# A Parsing MathML

Overview: Mathematical Markup Language (MathML) Version 2.0 (2nd Edition)
Previous: 8 Document Object Model for MathML
Next: B Content Markup Validation Grammar
A Parsing MathML
A.1 Use of MathML as Well-Formed XML
A.2 Using the MathML DTD
A.2.1 DOCTYPE Declaration for MathML
A.2.2 DTD Parameters
A.2.2.1 Namespace Prefix
A.2.2.2 Additional DTD Checking
A.2.3 MathML as a DTD Module
A.2.4 SGML
A.2.5 The MathML DTD
A.3 Using the MathML XML Schema
A.3.1 Associating the MathML Schema with MathML fragments
A.3.2 Character entity references

## A.1 Use of MathML as Well-Formed XML

A MathML document must be a well-formed XML documents using elements in the MathML namespace as defined by this specification, however it is not required that the document refer to any specific Document Type Definition or Schema that specifies MathML. It is sometimes advantagous not to specify such a language definition as these files are large, often much larger than the MathML expression and unless they have been previously cached by the MathML application, the time taken to fetch the DTD or schema may have an appreciable effect on the processing of the MathML document.

Note also that if no DTD is specified with a DOCTYPE declaration, that entity references (for example to refer to MathML characters by name) may not be used. The document should be encoded in an encoding (for example UTF-8) in which all needed characters may be encoded as character data, or characters may be referenced using numeric character references, for example &#x222B; rather than &int;

If a MathML fragment is parsed without a DTD, in other words as a well-formed XML fragment, it is the responsibility of the processing application to treat the white space characters occurring outside of token elements as not significant.

However, in many circumstances, especially while producing or editing MathML, it is useful to use a language definition, to constrain the editing process or to check the correctness of generated files. The following section, Section A.2 Using the MathML DTD, discusses the MathML DTD, which forms a normative part of the specification. Following that, Section A.3 Using the MathML XML Schema, discusses an alternative language definition using the W3C XML Schema language, [XMLSchemas]. One should note that the Schema definition of the language is currently stricter than the DTD version. That is, a Schema validating processor will declare invalid documents that are declared valid by a (DTD) validating XML parser. This is partly due to the fact that the XML Schema language may express additional constraints not expressable in the DTD, and partly due to the fact that for reasons of compatibility with earlier releases, the DTD is intentionally forgiving in some places and does not enforce constraints that are specified in the text of this specification.

J

## A.2 Using the MathML DTD

### A.2.1 DOCTYPE Declaration for MathML

MathML documents should be validated using the XML DTD for MathML, http://www.w3.org/Math/DTD/mathml2/mathml2.dtd J, which is also shown below in Section A.2.5 The MathML DTD.

Documents using this DTD should contain a doctype declaration of the form:

    <!DOCTYPE math
        PUBLIC "-//W3C//DTD MathML 2.0//EN"
               "http://www.w3.org/Math/DTD/mathml2/mathml2.dtd"
    >

J

The URI may be changed to that of a local copy of the DTD if required.

### A.2.2 DTD Parameters

The MathML DTD has several parameter entities that may be used to customise the behaviour of the XML parser. In the examples below these parameter entites are shown being used in the internal subset of the DTD, i.e. within `[]` inside the `<!DOCTYPE` declaration. If the MathML DTD is being used as a module in a larger document type, then these parameters entities may be set in the combined DTD and need not be explictly set in individual document instances. For example the combined XHTML + MathML DTD described below in Section A.2.3 MathML as a DTD Module sets each of these parameters to appropriate defaults.

#### A.2.2.1 Namespace Prefix

It is sometimes necessary, or convenient, to use the mechanisms described in [Modularization] which provide a namespace prefix on MathML element names. The DTD below is designed to allow this usage. If the parameter entity `MATHML.prefixed` is declared to be INCLUDE, using a declaration such as

    <!ENTITY % MATHML.prefixed "INCLUDE" >

either in the internal subset of the DOCTYPE declaration, or in the DTD file that is including the MathML DTD, then all MathML elements should be used with a prefix, for example `<m:mrow>`, `<m:apply>`, etc. The prefix defaults to `m` but another prefix may be declared by declaring in addition the parameter entity `MathML.prefix`. For example,

    <!ENTITY % MATHML.prefix   "mml" >

would set the prefix for the MathML namespace to `mml`.

So a complete declaration for a document using this prefix could be:

    <!DOCTYPE mml:math
        PUBLIC "-//W3C//DTD MathML 2.0//EN"
               "http://www.w3.org/Math/DTD/mathml2/mathml2.dtd" [
        <!ENTITY % MATHML.prefixed "INCLUDE">
        <!ENTITY % MATHML.prefix "mml">
    ]>
    <mml:math>
    ...

This use of parameter entities to control namespace prefixes follows the conventions specified in [Modularization].

In addition to the prefix for the MathML namespace, the DTD allows similar customization of other prefixes that may be used in attributes. The Xlink and W3C XML Schema Instance namespaces may be used with this DTD, with default prefixes `xlink` and `xsi` respectively. The entities `XLINK.prefix` and `Schema.prefix` may be set in the same way as `MATHML.prefix` above to use different prefixes. As these namespaces are used for attribute names, they must be used with explict prefixes, so there is no analogue of the `MATHML.prefixed` parameter in these cases. The following example uses the `s:schemaLocation` attribute (which is described below in Section A.3.1 Associating the MathML Schema with MathML fragments) with a non standard prefix, and uses a parameter entity in the internal subset of the DTD so that the file may be DTD valid as well as Schema valid.

    <!DOCTYPE math
        PUBLIC "-//W3C//DTD MathML 2.0//EN"
               "http://www.w3.org/Math/DTD/mathml2/mathml2.dtd" [
        <!ENTITY % Schema.prefix "s">
    ]>
    <math xmlns="http://www.w3.org/1998/Math/MathML"
          xmlns:s="http://www.w3.org/2001/XMLSchema-instance"
          s:schemaLocation="http://www.w3.org/1998/Math/MathML
                            http://www.w3.org/Math/XMLSchema/mathml2/mathml2.xsd">

    ...

Note that while the [Namespaces] Recommendation provides mechanisms to change the prefix at arbitrary points in the document, this flexibility is not provided in this DTD (and is probably not possible to specify in any DTD).

J

#### A.2.2.2 Additional DTD Checking

For reasons of backward compatibility, there are several constraints specified in this specification that are not enforced by the DTD by default. There are many constraints in the specification that may not be enforced by a DTD, however there are some additional constraints that could be checked. The parameter entity `MathMLStrict` may be set to `INCLUDE` to activate these stricter checks.

The syntax to set the parameter is as the same as for the previous examples:

    <!DOCTYPE math
        PUBLIC "-//W3C//DTD MathML 2.0//EN"
               "http://www.w3.org/Math/DTD/mathml2/mathml2.dtd" [
        <!ENTITY % MathMLstrict "INCLUDE">
    ]>

If this strict checking is enabled, the DTD will enforce that `mfrac` has exactly two child elements. Similarly for `msub`, `mover`, etc. The values of several attributes will be checked, for example the value of `mathvariant` is constrained to the list specified in Section 3.2.2 Mathematics style attributes common to token elements. The DTD will check that table makup, `mtr` and `mtd`, is only used correctly nested in `mtable`. Finally the use of Presentation MathML elements within Content MathML is restricted to those elements listed in section Section 5.2.3 Presentation Markup Contained in Content Markup.

J

### A.2.3 MathML as a DTD Module

Normally, however, a MathML expression does not constitute an entire XML document. MathML is designed to be used as the mathematics fragment of larger markup languages. In particular it is designed to be used as a module in documents marked up with the XHTML family of markup languages, as defined in [Modularization]. As a convenience, a version of the XHTML DTD, extended with this MathML module, is also provided as a concrete example. This version includes all the necessary declarations included into one file (in contrast to the standalone version of the MathML DTD which references several files for entity declarations etc.). To use this DTD, a document should contain the doctype declaration

    <!DOCTYPE html
        PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN"
               "http://www.w3.org/Math/DTD/mathml2/xhtml-math11-f.dtd"
    >

J

as above, the URI may be altered to that of a local copy of the DTD, and the namespace prefixes used for XHTML and MathML may be controlled by the use of parameter entities.

### A.2.4 SGML

If required, one may validate MathML documents using an SGML parser such as `nsgmls`, rather than a validating XML parser. In this case an SGML declaration defining the constraints of XML applicable to an SGML parser must be used. See [sgml-xml]J.

### A.2.5 The MathML DTD

The entity declarations for characters are referenced at the end of the DTD. These are linked to the character tables in Chapter 6 Characters, Entities and Fonts for each entity set.

Lists of the combined MathML set of character names, ordered by name or by Unicode value are also available.

