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Simplifying an expression in light of relationships between variables?

• To: mathgroup at smc.vnet.net
• Subject: [mg54263] Simplifying an expression in light of relationships between variables?
• From: "Steve W. Brewer" <ste-ve at ka-tech.com>
• Date: Mon, 14 Feb 2005 21:51:04 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

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? 

• Follow-Ups:
  • Re: Simplifying an expression in light of relationships between variables?
    • From: Chris Chiasson <chris.chiasson@gmail.com>
  • Re: Simplifying an expression in light of relationships between variables?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>