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Re: Simplification of vector and scalar products

• To: mathgroup at smc.vnet.net
• Subject: [mg39630] Re: Simplification of vector and scalar products
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 27 Feb 2003 00:26:59 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <b3hrkl$ij8$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

> I want to simplify vector and scalar products as for instance
> 
>        6 (a / 2) x b  //Simplify
> 
> where a and b are assumed to be vectors and "x" is the vector product..
> Simplify and FullSimplify do nothing, nor does the following command
> change anything:
> 
>        6 (a / 2) x b  /. p_ Cross[a_ / q_ , b_] => p Cross[a, b] / q

This does nothing because Mathematica store a/2 as Rational[1,2]*a
while a/q would be a*q^(-1) and the pattern with a_/q_ can't match,
but

6*Cross[a/2, b] /. Cross[a_.*q_, p_] /; NumericQ[a] :> a*Cross[q, p] 

work as expected.

> 
Regards
  Jens