-SMP">Mathematical Alphanumeric Symbols
Characters</a><br> 6.2.4 <a href="chapter6-d.html#chars.nonmark">Non-Marking Characters</a><br> 6.3 <a href="chapter6-d.html#id.6.3">Character Symbol Listings</a><br> 6.3.1 <a href="chapter6-d.html#chars.special">Special Constants</a><br> 6.3.2 <a href="chapter6-d.html#chars.byxxx">Character Tables (ASCII format)</a><br> 6.3.3 <a href="chapter6-d.html#chars.16x16-tables">Tables arranged by Unicode block</a><br> 6.3.4 <a href="chapter6-d.html#chars.math-negated-tables">Negated
Mathematical Characters</a><br> 6.3.5 <a href="chapter6-d.html#chars.math-variant-tables">Variant
Mathematical Characters</a><br> 6.3.6 <a href="chapter6-d.html#chars.letter-like-tables">Mathematical Alphanumeric Symbols</a><br> 6.3.7 <a href="chapter6-d.html#chars.entity.tables">MathML Character Names</a><br> 6.4 <a href="chapter6-d.html#id.6.4">Differences from Characters in MathML 1</a><br> 6.4.1 <a href="chapter6-d.html#id.6.4.1">Coverage</a><br> 6.4.2 <a href="chapter6-d.html#id.6.4.2">Fewer Non-marking Characters </a><br> 6.4.3 <a href="chapter6-d.html#id.6.4.3">ISO Tables</a><br> 6.4.4 <a href="chapter6-d.html#chars.char-status">Status of Character Encodings</a><br></div>
<div class="div1">
<div class="div2">
<h2><a name="chars.intro" id="chars.intro"></a>6.1 Introduction
</h2>
<p>
Notation and symbols have proved very important for
mathematics. Mathematics has grown in part because <span class="diff-del"> of the
succinctness and suggestiveness of its evolving notation<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span>
<span class="diff-add">its notation continually changes toward being succinct and
suggestive<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span>. There
have been many new signs <span class="diff-chg">developed<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span> for use in mathematical
notation, and mathematicians have not held back from making use
of many symbols originally <span class="diff-chg">introduced<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span> elsewhere. The result is
that mathematics makes use of a very large collection of
symbols. It is difficult to write mathematics fluently if these
characters are not available for use<span class="diff-del"> in coding<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span>. It is difficult
to read mathematics if corresponding glyphs are not available
for presentation on specific display devices.
</p>
<div class="diff-del">
<p>
This situation posed a problem for the first W3C Math Working Group
when it was brought into existence. It did not fall naturally within
the purview of developing a specification enabling mathematics to be
used with HTML and producing a DTD for <span class="diff-chg">the Working
Group<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span> to worry about more than
the entities allowed in the DTD. However, as experience has shown, a
long list of entities with no means to display them is of little use,
and a cause of frequent frustrations in trying to use a standard. On
the other hand, a large collection of glyphs and fonts representing
characters without a standard way to refer to them is not of much use
either.
</p><a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></div>
<p>
The W3C Math Working Group therefore took on directly the task of
specifying part of the full mechanism needed to proceed from
notation to final presentation, and started collaboration with
organizations undertaking specification of the rest.
</p>
<p>
This chapter of the MathML specification contains a listing of character names for
use <span class="diff-chg">with<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span> MathML, recommendations for their use, and
warnings to pay attention to the correct form of the corresponding code points
given in the UCS (Universal Character Set) as codified in Unicode and ISO 10646
[see <a href="appendixk-d.html#Unicode">[Unicode]</a> and the <a href="http://www.unicode.org/">Unicode
Web site</a>]. For simplicity we shall refer to this character set by the short
name Unicode. Though Unicode changes from time to time so that it is specified
exactly by using version numbers, unless this brings clarity on some point we
shall not use them. <span class="diff-chg">The specification of MathML 2.0
<span class="diff-add"><a href="appendixk-d.html#MathML2">[MathML2]</a><a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span> used to make use of some characters that were
not part of Unicode 3.0 but which had been proposed to the Unicode Technical
Committee (UTC), and thus for inclusion in ISO 10646. They have been included in
the revisions Unicode 3.1 and 3.2. As of the publication of the MathML 2.0 (Second Edition) the current version is Unicode
4.0.<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span> (For more detail about this see
<a href="chapter6-d.html#chars.char-status">Section 6.4.4 Status of Character Encodings</a>.)
</p>
<p>
<span class="diff-chg">
While a long process of review and adoption by UTC and ISO/IEC of the
characters of special interest to mathematics and MathML is now<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span>
complete <span class="diff-del">(<a href="http://www.unicode.org/unicode/alloc/Pipeline.html">Unicode Work
in Progress</a>)<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span> there remains the possibility of some further
modification of the lists of characters accepted<span class="diff-del">, of the code
assignments for those adopted, or of the names given them by Unicode<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span>.
To make sure any possible corrections to relevant standards are taken
into account, and for the latest character tables and font information,
see the <a href="http://www.w3.org/Math/">W3C Math Working Group
home page</a> and the <a href="http://www.unicode.org/">Unicode
site</a> <span class="diff-add">(see, for instance, <a href="http://www.unicode.org/unicode/alloc/Pipeline.html">Unicode Work
in Progress</a>)<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span>.
</p>
</div>
<div class="div2">
<h2><a name="chars.mathmlchars" id="chars.mathmlchars"></a>6.2 MathML Characters
</h2>
<p>
A MathML token element <a href="chapter3-d.html#presm.tokel">Section 3.2 Token Elements</a>, and <a href="chapter4-d.html#contm.tokenel">Section 4.4.1 Token Elements</a> takes as content a sequence of <em>MathML
Characters</em>. MathML Characters are defined to be either
Unicode characters legal in XML documents or <code>mglyph</code> elements.
