Overview

 
Constructing Artin Representations
      ArtinRepresentations(K) : FldNum -> SeqEnum
      K !! ch : FldNum, AlgChtrElt -> ArtRep
      PermutationCharacter(K) : FldNum -> ArtRep
      Determinant(A) : ArtRep -> ArtRep
      ChangeField(A,K) : ArtRep, FldNum -> ArtRep, BoolElt
      Example ArtRep_artin-const (H48E1)

 
Basic Invariants
      Field(A) : ArtRep -> FldNum
      Degree(A) : ArtRep -> RngIntElt
      Group(A) : ArtRep -> GrpPerm
      Character(A) : ArtRep -> AlgChtrElt
      Conductor(A) : ArtRep -> RngIntElt
      Decomposition(A) : ArtRep -> SeqEnum[Tup]
      RationalDecomposition(A) : ArtRep -> SeqEnum[Tup]
      Example ArtRep_artin-decompose (H48E2)
      DefiningPolynomial(A) : ArtRep -> RngUPolElt
      Minimize(A) : ArtRep -> ArtRep
      OptimizedRepresentation(A) : ArtRep -> ArtRep
      Kernel(A) : ArtRep -> FldNum
      Example ArtRep_artin-minimize (H48E3)
      IsIrreducible(A) : ArtRep -> BoolElt
      IsRamified(A, p) : ArtRep, RngIntElt -> BoolElt
      IsWildlyRamified(A, p) : ArtRep, RngIntElt -> BoolElt
      EulerFactor(A, p) : ArtRep, RngIntElt -> RngUPolElt
      EpsilonFactor(A) : ArtRep -> FldComElt
      RootNumber(A) : ArtRep -> FldComElt
      EpsilonFactor(A,p) : ArtRep, RngIntElt -> FldComElt
      RootNumber(A,p) : ArtRep, RngIntElt -> FldComElt
      EpsilonFactor(A,infty) : ArtRep, Infty -> FldComElt
      Example ArtRep_artin-invariants (H48E4)
      DirichletCharacter(A) : ArtRep -> GrpDrchElt
      HeckeCharacter(A) : ArtRep -> GrpHeckeElt
      ArtinRepresentation(ch) : GrpDrchElt -> ArtRep
      Example ArtRep_one-dim-artin-reps (H48E5)

 
Arithmetic
      A1 + A2: ArtRep, ArtRep -> ArtRep
      A1 - A2: ArtRep, ArtRep -> ArtRep
      A1 * A2: ArtRep, ArtRep -> ArtRep
      A1 eq A2: ArtRep, ArtRep -> BoolElt
      A1 ne A2: ArtRep, ArtRep -> BoolElt
      Example ArtRep_artin-arith1 (H48E6)
      Example ArtRep_artin-arith2 (H48E7)

 
Implementation Notes

 
Bibliography

[Next][Prev] [____] [Up] [Index] [Root]