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      <h1>
         <a id="changes">

         </a>J Changes (Non-Normative)</h1><!-- TOP NAVIGATION BAR -->
      <div class="minitoc">

  Overview: <a href="overview.xml">Mathematical Markup Language (MathML) Version 2.0 (2nd Edition)
</a>
         <br class="html-compat"/>
  Previous: I <a href="appendixi.xml">Working Group Membership and Acknowledgments</a>
         <br class="html-compat"/>
  Next: K <a href="appendixk.xml">References</a>
         <br class="html-compat"/>
         <br class="html-compat"/>J <a href="appendixj.xml">Changes (Non-Normative)</a>
         <br class="html-compat"/>    J.1 <a href="appendixj.xml#changes.mathml2.0-2.02e">Changes between MathML 2.0 and MathML 2.0 2nd Edition</a>
         <br class="html-compat"/>    J.2 <a href="appendixj.xml#changes.mathml1.01-2.0">Changes between MathML 1.01 and MathML 2.0</a>
         <br class="html-compat"/>
      </div>
      <div class="div1">
         <div class="div2">

            <h2>
               <a id="changes.mathml2.0-2.02e">

               </a>J.1 Changes between MathML 2.0 and MathML 2.0 2nd Edition</h2>
            <ul>
               <li>
                  <p>Changes to <a href="overview.xml#status">
                        <b>Status</b>
                     </a>.</p>
                  <ul>
                     <li>
                        <a id="d0e51800">

                        </a>
                        <p>New text in <a href="overview.xml#status">
                              <b>Status</b>
                           </a>.</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>Changes to <a href="chapter2.xml#fund.overview">
                        <b>2.1 MathML Overview</b>
                     </a>.</p>
                  <ul>
                     <li>
                        <a id="d0e51811">

                        </a>
                        <p>Modify description of entity usage in <a href="chapter2.xml#fund.pres">
                              <b>2.3.1 Presentation Examples</b>
                           </a>.</p>
                     </li>
                     <li>
                        <a id="d0e51816">

                        </a>
                        <p>Correct the MathML and default rendering of quatratic
formula example in <a href="chapter2.xml#fund.cont">
                              <b>2.3.2 Content Examples</b>
                           </a>.</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>Changes to <a href="chapter3.xml">
                        <b>3 Presentation Markup</b>
                     </a>.</p>
                  <ul>
                     <li>
                        <a id="d0e51827">

                        </a>
                        <p>Delete references to Negative Space Characters in <a href="chapter3.xml#presm.mtext">
                              <b>3.2.6 Text (mtext)</b>
                           </a> and <a href="chapter3.xml#presm.mstyle">
                              <b>3.3.4 Style Change (mstyle)</b>
                           </a>.</p>
                     </li>
                     <li>
                        <a id="d0e51834">

                        </a>
                        <p>The example in<a href="chapter3.xml#presm.menclose">
                              <b>3.3.9 Enclose Expression Inside Notation
  (menclose)</b>
                           </a>
  omitted units in the <code>columnspacing
</code> and <code>rowspacing
</code> attributes.</p>
                     </li>
                     <li>
                        <a id="d0e51845">

                        </a>
                        <p>Correct the example MathML in <a href="chapter3.xml#presm.malign">
                              <b>3.5.5 Alignment Markers</b>
                           </a>.</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>Changes to <a href="chapter4.xml">
                        <b>4 Content Markup</b>
                     </a>.</p>
                  <ul>
                     <li>
                        <a id="d0e51856">

                        </a>
                        <p>The descriptions of the "scientific, or e notation" (1.234e5) in
<a href="chapter4.xml#contm.typeattrib">
                              <b>4.3.2.9 
type</b>
                           </a>, <a href="chapter4.xml#contm.ci">
                              <b>4.4.1.2 Identifier (ci)</b>
                           </a> and
Appendices C and D became inconsistent in the final 
draft of MathML2. The older names float and floating-point remained, and the
description of type="e-notation" in Chapter 4 (but not Appendix C)
described its use with the example 1.234 e 5
 where e was used as a separator rather than the <code>sep
</code> element 
</p>
                     </li>
                     <li>
                        <a id="d0e51866">

                        </a>
                        <p>Correct the example MathML in <a href="chapter4.xml#contm.genatt">
                              <b>4.3.3.2 General Attributes</b>
                           </a>.</p>
                     </li>
                     <li>
                        <a id="d0e51871">

                        </a>
                        <p>Add note to <a href="chapter4.xml#contm.forall">
                              <b>4.4.3.17 Universal quantifier (forall)</b>
                           </a> observing that the mathematical expressions in the
examples are false.</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>Changes to <a href="chapter5.xml">
                        <b>5 Combining Presentation and Content Markup</b>
                     </a>.</p>
                  <ul>
                     <li>
                        <a id="d0e51882">