The latter are used to represent
characters that do not have a Unicode encoding, as described in
<a href="chapter3-d.html#presm.mglyph">Section 3.2.9 Accessing glyphs for
characters from MathML
(mglyph)</a>.
<span class="diff-chg"> Because the Unicode UCS provided
approximately one thousand special alphabetic characters for the use
of mathematics with Unicode 3.1, and over 900 further
special symbols in Unicode 3.2, the need for
<code>mglyph</code> should be rare. <a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>
</p>
<div class="div3">
<h3><a name="chars.unicodechars" id="chars.unicodechars"></a>6.2.1 Unicode Character Data
</h3>
<p>
As always in XML, any character allowed by XML may be used in MathML
in an XML document. The legal characters have the hexadecimal code
numbers 09 (tab = U+0009), 0A (line feed = U+000A), 0D (carriage
return = U+000D), 20-D7FF (U+0020..U+D7FF), E000-FFFD
(U+E000..U+FFFD), and 10000-10FFFF (U+010000..U+10FFFF). The
<span class="diff-chg">notation, just introduced in parentheses,<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>
beginning with U+ is <span class="diff-chg">that<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> recommended by Unicode
for referring to Unicode characters [see <a href="appendixk-d.html#Unicode">[Unicode]</a>, page
xxviii]. The exclusions above code number D7FF are of the blocks used
in surrogate pairs, and the two characters guaranteed not to be
Unicode characters at all. U+FFFE is excluded to allow determination
of byte order in certain encodings.
</p>
<p>
There are essentially three different ways of encoding character data.
</p>
<ul>
<li>
<p>
Using characters directly: For example, an A may be entered as 'A'
from a keyboard (character <span class="diff-chg">U+0041<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>). This option is only available
if the character encoding specified for the XML document includes
the character. Most commonly used encodings will have 'A' in the
ASCII position. In many encodings, characters may need more than
one byte. Note that if the document is, for example, encoded in
Latin-1 (ISO-8859-1) then <em>only</em> the characters in that
encoding are available directly. <span class="diff-del">Unfortunately, most mathematical
symbols may not be encoded as character data in this way.<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>
<span class="diff-add">Using UTF-8 or UTF-16, the only two encodings that
all XML processors are required to accept, mathematical symbols can
be encoded as character data.<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>
</p>
</li>
<li>
<p>
Using numeric XML character references: Using this notation, 'A' may be
represented as &<span class="diff-chg">#65;<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> (decimal) or &#x41; (hex).
Note that the numbers always refer to the Unicode encoding (and not to
the character encoding used in the XML file). By using <span class="diff-chg">character<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>
references it is always possible to access the entire Unicode range.
For a general XML vocabulary, there is a disadvantage to this approach:
character references may not be used in XML element or attribute
names. However, this is not an issue for MathML, as all element names in
MathML are restricted to ASCII characters.
</p>
</li>
<li>
<p>
Using entity references: The MathML DTD defines internal entities that
expand to character data. Thus for example the entity reference
&eacute; may be used rather than the character reference
"&#xE9; or, if, for example, the document is encoded in
ISO-8859-1, the character é. An XML fragment that uses an entity
reference which is not defined in a DTD is not well-formed; therefore
it will be rejected by an XML parser. For this reason
<em>every</em> fragment using entity references <em>must</em>
use a DOCTYPE declaration which specifies the MathML DTD, or a DTD
that at least declares any entity reference used in the MathML
instance. The need to use a DOCTYPE complicates inclusion of MathML in
some documents. However, entity references are very useful for small
illustrative examples, and are used in most examples in this document.
</p>
<div class="diff-del">
<p>
For this reason entity references are perhaps not optimal for use in
generated MathML, however they are very useful for small illustrative
examples, as used in this document.
</p><a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></div>
</li>
</ul>
</div>
<div class="div3">
<h3><a name="chars.mglyph" id="chars.mglyph"></a>6.2.2 Special Characters Not in Unicode
</h3>
<p>
For special purposes, one may need to use a character which is not in
Unicode<span class="diff-del">, even with the expected additions<a href="appendixj-d.html#d0e55670"><sub class="diff-link">J</sub></a></span>.
In these cases
one may use the <a href="chapter3-d.html#presm.mglyph"><code>mglyph</code></a>
element for direct access to a glyph from some font and creation of
a MathML <span class="diff-chg">substitute for the corresponding character<a href="appendixj-d.html#d0e55670"><sub class="diff-link">J</sub></a></span>.
All MathML token elements that accept character data also accept an
<code>mglyph</code> in their content.
</p>
<p>
Beware, however, that the font chosen may not be available to all
MathML processors.
</p>
</div>
<div class="div3">
<h3><a name="chars.BMP-SMP" id="chars.BMP-SMP"></a>6.2.3 Mathematical Alphanumeric Symbols
Characters
</h3>
<p>
A noticeable feature of mathematical and scientific writing is the use
of single letters to denote variables and constants in a given
context. The increasing complexity of science has led to the use of
certain common alphabet and font variations to provide enough special
symbols of this letter-like type. These denotations are in fact
<em>not</em> letters that may be used to make up words with
recognized meanings, but individual carriers of semantics themselves.
