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Volume integrals in Content MathML

From: JB Collins <joebmath@yahoo.com>
Date: Mon, 3 Nov 2008 18:19:34 -0800 (PST)
To: www-math@w3.org
Message-ID: <578955.35486.qm@web57606.mail.re1.yahoo.com>
Assume that the mass of an object is given by the volume integral of its mass density.
In LaTeX:

$\int \rho({\bf r}) d^3{\bf r}$

The (unambiguous) interpretation of this is the integration of the density over all 3-space, regardless of the basis in which the vector, r, may later be expressed.

Can this be expressed in Content MathML compactly, without the assumption of a basis?

Certainly if I assume a basis, e.g., Cartesian coordinates, then I could express the integral as

<apply>
   <int/> 
      <bvar> <ci>x</ci> </bvar>
      <lowlimit><minfinity/></lowlimit>
      <uplimit><infinity/></uplimit>
   <apply>
      <int/>
         <bvar> <ci>y</ci> </bvar>
         <lowlimit><minfinity/></lowlimit>
         <uplimit><infinity/></uplimit>
      <apply>
         <int/>
            <bvar> <ci>z</ci> </bvar>
            <lowlimit><minfinity/></lowlimit>
            <uplimit><infinity/></uplimit>
         <apply>
            <fn>&rho</fn>
            <vector> <ci>x</ci> <ci>y</ci> <ci>z</ci> </vector>
         </apply>
      </apply>
   </apply>
</apply>


Regards,
Joe C.


      
Received on Tuesday, 4 November 2008 02:20:23 GMT

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