In order to accommodate XML namespace prefixes, the DTD does not directly refer to an element name such as `mrow` but instead always refers to the name via a parameter entity such as `%mrow.qname;`. The definitions of these parameter entities are in the file but are not shown here. They are simply declarations such as the following, one for each MathML element.

    <!ENTITY % mrow.qname           "%MATHML.pfx;mrow" >

Here we give the main body of the DTD. The full DTD, as well as the XHTML-Math DTD, is available as a gzipped tar archive.

    <!-- MathML 2.0 DTD  ....................................................... -->
    <!-- file: mathml2.dtd
    -->

    <!-- MathML 2.0 DTD

         This is the Mathematical Markup Language (MathML) 2.0, an XML
         application for describing mathematical notation and capturing
         both its structure and content.

         Copyright &#xa9; 1998-2003 W3C&#xae; (MIT, ERCIM, Keio), All Rights
         Reserved. W3C liability, trademark, document use and software
         licensing rules apply.

         Permission to use, copy, modify and distribute the MathML 2.0 DTD and
         its accompanying documentation for any purpose and without fee is
         hereby granted in perpetuity, provided that the above copyright notice
         and this paragraph appear in all copies.  The copyright holders make
         no representation about the suitability of the DTD for any purpose.

         It is provided "as is" without expressed or implied warranty.

            Revision:   $Id: parsing.xml,v 1.68 2003/06/30 09:54:56 davidc Exp $

         This entity may be identified by the PUBLIC and SYSTEM identifiers:

           PUBLIC "-//W3C//DTD MathML 2.0//EN"
           SYSTEM "mathml2.dtd"

         Revisions: editor and revision history at EOF
    -->
    <!-- Entity used to enable marked sections which enforces stricterJ
         checking of MathML syntax rulesJ
    -->
    <!ENTITY % MathMLstrict "IGNORE">J

    <!-- MathML Qualified Names module ............................... -->
    <!ENTITY % mathml-qname.module "INCLUDE" >
    <![%mathml-qname.module;[
    <!ENTITY % mathml-qname.mod
         PUBLIC "-//W3C//ENTITIES MathML 2.0 Qualified Names 1.0//EN"
                "mathml2-qname-1.mod" >
    %mathml-qname.mod;]]>

    <!-- if %NS.prefixed; is INCLUDE, include all NS attributes,
         otherwise just those associated with MathML
    -->
    <![%NS.prefixed;[
      <!ENTITY % MATHML.NamespaceDecl.attrib
             "%NamespaceDecl.attrib;"
    >
    ]]>
    <!ENTITY % MATHML.NamespaceDecl.attrib
         "%MATHML.xmlns.attrib;"
    >

    <!-- Attributes shared by all elements  .......................... -->

    <!ENTITY % MATHML.Common.attrib
         "%MATHML.NamespaceDecl.attrib;
          %XLINK.prefix;:href   CDATA           #IMPLIEDJ
          %XLINK.prefix;:type   CDATA           #IMPLIEDJ
          class        CDATA                    #IMPLIED
          style        CDATA                    #IMPLIED
          id           ID                       #IMPLIED
          xref         IDREF                    #IMPLIED
          other        CDATA                    #IMPLIED"
    >

    <!-- Presentation element set  ................................... -->

    <!-- Attribute definitions -->

    <!ENTITY % att-fontsize
         "fontsize     CDATA                    #IMPLIED" >
    <!ENTITY % att-fontweight
         "fontweight   ( normal | bold )        #IMPLIED" >
    <!ENTITY % att-fontstyle
         "fontstyle    ( normal | italic )      #IMPLIED" >
    <!ENTITY % att-fontfamily
         "fontfamily   CDATA                    #IMPLIED" >
    <!ENTITY % att-color
         "color        CDATA                    #IMPLIED" >

    <!-- MathML2 typographically-distinguished symbol attributes -->

    <![%MathMLstrict;[
      <!ENTITY % att-mathvariant
         "mathvariant     ( normal | bold | italic | bold-italic | double-struck |
                            bold-fraktur | script | bold-script | fraktur |
                            sans-serif | bold-sans-serif | sans-serif-italic |
                            sans-serif-bold-italic | monospace )
                                                                       #IMPLIED" >
    ]]>J
    <!ENTITY % att-mathvariant
         "mathvariant     CDATA                    #IMPLIED" >
    <!ENTITY % att-mathsize
         "mathsize     CDATA                    #IMPLIED" >
    <!ENTITY % att-mathcolor
         "mathcolor     CDATA                    #IMPLIED" >
    <!ENTITY % att-mathbackground
         "mathbackground     CDATA                    #IMPLIED" >

    <!ENTITY % att-fontinfo
         "%att-fontsize;
          %att-fontweight;
          %att-fontstyle;
          %att-fontfamily;
          %att-color;
          %att-mathvariant;
          %att-mathsize;
          %att-mathcolor;
          %att-mathbackground;"
    >

    <!ENTITY % att-form
         "form         ( prefix | infix | postfix )  #IMPLIED" >
    <!ENTITY % att-fence
         "fence        ( true | false )         #IMPLIED" >
    <!ENTITY % att-separator
         "separator    ( true | false )         #IMPLIED" >
    <!ENTITY % att-lspace
         "lspace       CDATA                    #IMPLIED" >
    <!ENTITY % att-rspace
         "rspace       CDATA                    #IMPLIED" >
    <!ENTITY % att-stretchy
         "stretchy     ( true | false )         #IMPLIED" >
    <!ENTITY % att-symmetric
         "symmetric    ( true | false )         #IMPLIED" >
    <!ENTITY % att-maxsize
         "maxsize      CDATA                    #IMPLIED" >
    <!ENTITY % att-minsize
         "minsize      CDATA                    #IMPLIED" >
    <!ENTITY % att-largeop
         "largeop      ( true | false)          #IMPLIED" >
    <!ENTITY % att-movablelimits
         "movablelimits ( true | false )        #IMPLIED" >
    <!ENTITY % att-accent
         "accent       ( true | false )         #IMPLIED" >

