<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE document PUBLIC "-//CNX//DTD CNXML 0.5 plus MathML//EN" "http://cnx.rice.edu/cnxml/0.5/DTD/cnxml_mathml.dtd">
<document xmlns="http://cnx.rice.edu/cnxml" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:bib="http://bibtexml.sf.net/" xmlns:md="http://cnx.rice.edu/mdml/0.4" id="m0046">

  <name>MathML Test Suite</name>


  <content>

    <section id="cnxmltests">
      <name>CNXML Tests</name>
      <para id="intro">
	This module is a test suite for many MathML
      functions.
      </para>

     <para id="entitytest">
        <name>Entity Tests</name>
        <list id="listtest" type="nameditem">
	  <item><name>A script</name></item>
          <item><name>B script</name>ℬ</item>
          <item><name>C script</name></item>
          <item><name>D script</name></item>
	  <item><name>E script</name>ℰ</item>
          <item><name>F script</name>ℱ</item>
          <item><name>G script</name></item>
          <item><name>H script</name>ℋ</item>
          <item><name>I script</name>ℐ</item>
	  <item><name>J script</name></item>
          <item><name>K script</name></item>
          <item><name>L script</name>ℒ</item>
          <item><name>M script</name>ℳ</item>
          <item><name>N script</name></item>
	  <item><name>O script</name></item>
          <item><name>P script</name></item>
          <item><name>Q script</name></item>
          <item><name>R script</name>ℛ</item>
          <item><name>S script</name></item>
	  <item><name>T script</name></item>
          <item><name>U script</name></item>
          <item><name>V script</name></item>
          <item><name>W script</name></item>
	  <item><name>X script</name></item>
          <item><name>Y script</name></item>
          <item><name>Z script</name></item>
          <item><name>Section Symbol</name>§</item>
	</list>

	  <list id="listtest2" type="nameditem"><name>Greek Characters</name>
	  <item><name>Alpha</name>Αα</item>
          <item><name>Beta</name>Ββ</item>
          <item><name>Gamma</name>Γγ</item>
          <item><name>Delta</name>Δδ</item>
	  <item><name>Epsilon</name>Εε</item>
          <item><name>Zeta</name>Ζζ</item>
          <item><name>Eta</name>Ηη</item>
          <item><name>Theta</name>Θθ</item>
          <item><name>Iota</name>Ιι</item>
	  <item><name>Kappa</name>Κκ</item>
          <item><name>Lambda</name>Λλ</item>
          <item><name>Mu</name>Μμ</item>
          <item><name>Nu</name>Νν</item>
          <item><name>Xi</name>Ξξ</item>
	  <item><name>Omicron</name>Οο</item>
          <item><name>Pi</name>Ππ</item>
          <item><name>Rho</name>Ρρ</item>
          <item><name>Sigma</name>Σσς</item>
          <item><name>Tau</name>Ττ</item>
	  <item><name>Upsilon</name>Υυ</item>
          <item><name>Phi</name>Φφ</item>
          <item><name>Chi</name>Χχ</item>
          <item><name>Psi</name>Ψψ</item>
	  <item><name>Omega</name>Ωω</item>
	</list>


	<list id="others" type="named-item">
	  <name>Accents and diacritial marks</name>
	  <item><name>alpha with accent and unvoiced aspiation mark</name>ά̓</item>
	  <item><name>epsilon with accent</name>έ</item>
	  <item><name>eta with a little hat (inverted
	  breve)</name>η̑</item>
	  <item><name>eta with accent</name>ή</item>
	  <item><name>eta with accent and voiced aspiration
	  mark*</name>ή̔</item>
	  <item><name>alpha with unvoiced aspiration
	  mark*</name>ἀ</item>
	  <item><name>iota with little
	  hat*</name>ι̑</item>
	  <item><name>epsilon with
	  aspiration</name>ἐ</item>
	  <item><name>omega with accent</name>ό</item>
	  <item><name>final sigma</name>ς</item>
	  <item><name>iota with
	  aspiration*</name>ἰ</item>
	  <item><name>omega with
	  aspiraction*</name>ὀ</item>
	  <item><name>iota with diaresis</name>ϊ</item>
	  <item><name>e with capon</name>ě</item>
	</list>

	<list id="math-accents" type="named-item">
	  <name>Presentation MathML accents</name>
	  <item>
	    <name>mover: right-arrow</name>
	    <m:math>
	      <m:mover accent="true">
		<m:mi>F</m:mi>
		<m:mo form="postfix" accent="true">⃗</m:mo>
	      </m:mover>
	    </m:math>
	  </item>
	  <item>
	    <name>mover: double dot (diaresis)</name>
	    <m:math>
	      <m:mover accent="true">
		<m:mi>x</m:mi>
		<m:mo form="postfix" accent="true">¨</m:mo>
	      </m:mover>
	    </m:math>
	  </item>
	  <item>
	    <name>mover: single dot</name>
	    <m:math>
	      <m:mover accent="true">
		<m:mi>x</m:mi>
		<m:mo form="postfix" accent="true">˙</m:mo>
	      </m:mover>  
	    </m:math>
	  </item>
	</list>

        <list id="spanishcharacters" type="named-item"><name>Spanish Characters</name>
          <item><name>aacute</name>á</item> 
          <item><name>eacute</name>é</item>
          <item><name>iacute</name>í</item>
          <item><name>oacute</name>ó</item>
          <item><name>uacute</name>ú</item>
	  <item><name>N tilde</name>ñ</item>
          <item><name>upside down exclamation</name>¡</item> 
        </list>
      </para>
    </section>


    <section id="mathsymbols">
      <name>Math Symbols</name>
      <para id="mathsymbolspara">
	<m:math display="block"><m:ci>·</m:ci></m:math>
	<m:math display="block"><m:ci>∑</m:ci></m:math>
	<m:math display="block"><m:ci>∏</m:ci></m:math>
	<m:math display="block"><m:ci>∫</m:ci></m:math>
	<m:math display="block"><m:ci>ℝ</m:ci></m:math>
	<m:math display="block"><m:ci>ℚ </m:ci></m:math>
	<m:math display="block"><m:ci>𝔼</m:ci></m:math>
	<m:math display="block"><m:ci>𝔽</m:ci></m:math>
      </para>
    </section>
      
    
    <section id="mathmltest">
      <name>MathML Elements</name>

      <section id="presentation">
	<name>Presentation MathML</name>

	
	<equation id="msub">
	  <name>Msub</name>
	  <m:math display="block">
	    <m:ci>
	      <m:msub>
		<m:mi>X</m:mi>
		<m:mi>Y</m:mi>
	      </m:msub>
	    </m:ci>
	  </m:math>
	</equation>

<equation id="msub2">
	  <name>Msub</name>
	  <m:math display="block">
	    <m:ci>
	      <m:msub>
		<m:mi>X</m:mi>
		<m:mrow>
                  <m:mi>A</m:mi>
                  <m:mo>+</m:mo>
                  <m:mi>B</m:mi>
                </m:mrow>
	      </m:msub>
	    </m:ci>
	  </m:math>
	</equation>

