/*************************************************************
 *
 *  MathJax/extensions/MathML/mml3.js
 *
 *  This file implements an XSLT transform to convert some MathML 3 
 *  constructs to constructs MathJax can render. The transform is
 *  performed in a pre-filter for the MathML input jax, so that the
 *  Show Math As menu will still show the Original MathML correctly,
 *  but the transformed MathML can be obtained from the regular MathML menu.
 *  
 *  To load it, include
 *  
 *      MathML: {
 *        extensions: ["mml3.js"]
 *      }
 *  
 *  in your configuration.
 * 
 *  A portion of this file is taken from mml3mj.xsl which is
 *  Copyright (c) David Carlisle 2008-2015
 *  and is used by permission of David Carlisle, who has agreed to allow us
 *  to release it under the Apache2 license (see below).  That portion is
 *  indicated via comments.
 *   
 *  The remainder falls under the copyright that follows.
 *  ---------------------------------------------------------------------
 *  
 *  Copyright (c) 2013-2020 The MathJax Consortium
 *  
 *  Licensed under the Apache License, Version 2.0 (the "License");
 *  you may not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *  
 *      http://www.apache.org/licenses/LICENSE-2.0
 *  
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS,
 *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 */


MathJax.Extension["MathML/mml3"] = {
  version: "2.7.9"
};

MathJax.Hub.Register.StartupHook("MathML Jax Ready",function () {

  var MATHML = MathJax.InputJax.MathML,
      PARSE = MATHML.Parse.prototype;

  MATHML.prefilterHooks.Add(function (data) {
    if (!MATHML.mml3XSLT) return;

    // Parse the <math> but use MATHML.Parse's preProcessMath to apply the normal preprocessing.
    if (!MATHML.ParseXML) {MATHML.ParseXML = MATHML.createParser()}
    var doc = MATHML.ParseXML(PARSE.preProcessMath(data.math));

    // Now transform the <math> using the mml3 stylesheet.
    var newdoc = MATHML.mml3XSLT.transformToDocument(doc);

    if ((typeof newdoc) === "string") {
      // Internet Explorer returns a string, so just use it.
      data.math = newdoc;
    } else if (window.XMLSerializer) {
      // Serialize the <math> again. We could directly provide the DOM content
      // but other prefilterHooks may assume data.math is still a string.
      var serializer = new XMLSerializer();
      data.math = serializer.serializeToString(newdoc.documentElement, doc);
    }
  });

  /*
   *  The following is derived from mml3mj.xsl
   *  (https://github.com/davidcarlisle/web-xslt/blob/master/ctop/mml3mj.xsl)
   *  which is Copyright (c) David Carlisle 2008-2015.
   *  It is used by permission of David Carlisle, who has agreed to allow it to
   *  be released under the Apache License, Version 2.0.
   */
  var BROWSER = MathJax.Hub.Browser;
  var exslt = '';
  if (BROWSER.isEdge || BROWSER.isMSIE) {
    exslt = 'urn:schemas-microsoft-com:xslt'
  } else {
    exslt = 'http://exslt.org/common';
  }
  var mml3Stylesheet =
    '<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform" ' +
    '		xmlns:m="http://www.w3.org/1998/Math/MathML"' +
    '		xmlns:c="' + exslt + '"' +
    '		exclude-result-prefixes="m c">' +
    '<xsl:output indent="yes" omit-xml-declaration="yes"/>' +
    '<xsl:output indent="yes" omit-xml-declaration="yes"/><xsl:template match="*">' +
    ' <xsl:copy>' +
    '  <xsl:copy-of select="@*"/>' +
    '  <xsl:apply-templates/>' +
    ' </xsl:copy>' +
    '</xsl:template><xsl:template match="m:*[@dir=\'rtl\']"  priority="10">' +
    ' <xsl:apply-templates mode="rtl" select="."/>' +
    '</xsl:template><xsl:template match="@*" mode="rtl">' +
    ' <xsl:copy-of select="."/>' +
    ' <xsl:attribute name="dir">ltr</xsl:attribute>' +
    '</xsl:template>' +
    '<xsl:template match="*" mode="rtl">' +
    ' <xsl:copy>' +
    '  <xsl:apply-templates select="@*" mode="rtl"/>' +
    '  <xsl:for-each select="node()">' +
    '   <xsl:sort data-type="number" order="descending" select="position()"/>' +
    '   <xsl:text> </xsl:text>' +
    '   <xsl:apply-templates mode="rtl" select="."/>' +
