Comment #5 on issue 2075 by asmeurer: solve fails for eq1=1 + 2*y/b - (e + x)**2/a; eq3=1 + 2*y/d - (x - e)**2/c
http://code.google.com/p/sympy/issues/detail?id=2075
Those are used internally by Poly to determine what the coefficients of a polynomial come from. ZZ means the integers and QQ means the rational numbers. [] means polynomial and () means rational function (polynomial over polynomial). The letters are the variables (of the coefficients). So an element of ZZ[a, b] might be 2*a + 3*a*b**2. An element of QQ(a, b, c) might be 3/2*a/(b + 1) - c. I'd point you to the Wikipedia article, but it is way in depth, and would likely just confuse you more.
Obviously, if something is an element of ZZ(a, b, e) then it is also an element of ZZ(a, b, c, d, e), but it requires some work internally because the variables have to be renumbered and the internal representation remade. There are functions for this to do that in the internal part of polys (see that 6abbf commit above), but it obviously hasn't been fully implemented anywhere yet.
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