Writing a string of such symbols is usually interpreted in terms of
some composition law, for instance, multiplication. Many letter-like
symbols may be quickly interpreted by specialists in a given area as
of a certain mathematical type: for instance, bold symbols, whether
based on Latin or Greek letters, as vectors in physics or engineering,
or fraktur symbols as Lie algebras in part of pure mathematics. Again,
in given areas of science, some constants are recognizable letter
forms. When you look carefully at the range of letter-like
mathematical symbols in common use today, as the STIX project
supported by major scientific and technical publishers did, you come
up with perhaps surprisingly many. A proposal to facilitate
mathematical publishing by inclusion of mathematical alphabetic
symbols in the UCS was made, and has been favorably handled.
</p>
<p>
The <span class="diff-chg">additional<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> Mathematical Alphanumeric Symbols
<span class="diff-chg">provided<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> in Unicode 3.1 have
<span class="diff-del">provisional <a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>code points in <em>Plane 1</em>, that is, in the first
plane with Unicode values higher than 2<sup>16</sup>. This plane of
characters is also known as the Secondary Multilingual Plane (SMP),
in contrast to the Basic Multilingual Plane (BMP) which <span class="diff-chg">
was originally the entire extent of Unicode<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>. Support for Plane 1 characters in currently
deployed software is not always reliable, and in particular support
for these Mathematical Alphanumeric Symbol characters is not likely to be
widespread until after <span class="diff-chg">public fonts covering the characters
adopted for mathematics are available<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>.
</p>
<p>
As discussed in <a href="chapter3-d.html#presm.commatt">Section 3.2.2 Mathematics style attributes common to token
elements</a>, MathML offers an
alternative mechanism to specify mathematical alphabetic
characters<span class="diff-chg">. This alternative spans the gap between the
specification of Unicode 3.1 and its associated deployment in software and
fonts.<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>
Namely, one uses the <code>mathvariant</code>
attribute on the surrounding token element, which will most commonly
be <code>mi</code>. In this section we detail the
correspondence that a MathML processor should apply between certain
characters in <em>Plane 0</em> (BMP) of Unicode, modified by the
<code>mathvariant</code> attribute, and the Plane 1
Mathematical Alphanumeric Symbol characters.
</p>
<p>The basic idea of the correspondence is fairly simple.
For example, a Mathematical Fraktur alphabet is <span class="diff-chg">
in Plane 1<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>, and
the code point for Mathematical Fraktur A is
<span class="diff-chg">U+1D504<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>.
Thus using these <span class="diff-del">proposed<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> characters, a typical example might be
</p><pre>
<mi>&#x1D504;</mi>
</pre><p>
However, an alternative, equivalent markup would be to use
the standard A and modify the identifier using the
<code>mathvariant</code> attribute, as follows:
</p><pre>
<mi mathvariant="fraktur">A</mi>
</pre><p>
The exact correspondence between a mathematical alphabetic character
and an unstyled character is complicated by the fact that certain
characters that were already present in Unicode are not in the
'expected' sequence.
</p>
<p>
The detailed correspondence is shown in the tables given in
<a href="chapter6-d.html#chars.letter-like-tables">Section 6.3.6 Mathematical Alphanumeric Symbols</a>.
</p>
<p>
Mathematical Alphanumeric Symbol characters should not be used for styled text.
For example, Mathematical Fraktur A must not be used to just select
a blackletter font for an uppercase A. Doing this sort of thing
would create problems for searching, restyling (e.g. for accessibility),
and many other kinds of processing.
</p>
</div>
<div class="div3">
<h3><a name="chars.nonmark" id="chars.nonmark"></a>6.2.4 Non-Marking Characters
</h3>
<p>
Some characters, although important for the quality of print or
alternative rendering, do not have glyph marks that correspond
directly <span class="diff-add">to them<a href="appendixj-d.html#d0e55636"><sub class="diff-link">J</sub></a></span>. They are called here non-marking characters.<span class="diff-del">Below we have
a table of those adopted for the purposes of MathML.<a href="appendixj-d.html#d0e55636"><sub class="diff-link">J</sub></a></span>
Their roles are
discussed in <a href="chapter3-d.html">Chapter 3 Presentation Markup</a> and <a href="chapter4-d.html">Chapter 4 Content Markup</a><span class="diff-del">,
respectively. The values of the spaces given are
recommendations. Some of these characters are among those with new
Unicode values, and some are given as combinations of Unicode
characters employing the new special mathematics modifier character
(U0FE00). The correspondence between the spacing amounts mentioned
below and those in the Unicode descriptions is not exact, but the
matches are good<a href="appendixj-d.html#d0e55636"><sub class="diff-link">J</sub></a></span>.
</p>
<p>In MathML 2 control of page composition, such as line-breaking, is
effected by the use of the proper attributes on the <code>mspace</code> element.
</p>
<div class="diff-chg">
<p>The characters below are not simple spacers. They are
especially important new additions to the UCS because they provide
textual clues which can increase the quality of print rendering,
permit correct audio rendering, and allow the unique recovery of
mathematical semantics from text which is visually ambiguous.