    '  </xsl:for-each>' +
    ' </xsl:copy>' +
    '</xsl:template><xsl:template match="@open" mode="rtl">' +
    ' <xsl:attribute name="close"><xsl:value-of select="."/></xsl:attribute>' +
    '</xsl:template><xsl:template match="@open[.=\'(\']" mode="rtl">' +
    ' <xsl:attribute name="close">)</xsl:attribute>' +
    '</xsl:template><xsl:template match="@open[.=\')\']" mode="rtl">' +
    ' <xsl:attribute name="close">(</xsl:attribute>' +
    '</xsl:template>' +
    '<xsl:template match="@open[.=\'[\']" mode="rtl">' +
    ' <xsl:attribute name="close">]</xsl:attribute>' +
    '</xsl:template>' +
    '<xsl:template match="@open[.=\']\']" mode="rtl">' +
    ' <xsl:attribute name="close">[</xsl:attribute>' +
    '</xsl:template>' +
    '<xsl:template match="@open[.=\'{\']" mode="rtl">' +
    ' <xsl:attribute name="close">}</xsl:attribute>' +
    '</xsl:template>' +
    '<xsl:template match="@open[.=\'}\']" mode="rtl">' +
    ' <xsl:attribute name="close">{</xsl:attribute>' +
    '</xsl:template>' +
    '<xsl:template match="@close" mode="rtl">' +
    ' <xsl:attribute name="open"><xsl:value-of select="."/></xsl:attribute>' +
    '</xsl:template><xsl:template match="@close[.=\'(\']" mode="rtl">' +
    ' <xsl:attribute name="open">)</xsl:attribute>' +
    '</xsl:template><xsl:template match="@close[.=\')\']" mode="rtl">' +
    ' <xsl:attribute name="open">(</xsl:attribute>' +
    '</xsl:template>' +
    '<xsl:template match="@close[.=\'[\']" mode="rtl">' +
    ' <xsl:attribute name="open">]</xsl:attribute>' +
    '</xsl:template>' +
    '<xsl:template match="@close[.=\']\']" mode="rtl">' +
    ' <xsl:attribute name="open">[</xsl:attribute>' +
    '</xsl:template>' +
    '<xsl:template match="@close[.=\'{\']" mode="rtl">' +
    ' <xsl:attribute name="open">}</xsl:attribute>' +
    '</xsl:template>' +
    '<xsl:template match="@close[.=\'}\']" mode="rtl">' +
    ' <xsl:attribute name="open">{</xsl:attribute>' +
    '</xsl:template><xsl:template match="m:mfrac[@bevelled=\'true\']" mode="rtl">' +
    ' <m:mrow>' +
    '  <m:msub><m:mi></m:mi><xsl:apply-templates select="*[2]" mode="rtl"/></m:msub>' +
    '  <m:mo>&#x5c;</m:mo>' +
    '  <m:msup><m:mi></m:mi><xsl:apply-templates select="*[1]" mode="rtl"/></m:msup>' +
    ' </m:mrow>' +
    '</xsl:template><xsl:template match="m:mfrac" mode="rtl">' +
    ' <xsl:copy>' +
    '  <xsl:apply-templates mode="rtl" select="@*|*"/>' +
    ' </xsl:copy>' +
    '</xsl:template><xsl:template match="m:mroot" mode="rtl">' +
    ' <m:msup>' +
    '  <m:menclose notation="top right">' +
    '   <xsl:apply-templates mode="rtl" select="@*|*[1]"/>' +
    '  </m:menclose>' +
    '  <xsl:apply-templates mode="rtl" select="*[2]"/>' +
    ' </m:msup>' +
    '</xsl:template>' +
    '<xsl:template match="m:msqrt" mode="rtl">' +
    ' <m:menclose notation="top right">' +
    '  <xsl:apply-templates mode="rtl" select="@*|*[1]"/>' +
    ' </m:menclose>' +
    '</xsl:template><xsl:template match="m:mtable|m:munder|m:mover|m:munderover" mode="rtl" priority="2">' +
    ' <xsl:copy>' +
    '  <xsl:apply-templates select="@*" mode="rtl"/>' +
    '  <xsl:apply-templates mode="rtl">' +
    '  </xsl:apply-templates>' +
    ' </xsl:copy>' +
    '</xsl:template>' +
    '<xsl:template match="m:msup" mode="rtl" priority="2">' +
    ' <m:mmultiscripts>' +
    '  <xsl:apply-templates select="*[1]" mode="rtl"/>' +
    '  <m:mprescripts/>' +
    '  <m:none/>' +
    '  <xsl:apply-templates select="*[2]" mode="rtl"/>' +
    ' </m:mmultiscripts>' +
    '</xsl:template>' +
    '<xsl:template match="m:msub" mode="rtl" priority="2">' +
    ' <m:mmultiscripts>' +
    '  <xsl:apply-templates select="*[1]" mode="rtl"/>' +
    '  <m:mprescripts/>' +
    '  <xsl:apply-templates select="*[2]" mode="rtl"/>' +
    '  <m:none/>' +
    ' </m:mmultiscripts>' +
    '</xsl:template>' +
    '<xsl:template match="m:msubsup" mode="rtl" priority="2">' +
    ' <m:mmultiscripts>' +
    '  <xsl:apply-templates select="*[1]" mode="rtl"/>' +
    '  <m:mprescripts/>' +
    '  <xsl:apply-templates select="*[2]" mode="rtl"/>' +
    '  <xsl:apply-templates select="*[3]" mode="rtl"/>' +
