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)
Bibliography
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Version: V2.19 of
Wed Apr 24 15:09:57 EST 2013