Overview: Mathematical Markup Language (MathML) Version 2.0
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A Parsing MathML
A.1 DOCTYPE Declaration for MathML
A.2 MathML as a DTD Module
A.3 Namespace prefix declarations
A.4 Use of MathML without a DTD
A.5 SGML
A.6 The MathML DTD
MathML documents should be validated using the XML DTD for MathML, which is also shown below in Section A.6 [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/TR/MathML2/dtd/mathml2.dtd"
>
The URI may be changed to that of a local copy of the DTD if required.
If a namespace prefix is being used, so that for example the document element is:
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> ... </mml:math>
then the prefix must be declared in the local subset of the DTD, as follows:
<!DOCTYPE mml:math
PUBLIC "-//W3C//DTD MathML 2.0//EN"
"http://www.w3.org/TR/MathML2/dtd/mathml2.dtd" [
<!ENTITY % MATHML.prefixed "INCLUDE">
<!ENTITY % MATHML.prefix "mml">
]>
This use of parameter entities to control namespace prefixes follows the conventions specified in [Modularization].
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/TR/MathML2/dtd/xhtml-math11-f.dtd"
>
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.
As mentioned above, 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 local 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 "math" >
would set the prefix for the MathML namespace to math:.
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).
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.
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.
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 the
note on SGML and XML.
Some older SGML systems may not be able to process files referring to plane 1 characters (those with Unicode values above hex FFFF).
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 zip 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 1998-2000 World Wide Web Consortium
(Massachusetts Institute of Technology, Institut National de
Recherche en Informatique et en Automatique, Keio University).
All Rights Reserved.
Permission to use, copy, modify and distribute the XHTML 1.1 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: appendixa.html,v 1.2 2001/01/08 15:09:42 dom 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
-->
<!-- 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:href CDATA #IMPLIED
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 -->
<!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" >
<!ENTITY % att-rowalign
"rowalign CDATA #IMPLIED" >
<!ENTITY % att-columnalign
"columnalign CDATA #IMPLIED" >
<!ENTITY % att-columnwidth
"columnwidth CDATA #IMPLIED" >
<!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-framespacing
"framespacing CDATA #IMPLIED" >
<!ENTITY % att-equalrows
"equalrows CDATA #IMPLIED" >
<!ENTITY % att-equalcolumns
"equalcolumns CDATA #IMPLIED" >
<!ENTITY % att-tableinfo
"%att-align;
%att-rowalign;
%att-columnalign;
%att-columnwidth;
%att-groupalign;
%att-alignmentscope;
%att-rowspacing;
%att-columnspacing;
%att-rowlines;
%att-columnlines;
%att-frame;
%att-framespacing;
%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" >
<!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;
%att-linethickness;
>
<!ATTLIST %msqrt.qname;
%MATHML.Common.attrib;
>
<!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-actiontype;
%att-selection;
>
<!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 -->
<!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;
%att-groupalign;
>
<!ATTLIST %mlabeledtr.qname;
%MATHML.Common.attrib;
%att-rowalign;
%att-columnalign;
%att-groupalign;
>
<!ATTLIST %mtd.qname;
%MATHML.Common.attrib;
%att-rowalign;
%att-columnalign;
%att-groupalign;
%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 -->
<!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 -->
<!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)
-->
<!ENTITY % ContentExpression
"(%Content; | %PresInCont;)*" >
<!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; (%ContentExpression;) >
<!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.
