- Introduction
- Creation
- Ray Class Groups
- Selmer Groups
- Maps
- InducedMap(m1, m2, h, c) : Map, Map, Map, RngIntElt -> Map
- InducedAutomorphism(r, h, c) : Map, Map, RngIntElt -> Map
- Example FldAb_inducedMap (H41E4)
- Abelian Extensions
- Binary Operations
- Galois Module Structure
- Conversion to Number Fields
- Invariants
- Discriminant(A) : FldAb -> RngOrdIdl, [RngIntElt]
- AbsoluteDiscriminant(A) : FldAb -> RngIntElt
- Conductor(A) : FldAb -> RngOrdIdl, [RngIntElt]
- Degree(A) : FldAb -> RngIntElt
- AbsoluteDegree(A) : FldAb -> RngIntElt
- CoefficientRing(A) : FldAb -> Fld
- BaseRing(A) : FldAb -> Rng
- NormGroup(A) : FldAb -> Map, RngOrdIdl, [RngIntElt]
- DecompositionField(p, A) : RngOrdIdl, FldAb -> FldAb
- DecompositionField(p, A) : PlcNumElt, FldAb -> FldAb
- DecompositionGroup(p, A) : RngIntElt, FldAb -> GrpAb
- DecompositionGroup(p, A) : PlcNumElt, FldAb -> GrpAb
- DecompositionType(A, p) : FldAb, RngOrdIdl -> [Tpl]
- DecompositionType(A, p) : FldAb, PlcNumElt -> [Tpl]
- DecompositionType(A, p) : FldAb, RngIntElt -> [Tpl]
- DecompositionTypeFrequency(A, l) : FldAb, [ ] -> Mset
- DecompositionTypeFrequency(A, a, b) : FldAb, RngIntElt, RngIntElt -> Mset
- Automorphisms
- ArtinMap(A) : FldAb -> Map
- FrobeniusAutomorphism(A, p) : FldAb, RngOrdIdl -> Map
- AutomorphismGroup(A) : FldAb -> GrpFP, [Map], Map
- ProbableAutomorphismGroup(A) : FldAb -> GrpFP, SeqEnum
- ImproveAutomorphismGroup(F, E) : FldAb, SeqEnum -> GrpFP, SeqEnum
- Example FldAb_ProbableAutomorphismGroup (H41E8)
- AbsoluteGaloisGroup(A) : FldAb -> GrpPerm, SeqEnum, GaloisData
- TwoCocycle(A) : FldAb -> UserProgram
- Norm Equations
- IsLocalNorm(A, x, p) : FldAb, RngOrdElt, RngOrdIdl -> BoolElt
- IsLocalNorm(A, x, i) : FldAb, RngOrdElt, RngIntElt -> BoolElt
- IsLocalNorm(A, x, p) : FldAb, RngOrdElt, PlcNumElt -> BoolElt
- IsLocalNorm(A, x) : FldAb, RngOrdElt -> BoolElt
- Knot(A) : FldAb -> GrpAb
- NormEquation(A, x) : FldAb, RngOrdElt -> BoolElt, [RngOrdElt]
- IsNorm(A, x) : FldAb, RngOrdElt -> BoolElt
- Example FldAb_norm-equation (H41E9)
- Attributes
- Group Theoretic Functions
- Bibliography
V2.28, 13 July 2023