Comment #3 on issue 2329 by [email protected]: Should Poly use an algebraic domain by default?
http://code.google.com/p/sympy/issues/detail?id=2329

But shouldn't ZZ[I] raise an exception?

It would be nice, but then people would complain that `I` can't be a generator in the context of symbolic manipulation (not algebraic computations). The current state of art is something that is convenient in the former case and allows to do the later when needed.

EX doesn't solve zero equivalence problem in general, whereas algebraic domains do, but for most common cases EX is sufficient and is faster than algebraics (because it doesn't require computing minimal polynomials, field isomorphisms, etc. (which are very expensive -> Groebner bases, PSLQ)). And if you want to do meaningful algebraic computing, then you make have to setup the appropriate domain explicitly anyway, for example factor(x**4 + 1) over I or sqrt(2) or I + sqrt(2).

This is also how Mathematica works more or less.

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