
<!-- MathML 3.0 DTD  ....................................................... -->
<!-- file: mathml3.dtd
-->

<!-- MathML 3.0 DTD

     This is the Mathematical Markup Language (MathML) 3.0, an XML
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     both its structure and content.

     Copyright &#xa9; 1998-2014 W3C&#xae; (MIT, ERCIM, Keio, Beihang), All Rights 
     Reserved. W3C liability, trademark, document use and software
     licensing rules apply. 

     Permission to use, copy, modify and distribute the MathML 3.0 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.

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

       PUBLIC "-//W3C//DTD MathML 3.0//EN"
       SYSTEM "mathml3.dtd"

-->

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<!ENTITY % mathml-qname.mod
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<!ENTITY % htmlmathmlent PUBLIC "-//W3C//ENTITIES HTML MathML Set//EN//XML" "htmlmathml-f.ent">
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  %DefEncAtt;>

<!ELEMENT %sech.qname; EMPTY>
<!ATTLIST %sech.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %csch.qname; EMPTY>
<!ATTLIST %csch.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %coth.qname; EMPTY>
<!ATTLIST %coth.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %arcsin.qname; EMPTY>
<!ATTLIST %arcsin.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %arccos.qname; EMPTY>
<!ATTLIST %arccos.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %arctan.qname; EMPTY>
<!ATTLIST %arctan.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %arccosh.qname; EMPTY>
<!ATTLIST %arccosh.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %arccot.qname; EMPTY>
<!ATTLIST %arccot.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %arccoth.qname; EMPTY>
<!ATTLIST %arccoth.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %arccsc.qname; EMPTY>
<!ATTLIST %arccsc.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %arccsch.qname; EMPTY>
<!ATTLIST %arccsch.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %arcsec.qname; EMPTY>
<!ATTLIST %arcsec.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %arcsech.qname; EMPTY>
<!ATTLIST %arcsech.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %arcsinh.qname; EMPTY>
<!ATTLIST %arcsinh.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %arctanh.qname; EMPTY>
<!ATTLIST %arctanh.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %mean.qname; EMPTY>
<!ATTLIST %mean.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %sdev.qname; EMPTY>
<!ATTLIST %sdev.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %variance.qname; EMPTY>
<!ATTLIST %variance.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %median.qname; EMPTY>
<!ATTLIST %median.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %mode.qname; EMPTY>
<!ATTLIST %mode.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %vector.qname; ((%BvarQ;),(%DomainQ;),(%ContExp;)*)>
<!ATTLIST %vector.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %matrix.qname; ((%BvarQ;),(%DomainQ;),(%ContExp;)*)>
<!ATTLIST %matrix.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %matrixrow.qname; ((%BvarQ;),(%DomainQ;),(%ContExp;)*)>
<!ATTLIST %matrixrow.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %determinant.qname; EMPTY>
<!ATTLIST %determinant.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %transpose.qname; EMPTY>
<!ATTLIST %transpose.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %selector.qname; EMPTY>
<!ATTLIST %selector.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %vectorproduct.qname; EMPTY>
<!ATTLIST %vectorproduct.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %scalarproduct.qname; EMPTY>
<!ATTLIST %scalarproduct.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %outerproduct.qname; EMPTY>
<!ATTLIST %outerproduct.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %integers.qname; EMPTY>
<!ATTLIST %integers.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %reals.qname; EMPTY>
<!ATTLIST %reals.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %rationals.qname; EMPTY>
<!ATTLIST %rationals.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %naturalnumbers.qname; EMPTY>
<!ATTLIST %naturalnumbers.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %complexes.qname; EMPTY>
<!ATTLIST %complexes.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %primes.qname; EMPTY>
<!ATTLIST %primes.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %emptyset.qname; EMPTY>
<!ATTLIST %emptyset.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %exponentiale.qname; EMPTY>
<!ATTLIST %exponentiale.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %imaginaryi.qname; EMPTY>
<!ATTLIST %imaginaryi.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %notanumber.qname; EMPTY>
<!ATTLIST %notanumber.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %true.qname; EMPTY>
<!ATTLIST %true.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %false.qname; EMPTY>
<!ATTLIST %false.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %pi.qname; EMPTY>
<!ATTLIST %pi.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %eulergamma.qname; EMPTY>
<!ATTLIST %eulergamma.qname;
  %CommonAtt;
  %DefEncAtt;>

