Documentation

abelian
- Abelian Extensions (CLASS FIELD THEORY)
- Abelian Extensions (CLASS FIELD THEORY)
- Abelian Group Functions (MATRIX GROUPS OVER GENERAL RINGS)
- ABELIAN GROUPS
- Abelian Quotient (FINITELY PRESENTED GROUPS)
- Abelian Quotient (INTRODUCTION TO FP-GROUPS [FINITELY-PRESENTED GROUPS])
- CLASS FIELD THEORY
- Construction of a Generic Abelian Group (ABELIAN GROUPS)
- Elliptic Curves (MODULAR FORMS)
- The Abelian Quotient Structure of a Group (POLYCYCLIC GROUPS)
abelian-extension
- CLASS FIELD THEORY
abelian-extension-attributes
- FldAb_abelian-extension-attributes (Example H41E11)
abelian-extensions
- Abelian Extensions (CLASS FIELD THEORY)
abelian-extensions-basics
- Abelian Extensions (CLASS FIELD THEORY)
abelian-group
- AbelianBasis(G) : GrpMat -> [ GrpMatElt ], [ RngIntElt ]
- Abelian Group Functions (MATRIX GROUPS OVER GENERAL RINGS)
abelian-structure
- The Abelian Quotient Structure of a Group (POLYCYCLIC GROUPS)
abelian-varieties
- Elliptic Curves (MODULAR FORMS)
abelian_group
- Abelian Group Structure (ELLIPTIC CURVES OVER FINITE FIELDS)
abelian_group_jacobian
- Abelian Group Structure (HYPERELLIPTIC CURVES)
AbelianBasis
- AbelianBasis(A) : GrpAb -> [ GrpAbElt ], [ RngIntElt ]
- PrimaryAbelianBasis(A) : GrpAb -> [ GrpAbElt ], [ RngIntElt ]
- PrimaryAbelianBasis(G) : GrpFin -> [ GrpFinElt ], [ RngIntElt ]
- PrimaryAbelianBasis(G) : GrpMat -> [ GrpMatElt ], [ RngIntElt ]
- PrimaryAbelianBasis(G) : GrpPC -> [ GrpPCElt ], [ RngIntElt ]
- PrimaryAbelianBasis(G) : GrpPerm -> [ GrpPermElt ], [ RngIntElt ]
AbelianExtension
- AbelianExtension(D, U) : DivFunElt, GrpAb -> FldFunAb
- AbelianExtension(K) : FldAlg -> FldAb
- AbelianExtension(psi) : GrpHecke -> FldAb
- AbelianExtension(I) : RngOrdIdl -> FldAb
- AbelianExtension(I, P) : RngOrdIdl, [RngIntElt] -> FldAb
- RayClassField(m) : Map -> FldAb
AbelianFPGroup
- AbelianFPGroup([n₁,...,n_r]): [ RngIntElt ] -> GrpFP
AbelianGroup
- AbelianGroup(GrpAb, Q) : Cat, [ RngIntElt ] -> GrpAb
- AbelianGroup(C, Q) : Cat, [ RngIntElt ] -> GrpFin
- AbelianGroup(GrpPerm, Q) : Cat, [ RngIntElt ] -> GrpPerm
- AbelianGroup(GrpGPC, Q) : Cat, [RngIntElt] -> GrpGPC
- AbelianGroup(GrpPC, Q) : Cat, [RngIntElt] -> GrpPC
- AbelianGroup(G) : Grp -> GrpAb, Hom
- AbelianGroup(G) : GrpDrch -> GrpAb, Map
- AbelianGroup(G) : GrpGPC -> GrpAb, Map
- AbelianGroup(G) : GrpPC -> GrpAb, Map
- AbelianGroup(J) : JacHyp -> GrpAb, Map
- AbelianGroup< X | R > : List(Var), List(GrpAbRel) -> GrpAb, Hom(GrpAb)
- AbelianGroup(G) : ModAbVarSubGrp -> GrpAb, Map, Map
- AbelianGroup(A: parameters) : GrpAbGen -> GrpAb, Map
- AbelianGroup(H) : SetPtEll -> GrpAb, Map
- AbelianGroup([n₁,...,n_r]): [ RngIntElt ] -> GrpAb
- Group< X | R > : List(Identifiers), List(GrpFPRel) -> GrpFP, Hom(Grp)
- MordellWeilGroup(H: parameters) : SetPtEll -> GrpAb, Map, BoolElt, BoolElt
- CrvEllFldFin_AbelianGroup (Example H129E6)
- GrpAb_AbelianGroup (Example H75E3)
AbelianGroup2
- GrpAb_AbelianGroup2 (Example H75E4)
AbelianInvariants
- AbelianInvariants(A) : GrpAb -> [ RngIntElt ]
- PrimaryAbelianInvariants(A) : GrpAb -> [ RngIntElt ]
- PrimaryAbelianInvariants(G) : GrpFin -> [ RngIntElt ]
- PrimaryAbelianInvariants(G) : GrpMat -> [ RngIntElt ]
- PrimaryAbelianInvariants(G) : GrpPC -> [RngIntElt]
- PrimaryAbelianInvariants(G) : GrpPerm -> [ RngIntElt ]
AbelianLieAlgebra
- AbelianLieAlgebra(R, n) : Rng, RngIntElt -> AlgLie
AbelianNormalQuotient
- AbelianNormalQuotient(G, H) : GrpPerm, GrpPerm -> GrpPerm, Hom(GrpPerm), GrpPerm
AbelianNormalSubgroup
- AbelianNormalSubgroup(G) : GrpPerm -> GrpPerm
Abelianp
- AbelianpExtension(m, p) : Map, RngIntElt -> FldAb
AbelianpExtension
- AbelianpExtension(m, p) : Map, RngIntElt -> FldAb
AbelianQuotient
- AbelianQuotient(G) : Grp -> GrpAb, Hom
- AbelianQuotient(G) : GrpFP -> GrpAb, Map
- AbelianQuotient(G) : GrpGPC -> GrpAb, Map
- AbelianQuotient(G) : GrpMat -> GrpAb, Map
- AbelianQuotient(G) : GrpPC -> GrpAb, Map
- AbelianQuotient(G) : GrpPerm -> GrpAb, Map
AbelianQuotientInvariants
- AQInvariants(G) : GrpFP -> [ RngIntElt ]
- AbelianQuotientInvariants(G) : GrpFP -> [ RngIntElt ]
- AbelianQuotientInvariants(H) : GrpFP -> [ RngIntElt ]
- AbelianQuotientInvariants(G, n) : GrpFP, RngIntElt -> [ RngIntElt ]
- AbelianQuotientInvariants(H, n) : GrpFP, RngIntElt -> [ RngIntElt ]
- AbelianQuotientInvariants(G) : GrpGPC -> [ RngIntElt ]
- AbelianQuotientInvariants(G) : GrpPC -> SeqEnum
AbelianSubfield
- FixedField(A, U) : FldAb, GrpAb -> FldAb
- AbelianSubfield(A, U) : FldAb, GrpAb -> FldAb
AbelianSubgroups
- CyclicSubgroups(G) : GrpPC -> SeqEnum
- ElementaryAbelianSubgroups(G) : GrpPC -> SeqEnum
- NilpotentSubgroups(G) : GrpPC -> SeqEnum
- AbelianSubgroups(G) : GrpPC -> SeqEnum
- AbelianSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
- AbelianSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]

V2.28, 13 July 2023

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