    <!ENTITY % att-opinfo
         "%att-form;
          %att-fence;
          %att-separator;
          %att-lspace;
          %att-rspace;
          %att-stretchy;
          %att-symmetric;
          %att-maxsize;
          %att-minsize;
          %att-largeop;
          %att-movablelimits;
          %att-accent;"
    >
    <!ENTITY % att-width
         "width        CDATA                    #IMPLIED" >
    <!ENTITY % att-height
         "height       CDATA                    #IMPLIED" >
    <!ENTITY % att-depth
         "depth        CDATA                    #IMPLIED" >
    <!ENTITY % att-linebreak
         "linebreak    CDATA                    #IMPLIED" >
    <!ENTITY % att-sizeinfo
         "%att-width;
          %att-height;
          %att-depth;"
    >
    <!ENTITY % att-lquote
         "lquote       CDATA                    #IMPLIED" >
    <!ENTITY % att-rquote
         "rquote       CDATA                    #IMPLIED" >
    <!ENTITY % att-linethickness
         "linethickness CDATA                   #IMPLIED" >
    <!ENTITY % att-scriptlevel
         "scriptlevel  CDATA                    #IMPLIED" >
    <!ENTITY % att-displaystyle
         "displaystyle ( true | false )         #IMPLIED" >
    <!ENTITY % att-scriptsizemultiplier
         "scriptsizemultiplier CDATA            #IMPLIED" >
    <!ENTITY % att-scriptminsize
         "scriptminsize CDATA                   #IMPLIED" >
    <!ENTITY % att-background
         "background   CDATA                    #IMPLIED" >
    <!ENTITY % att-veryverythinmathspace
         "veryverythinmathspace   CDATA         #IMPLIED" >
    <!ENTITY % att-verythinmathspace
         "verythinmathspace   CDATA             #IMPLIED" >
    <!ENTITY % att-thinmathspace
         "thinmathspace   CDATA                 #IMPLIED" >
    <!ENTITY % att-mediummathspace
         "mediummathspace   CDATA               #IMPLIED" >
    <!ENTITY % att-thickmathspace
         "thickmathspace   CDATA                #IMPLIED" >
    <!ENTITY % att-verythickmathspace
         "verythickmathspace   CDATA            #IMPLIED" >
    <!ENTITY % att-veryverythickmathspace
         "veryverythickmathspace   CDATA        #IMPLIED" >
    <!ENTITY % att-open
         "open         CDATA                    #IMPLIED" >
    <!ENTITY % att-close
         "close        CDATA                    #IMPLIED" >
    <!ENTITY % att-separators
         "separators   CDATA                    #IMPLIED" >
    <!ENTITY % att-subscriptshift
         "subscriptshift CDATA                  #IMPLIED" >
    <!ENTITY % att-superscriptshift
         "superscriptshift CDATA                #IMPLIED" >
    <!ENTITY % att-accentunder
         "accentunder  ( true | false )         #IMPLIED" >
    <!ENTITY % att-align
         "align        CDATA                    #IMPLIED" >
    <![%MathMLstrict;[
      <!ENTITY % att-numalignJ
         "numalign     ( left | center | right )         #IMPLIED" >
      <!ENTITY % att-denomalign
         "denomalign   ( left | center | right )         #IMPLIED" >
    ]]>J
    <!ENTITY % att-numalignJ
         "numalign        CDATA                    #IMPLIED" >J
    <!ENTITY % att-denomalignJ
         "denomalign        CDATA                    #IMPLIED" >J
    <!ENTITY % att-rowalign-listJ
         "rowalign     CDATA                    #IMPLIED" >J
    <!ENTITY % att-columnalign-listJ
         "columnalign  CDATA                    #IMPLIED" >J
    <![%MathMLstrict;[
      <!ENTITY % att-rowalign
         "rowalign     ( top | bottom |	center | baseline | axis )    #IMPLIED" >
      <!ENTITY % att-columnalign
         "columnalign  ( left | center | right )        #IMPLIED" >
    ]]>J
    <!ENTITY % att-rowalign
         "rowalign     CDATA                    #IMPLIED" >
    <!ENTITY % att-columnalign
         "columnalign  CDATA                    #IMPLIED" >
    <!ENTITY % att-columnwidth
         "columnwidth  CDATA                    #IMPLIED" >
    <!ENTITY % att-groupalign-listJ
         "groupalign   CDATA                    #IMPLIED" >J
    <![%MathMLstrict;[
      <!ENTITY % att-groupalign
         "groupalign   ( left | right | center | decimalpoint )   #IMPLIED" >
    ]]>J
    <!ENTITY % att-groupalign
         "groupalign   CDATA                    #IMPLIED" >
    <!ENTITY % att-alignmentscope
         "alignmentscope CDATA                  #IMPLIED" >
    <!ENTITY % att-rowspacing
         "rowspacing   CDATA                    #IMPLIED" >
    <!ENTITY % att-columnspacing
         "columnspacing CDATA                   #IMPLIED" >
    <!ENTITY % att-rowlines
         "rowlines     CDATA                    #IMPLIED" >
    <!ENTITY % att-columnlines
         "columnlines  CDATA                    #IMPLIED" >
    <!ENTITY % att-frame
         "frame       ( none | solid | dashed ) #IMPLIED" >
    <!ENTITY % att-sideJ
         "side       ( left | right | leftoverlap | rightoverlap ) #IMPLIED" >J
    <!ENTITY % att-framespacing
         "framespacing CDATA                    #IMPLIED" >
    <!ENTITY % att-minlabelspacingJ
         "minlabelspacing CDATA                 #IMPLIED" >J
    <![%MathMLstrict;[
      <!ENTITY % att-equalrows
         "equalrows    ( true | false )         #IMPLIED" >
      <!ENTITY % att-equalcolumns
         "equalcolumns ( true | false )         #IMPLIED" >
    ]]>J
    <!ENTITY % att-equalrows
         "equalrows    CDATA                    #IMPLIED" >
    <!ENTITY % att-equalcolumns
         "equalcolumns CDATA                    #IMPLIED" >

    <!ENTITY % att-tableinfo
         "%att-align;
          %att-rowalign-list;J
          %att-columnalign-list;J
          %att-columnwidth;
          %att-groupalign-list;J
          %att-alignmentscope;
          %att-side;J
          %att-rowspacing;
          %att-columnspacing;
          %att-rowlines;
          %att-columnlines;
          %att-width;J
          %att-frame;
          %att-framespacing;
          %att-minlabelspacing;J
          %att-equalrows;
          %att-equalcolumns;
          %att-displaystyle;"
    >

    <!ENTITY % att-rowspan
         "rowspan      CDATA                    #IMPLIED" >
    <!ENTITY % att-columnspan
         "columnspan   CDATA                    #IMPLIED" >
    <!ENTITY % att-edge
         "edge         ( left | right )         #IMPLIED" >
    <!ENTITY % att-actiontype
         "actiontype   CDATA                    #IMPLIED" >
    <!ENTITY % att-selection
         "selection    CDATA                    #IMPLIED" >

    <!ENTITY % att-name
         "name         CDATA                    #IMPLIED" >
    <!ENTITY % att-alt
         "alt          CDATA                    #IMPLIED" >
    <!ENTITY % att-index
         "index        CDATA                    #IMPLIED" >

    <![%MathMLstrict;[
      <!ENTITY % att-bevelled
         "bevelled      ( true | false )        #IMPLIED" >
    ]]>J
    <!ENTITY % att-bevelled
         "bevelled      CDATA                    #IMPLIED" >

    <!-- Presentation schemata with content -->

    <!ENTITY % ptoken
         "%mi.qname; | %mn.qname; | %mo.qname;
          | %mtext.qname; | %ms.qname;" >

    <!ATTLIST %mi.qname;
          %MATHML.Common.attrib;
          %att-fontinfo;
    >

    <!ATTLIST %mn.qname;
          %MATHML.Common.attrib;
          %att-fontinfo;
    >

    <!ATTLIST %mo.qname;
          %MATHML.Common.attrib;
          %att-fontinfo;
          %att-opinfo;
    >

    <!ATTLIST %mtext.qname;
          %MATHML.Common.attrib;
          %att-fontinfo;
    >

    <!ATTLIST %ms.qname;
          %MATHML.Common.attrib;
          %att-fontinfo;
          %att-lquote;
          %att-rquote;
    >

    <!-- Empty presentation schemata -->

    <!ENTITY % petoken
         "%mspace.qname;" >
    <!ELEMENT %mspace.qname;  EMPTY >

    <!ATTLIST %mspace.qname;
          %att-sizeinfo;
          %att-linebreak;
          %MATHML.Common.attrib;
    >

    <!-- Presentation: general layout schemata -->

    <!ENTITY % pgenschema
         "%mrow.qname; | %mfrac.qname; | %msqrt.qname; | %mroot.qname;
          | %menclose.qname; | %mstyle.qname; | %merror.qname;
          | %mpadded.qname; | %mphantom.qname; | %mfenced.qname;" >

    <!ATTLIST %mrow.qname;
          %MATHML.Common.attrib;
    >

    <!ATTLIST %mfrac.qname;
          %MATHML.Common.attrib;
          %att-bevelled;J
          %att-numalign;J
          %att-denomalign;J
          %att-linethickness;
    >

    <!ATTLIST %msqrt.qname;
          %MATHML.Common.attrib;
    >

    <![%MathMLstrict;[
      <!ATTLIST %menclose.qname;
          %MATHML.Common.attrib;
          notation ( longdiv | actuarial | radical ) 'longdiv' >
    ]]>J
    <!ATTLIST %menclose.qname;
          %MATHML.Common.attrib;
          notation CDATA 'longdiv' >

    <!ATTLIST %mroot.qname;
          %MATHML.Common.attrib;
    >

    <!ATTLIST %mstyle.qname;
          %MATHML.Common.attrib;
          %att-fontinfo;
          %att-opinfo;
          %att-lquote;
          %att-rquote;
          %att-linethickness;
          %att-scriptlevel;
          %att-scriptsizemultiplier;
          %att-scriptminsize;
          %att-background;
          %att-veryverythinmathspace;
          %att-verythinmathspace;
          %att-thinmathspace;
          %att-mediummathspace;
          %att-thickmathspace;
          %att-verythickmathspace;
          %att-veryverythickmathspace;
          %att-open;
          %att-close;
          %att-separators;
          %att-subscriptshift;
          %att-superscriptshift;
          %att-accentunder;
          %att-tableinfo;
          %att-rowspan;
          %att-columnspan;
          %att-edge;
          %att-selection;
          %att-bevelled;J
          %att-height;J
          %att-depth;J
    >

    <!ATTLIST %merror.qname;
          %MATHML.Common.attrib;
    >

    <!ATTLIST %mpadded.qname;
          %MATHML.Common.attrib;
          %att-sizeinfo;
          %att-lspace;
    >

    <!ATTLIST %mphantom.qname;
          %MATHML.Common.attrib;
    >

    <!ATTLIST %mfenced.qname;
          %MATHML.Common.attrib;
          %att-open;
          %att-close;
          %att-separators;
    >

    <!-- Presentation layout schemata: scripts and limits -->

    <!ENTITY % pscrschema
         "%msub.qname; | %msup.qname; | %msubsup.qname; | %munder.qname;
          | %mover.qname; | %munderover.qname; | %mmultiscripts.qname;" >

    <!ATTLIST %msub.qname;
          %MATHML.Common.attrib;
          %att-subscriptshift;
    >

    <!ATTLIST %msup.qname;
          %MATHML.Common.attrib;
          %att-superscriptshift;
    >