<!ELEMENT %infinity.qname; EMPTY>
<!ATTLIST %infinity.qname;
  %CommonAtt;
  %DefEncAtt;>

<!-- end of mathml3-common.rng -->

<!ENTITY % MathExpression "%ContExp;|%PresentationExpression;">

<!-- end of mathml3-content.rng -->

<!-- start of mathml3-presentation.rng -->

<!ENTITY % ImpliedMrow "(%MathExpression;)*">

<!ENTITY % TableRowExpression "%mtr.qname;|%mlabeledtr.qname;">

<!ENTITY % TableCellExpression "%mtd.qname;">

<!ENTITY % MstackExpression "%MathExpression;|%mscarries.qname;
                             |%msline.qname;|%msrow.qname;|%msgroup.qname;">

<!ENTITY % MsrowExpression "%MathExpression;|%none.qname;">

<!ENTITY % MultiScriptExpression "(%MathExpression;|%none.qname;),
                                  (%MathExpression;|%none.qname;)">

<!ENTITY % mpadded-length "CDATA">

<!ENTITY % linestyle "none|solid|dashed">

<!ENTITY % verticalalign "top|bottom|center|baseline|axis">

<!ENTITY % columnalignstyle "left|center|right">

<!ENTITY % notationstyle "longdiv|actuarial|radical|box|roundedbox
                          |circle|left|right|top|bottom|updiagonalstrike
                          |downdiagonalstrike|verticalstrike
                          |horizontalstrike|madruwb">

<!ENTITY % idref "#PCDATA">

<!ENTITY % unsigned-integer "CDATA">

<!ENTITY % integer "CDATA">

<!ENTITY % number "CDATA">

<!ENTITY % character "CDATA">

<!ENTITY % color "CDATA">

<!ENTITY % group-alignment "left|center|right|decimalpoint">

<!ENTITY % group-alignment-list "#PCDATA">

<!ENTITY % group-alignment-list-list "#PCDATA">

<!ENTITY % positive-integer "CDATA">

<!ENTITY % token.content "#PCDATA|%mglyph.qname;|%malignmark.qname;">

<!ELEMENT %mi.qname; (%token.content;)*>

<!ENTITY % length "CDATA">

<!ENTITY % DeprecatedTokenAtt "
  fontfamily CDATA #IMPLIED
  fontweight (normal|bold) #IMPLIED
  fontstyle (normal|italic) #IMPLIED
  fontsize %length; #IMPLIED
  color %color; #IMPLIED
  background CDATA #IMPLIED">

<!ENTITY % TokenAtt "
  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
               |initial|tailed|looped|stretched) #IMPLIED
  mathsize CDATA #IMPLIED
  dir (ltr|rtl) #IMPLIED
  %DeprecatedTokenAtt;">

<!ENTITY % CommonPresAtt "
  mathcolor %color; #IMPLIED
  mathbackground CDATA #IMPLIED">

