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Re: Symbolic tensor analysis in Mathematica 8


On Friday, March 16, 2012 4:35:24 AM UTC-7, Misery Slave wrote:
> Hello,
> 
> Recently I begun to use Mathematica. For now I'm trying to learn to
> use it properly.
> The first tasks I would like to play with, are vector and tensor
> analysis.
> The question is:
> For simplicity I would like to have vector definition:
> 
> v={v1,v2,v3} or v={vx,vy,vz}
> 
> where 1,2,3 or x,y,z are subscripts or superscripts. How do I achieve
> that? When I write something like that I get the recursion which I do
> not want. And the other thing is: how do I tell Mathematica that for
> example vx is a function of x,y,z to get something like:
> 
> vx=f(x,y,z), vy=g(x,y,z), vz=h(x,y,z)
> 
> to describe vector field. But during derivations I may not know
> formulas for f,g,h. But when counting the derivative I would like to
> get
> 
> Dv/dx={f'(x,y,z),g'(x,y,z),h'(x,y,z)}
> and so on.
> 
> Thanks in advance and
> Best regards,
> Misery

You may find the following posts useful:

(a)
General discussion on how to make subscript notation work:
http://mathematica.stackexchange.com/questions/3020/why-cant-i-define-vector-v-as-having-subscripted-elements-v-1-v-2-v-3

(b)
More specific example of how I would display objects for vector analysis:
https://groups.google.com/d/msg/comp.soft-sys.math.mathematica/VBXq2LPmxD8/YeNpmyOWUYwJ

Jens



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