                        </a>
                        <p>Correct the complexity of parallel markup given in <a href="chapter5.xml#mixing.parallel">
                              <b>5.3 Parallel Markup</b>
                           </a> to O(n log n).</p>
                     </li>
                     <li>
                        <a id="d0e51887">

                        </a>
                        <p>Correct the example MathML in <a href="chapter5.xml#mixing.sheet">
                              <b>5.4.3 Style Sheets for Extensions</b>
                           </a>.</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>Changes to <a href="appendixa.xml">
                        <b>A Parsing MathML</b>
                     </a>.</p>
                  <ul>
                     <li>
                        <a id="d0e51898">

                        </a>
                        <p>New section, <a href="appendixa.xml#parsing.wellformed">
                              <b>A.1 Use of MathML as Well-Formed
XML</b>
                           </a> describing use without a DTD.</p>
                     </li>
                     <li>
                        <a id="d0e51903">

                        </a>
                        <p>The location of the MathML DTDs  described in <a href="appendixa.xml#parsing.doctype">
                              <b>A.2.1 DOCTYPE Declaration for MathML</b>
                           </a> and  <a href="appendixa.xml#parsing.module">
                              <b>A.2.3 MathML as a DTD Module</b>
                           </a> are now in the Math Working group area rather
than distributed with this Recommendation.</p>
                     </li>
                     <li>
                        <a id="d0e51910">

                        </a>
                        <p>New sections descriping parameterisation possibilities for
the DTD: <a href="appendixa.xml#parsing.dtd.prefix">
                              <b>A.2.2.1 Namespace Prefix</b>
                           </a>, <a href="appendixa.xml#parsing.dtd.plane1">
                              <b>A.2.2.2 Plane 1 Characters</b>
                           </a>
and <a href="appendixa.xml#parsing.dtd.strict">
                              <b>A.2.2.3 Additional DTD Checking</b>
                           </a>.</p>
                     </li>
                     <li>
                        <a id="d0e51919">

                        </a>
                        <p>The MathML DTD as shown in <a href="appendixa.xml#parsing.dtd">
                              <b>A.2.5 The MathML DTD</b>
                           </a>
Incorporates several corrections as listed in the MathML 2.0
Errata document.</p>
                     </li>
                     <li>
                        <a id="d0e51924">

                        </a>
                        <p>New section, <a href="appendixa.xml#parsing.usingxsd">
                              <b>A.3 Using the MathML XML Schema</b>
                           </a> describing the
use of the W3C XML Schema for MathML.</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>Changes to <a href="appendixb.xml">
                        <b>B Content Markup Validation Grammar</b>
                     </a>.</p>
                  <ul>
                     <li>
                        <a id="d0e51935">

                        </a>
                        <p>Many corrections, and new display format for the productions
given in the grammar for Content Markup in <a href="appendixb.xml">
                              <b>B Content Markup Validation Grammar</b>
                           </a>.</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>Changes to <a href="appendixc.xml">
                        <b>C Content Element Definitions</b>
                     </a>.</p>
                  <ul>
                     <li>
                        <a id="d0e51946">

                        </a>
                        <p>Many corrections to the MathML Examples in <a href="appendixc.xml#cedef.Token.Elements">
                              <b>C.2.1 Token Elements</b>
                           </a>.</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>Changes to <a href="appendixf.xml">
                        <b>F Operator Dictionary</b>
                     </a>.</p>
                  <ul>
                     <li>
                        <a id="d0e51957">

                        </a>
                        <p>Blank lines in <a href="appendixf.xml#oper-dict.entries">
                              <b>F.5 Operator dictionary entries</b>
                           </a> used in the inferred
mrow grouping algorithm were omitted. 
They have been restored based on the groupings in MathML 1.01.
</p>
                     </li>
                  </ul>
               </li>
            </ul>
         </div>
         <div class="div2">

            <h2>
               <a id="changes.mathml1.01-2.0">

               </a>J.2 Changes between MathML 1.01 and MathML 2.0</h2>
            <ul>
               <li>
                  <p>changes to <a href="chapter1.xml">
                        <b>1 Introduction</b>
                     </a> 

                  </p>
                  <ul>
                     <li>
                        <p>rewritten to reflect developments since publication of
the MathML 1.0 Recommendation, for example XML, XSL, CSS and schemas</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>changes to <a href="chapter2.xml">
                        <b>2 MathML Fundamentals</b>
                     </a>