    <!ATTLIST %msubsup.qname;
          %MATHML.Common.attrib;
          %att-subscriptshift;
          %att-superscriptshift;
    >

    <!ATTLIST %munder.qname;
          %MATHML.Common.attrib;
          %att-accentunder;
    >

    <!ATTLIST %mover.qname;
          %MATHML.Common.attrib;
          %att-accent;
    >

    <!ATTLIST %munderover.qname;
          %MATHML.Common.attrib;
          %att-accent;
          %att-accentunder;
    >

    <!ATTLIST %mmultiscripts.qname;
          %MATHML.Common.attrib;
          %att-subscriptshift;
          %att-superscriptshift;
    >

    <!-- Presentation layout schemata: empty elements for scripts -->

    <!ENTITY % pscreschema
         "%mprescripts.qname; | %none.qname;" >

    <!ELEMENT %mprescripts.qname;  EMPTY >
    <!ATTLIST %mprescripts.qname;
          %MATHML.xmlns.attrib; >

    <!ELEMENT %none.qname;  EMPTY >
    <!ATTLIST %none.qname;
          %MATHML.xmlns.attrib; >

    <!-- Presentation layout schemata: tables -->

    <![%MathMLstrict;[
    <!-- in strict mode only allow mtable at top level.
         mtr ,mlabledtr and mtd only allowed inside mtable.
    -->
      <!ENTITY % ptabschema    "%mtable.qname;" >
    ]]>J

    <!ENTITY % ptabschema
         "%mtable.qname; | %mtr.qname; | %mlabeledtr.qname; | %mtd.qname;" >

    <!ATTLIST %mtable.qname;
          %MATHML.Common.attrib;
          %att-tableinfo;
    >

    <!ATTLIST %mtr.qname;
          %MATHML.Common.attrib;
          %att-rowalign;
          %att-columnalign-list;J
          %att-groupalign-list;J
    >

    <!ATTLIST %mlabeledtr.qname;
          %MATHML.Common.attrib;
          %att-rowalign;
          %att-columnalign-list;J
          %att-groupalign-list;J
    >

    <!ATTLIST %mtd.qname;
          %MATHML.Common.attrib;
          %att-rowalign;
          %att-columnalign;
          %att-groupalign-list;J
          %att-rowspan;
          %att-columnspan;
    >
    <!ENTITY % plschema
         "%pgenschema; | %pscrschema; | %ptabschema;" >

    <!-- Empty presentation layout schemata -->

    <!ENTITY % peschema
         "%maligngroup.qname; | %malignmark.qname;" >

    <!ELEMENT %malignmark.qname;  EMPTY >

    <!ATTLIST %malignmark.qname;
          %att-edge; >

    <!ELEMENT %maligngroup.qname;  EMPTY >
    <!ATTLIST %maligngroup.qname;
          %MATHML.Common.attrib;
          %att-groupalign;
    >

    <!ELEMENT %mglyph.qname;  EMPTY >
    <!ATTLIST %mglyph.qname;
          %att-alt;
          %att-fontfamily;
          %att-index; >

    <!-- Presentation action schemata -->

    <!ENTITY % pactions
         "%maction.qname;" >
    <!ATTLIST %maction.qname;
          %MATHML.Common.attrib;
          %att-actiontype;
          %att-selection;
    >

    <!-- The following entity for substitution into
         content constructs excludes elements that
         are not valid as expressions.
    -->

    <!ENTITY % PresInCont
         "%ptoken; | %petoken; |
          %plschema; | %peschema; | %pactions;" >

    <!-- Presentation entity: all presentation constructs -->

    <![%MathMLstrict;[
    <!-- In strict mode don't allow prescripts and none at top level.-->
      <!ENTITY % Presentation "%PresInCont;">
    ]]>J
    <!ENTITY % Presentation
         "%ptoken; | %petoken; | %pscreschema; |
          %plschema; | %peschema; | %pactions;">

    <!-- Content element set  ........................................ -->

    <!-- Attribute definitions -->

    <!ENTITY % att-base
         "base         CDATA                    '10'" >
    <!ENTITY % att-closure
         "closure      CDATA                    'closed'" >
    <!ENTITY % att-definition
         "definitionURL CDATA                   ''" >
    <!ENTITY % att-encoding
         "encoding     CDATA                    ''" >
    <!ENTITY % att-nargs
         "nargs        CDATA                    '1'" >
    <!ENTITY % att-occurrence
         "occurrence   CDATA                    'function-model'" >
    <!ENTITY % att-order
         "order        CDATA                    'numeric'" >
    <!ENTITY % att-scope
         "scope        CDATA                    'local'" >
    <!ENTITY % att-type
         "type         CDATA                    #IMPLIED" >

    <!-- Content elements: leaf nodes -->

    <!ENTITY % ctoken
         "%csymbol.qname; | %ci.qname; | %cn.qname;" >

    <!ATTLIST %ci.qname;
          %MATHML.Common.attrib;
          %att-type;
          %att-definition;
          %att-encoding;
    >

    <!ATTLIST %csymbol.qname;
          %MATHML.Common.attrib;
          %att-encoding;
          %att-type;
          %att-definition;
    >

    <!ATTLIST %cn.qname;
          %MATHML.Common.attrib;
          %att-type;
          %att-base;
          %att-definition;
          %att-encoding;
    >

    <!-- Content elements: specials -->

    <!ENTITY % cspecial
         "%apply.qname; | %reln.qname; |
          %lambda.qname;" >

    <!ATTLIST %apply.qname;
          %MATHML.Common.attrib;
    >

    <!ATTLIST %reln.qname;
          %MATHML.Common.attrib;
    >

    <!ATTLIST %lambda.qname;
          %MATHML.Common.attrib;
    >

    <!-- Content elements: others -->

    <!ENTITY % cother
         "%condition.qname; | %declare.qname; | %sep.qname;" >

    <!ATTLIST %condition.qname;
          %MATHML.Common.attrib;
    >

    <!ATTLIST %declare.qname;
          %MATHML.Common.attrib;
          %att-type;
          %att-scope;
          %att-nargs;
          %att-occurrence;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %sep.qname;  EMPTY >
    <!ATTLIST %sep.qname;
          %MATHML.xmlns.attrib; >

    <!-- Content elements: semantic mapping -->

    <![%MathMLstrict;[
    <!-- in strict mode only allow semantics at top level.
         annotation and annotation-xml only allowed in semantics
    -->
      <!ENTITY % csemantics  "%semantics.qname;" >
    ]]>J
    <!ENTITY % csemantics
         "%semantics.qname; | %annotation.qname; |
          %annotation-xml.qname;" >

    <!ATTLIST %semantics.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ATTLIST %annotation.qname;
          %MATHML.Common.attrib;
          %att-encoding;
    >

    <!ATTLIST %annotation-xml.qname;
          %MATHML.Common.attrib;
          %att-encoding;
    >

    <!-- Content elements: constructors -->

    <!ENTITY % cconstructor
         "%interval.qname; | %list.qname; | %matrix.qname;
          | %matrixrow.qname; | %set.qname; | %vector.qname;
          | %piecewise.qname; " >

    <!ATTLIST %interval.qname;
          %MATHML.Common.attrib;
          %att-closure;
    >

    <!ATTLIST %set.qname;
          %MATHML.Common.attrib;
          %att-type;
    >

    <!ATTLIST %list.qname;
          %MATHML.Common.attrib;
          %att-order;
    >

    <!ATTLIST %vector.qname;
          %MATHML.Common.attrib;
    >

    <!ATTLIST %matrix.qname;
          %MATHML.Common.attrib;
    >

    <!ATTLIST %matrixrow.qname;
          %MATHML.Common.attrib;
    >

    <!ATTLIST %piecewise.qname;
          %MATHML.Common.attrib;
    >

    <!ATTLIST %piece.qname;
          %MATHML.Common.attrib;
    >

    <!ATTLIST %otherwise.qname;
          %MATHML.Common.attrib;
    >

    <!-- Content elements: symbols -->

    <!ENTITY % c0ary
        "%integers.qname; |
         %reals.qname; |
         %rationals.qname; |
         %naturalnumbers.qname; |
         %complexes.qname; |
         %primes.qname; |
         %exponentiale.qname; |
         %imaginaryi.qname; |
         %notanumber.qname; |
         %true.qname; |
         %false.qname; |
         %emptyset.qname; |
         %pi.qname; |
         %eulergamma.qname; |
         %infinity.qname;" >

