GALOIS RINGS

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 (H60E1)

 
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 (H60E2)