    ' </m:mmultiscripts>' +
    '</xsl:template>' +
    '<xsl:template match="m:mmultiscripts" mode="rtl" priority="2">' +
    ' <m:mmultiscripts>' +
    '  <xsl:apply-templates select="*[1]" mode="rtl"/>' +
    '  <xsl:for-each  select="m:mprescripts/following-sibling::*[position() mod 2 = 1]">' +
    '   <xsl:sort data-type="number" order="descending" select="position()"/>' +
    '   <xsl:apply-templates select="."  mode="rtl"/>' +
    '   <xsl:apply-templates select="following-sibling::*[1]"  mode="rtl"/>' +
    '  </xsl:for-each>' +
    '  <m:mprescripts/>' +
    '  <xsl:for-each  select="m:mprescripts/preceding-sibling::*[position()!=last()][position() mod 2 = 0]">' +
    '   <xsl:sort data-type="number" order="descending" select="position()"/>' +
    '   <xsl:apply-templates select="."  mode="rtl"/>' +
    '   <xsl:apply-templates select="following-sibling::*[1]"  mode="rtl"/>' +
    '  </xsl:for-each>' +
    ' </m:mmultiscripts>' +
    '</xsl:template>' +
    '<xsl:template match="m:mmultiscripts[not(m:mprescripts)]" mode="rtl" priority="3">' +
    ' <m:mmultiscripts>' +
    '  <xsl:apply-templates select="*[1]" mode="rtl"/>' +
    '  <m:mprescripts/>' +
    '  <xsl:for-each  select="*[position() mod 2 = 0]">' +
    '   <xsl:sort data-type="number" order="descending" select="position()"/>' +
    '   <xsl:apply-templates select="."  mode="rtl"/>' +
    '   <xsl:apply-templates select="following-sibling::*[1]"  mode="rtl"/>' +
    '  </xsl:for-each>' +
    ' </m:mmultiscripts>' +
    '</xsl:template>' +
    '<xsl:template match="text()[.=\'(\']" mode="rtl">)</xsl:template>' +
    '<xsl:template match="text()[.=\')\']" mode="rtl">(</xsl:template>' +
    '<xsl:template match="text()[.=\'{\']" mode="rtl">}</xsl:template>' +
    '<xsl:template match="text()[.=\'}\']" mode="rtl">{</xsl:template>' +
    '<xsl:template match="text()[.=\'&lt;\']" mode="rtl">&gt;</xsl:template>' +
    '<xsl:template match="text()[.=\'&gt;\']" mode="rtl">&lt;</xsl:template>' +
    '<xsl:template match="text()[.=\'&#x2208;\']" mode="rtl">&#x220b;</xsl:template>' +
    '<xsl:template match="text()[.=\'&#x220b;\']" mode="rtl">&#x2208;</xsl:template>' +
    '<xsl:template match="@notation[.=\'radical\']" mode="rtl">' +
    ' <xsl:attribute name="notation">top right</xsl:attribute>' +
    '</xsl:template>' +
    '<xsl:template match="m:mlongdiv|m:mstack" mode="rtl">' +
    ' <m:mrow dir="ltr">' +
    ' <xsl:apply-templates select="."/>' +
    ' </m:mrow>' +
    '</xsl:template>' +
    '<xsl:template match="m:mstack" priority="11">' +
    ' <xsl:variable name="m">' +
    '  <m:mtable columnspacing="0em">' +
    '   <xsl:copy-of select="@align"/>' +
    '  <xsl:variable name="t">' +
    '   <xsl:apply-templates select="*" mode="mstack1">' +
    '    <xsl:with-param name="p" select="0"/>' +
    '   </xsl:apply-templates>' +
    '  </xsl:variable>' +
    '  <xsl:variable name="maxl">' +
    '   <xsl:for-each select="c:node-set($t)/*/@l">' +
    '    <xsl:sort data-type="number" order="descending"/>' +
    '    <xsl:if test="position()=1">' +
    '     <xsl:value-of select="."/>' +
    '    </xsl:if>' +
    '   </xsl:for-each>' +
    '  </xsl:variable>' +
    '  <xsl:for-each select="c:node-set($t)/*[not(@class=\'mscarries\') or following-sibling::*[1]/@class=\'mscarries\']">' +
    '<xsl:variable name="c" select="preceding-sibling::*[1][@class=\'mscarries\']"/>' +
    '   <xsl:text>&#10;</xsl:text>' +
    '   <m:mtr>' +
    '    <xsl:copy-of select="@class[.=\'msline\']"/>' +
    '    <xsl:variable name="offset" select="$maxl - @l"/>' +
    '    <xsl:choose>' +
    '     <xsl:when test="@class=\'msline\' and @l=\'*\'">' +
    '      <xsl:variable name="msl" select="*[1]"/>' +
    '      <xsl:for-each select="(//node())[position()&lt;=$maxl]">' +
    '       <xsl:copy-of select="$msl"/>' +
    '      </xsl:for-each>' +
    '     </xsl:when>' +
    '     <xsl:when test="$c">' +
    '      <xsl:variable name="ldiff" select="$c/@l - @l"/>' +
    '      <xsl:variable name="loffset" select="$maxl - $c/@l"/>' +
    '      <xsl:for-each select="(//*)[position()&lt;= $offset]">' +
