Introduction

 
Creation Functions

      Creation of Structures
            ValuationRing(Q, p) : FldRat, RngIntElt -> RngVal
            ValuationRing(F, f) : FldFunRat, RngUPolElt -> RngVal
            ValuationRing(F) : FldFunRat -> RngVal
            ValuationRing(K, p) : FldNum, RngOrdIdl -> RngVal

      Creation of Elements
            V ! r : RngVal, FldFunElt -> RngValElt

 
Structure Operations

      Related Structures
            FieldOfFractions(V) : RngVal -> Rng

      Numerical Invariants

 
Element Operations

      Arithmetic Operations
            v div w : RngValElt, RngValElt -> RngValElt

      Equality and Membership

      Parent and Category

      Predicates on Ring Elements

      Other Element Functions
            EuclideanNorm(v) : RngValElt -> RngIntElt
            Quotrem(v, w) : RngValElt, RngValElt -> RngValElt, RngValElt
            GreatestCommonDivisor(v, w) : RngValElt, RngValElt -> RngValElt
            ExtendedGreatestCommonDivisor(v, w) : RngValElt, RngValElt -> RngValElt, RngValElt, RngValElt

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