      </section>

      <section id="content">
	<name>Content MathML</name>
	
	
	<section id="tokenelements">
	  <name>Token Elements</name>

	  <equation id="ci">
	    <name>ci</name>
	    <m:math>
	      <m:ci>X</m:ci>
	    </m:math>
	  </equation>
	  
	  <equation id="vector">
	    <name>ci type='vector'</name>
	    <m:math display="block">
	      <m:ci type="vector">W</m:ci>
	    </m:math>
	  </equation>

	  <equation id="vectorsubscript">
	    <name>ci type='vector' with subscript</name>
	    <m:math display="block">
	      <m:ci type="vector">
		<m:msub>
		  <m:mi>X</m:mi>
		  <m:mi>y</m:mi>
		</m:msub>
	      </m:ci>
	    </m:math>
	  </equation>

	  <equation id="cnsub">
	    <name>Cn with subscript</name>
	    <m:math display="block">
	      <m:cn>
		<m:msub>
		  <m:mn>1</m:mn>
		  <m:mn>0</m:mn>
		</m:msub>
	      </m:cn>
	    </m:math>
	  </equation>

          <equation id="omegaover">
           <name>Omega with Over</name>
             <m:math>
    <m:ci><m:mover>
	<m:msub>
	  <m:mi>ω</m:mi>
	  <m:mi>c</m:mi>
	</m:msub>
	<m:mo>˜</m:mo>
      </m:mover></m:ci>
  </m:math>    
  </equation>

	  <equation id="function">
	    <name>Function</name>
	    <m:math>
	      <m:apply>
		<m:ci type="fn">x</m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="fndeprecated"><name>Fn deprecated</name>
	  <m:math display="block">
	    <m:apply>
	      <m:fn>
		<m:apply>
		  <m:plus/>
		  <m:ci> f </m:ci>
		  <m:ci> g </m:ci>
		</m:apply>
	      </m:fn>
	      <m:ci>z</m:ci>
	    </m:apply>
	  </m:math>
	</equation><equation id="fnpower">
	    <name>Function of Power</name>
	    <m:math>
	      <m:apply>
		<m:ci type="fn">f</m:ci>
		<m:apply>
		  <m:power/>
		  <m:apply>
		    <m:ci type="fn">x</m:ci>
		    <m:ci>t</m:ci>
		  </m:apply>
		  <m:cn>2</m:cn>
		</m:apply>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="functiondiff">
	    <name>Function Diff</name>
	    <m:math>
	      <m:apply>
		<m:diff/>
		<m:apply>
		  <m:ci type="fn">φ</m:ci>
		  <m:ci>t</m:ci>
		</m:apply>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="subtest">
	    <name>Function with Subscript</name>
	    <m:math>
	      <m:apply>
		<m:ci type="fn">
		  <m:msub>
		    <m:mi>ℛ</m:mi>
		    <m:mi>s</m:mi>
		  </m:msub>
		</m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="powersubsup">
	    <name>Function with Subsup and Power</name>
	    <m:math>
	      <m:apply>
	      <m:power/>
		<m:apply>
		  <m:ci type="fn">
		    <m:msubsup>
		      <m:mi>x</m:mi>
		      <m:mn>0</m:mn>
		      <m:mi>n</m:mi>
		    </m:msubsup>
		  </m:ci>
		  <m:ci>t</m:ci>
		</m:apply>
		<m:ci>z</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="twovariablefunction">
	    <name>Function with Power and Two Variables</name>
	    <m:math>
	      <m:apply>
		<m:power/>
		<m:apply>
		  <m:ci type="fn">x</m:ci>
		  <m:apply>
		    <m:plus/>
		    <m:ci>z</m:ci>
		    <m:ci>y</m:ci>
		  </m:apply>
		  <m:apply>
		    <m:plus/>
		    <m:ci>w</m:ci>
		    <m:ci>q</m:ci>
		  </m:apply>
		</m:apply>
		<m:ci>α</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="discrete">
	    <name>Discrete Function</name>
	    <m:math>
	      <m:apply>
		<m:ci type="fn" class="discrete">x</m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>
	  
	  <equation id="subscriptfunctiontest">
	    <name>Discrete Function with Subscript</name>
	    <m:math>
	      <m:apply>
		<m:ci type="fn" class="discrete">
		  <m:msub>
		    <m:mi>x</m:mi>
		    <m:mi>c</m:mi>
		  </m:msub>
		</m:ci>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <section id="csymbols">
	    <name>Csymbol Tests</name>

	     <equation id="adjoint2">
	      <name>Adjoint</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#adjoint"/>
		  <m:ci>X</m:ci>
		</m:apply>
	      </m:math>
            </equation> 

	    <equation id="adjoint">
	      <name>Adjoint</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#adjoint"/>
		  <m:apply>
		    <m:plus/>
		    <m:ci>x</m:ci>
		    <m:ci>y</m:ci>
		  </m:apply>
		</m:apply>
	      </m:math>
            </equation> 

           <equation id="directionaldiff">
              <name>Directional diff</name>
	      <m:math>
             <m:apply>
               <m:diff definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#vectorderivative"/>
                <m:bvar><m:ci>y</m:ci></m:bvar>
               <m:ci>x</m:ci>
              </m:apply>
	      </m:math>
            </equation>



	    <equation id="piecewiseprob">
	      <name>Stochastic Process</name>
	      <m:math> 
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#stochastic"/> 
		  <m:apply>
		    <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#stochasticpiece"/> 
		    <m:cn> 0 </m:cn> 
		    <m:ci>p</m:ci>
		    </m:apply>
		  <m:apply>
		    <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#stochasticpiece"/> 
		    <m:cn> 1 </m:cn> 
		    <m:apply> 
		      <m:minus/>
		      <m:cn>1</m:cn>
		      <m:ci>p</m:ci>
		    </m:apply>
		  </m:apply>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="mutualinformation">
	      <name>Mutual Information</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#mutualinformation"/>
		  <m:ci>x</m:ci>
		  <m:ci>y</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="distance">
	      <name>Distance</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#distance"/>
		  <m:ci>x</m:ci>
		  <m:ci>y</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="normaldist">
	      <name>Normal Distribution</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#normaldistribution"/>
		  <m:cn>0</m:cn>
		  <m:ci>y</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="distributedin">
	      <name>Distributed In</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#distributedin"/>
		  <m:ci>r</m:ci>
		  <m:apply>
		    <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#normaldistribution"/>
		    <m:cn>0</m:cn>
		    <m:apply>
		      <m:power/>
		      <m:ci>σ</m:ci>
		      <m:cn>2</m:cn>
		    </m:apply>
		  </m:apply>
		</m:apply>
	      </m:math>
	    </equation>
	    
	    <equation id="estimate">
	      <name>Estimate</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#estimate"/>
		  <m:ci>x</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	     
	    <equation id="estimate4">
	      <name>Estimate</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#estimate"/>
		  <m:ci><m:msub><m:mi>x</m:mi><m:mi>y</m:mi>
		    </m:msub></m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="estimate5">
	      <name>Estimate with msub</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#estimate"/>
		  <m:ci><m:msub><m:mi>x</m:mi><m:mn>2</m:mn>
		    </m:msub></m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="estimate6">
	      <name>Estimate with msub</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#estimate"/>
		  <m:ci><m:msub><m:mi>x</m:mi><m:mn>2</m:mn>
		    </m:msub></m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	     <equation id="estimate7">
	      <name>Estimate with complex msub</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#estimate"/>
		  <m:ci><m:msub><m:mi>x</m:mi><m:mrow><m:mi>a</m:mi><m:mi>b</m:mi><m:mi>c</m:mi>
		      </m:mrow>
		    </m:msub></m:ci>
		</m:apply>
	      </m:math>
	    </equation>