    '       <xsl:variable name="pn" select="position()"/>' +
    '       <xsl:variable name="cy" select="$c/*[position()=$pn - $loffset]"/>' +
    '	 <m:mtd>' +
    '	  <xsl:if test="$cy/*">' +
    '	  <m:mover><m:mphantom><m:mn>0</m:mn></m:mphantom><m:mpadded width="0em" lspace="-0.5width">' +
    '	  <xsl:copy-of select="$cy/*"/></m:mpadded></m:mover>' +
    '	  </xsl:if>' +
    '	 </m:mtd>' +
    '      </xsl:for-each>' +
    '      <xsl:for-each select="*">' +
    '       <xsl:variable name="pn" select="position()"/>' +
    '       <xsl:variable name="cy" select="$c/*[position()=$pn + $ldiff]"/>' +
    '       <xsl:copy>' +
    '	<xsl:copy-of select="@*"/>' +
    '	<xsl:variable name="b">' +
    '	 <xsl:choose>' +
    '	  <xsl:when test="not(string($cy/@crossout) or $cy/@crossout=\'none\')"><xsl:copy-of select="*"/></xsl:when>' +
    '	  <xsl:otherwise>' +
    '	   <m:menclose notation="{$cy/@crossout}"><xsl:copy-of select="*"/></m:menclose>' +
    '	  </xsl:otherwise>' +
    '	 </xsl:choose>' +
    '	</xsl:variable>' +
    '	<xsl:choose>' +
    '	 <xsl:when test="$cy/m:none or not($cy/*)"><xsl:copy-of select="$b"/></xsl:when>' +
    '	 <xsl:when test="not(string($cy/@location)) or $cy/@location=\'n\'">' +
    '	  <m:mover>' +
    '	   <xsl:copy-of select="$b"/><m:mpadded width="0em" lspace="-0.5width">' +
    '	   <xsl:copy-of select="$cy/*"/>' +
    '	  </m:mpadded>' +
    '	  </m:mover>' +
    '	 </xsl:when>' +
    '	 <xsl:when test="$cy/@location=\'nw\'">' +
    '	  <m:mmultiscripts><xsl:copy-of select="$b"/><m:mprescripts/><m:none/><m:mpadded lspace="-1width" width="0em"><xsl:copy-of select="$cy/*"/></m:mpadded></m:mmultiscripts>' +
    '	 </xsl:when>' +
    '	 <xsl:when test="$cy/@location=\'s\'">' +
    '	  <m:munder><xsl:copy-of select="$b"/><m:mpadded width="0em" lspace="-0.5width"><xsl:copy-of select="$cy/*"/></m:mpadded></m:munder>' +
    '	 </xsl:when>' +
    '	 <xsl:when test="$cy/@location=\'sw\'">' +
    '	  <m:mmultiscripts><xsl:copy-of select="$b"/><m:mprescripts/><m:mpadded lspace="-1width" width="0em"><xsl:copy-of select="$cy/*"/></m:mpadded><m:none/></m:mmultiscripts>' +
    '	 </xsl:when>' +
    '	 <xsl:when test="$cy/@location=\'ne\'">' +
    '	  <m:msup><xsl:copy-of select="$b"/><m:mpadded width="0em"><xsl:copy-of select="$cy/*"/></m:mpadded></m:msup>' +
    '	 </xsl:when>' +
    '	 <xsl:when test="$cy/@location=\'se\'">' +
    '	  <m:msub><xsl:copy-of select="$b"/><m:mpadded width="0em"><xsl:copy-of select="$cy/*"/></m:mpadded></m:msub>' +
    '	 </xsl:when>' +
    '	 <xsl:when test="$cy/@location=\'w\'">' +
    '	  <m:msup><m:mrow/><m:mpadded lspace="-1width" width="0em"><xsl:copy-of select="$cy/*"/></m:mpadded></m:msup>' +
    '	  <xsl:copy-of select="$b"/>' +
    '	 </xsl:when>' +
    '	 <xsl:when test="$cy/@location=\'e\'">' +
    '	  <xsl:copy-of select="$b"/>' +
    '	  <m:msup><m:mrow/><m:mpadded width="0em"><xsl:copy-of select="$cy/*"/></m:mpadded></m:msup>' +
    '	 </xsl:when>' +
    '	 <xsl:otherwise>' +
    '	  <xsl:copy-of select="$b"/>' +
    '	 </xsl:otherwise>' +
    '	</xsl:choose>' +
    '       </xsl:copy>' +
    '      </xsl:for-each>' +
    '     </xsl:when>' +
    '     <xsl:otherwise>' +
    '      <xsl:for-each select="(//*)[position()&lt;= $offset]"><m:mtd/></xsl:for-each>' +
    '      <xsl:copy-of select="*"/>' +
    '     </xsl:otherwise>' +
    '    </xsl:choose>' +
    '   </m:mtr>' +
    '  </xsl:for-each>' +
    ' </m:mtable>' +
    '</xsl:variable>' +
    '<xsl:apply-templates mode="ml" select="c:node-set($m)"/>' +
    '</xsl:template>' +
    '<xsl:template match="*" mode="ml">' +
    ' <xsl:copy>' +
    '  <xsl:copy-of select="@*"/>' +
    '  <xsl:apply-templates mode="ml"/>' +
    ' </xsl:copy>' +
    '</xsl:template>' +
    '<xsl:template mode="ml" match="m:mtr[following-sibling::*[1][@class=\'msline\']]">' +
    ' <m:mtr>' +
    '  <xsl:copy-of select="@*"/>' +
    '  <xsl:variable name="m" select="following-sibling::*[1]/m:mtd"/>' +
    '  <xsl:for-each select="m:mtd">' +
    '   <xsl:variable name="p" select="position()"/>' +
    '   <m:mtd>' +
    '    <xsl:copy-of select="@*"/>' +
