What is the difficulty in factoring polynomials with multiple roots over 
the p-adic ring? 

[[[ R.<x>=Qp(5)[]
f=x^2
g=gcd(f,f.derivative())
(f/g).factor() ]]]

returns the following error:

sage.rings.padics.precision_error.PrecisionError: p-adic factorization
not well-defined since the discriminant is zero up to the requestion
p-adic precision


this works fine over the rationals:


[[[ R.<x>=QQ[]
f=x^2
g=gcd(f,f.derivative())
(f/g).factor() ]]]

I'm not well versed in p-adics, is this impossible or just not implemented?

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