            <equation id="estimate8">
	      <name>Estimate</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#estimate"/>
		  <m:ci><m:msub><m:mi>x</m:mi><m:mrow><m:mi>y</m:mi><m:mo>+</m:mo><m:mi>X</m:mi></m:mrow>
		    </m:msub></m:ci>
		</m:apply>
	      </m:math>
	    </equation>




	    <equation id="cdf">
	      <name>CDF</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#cdf">C</m:csymbol>
		  <m:ci>r</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="cdf2">
	      <name>CDF wit condition</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#cdf">C</m:csymbol>
		  <m:condition>
		    <m:ci>θ</m:ci>
		  </m:condition>
		  <m:ci>r</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	        <equation id="cdf3">
	      <name>CDF with multiple conditions</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#cdf">C</m:csymbol>
		  <m:condition>
		    <m:ci>θ</m:ci>
		  </m:condition>
		  <m:condition>
		    <m:ci>β</m:ci>
		  </m:condition>
		  <m:ci>r</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="cdf4">
	      <name>CDF with multiple conditions and bvar</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#cdf">C</m:csymbol>
		  <m:bvar>
		    <m:ci>x</m:ci>
		  </m:bvar>
		  <m:condition>
		    <m:ci>θ</m:ci>
		  </m:condition>
		  <m:condition>
		    <m:ci>β</m:ci>
		  </m:condition>
		  <m:ci>r</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    

	    <equation id="pdf">
	      <name>PDF</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#pdf"><m:msup><m:mi>P</m:mi><m:mi>a</m:mi>
		    </m:msup></m:csymbol>
		  <m:bvar><m:ci>x</m:ci>
		  </m:bvar>
		  <m:ci>r</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    
	    <equation id="pdf2">
	      <name>PDF with condition</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#pdf">P</m:csymbol>
		  <m:bvar><m:ci>x</m:ci>
		  </m:bvar>
		  <m:condition>
		    <m:ci>θ</m:ci>
		  </m:condition>
		  <m:ci>r</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="pdf10">
	      <name>PDF with multiple conditions</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#pdf">P</m:csymbol>
		  <m:bvar><m:ci>x</m:ci>
		  </m:bvar>
		  <m:condition>
		    <m:ci>θ</m:ci>
		  </m:condition>
		  <m:condition>
		    <m:ci>β</m:ci>
		  </m:condition>
		  <m:ci>r</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="pdf3">
	       <name>PDF multiple arguments with condition</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#pdf">P</m:csymbol>
		  <m:bvar><m:ci>x</m:ci>
		  </m:bvar>
		  <m:bvar><m:ci>y</m:ci>
		  </m:bvar>
		  <m:condition>
		    <m:ci>θ</m:ci>
		  </m:condition>
		  <m:ci>r</m:ci>
		  <m:ci>s</m:ci>
		</m:apply>
	      </m:math>
	    </equation>


	    <equation id="estimate2">
	      <name>Estimate of Function</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#estimate"/>
		  <m:apply>
		    <m:ci type="fn">P</m:ci>
		    <m:ci>x</m:ci>
		  </m:apply>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="estimate3">
	      <name>Estimate of Function</name>
	      <m:math>
		<m:apply>
		  <m:apply>
		    <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#estimate"/>
		    <m:ci>P</m:ci>
		  </m:apply>
		  <m:ci>x</m:ci>
		</m:apply>
	      </m:math>
	    </equation>


	    <equation id="expectedvalue">
	      <name>Expected Value</name>
	      <m:math>
		  <m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#expectedvalue"/>
		  <m:ci>x</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

              <equation id="expectedvalue2">
	      <name>Expected Value w/bvar and condition</name>
	      <m:math>
		  <m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#expectedvalue"/>
                  <m:bvar>
		    <m:ci>x</m:ci>
		  </m:bvar>
		  <m:condition>
		    <m:ci>θ</m:ci>
		  </m:condition>
		  <m:ci><m:msub>
		      <m:mover>
			<m:mi>θ</m:mi>
			<m:mi>̂</m:mi>
		      </m:mover>
		      <m:mi>MMSE</m:mi>
		    </m:msub></m:ci>
		</m:apply>
	      </m:math>
	    </equation>	

	     <equation id="expectedvalue3">
	      <name>Expected Value w condition</name>
	      <m:math>
		  <m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#expectedvalue"/>
                 
		  <m:condition>
		    <m:ci>θ</m:ci>
		  </m:condition>
		  <m:ci><m:msub>
		      <m:mover>
			<m:mi>θ</m:mi>
			<m:mi>̂</m:mi>
		      </m:mover>
		      <m:mi>MMSE</m:mi>
		    </m:msub></m:ci>
		</m:apply>
	      </m:math>
	    </equation>	

	    
	     <equation id="expectedvalue4">
	      <name>Expected Value multiple conditions</name>
	      <m:math>
		  <m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#expectedvalue"/>
                 
		  <m:condition>
		    <m:ci>θ</m:ci>
		  </m:condition>
		  <m:condition>
		    <m:ci>ω</m:ci>
		  </m:condition>
		  <m:condition>
		    <m:ci>φ</m:ci>
		  </m:condition>
		  <m:ci><m:msub>
		      <m:mover>
			<m:mi>θ</m:mi>
			<m:mi>̂</m:mi>
		      </m:mover>
		      <m:mi>MMSE</m:mi>
		    </m:msub></m:ci>
		</m:apply>
	      </m:math>
	    </equation>	

	    <equation id="probabliltytest1">
	      <name>Probability</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#probability"/>
		  <m:ci>X</m:ci>
		</m:apply>
	      </m:math>
	    </equation>
	    
	    <equation id="probabliltytest2">
	      <name>Probability with multiple arguments</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#probability"/>		 
		  <m:ci>X</m:ci>
                  <m:ci>Y</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="complement">
	      <name>Complement</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#complement"/>
		  <m:apply>
		    <m:ci type="fn">x</m:ci>
		    <m:ci>y</m:ci>
		  </m:apply>
		</m:apply>
	      </m:math>
	    </equation>
		  
	    