</p><a href="appendixj-d.html#d0e55636"><sub class="diff-link">J</sub></a></div>
<table id="chars.table-white">
<thead>
<tr>
<th rowspan="1" colspan="1">Character name</th>
<th rowspan="1" colspan="1">Unicode</th>
<th rowspan="1" colspan="1">Description</th>
</tr>
</thead>
<tbody>
<tr class="diff-del">
<td rowspan="1" colspan="1"><code>&Tab;</code></td>
<td rowspan="1" colspan="1">00009</td>
<td rowspan="1" colspan="1">tabulator stop; horizontal tabulation</td>
</tr>
<tr class="diff-del">
<td rowspan="1" colspan="1"><code>&NewLine;</code></td>
<td rowspan="1" colspan="1">0000A</td>
<td rowspan="1" colspan="1">force a line break; line feed</td>
</tr>
<tr class="diff-del">
<td rowspan="1" colspan="1"><code>&Space;</code></td>
<td rowspan="1" colspan="1">00020</td>
<td rowspan="1" colspan="1">one em of space in the current font</td>
</tr>
<tr class="diff-del">
<td rowspan="1" colspan="1"><code>&NonBreakingSpace;</code></td>
<td rowspan="1" colspan="1">000A0</td>
<td rowspan="1" colspan="1">space that is not a legal breakpoint</td>
</tr>
<tr class="diff-del">
<td rowspan="1" colspan="1"><code>&ZeroWidthSpace;</code></td>
<td rowspan="1" colspan="1">0200B</td>
<td rowspan="1" colspan="1">space of no width at all</td>
</tr>
<tr class="diff-del">
<td rowspan="1" colspan="1"><code>&VeryThinSpace;</code></td>
<td rowspan="1" colspan="1">0200A</td>
<td rowspan="1" colspan="1">space of width 1/18 em</td>
</tr>
<tr class="diff-del">
<td rowspan="1" colspan="1"><code>&ThinSpace;</code></td>
<td rowspan="1" colspan="1">02009</td>
<td rowspan="1" colspan="1">space of width 3/18 em</td>
</tr>
<tr class="diff-del">
<td rowspan="1" colspan="1"><code>&MediumSpace;</code></td>
<td rowspan="1" colspan="1">02005</td>
<td rowspan="1" colspan="1">space of width 4/18 em</td>
</tr>
<tr class="diff-del">
<td rowspan="1" colspan="1"><code>&ThickSpace;</code></td>
<td rowspan="1" colspan="1">02009-0200A-0200A</td>
<td rowspan="1" colspan="1">space of width 5/18 em</td>
</tr>
<tr class="diff-del">
<td rowspan="1" colspan="1"><code>&NegativeVeryThinSpace;</code></td>
<td rowspan="1" colspan="1">0200A-0FE00</td>
<td rowspan="1" colspan="1">space of width -1/18 em</td>
</tr>
<tr class="diff-del">
<td rowspan="1" colspan="1"><code>&NegativeThinSpace;</code></td>
<td rowspan="1" colspan="1">02009-0FE00</td>
<td rowspan="1" colspan="1">space of width -3/18 em</td>
</tr>
<tr class="diff-del">
<td rowspan="1" colspan="1"><code>&NegativeMediumSpace;</code></td>
<td rowspan="1" colspan="1">0205F-0FE00</td>
<td rowspan="1" colspan="1">space of width -4/18 em</td>
</tr>
<tr class="diff-del">
<td rowspan="1" colspan="1"><code>&NegativeThickSpace;</code></td>
<td rowspan="1" colspan="1">02005-0FE00</td>
<td rowspan="1" colspan="1">space of width -5/18 em</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><code>&InvisibleTimes;</code></td>
<td rowspan="1" colspan="1">02062</td>
<td rowspan="1" colspan="1">marks multiplication when it is understood without a mark
(<a href="chapter3-d.html#presm.mo">Section 3.2.5 Operator, Fence, Separator or Accent
(mo)</a></td>
</tr>
<tr>
<td rowspan="1" colspan="1"><code>&InvisibleComma;</code></td>
<td rowspan="1" colspan="1">02063</td>
<td rowspan="1" colspan="1">used as a separator, e.g., in indices (<a href="chapter3-d.html#presm.mo">Section 3.2.5 Operator, Fence, Separator or Accent
(mo)</a></td>
</tr>
<tr>
<td rowspan="1" colspan="1"><code>&ApplyFunction;</code></td>
<td rowspan="1" colspan="1">02061</td>
<td rowspan="1" colspan="1">character showing function application in presentation tagging
(<a href="chapter3-d.html#presm.mo">Section 3.2.5 Operator, Fence, Separator or Accent
(mo)</a></td>
</tr>
</tbody>
</table>
</div>
</div>
<div class="div2">
<h2><a name="id.6.3" id="id.6.3"></a>6.3 Character Symbol Listings
</h2>
<p>The Universal Character Set (UCS) of Unicode and ISO 10646
continues to evolve, see <a href="chapter6-d.html#chars.char-status">Section 6.4.4 Status of Character Encodings</a>.
<span class="diff-add">At the time of writing the standard is Unicode 4.0.<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span>
<span class="diff-del">A small
number of the changes recently introduced, relative to those resulting
from the needs of Asian languages, are those designed exactly to
facilitate the use of Unicode by the 'equation-writing' community.
This specification is written on the assumption that the code
assignments suggested to ISO/IEC JTC1/SC2/WG2 by the UTC will be
confirmed as they are in public draft forms of Unicode 3.1 and 3.2.<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span>
<span class="diff-chg">As before, we can only reiterate that for latest developments on
details of character standards as far as they influence mathematical
formalism the <a href="http://www.w3.org/Math/">home page of the
W3C Math Activity</a> should be consulted.<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span></p>
<p>The characters are given with entity names as well as Unicode
numbers. To facilitate comprehension of a fairly large list of names,
which totals over 2000 in this case, we offer more than one way to find
to a given character. A corresponding full set of entity declarations
is in the DTD in <a href="appendixa-d.html">Appendix A Parsing MathML</a>. For discussion of entity
declarations see that appendix.
