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Re: Working with vectors symbolically

• To: mathgroup at smc.vnet.net
• Subject: [mg93630] Re: Working with vectors symbolically
• From: David Bailey <dave at removedbailey.co.uk>
• Date: Tue, 18 Nov 2008 07:23:26 -0500 (EST)
• References: <gfrjv6$lo5$1@smc.vnet.net>

cool-RR wrote:
> I need a CAS for working with vectors symbolically. I am accustomed to
> using Mathematica for my symbolic math work, but it seems that
> Mathematica is not up for the task. So I am hoping that you can either
> show me how to do it in Mathematica, or refer me to some other CAS
> that can handle this. [Do this my email to the author - moderator]
> What I do are equations relating to electromagnetic fields. I have
> long equations which are filled with scalar products and cross
> products of vectors. Right now I have to simplify these equations by
> hand. I want to be able to simplify them automatically... Also taking
> limits. Mathematica has trouble taking limits on equations involving
> vectors.
> 
> So anyone has any advice to offer?
> 
> Thanks,
> Ram Rachum.
> 
By supplying your own rules, it is possible to program all sorts of 
algebraic systems - commutative or non-commutative - using Mathematica.

This is often quite easy, because you end up with a few simple rules 
that get applied over and over again to produce complicated results.

Writing your own rules may be much easier than trying to find a 
pre-built system that supplies exactly what you need. For example, you 
can decide all sorts of details for yourself - such as how to represent 
scalar quantities, distinguish between symbolic vectors and scalars, etc.

Someone may suggest some existing package, but failing that, why not 
post a few specific examples of the transformations you wish to achieve?

David Bailey
http://www.dbaileyconsultancy.co.uk