<!-- 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: mathml2.dtd,v 1.20 2000/12/06 19:03:13 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
-->


<!-- 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                 
     "