</p>
<p>
The characters are listed by name, and sample glyphs provided for all
of them. Each character name is accompanied by a code for a character
grouping chosen from a list given below, a short verbal description,
and a Unicode hex code drawn from ISO 10646<span class="diff-del">, now extended in
accordance with the proposal forwarded by the UTC to ISO/IEC WG2 in
March 2000<a href="appendixj-d.html#d0e55629"><sub class="diff-link">J</sub></a></span>.
</p>
<p>The character listings by alphabetical and Unicode order in
<a href="chapter6-d.html#chars.entity.tables">Section 6.3.7 MathML Character Names</a> are in harmony with the ISO
character sets given, in that if some part of a set is included then
the entire set is included.
</p>
<div class="div3">
<h3><a name="chars.special" id="chars.special"></a>6.3.1 Special Constants
</h3>
<p> To begin we list separately a few of the special characters which
MathML has introduced. These <span class="diff-chg">now have<a href="appendixj-d.html#d0e55641"><sub class="diff-link">J</sub></a></span>
Unicode values. Rather like the non-marking <span class="diff-chg">characters<a href="appendixj-d.html#d0e55641"><sub class="diff-link">J</sub></a></span> above, they provide very useful
capabilities in the context of machinable mathematics.<span class="diff-del"> It might be
imagined there could also be entries below for <code>&true;</code>, <code>&false;</code> and <code>&NotANumber;</code>, but these do not yet have Unicode
points assigned. They can be introduced by the character extension
mechanisms provided by the <code>mglyph</code> and <code>csymbol</code> elements.<a href="appendixj-d.html#d0e55641"><sub class="diff-link">J</sub></a></span>
</p>
<table>
<thead>
<tr>
<th rowspan="1" colspan="1">Entity name</th>
<th rowspan="1" colspan="1">Unicode</th>
<th rowspan="1" colspan="1">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="1" colspan="1"><code>&CapitalDifferentialD;</code></td>
<td rowspan="1" colspan="1">02145</td>
<td rowspan="1" colspan="1">D for use in differentials, e.g. within integrals</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><code>&DifferentialD;</code></td>
<td rowspan="1" colspan="1">02146</td>
<td rowspan="1" colspan="1">d for use in differentials, e.g. within integrals</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><code>&ExponentialE;</code></td>
<td rowspan="1" colspan="1">02147</td>
<td rowspan="1" colspan="1">e for use for the exponential base of the natural logarithms</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><code>&ImaginaryI;</code></td>
<td rowspan="1" colspan="1">02148</td>
<td rowspan="1" colspan="1">i for use as a square root of -1</td>
</tr>
</tbody>
</table>
</div>
<div class="div3">
<h3><a name="chars.byxxx" id="chars.byxxx"></a>6.3.2 Character Tables (ASCII format)
</h3>
<p>The first table offered is a very large ASCII listing of characters
considered particularly relevant to mathematics. This is given in
<span class="diff-chg"><a href="bycodes-d.html">Unicode order</a><a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>.
Most, but not all, of these characters have MathML names
defined via entity declarations in the DTD. Those that do not are
usually symbols which seem mathematically peripheral, such as dingbats,
machine graphics or technical symbols.
</p>
<p>
A second table lists those characters that do have MathML entity
names, <a href="byalpha-d.html">ordered alphabetically</a>, with
a lower-case letter preceding its upper-case counterpart.
</p>
</div>
<div class="div3">
<h3><a name="chars.16x16-tables" id="chars.16x16-tables"></a>6.3.3 Tables arranged by Unicode block
</h3>
<p>
The tables in this section detail Unicode code points (displayed with
256 code points per table) that have mathematically significant
characters. The sample glyph images link to the <a href="bycodes-d.html">table of characters ordered by Unicode</a> given
in the previous section.<span class="diff-del"> As shown in the key for each table, the
status of each character (for example in Unicode 3.0 or in the
proposed additions) is indicated by a CSS class on the table cell
(which by default is indicated by varying the background color).<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> The
names of the blocks are those of the Unicode blocks included in the
numerical range given; bracketing indicates <span class="diff-add">glyphs
for<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> characters of that type are not shown in these tables.
</p>
<table id="chars.table-unicode-block">
<thead>
<tr>
<th rowspan="1" colspan="1">Block Range</th>
<th rowspan="1" colspan="1">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="1" colspan="1"><a href="000-d.html">00000 - 000FF</a></td>
<td rowspan="1" colspan="1">Controls and Basic Latin, and Latin-1 Supplement</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="001-d.html">00100 - 001FF</a></td>
<td rowspan="1" colspan="1">Latin Extended-A, Latin Extended-B</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="002-d.html">00200 - 002FF</a></td>
<td rowspan="1" colspan="1">IPA Extensions, Spacing Modifier Letters</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="003-d.html">00300 - 003FF</a></td>
<td rowspan="1" colspan="1">Combining Diacritical Marks, Greek [and Coptic]
</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="004-d.html">00400 - 004FF</a></td>
<td rowspan="1" colspan="1">Cyrillic</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="020-d.html">02000 - 020FF</a></td>
<td rowspan="1" colspan="1">General Punctuation, Superscripts and Subscripts, Currency Symbols,
Combining Diacritical Marks for Symbols
</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="021-d.html">02100 - 021FF</a></td>
<td rowspan="1" colspan="1">Letter-like Symbols, Number Forms, Arrows</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="022-d.html">02200 - 022FF</a></td>
<td rowspan="1" colspan="1">Mathematical Operators</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="023-d.html">02300 - 023FF</a></td>
<td rowspan="1" colspan="1">Miscellaneous
Technical