                  </p>
                  <ul>
                     <li>
                        <p>rewritten to reflect developments since publication of
the MathML 1.0 Recommendation, for example XML, XSL, CSS and schemas</p>
                     </li>
                     <li>
                        <p>examples were rewritten to reflect good MathML 2.0 practice</p>
                     </li>
                     <li>
                        <p>descriptions of attribute values were updated to reflect
MathML 2.0</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>changes to <a href="chapter3.xml">
                        <b>3 Presentation Markup</b>
                     </a>

                  </p>
                  <ul>
                     <li>
                        <p>introduced a new section on bidirectional layout of
mathematics</p>
                     </li>
                     <li>
                        <p>introduced new mathematics style attributes
<code>mathvariant
</code>,
<code>mathsize
</code>,
<code>mathweight
</code>, and
<code>mathcolor
</code> on token elements, and deprecated the
use of
<code>fontfamily
</code>,
<code>fontsize
</code>,
<code>fontweight
</code>,
<code>fontstyle
</code> and
<code>color
</code>.
</p>
                     </li>
                     <li>
                        <p>introduced new elements <b>mglyph
</b>, <b>menclose
</b>
and <b>mlabeledtr
</b> and updated related text accordingly</p>
                     </li>
                     <li>
                        <p>added attributes <b>beveled
</b>, <b>numalign
</b> and
<b>denomalign
</b> to <b>mfrac
</b>
                        </p>
                     </li>
                     <li>
                        <p>added a linebreaking attribute to <b>mspace
</b>
                        </p>
                     </li>
                     <li>
                        <p>required <b>mtr
</b> and <b>mtd
</b> elements to be
explicit instead of allowing them to be inferred. </p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>changes to <a href="chapter4.xml">
                        <b>4 Content Markup</b>
                     </a>

                  </p>
                  <ul>
                     <li>
                        <p>deprecated the use of <b>reln
</b> and <b>fn
</b> and
changed the use of <b>apply
</b> accordingly</p>
                     </li>
                     <li>
                        <p>introduced <b>csymbol
</b> and added a discussion about the
relation to the deprecated <b>fn
</b> element</p>
                     </li>
                     <li>
                        <p>introduced new content elements
<b>domain
</b>,
<b>codomain
</b>,
<b>image
</b>,
<b>domainofapplication
</b>,
<b>arg
</b>,
<b>real
</b>,
<b>imaginary
</b>,
<b>lcm
</b>,
<b>floor
</b>,
<b>ceiling
</b>,
<b>equivalent
</b>,
<b>approx
</b>,
<b>divergence
</b>,
<b>grad
</b>,
<b>curl
</b>,
<b>laplacian
</b>,
<b>card
</b>,
<b>cartesianproduct
</b>,
<b>momentabout
</b>,
<b>vectorproduct
</b>,
<b>scalarproduct
</b>,
<b>outerproduct
</b>,
<b>integers
</b>,
<b>reals
</b>,
<b>rationals
</b>,
<b>naturalnumbers
</b>,
<b>complexes
</b>,
<b>primes
</b>,
<b>exponentiale
</b>,
<b>imaginaryi
</b>,
<b>notanumber
</b>,
<b>true
</b>,
<b>false
</b>,
<b>emptyset
</b>,
<b>pi
</b>,
<b>eulergamma
</b>,
<b>infinity
</b>,
<b>piecewise
</b>,
<b>piece
</b> and
<b>otherwise
</b>

                        </p>
                     </li>
                     <li>
                        <p>corrected examples and fixed typos</p>
                     </li>
                     <li>
                        <p>expanded the attribute <b>definitionURL
</b> to allow a URL
or a URI as a value</p>
                     </li>
                     <li>
                        <p>clarified the use of presentation markup inside
<b>cn
</b>
                        </p>
                     </li>
                     <li>
                        <p>made use of <b>encoding
</b> attribute more
uniform</p>
                     </li>
                     <li>
                        <p>changed description of the use of <b>bvar
</b> in
combination with <b>min
</b> and <b>max
</b>
                        </p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>changes to <a href="chapter5.xml">
                        <b>5 Combining Presentation and Content Markup</b>
                     </a>

                  </p>
                  <ul>
                     <li>
                        <p>added description of content-faithful transformation</p>
                     </li>
                     <li>
                        <p>updated examples to reflect MathML 2.0</p>
                     </li>
                     <li>
                        <p>define list of content that can appear in presentation</p>
                     </li>
                     <li>
                        <p>add attribute <b>xref
</b> for cross-referencing purposes</p>
                     </li>
                     <li>
                        <p>added examples using XLink and namespaces</p>
                     </li>
                     <li>
                        <p>make use of <b>encoding
</b> attribute more uniform</p>
                     </li>
                     <li>
                        <p>miscellaneous typographical corrections</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>changes to <a href="chapter6.xml">
                        <b>6 Characters, Entities and Fonts</b>
                     </a>

