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.

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    $\begingroup$ Structures with operations that satisfy "identities" are called varieties (in formal logic, esp. universal algebra), but I haven't come across what you describe online. $\endgroup$
    – hardmath
    Jun 10 '14 at 22:27
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    $\begingroup$ I would like to write the site you ask about before I die, but this way on it's gonna take me a lot. So far, this is the best I've seen around: math.chapman.edu/~jipsen/structures/doku.php. No better or more complete/wide sources are known to me. $\endgroup$ Jun 16 '14 at 13:30

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