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Re: Semantic information for math representations of physics

From: Roger I Martin PhD <hypernexdev@hypernexinc.com>
Date: Wed, 09 Feb 2005 15:13:24 -0500
Message-ID: <420A6EE4.3060202@hypernexinc.com>
CC: www-math@w3.org

JB Collins wrote:

>It seems to me that what you are offering supports
>translation into available numerical library calls.
>The problem I am facing is that physicists often "roll
>their own" numerical methods - and for good reason.
>General purpose methods, say for example a Runge-Kutta
>integrator, works well for general use. When high
>performance is required, however, an integrator
>specific to the equation of interest will generally
>work more efficiently.
>
Going to an integrator of the specific equation is where I'm going.  Not 
an available numerical library call.  Differentiation is easier example 
but I'm applying the rules of integration whenever possible to avoid 
numerical integrators. That is the difference.  The simple example 
again.  The integral of ln(x) from 1 to 2.  The system does not go to 
Romberg http://mathworld.wolfram.com/RombergIntegration.html, discretise 
the function but returns a compiled class with the answer ln(2).   The 
specialized integrator can be written by the physicist  in mathml and 
run.  If I use http://mathworld.wolfram.com/Runge-KuttaMethod.html then 
I write it in mathml with the equation of interest embedded in it.  What 
I'm thinking about is giving the physicists the ability to often "roll 
their own" numerical methods without writing a line of code or calling a 
numerical library.

>This latter case happens all of
>the time. Don't get me wrong: physicists use the
>general purpose libraries all of the time, also. But
>support for documenting the translation of
>mathematical descriptions to discrete representations
>is required for both cases.
>
>Regards,
>Joe Collins
>Naval Research Lab
>
>--- Roger I Martin PhD <hypernexdev@hypernexinc.com>
>wrote:
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Received on Wednesday, 9 February 2005 20:11:16 GMT

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