</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="024-d.html">02400 - 024FF</a></td>
<td rowspan="1" colspan="1">Control Pictures, Optical Character Recognition, Enclosed Alphanumerics</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="025-d.html">02500 - 025FF</a></td>
<td rowspan="1" colspan="1">Box Drawing, Block Elements, Geometric Shapes</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="026-d.html">02600 - 026FF</a></td>
<td rowspan="1" colspan="1">Miscellaneous Symbols </td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="027-d.html">02700 - 027FF</a></td>
<td rowspan="1" colspan="1">Dingbats</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="029-d.html">02900 - 029FF</a></td>
<td rowspan="1" colspan="1">Supplemental Arrows, Miscellaneous Mathematical Symbols</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="02A-d.html">02A00 - 02AFF</a></td>
<td rowspan="1" colspan="1">Supplemental Mathematical Operators</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="030-d.html">03000 - 030FF</a></td>
<td rowspan="1" colspan="1">CJK Symbols and Punctuation, [Hiragana, Katakana]</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="0FB-d.html">0FB00 - 0FBFF</a></td>
<td rowspan="1" colspan="1">Alphabetic Presentation Forms </td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="0FE-d.html">0FE00 - 0FEFF</a></td>
<td rowspan="1" colspan="1">[Combining Half Marks, CJK Compatibility Forms, Small Form Variants,
Arabic Presentation Forms-B]
</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="1D4-d.html">1D400 - 1D4FF</a></td>
<td rowspan="1" colspan="1">Mathematical Styled Latin (Bold, Italic, Bold Italic, Script,
Bold Script begins)
</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="1D5-d.html">1D500 - 1D5FF</a></td>
<td rowspan="1" colspan="1">Mathematical Styled Latin (Bold Script ends, Fraktur, Double-struck,
Bold Fraktur, Sans-serif, Sans-serif Bold begins)
</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="1D6-d.html">1D600 - 1D6FF</a></td>
<td rowspan="1" colspan="1">Mathematical Styled Latin (Sans-serif Bold ends, Sans-serif Italic,
Sans-serif Bold Italic, Monospace, Bold), Mathematical Styled Greek (Bold, Italic begins)
</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="1D7-d.html">1D700 - 1D7FF</a></td>
<td rowspan="1" colspan="1">Mathematical Styled Greek (Italic continued, Bold Italic,
Sans-serif Bold), Mathematical Styled Digits
</td>
</tr>
</tbody>
</table>
</div>
<div class="div3">
<h3><a name="chars.math-negated-tables" id="chars.math-negated-tables"></a>6.3.4 Negated
Mathematical Characters
</h3>
<p>
In addition to the Unicode Characters so far listed, one may use the
combining characters <span class="diff-chg">U+0338<a href="appendixj-d.html#d0e55646"><sub class="diff-link">J</sub></a></span> (/),
<span class="diff-chg">U+20D2<a href="appendixj-d.html#d0e55646"><sub class="diff-link">J</sub></a></span> (|) and <span class="diff-chg">U+20E5<a href="appendixj-d.html#d0e55646"><sub class="diff-link">J</sub></a></span> (\) to produce
negated or <span class="diff-chg">canceled<a href="appendixj-d.html#d0e55646"><sub class="diff-link">J</sub></a></span> 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.
</p>
<p>
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 <span class="diff-chg">U+003D+00338<a href="appendixj-d.html#d0e55646"><sub class="diff-link">J</sub></a></span> which amounts to
<span class="diff-chg">U+2260<a href="appendixj-d.html#d0e55646"><sub class="diff-link">J</sub></a></span>, or it does not as is the
case for <span class="diff-chg">U+2202+0338<a href="appendixj-d.html#d0e55646"><sub class="diff-link">J</sub></a></span>. The common cases of
negations, <span class="diff-chg">of the latter type<a href="appendixj-d.html#d0e55646"><sub class="diff-link">J</sub></a></span>,
that have been identified are listed in the table
</p>
<ul>
<li>
<p><a href="cancellations-d.html">cancellations</a></p>
</li>
</ul>
<p>
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.
<span class="diff-add">For further information on these matters see
the Unicode Standard Annex 15, Unicode Normalization Forms
<a href="appendixk-d.html#UAX15">[UAX15]</a>, especially
the discussion of Normalization Form C.<a href="appendixj-d.html#d0e55646"><sub class="diff-link">J</sub></a></span>
</p>
</div>
<div class="div3">
<h3><a name="chars.math-variant-tables" id="chars.math-variant-tables"></a>6.3.5 Variant
Mathematical Characters
</h3>
<p>
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 <span class="diff-chg">in<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>
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.
</p>
<ul>
<li>
<p><a href="variants-d.html">variants</a></p>
</li>
</ul>
</div>
<div class="div3">
<h3><a name="chars.letter-like-tables" id="chars.letter-like-tables"></a>6.3.6 Mathematical Alphanumeric Symbols
</h3>
<p>
Here we list the special mathematical alphabets. Note that the names
for these alphabetic runs should be regarded as conventions resulting
from recent tradition in the typesetting of mathematical formulas,
rather than as fixing exactly and forever the styles which are to be
used. Of course, they do correspond to the styles presently most
common. But, for instance, there may be font variations in the glyphs
from double-struck, open-face or blackboard bold fonts, all of which
would naturally be used for the characters in the range here labelled
Double-struck. Similar considerations would apply to appellations
such as fraktur and gothic, or script and calligraphic.
</p>
<p>
As discussed above, the use of these characters is formally equivalent
to the use of characters in Plane 0, together with a suitable value
for the <code>mathvariant</code> attribute. The
correspondence is given in the character tables. Most of these
characters come from the <span class="diff-del">proposed<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> additions to Plane 1, however a few
characters (such as the double-struck letters N, P, Z, Q, R, C, H
representing common number sets) were already present in Unicode 3.0
and retain their original positions. These characters are highlighted
in the tables.