	    <equation id="probabliltytest">
	      <name>Probability with Condition</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#probability"/>
		  <m:condition>
		    <m:apply>
		      <m:in/>
		      <m:ci>X</m:ci>
		      <m:reals/>
		    </m:apply>
		  </m:condition>
		  <m:ci>X</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="argmintest6">
	      <name>argmin</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#argmin"/>
		  <m:ci>X</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="argmintest">
	      <name>Argmin with Condition</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#argmin"/>
		  <m:condition>
		    <m:ci>C</m:ci>
		  </m:condition>
		  <m:ci>X</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="argmintest2">
	      <name>Argmin with domainofapplication</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#argmin"/>
		  <m:domainofapplication>
		    <m:ci>D</m:ci>
		  </m:domainofapplication>
		  <m:ci>X</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="argmintest5">
	      <name>argmax</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#argmax"/>
		  <m:ci>X</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="argmaxtest">
	      <name>Argmax with condition</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#argmax"/>
		  <m:condition>
		    <m:ci>C</m:ci>
		  </m:condition>
		  <m:ci>X</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="argmaxtest2">
	      <name>Argmax with domainofapplication</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#argmax"/>
		  <m:domainofapplication>
		    <m:ci>C</m:ci>
		  </m:domainofapplication>
		  <m:ci>X</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="convolutiontest">
	      <name>Convolution</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#convolve"/>
		  <m:ci>X</m:ci>
		  <m:ci>Y</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="probtest">
	      <name>Probability</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#probability"/>
		  <m:apply>
		    <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#giventhat"/>
		    <m:ci>A</m:ci>
		    <m:ci>B</m:ci>
		  </m:apply>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="evaluateat">
	      <name>Evaluateat with interval</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#evaluateat"/>
		  <m:interval>
		    <m:cn>1</m:cn>
		    <m:cn>2</m:cn>
		  </m:interval>
		  <m:apply>
		    <m:ci type="fn">F</m:ci>
		    <m:ci>x</m:ci>
		  </m:apply>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="evaluateat2">
	      <name>Evaluate with bvar and interval</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#evaluateat"/>
		  <m:bvar>
		    <m:ci>t</m:ci>
		  </m:bvar>
		  <m:interval>
		    <m:cn>1</m:cn>
		    <m:cn>2</m:cn>
		  </m:interval>
		  <m:apply>
		    <m:ci type="fn">F</m:ci>
		    <m:ci>x</m:ci>
		  </m:apply>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="evaluateat3">
	      <name>Evaluateat with condition</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#evaluateat"/>
		  <m:condition>
		    <m:ci>z</m:ci>
		  </m:condition>
		  <m:apply>
		    <m:ci type="fn">F</m:ci>
		    <m:ci>x</m:ci>
		  </m:apply>
		</m:apply>
	      </m:math>
	    </equation>

	     <equation id="evaluateat100">
	      <name>Evaluateat with multiple conditions</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#evaluateat"/>
		  <m:condition>
		    <m:ci>z</m:ci>
		  </m:condition>
		  <m:condition>
		    <m:ci>a</m:ci>
		  </m:condition>
		  <m:apply>
		    <m:ci type="fn">F</m:ci>
		    <m:ci>x</m:ci>
		  </m:apply>
		</m:apply>
	      </m:math>
	    </equation>

	    

	    <equation id="evaluateat4">
	      <name>Evaluate with bvar and condition</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#evaluateat"/>
		  <m:bvar>
		    <m:ci>t</m:ci>
		  </m:bvar>
		  <m:condition>
		    <m:ci>y</m:ci>
		  </m:condition>
		  <m:apply>
		    <m:ci type="fn">F</m:ci>
		    <m:ci>x</m:ci>
		  </m:apply>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="evaluateat5">
	      <name>Evaluate with lowlimit/uplimit</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#evaluateat"/>
		  <m:lowlimit>
		    <m:ci>z</m:ci>
		  </m:lowlimit>
		  <m:uplimit>
		    <m:ci>x</m:ci>
		  </m:uplimit>
		  <m:apply>
		    <m:ci type="fn">F</m:ci>
		    <m:ci>x</m:ci>
		  </m:apply>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="evaluateat6">
	      <name>Evaluate with bvar and lowlimit/uplimit</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#evaluateat"/>
		  <m:bvar>
		    <m:ci>t</m:ci>
		  </m:bvar>
		  <m:lowlimit>
		    <m:ci>y</m:ci>
		  </m:lowlimit>
		  <m:uplimit>
		    <m:ci>t</m:ci>
		  </m:uplimit>
		  <m:apply>
		    <m:ci type="fn">F</m:ci>
		    <m:ci>x</m:ci>
		  </m:apply>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="csymboltest3">
	      <name>Surface Integral with bvar and domainofapplication</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#surfaceintegral"/>
		  <m:bvar><m:ci>x</m:ci>
		  </m:bvar>
		  <m:domainofapplication><m:ci>S</m:ci>
		  </m:domainofapplication>
		  <m:ci>X</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="csymboltest2">
	      <name>Surface Intgral with bvar and condition</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#surfaceintegral"/>
		  <m:bvar><m:ci>x</m:ci>
		  </m:bvar>
		  <m:condition><m:ci>S</m:ci>
		  </m:condition>
		  <m:ci>X</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="csymboltest">
	      <name>Surface Integral with bvar and lowlimit/uplimit</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#surfaceintegral"/>
		  <m:bvar><m:ci>x</m:ci>
		  </m:bvar>
		  <m:lowlimit>
		    <m:cn>1</m:cn>
		  </m:lowlimit>
		  <m:uplimit>
		    <m:cn>3</m:cn>
		  </m:uplimit>
		  <m:ci>X</m:ci>
		</m:apply>
	      </m:math>
	    </equation>


	    <equation id="csymboltest6">
	      <name>Surface Integral with bvar</name>
	      <m:math>
		<m:apply>
		  <m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#surfaceintegral"/>
		  <m:bvar><m:ci>x</m:ci>
		  </m:bvar>
		  <m:ci>X</m:ci>
		</m:apply>
	      </m:math>
	    </equation>
	    
	    
	  </section>

	</section>

	<section id="basiccontentelements">
	  <name>Basic Content Elements</name>

	  <equation id="complexcarts">
	    <name>Mult. Complex Cartesians</name>
	    <m:math>
	      <m:apply>
		<m:times/>
		<m:cn type="complex-cartesian">2<m:sep/>3</m:cn>
		<m:cn type="complex-cartesian">2<m:sep/>-3</m:cn>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="apply">
	    <name>Apply</name>
	    <m:math>
	      <m:apply>
		<m:ci>A</m:ci>
		<m:ci>B</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="compose">
	    <name>Composition</name>
	    <m:math>
	      <m:apply>
		<m:apply>
		  <m:compose/>
		  <m:ci>x</m:ci>
		  <m:ci>y</m:ci>
		</m:apply>
		<m:ci>z</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="difftestli3">
	    <name>Inverse of a Function</name>
	    <m:math>
	      <m:apply>
		<m:inverse/>
		<m:apply>
		  <m:ci type="fn">u</m:ci>
		  <m:ci>t</m:ci>
		</m:apply>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="difftestlicompose">
	    <name>Apply/Apply/Plus</name>
	    <m:math>
	      <m:apply>
		<m:apply>
		  <m:plus/>
		  <m:ci>F</m:ci>
		  <m:ci>G</m:ci>
		</m:apply>
		<m:ci>x</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  
	  <equation id="difftestli">
	    <name>Apply/Apply/Diff</name>
	    <m:math>
	      <m:apply>
		<m:apply>
		  <m:diff/>
		  <m:ci>u</m:ci>
		</m:apply>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="difftestlicompose2">
	    <name>Apply/Apply/Diff/Apply/Plus</name>
	    <m:math>
	      <m:apply>
		<m:apply>
		  <m:diff/>
                  <m:degree><m:cn>1</m:cn></m:degree>
		  <m:apply>
		    <m:plus/>
		    <m:ci>F</m:ci>
		    <m:ci>G</m:ci>
		  </m:apply>
		</m:apply>
		<m:ci>x</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	    <equation id="applyapplypower">
	    <name>Apply/Apply/Power</name>
	    <m:math>
	      <m:apply>
		<m:apply>
		  <m:power/>
		  <m:ci>x</m:ci>
		  <m:cn>2</m:cn>
		</m:apply>
		<m:ci>2</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>


