In characteristic 0 are there problems:

sage: T=SR(pAdicField(5)(1/3))
sage: T.pyobject()
2 + 3*5 + 5^2 + 3*5^3 + 5^4 + 3*5^5 + 5^6 + 3*5^7 + 5^8 + 3*5^9 + 5^10
+ 3*5^11 + 5^12 + 3*5^13 + 5^14 + 3*5^15 + 5^16 + 3*5^17 + 5^18 +
3*5^19 + O(5^20)

(fair enough - it just gets wrapped)

sage: T=SR(pAdicField(5)['x']([1/3]))
sage: T.pyobject()
[same thing

sage: T=SR(pAdicField(5)['x']([1/3,1]))
TypeError:

[sic -- really just a blank type-error]

sage: f=(exp(SR(pAdicField(5)(1/3))*x+x^2)+exp(RR(1.0)*x^2)).diff()
sage: f(x=5)
10*e^25 + 2 + 4*5 + 4*5^2 + 3*5^3 + 2*5^4 + 3*5^5 + 4*5^6 + 4*5^7 +
5^9 + 3*5^10 + 2*5^11 + 3*5^13 + 2*5^14 + 4*5^15 + 5^16 + 2*5^17 +
4*5^19 + O(5^20)



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