    '    <xsl:choose>' +
    '     <xsl:when test="$m[$p]/m:mpadded">' +
    '      <m:menclose notation="bottom">' +
    '       <m:mpadded depth=".1em" height="1em" width=".4em">' +
    '	<xsl:copy-of select="*"/>' +
    '       </m:mpadded>' +
    '      </m:menclose>' +
    '     </xsl:when>' +
    '     <xsl:otherwise>' +
    '      <xsl:copy-of select="*"/>' +
    '     </xsl:otherwise>' +
    '    </xsl:choose>' +
    '   </m:mtd>' +
    '  </xsl:for-each>' +
    ' </m:mtr>' +
    '</xsl:template><xsl:template mode="ml" match="m:mtr[not(preceding-sibling::*)][@class=\'msline\']" priority="3">' +
    ' <m:mtr>' +
    '  <xsl:copy-of select="@*"/>' +
    '  <xsl:for-each select="m:mtd">' +
    '   <m:mtd>' +
    '    <xsl:copy-of select="@*"/>' +
    '    <xsl:if test="m:mpadded">' +
    '     <m:menclose notation="bottom">' +
    '      <m:mpadded depth=".1em" height="1em" width=".4em">' +
    '       <m:mspace width=".2em"/>' +
    '      </m:mpadded>' +
    '     </m:menclose>' +
    '    </xsl:if>' +
    '   </m:mtd>' +
    '  </xsl:for-each>' +
    ' </m:mtr>' +
    '</xsl:template><xsl:template mode="ml" match="m:mtr[@class=\'msline\']" priority="2"/>' +
    '<xsl:template mode="mstack1" match="*">' +
    ' <xsl:param name="p"/>' +
    ' <xsl:param name="maxl" select="0"/>' +
    ' <m:mtr l="{1 + $p}">' +
    '  <xsl:if test="ancestor::mstack[1]/@stackalign=\'left\'">' +
    '   <xsl:attribute name="l"><xsl:value-of  select="$p"/></xsl:attribute>' +
    '  </xsl:if>' +
    '  <m:mtd><xsl:apply-templates select="."/></m:mtd>' +
    ' </m:mtr>' +
    '</xsl:template>' +
    '<xsl:template mode="mstack1" match="m:msrow">' +
    ' <xsl:param name="p"/>' +
    ' <xsl:param name="maxl" select="0"/>' +
    ' <xsl:variable  name="align1" select="ancestor::m:mstack[1]/@stackalign"/>' +
    ' <xsl:variable name="align">' +
    '  <xsl:choose>' +
    '   <xsl:when test="string($align1)=\'\'">decimalpoint</xsl:when>' +
    '   <xsl:otherwise><xsl:value-of select="$align1"/></xsl:otherwise>' +
    '  </xsl:choose>' +
    ' </xsl:variable>' +
    ' <xsl:variable name="row">' +
    '  <xsl:apply-templates mode="mstack1" select="*">' +
    '   <xsl:with-param name="p" select="0"/>' +
    '  </xsl:apply-templates>' +
    ' </xsl:variable>' +
    ' <xsl:text>&#10;</xsl:text>' +
    ' <xsl:variable name="l1">' +
    '  <xsl:choose>' +
    '   <xsl:when test="$align=\'decimalpoint\' and m:mn">' +
    '    <xsl:for-each select="c:node-set($row)/m:mtr[m:mtd/m:mn][1]">' +
    '     <xsl:value-of select="number(sum(@l))+count(preceding-sibling::*/@l)"/>' +
    '    </xsl:for-each>' +
    '   </xsl:when>' +
    '   <xsl:when test="$align=\'right\' or $align=\'decimalpoint\'">' +
    '    <xsl:value-of select="count(c:node-set($row)/m:mtr/m:mtd)"/>' +
    '   </xsl:when>' +
    '   <xsl:otherwise>' +
    '    <xsl:value-of select="0"/>' +
    '   </xsl:otherwise>' +
    '  </xsl:choose>' +
    ' </xsl:variable>' +
    ' <m:mtr class="msrow" l="{number($l1) + number(sum(@position)) +$p}">' +
    '  <xsl:copy-of select="c:node-set($row)/m:mtr/*"/>' +
    ' </m:mtr>' +
    '</xsl:template><xsl:template mode="mstack1" match="m:mn">' +
    ' <xsl:param name="p"/>' +
    ' <xsl:variable name="align1" select="ancestor::m:mstack[1]/@stackalign"/>' +
    ' <xsl:variable name="dp1" select="ancestor::*[@decimalpoint][1]/@decimalpoint"/>' +
    ' <xsl:variable name="align">' +
    '  <xsl:choose>' +
    '   <xsl:when test="string($align1)=\'\'">decimalpoint</xsl:when>' +
    '   <xsl:otherwise><xsl:value-of select="$align1"/></xsl:otherwise>' +
    '  </xsl:choose>' +
    ' </xsl:variable>' +
    ' <xsl:variable name="dp">' +
    '  <xsl:choose>' +
    '   <xsl:when test="string($dp1)=\'\'">.</xsl:when>' +
    '   <xsl:otherwise><xsl:value-of select="$dp1"/></xsl:otherwise>' +
    '  </xsl:choose>' +
    ' </xsl:variable>' +
    ' <m:mtr l="$p">' +
    '  <xsl:variable name="mn" select="normalize-space(.)"/>' +
    '  <xsl:variable name="len" select="string-length($mn)"/>' +
    '  <xsl:choose>' +
    '   <xsl:when test="$align=\'right\' or ($align=\'decimalpoint\' and not(contains($mn,$dp)))">' +