	  <equation id="difftestli4">
	    <name>Apply/Apply/Inverse</name>
	    <m:math>
	      <m:apply>
		<m:apply>
		  <m:inverse/>
		  <m:ci type="fn">u</m:ci>
		</m:apply>
		<m:ci>t</m:ci>
	      </m:apply>
	    </m:math>
	  </equation> 


	</section>

	<section id="arithmatic">
	  <name>Arithmatic Algebra and Logic</name>

	  <equation id="maxaplain">
	    <name>Max</name>
	    <m:math>
	      <m:apply>
		<m:max/>
		<m:ci> a </m:ci>
		<m:ci> b </m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="minplain">
	    <name>Min</name>
	    <m:math>
	      <m:apply>
		<m:min/>
		<m:ci> a </m:ci>
		<m:ci> b </m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	    <equation id="mintest">
	      <name>min</name>
	      <m:math>
		<m:apply>
		  <m:min/>
		  <m:ci>X</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="mintest2">
	      <name>Min with Condition</name>
	      <m:math>
		<m:apply>
		  <m:min/>
		  <m:condition>
		    <m:ci>C</m:ci>
		  </m:condition>
		  <m:ci>X</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="mintest3">
	      <name>Min with domainofapplication</name>
	      <m:math>
		<m:apply>
		  <m:min/>
		  <m:domainofapplication>
		    <m:ci>D</m:ci>
		  </m:domainofapplication>
		  <m:ci>X</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	   <equation id="mintest4">
	      <name>Min with domainofapplication and condition and
	      multiple bvars</name>
	      <m:math>
		<m:apply>
		  <m:min/>
		<m:domainofapplication>
		  <m:ci>D</m:ci>
		</m:domainofapplication>
		<m:bvar>
		  <m:ci>V</m:ci>
		</m:bvar>
		<m:bvar>
		  <m:ci>T</m:ci>
		</m:bvar>
		<m:condition>
		  <m:apply>
		    <m:in/>
		    <m:ci>a</m:ci>
		    <m:ci>b</m:ci>
		  </m:apply>
		</m:condition>
		<m:ci>X</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	   <equation id="maxtest4">
	      <name>Max with domainofapplication and condition and
	      multiple bvars</name>
	      <m:math>
		<m:apply>
		  <m:max/>
		<m:domainofapplication>
		  <m:ci>D</m:ci>
		</m:domainofapplication>
		<m:bvar>
		  <m:ci>V</m:ci>
		</m:bvar>
		<m:bvar>
		  <m:ci>T</m:ci>
		</m:bvar>
		<m:condition>
		  <m:apply>
		    <m:in/>
		    <m:ci>a</m:ci>
		    <m:ci>b</m:ci>
		  </m:apply>
		</m:condition>
		<m:ci>X</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	    <equation id="maxtest2">
	      <name>Max with Condition</name>
	      <m:math>
		<m:apply>
		  <m:max/>
		  <m:condition>
		    <m:ci>C</m:ci>
		  </m:condition>
		  <m:ci>X</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

	    <equation id="maxtest3">
	      <name>Max with domainofapplication</name>
	      <m:math>
		<m:apply>
		  <m:max/>
		  <m:domainofapplication>
		    <m:ci>D</m:ci>
		  </m:domainofapplication>
		  <m:ci>X</m:ci>
		</m:apply>
	      </m:math>
	    </equation>

        <equation id="infimum">
	    <name>Infimum with bvar and condition</name>
	    <m:math> 
	      <m:apply> 
		<m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#infimum"/> 
		<m:bvar> 
		  <m:ci>x</m:ci> 
		</m:bvar> 
		<m:condition> 
		  <m:apply> 
		    <m:notin/> 
		    <m:ci> x </m:ci> 
		    <m:ci type="set"> B </m:ci> 
		  </m:apply> 
		</m:condition> 
		<m:apply> 
		  <m:power/> 
		  <m:ci> x </m:ci> 
		  <m:cn> 2 </m:cn> 
		</m:apply> 
	      </m:apply> 
	    </m:math>
	  </equation>

	  <equation id="minus">
	    <name>Minus</name>
	    <m:math>
	      <m:apply>
		<m:minus/>
		<m:ci>a</m:ci>
		<m:ci>b</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>
	  
	  <equation id="quotient">
	    <name>Quotient</name>
	    <m:math>
	      <m:apply>
		<m:quotient/>
		<m:ci>a</m:ci>
		<m:ci>b</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="times">
	    <name>Times</name>
	    <m:math display="block">
	      <m:apply>
		<m:times/>
		<m:ci>x</m:ci>
		<m:ci>y</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="powertest">
	    <name>Power Test</name>
	    <m:math>
	      <m:apply>
		<m:power/>
		<m:apply>
		  <m:minus/>
		  <m:cn>1</m:cn>
		</m:apply>
		<m:apply>
		  <m:ci type="fn">b</m:ci>
		  <m:ci>n</m:ci>
		</m:apply>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="functionpower">
	    <name>Power of a Function</name>
	    <m:math>
	      <m:apply>
		<m:power/>
		<m:apply>
		  <m:ci type="fn"><m:msub><m:mi>S</m:mi><m:mn>0</m:mn></m:msub></m:ci>
		  <m:ci>n</m:ci>
		</m:apply>
		<m:cn>2</m:cn>
	      </m:apply>
	    </m:math>
	  </equation>

	 
	  <equation id="powerdiscrete">
	    <name>Power of a Discrete Function</name>
	    <m:math>
	      <m:apply>
		<m:power/>
		<m:apply>
		  <m:ci type="fn" class="discrete">x</m:ci>
		  <m:ci>t</m:ci>
		</m:apply>
		<m:cn>2</m:cn>
	      </m:apply>
	    </m:math>
	  </equation>
 

	  <equation id="and">
	    <name>And</name>
	    <m:math display="block">
	      <m:apply>
		<m:and/>
		<m:ci>a</m:ci>
		<m:ci>c</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="or">
	    <name>Or</name>
	    <m:math display="block">
	      <m:apply>
		<m:or/>
		<m:ci>a</m:ci>
		<m:ci>c</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="nottest">
	    <name>Not Test</name>
	    <m:math>
	      <m:apply>
		<m:ci>W</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="xortest">
	    <name>XOR test</name>
	    <m:math>
	      <m:apply>
		<m:xor/>
		<m:ci>a</m:ci>
		<m:ci>b</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	    <equation id="xortest2">
	    <name>XOR test 2</name>
	    <m:math>
	      <m:apply>
		<m:times/>
		<m:ci type="matrix">H</m:ci>
		<m:apply>
		  <m:xor/>
		  <m:ci>a</m:ci>
		<m:ci>b</m:ci>
		</m:apply>
	      </m:apply>
	    </m:math>
	  </equation>


