How do define an unspecified function that is additive or multiplicative?

Question

How can I define unknown functions that have certain algebraic properties?

Example: I want to define the conjugation operator with the properties:

bar(a+b) = bar(a) + bar(b) and bar(a*b) = bar(a)*bar(b).

The goal is that maple should then use these properties to simplify a polynomial expression involving bars.

Answer 1

The command define might help with this somewhat. This creates evaluation rules rather than simplification rules for your operator, however.