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MathGroup Archive 2005

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Re: question: re-organising equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55214] Re: question: re-organising equations
  • From: dh <dh at metrohm.ch>
  • Date: Thu, 17 Mar 2005 03:28:32 -0500 (EST)
  • References: <d19306$ngr$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com


OneTel wrote:
> I have a set of simultaneous equations which are very long and so I will 
> not include them here. They take the form of:
> 
>     x = f(A,B,C,D)
>     y = f(A,B,C,D)
>     z = f(A,B,C,D)
>     w = f(A,B,C,D)
> 
> I would like to re-organise these into the form:
>    
>     A = f(x,y,z,w)
>     B = f(x,y,z,w)
>     C = f(x,y,z,w)
>     D = f(x,y,z,w)
> 

Hello
This can be done e.g. with the functione "Solve".
Success will depend on the form of your equations. If they are linear, 
then it is easy can always be done (provided the equations are not 
degenerate).
For polynomial equations up to quartic it can be done in principle, but 
it is getting messy very fast. For higher polynimial equations there is 
in general no explizite solution. But special cases may be solved 
nontheless. The same is true for non polynomial cases, no general 
solution, but many special ones.
If everything breaks, there is always the possibility to recurse to 
numerical or other (e.g. basis sets) approximations.
Daniel


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