reduce-historical/r38/packages/mathml/examples.mml

%  Description: This file contains a long list of examples demonstrating the abilities of
%               the translator. Most of these examples come straight from the MathML spec. They
%               were used during the development of the interface and should all be correctly
%               translated into OpenMath.
%
%  Version 17 April 2000
%
%  Author: Luis Alvarez Sobreviela
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%       


mml2om();
<math>
  <apply><sin/>
     <apply><plus/>
       <apply><cos/>
         <ci> x </ci>
       </apply>
       <apply><power/>
         <ci> x </ci>
         <cn> 3 </cn>
       </apply>
     </apply>
   </apply>
</math>            


mml2om();
<math>
  <apply><sin/>
     <apply><plus/>
       <apply><cos/>
         <ci> x </ci>
       </apply>
       <apply><power/>
         <ci type="real"> x </ci>
         <cn> 3 </cn>
       </apply>
     </apply>
   </apply>
</math>      


mml2om();
<math>
  <set type=normal>
     <ci> b </ci>
     <cn> 2 </cn>
     <ci> c </ci>
   </set>
</math>


mml2om();
<math>
  <set type="multiset">
     <ci> b </ci>
     <cn> 2 </cn>
     <ci> c </ci>
   </set>
</math>


mml2om();
<math>
  <vector>
     <ci> b </ci>
     <cn> 2 </cn>
     <ci> c </ci>
   </vector>
</math>

mml2om();
<math>
  <interval closure=closed>
     <ci> b </ci>
     <cn> 2 </cn>
   </interval>
</math>

mml2om();
<math>
  <interval closure=open>
     <ci> b </ci>
     <cn> 2 </cn>
   </interval>
</math>

mml2om();
<math>
  <interval closure=open-closed>
     <ci> b </ci>
     <cn> 2 </cn>
   </interval>
</math>


mml2om();
<math>
  <interval closure=closed-open>
     <ci> b </ci>
     <cn> 2 </cn>
   </interval>
</math>


mml2om();
<math>
   <cn type="complex-cartesian"> 6 <sep/> 3 </cn>
</math>

mml2om();
<math>
   <cn type="complex-polar"> 6 <sep/> 3 </cn>
</math>

mml2om();
<math>
   <cn type="integer" base="10"> 6 </cn>
</math>

mml2om();
<math>
  <apply><sum/>
     <bvar>
       <ci> x </ci>
     </bvar>
     <lowlimit>
       <ci> a </ci>
     </lowlimit>
     <uplimit>
       <ci> b </ci>
     </uplimit>
      <apply><plus/>
         <ci> x </ci>
         <apply><sin/>
            <ci> y </ci>
         </apply>
      </apply>
   </apply>
</math>


              
mml2om();
<math>
  <apply><int/>
     <bvar>
       <ci> x </ci>
     </bvar>
     <lowlimit>
       <ci> a </ci>
     </lowlimit>
     <uplimit>
       <ci> b </ci>
     </uplimit>
     <apply><fn><ci> f </ci></fn>
       <ci> x </ci>
     </apply>
   </apply>
</math>  



mml2om();
<math>
   <lambda>
      <bvar>
         <ci> x </ci>
      </bvar>
      <apply><sin/>
         <ci> x </ci>
      </apply>
   </lambda>
</math>          
    

mml2om();
<math>
 <apply><limit/>
     <bvar>
       <ci> x </ci>
     </bvar>
     <lowlimit>
       <cn> 0 </cn>
     </lowlimit>
     <apply><sin/>
       <ci> x </ci>
     </apply>
   </apply>
</math>
 
mml2om();            
<math>
  <apply><limit/>
    <bvar>
      <ci> x </ci>
    </bvar>
    <condition>
      <apply>
        <tendsto type="above"/>
        <ci> x </ci>
        <ci> a </ci>
      </apply>
    </condition>
    <apply><sin/>
       <ci> x </ci>
    </apply>
  </apply>
</math>


