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MathGroup Archive 2005

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Re: Simplifying an expression in light of relationships between variables?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54283] Re: [mg54263] Simplifying an expression in light of relationships between variables?
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Wed, 16 Feb 2005 14:36:02 -0500 (EST)
  • Reply-to: hanlonr at cox.net
  • Sender: owner-wri-mathgroup at wolfram.com

cond={d==a+b,e==c+d};

Simplify[#,cond]& /@ 
  {a+b,d-b,a+b+c,e-c,e-c-b}

{d,d-b,e,d,d-b}

FullSimplify[#,cond]& /@ 
  {a+b,d-b,a+b+c,e-c,e-c-b}

{d,d-b,e,d,d-b}

For reasons unknown to me, d-b won't simplify.  Hit it with a hammer.

Simplify[#,cond] /. d-b:>a& /@ 
  {a+b,d-b,a+b+c,e-c,e-c-b}

{d,a,e,d,a}


Bob Hanlon

> 
> From: "Steve W. Brewer" <ste-ve at ka-tech.com>
To: mathgroup at smc.vnet.net
> Date: 2005/02/14 Mon PM 09:51:04 EST
> To: mathgroup at smc.vnet.net
> Subject: [mg54283] [mg54263] Simplifying an expression in light of relationships 
between variables?
> 
> Suppose I have a few variables that are related in the following way:
> 
> d == a + b
> e == c + d
> 
> 
> 
> I want Simplify and FullSimplify to consider these relationships when 
> performing simplification.  For example:
> 
> FullSimplify[a + b]
> 
> d
> 
> 
> 
> FullSimplify[d - b]
> 
> a
> 
> 
> 
> FullSimplify[a + b + c]
> 
> e
> 
> 
> 
> FullSimplify[e - c]
> 
> d
> 
> 
> 
> FullSimplify[e - c - b]
> 
> a
> 
> 
> 
> Is there a straightforward way to get this behavior?  I've tried 
> experimenting with TransformationFunctions, but it looks like I need to 
> include every possible permutation for it to work, for example:
> 
> TransformationFunctions ->
>    {Automatic,
>     # /. (d -> a + b)&,
>     # /. (a + b -> d)&,
>     # /. (a -> d - b)&,
>     # /. (d - b -> a)&,
>     # /. (b -> d - a)&,
>     # /. (d - a -> b)&,
>     ... }
> 
> 
> 
> This is unwieldy even in this simple example, and it rapidly becomes 
> unmanageable as the number of variables and relationships increases.
> 
> 
> Is there an easier way? 
> 
> 


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