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GALOIS RINGS

 
Acknowledgements
 
Introduction
 
Creation Functions
      Creation of Structures
      Names
      Creation of Elements
      Sequence Conversions
 
Structure Operations
      Related Structures
      Numerical Invariants
      Ring Predicates and Booleans
 
Element Operations
      Arithmetic Operators
      Euclidean Operations
      Equality and Membership
      Parent and Category
      Predicates on Ring Elements







DETAILS

 
Introduction

 
Creation Functions

      Creation of Structures
            GaloisRing(q, d) : RngIntElt, RngIntElt -> RngGal
            GaloisRing(p, a, d) : RngIntElt, RngIntElt, RngIntElt -> RngGal
            GaloisRing(q, D) : RngIntElt, RngUPol -> RngGal
            GaloisRing(p, a, D) : RngIntElt, RngIntElt, RngUPol -> RngGal

      Names
            AssignNames(~R, [f]) : RngGal, [ MonStgElt ]) ->
            Name(R, 1) : RngGal, RngIntElt -> RngGalElt

      Creation of Elements
            R . 1 : RngGal -> RngGalElt
            R ! a : RngGal, RngElt -> RngGalElt
            Random(R) : RngGal -> RngGalElt

      Sequence Conversions
            ElementToSequence(a) : RngGalElt -> [ RngIntResElt ]
            Example RngGal_Create (H48E1)

 
Structure Operations

      Related Structures

      Numerical Invariants
            Characteristic(R) : RngGal -> RngIntElt
            # R : RngGal -> RngIntElt
            Degree(R) : RngGal -> RngIntElt
            ResidueField(R) : RngGal -> FldFin

      Ring Predicates and Booleans

 
Element Operations

      Arithmetic Operators

      Euclidean Operations

      Equality and Membership

      Parent and Category

      Predicates on Ring Elements
            Example RngGal_Create (H48E2)

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Version: V2.19 of Mon Dec 17 14:40:36 EST 2012