mml2om();
<math>
   <apply><not/>
      <apply><exists/>
         <bvar>
            <ci> x </ci>
         </bvar>
         <bvar>
            <ci> y </ci>
         </bvar>
         <bvar>
            <ci> z </ci>
         </bvar>
         <bvar>
            <ci> n </ci>
         </bvar>
         <apply><and/>
            <apply><gt/>
               <ci> n </ci>
               <cn type="integer"> 2 </cn>
            </apply>
            <apply><eq/>
               <apply><plus/>
                  <apply><power/>
                     <ci> x </ci>
                     <ci> n </ci>
                  </apply>
                  <apply><power/>
                     <ci> y </ci>
                     <ci> n </ci>
                  </apply>
               </apply>
               <apply><power/>
                  <ci> z </ci>
                  <ci> n </ci>
               </apply>
            </apply>
         </apply>
      </apply>
   </apply>
</math>      



mml2om();
<math>
  <matrix>
     <matrixrow>
       <cn> 0 </cn> <cn> 1 </cn> <cn> 0 </cn>
     </matrixrow>
     <matrixrow>
       <cn> 0 </cn> <cn> 0 </cn> <cn> 1 </cn>
     </matrixrow>
     <matrixrow>
       <cn> 1 </cn> <cn> 0 </cn> <cn> 0 </cn>
     </matrixrow>
   </matrix>
</math>

mml2om();
<math>
   <apply><int/>
      <bvar>
         <ci>x</ci>
      </bvar>
      <apply><power/>
         <ci>x</ci>
         <cn type="integer">2</cn>
      </apply>
   </apply>
</math>
     
mml2om();
<math>
   <apply><int/>
      <bvar>
         <ci> x </ci>
      </bvar>
      <apply><sin/>
         <ci> x </ci>
      </apply>
   </apply>
</math>                    


mml2om();
<math>
<apply><sum/>
     <bvar>
       <ci> x </ci>
     </bvar>
     <lowlimit>
       <ci> a </ci>
     </lowlimit>
     <uplimit>
       <ci> b </ci>
     </uplimit>
     <apply><fn><ci> f </ci></fn>
       <ci> x </ci>
     </apply>
   </apply>
</math>
                 


mml2om();
<math>
  <apply><diff/>
    <bvar>
      <ci> x </ci>
   </bvar>
    <apply><fn><ci>f</ci></fn>
       <ci> x </ci>
    </apply>
  </apply>
</math>
 

mml2om();
<math>
  <apply><diff/>
    <bvar>
      <ci> x </ci>
      <degree> 
        <cn> 2 </cn>
      </degree> 
   </bvar>
    <apply><fn><ci>f</ci></fn>
       <ci> x </ci>
    </apply>
  </apply>
</math>
 

mml2om();
<math>
  <apply><diff/>
    <bvar>
      <ci> x </ci>
      <degree> 
        <cn> 3 </cn>
      </degree> 
   </bvar>
    <apply><fn><ci>f</ci></fn>
       <ci> x </ci>
    </apply>
  </apply>
</math>
 



mml2om();
<math>
  <set type=normal>
     <ci> b </ci>
     <ci> a </ci>
     <ci> c </ci>
  </set>
</math>

mml2om();
<math>
   <list>
     <ci> b </ci>
     <ci> a </ci>
     <ci> c </ci>
   </list>
</math>

mml2om();
<math>
<list order="lexicographic">
     <ci> b </ci>
     <ci> a </ci>
     <ci> c </ci>
   </list>
</math>

mml2om();
<math>
<apply><union definitionurl="www.nag.co.uk"/>
     <ci type="set"> A </ci>
     <ci type="set"> B </ci>
   </apply>
</math>

mml2om();
<math>
<apply><union/>
  <set type="normal">
     <ci> b </ci>
     <cn> 2 </cn>
     <ci> c </ci>
   </set>
   <set>
     <ci> b </ci>
     <ci> r </ci>
     <cn> 2 </cn>
     <cn> 4 </cn>
     <ci> c </ci>
   </set>
   </apply>
</math>

mml2om();
<math>
<apply><intersect definitionurl="www.mit.edu"/>
     <ci type="set"> A </ci>
     <ci type="set"> B </ci>
   </apply>
</math>

mml2om();
<math>
<apply><intersect/>
  <set>
     <ci> b </ci>
     <cn> 2 </cn>
     <ci> c </ci>
   </set>
   <set>
     <ci> b </ci>
     <ci> r </ci>
     <cn> 2 </cn>
     <cn> 4 </cn>
     <ci> c </ci>
   </set>
 </apply>
</math>


mml2om();
<math>
<reln><in definitionurl="www.www.www"/>
     <ci> a </ci>
     <ci type="set"> A </ci>
   </reln>
</math>

