UniformizingElement returns the element of valuation 1 and InertialElement returns the element adjoined in making the unramified part of the extension. ChangePrecision allows the precision of a ring or field or an element thereof to be altered. Random and Representative have both been provided for local rings. The sequence conversions given by LocseqInert, InertseqPadic, Locseq and ElementToSequence provide several different ways to represent an element of a local ring or field as a sequence. Arithmetic and Predicates are provided as usual.
Parent returns the local ring or field that an element is contained in.
To consider an element to have full precision apply Expand. The valuation of an element is returned by Valuation. The logarithm of an element is computed by Log and the exponential by Exp. The norm and trace of a local element over the p-adic substructure can be calculated using Norm and Trace. The greatest common divisor of two polynomials over a local ring can be calculated using the GreatestCommonDivisor function.