	  <equation id="foralltest2">
	    <m:math>
	      <m:apply>
		<m:forall/>
		<m:bvar>
		  <m:ci>k</m:ci>
		</m:bvar> 
		<m:bvar>
		  <m:ci>l</m:ci>
		</m:bvar> 
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="foralltest">
	    <name>Forall test</name>
	    
	    <m:math>
	      <m:apply>
		<m:forall/>	   
		<m:bvar>
		  <m:ci>x</m:ci>
		</m:bvar>
		<m:condition>
		  <m:apply>
		    <m:in/>
		    <m:ci>x</m:ci>
		    <m:set>
		      <m:cn>0</m:cn>
		      <m:cn>1</m:cn>
		      <m:cn>2</m:cn>
		    </m:set>
		  </m:apply>
		</m:condition>
		<m:condition>
		  <m:apply>
		    <m:in/>
		    <m:ci>x</m:ci>
		    <m:ci>ℤ</m:ci>
		  </m:apply>
		</m:condition>
		<m:apply>
		  <m:eq/>
		  <m:ci>y</m:ci>
		  <m:apply>
		    <m:plus/>
		    <m:apply>
		      <m:times/>
		      <m:cn>2</m:cn>
		      <m:ci>x</m:ci>
		    </m:apply>
		    <m:cn>3</m:cn>
		  </m:apply>
		</m:apply>
	      </m:apply>
	    </m:math>
	  </equation>

        <para id="forallinline">This is a test of the above as inline math:
          <m:math>
	      <m:apply>
		<m:forall/>
		<m:bvar>
		  <m:ci>x</m:ci>
		</m:bvar>
		<m:condition>
		  <m:apply>
		    <m:in/>
		    <m:ci>x</m:ci>
		    <m:set>
		      <m:cn>0</m:cn>
		      <m:cn>1</m:cn>
		      <m:cn>2</m:cn>
		    </m:set>
		  </m:apply>
		</m:condition>
		<m:condition>
		  <m:apply>
		    <m:in/>
		    <m:ci>x</m:ci>
		    <m:ci>ℤ</m:ci>
		  </m:apply>
		</m:condition>
		<m:apply>
		  <m:eq/>
		  <m:ci>y</m:ci>
		  <m:apply>
		    <m:plus/>
		    <m:apply>
		      <m:times/>
		      <m:cn>2</m:cn>
		      <m:ci>x</m:ci>
		    </m:apply>
		    <m:cn>3</m:cn>
		  </m:apply>
		</m:apply>
	      </m:apply>
	    </m:math>
        </para>	  


        <equation id="forallsimple">
          <name>Forall x, x</name>
          <m:math>
            <m:apply>
              <m:forall/>
              <m:bvar>
                <m:ci>x</m:ci>
              </m:bvar>
              <m:ci>x</m:ci>
            </m:apply>
          </m:math>
        </equation>

        <equation id="forallwithtrailingand">
          <name>Forall x,(x) and y</name>
          <m:math>
            <m:apply>
              <m:and/>
              <m:apply>
              <m:forall/>
              <m:bvar>
                <m:ci>x</m:ci>
              </m:bvar>
              <m:ci>x</m:ci>

            </m:apply>
            <m:ci>y</m:ci>
            </m:apply>
          </m:math>
        </equation>

        <equation id="forallwithincludedand">
          <name>Forall x,(x and y)</name>
          <m:math>
              <m:apply>
              <m:forall/>
              <m:bvar>
                <m:ci>x</m:ci>
              </m:bvar>
              <m:apply><m:and/>
              <m:ci>x</m:ci>
              <m:ci>y</m:ci>
              </m:apply>
            </m:apply>
          </m:math>
        </equation>

          <equation id="xandyorz">
            <name>x and y or z : or(and(x,y),z)</name>
            <m:math>
               <m:apply> <m:or/>
                <m:apply>
                <m:and/>

                <m:ci>x</m:ci>
                <m:ci>y</m:ci>
                </m:apply>
               <m:ci>z</m:ci>
              </m:apply>
            </m:math>
          </equation>

          <equation id="anotherxandyorz">
            <name>x and (y or z): and(x,or(y,z))</name>
            <m:math>
                <m:apply>
                <m:and/>
                <m:ci>x</m:ci>
                <m:apply> <m:or/>
                 <m:ci>y</m:ci>
                 <m:ci>z</m:ci>
                </m:apply>
              </m:apply>
            </m:math>
          </equation>

	  <equation id="conjugatetest">
	    <name>Conjugate Test</name>
	    <m:math>
	      <m:apply>
		<m:conjugate/>
		<m:ci>x</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="remainder">
	    <name>Remainder</name>
	    <m:math>
	      <m:apply>
		<m:rem/>
		<m:ci>a</m:ci>
		<m:ci>b</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	</section>

	<section id="relations">
	  <name>Relations</name>
	  
	  <equation id="equals">
	    <name>Equals</name>
	    <m:math>
	      <m:apply>
		<m:eq/>
		<m:ci>a</m:ci>
		<m:ci>b</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>
	  


	  <equation id="equalslong">
	    <name>Equals with Line Breaking</name>
	    <m:math>
	      <m:apply>
		<m:eq/>
		<m:ci>a</m:ci>
		<m:ci>b</m:ci>
		<m:ci>c</m:ci>
		<m:ci>d</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="real">
	    <name>Real</name>
	    <m:math display="block">
	      <m:apply>
		<m:real/>
		<m:ci>x</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>
	  
	</section>

	<section id="calculusvectorcal">
	  <name>Calculus and Vector Calculus</name>
	  
	  <equation id="integraltest">
	    <name>Int</name>
	    <m:math>
	      <m:apply>
		<m:int/>
		<m:bvar>
		  <m:ci>x</m:ci>
		</m:bvar>
		<m:ci>y</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

 
           
	  <equation id="integraltest1000">
	    <name>Int</name>
	    <m:math>
	      <m:apply>
		<m:int/>
		<m:bvar>
		  <m:ci>x</m:ci>
		</m:bvar>
		<m:apply>
                  <m:minus/>
                   <m:ci>a</m:ci>
                    <m:ci>b</m:ci>
                </m:apply>
	      </m:apply>
	    </m:math>
	  </equation> 
                  

	   <equation id="integraltest2">
	    <name>Int with domain of application and nothing else</name>
	    <m:math>
	      <m:apply>
		<m:int/>
		<m:bvar>
		  <m:ci>x</m:ci>
		</m:bvar>
		<m:domainofapplication>
		  <m:reals/>
		</m:domainofapplication>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="difftest">
	    <name>Diff</name>
	    <m:math>
	      <m:apply>
		<m:diff/>
		<m:ci> f </m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="difftestplus">
	    <name>Diff of Sum</name>
	    <m:math>
	      <m:apply>
		<m:diff/>
		<m:apply>
		  <m:plus/>
		  <m:ci> f </m:ci>
		  <m:ci>g</m:ci>
		</m:apply>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="degreediff">
	    <name>Diff with degree</name>
	    <m:math>
	      <m:apply>
		<m:diff/>
		<m:degree><m:cn>5</m:cn>
		</m:degree>
		<m:ci type="fn">u</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="degreediff2">
	    <m:math>
	      <m:apply>
		<m:diff/>
		<m:degree>
		  <m:ci>y</m:ci>
		</m:degree>
		<m:ci>f</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>
	  