mml2om();
<math>
 <reln><notin definitionurl="www.www.www"/>
   <ci> a </ci>
   <ci> A </ci>
 </reln>
</math>

mml2om();
<math>
<reln><prsubset definitionurl="www.www.www"/>
     <ci> A </ci>
     <ci> B </ci>
   </reln>
</math>

mml2om();
<math>
<reln><notsubset definitionurl="www.www.www"/>
     <ci> A </ci>
     <ci> B </ci>
   </reln>
</math>

mml2om();
<math>
<reln><notprsubset definitionurl="www.www.www"/>
     <ci> A </ci>
     <ci> B </ci>
   </reln>
</math>

mml2om();
<math>
<apply><setdiff definitionurl="www.www.www"/>
     <ci> A </ci>
     <ci> B </ci>
   </apply>
</math>

mml2om();
<math>
<apply><sum/>
     <bvar>
       <ci> x </ci>
     </bvar>
     <lowlimit>
       <ci> a </ci>
     </lowlimit>
     <uplimit>
       <ci> b </ci>
     </uplimit>
     <apply><fn><ci> f </ci></fn>
       <ci> x </ci>
     </apply>
   </apply>
</math>



mml2om();
<math>
<apply><product/>
     <bvar>
       <ci> x </ci>
     </bvar>
     <lowlimit>
       <ci> a </ci>
     </lowlimit>
     <uplimit>
       <ci> b </ci>
     </uplimit>
     <apply><fn><ci> f </ci></fn>
       <ci> x </ci>
     </apply>
   </apply>
</math>

mml2om();
<math>
 <apply><limit/>
   <bvar>
     <ci> V </ci>
   </bvar>
   <condition>
     <apply>
       <tendsto type=above/>
       <ci> V </ci>
       <cn> 0 </cn>
     </apply>
   </condition>
   <apply><divide/>
     <apply><int/>
       <bvar>
         <ci> S</ci>
       </bvar>
       <ci> a </ci>
     </apply>
     <ci> V </ci>
   </apply>
 </apply>
</math>               

mml2om();
<math>
<apply><limit/>
     <bvar>
       <ci> x </ci>
     </bvar>
     <lowlimit>
       <cn> 0 </cn>
     </lowlimit>
     <apply><sin/>
       <ci> x </ci>
     </apply>
   </apply>
</math>

mml2om();
<math>
<apply><limit/>
     <bvar>
       <ci> x </ci>
     </bvar>
     <condition>
       <reln>
         <tendsto type="above"/>
         <ci> x </ci>
         <ci> a </ci>
       </reln>
     </condition>
     <apply><sin/>
        <ci> x </ci>
     </apply>
   </apply>
</math>


mml2om();
<math>
<apply><sin/>
     <apply><plus/>
       <apply><cos/>
         <ci> x </ci>
       </apply>
       <apply><power/>
         <ci> x </ci>
         <cn> 3 </cn>
       </apply>
     </apply>
   </apply>
</math>

mml2om();
<math>
<apply><mean/>
     <ci> b </ci>
     <ci> r </ci>
     <cn> 2 </cn>
     <cn> 4 </cn>
     <ci> c </ci>
   </apply>
</math>

mml2om();
<math>
<apply><sdev/>
     <ci> b </ci>
     <ci> r </ci>
     <cn> 2 </cn>
     <cn> 4 </cn>
     <ci> c </ci>
   </apply>
</math>

mml2om();
<math>
 <apply><var/>
     <ci> b </ci>
     <ci> r </ci>
     <cn> 2 </cn>
     <cn> 4 </cn>
     <ci> c </ci>
 </apply>
</math>


mml2om();
<math>
<vector>
     <cn> 1 </cn>
     <cn> 2 </cn>
     <cn> 3 </cn>
     <ci> x </ci>
   </vector>
</math>

mml2om();
<math>
<matrix>
     <matrixrow>
       <cn> 0 </cn> <cn> 1 </cn> <cn> 0 </cn>
     </matrixrow>
     <matrixrow>
       <cn> 0 </cn> <cn> 0 </cn> <cn> 1 </cn>
     </matrixrow>
     <matrixrow>
       <cn> 1 </cn> <cn> 0 </cn> <cn> 0 </cn>
     </matrixrow>
   </matrix>
</math>

