Gene writes: << Factorization is not unique. Let p(x) be any power series with integer coefficients beginning with 1. Then 1/p(x) is also a power series with integer coefficients beginning with 1. Then any factor f(x) can be replaced by p(x) (f(x)/p(x)). Neil wrote:

There are lots of algorithms for factoring in Z[x]. But what about power series with integer coefficients? Is there a good algorithm? Knuth Vol 2 is silent. Any hints would be appreciated! There are two versions, depending on whether you work to order n, or with the full power series. . . .

...

Still, formal power series Z[[x]] over Z might be a unique factorization domain (and surely this is known to algebraists). The non-uniqueness Gene points out looks like a big pain, but at least so far this is only the non-uniquenss that comes about from multiplication & division by the *units* in Z[[x]]. It looks as though there might be a Euclideanesque "algorithm" to find the GCD of two members of Z[[x]] -- but it typically involves infinitely many steps. Still, if it works that would imply Z[[x]] is a UFD. --Dan