<!ATTLIST %mi.qname;
  %CommonAtt;
  %CommonPresAtt;
  %TokenAtt;>

<!ELEMENT %mn.qname; (%token.content;)*>

<!ATTLIST %mn.qname;
  %CommonAtt;
  %CommonPresAtt;
  %TokenAtt;>

<!ELEMENT %mo.qname; (%token.content;)*>

<!ATTLIST %mo.qname;
  %CommonAtt;
  %CommonPresAtt;
  %TokenAtt;
  form (prefix|infix|postfix) #IMPLIED
  fence (true|false) #IMPLIED
  separator (true|false) #IMPLIED
  lspace %length; #IMPLIED
  rspace %length; #IMPLIED
  stretchy (true|false) #IMPLIED
  symmetric (true|false) #IMPLIED
  maxsize CDATA #IMPLIED
  minsize %length; #IMPLIED
  largeop (true|false) #IMPLIED
  movablelimits (true|false) #IMPLIED
  accent (true|false) #IMPLIED
  linebreak (auto|newline|nobreak|goodbreak|badbreak) #IMPLIED
  lineleading %length; #IMPLIED
  linebreakstyle (before|after|duplicate|infixlinebreakstyle) #IMPLIED
  linebreakmultchar CDATA #IMPLIED
  indentalign (left|center|right|auto|id) #IMPLIED
  indentshift %length; #IMPLIED
  indenttarget CDATA #IMPLIED
  indentalignfirst (left|center|right|auto|id|indentalign) #IMPLIED
  indentshiftfirst CDATA #IMPLIED
  indentalignlast (left|center|right|auto|id|indentalign) #IMPLIED
  indentshiftlast CDATA #IMPLIED>

<!ELEMENT %mtext.qname; (%token.content;)*>

<!ATTLIST %mtext.qname;
  %CommonAtt;
  %CommonPresAtt;
  %TokenAtt;>

<!ELEMENT %mspace.qname; EMPTY>

<!ATTLIST %mspace.qname;
  %CommonAtt;
  %CommonPresAtt;
  %TokenAtt;
  width %length; #IMPLIED
  height %length; #IMPLIED
  depth %length; #IMPLIED
  linebreak (auto|newline|nobreak|goodbreak|badbreak
             |indentingnewline) #IMPLIED
  indentalign (left|center|right|auto|id) #IMPLIED
  indentshift %length; #IMPLIED
  indenttarget CDATA #IMPLIED
  indentalignfirst (left|center|right|auto|id|indentalign) #IMPLIED
  indentshiftfirst CDATA #IMPLIED
  indentalignlast (left|center|right|auto|id|indentalign) #IMPLIED
  indentshiftlast CDATA #IMPLIED>

<!ELEMENT %ms.qname; (%token.content;)*>

<!ATTLIST %ms.qname;
  %CommonAtt;
  %CommonPresAtt;
  %TokenAtt;
  lquote CDATA #IMPLIED
  rquote CDATA #IMPLIED>

<!ENTITY % mglyph.deprecatedattributes "
  index %integer; #IMPLIED
  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
               |initial|tailed|looped|stretched) #IMPLIED
  mathsize CDATA #IMPLIED
  %DeprecatedTokenAtt;">

<!ENTITY % mglyph.attributes "
  %CommonAtt;
  %CommonPresAtt;
  src CDATA #IMPLIED
  width %length; #IMPLIED
  height %length; #IMPLIED
  valign %length; #IMPLIED
  alt CDATA #IMPLIED">

<!ELEMENT %mglyph.qname; EMPTY>
<!ATTLIST %mglyph.qname;
  %mglyph.attributes;
  %mglyph.deprecatedattributes;>

<!ELEMENT %msline.qname; EMPTY>

<!ATTLIST %msline.qname;
  %CommonAtt;
  %CommonPresAtt;
  position %integer; #IMPLIED
  length %unsigned-integer; #IMPLIED
  leftoverhang %length; #IMPLIED
  rightoverhang %length; #IMPLIED
  mslinethickness CDATA #IMPLIED>

<!ELEMENT %none.qname; EMPTY>

<!ATTLIST %none.qname;
  %CommonAtt;
  %CommonPresAtt;>

<!ELEMENT %mprescripts.qname; EMPTY>

<!ATTLIST %mprescripts.qname;
  %CommonAtt;
  %CommonPresAtt;>

<!ELEMENT %malignmark.qname; EMPTY>

<!ATTLIST %malignmark.qname;
  %CommonAtt;
  %CommonPresAtt;
  edge (left|right) #IMPLIED>