mml2om();
<math>
<apply><determinant/>
<matrix>
     <matrixrow>
       <cn> 3 </cn> <cn> 1 </cn> <cn> 5 </cn>
     </matrixrow>
     <matrixrow>
       <cn> 7 </cn> <cn> 0 </cn> <cn> 2 </cn>
     </matrixrow>
     <matrixrow>
       <cn> 1 </cn> <cn> 7 </cn> <cn> 8 </cn>
     </matrixrow>
   </matrix>
</apply>
</math>

mml2om();
<math>
<apply><transpose/>
<matrix>
     <matrixrow>
       <cn> 3 </cn> <cn> 1 </cn> <cn> 5 </cn>
     </matrixrow>
     <matrixrow>
       <cn> 7 </cn> <cn> 0 </cn> <cn> 2 </cn>
     </matrixrow>
     <matrixrow>
       <cn> 1 </cn> <cn> 7 </cn> <cn> 8 </cn>
     </matrixrow>
   </matrix>
</apply>
</math>

mml2om();
<math>
<apply><selector/>
     <matrix>
       <matrixrow>
         <cn> 1 </cn> <cn> 2 </cn>
       </matrixrow>
       <matrixrow>
         <cn> 3 </cn> <cn> 4 </cn>
       </matrixrow>
     </matrix>
     <cn> 1 </cn>
   </apply>
</math>

mml2om();
<math>
<apply><select/>
     <matrix>
       <matrixrow>
         <cn> 1 </cn> <cn> 2 </cn>
       </matrixrow>
       <matrixrow>
         <cn> 3 </cn> <cn> 4 </cn>
       </matrixrow>
     </matrix>
     <cn> 2 </cn>
     <cn> 2 </cn>
   </apply>
</math>

mml2om();
<math>
<apply><determinant/>
 <matrix>
      <matrixrow>
         <ci>a</ci>
         <cn type="integer">1</cn>
      </matrixrow>
      <matrixrow>
         <cn type="integer">2</cn>
         <ci>s</ci>
      </matrixrow>
   </matrix>
</apply>
</math>


mml2om();
<math>
 <apply><determinant/>
  <apply><transpose/>
   <matrix>
      <matrixrow>
         <cn type="integer">1</cn>
         <cn type="integer">2</cn>
         <cn type="integer">3</cn>
         <cn type="integer">4</cn>
      </matrixrow>
      <matrixrow>
         <cn type="integer">1</cn>
         <cn type="integer">2</cn>
         <cn type="integer">1</cn>
         <cn type="integer">2</cn>
      </matrixrow>
      <matrixrow>
         <cn type="integer">2</cn>
         <cn type="integer">3</cn>
         <cn type="integer">2</cn>
         <cn type="integer">1</cn>
      </matrixrow>
      <matrixrow>
         <cn type="integer">2</cn>
         <cn type="integer">1</cn>
         <cn type="integer">1</cn>
         <cn type="integer">1</cn>
      </matrixrow>
   </matrix>
  </apply>
 </apply>
</math>


mml2om();
<math>
   <apply><plus/>
      <apply><times/>
         <cn type="integer">2</cn>
         <apply><cos/>
            <ci>x</ci>
         </apply>
         <ci>x</ci>
      </apply>
      <apply><minus/>
         <apply><times/>
            <apply><sin/>
               <ci>x</ci>
            </apply>
            <apply><power/>
               <ci>x</ci>
               <cn type="integer">2</cn>
            </apply>
         </apply>
      </apply>
   </apply>
</math>


mml2om();
<math>
   <list>
      <reln><eq/>
         <ci>x</ci>
         <apply><plus/>
            <cn type="constant">&ImaginaryI;</cn>
            <apply><minus/>
               <cn type="integer">1</cn>
            </apply>
         </apply>
      </reln>
      <reln><eq/>
         <ci>x</ci>
         <apply><plus/>
            <apply><minus/>
               <cn type="constant">&ImaginaryI;</cn>
            </apply>
            <apply><minus/>
               <cn type="integer">1</cn>
            </apply>
         </apply>
      </reln>
   </list>
</math>