    <!ELEMENT %integers.qname;  EMPTY >
    <!ATTLIST %integers.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %reals.qname;  EMPTY >
    <!ATTLIST %reals.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %rationals.qname;  EMPTY >
    <!ATTLIST %rationals.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %naturalnumbers.qname;  EMPTY >
    <!ATTLIST %naturalnumbers.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %complexes.qname;  EMPTY >
    <!ATTLIST %complexes.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %primes.qname;  EMPTY >
    <!ATTLIST %primes.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %exponentiale.qname;  EMPTY >
    <!ATTLIST %exponentiale.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %imaginaryi.qname;  EMPTY >
    <!ATTLIST %imaginaryi.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %notanumber.qname;  EMPTY >
    <!ATTLIST %notanumber.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %true.qname;  EMPTY >
    <!ATTLIST %true.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %false.qname;  EMPTY >
    <!ATTLIST %false.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %emptyset.qname;  EMPTY >
    <!ATTLIST %emptyset.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %pi.qname;  EMPTY >
    <!ATTLIST %pi.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %eulergamma.qname;  EMPTY >
    <!ATTLIST %eulergamma.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %infinity.qname;  EMPTY >
    <!ATTLIST %infinity.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!-- Content elements: operators -->

    <!ENTITY % cfuncop1ary
         "%inverse.qname; | %ident.qname;|
          %domain.qname; |  %codomain.qname; |
          %image.qname;  " >

    <!ELEMENT %inverse.qname;  EMPTY >
    <!ATTLIST %inverse.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %domain.qname;  EMPTY >
    <!ATTLIST %domain.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %codomain.qname;  EMPTY >
    <!ATTLIST %codomain.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %image.qname;  EMPTY >
    <!ATTLIST %image.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % cfuncopnary
         "%fn.qname; | %compose.qname;" >

    <!ATTLIST %fn.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %ident.qname;  EMPTY >
    <!ATTLIST %ident.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %compose.qname;  EMPTY >
    <!ATTLIST %compose.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % carithop1ary
         "%abs.qname; | %conjugate.qname; | %exp.qname; | %factorial.qname; |
          %arg.qname; | %real.qname; | %imaginary.qname; |
          %floor.qname; | %ceiling.qname;" >

    <!ELEMENT %exp.qname;  EMPTY >
    <!ATTLIST %exp.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %abs.qname;  EMPTY >
    <!ATTLIST %abs.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %arg.qname;  EMPTY >
    <!ATTLIST %arg.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %real.qname;  EMPTY >
    <!ATTLIST %real.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %imaginary.qname;  EMPTY >
    <!ATTLIST %imaginary.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %conjugate.qname;  EMPTY >
    <!ATTLIST %conjugate.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %factorial.qname;  EMPTY >
    <!ATTLIST %factorial.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %floor.qname;  EMPTY >
    <!ATTLIST %floor.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %ceiling.qname;  EMPTY >
    <!ATTLIST %ceiling.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >
    <!ENTITY % carithop1or2ary
         "%minus.qname;" >

    <!ELEMENT %minus.qname;  EMPTY >
    <!ATTLIST %minus.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % carithop2ary
         "%quotient.qname; | %divide.qname; | %power.qname; | %rem.qname;" >

    <!ELEMENT %quotient.qname;  EMPTY >
    <!ATTLIST %quotient.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %divide.qname;  EMPTY >
    <!ATTLIST %divide.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %power.qname;  EMPTY >
    <!ATTLIST %power.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %rem.qname;  EMPTY >
    <!ATTLIST %rem.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % carithopnary
         "%plus.qname; | %times.qname; | %max.qname;
          | %min.qname; | %gcd.qname; | %lcm.qname;" >

    <!ELEMENT %plus.qname;  EMPTY >
    <!ATTLIST %plus.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %max.qname;  EMPTY >
    <!ATTLIST %max.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %min.qname;  EMPTY >
    <!ATTLIST %min.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %times.qname;  EMPTY >
    <!ATTLIST %times.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %gcd.qname;  EMPTY >
    <!ATTLIST %gcd.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %lcm.qname;  EMPTY >
    <!ATTLIST %lcm.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % carithoproot
         "%root.qname;" >

    <!ELEMENT %root.qname;  EMPTY >
    <!ATTLIST %root.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % clogicopquant
         "%exists.qname; | %forall.qname;" >

    <!ELEMENT %exists.qname;  EMPTY >
    <!ATTLIST %exists.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %forall.qname;  EMPTY >
    <!ATTLIST %forall.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % clogicopnary
         "%and.qname; | %or.qname; | %xor.qname;" >

    <!ELEMENT %and.qname;  EMPTY >
    <!ATTLIST %and.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %or.qname;  EMPTY >
    <!ATTLIST %or.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %xor.qname;  EMPTY >
    <!ATTLIST %xor.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % clogicop1ary
         "%not.qname;" >

    <!ELEMENT %not.qname;  EMPTY >
    <!ATTLIST %not.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % clogicop2ary
         "%implies.qname;" >

    <!ELEMENT %implies.qname;  EMPTY >
    <!ATTLIST %implies.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % ccalcop
         "%log.qname; | %int.qname; | %diff.qname; | %partialdiff.qname; |
          %divergence.qname; | %grad.qname; | %curl.qname; | %laplacian.qname;" >

    <!ELEMENT %divergence.qname;  EMPTY >
    <!ATTLIST %divergence.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %grad.qname;  EMPTY >
    <!ATTLIST %grad.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %curl.qname;  EMPTY >
    <!ATTLIST %curl.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %laplacian.qname;  EMPTY >
    <!ATTLIST %laplacian.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %log.qname;  EMPTY >
    <!ATTLIST %log.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %int.qname;  EMPTY >
    <!ATTLIST %int.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %diff.qname;  EMPTY >
    <!ATTLIST %diff.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %partialdiff.qname;  EMPTY >
    <!ATTLIST %partialdiff.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % ccalcop1ary
         "%ln.qname;" >

    <!ELEMENT %ln.qname;  EMPTY >
    <!ATTLIST %ln.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % csetop1ary
         "%card.qname;" >

    <!ELEMENT %card.qname;  EMPTY >
    <!ATTLIST %card.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % csetop2ary
         "%setdiff.qname;" >

    <!ELEMENT %setdiff.qname;  EMPTY >
    <!ATTLIST %setdiff.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % csetopnary
         "%union.qname; | %intersect.qname; | %cartesianproduct.qname; " >

    <!ELEMENT %union.qname;  EMPTY >
    <!ATTLIST %union.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %intersect.qname;  EMPTY >
    <!ATTLIST %intersect.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %cartesianproduct.qname;  EMPTY >
    <!ATTLIST %cartesianproduct.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % cseqop
         "%sum.qname; | %product.qname; | %limit.qname;" >

    <!ELEMENT %sum.qname;  EMPTY >
    <!ATTLIST %sum.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %product.qname;  EMPTY >
    <!ATTLIST %product.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %limit.qname;  EMPTY >
    <!ATTLIST %limit.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % ctrigop
         "%sin.qname; | %cos.qname; | %tan.qname;
          | %sec.qname; | %csc.qname; | %cot.qname;
          | %sinh.qname; | %cosh.qname; | %tanh.qname;
          | %sech.qname; | %csch.qname; | %coth.qname;
          | %arcsin.qname; | %arccos.qname; | %arctan.qname;
          | %arccosh.qname; | %arccot.qname; | %arccoth.qname;
          | %arccsc.qname; | %arccsch.qname; | %arcsec.qname;
          | %arcsech.qname; | %arcsinh.qname; | %arctanh.qname;
          " >

    <!ELEMENT %sin.qname;  EMPTY >
    <!ATTLIST %sin.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %cos.qname;  EMPTY >
    <!ATTLIST %cos.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %tan.qname;  EMPTY >
    <!ATTLIST %tan.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %sec.qname;  EMPTY >
    <!ATTLIST %sec.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %csc.qname;  EMPTY >
    <!ATTLIST %csc.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %cot.qname;  EMPTY >
    <!ATTLIST %cot.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %sinh.qname;  EMPTY >
    <!ATTLIST %sinh.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %cosh.qname;  EMPTY >
    <!ATTLIST %cosh.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %tanh.qname;  EMPTY >
    <!ATTLIST %tanh.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %sech.qname;  EMPTY >
    <!ATTLIST %sech.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %csch.qname;  EMPTY >
    <!ATTLIST %csch.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %coth.qname;  EMPTY >
    <!ATTLIST %coth.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %arcsin.qname;  EMPTY >
    <!ATTLIST %arcsin.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %arccos.qname;  EMPTY >
    <!ATTLIST %arccos.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %arctan.qname;  EMPTY >
    <!ATTLIST %arctan.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %arccosh.qname;  EMPTY >
    <!ATTLIST %arccosh.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %arccot.qname;  EMPTY >
    <!ATTLIST %arccot.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %arccoth.qname;  EMPTY >
    <!ATTLIST %arccoth.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %arccsc.qname;  EMPTY >
    <!ATTLIST %arccsc.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %arccsch.qname;  EMPTY >
    <!ATTLIST %arccsch.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %arcsec.qname;  EMPTY >
    <!ATTLIST %arcsec.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %arcsech.qname;  EMPTY >
    <!ATTLIST %arcsech.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %arcsinh.qname;  EMPTY >
    <!ATTLIST %arcsinh.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %arctanh.qname;  EMPTY >
    <!ATTLIST %arctanh.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % cstatopnary
         "%mean.qname; | %sdev.qname; |
          %variance.qname; | %median.qname; |
          %mode.qname;" >

