Question: Non-default Set Orderings

I want to learn about why sometimes different algebraic expressions are ordered differently, and what would be the best way to instruct maple to chose a different "rule" for which a set of arithmetic functions are ordered, while still maintaining the axiom of uniqueness. 

I figured this would be accomplished on a case by case basis, and it may involve just using lists instead,defining a procedure to produce the desired ordering for any given set of functions, and using the "remove" command to replace the set "difference" operator and the Join command for the lists in place of the union operator. Then of course using the "Remove Duplicates" option from ListTools to impose the axiom of unique elements. 

Is this the best way to go about this, or is there a much simpler way, that includes an abstract algebra package that I'm unaware of thus far?