mml2om();
<math>
   <apply><plus/>
      <apply><minus/>
         <apply><times/>
            <apply><cos/>
               <apply><times/>
                  <ci>x</ci>
                  <ci>y</ci>
               </apply>
            </apply>
            <ci>x</ci>
            <ci>y</ci>
         </apply>
      </apply>
      <apply><times/>
         <apply><power/>
            <cn type="integer">2</cn>
            <apply><times/>
               <ci>x</ci>
               <ci>y</ci>
            </apply>
         </apply>
         <apply><power/>
            <apply><log/>
               <cn type="integer">2</cn>
            </apply>
            <cn type="integer">2</cn>
         </apply>
         <ci>x</ci>
         <ci>y</ci>
      </apply>
      <apply><times/>
         <apply><power/>
            <cn type="integer">2</cn>
            <apply><times/>
               <ci>x</ci>
               <ci>y</ci>
            </apply>
         </apply>
         <apply><log/>
            <cn type="integer">2</cn>
         </apply>
      </apply>
      <apply><minus/>
         <apply><sin/>
            <apply><times/>
               <ci>x</ci>
               <ci>y</ci>
            </apply>
         </apply>
      </apply>
      <cn type="integer">1</cn>
   </apply>
</math>


mml2om();
<math>
 <reln><eq/>
  <cn>2</cn>
  <cn>2</cn>
  <cn>2</cn>
 </reln>
</math>

mml2om();
<math>
 <reln><eq/>
  <cn>2</cn>
  <ci>A</ci>
  <ci>u</ci>
 </reln>
</math>

mml2om();
<math>
 <reln><neq/>
  <cn>2</cn>
  <cn>2</cn>
 </reln>
</math>

mml2om();
<math>
 <reln><neq/>
  <cn>2</cn>
  <ci>A</ci>
 </reln>
</math>

mml2om();
<math>
 <reln><lt/>
  <cn>2</cn>
  <cn>2</cn>
  <cn>2</cn>
 </reln>
</math>

mml2om();
<math>
 <reln><lt/>
  <cn>2</cn>
  <ci>A</ci>
  <ci>u</ci>
 </reln>
</math>

mml2om();
<math>
 <reln><gt/>
  <cn>2</cn>
  <cn>2</cn>
  <cn>2</cn>
 </reln>
</math>

mml2om();
<math>
 <reln><gt/>
  <cn>2</cn>
  <ci>A</ci>
  <ci>u</ci>
 </reln>
</math>

mml2om();
<math>
 <reln><geq/>
  <cn>2</cn>
  <cn>2</cn>
  <cn>2</cn>
 </reln>
</math>

mml2om();
<math>
 <reln><geq/>
  <cn>2</cn>
  <ci>A</ci>
  <ci>u</ci>
 </reln>
</math>

mml2om();
<math>
 <reln><leq/>
  <cn>2</cn>
  <cn>2</cn>
  <cn>2</cn>
 </reln>
</math>

mml2om();
<math>
 <reln><leq/>
  <cn>2</cn>
  <ci>A</ci>
  <ci>u</ci>
 </reln>
</math>

%The following examples work perfectly when read
%in by mml2om() and prove that the tags employed
%work correctly. The ir output can then be used
%to see if the mathml produced works:

mml2om();
<math>
   <apply><int/>
      <bvar>
         <ci>x</ci>
      </bvar>
      <lowlimit>
         <cn type="integer">0</cn>
      </lowlimit>
      <uplimit>
         <cn type="integer">1</cn>
      </uplimit>
      <apply><power/>
         <ci>x</ci>
         <cn type="integer">2</cn>
      </apply>
   </apply>
</math>           


mml2om();
<math>
   <apply><int/>
      <bvar>
         <ci>x</ci>
      </bvar>
      <lowlimit>
         <cn type="integer">1</cn>
      </lowlimit>
      <uplimit>
         <cn type="constant">&infin;</cn>
      </uplimit>
      <ci>x</ci>
   </apply>
</math>       

mml2om();
<math>       
 <apply><int/>
   <bvar>
     <ci> x </ci>
   </bvar>
   <interval>
      <ci> a </ci>
      <ci> b </ci>
    </interval>
   <apply><cos/>
     <ci> x </ci>
   </apply>
 </apply>
</math>       

