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Magma
Computer • algebra
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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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V2.28, 13 July 2023