Introduction

 
Creation Functions

      Creation of Cyclotomic Fields
            CyclotomicField(m) : RngIntElt -> FldCyc
            CyclotomicPolynomial(m) : RngIntElt -> RngUPolElt
            MinimalField(a) : FldRatElt -> FldRat
            MinimalField(S) : [ FldCycElt ] -> FldCyc
            Example FldCyc_creation (H38E1)

      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

      Invariants
            Conductor(K) : FldCyc -> RngIntElt, [RngIntElt]
            CyclotomicOrder(K) : FldCyc -> RngIntElt
            CyclotomicAutomorphismGroup(K) : FldCyc -> GrpAb, Map
            CyclotomicRelativeField(k, K) : FldCyc, FldCyc -> FldNum

 
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 (H38E2)

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