<!ELEMENT %maligngroup.qname; EMPTY>

<!ATTLIST %maligngroup.qname;
  %CommonAtt;
  %CommonPresAtt;
  groupalign (left|center|right|decimalpoint) #IMPLIED>

<!ELEMENT %mrow.qname; (%MathExpression;)*>

<!ATTLIST %mrow.qname;
  %CommonAtt;
  %CommonPresAtt;
  dir (ltr|rtl) #IMPLIED>

<!ELEMENT %mfrac.qname; ((%MathExpression;),(%MathExpression;))>

<!ATTLIST %mfrac.qname;
  %CommonAtt;
  %CommonPresAtt;
  linethickness CDATA #IMPLIED
  numalign (left|center|right) #IMPLIED
  denomalign (left|center|right) #IMPLIED
  bevelled (true|false) #IMPLIED>

<!ELEMENT %msqrt.qname; (%ImpliedMrow;)>

<!ATTLIST %msqrt.qname;
  %CommonAtt;
  %CommonPresAtt;>

<!ELEMENT %mroot.qname; ((%MathExpression;),(%MathExpression;))>

<!ATTLIST %mroot.qname;
  %CommonAtt;
  %CommonPresAtt;>

<!ELEMENT %mstyle.qname; (%ImpliedMrow;)>

<!ENTITY % mstyle.deprecatedattributes "
  %DeprecatedTokenAtt;
  veryverythinmathspace %length; #IMPLIED
  verythinmathspace %length; #IMPLIED
  thinmathspace %length; #IMPLIED
  mediummathspace %length; #IMPLIED
  thickmathspace %length; #IMPLIED
  verythickmathspace %length; #IMPLIED
  veryverythickmathspace %length; #IMPLIED">

<!ENTITY % mstyle.generalattributes "
  accent (true|false) #IMPLIED
  accentunder (true|false) #IMPLIED
  align (left|right|center) #IMPLIED
  alignmentscope CDATA #IMPLIED
  bevelled (true|false) #IMPLIED
  charalign (left|center|right) #IMPLIED
  charspacing CDATA #IMPLIED
  close CDATA #IMPLIED
  columnalign CDATA #IMPLIED
  columnlines CDATA #IMPLIED
  columnspacing CDATA #IMPLIED
  columnspan %positive-integer; #IMPLIED
  columnwidth CDATA #IMPLIED
  crossout CDATA #IMPLIED
  denomalign (left|center|right) #IMPLIED
  depth %length; #IMPLIED
  dir (ltr|rtl) #IMPLIED
  edge (left|right) #IMPLIED
  equalcolumns (true|false) #IMPLIED
  equalrows (true|false) #IMPLIED
  fence (true|false) #IMPLIED
  form (prefix|infix|postfix) #IMPLIED
  frame (%linestyle;) #IMPLIED
  framespacing CDATA #IMPLIED
  groupalign CDATA #IMPLIED
  height %length; #IMPLIED
  indentalign (left|center|right|auto|id) #IMPLIED
  indentalignfirst (left|center|right|auto|id|indentalign) #IMPLIED
  indentalignlast (left|center|right|auto|id|indentalign) #IMPLIED
  indentshift %length; #IMPLIED
  indentshiftfirst CDATA #IMPLIED
  indentshiftlast CDATA #IMPLIED
  indenttarget CDATA #IMPLIED
  largeop (true|false) #IMPLIED
  leftoverhang %length; #IMPLIED
  length %unsigned-integer; #IMPLIED
  linebreak (auto|newline|nobreak|goodbreak|badbreak) #IMPLIED
  linebreakmultchar CDATA #IMPLIED
  linebreakstyle (before|after|duplicate|infixlinebreakstyle) #IMPLIED
  lineleading %length; #IMPLIED
  linethickness CDATA #IMPLIED
  location (w|nw|n|ne|e|se|s|sw) #IMPLIED
  longdivstyle CDATA #IMPLIED
  lquote CDATA #IMPLIED
  lspace %length; #IMPLIED
  mathsize CDATA #IMPLIED
  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
               |initial|tailed|looped|stretched) #IMPLIED
  maxsize CDATA #IMPLIED
  minlabelspacing %length; #IMPLIED
  minsize %length; #IMPLIED
  movablelimits (true|false) #IMPLIED
  mslinethickness CDATA #IMPLIED
  notation CDATA #IMPLIED
  numalign (left|center|right) #IMPLIED
  open CDATA #IMPLIED
  position %integer; #IMPLIED
  rightoverhang %length; #IMPLIED
  rowalign CDATA #IMPLIED
  rowlines CDATA #IMPLIED
  rowspacing CDATA #IMPLIED
  rowspan %positive-integer; #IMPLIED
  rquote CDATA #IMPLIED
  rspace %length; #IMPLIED
  selection %positive-integer; #IMPLIED
  separator (true|false) #IMPLIED
  separators CDATA #IMPLIED
  shift %integer; #IMPLIED
  side (left|right|leftoverlap|rightoverlap) #IMPLIED
  stackalign (left|center|right|decimalpoint) #IMPLIED
  stretchy (true|false) #IMPLIED
  subscriptshift %length; #IMPLIED
  superscriptshift %length; #IMPLIED
  symmetric (true|false) #IMPLIED
  valign %length; #IMPLIED
  width %length; #IMPLIED">