-->
<!ELEMENT %mstyle.qname; (%PresExpression;) >
<!ELEMENT %merror.qname; (%PresExpression;) >
<!ELEMENT %mphantom.qname; (%PresExpression;) >
<!ELEMENT %mrow.qname; (%PresExpression;) >
<!ELEMENT %mfrac.qname; (%PresExpression;) >
<!ELEMENT %msqrt.qname; (%PresExpression;) >
<!ELEMENT %menclose.qname; (%PresExpression;) >
<!ELEMENT %mroot.qname; (%PresExpression;) >
<!ELEMENT %msub.qname; (%PresExpression;) >
<!ELEMENT %msup.qname; (%PresExpression;) >
<!ELEMENT %msubsup.qname; (%PresExpression;) >
<!ELEMENT %mmultiscripts.qname; (%PresExpression;) >
<!ELEMENT %munder.qname; (%PresExpression;) >
<!ELEMENT %mover.qname; (%PresExpression;) >
<!ELEMENT %munderover.qname; (%PresExpression;) >
<!ELEMENT %mtable.qname; (%PresExpression;) >
<!ELEMENT %mtr.qname; (%PresExpression;) >
<!ELEMENT %mlabeledtr.qname; (%PresExpression;) >
<!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" >
<!ENTITY % att-display
"display CDATA #IMPLIED" >
<!ENTITY % att-topinfo
"%MATHML.Common.attrib;
%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"
"isoamsa.ent" >
%ent-isoamsa;
<!ENTITY % ent-isoamsb
PUBLIC "-//W3C//ENTITIES Added Math Symbols: Binary Operators for MathML 2.0//EN"
"isoamsb.ent" >
%ent-isoamsb;
<!ENTITY % ent-isoamsc
PUBLIC "-//W3C//ENTITIES Added Math Symbols: Delimiters for MathML 2.0//EN"
"isoamsc.ent" >
%ent-isoamsc;
<!ENTITY % ent-isoamsn
PUBLIC "-//W3C//ENTITIES Added Math Symbols: Negated Relations for MathML 2.0//EN"
"isoamsn.ent" >
%ent-isoamsn;
<!ENTITY % ent-isoamso
PUBLIC "-//W3C//ENTITIES Added Math Symbols: Ordinary for MathML 2.0//EN"
"isoamso.ent" >
%ent-isoamso;
<!ENTITY % ent-isoamsr
PUBLIC "-//W3C//ENTITIES Added Math Symbols: Relations for MathML 2.0//EN"
"isoamsr.ent" >
%ent-isoamsr;
<!ENTITY % ent-isogrk3
PUBLIC "-//W3C//ENTITIES Greek Symbols for MathML 2.0//EN"
"isogrk3.ent" >
%ent-isogrk3;
<!ENTITY % ent-isomfrk
PUBLIC "-//W3C//ENTITIES Math Alphabets: Fraktur for MathML 2.0//EN"
"isomfrk.ent" >
%ent-isomfrk;
<!ENTITY % ent-isomopf
PUBLIC "-//W3C//ENTITIES Math Alphabets: Open Face for MathML 2.0//EN"
"isomopf.ent" >
%ent-isomopf;
<!ENTITY % ent-isomscr
PUBLIC "-//W3C//ENTITIES Math Alphabets: Script for MathML 2.0//EN"
"isomscr.ent" >
%ent-isomscr;
<!ENTITY % ent-isotech
PUBLIC "-//W3C//ENTITIES General Technical for MathML 2.0//EN"
"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"
"isobox.ent" >
%ent-isobox;
<!ENTITY % ent-isocyr1
PUBLIC "-//W3C//ENTITIES Russian Cyrillic for MathML 2.0//EN"
"isocyr1.ent" >
%ent-isocyr1;
<!ENTITY % ent-isocyr2
PUBLIC "-//W3C//ENTITIES Non-Russian Cyrillic for MathML 2.0//EN"
"isocyr2.ent" >
%ent-isocyr2;
<!ENTITY % ent-isodia
PUBLIC "-//W3C//ENTITIES Diacritical Marks for MathML 2.0//EN"
"isodia.ent" >
%ent-isodia;
<!ENTITY % ent-isolat1
PUBLIC "-//W3C//ENTITIES Added Latin 1 for MathML 2.0//EN"
"isolat1.ent" >
%ent-isolat1;
<!ENTITY % ent-isolat2
PUBLIC "-//W3C//ENTITIES Added Latin 2 for MathML 2.0//EN"
"isolat2.ent" >
%ent-isolat2;
<!ENTITY % ent-isonum
PUBLIC "-//W3C//ENTITIES Numeric and Special Graphic for MathML 2.0//EN"
"isonum.ent" >
%ent-isonum;
<!ENTITY % ent-isopub
PUBLIC "-//W3C//ENTITIES Publishing for MathML 2.0//EN"
"isopub.ent" >
%ent-isopub;
<!-- New characters defined by MathML ............................ -->
<!ENTITY % ent-mmlextra
PUBLIC "-//W3C//ENTITIES Extra for MathML 2.0//EN"
"mmlextra.ent" >
%ent-mmlextra;
<!-- MathML aliases for characters defined above ................. -->
<!ENTITY % ent-mmlalias
PUBLIC "-//W3C//ENTITIES Aiases for MathML 2.0//EN"
"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 2000-10-31
David Carlisle
-->
<!-- end of MathML 2.0 DTD ................................................ -->
<!-- ....................................................................... -->
Overview: Mathematical Markup Language (MathML) Version 2.0
Previous: 8 Document Object Model for MathML
Next: B Content Markup Validation Grammar