    '    <xsl:attribute name="l"><xsl:value-of select="$p + $len"/></xsl:attribute>' +
    '   </xsl:when>' +
    '   <xsl:when test="$align=\'center\'">' +
    '    <xsl:attribute name="l"><xsl:value-of select="round(($p + $len) div 2)"/></xsl:attribute>' +
    '   </xsl:when>' +
    '   <xsl:when test="$align=\'decimalpoint\'">' +
    '    <xsl:attribute name="l"><xsl:value-of select="$p + string-length(substring-before($mn,$dp))"/></xsl:attribute>' +
    '   </xsl:when>' +
    '  </xsl:choose>  <xsl:for-each select="(//node())[position() &lt;=$len]">' +
    '   <xsl:variable name="pos" select="position()"/>' +
    '   <m:mtd><m:mn><xsl:value-of select="substring($mn,$pos,1)"/></m:mn></m:mtd>' +
    '  </xsl:for-each>' +
    ' </m:mtr>' +
    '</xsl:template>' +
    '<xsl:template match="m:msgroup" mode="mstack1">' +
    ' <xsl:param name="p"/>' +
    ' <xsl:variable name="s" select="number(sum(@shift))"/>' +
    ' <xsl:variable name="thisp" select="number(sum(@position))"/>' +
    ' <xsl:for-each select="*">' +
    '  <xsl:apply-templates mode="mstack1" select=".">' +
    '   <xsl:with-param name="p" select="number($p)+$thisp+(position()-1)*$s"/>' +
    '  </xsl:apply-templates>' +
    ' </xsl:for-each>' +
    '</xsl:template>' +
    '<xsl:template match="m:msline" mode="mstack1">' +
    ' <xsl:param name="p"/>' +
    ' <xsl:variable  name="align1" select="ancestor::m:mstack[1]/@stackalign"/>' +
    ' <xsl:variable name="align">' +
    '  <xsl:choose>' +
    '   <xsl:when test="string($align1)=\'\'">decimalpoint</xsl:when>' +
    '   <xsl:otherwise><xsl:value-of select="$align1"/></xsl:otherwise>' +
    '  </xsl:choose>' +
    ' </xsl:variable>' +
    ' <m:mtr class="msline">' +
    '  <xsl:attribute name="l">' +
    '   <xsl:choose>' +
    '    <xsl:when test="not(string(@length)) or @length=0">*</xsl:when>' +
    '    <xsl:when test="string($align)=\'right\' or string($align)=\'decimalpoint\' "><xsl:value-of select="$p+ @length"/></xsl:when>' +
    '    <xsl:otherwise><xsl:value-of select="$p"/></xsl:otherwise>' +
    '   </xsl:choose>' +
    '  </xsl:attribute>' +
    '  <xsl:variable name="w">' +
    '   <xsl:choose>' +
    '    <xsl:when test="@mslinethickness=\'thin\'">0.1em</xsl:when>' +
    '    <xsl:when test="@mslinethickness=\'medium\'">0.15em</xsl:when>' +
    '    <xsl:when test="@mslinethickness=\'thick\'">0.2em</xsl:when>' +
    '    <xsl:when test="@mslinethickness"><xsl:value-of select="@mslinethickness"/></xsl:when>' +
    '    <xsl:otherwise>0.15em</xsl:otherwise>' +
    '   </xsl:choose>' +
    '  </xsl:variable>' +
    '  <xsl:choose>' +
    '   <xsl:when test="not(string(@length)) or @length=0">' +
    '    <m:mtd class="mslinemax">' +
    '     <m:mpadded lspace="-0.2em" width="0em" height="0em">' +
    '      <m:mfrac linethickness="{$w}">' +
    '       <m:mspace width=".4em"/>' +
    '       <m:mrow/>' +
    '      </m:mfrac>' +
    '     </m:mpadded>' +
    '    </m:mtd>' +
    '   </xsl:when>' +
    '   <xsl:otherwise>' +
    '    <xsl:variable name="l" select="@length"/>' +
    '    <xsl:for-each select="(//node())[position()&lt;=$l]">' +
    '     <m:mtd class="msline">' +
    '      <m:mpadded lspace="-0.2em" width="0em" height="0em">' +
    '       <m:mfrac linethickness="{$w}">' +
    '	<m:mspace width=".4em"/>' +
    '	<m:mrow/>' +
    '       </m:mfrac>' +
    '      </m:mpadded>' +
    '     </m:mtd>' +
    '    </xsl:for-each>' +
    '   </xsl:otherwise>' +
    '  </xsl:choose>' +
    ' </m:mtr>' +
    '</xsl:template>' +
    '<xsl:template match="m:mscarries" mode="mstack1">' +
    ' <xsl:param name="p"/>' +
    ' <xsl:variable  name="align1" select="ancestor::m:mstack[1]/@stackalign"/>' +
    ' <xsl:variable name="l1">' +
    '  <xsl:choose>' +
    '   <xsl:when test="string($align1)=\'left\'">0</xsl:when>' +
    '   <xsl:otherwise><xsl:value-of select="count(*)"/></xsl:otherwise>' +
    '  </xsl:choose>' +
    ' </xsl:variable>' +
    ' <m:mtr class="mscarries" l="{$p + $l1 + sum(@position)}">' +
    '  <xsl:apply-templates select="*" mode="msc"/>' +
    ' </m:mtr>' +
