Creation of Cyclotomic Fields
CyclotomicField(m) : RngIntElt -> FldCyc
CyclotomicPolynomial(m) : RngIntElt -> RngUPolElt
MinimalField(a) : FldRatElt -> FldRat
MinimalField(S) : [ FldCycElt ] -> FldCyc
Example FldCyc_creation (H36E1)
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 }
Invariants
Conductor(K) : FldCyc -> RngIntElt, [RngIntElt]
CyclotomicOrder(K) : FldCyc -> RngIntElt
CyclotomicAutomorphismGroup(K) : FldCyc -> GrpAb, Map
CyclotomicRelativeField(k, K) : FldCyc, FldCyc -> FldNum
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 (H36E2)
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Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012