    <!ELEMENT %mean.qname;  EMPTY >
    <!ATTLIST %mean.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %sdev.qname;  EMPTY >
    <!ATTLIST %sdev.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %variance.qname;  EMPTY >
    <!ATTLIST %variance.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %median.qname;  EMPTY >
    <!ATTLIST %median.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %mode.qname;  EMPTY >
    <!ATTLIST %mode.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % cstatopmoment
         "%moment.qname;" >

    <!ELEMENT %moment.qname;  EMPTY >
    <!ATTLIST %moment.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % clalgop1ary
         "%determinant.qname; |
          %transpose.qname;" >

    <!ELEMENT %determinant.qname;  EMPTY >
    <!ATTLIST %determinant.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %transpose.qname;  EMPTY >
    <!ATTLIST %transpose.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % clalgop2ary
         "%vectorproduct.qname;
          | %scalarproduct.qname;
          | %outerproduct.qname;" >

    <!ELEMENT %vectorproduct.qname;  EMPTY >
    <!ATTLIST %vectorproduct.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %scalarproduct.qname;  EMPTY >
    <!ATTLIST %scalarproduct.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %outerproduct.qname;  EMPTY >
    <!ATTLIST %outerproduct.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % clalgopnary
         "%selector.qname;" >

    <!ELEMENT %selector.qname;  EMPTY >
    <!ATTLIST %selector.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!-- Content elements: relations -->

    <!ENTITY % cgenrel2ary
         "%neq.qname; | %factorof.qname;" >

    <!ELEMENT %neq.qname;  EMPTY >
    <!ATTLIST %neq.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %factorof.qname;  EMPTY >
    <!ATTLIST %factorof.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % cgenrelnary
         "%eq.qname; | %leq.qname; | %lt.qname; | %geq.qname;
          | %gt.qname;| %equivalent.qname; | %approx.qname;" >

    <!ELEMENT %eq.qname;  EMPTY >
    <!ATTLIST %eq.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %equivalent.qname;  EMPTY >
    <!ATTLIST %equivalent.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %approx.qname;  EMPTY >
    <!ATTLIST %approx.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %gt.qname;  EMPTY >
    <!ATTLIST %gt.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %lt.qname;  EMPTY >
    <!ATTLIST %lt.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %geq.qname;  EMPTY >
    <!ATTLIST %geq.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %leq.qname;  EMPTY >
    <!ATTLIST %leq.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % csetrel2ary
         "%in.qname; | %notin.qname; | %notsubset.qname; | %notprsubset.qname;" >

    <!ELEMENT %in.qname;  EMPTY >
    <!ATTLIST %in.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %notin.qname;  EMPTY >
    <!ATTLIST %notin.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %notsubset.qname;  EMPTY >
    <!ATTLIST %notsubset.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %notprsubset.qname;  EMPTY >
    <!ATTLIST %notprsubset.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % csetrelnary
         "%subset.qname; | %prsubset.qname;" >

    <!ELEMENT %subset.qname;  EMPTY >
    <!ATTLIST %subset.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ELEMENT %prsubset.qname;  EMPTY >
    <!ATTLIST %prsubset.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
    >

    <!ENTITY % cseqrel2ary
         "%tendsto.qname;" >

    <!ELEMENT %tendsto.qname;  EMPTY >
    <!ATTLIST %tendsto.qname;
          %MATHML.Common.attrib;
          %att-definition;
          %att-encoding;
          %att-type;
    >

    <!-- Content elements: quantifiers -->

    <!ENTITY % cquantifier
         "%lowlimit.qname; | %uplimit.qname; | %bvar.qname;
          | %degree.qname; | %logbase.qname;
          | %momentabout.qname; | %domainofapplication.qname; " >

    <!ATTLIST %lowlimit.qname;
          %MATHML.Common.attrib;
    >

    <!ATTLIST %uplimit.qname;
          %MATHML.Common.attrib;
    >

    <!ATTLIST %bvar.qname;
          %MATHML.Common.attrib;
    >

    <!ATTLIST %degree.qname;
          %MATHML.Common.attrib;
    >

    <!ATTLIST %logbase.qname;
          %MATHML.Common.attrib;
    >

    <!ATTLIST %momentabout.qname;
          %MATHML.Common.attrib;
    >

    <!ATTLIST %domainofapplication.qname;
          %MATHML.Common.attrib;
    >

    <!-- Operator groups -->

    <!ENTITY % cop1ary
         "%cfuncop1ary; | %carithop1ary; | %clogicop1ary; |
          %ccalcop1ary; | %ctrigop; | %clalgop1ary; |
          %csetop1ary;" >

    <!ENTITY % cop2ary
         "%carithop2ary; | %clogicop2ary;| %clalgop2ary; | %csetop2ary;" >

    <!ENTITY % copnary
         "%cfuncopnary; | %carithopnary; | %clogicopnary; |
          %csetopnary; | %cstatopnary; | %clalgopnary;" >

    <!ENTITY % copmisc
         "%carithoproot; | %carithop1or2ary; | %ccalcop; |
          %cseqop; | %cstatopmoment; | %clogicopquant;" >

    <!-- Relation groups -->

    <!ENTITY % crel2ary
         "%cgenrel2ary; | %csetrel2ary; | %cseqrel2ary;" >

    <!ENTITY % crelnary
         "%cgenrelnary; | %csetrelnary;" >

    <!-- Content constructs: all -->

    <!ENTITY % Content
         "%ctoken; | %cspecial; | %cother; | %csemantics; | %c0ary;
          | %cconstructor; | %cquantifier; | %cop1ary; | %cop2ary;
          | %copnary; |%copmisc; | %crel2ary; | %crelnary;" >

    <!-- Content constructs for substitution in presentation structures -->

    <!ENTITY % ContInPres
         "%ci.qname; |%csymbol.qname;| %cn.qname; | %c0ary; |
          %apply.qname; | %fn.qname; |
          %lambda.qname; | %reln.qname; |
          %cconstructor; |
          %semantics.qname; |%declare.qname;" >

    <!-- ............................................................. -->
    <!-- Recursive definition for content of expressions. Include
         presentation constructs at lowest level so presentation
         layout schemata hold presentation or content elements.
         Include content constructs at lowest level so content
         elements hold PCDATA or presentation elements at leaf
         level (for permitted substitutable elements in context)
    -->
    <![%MathMLstrict;[
    <!-- in strict mode don't allow presentation in content
         except where allowed by chapter 5:
         ci, cn, csymbol, semantics
    -->
      <!ENTITY % ContentExpression  "(%Content;)*" >
      <!ENTITY % semanticsContentExpression
           "(%Content; | %PresInCont; |
             %annotation.qname; | %annotation-xml.qname;)*" >
    ]]>J
    <!ENTITY % ContentExpression
         "(%Content; | %PresInCont;)*" >
    <!ENTITY % semanticsContentExpression    "%ContentExpression;">

    <!ENTITY % PresExpression
         "(%Presentation; | %ContInPres;)*" >
    <!ENTITY % MathExpression
         "(%PresInCont; | %ContInPres;)*" >

    <!-- PCDATA or MathML character elements -->
    <!ENTITY % MathMLCharacters
         "#PCDATA | %mglyph.qname; " >

    <!-- Content elements: tokens                       -->
    <!-- (may contain embedded presentation constructs) -->

    <!ELEMENT %ci.qname;                 (%MathMLCharacters; | %PresInCont;)* >
    <!ELEMENT %csymbol.qname;            (%MathMLCharacters; | %PresInCont;)* >
    <!ELEMENT %cn.qname;                 (%MathMLCharacters; | %sep.qname; | %PresInCont;)* >

    <!-- Content elements: special -->

    <!ELEMENT %apply.qname;              (%ContentExpression;) >
    <!ELEMENT %reln.qname;               (%ContentExpression;) >
    <!ELEMENT %lambda.qname;             (%ContentExpression;) >

    <!-- Content elements: other -->

    <!ELEMENT %condition.qname;          (%ContentExpression;) >
    <!ELEMENT %declare.qname;            (%ContentExpression;) >

    <!-- Content elements: semantics -->

    <!ELEMENT %semantics.qname;          (%semanticsContentExpression;) >
    <!ENTITY % Annotation.content  "( #PCDATA )" >
    <!ELEMENT %annotation.qname;         %Annotation.content; >

    <!ENTITY % Annotation-xml.content "ANY" >
    <!ELEMENT %annotation-xml.qname;     %Annotation-xml.content; >