    '</xsl:template><xsl:template match="*" mode="msc">' +
    ' <m:mtd>' +
    '  <xsl:copy-of select="../@location|../@crossout"/>' +
    '  <xsl:choose>' +
    '   <xsl:when test="../@scriptsizemultiplier">' +
    '    <m:mstyle mathsize="{round(../@scriptsizemultiplier div .007)}%">' +
    '     <xsl:apply-templates select="."/>' +
    '    </m:mstyle>' +
    '   </xsl:when>' +
    '   <xsl:otherwise>' +
    '    <xsl:apply-templates select="."/>' +
    '   </xsl:otherwise>' +
    '  </xsl:choose>' +
    ' </m:mtd>' +
    '</xsl:template><xsl:template match="m:mscarry" mode="msc">' +
    ' <m:mtd>' +
    ' <xsl:copy-of select="@location|@crossout"/>' +
    '  <xsl:choose>' +
    '   <xsl:when test="../@scriptsizemultiplier">' +
    '    <m:mstyle mathsize="{round(../@scriptsizemultiplier div .007)}%">' +
    '     <xsl:apply-templates/>' +
    '    </m:mstyle>' +
    '   </xsl:when>' +
    '   <xsl:otherwise>' +
    '    <xsl:apply-templates/>' +
    '   </xsl:otherwise>' +
    '  </xsl:choose>' +
    ' </m:mtd>' +
    '</xsl:template>' +
    '<xsl:template match="m:mlongdiv" priority="11">' +
    ' <xsl:variable name="ms">' +
    '  <m:mstack>' +
    '   <xsl:copy-of select="(ancestor-or-self::*/@decimalpoint)[last()]"/>' +
    '   <xsl:choose>' +
    '    <xsl:when test="@longdivstyle=\'left)(right\'">' +
    '     <m:msrow>' +
    '      <m:mrow><xsl:copy-of select="*[1]"/></m:mrow>' +
    '      <m:mo>)</m:mo>' +
    '      <xsl:copy-of select="*[3]"/>' +
    '      <m:mo>(</m:mo>' +
    '      <xsl:copy-of select="*[2]"/>' +
    '     </m:msrow>' +
    '    </xsl:when>' +
    '    <xsl:when test="@longdivstyle=\'left/\right\'">' +
    '     <m:msrow>' +
    '      <m:mrow><xsl:copy-of select="*[1]"/></m:mrow>' +
    '      <m:mo>/</m:mo>' +
    '      <xsl:copy-of select="*[3]"/>' +
    '      <m:mo>\</m:mo>' +
    '      <xsl:copy-of select="*[2]"/>' +
    '     </m:msrow>' +
    '    </xsl:when>' +
    '    <xsl:when test="@longdivstyle=\':right=right\'">' +
    '     <m:msrow>' +
    '      <xsl:copy-of select="*[3]"/>' +
    '      <m:mo>:</m:mo>' +
    '      <xsl:copy-of select="*[1]"/>' +
    '      <m:mo>=</m:mo>' +
    '      <xsl:copy-of select="*[2]"/>' +
    '     </m:msrow>' +
    '    </xsl:when>' +
    '    <xsl:when test="@longdivstyle=\'stackedrightright\'' +
    '		    or @longdivstyle=\'mediumstackedrightright\'' +
    '		    or @longdivstyle=\'shortstackedrightright\'' +
    '		    or @longdivstyle=\'stackedleftleft\'' +
    '		    ">' +
    '     <xsl:attribute name="align">top</xsl:attribute>' +
    '     <xsl:copy-of select="*[3]"/>' +
    '    </xsl:when>' +
    '    <xsl:when test="@longdivstyle=\'stackedleftlinetop\'">' +
    '     <xsl:copy-of select="*[2]"/>' +
    '     <m:msline length="{string-length(*[3])-1}"/>' +
    '     <m:msrow>' +
    '      <m:mrow>' +
    '     <m:menclose notation="bottom right">' +
    '      <xsl:copy-of select="*[1]"/>' +
    '     </m:menclose>' +
    '      </m:mrow>' +
    '      <xsl:copy-of select="*[3]"/>' +
    '     </m:msrow>' +
    '    </xsl:when>' +
    '    <xsl:when test="@longdivstyle=\'righttop\'">' +
    '     <xsl:copy-of select="*[2]"/>' +
    '     <m:msline length="{string-length(*[3])}"/>' +
    '     <m:msrow>' +
    '      <xsl:copy-of select="*[3]"/>' +
    '      <m:menclose notation="top left bottom">' +
    '       <xsl:copy-of select="*[1]"/></m:menclose>' +
    '     </m:msrow>' +
    '    </xsl:when>' +
    '    <xsl:otherwise>' +
    '     <xsl:copy-of select="*[2]"/>' +
    '     <m:msline length="{string-length(*[3])}"/>' +
    '     <m:msrow>' +
    '      <m:mrow><xsl:copy-of select="*[1]"/></m:mrow>' +
    '      <m:mo>)</m:mo>' +
    '      <xsl:copy-of select="*[3]"/>' +
    '     </m:msrow>' +
    '    </xsl:otherwise>' +
    '   </xsl:choose>' +
    '   <xsl:copy-of select="*[position()&gt;3]"/>' +
    '  </m:mstack>' +
    ' </xsl:variable>' +
    ' <xsl:choose>' +
    '  <xsl:when test="@longdivstyle=\'stackedrightright\'">' +
    '   <m:menclose notation="right">' +
    '    <xsl:apply-templates select="c:node-set($ms)"/>' +
    '   </m:menclose>' +
