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Factorization of polynomials over non-fields is generally not implemented, with a notable exception of ZZ. There is no (yet?) such implementation for Gaussian integers.

As for I0, apparently it denotes the generator of ZZ[I] to distinguish it from I, which is a generator of QQ[I]. Btw, it is more straightforward to use GaussianIntegers() rather than ZZ[I]. Check this out:

print( GaussianIntegers() )
print( ZZ[I] )
print( I.parent() )
print( ZZ[I](I).parent() )

Factorization of polynomials over non-fields is generally not implemented, with a notable exception of ZZ. There is no (yet?) such implementation for non-monic polynomials over Gaussian integers.

As for I0, apparently it denotes the generator of ZZ[I] to distinguish it from I, which is a generator of QQ[I]. Btw, it is more straightforward to use GaussianIntegers() rather than ZZ[I]. Check this out:

print( GaussianIntegers() )
print( ZZ[I] )
print( I.parent() )
print( ZZ[I](I).parent() )