	  <equation id="difftest2">
	    <name>Diff with bvar</name>
	    <m:math>
	      <m:apply>
		<m:diff/>
		<m:bvar>
		  <m:ci> x </m:ci>
		</m:bvar>
		<m:apply><m:ci type="fn"> f </m:ci>
		  <m:ci> x </m:ci>
		</m:apply>
	      </m:apply>
	    </m:math>
	  </equation>
	  
	  <equation id="difftest3">
	    <name>diff with bvar and bvar/degree</name>
	    <m:math>
	      <m:apply>
		<m:diff/>
		<m:bvar>
		  <m:ci> x </m:ci>
		  <m:degree><m:cn>2</m:cn>
		  </m:degree>
		</m:bvar>
		<m:apply><m:ci type="fn"> f </m:ci>
		  <m:ci> x </m:ci>
		</m:apply>
	      </m:apply>
	    </m:math>
	  </equation>

      
	  <equation id="difftestli2">
	    <name>Diff of a Function</name>
	    <m:math>
	      <m:apply>
		<m:diff/>
		<m:apply>
		  <m:ci type="fn">u</m:ci>
		  <m:ci>t</m:ci>
		</m:apply>
	      </m:apply>
	    </m:math>
	  </equation>

   

   

	  <equation id="partialdifftest">
	    <name>Partial Diff</name>
	    <m:math>
	      <m:apply>
		<m:partialdiff/>
		<m:bvar>
		  <m:ci>x</m:ci>
		</m:bvar>
		<m:degree><m:ci>4</m:ci>
		</m:degree>
		<m:ci>f</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  
	  <equation id="difftest100000">
	    <name>Partial Diff with multiple bvar</name>
	    <m:math>
	      <m:apply>
		<m:partialdiff/>
		<m:bvar><m:ci>x </m:ci></m:bvar>
		<m:bvar><m:ci>y</m:ci></m:bvar>
		<m:apply>
		  <m:ci type="fn">f</m:ci>
		  <m:ci>x</m:ci>
		  <m:ci>y</m:ci>
		</m:apply>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="difftest111">
	    <name>Partial Diff with Degree</name>
	    <m:math>
	      <m:apply>
		<m:partialdiff/>
		<m:degree><m:cn>2</m:cn>
		</m:degree>
		<m:ci>f</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="difftest1112">
	    <name>Partial Diff with Degree</name>
	    <m:math>
	      <m:apply>
		<m:partialdiff/>
		<m:degree><m:cn>2</m:cn>
		</m:degree>
		<m:apply>
		  <m:ci type="fn">f</m:ci>
		  <m:ci>x</m:ci>
		</m:apply>		    
	      </m:apply>
	    </m:math>
	  </equation>

	  

	  
	  <equation id="gradtest">
	    <name>Grad Test</name>
	    <m:math>
	      <m:apply>
		<m:grad/>
		<m:ci>T</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="curltest">
	    <name>Curl Test</name>
	    <m:math>
	      <m:apply>
		<m:curl/>
		<m:ci>R</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="normtest">
	    <name>Norm Test</name>
	    <m:math>
	      <m:apply>
		<m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#norm"/>
		<m:ci>x</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>
	  
	  <equation id="normtest2">
	    <name>Norm Test with Domain of Application</name>
	    <m:math>
	      <m:apply>
		<m:csymbol definitionURL="http://cnx.rice.edu/cd/cnxmath.ocd#norm"/>
		<m:domainofapplication>
		  <m:integers/>
		</m:domainofapplication>
		<m:ci>x</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>
	  
	   
	</section>

	

	<section id="theoryofsets">
	  <name>Theory of Sets</name>
	  
	  
	  <equation id="set">
	    <name>Set</name>
	    <m:math>
	      <m:set>
		<m:cn>0</m:cn>
		<m:cn>1</m:cn>
		<m:cn>2</m:cn>
	      </m:set>
	    </m:math>
	  </equation>

	  <equation id="prset">
	    <name>Proper Subset</name>
	    <m:math>
	      <m:apply>
		<m:prsubset/>
		<m:ci>X</m:ci>
		<m:ci>Y</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	</section>

	<section id="sequencesandseries">
	  <name>Sequences and Series</name>
           
          <equation id="sumalone">
           <name>Sum with nothing</name>
           <m:math>
            <m:apply>
             <m:sum/>
             <m:ci>x</m:ci>
            </m:apply>
           </m:math>
           </equation>
	  
	   <equation id="sumbvar">
           <name>Sum with Bvar</name>
	    <m:math>
            <m:apply>
		<m:sum/>
		<m:bvar><m:ci>x</m:ci></m:bvar>
		<m:ci>x</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="sumbvarmult">
           <name>Sum with Mulitple Bvar</name>
           <m:math>
            <m:apply>
             <m:sum/>
              <m:bvar><m:ci>x</m:ci></m:bvar>
		<m:bvar><m:ci>y</m:ci></m:bvar>
             <m:ci>x</m:ci>
            </m:apply>
           </m:math>
           </equation>

	  <equation id="sumtest">
	    <name>Sum with Limits and Condition</name>
	    <m:math>
	      <m:apply>
		<m:sum/>
		<m:bvar>
		  <m:ci>x</m:ci>
		</m:bvar>
		<m:lowlimit>
		  <m:ci>0</m:ci>
		</m:lowlimit>
		<m:uplimit>
		  <m:infinity/>
		</m:uplimit>
		<m:condition>
		  <m:apply>
		    <m:in/>
		    <m:ci>x</m:ci>
		    <m:reals/>
		  </m:apply>
		</m:condition>
		<m:apply>
		  <m:power/>
		  <m:ci>x</m:ci>
		  <m:cn>3</m:cn>
		</m:apply>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="sumdomaincondition">
	    <name>Sum with Domainofapplication and Condition</name>
	    <m:math>
	      <m:apply>
		<m:sum/>
		<m:bvar>
		  <m:ci>x</m:ci>
		</m:bvar>
		<m:condition>
		  <m:apply>
		    <m:in/>
		    <m:ci>x</m:ci>
		    <m:reals/>
		  </m:apply>
		</m:condition>
		<m:domainofapplication>
		  <m:set>
		    <m:ci>n</m:ci>
		    <m:ci>…</m:ci>
		    <m:ci>
		      <m:msub>
			<m:mi>n</m:mi>
			<m:mi>m</m:mi>
		      </m:msub>
		    </m:ci>
		  </m:set>
		</m:domainofapplication>
		<m:apply>
		  <m:power/>
		  <m:ci>x</m:ci>
		  <m:cn>3</m:cn>
		</m:apply>
	      </m:apply> 
	    </m:math>
	  </equation>


