Updates:
Status: Invalid
Comment #2 on issue 2739 by [email protected]: this composition doesn't
decompose
http://code.google.com/p/sympy/issues/detail?id=2739
In the second case, composition gives trivial result: x**2 - x. This
polynomial doesn't have functional decomposition with Kozen's algorithm,
although it has trivial factorization. This is an implication of the first
point from the docstring. In general you can't expect that compositions
with linear polynomials will decompose at all or decompose the way you
want. In other words, the algorithm can't decide which shift should be
considered (in your case it was -1) and [x - 1, x] is not a functional
decomposition (but factorization). Similar argumentation applies to other
cases from the docstring. Thus you should *never* assume that:
a.compose(b).decompose() in [[a, b], [b, a]].
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