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VALUATION RINGS

 
Acknowledgements
 
Introduction
 
Creation Functions
      Creation of Structures
      Creation of Elements
 
Structure Operations
      Related Structures
      Numerical Invariants
 
Element Operations
      Arithmetic Operations
      Equality and Membership
      Parent and Category
      Predicates on Ring Elements
      Other Element Functions







DETAILS

 
Introduction

 
Creation Functions

      Creation of Structures
            ValuationRing(Q, p) : FldRat, RngIntElt -> RngVal
            ValuationRing(F, f) : FldFun, RngUPolElt -> RngVal
            ValuationRing(F) : FldFun -> 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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Version: V2.19 of Wed Apr 24 15:09:57 EST 2013