Artin Representations
- Overview
- Constructing Artin Representations
- Basic Invariants
Field(A): ArtRep → FldNumBaseField(A): ArtRep → FldDegree(A): ArtRep → RngIntEltDimension(A): ArtRep → RngIntEltGroup(A): ArtRep → GrpPermCharacter(A): ArtRep → AlgChtrEltConductor(A): ArtRep → RngIntEltDecomposition(A): ArtRep → SeqEnum[Tup]RationalDecomposition(A): ArtRep → SeqEnum[Tup]- Example: Decomposing Artin Representations
DefiningPolynomial(A): ArtRep → RngUPolEltMinimize(A): ArtRep → ArtRepOptimizedRepresentation(A): ArtRep → ArtRepKernel(A): ArtRep → FldNum- Example: Minimising an Artin Representation
IsIrreducible(A): ArtRep → BoolEltIsRamified(A, p): ArtRep, RngIntElt → BoolEltIsWildlyRamified(A, p): ArtRep, RngIntElt → BoolEltEulerFactor(A, p): ArtRep, RngIntElt → RngUPolEltEpsilonFactor(A): ArtRep → FldComEltRootNumber(A): ArtRep → FldComEltEpsilonFactor(A,p): ArtRep, RngIntElt → FldComEltRootNumber(A,p): ArtRep, RngIntElt → FldComEltEpsilonFactor(A,infty): ArtRep, Infty → FldComEltRootNumber(A,infty): ArtRep, Infty → FldComElt- Example: Invariants of Artin Representations
DirichletCharacter(A): ArtRep → GrpDrchEltHeckeCharacter(A): ArtRep → GrpHeckeEltArtinRepresentation(ch): GrpDrchElt → ArtRep- Example: One-Dimensional Artin Representations
- Arithmetic
- Implementation Notes
- Bibliography