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ARTIN REPRESENTATIONS

 
Acknowledgements
 
Overview
 
Constructing Artin Representations
 
Basic Invariants
 
Arithmetic
 
Implementation Notes
 
Bibliography







DETAILS

 
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 (H44E1)

 
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]
      DefiningPolynomial(A) : ArtRep -> RngUPolElt
      Minimize(A) : ArtRep -> ArtRep
      Kernel(A) : ArtRep -> FldNum
      Example ArtRep_artin-minimize (H44E2)
      IsIrreducible(A) : ArtRep -> BoolElt
      IsRamified(A, p) : ArtRep, RngIntElt -> BoolElt
      IsWildlyRamified(A, p) : ArtRep, RngIntElt -> BoolElt
      EulerFactor(A, p) : ArtRep, RngIntElt -> RngUPolElt
      Example ArtRep_artin-invariants (H44E3)
      DirichletCharacter(A) : ArtRep -> GrpDrchElt
      ArtinRepresentation(ch) : GrpDrchElt -> ArtRep
      Example ArtRep_one-dim-artin-reps (H44E4)

 
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 (H44E5)
      Example ArtRep_artin-arith2 (H44E6)

 
Implementation Notes

 
Bibliography

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Version: V2.19 of Mon Dec 17 14:40:36 EST 2012