       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?

```

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