    <!-- Content elements: constructors -->

    <!ELEMENT %interval.qname;           (%ContentExpression;) >
    <!ELEMENT %set.qname;                (%ContentExpression;) >
    <!ELEMENT %list.qname;               (%ContentExpression;) >
    <!ELEMENT %vector.qname;             (%ContentExpression;) >
    <!ELEMENT %matrix.qname;             (%ContentExpression;) >
    <!ELEMENT %matrixrow.qname;          (%ContentExpression;) >

    <!ELEMENT %piecewise.qname;          ((%piece.qname;)*, (%otherwise.qname;)? ) >
    <!ELEMENT %piece.qname;              (%ContentExpression;) >
    <!ELEMENT %otherwise.qname;          (%ContentExpression;) >

    <!-- Content elements: operator (user-defined) -->

    <!ELEMENT %fn.qname;                 (%ContentExpression;) >

    <!-- Content elements: quantifiers -->

    <!ELEMENT %lowlimit.qname;           (%ContentExpression;) >
    <!ELEMENT %uplimit.qname;            (%ContentExpression;) >
    <!ELEMENT %bvar.qname;               (%ContentExpression;) >
    <!ELEMENT %degree.qname;             (%ContentExpression;) >
    <!ELEMENT %logbase.qname;            (%ContentExpression;) >
    <!ELEMENT %momentabout.qname;        (%ContentExpression;) >
    <!ELEMENT %domainofapplication.qname; (%ContentExpression;) >

    <!-- ............................................................. -->
    <!-- Presentation layout schemata contain tokens,
         layout and content schemata.
    -->

    <![%MathMLstrict;[
    <!-- In strict mode enforce mfrac has exactly two children
          same for msub etc -->
      <!ENTITY % onePresExpression
           "(%Presentation; | %ContInPres;)" >
      <!ENTITY % twoPresExpression
           "(%onePresExpression;,%onePresExpression;)" >
      <!ENTITY % threePresExpression
           "(%onePresExpression;,%onePresExpression;,%onePresExpression;)" >
      <!ENTITY % mtrPresExpression
           "(%mtr.qname;|%mlabeledtr.qname;)*" >
      <!ENTITY % mtdPresExpression
           "(%mtd.qname;)*" >
      <!ENTITY % prscrPresExpression " (%onePresExpression;,
      ((%onePresExpression;|%none.qname;),(%onePresExpression;|%none.qname;))*,
      (%mprescripts.qname;,
      ((%onePresExpression;|%none.qname;),(%onePresExpression;|%none.qname;))*)?
      )">
    ]]>J

    <!-- By default keep them as they were in MathML 2.0  -->
    <!ENTITY % onePresExpression   "%PresExpression;">
    <!ENTITY % twoPresExpression   "%PresExpression;">
    <!ENTITY % threePresExpression "%PresExpression;">
    <!ENTITY % mtrPresExpression   "%PresExpression;">
    <!ENTITY % mtdPresExpression   "%PresExpression;">
    <!ENTITY % prscrPresExpression "%PresExpression;">

    <!ELEMENT %mstyle.qname;             (%PresExpression;) >
    <!ELEMENT %merror.qname;             (%PresExpression;) >
    <!ELEMENT %mphantom.qname;           (%PresExpression;) >
    <!ELEMENT %mrow.qname;               (%PresExpression;) >
    <!ELEMENT %mfrac.qname;              (%twoPresExpression;) >
    <!ELEMENT %msqrt.qname;              (%PresExpression;) >
    <!ELEMENT %menclose.qname;           (%PresExpression;) >
    <!ELEMENT %mroot.qname;              (%twoPresExpression;) >
    <!ELEMENT %msub.qname;               (%twoPresExpression;) >
    <!ELEMENT %msup.qname;               (%twoPresExpression;) >
    <!ELEMENT %msubsup.qname;            (%threePresExpression;) >
    <!ELEMENT %mmultiscripts.qname;      (%prscrPresExpression;) >
    <!ELEMENT %munder.qname;             (%twoPresExpression;) >
    <!ELEMENT %mover.qname;              (%twoPresExpression;) >
    <!ELEMENT %munderover.qname;         (%threePresExpression;) >
    <!ELEMENT %mtable.qname;             (%mtrPresExpression;) >
    <!ELEMENT %mtr.qname;                (%mtdPresExpression;) >
    <!ELEMENT %mlabeledtr.qname;         (%mtdPresExpression;) >
    <!ELEMENT %mtd.qname;                (%PresExpression;) >
    <!ELEMENT %maction.qname;            (%PresExpression;) >
    <!ELEMENT %mfenced.qname;            (%PresExpression;) >
    <!ELEMENT %mpadded.qname;            (%PresExpression;) >

    <!-- Presentation elements contain PCDATA or malignmark constructs. -->

    <!ELEMENT %mi.qname;                 (%MathMLCharacters; |
          %malignmark.qname;)* >
    <!ELEMENT %mn.qname;                 (%MathMLCharacters; |
          %malignmark.qname;)* >
    <!ELEMENT %mo.qname;                 (%MathMLCharacters; |
          %malignmark.qname;)* >
    <!ELEMENT %mtext.qname;              (%MathMLCharacters; |
          %malignmark.qname;)* >
    <!ELEMENT %ms.qname;                 (%MathMLCharacters; |
          %malignmark.qname;)* >

    <!-- Browser interface definition  ............................... -->

    <!-- Attributes for top-level element "math" -->

    <!ENTITY % att-macros
         "macros       CDATA                    #IMPLIED" >
    <!ENTITY % att-mode
         "mode         CDATA                    #IMPLIED" >
    <![%MathMLstrict;[
      <!ENTITY % att-display
         "display      ( block | inline )                    'inline'" >
    ]]>J
    <!ENTITY % att-display
         "display      CDATA                    #IMPLIED" >

    <!ENTITY % att-schemalocation
         "%Schema.prefix;:schemaLocation CDATA  #IMPLIED">J

    <!ENTITY % att-topinfo
         "%MATHML.Common.attrib;
          %att-schemalocation;J
          %att-macros;
          %att-mode;
          %att-display;" >

    <!-- Attributes for browser interface element -->

    <!ENTITY % att-baseline
         "baseline     CDATA                    #IMPLIED" >
    <!ENTITY % att-overflow
         "overflow  ( scroll | elide | truncate | scale ) 'scroll'" >
    <!ENTITY % att-altimg
         "altimg       CDATA                    #IMPLIED" >
    <!ENTITY % att-alttext
         "alttext      CDATA                    #IMPLIED" >

    <!ENTITY % att-browif
         "%att-type;
          %att-name;
          %att-height;
          %att-width;
          %att-baseline;
          %att-overflow;
          %att-altimg;
          %att-alttext;" >

    <!-- ............................................................. -->
    <!-- The top-level element "math" contains MathML encoded
         mathematics. The "math" element has the browser info
         attributes iff it is also the browser interface element.
    -->

    <!ELEMENT %math.qname;               (%MathExpression;) >

    <!ATTLIST %math.qname;
          %att-topinfo;
          %att-browif; >

    <!-- MathML Character Entities .............................................. -->
    <!ENTITY % mathml-charent.module "INCLUDE" >
    <![%mathml-charent.module;[
    <!-- Entity sets from ISO Technical Report 9573-13 ..... -->

    <!ENTITY % ent-isoamsa
          PUBLIC "-//W3C//ENTITIES Added Math Symbols: Arrow Relations for MathML 2.0//EN"
                 "iso9573-13/isoamsa.ent" >
    %ent-isoamsa;

    <!ENTITY % ent-isoamsb
          PUBLIC "-//W3C//ENTITIES Added Math Symbols: Binary Operators for MathML 2.0//EN"
                 "iso9573-13/isoamsb.ent" >
    %ent-isoamsb;

    <!ENTITY % ent-isoamsc
          PUBLIC "-//W3C//ENTITIES Added Math Symbols: Delimiters for MathML 2.0//EN"
                 "iso9573-13/isoamsc.ent" >
    %ent-isoamsc;

    <!ENTITY % ent-isoamsn
          PUBLIC "-//W3C//ENTITIES Added Math Symbols: Negated Relations for MathML 2.0//EN"
                 "iso9573-13/isoamsn.ent" >
    %ent-isoamsn;

    <!ENTITY % ent-isoamso
          PUBLIC "-//W3C//ENTITIES Added Math Symbols: Ordinary for MathML 2.0//EN"
                 "iso9573-13/isoamso.ent" >
    %ent-isoamso;

    <!ENTITY % ent-isoamsr
          PUBLIC "-//W3C//ENTITIES Added Math Symbols: Relations for MathML 2.0//EN"
                 "iso9573-13/isoamsr.ent" >
    %ent-isoamsr;

