- most operations in computer algebra are some form of simplification
- here is a question on what representation to use for algebraic
expressions: which form is simpler?

- is a canonical simplification operator if and only if

- the canonical simplification operator gives us an unique form
for equivalent formulas: it defines a unique representative for
each class of equivalent algebraic expressions
- most often non-canonical simplification for general algebraic
expressions is used in computer algebra programs--typically, a
combination of canonical simplification and pattern matching

Richard Liska