                  </p>
                  <ul>
                     <li>
                        <p>added a new section describing the methods of using Unicode
data within MathML</p>
                     </li>
                     <li>
                        <p>added a new section describing the correspondence between
Math Alphabet characters and the <code>mathvariant
</code>
attribute</p>
                     </li>
                     <li>
                        <p>completely revised and reformatted the MathML character
tables to reflect changes in Unicode since MathML 1.01</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>changes to <a href="chapter7.xml">
                        <b>7 The MathML Interface</b>
                     </a>

                  </p>
                  <ul>
                     <li>
                        <p>reworked the text in acknowledgement of the fact that the top-level and 
interface elements for MathML are now in practice the same</p>
                     </li>
                     <li>
                        <p>rewrote the text about linking to reflect changes in XLink
since MathML 1.01</p>
                     </li>
                     <li>
                        <p>revised material about interactions with embedded renderers to 
reflect the current state of DOM implementation</p>
                     </li>
                     <li>
                        <p>added a definition of deprecated features in MathML 2</p>
                     </li>
                     <li>
                        <p>updated the text to reflect the use of namespaces and the
introduction of XHTML.
2.0</p>
                     </li>
                     <li>
                        <p>added a new section on the appropriate use of CSS and the
new mathematics style attributes in rendering environments with
support CSS</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>changes to <a href="chapter8.xml">
                        <b>8 Document Object Model for MathML</b>
                     </a>

                  </p>
                  <ul>
                     <li>
                        <p>this is a completely new chapter</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>changes to <a href="appendixa.xml">
                        <b>A Parsing MathML</b>
                     </a>

                  </p>
                  <ul>
                     <li>
                        <p>renamed attribute <b>occurence
</b> to <b>occurrence
</b>
                        </p>
                     </li>
                     <li>
                        <p>added global attribute <b>xref
</b>
                        </p>
                     </li>
                     <li>
                        <p>add links to tables for each entity set</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>changes to <a href="appendixb.xml">
                        <b>B Content Markup Validation Grammar</b>
                     </a>

                  </p>
                  <ul>
                     <li>
                        <p>Updated to reflect MathML 2.0.</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>changes to <a href="appendixc.xml">
                        <b>C Content Element Definitions</b>
                     </a>

                  </p>
                  <ul>
                     <li>
                        <p>completely rewritten to reflect changes in MathML 2.0</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>changes to <a href="appendixf.xml">
                        <b>F Operator Dictionary</b>
                     </a>

                  </p>
                  <ul>
                     <li>
                        <p>entries in operator dictionary are parametrized</p>
                     </li>
                     <li>
                        <p>operator dictionary has become a non-normative part of the specification</p>
                     </li>
                     <li>
                        <p>new entries were added to operator dictionary</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>changes to <a href="appendixd.xml">
                        <b>D Document Object Model for MathML</b>
                     </a>

                  </p>
                  <ul>
                     <li>
                        <p>this is a completely new appendix, containing the IDL definitions 
</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>changes to <a href="appendixh.xml">
                        <b>H Glossary</b>
                     </a>

                  </p>
                  <ul>
                     <li>
                        <p>added entries for XSL, XSLT and XSL FO</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>changes to <a href="appendixi.xml">
                        <b>I Working Group Membership and Acknowledgments</b>
                     </a> 

                  </p>
                  <ul>
                     <li>
                        <p>all members of first and second Math Working Group are listed</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>changes to <a href="">
                        <b>J Changes</b>
                     </a>

                  </p>
                  <ul>
                     <li>
                        <p>completely new appendix, based on the logs obtained from CVS</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>changes to <a href="appendixk.xml">
                        <b>K References</b>
                     </a>

                  </p>
                  <ul>
                     <li>
                        <p>added and updated many entries</p>
                     </li>
                  </ul>
               </li>
               <li>
                  <p>general changes
</p>
                  <ul>
                     <li>
                        <p>text of specification now in XML form, with HTML and XHTML rendering by
means of XSLT, and PDF rendering by means of XSLT and T<sub>E</sub>X</p>
                     </li>
                     <li>
                        <p>fixed errors in spelling and notation</p>
                     </li>
                     <li>
                        <p>normative examples of formulas are images, with a LaT<sub>E</sub>X equivalent</p>
                     </li>
                     <li>
                        <p>non-normative examples of formulas are HTML constructions wherever possible</p>
                     </li>
                     <li>
                        <p>improved cross-referencing</p>
                     </li>
                  </ul>
               </li>
            </ul>
         </div>
      </div>
      <div class="minitoc">

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