</p>
<ul>
<li>
<p><a href="bold-d.html">Bold</a></p>
</li>
<li>
<p><a href="italic-d.html">Italic</a></p>
</li>
<li>
<p><a href="bold-italic-d.html">Bold Italic</a></p>
</li>
<li>
<p><a href="double-struck-d.html">Double-struck</a></p>
</li>
<li>
<p><a href="script-d.html">Script</a></p>
</li>
<li>
<p><a href="bold-script-d.html">Bold Script</a></p>
</li>
<li>
<p><a href="fraktur-d.html">Fraktur</a></p>
</li>
<li>
<p><a href="bold-fraktur-d.html">Bold Fraktur</a></p>
</li>
<li>
<p><a href="sans-serif-d.html">Sans-serif</a></p>
</li>
<li>
<p><a href="bold-sans-serif-d.html">Bold Sans-serif</a></p>
</li>
<li>
<p><a href="sans-serif-italic-d.html">Sans-serif Italic</a></p>
</li>
<li>
<p><a href="sans-serif-bold-italic-d.html">Sans-serif Bold Italic</a></p>
</li>
<li>
<p><a href="monospace-d.html">Monospace</a></p>
</li>
</ul>
</div>
<div class="div3">
<h3><a name="chars.entity.tables" id="chars.entity.tables"></a>6.3.7 MathML Character Names
</h3>
<p>
This section corresponds closely with the entity definitions in the DTD
described in <a href="appendixa-d.html">Appendix A Parsing MathML</a>. All of the entity sets except the
last correspond to entity sets defined by ISO 8879 or ISO 9573-13.
</p>
<table>
<thead>
<tr>
<th rowspan="1" colspan="1">ISO Handle</th>
<th rowspan="1" colspan="1">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td rowspan="1" colspan="1"><a href="isoamsa-d.html">ISOAMSA</a></td>
<td rowspan="1" colspan="1"> Added Mathematical Symbols: Arrows</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="isoamsb-d.html">ISOAMSB</a></td>
<td rowspan="1" colspan="1">Added Mathematical Symbols: Binary Operators</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="isoamsc-d.html">ISOAMSC</a></td>
<td rowspan="1" colspan="1">Added Mathematical Symbols: Delimiters</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="isoamsn-d.html">ISOAMSN</a></td>
<td rowspan="1" colspan="1">Added Mathematical Symbols: Negated Relations</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="isoamso-d.html">ISOAMSO</a></td>
<td rowspan="1" colspan="1">Added Mathematical Symbols: Ordinary</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="isoamsr-d.html">ISOAMSR</a></td>
<td rowspan="1" colspan="1">Added Mathematical Symbols: Relations</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="isobox-d.html">ISOBOX</a></td>
<td rowspan="1" colspan="1">Box and Line Drawing</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="isocyr1-d.html">ISOCYR1</a></td>
<td rowspan="1" colspan="1">Cyrillic-1</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="isocyr2-d.html">ISOCYR2</a></td>
<td rowspan="1" colspan="1">Cyrillic-2</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="isodia-d.html">ISODIA</a></td>
<td rowspan="1" colspan="1">Diacritical Marks</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="isogrk3-d.html">ISOGRK3</a></td>
<td rowspan="1" colspan="1">Greek-3</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="isolat1-d.html">ISOLAT1</a></td>
<td rowspan="1" colspan="1">Latin-1</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="isolat2-d.html">ISOLAT2</a></td>
<td rowspan="1" colspan="1">Latin-2</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="isomfrk-d.html">ISOMFRK</a></td>
<td rowspan="1" colspan="1">Mathematical Fraktur</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="isomopf-d.html">ISOMOPF</a></td>
<td rowspan="1" colspan="1">Mathematical Openface (Double-struck)</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="isomscr-d.html">ISOMSCR</a></td>
<td rowspan="1" colspan="1">Mathematical Script</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="isonum-d.html">ISONUM</a></td>
<td rowspan="1" colspan="1">Numeric and Special Graphic</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="isopub-d.html">ISOPUB</a></td>
<td rowspan="1" colspan="1">Publishing</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="isotech-d.html">ISOTECH</a></td>
<td rowspan="1" colspan="1">General Technical</td>
</tr>
<tr>
<td rowspan="1" colspan="1"><a href="mmlextra-d.html">MMLEXTRA</a></td>
<td rowspan="1" colspan="1">Extra Names added by MathML</td>
</tr>
</tbody>
</table>
</div>
</div>
<div class="div2">
<h2><a name="id.6.4" id="id.6.4"></a>6.4 Differences from Characters in MathML 1
</h2>
<div class="div3">
<h3><a name="id.6.4.1" id="id.6.4.1"></a>6.4.1 Coverage
</h3>
<p>
We have excluded a very few other characters that may have appeared in
the corresponding lists in MathML 1. Those characters thus
<em>lost</em> will be found to be used very infrequently in the
experience of mathematical publishers, or simply to be completely
unacceptable for inclusion in Unicode. However MathML 2 does provide
the <code>mglyph</code> element to accommodate new
characters that authors may wish to introduce.
</p>
</div>
<div class="div3">
<h3><a name="id.6.4.2" id="id.6.4.2"></a>6.4.2 Fewer Non-marking Characters
</h3>
<p>It used to be in MathML 1.0 that there were a number more
non-marking character entities listed. These were concerned with
composition control, such as line-breaking. In MathML 2 such control
is effected by the use of the proper attributes on the <code>mspace</code> element.