    '   <m:mtable align="top">' +
    '    <m:mtr>' +
    '     <m:menclose notation="bottom">' +
    '      <xsl:copy-of select="*[1]"/>' +
    '     </m:menclose>' +
    '    </m:mtr>' +
    '    <m:mtr>' +
    '     <mtd><xsl:copy-of select="*[2]"/></mtd>' +
    '    </m:mtr>' +
    '   </m:mtable>' +
    '  </xsl:when>' +
    '    <xsl:when test="@longdivstyle=\'mediumstackedrightright\'">' +
    '    <xsl:apply-templates select="c:node-set($ms)"/>' +
    '   <m:menclose notation="left">' +
    '   <m:mtable align="top">' +
    '    <m:mtr>' +
    '     <m:menclose notation="bottom">' +
    '      <xsl:copy-of select="*[1]"/>' +
    '     </m:menclose>' +
    '    </m:mtr>' +
    '    <m:mtr>' +
    '     <mtd><xsl:copy-of select="*[2]"/></mtd>' +
    '    </m:mtr>' +
    '   </m:mtable>' +
    '   </m:menclose>' +
    '  </xsl:when>' +
    '  <xsl:when test="@longdivstyle=\'shortstackedrightright\'">' +
    '    <xsl:apply-templates select="c:node-set($ms)"/>' +
    '   <m:mtable align="top">' +
    '    <m:mtr>' +
    '     <m:menclose notation="left bottom">' +
    '      <xsl:copy-of select="*[1]"/>' +
    '     </m:menclose>' +
    '    </m:mtr>' +
    '    <m:mtr>' +
    '     <mtd><xsl:copy-of select="*[2]"/></mtd>' +
    '    </m:mtr>' +
    '   </m:mtable>' +
    '  </xsl:when>' +
    '  <xsl:when test="@longdivstyle=\'stackedleftleft\'">' +
    '   <m:mtable align="top">' +
    '    <m:mtr>' +
    '     <m:menclose notation="bottom">' +
    '      <xsl:copy-of select="*[1]"/>' +
    '     </m:menclose>' +
    '    </m:mtr>' +
    '    <m:mtr>' +
    '     <mtd><xsl:copy-of select="*[2]"/></mtd>' +
    '    </m:mtr>' +
    '   </m:mtable>' +
    '   <m:menclose notation="left">' +
    '    <xsl:apply-templates select="c:node-set($ms)"/>' +
    '   </m:menclose>' +
    '  </xsl:when>' +
    '  <xsl:otherwise>' +
    '   <xsl:apply-templates select="c:node-set($ms)"/>' +
    '  </xsl:otherwise>' +
    ' </xsl:choose>' +
    '</xsl:template>' +
    '<xsl:template match="m:menclose[@notation=\'madruwb\']" mode="rtl">' +
    ' <m:menclose notation="bottom right">' +
    '  <xsl:apply-templates mode="rtl"/>' +
    ' </m:menclose>' +
    '</xsl:template></xsl:stylesheet>';

  /*
   *  End of mml3mj.xsl material.
   */

  var mml3;
  if (window.XSLTProcessor) {
    // standard method: just use an XSLTProcessor and parse the stylesheet
    if (!MATHML.ParseXML) {MATHML.ParseXML = MATHML.createParser()}
    MATHML.mml3XSLT = new XSLTProcessor();
    MATHML.mml3XSLT.importStylesheet(MATHML.ParseXML(mml3Stylesheet));
  } else if (MathJax.Hub.Browser.isMSIE) {
    // nonstandard methods for Internet Explorer
    if (MathJax.Hub.Browser.versionAtLeast("9.0") || (document.documentMode||0) >= 9) {
      // For Internet Explorer >= 9, use createProcessor
      mml3 = new ActiveXObject("Msxml2.FreeThreadedDOMDocument");
      mml3.loadXML(mml3Stylesheet);
      var xslt = new ActiveXObject("Msxml2.XSLTemplate");
      xslt.stylesheet = mml3;
      MATHML.mml3XSLT = {
        mml3: xslt.createProcessor(),
        transformToDocument: function(doc) {
          this.mml3.input = doc;
          this.mml3.transform();
          return this.mml3.output;
        }
      }
    } else {
      // For Internet Explorer <= 8, use transformNode
      mml3 = MATHML.createMSParser();
      mml3.async = false;
      mml3.loadXML(mml3Stylesheet);
      MATHML.mml3XSLT = {
        mml3: mml3,
        transformToDocument: function(doc) {
          return doc.documentElement.transformNode(this.mml3);
        }
      }
    }
  } else {
    // No XSLT support. Do not change the <math> content.
    MATHML.mml3XSLT = null;
  }
  
  // Tweak CSS to avoid some browsers rearranging HTML output
  MathJax.Ajax.Styles({
    ".MathJax .mi, .MathJax .mo, .MathJax .mn, .MathJax .mtext": {
      direction: "ltr",
      display: "inline-block"
    },
    ".MathJax .ms, .MathJax .mspace, .MathJax .mglyph": {
      direction: "ltr",
      display: "inline-block"
    }
  });

  MathJax.Hub.Startup.signal.Post("MathML mml3.js Ready");
});

MathJax.Ajax.loadComplete("[MathJax]/extensions/MathML/mml3.js");