I'm working on an abstract algebra library in Python, and I'm trying to include as many functions that analyze algebraic structures, returning true or false based on whether or not the algebra satisfies a certain identity or not. I've found a good list of these in the Magma package provided by Maple, but I want something similar but for algebraic structures with two binary operators.
Of course, I'll include the obvious: isDistributive(), isRing(), isField(), etc... but I want to be as complete as possible, so if there was a reference somewhere online with a large number of properties/identities/different types of algebras with two binary operators, or possibly an existing CAS that implements something like this, that would be very helpful.