</p>
</div>
<div class="div3">
<h3><a name="id.6.4.3" id="id.6.4.3"></a>6.4.3 ISO Tables
</h3>
<p>
The character listings by alphabetical and Unicode order in <a href="chapter6-d.html#chars.entity.tables">Section 6.3.7 MathML Character Names</a> have now been brought more into line with
the corresponding ISO character sets than was the case in MathML 1.0,
in that if some part of a set is included then the entire set is
included. In addition, the group ISOCHEM has been dropped as more
properly the concern of chemists. All the ISO mathematical alphabets
are listed, since there are now Unicode characters to point to,
in particular the bold Greek of ISOGRK3. These changes have also been
reflected in the entity declarations in the DTD in <a href="appendixa-d.html">Appendix A Parsing MathML</a>.
</p>
</div>
<div class="div3">
<h3><a name="chars.char-status" id="chars.char-status"></a>6.4.4 Status of Character Encodings
</h3>
<p>A significant change
<span class="diff-chg">after MathML 1.0 occurred in<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> the movement toward
adoption of more characters for mathematics in the UCS
and availability of public fonts for mathematics. The
encoding of characters in the UCS is done
jointly by the Unicode Technical Committee and by ISO/IEC
JTC1/SC2/WG2. The process of encoding takes quite some time from the
deliberation of first proposals to the final approval.
The characters mentioned in this chapter and listed in the associated
tables <span class="diff-chg">have been though the<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> various stages
of this approval process.<span class="diff-del"> This section
gives detailed information about the stages relevant to this
specification and gives an overview of the characters affected. The
lists, as well as other places that discuss characters, mention
any cases when
characters are not fully approved or show this graphically.
Updates on the status of the characters will be provided by updates
to this specification, by errata to this
specification, and by notices on the
<a href="http://www.w3.org/Math/">W3C Math home page</a>.
The final word on all Unicode matters is naturally to be found
at <a href="http://www.unicode.org/">the Unicode Consortium</a>.<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span></p>
<p>
<span class="diff-chg">At the time of the preparation of the MathML 2.0
specification <span class="diff-add"><a href="appendixk-d.html#MathML2">[MathML2]</a><a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> the characters relevant to mathematics fell <a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>
into three categories:
<span class="diff-chg">fully<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> accepted characters, characters in final (JTC1) ISO/IEC ballot,
and characters before the final ISO/IEC ballot.
</p>
<ul>
<li>
<p>
Fully accepted characters <span class="diff-chg">included <a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span>a large number of Latin, Greek, and
Cyrillic letters, a large number of Mathematical Operators and
symbols, including arrows, and so on. Fully accepted characters
<span class="diff-chg">were<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> exactly those that are
<span class="diff-chg">in<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> both Unicode 3.0 <a href="appendixk-d.html#Unicode">[Unicode]</a> and ISO/IEC 10646-1:2000 <a href="appendixk-d.html#ISOIEC10646-1">[ISOIEC10646-1]</a>, which are identical code point by code point.
<span class="diff-del">Fully
accepted characters are not specially marked or mentioned in this
specification; they do not pose any unusual implementation problems
other than possibly finding fonts to display them<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> Those of obvious
special interest to mathematics <span class="diff-chg">numbered<a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></span> over
1,500, depending on how you count.
</p>
</li>
<li>
<div class="diff-chg">
<p>
In April 2001, the Mathematical Alphanumeric Symbols came up for a final ballot
together with a large number of ideographs and other
characters not directly relevant for mathematics. There were just
about 1,000 of these. The additions were published as ISO/IEC 10646-2,
and became part of Unicode 3.1.
</p><a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></div>
<div class="diff-del">
<p>
While acceptance of this ballot seems more likely than rejection,
implementers and users of MathML have to be aware that until the final
acceptance, they are using the code points of characters in final
ballot at their own risk. Entities (see <a href="chapter6-d.html#chars.entity.tables">Section 6.3.7 MathML Character Names</a>) and the <code>mathvariant</code> attribute (see <a href="chapter3-d.html#presm.commatt">Section 3.2.2 Mathematics style attributes common to token
elements</a>) can be used to avoid that risk.
</p><a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></div>
</li>
<li>
<div class="diff-chg">
<p>
Characters relevant to MathML that were before final ballot made up a long list
of operators and symbols, including some special constants and
non-marking characters (see <a href="chapter6-d.html#chars.nonmark">Section 6.2.4 Non-Marking Characters</a> and
<a href="chapter6-d.html#chars.special">Section 6.3.1 Special Constants</a>). They numbered about 590 in all.
With some small technical improvements and compromises the proposed additions
accepted were published as an amendment to [ISO/IEC
10646-1], and became part of Unicode 3.2.
</p><a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></div>
<div class="diff-chg">
<p>
Even with the good will shown to the mathematical community by the
Unicode process a small number of characters of special interest
to some may not yet have been included. The obvious solution of
avoiding their use may not satisfy all. For these characters the
Unicode mechanism involving Private Use Area codes could be deployed,
in spite of all the dangers of confusion and collisions of conventions
this brings with it. However, this is the situation for which
<a href="chapter3-d.html#presm.mglyph"><code>mglyph</code></a>
was introduced. The use of <a href="chapter3-d.html#presm.mglyph"><code>mglyph</code></a>
is recommended to refer to symbols not included in Unicode.
</p><a href="appendixj-d.html#d0e55651"><sub class="diff-link">J</sub></a></div>
</li>
</ul>
</div>
</div>
</div>
<div class="minitoc">
Overview: <a href="overview-d.html">Mathematical Markup Language (MathML) Version 2.0 (Second Edition)</a><br>
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