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Re: Semantic information for math representations of physics

From: Roger I Martin PhD <hypernexdev@hypernexinc.com>
Date: Thu, 03 Feb 2005 14:18:10 -0500
Message-ID: <420278F2.5000302@hypernexinc.com>
CC: www-math@w3.org

>It seems to me that others are thinking along these
>lines as well. (Set me straight if you think
>otherwise). I am still exploring available tools and
>trying to define exactly what I need to build for
>myself.
>
>  
>
Maybe an example would clarify if we are thinking along the same lines:

Are you interested in having douments with for example

http://mathworld.wolfram.com/NURBSCurve.html written
in mathml and then a system to transform it:

   <apply>
       <eq/>
       <apply>
           <csymbol type="vector">C</csymbol>
           <ci >t</ci>
       </apply>
      <apply>
           <divide/>
           <apply>
               <sum />
               <bvar>
                   <ci type="integer">i</ci>
               </bvar>
               <lowlimit>
                   <cn>0</cn>
               </lowlimit>
               <uplimit>
                   <ci type="integer">n</ci>
               </uplimit>
               <apply>
                   <times/>
                   <apply>
                       <selector/>
                       <ci>w</ci>
                       <ci>i</ci>
                   </apply>
                   <apply>
                       <selector/>
                       <ci type="vector">d</ci>
                       <ci>i</ci>
                   </apply>
                   <apply>
                       <csymbol>N</csymbol>
                       <ci type="integer">i</ci>
                       <ci type="integer">p</ci>
                       <apply>
                           <selector/>
                           <ci>knot</ci>
                           <ci type="integer">i</ci>
                       </apply>
                       <ci>t</ci>
                   </apply>
               </apply>
           </apply>
           <apply>
               <sum />
               <bvar>
                   <ci type="integer">i</ci>
               </bvar>
               <lowlimit>
                   <cn>0</cn>
               </lowlimit>
               <uplimit>
                   <ci>n</ci>
               </uplimit>
               <apply>
                   <times/>
                   <apply>
                       <selector/>
                       <ci>w</ci>
                       <ci>i</ci>
                   </apply>
                   <apply>
                       <csymbol>N</csymbol>
                       <ci type="integer">i</ci>
                       <ci>p</ci>
                       <apply>
                           <selector/>
                           <ci>knot</ci>
                           <ci type="integer">i</ci>
                       </apply>
                       <ci>t</ci>
                   </apply>
               </apply>
           </apply>
       </apply>
   </apply>

to compilable and runnable at runtime Java code:

   public javax.vecmath.GVector C(double t)
   {
         javax.vecmath.GVector C=null;
       C=divide((new
com.pombi.mathml.lang.OperatorAdapter(){ public
javax.vecmath.GVector vectorSum(double t){
         javax.vecmath.GVector sum=new
javax.vecmath.GVector(3);
         for(int i=0;i<=n;i++)
         {
            sum.add(times(new
Object[]{w[(int)i],d[(int)i],N(i, p, knot, t)}));
         }
               return sum;
               }}).vectorSum(t),(new
com.pombi.mathml.lang.OperatorAdapter(){ public double
sum(double t){
               double sum=0.0;
               for(int i=0;i<n;i++)
               {
                                sum+=((w[(int)i]*N(i,
p, knot, t)));
                             }
               return sum;
               }}).sum(t));
       return C;
   }

Then have a bean or web service environment to use the equation in numeric modeling and solutions?  
If so we are thinking along the same lines.  I'm aware of many cases where numeric computer code
 does not necessarily reflect the intend of the physicist's/scientist's more abstract mathematical
 model or produce the correct results:-)  And said code is not the place to start working on the model
 or new functional implementation.  Most of the time the code cannot be trusted and starting from scratch is 
recommended. Applying a more abstract level that directly matches and retains the intentions of 
physicists/scientists while being able to utilize cpus for computation is very attractive.

r,

Roger
Received on Thursday, 3 February 2005 19:16:05 GMT

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