	  <equation id="productlimitscondtest">
	    <name>Product with Limits and Condition</name>
	    <m:math>
	      <m:apply>
		<m:product/>
		<m:bvar>
		  <m:ci>x</m:ci>
		</m:bvar>
		<m:lowlimit>
		  <m:ci>0</m:ci>
		</m:lowlimit>
		<m:uplimit>
		  <m:infinity/>
		</m:uplimit>
		<m:condition>
		  <m:apply>
		    <m:in/>
		    <m:ci>x</m:ci>
		    <m:reals/>
		  </m:apply>
		</m:condition>
		<m:apply>
		  <m:power/>
		  <m:ci>x</m:ci>
		  <m:cn>3</m:cn>
		</m:apply>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="productdomaincondition">
	    <name>Product with Domainofapplication and Condition</name>
	    <m:math>
	      <m:apply>
		<m:product/>
		<m:bvar>
		  <m:ci>x</m:ci>
		</m:bvar>
		<m:condition>
		  <m:apply>
		    <m:in/>
		    <m:ci>x</m:ci>
		    <m:reals/>
		  </m:apply>
		</m:condition>
		<m:domainofapplication>
		  <m:set>
		    <m:ci>n</m:ci>
		    <m:ci>…</m:ci>
		    <m:ci>
		      <m:msub>
			<m:mi>n</m:mi>
			<m:mi>m</m:mi>
		      </m:msub>
		    </m:ci>
		  </m:set>
		</m:domainofapplication>
		<m:apply>
		  <m:power/>
		  <m:ci>x</m:ci>
		  <m:cn>3</m:cn>
		</m:apply>
	      </m:apply> 
	    </m:math>
	  </equation>

	  <equation id="producttimestest">
	    <name>Product Times Test</name>
	    <m:math>
	      <m:apply>
		<m:sum/>
		<m:bvar>
		  <m:ci>j</m:ci>
		</m:bvar>
		<m:apply>
		  <m:times/>
		  <m:ci>w</m:ci>
		  <m:apply>
		    <m:product/>
		    <m:bvar>
		      <m:ci>i</m:ci>
		    </m:bvar>
		    <m:lowlimit>
		      <m:cn>1</m:cn>
		    </m:lowlimit>
		    <m:uplimit>
		      <m:cn>2</m:cn>
		    </m:uplimit>
		    <m:ci>x</m:ci>
		  </m:apply>
		</m:apply>
	      </m:apply>
	    </m:math>
	  </equation>

	</section>
	
	<section id="elementaryclassicalfunctions">
	  <name>Elementary Classical Functions</name>

	  <equation id="sin">
	    <name>Sin</name>
	    <m:math>
	      <m:apply>
		<m:sin/>
		<m:ci>x</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	</section>
	
	<section id="statistics">
	  <name>Statistics</name>
	  
	  <equation id="meantest">
	    <name>Mean Test</name>
	    <m:math>
	      <m:apply>
		<m:mean/>
		<m:ci>m</m:ci>
		<m:ci>n</m:ci>
		<m:ci>o</m:ci>
	      </m:apply>
	    </m:math>
	  </equation> 


	  <equation id="meantimestest">
	    <name>Mean Times Test</name>
	    <m:math>
	      <m:apply>
		<m:times/>
		<m:apply>
		  <m:mean/>
		  <m:ci>X</m:ci>
		</m:apply>
		<m:apply>
		  <m:mean/>
		  <m:ci>Y</m:ci>
		</m:apply>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="moment">
	    <name>Moment</name>
	    <m:math>
	      <m:apply>
		<m:moment/>
		<m:degree>
		  <m:cn>3</m:cn>
		</m:degree>
		<m:momentabout>
		  <m:ci>p</m:ci>
		</m:momentabout>
		<m:ci>x</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	</section>

	<section id="linearalgebra">
	  <name>Linear Algera</name>

	  <equation id="selector">
	    <name>Selector</name>
	    <m:math>
	      <m:apply>
		<m:selector/>
		<m:apply>
		  <m:inverse/>
		    <m:ci>x</m:ci>
		</m:apply>
		<m:ci>i</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>
	  
	  <equation id="vectorentitytest">
	    <name>Vector Entity Test</name>
	    <m:math display="block">
	      <m:ci type="vector">π</m:ci>
	    </m:math>
	  </equation>  

	  <equation id="vectorproducttest">
	    <name>Vector Product Test</name>
	    <m:math>
	      <m:apply>
		<m:vectorproduct/>
		<m:ci>C</m:ci>
		<m:ci>D</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>
	  
	  <equation id="scalarproducttest">
	    <name>Scalar Product Test</name>
	    <m:math>
	      <m:apply>
		<m:scalarproduct/>
		<m:ci type="vector">A</m:ci>
		<m:ci type="vector">B</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="outerproducttest">
	    <name>Outer Product Test</name>
	    <m:math>
	      <m:apply>
		<m:outerproduct/>
		<m:ci>V</m:ci>
		<m:ci>X</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	</section>

	<section id="semanticmappingelements">
	  <name>Semantic Mapping Elements</name>

	  <equation id="annotation">
	    <name>Annotation</name>
	    <m:math>
	    </m:math>
	  </equation>

	</section>

	<section id="constantandsymbol">
	  <name>Constant and Symbol Elements</name>
	  
	  <equation id="integers">
	    <name>Integers</name>
	    <m:math>
	      <m:integers/>
	    </m:math>
	  </equation>
	  
	</section>

	<section id="otherconnexionsmath">
	  <name>Other MathML Tests</name>
	  
	  <equation id="moapply2">
	    <name>Applying an m:ci to a single m:ci</name>
	    <m:math>
	      <m:apply>
		<m:ci><m:mo>∠</m:mo></m:ci>
		<m:apply>
		  <m:ci type="fn">x</m:ci>
		  <m:ci>t</m:ci>
		</m:apply>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="ciapply">
	    <name>Applying a ci with an mo in it</name>
	    <m:math>
	      <m:apply>
		<m:ci><m:mo>≫</m:mo></m:ci>
		<m:ci>x</m:ci>
		<m:ci>y</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="ciapply3">
	    <name>Applying a ci with an mo in it</name>
	    <m:math>
	      <m:apply>
		<m:ci><m:mo>≫</m:mo></m:ci>
		<m:ci>x</m:ci>
		<m:ci>y</m:ci>
		<m:ci>z</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>

	  <equation id="ciapply4">
	    <name>Laplace in ci</name>
	    <m:math>
	      <m:apply>
		<m:ci><m:mo>ℒ</m:mo></m:ci>
		<m:ci>x</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>  

	  <equation id="ciapply5">
	    <name>Fourier Transform in ci</name>
	    <m:math>
	      <m:apply>
		<m:ci><m:mo>ℱ</m:mo></m:ci>
		<m:ci>x</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>  

	   <equation id="ciapply6">
	    <name>Apply ci to apply</name>
	    <m:math>
	      <m:apply>
		<m:ci><m:mo>∠</m:mo></m:ci>
		<m:apply>
		  <m:plus/>
		  <m:ci>a</m:ci>
		  <m:ci>b</m:ci>
		</m:apply>
	      </m:apply>
	    </m:math>
	  </equation>  
	  <equation id="ciapply2">
	    <name>Applying a ci with an mo in it</name>
	    <m:math>
	      <m:apply>
		<m:ci><m:mo>≫</m:mo></m:ci>
		<m:ci>x</m:ci>
	      </m:apply>
	    </m:math>
	  </equation>
	</section>
      </section>
    </section>
  </content>

 

</document>
