Documentation

galois-cohomology
- Galois Cohomology (GROUPS OF LIE TYPE)
galois-module-structure
- Galois Module Structure (CLASS FIELD THEORY)
galois-ring
- GALOIS RINGS
galois-subfield
- FldFunG_galois-subfield (Example H45E16)
- RngOrdGal_galois-subfield (Example H40E5)
galois-theory
- GALOIS GROUPS AND AUTOMORPHISMS
- Galois Theory (NUMBER FIELDS)
GaloisCohomology
- GaloisCohomology(A) : GGrp -> SeqEnum
GaloisConjugacyRepresentatives
- GaloisConjugacyRepresentatives(G) : GrpDrch -> [GrpDrchElt]
GaloisConjugate
- GaloisConjugate(x, j) : AlgChtrElt, RngIntElt -> AlgChtrElt
GaloisField
- GaloisField(q) : RngIntElt -> FldFin
- GF(q) : RngIntElt -> FldFin
- FiniteField(q) : RngIntElt -> FldFin
- FiniteField(p, n) : RngIntElt, RngIntElt -> FldFin
GaloisGroup
- GaloisGroup(K, k) : FldFin, FldFin -> GrpPerm, [FldFinElt]
- GaloisGroup(F) : FldFun -> GrpPerm, [RngElt], GaloisData
- GaloisGroup(K) : FldNum -> GrpPerm, SeqEnum, GaloisData
- GaloisGroup(K) : FldNum -> GrpPerm, [RngElt], GaloisData
- GaloisGroup(f) : RngUPolElt -> GrpPerm, [ RngElt ], GaloisData
- GaloisGroup(f) : RngUPolElt[FldPad] -> GrpPerm, SeqEnum, UserProgram
- GaloisGroup(f) : RngUPolElt[RngInt] -> GrpPerm, SeqEnum, GaloisData
- Group(A) : GalRep -> GrpPerm
GaloisGroupInvariant
- GaloisGroupInvariant(G, H) : GrpPerm, GrpPerm -> RngSLPolElt
GaloisGroups
- FldFunG_GaloisGroups (Example H45E13)
- RngOrdGal_GaloisGroups (Example H40E4)
GaloisGroups2
- FldFunG_GaloisGroups2 (Example H45E14)
GaloisImage
- GaloisImage(x, i) : RngPadElt, RngIntElt -> RngPadElt
GaloisOrbit
- GaloisOrbit(x) : AlgChtrElt -> { AlgChtrElt }
GaloisProof
- GaloisProof(f, S) : RngUPolElt, GaloisData -> BoolElt
GaloisQuotient
- GaloisQuotient(K, Q) : FldNum, GrpPerm -> SeqEnum[RngUPolElt]
GaloisRepresentation
- GaloisRepresentation(A,p) : ArtRep,RngIntElt -> GalRep
- GaloisRepresentation(E) : CrvEll -> GalRep
- GaloisRepresentation(E,p) : CrvEll,RngIntElt -> GalRep
- GaloisRepresentation(E,P) : CrvEll,RngOrdIdl -> GalRep
- GaloisRepresentation(C,P) : CrvHyp[FldNum],RngOrdIdl -> GalRep
- GaloisRepresentation(C) : CrvHyp[FldPad] -> GalRep
- GaloisRepresentation(C,p) : CrvHyp[FldRat], RngIntElt -> GalRep
- GaloisRepresentation(chi,p) : GrpDrchElt,RngIntElt -> GalRep
- GaloisRepresentation(f,p) : ModFrmElt,RngIntElt -> GalRep
- GaloisRepresentation(pi) : RepLoc -> GalRep
GaloisRepresentations
- GaloisRepresentations(F,K) : FldPad,FldPad -> SeqEnum[GalRep]
- GaloisRepresentations(f) : RngUPolEltFldPad -> SeqEnum[GalRep]
GaloisRing
- GR(q, d) : RngIntElt, RngIntElt -> RngGal
- GaloisRing(q, d) : RngIntElt, RngIntElt -> RngGal
- GaloisRing(p, a, d) : RngIntElt, RngIntElt, RngIntElt -> RngGal
- GaloisRing(p, a, D) : RngIntElt, RngIntElt, RngUPol -> RngGal
- GaloisRing(q, D) : RngIntElt, RngUPol -> RngGal
GaloisRoot
- GaloisRoot(f, i, S) : RngUPolElt, RngIntElt, GaloisData -> RngElt
GaloisSplittingField
- GaloisSplittingField(f) : RngUPolElt -> FldFun, [FldFunElt], GrpPerm, [[FldFunElt]]
- GaloisSplittingField(f) : RngUPolElt -> FldNum, [FldNumElt], GrpPerm, [[FldNumElt]]
GaloisSubfieldTower
- GaloisSubfieldTower(S, L) : GaloisData, [GrpPerm] -> FldNum, [Tup<RngSLPolElt, RngUPolElt, [GrpPermElt]>], UserProgram, UserProgram
GaloisSubgroup
- GaloisSubgroup(K, U) : FldNum, GrpPerm -> RngUPolElt, RngSLPolElt
GalRep
- LOCAL GALOIS REPRESENTATIONS
galrep
- Example: Local and Global Epsilon Factors for Dirichlet Characters (LOCAL GALOIS REPRESENTATIONS)
- Example: Reconstructing a Galois Representation from its Euler Factors (LOCAL GALOIS REPRESENTATIONS)
galrep-artin
- GalRep_galrep-artin (Example H57E15)
galrep-automorphism
- GalRep_galrep-automorphism (Example H57E28)
galrep-basechange
- GalRep_galrep-basechange (Example H57E50)
galrep-character
- GalRep_galrep-character (Example H57E26)
galrep-conductor
- GalRep_galrep-conductor (Example H57E37)
galrep-crvhyp-nf
- GalRep_galrep-crvhyp-nf (Example H57E21)
galrep-crvhyp-Q
- GalRep_galrep-crvhyp-Q (Example H57E20)
galrep-crvhyp-Qp
- GalRep_galrep-crvhyp-Qp (Example H57E19)
galrep-cyclotomiccharacter
- GalRep_galrep-cyclotomiccharacter (Example H57E4)
galrep-decomposition
- GalRep_galrep-decomposition (Example H57E40)
galrep-definingpolynomial
- GalRep_galrep-definingpolynomial (Example H57E27)
galrep-degree
- GalRep_galrep-degree (Example H57E23)
galrep-determinant
- GalRep_galrep-determinant (Example H57E46)
galrep-difference
- GalRep_galrep-difference (Example H57E42)
galrep-dirichlet
- GalRep_galrep-dirichlet (Example H57E14)
galrep-E
- GalRep_galrep-E (Example H57E16)
galrep-E-P
- GalRep_galrep-E-P (Example H57E18)
galrep-E-p
- GalRep_galrep-E-p (Example H57E17)
galrep-eq
- GalRep_galrep-eq (Example H57E45)
galrep-eulerfactor
- GalRep_galrep-eulerfactor (Example H57E29)
galrep-f-p
- GalRep_galrep-f-p (Example H57E22)
galrep-factorization
- GalRep_galrep-factorization (Example H57E30)
galrep-frobeniuselement
- GalRep_galrep-frobeniuselement (Example H57E25)

V2.28, 13 July 2023

Magma is maintained and distributed by the Computational Algebra Group, School of Mathematics and Statistics, University of Sydney.