The SeriesPrinting attribute allows the user to specify the print style of a p-adic element. Prime returns the prime number that has valuation 1 in the p-adic ring or field. ResidueClassField returns the quotient of the p-adic ring by its unique maximal ideal. In the case of fields, the residue class field is defined to be that of its ring of integers. UniformizingElement returns the prime of the p-adic ring or field as an element of that ring or field.
Precision returns the precision of the ring or field.
This is used as the default precision to create elements of that ring or field with. ChangePrecision allows the user to change the precision of a ring or field or an element in either. The function Random has been provided to generate random elements in a p-adic ring. GreatestCommonDivisor is now available for polynomials over fixed precision p-adic rings. The function NewtonPolygon and the associated machinery can be used to compute the valuations of the roots of a polynomial over a p-adic ring and the number of roots that have that valuation.