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>