%this example is MathML1.0 and when passed
%through function mml2om() it translates it to
%MathML2.0

mml2om();
<math>
  <apply><diff/>
    <bvar>
      <ci> x </ci>
      <degree>
        <cn> 2 </cn>
      </degree>
    </bvar>
    <apply><fn><ci>f</ci></fn>
       <ci> x </ci>
    </apply>
  </apply>
</math>             



mml2om();
<math>
  <list>
    <apply><plus/>
       <ci> x </ci>
       <ci> y </ci>
    </apply>
    <cn> 3 </cn>
    <cn> 7 </cn>
  </list>
</math>       

mml2om();
<math>       
  <interval closure="open-closed">
    <ci> a </ci>
    <ci> b </ci>
  </interval>
</math>       

mml2om();
<math>
   <interval>
     <ci> a </ci>
     <ci> b </ci>
   </interval>
</math>

mml2om();
<math>
   <list>
      <list>
         <reln><eq/>
            <ci>x</ci>
            <apply>
               <csymbol definitionURL="..." encoding="...">
                  <ci>root_of</ci>
               </csymbol>
               <apply><plus/>
                  <apply><minus/>
                     <apply><power/>
                        <ci>y</ci>
                        <ci>x_</ci>
                     </apply>
                  </apply>
                  <apply><minus/>
                     <apply><times/>
                        <apply><int/>
                           <bvar>
                              <ci>x_</ci>
                           </bvar>
                           <apply><power/>
                              <ci>x_</ci>
                              <ci>x_</ci>
                           </apply>
                        </apply>
                        <ci>y</ci>
                     </apply>
                  </apply>
                  <ci>x_</ci>
                  <ci>y</ci>
               </apply>
               <ci>x_</ci>
               <ci>tag_1</ci>
            </apply>
         </reln>
         <reln><eq/>
            <ci>a</ci>
            <apply><plus/>
               <ci>x</ci>
               <ci>y</ci>
            </apply>
         </reln>
      </list>
   </list>
</math>          
mml2om();
<math>
   <list>
      <list>
         <reln><eq/>
            <ci>x</ci>
            <apply>
               <csymbol definitionURL="..." encoding="...">
                  <ci>root_of</ci>
               </csymbol>
               <apply><plus/>
                  <apply><times/>
                     <apply><exp/>
                        <apply><plus/>
                           <cn type="constant">&ImaginaryI;</cn>
                           <ci>x_</ci>
                        </apply>
                     </apply>
                     <ci>y</ci>
                  </apply>
                  <apply><exp/>
                     <apply><plus/>
                        <cn type="constant">&ImaginaryI;</cn>
                        <ci>x_</ci>
                     </apply>
                  </apply>
                  <apply><power/>
                     <ci>x_</ci>
                     <apply><plus/>
                        <ci>y</ci>
                        <cn type="integer">1</cn>
                     </apply>
                  </apply>
                  <apply><times/>
                     <apply><int/>
                        <bvar>
                           <ci>x_</ci>
                        </bvar>
                        <apply><power/>
                           <ci>x_</ci>
                           <ci>x_</ci>
                        </apply>
                     </apply>
                     <apply><power/>
                        <ci>y</ci>
                        <cn type="integer">2</cn>
                     </apply>
                  </apply>
                  <apply><times/>
                     <apply><int/>
                        <bvar>
                           <ci>x_</ci>                  
                        </bvar>
                        <apply><power/>
                           <ci>x_</ci>
                           <ci>x_</ci>
                        </apply>
                     </apply>
                     <ci>y</ci>
                  </apply>
               </apply>
               <ci>x_</ci>
               <ci>tag_2</ci>
            </apply>
         </reln>
         <reln><eq/>
            <ci>z</ci>
            <ci>y</ci>
         </reln>
      </list>
   </list>
</math>                   


mml2om();
<math>
  <apply><curl/>
  <vector>
     <ci> b </ci>
     <cn> 2 </cn>
     <ci> c </ci>
   </vector>
  </apply>
</math>       

mml2om();
<math>
  <apply><divergence/>
  <vector>
     <ci> b </ci>
     <cn> 2 </cn>
     <ci> c </ci>
   </vector>
  </apply>
</math>       

mml2om();
<math>
  <apply><laplacian/>
  <vector>
     <ci> b </ci>
     <cn> 2 </cn>
     <ci> c </ci>
   </vector>
  </apply>
</math>       

mml2om();
<math>
   <apply><forall/>
      <bvar>
         <ci> a </ci>
      </bvar>
      <apply><eq/>
         <apply><inverse/>
            <apply><inverse/>
               <ci> a </ci>
            </apply>
         </apply>
         <ci> a </ci>
      </apply>
   </apply>
</math>            

end;