Perhaps as a bit of explanation of why you may care about this and why our hand is forced:
Given symbolic expression A and B, what should bool(A == B) and bool(A != B) be? Python forces us that these are either True or False and since equality testing happens all over in Python, throwing an error isn't really an option either. It would seem the reasonable equality notion here is: "as functions in whatever variables are present". That's a notion of equality that is not always practically decidable and in fact is even theoretically undecidable in full generality (see Richardson's Theorem). It then seems reasonable to have bool(A==B) return True if equality can be established and False otherwise. That's generally what is attempted in sage. The question now arises for bool(A != B): what should it do for undecided cases? At least I was originally under the impression that a similar approach might be prudent to also return "False" for undecided, in which case bool(A==B) and bool(A!=B) aren't necesarily complementary: they could both be false. This is problematic in python, but even more important: the primitives in Maxima that we rely on don't even do this! We use "is(equal(A,B))" in maxima. In maxima, "is(equal(x,x^2))" returns "unknown" because there are values for x that make it True as well as values that make it False. So "unknown" doesn't mean "unable to determine if the two expressions describe the same function". With what I understand presently, I don't think we have a reasonable other option than to just make "bool(A!=B) == not bool(A==B)". Now would be a good time to voice concerns and help with finding alternatives, should they exist. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/sage-devel/40012127-c062-4d08-8066-708834a9d788n%40googlegroups.com.