<!ENTITY % mstyle.specificattributes "
  scriptlevel %integer; #IMPLIED
  displaystyle (true|false) #IMPLIED
  scriptsizemultiplier %number; #IMPLIED
  scriptminsize %length; #IMPLIED
  infixlinebreakstyle (before|after|duplicate) #IMPLIED
  decimalpoint %character; #IMPLIED">

<!ATTLIST %mstyle.qname;
  %CommonAtt;
  %CommonPresAtt;
  %mstyle.specificattributes;
  %mstyle.generalattributes;
  %mstyle.deprecatedattributes;>

<!ELEMENT %merror.qname; (%ImpliedMrow;)>

<!ATTLIST %merror.qname;
  %CommonAtt;
  %CommonPresAtt;>

<!ELEMENT %mpadded.qname; (%ImpliedMrow;)>

<!ATTLIST %mpadded.qname;
  %CommonAtt;
  %CommonPresAtt;
  height %mpadded-length; #IMPLIED
  depth %mpadded-length; #IMPLIED
  width %mpadded-length; #IMPLIED
  lspace %mpadded-length; #IMPLIED
  voffset %mpadded-length; #IMPLIED>

<!ELEMENT %mphantom.qname; (%ImpliedMrow;)>

<!ATTLIST %mphantom.qname;
  %CommonAtt;
  %CommonPresAtt;>

<!ELEMENT %mfenced.qname; (%MathExpression;)*>

<!ATTLIST %mfenced.qname;
  %CommonAtt;
  %CommonPresAtt;
  open CDATA #IMPLIED
  close CDATA #IMPLIED
  separators CDATA #IMPLIED>

<!ELEMENT %menclose.qname; (%ImpliedMrow;)>

<!ATTLIST %menclose.qname;
  %CommonAtt;
  %CommonPresAtt;
  notation CDATA #IMPLIED>

<!ELEMENT %msub.qname; ((%MathExpression;),(%MathExpression;))>

<!ATTLIST %msub.qname;
  %CommonAtt;
  %CommonPresAtt;
  subscriptshift %length; #IMPLIED>

<!ELEMENT %msup.qname; ((%MathExpression;),(%MathExpression;))>

<!ATTLIST %msup.qname;
  %CommonAtt;
  %CommonPresAtt;
  superscriptshift %length; #IMPLIED>

