- Introduction
- Acknowledgement
- Creation Functions
- Creation of Number Fields
- NumberField(f) : RngUPolElt -> FldNum
- RationalsAsNumberField() : -> FldNum
- NumberField(s) : [ RngUPolElt ] -> FldNum
- ext< F | s1, ..., sn > : FldNum, RngUPolElt, ..., RngUPolElt -> FldNum
- Example FldNum_Creation (H36E1)
- RadicalExtension(F, d, a) : Rng, RngIntElt, RngElt -> FldNum
- SplittingField(F) : FldNum -> FldNum, SeqEnum
- SplittingField(f) : RngUPolElt -> FldNum
- SplittingField(L) : [RngUPolElt] -> FldNum, [FldNumElt]
- sub< F | e1, ..., en > : FldAlg, FldAlgElt, ..., FldAlgElt -> FldAlg, Map
- MergeFields(F, L) : FldNum, FldNum -> SeqEnum
- Compositum(K, L) : FldNum, FldNum -> FldNum
- quo< FldNum : R | f > : RngUPol, RngUPolElt -> FldNum
- Example FldNum_CompositeFields (H36E2)
- OptimizedRepresentation(F) : FldNum -> FldNum, Map
- Example FldNum_opt-rep (H36E3)
- Maximal Orders
- Creation of Elements
- Creation of Homomorphisms
- Structure Operations
- General Functions
- Related Structures
- GroundField(F) : FldNum -> Fld
- AbsoluteField(F) : FldNum -> FldNum
- SimpleExtension(F) : FldNum -> FldNum
- RelativeField(F, L) : FldNum, FldNum -> FldNum
- Components(F) : FldNum -> [FldNum]
- Example FldNum_Compositum (H36E6)
- Embed(F, L, a) : FldNum, FldNum, FldNumElt ->
- Embed(F, L, a) : FldNum, FldNum, [FldNumElt] ->
- EmbeddingMap(F, L): FldNum, FldNum -> Map
- Example FldNum_em (H36E7)
- MinkowskiSpace(F) : FldNum -> Lat, Map
- Completion(K, P) : FldNum, RngOrdIdl -> FldLoc, Map
- Completion(K, P) : FldNum, PlcNumElt -> FldLoc, Map
- Representing Fields as Vector Spaces
- Invariants
- Basis Representation
- Ring Predicates
- Field Predicates
- Element Operations
- Class Group and Unit Group
- Galois Theory
- Solving Norm Equations
- Places and Divisors
- Creation of Structures
- Operations on Structures
- Creation of Elements
- Arithmetic with Places and Divisors
- Other Functions for Places and Divisors
- Valuation(a, p) : FldNumElt, PlcNumElt -> RngElt
- Valuation(I, p) : RngOrdFracIdl , PlcNumElt -> RngElt
- Support(D) : DivNumElt -> SeqEnum, SeqEnum
- Ideal(D) : DivNumElt -> RngOrdIdl
- Evaluate(x, p) : FldNumElt, PlcNumElt -> RngElt
- RealEmbeddings(a) : FldNumElt -> []
- RealSigns(a) : FldNumElt -> []
- IsReal(p) : PlcNumElt -> BoolElt
- IsComplex(p) : PlcNumElt -> BoolElt
- IsFinite(p) : PlcNumElt -> BoolElt
- IsInfinite(p) : PlcNumElt -> BoolElt, RngIntElt
- Extends(P, p) : PlcNumElt, PlcNumElt -> BoolElt
- InertiaDegree(P) : PlcNumElt -> RngIntElt
- Degree(D) : DivNumElt -> RngElt
- NumberField(P) : PlcNumElt -> FldNum
- ResidueClassField(P) : PlcNumElt -> Fld
- UniformizingElement(P) : PlcNumElt -> FldNumElt
- LocalDegree(P) : PlcNumElt -> RngIntElt
- RamificationIndex(P) : PlcNumElt -> RngIntElt
- DecompositionGroup(P) : PlcNumElt -> GrpPerm
- Number Field Database
- Bibliography
V2.28, 13 July 2023