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CYCLOTOMIC FIELDS

 
Introduction
 
Creation Functions
      Creation of Cyclotomic Fields
      Creation of Elements
 
Structure Operations
      Related Structures
      Invariants
 
Element Operations
      Predicates on Elements
      Conjugates







DETAILS

 
Introduction

 
Creation Functions

      Creation of Cyclotomic Fields
            CyclotomicField(m) : RngIntElt -> FldCyc
            CyclotomicPolynomial(m) : RngIntElt -> RngUPolElt
            MinimalField(a) : FldCycElt -> FldCyc
            MinimalField(S) : [ FldCycElt ] -> FldCyc
            Example FldCyc_creation (H50E1)

      Creation of Elements
            RootOfUnity(n) : RngIntElt -> FldCycElt
            RootOfUnity(n, K) : RngIntElt, FldCyc -> FldCycElt
            Minimise(~a) : FldCycElt ->
            Minimise(~s) : [ FldCycElt ] ->
            Minimise(a) : FldCycElt -> RngElt
            Minimise(s) : { FldCycElt } -> { RngElt }

 
Structure Operations

      Related Structures
            Algebra(K, J) : FldCyc, Fld -> AlgAss, Map
            VectorSpace(K, J) : FldCyc, Fld -> ModTupFld, Map

      Invariants
            Conductor(K) : FldCyc -> RngIntElt
            CyclotomicOrder(K) : FldCyc -> RngIntElt

 
Element Operations

      Predicates on Elements
            IsReal(a) : FldCycElt -> BoolElt

      Conjugates
            ComplexConjugate(a) : FldCycElt -> FldCycElt
            Conjugate(a, n) : FldCycElt, RngIntElt -> FldCycElt
            Conjugate(a, r) : FldCycElt, FldCycElt -> FldCycElt
            Example FldCyc_GaussianPeriods (H50E2)