<!ENTITY % msubsup.attributes "
  %CommonAtt;
  %CommonPresAtt;
  subscriptshift %length; #IMPLIED
  superscriptshift %length; #IMPLIED">

<!ELEMENT %msubsup.qname; ((%MathExpression;),(%MathExpression;),
                         (%MathExpression;))>
<!ATTLIST %msubsup.qname;
  %msubsup.attributes;>

<!ELEMENT %munder.qname; ((%MathExpression;),(%MathExpression;))>

<!ATTLIST %munder.qname;
  %CommonAtt;
  %CommonPresAtt;
  accentunder (true|false) #IMPLIED
  align (left|right|center) #IMPLIED>

<!ELEMENT %mover.qname; ((%MathExpression;),(%MathExpression;))>

<!ATTLIST %mover.qname;
  %CommonAtt;
  %CommonPresAtt;
  accent (true|false) #IMPLIED
  align (left|right|center) #IMPLIED>

<!ELEMENT %munderover.qname; ((%MathExpression;),(%MathExpression;),
                            (%MathExpression;))>

<!ATTLIST %munderover.qname;
  %CommonAtt;
  %CommonPresAtt;
  accent (true|false) #IMPLIED
  accentunder (true|false) #IMPLIED
  align (left|right|center) #IMPLIED>

<!ELEMENT %mmultiscripts.qname; ((%MathExpression;),
                               (%MultiScriptExpression;)*,
                               (%mprescripts.qname;,
                                (%MultiScriptExpression;)*)?)>

<!ATTLIST %mmultiscripts.qname;
  %msubsup.attributes;>

<!ELEMENT %mtable.qname; (%TableRowExpression;)*>

<!ATTLIST %mtable.qname;
  %CommonAtt;
  %CommonPresAtt;
  align CDATA #IMPLIED
  rowalign CDATA #IMPLIED
  columnalign CDATA #IMPLIED
  groupalign CDATA #IMPLIED
  alignmentscope CDATA #IMPLIED
  columnwidth CDATA #IMPLIED
  width CDATA #IMPLIED
  rowspacing CDATA #IMPLIED
  columnspacing CDATA #IMPLIED
  rowlines CDATA #IMPLIED
  columnlines CDATA #IMPLIED
  frame (%linestyle;) #IMPLIED
  framespacing CDATA #IMPLIED
  equalrows (true|false) #IMPLIED
  equalcolumns (true|false) #IMPLIED
  displaystyle (true|false) #IMPLIED
  side (left|right|leftoverlap|rightoverlap) #IMPLIED
  minlabelspacing %length; #IMPLIED>

<!ELEMENT %mlabeledtr.qname; (%TableCellExpression;)+>

<!ENTITY % mtr.attributes "
  %CommonAtt;
  %CommonPresAtt;
  rowalign (top|bottom|center|baseline|axis) #IMPLIED
  columnalign CDATA #IMPLIED
  groupalign CDATA #IMPLIED">

<!ATTLIST %mlabeledtr.qname;
  %mtr.attributes;>

<!ELEMENT %mtr.qname; (%TableCellExpression;)*>
<!ATTLIST %mtr.qname;
  %mtr.attributes;>

<!ELEMENT %mtd.qname; (%ImpliedMrow;)>

<!ATTLIST %mtd.qname;
  %CommonAtt;
  %CommonPresAtt;
  rowspan %positive-integer; #IMPLIED
  columnspan %positive-integer; #IMPLIED
  rowalign (top|bottom|center|baseline|axis) #IMPLIED
  columnalign (%columnalignstyle;) #IMPLIED
  groupalign CDATA #IMPLIED>

<!ELEMENT %mstack.qname; (%MstackExpression;)*>

<!ATTLIST %mstack.qname;
  %CommonAtt;
  %CommonPresAtt;
  align CDATA #IMPLIED
  stackalign (left|center|right|decimalpoint) #IMPLIED
  charalign (left|center|right) #IMPLIED
  charspacing CDATA #IMPLIED>