    <!ENTITY % ent-isogrk3
          PUBLIC "-//W3C//ENTITIES Greek Symbols for MathML 2.0//EN"
                 "iso9573-13/isogrk3.ent" >
    %ent-isogrk3;

    <!ENTITY % ent-isomfrk
          PUBLIC "-//W3C//ENTITIES Math Alphabets: Fraktur for MathML 2.0//EN"
                 "iso9573-13/isomfrk.ent" >
    %ent-isomfrk;

    <!ENTITY % ent-isomopf
          PUBLIC "-//W3C//ENTITIES Math Alphabets: Open Face for MathML 2.0//EN"
                 "iso9573-13/isomopf.ent" >
    %ent-isomopf;

    <!ENTITY % ent-isomscr
          PUBLIC "-//W3C//ENTITIES Math Alphabets: Script for MathML 2.0//EN"
                 "iso9573-13/isomscr.ent" >
    %ent-isomscr;

    <!ENTITY % ent-isotech
          PUBLIC "-//W3C//ENTITIES General Technical for MathML 2.0//EN"
                 "iso9573-13/isotech.ent" >
    %ent-isotech;

    <!-- Entity sets from informative annex to ISO 8879:1986 (SGML) ....... -->

    <!ENTITY % ent-isobox
          PUBLIC "-//W3C//ENTITIES Box and Line Drawing for MathML 2.0//EN"
                 "iso8879/isobox.ent" >
    %ent-isobox;

    <!ENTITY % ent-isocyr1
          PUBLIC "-//W3C//ENTITIES Russian Cyrillic for MathML 2.0//EN"
                 "iso8879/isocyr1.ent" >
    %ent-isocyr1;

    <!ENTITY % ent-isocyr2
          PUBLIC "-//W3C//ENTITIES Non-Russian Cyrillic for MathML 2.0//EN"
                 "iso8879/isocyr2.ent" >
    %ent-isocyr2;

    <!ENTITY % ent-isodia
          PUBLIC "-//W3C//ENTITIES Diacritical Marks for MathML 2.0//EN"
                 "iso8879/isodia.ent" >
    %ent-isodia;

    <!ENTITY % ent-isolat1
          PUBLIC "-//W3C//ENTITIES Added Latin 1 for MathML 2.0//EN"
                 "iso8879/isolat1.ent" >
    %ent-isolat1;

    <!ENTITY % ent-isolat2
          PUBLIC "-//W3C//ENTITIES Added Latin 2 for MathML 2.0//EN"
                 "iso8879/isolat2.ent" >
    %ent-isolat2;

    <!ENTITY % ent-isonum
          PUBLIC "-//W3C//ENTITIES Numeric and Special Graphic for MathML 2.0//EN"
                 "iso8879/isonum.ent" >
    %ent-isonum;

    <!ENTITY % ent-isopub
          PUBLIC "-//W3C//ENTITIES Publishing for MathML 2.0//EN"
                 "iso8879/isopub.ent" >
    %ent-isopub;

    <!-- New characters defined by MathML ............................ -->

    <!ENTITY % ent-mmlextra
          PUBLIC "-//W3C//ENTITIES Extra for MathML 2.0//EN"
                 "mathml/mmlextra.ent" >
    %ent-mmlextra;

    <!-- MathML aliases for characters defined above ................. -->

    <!ENTITY % ent-mmlalias
          PUBLIC "-//W3C//ENTITIES Aliases for MathML 2.0//EN"
                 "mathml/mmlalias.ent" >
    %ent-mmlalias;

    <!-- end of MathML Character Entity section -->]]>

    <!-- Revision History:

           Initial draft (syntax = XML) 1997-05-09
              Stephen Buswell
           Revised 1997-05-14
              Robert Miner
           Revised 1997-06-29 and 1997-07-02
              Stephen Buswell
           Revised 1997-12-15
              Stephen Buswell
           Revised 1998-02-08
              Stephen Buswell
           Revised 1998-04-04
              Stephen Buswell
           Entities and small revisions 1999-02-21
              David Carlisle
           Added attribute definitionURL to ci and cn 1999-10-11
              Nico Poppelier
           Additions for MathML 2  1999-12-16
              David Carlisle
           Namespace support 2000-01-14
              David Carlisle
           XHTML Compatibility 2000-02-23
              Murray Altheim
           New content elements 2000-03-26
              David Carlisle
           Further revisions for MathML2 CR draft 2000-07-11
              David Carlisle
           Further revisions for MathML2 CR draft 2000-10-31J
              David CarlisleJ
           Revisions for Unicode 3.2  2002-05-21J
              David CarlisleJ
           Add width and side attributes to mtable (to align with the specification)  2002-06-05J
              David CarlisleJ
           Use %XLINK.prefix rather than hardwired xlink:, add xlink:type 2002-06-12J
              David CarlisleJ
           Add missing numalign and denomalign attributes for mfrac 2002-07-05J
              David CarlisleJ
           Add MathMLstrict entity and related extra constraints 2002-12-05J
              David CarlisleJ
           Add support for xi:schemaLocation 2003-04-05J
              David CarlisleJ
           Removed actiontype from mstyle (to match spec) 2003-04-07J
              David CarlisleJ
           Additional constraints for MathMLstrict code (From SimonJ
           Pepping on www-math list) 2003-05-22J
              David CarlisleJ
           Add missing minlabelspacing attribute (From SimonJ
           Pepping on www-math list) 2003-05-22J
              David CarlisleJ
           Add missing height and depth attributes to mstyle (From SimonJ
           Pepping on www-math list) 2003-06-30J
              David CarlisleJ

    -->

    <!-- end of MathML 2.0 DTD  ................................................ -->
    <!-- ....................................................................... -->

## A.3 Using the MathML XML Schema

MathML fragments can be validated using the XML Schema for MathML, located at http://www.w3.org/Math/XMLSchema/mathml2/mathml2.xsd. The provided schema allows checking a MathML fragment in a stricter way than by performing DTD validation, in particular constrained attribute values such as `linethickness` are enforced by the schema. Additionally, XML Schemas have the advantage over DTDs of supporting the XML namespaces mechanism. Thus a MathML fragment can declare any namespace prefix (and possibly more than one), without the requirement that the author indicate it using a parameter entity, as described above.

In its current version the schema does not declare deprecated markup such as the `fn` element, so documents using such deprecated features will be declared invalid.

### A.3.1 Associating the MathML Schema with MathML fragments

Similarly to the DOCTYPE Declaration used in documents, it is possible to link a MathML fragment to the XML Schema, as shown below.

    <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"
              xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
              xsi:schemaLocation="http://www.w3.org/1998/Math/MathML
                http://www.w3.org/Math/XMLSchema/mathml2/mathml2.xsd">
    ...
    </mml:math>

The `xsi:schemaLocation` attribute belongs to the XML Schema instance namespace, defined in [XMLSchemas]. The value of the attribute is a pair of URIs: the first is the MathML namespace URI and the second is the location of the schema for that namespace. The second URI may be changed to that of a local copy if required.

As the XML Schema specification indicates, the use of the `schemaLocation` attribute is only a hint for schema processors: validation by a MathML-aware processor can be performed without requiring that the `schemaLocation` attribute be declared in the instance. Moreover, a processor can even ignore or override the specified schema URI, if it is directed to.

Note that the file `mathml.xsd` at the URI given above is only the main body of the schema, and is one of many files that constitute the MathML XML Schema. However the complete set of files is available as a gzipped tar archive for local use.

### A.3.2 Character entity references

Although validating a MathML fragment with the XML Schema provided performs more checks regarding the structure of the fragment than the DTD, DTD processing is still necessary if the MathML markup contains entity references for characters and symbols, as XML Schema does not provide a mechanism for expanding named entities. Therefore the MathML DOCTYPE declaration must still be present if one wishes to use entities for mathematical symbols, such as `&DifferentialD;`. An example of a MathML document linking to both the MathML DTD and the XML Schema is shown below.

    <!DOCTYPE mml:math
        PUBLIC "-//W3C//DTD MathML 2.0//EN"
               "http://www.w3.org/Math/DTD/mathml2/mathml2.dtd" [
        <!ENTITY % MATHML.prefixed "INCLUDE">
        <!ENTITY % MATHML.prefix "mml">
    ]>

    <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"
          xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
          xsi:schemaLocation="http://www.w3.org/1998/Math/MathML
                http://www.w3.org/Math/XMLSchema/mathml2/mathml2.xsd">
    ...
        <mml:mo> &DifferentialD; </mml:mo>
    ...
    </mml:math>

The use of character references to represent characters and symbols, such as `&#x2146;` (which is equivalent `to &DifferentialD;`) does not necessitate the use of a DOCTYPE declaration.

J
Overview: Mathematical Markup Language (MathML) Version 2.0 (2nd Edition)
Previous: 8 Document Object Model for MathML
Next: B Content Markup Validation Grammar