<!ELEMENT %mlongdiv.qname; ((%MstackExpression;),(%MstackExpression;),
                          (%MstackExpression;)+)>

<!ENTITY % msgroup.attributes "
  %CommonAtt;
  %CommonPresAtt;
  position %integer; #IMPLIED
  shift %integer; #IMPLIED">

<!ATTLIST %mlongdiv.qname;
  %msgroup.attributes;
  longdivstyle CDATA #IMPLIED>

<!ELEMENT %msgroup.qname; (%MstackExpression;)*>
<!ATTLIST %msgroup.qname;
  %msgroup.attributes;>

<!ELEMENT %msrow.qname; (%MsrowExpression;)*>

<!ATTLIST %msrow.qname;
  %CommonAtt;
  %CommonPresAtt;
  position %integer; #IMPLIED>

<!ELEMENT %mscarries.qname; (%MsrowExpression;|%mscarry.qname;)*>

<!ATTLIST %mscarries.qname;
  %CommonAtt;
  %CommonPresAtt;
  position %integer; #IMPLIED
  location (w|nw|n|ne|e|se|s|sw) #IMPLIED
  crossout CDATA #IMPLIED
  scriptsizemultiplier %number; #IMPLIED>

<!ELEMENT %mscarry.qname; (%MsrowExpression;)*>

<!ATTLIST %mscarry.qname;
  %CommonAtt;
  %CommonPresAtt;
  location (w|nw|n|ne|e|se|s|sw) #IMPLIED
  crossout CDATA #IMPLIED>

<!ELEMENT %maction.qname; (%MathExpression;)+>

<!ATTLIST %maction.qname;
  %CommonAtt;
  %CommonPresAtt;
  actiontype CDATA #REQUIRED
  selection %positive-integer; #IMPLIED>

<!-- end of mathml3-presentation.rng -->

<!-- start of mathml3-common.rng -->

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

<!ENTITY % NonMathMLAtt "">

<!ENTITY % math.deprecatedattributes "
  mode CDATA #IMPLIED
  macros CDATA #IMPLIED">

<!ATTLIST %math.qname;
  %CommonAtt;
  display (block|inline) #IMPLIED
  maxwidth %length; #IMPLIED
  overflow (linebreak|scroll|elide|truncate|scale) #IMPLIED
  altimg CDATA #IMPLIED
  altimg-width %length; #IMPLIED
  altimg-height %length; #IMPLIED
  altimg-valign CDATA #IMPLIED
  alttext CDATA #IMPLIED
  cdgroup CDATA #IMPLIED
  %math.deprecatedattributes;
  %CommonPresAtt;
  %mstyle.specificattributes;
  %mstyle.generalattributes;>

<!ENTITY % name "
  name CDATA #REQUIRED">

<!ENTITY % cd "
  cd CDATA #REQUIRED">

<!ENTITY % annotation.attributes "
  %CommonAtt;
  cd CDATA #IMPLIED
  name CDATA #IMPLIED
  %DefEncAtt;
  src CDATA #IMPLIED">

<!ELEMENT %annotation.qname; (#PCDATA)>
<!ATTLIST %annotation.qname;
  %annotation.attributes;>

<!ENTITY % annotation-xml.model "(%MathExpression;)*">

<!ENTITY % anyElement "">

<!ELEMENT %annotation-xml.qname; (%annotation-xml.model;)>
<!ATTLIST %annotation-xml.qname;
  %annotation.attributes;>

<!ELEMENT %semantics.qname; ((%MathExpression;),
                           (%annotation.qname;|%annotation-xml.qname;)*)>

<!ATTLIST %semantics.qname;
  %CommonAtt;
  %DefEncAtt;
  cd CDATA #IMPLIED
  name CDATA #IMPLIED>