[____] [____] [_____] [____] [__] [Index] [Root]
Index A
Construction of an A-Module (MODULES OVER A MATRIX ALGEBRA)
A`IsAbelian : FldAb -> Bool
A`IsCentral : FldAb -> Bool
A`IsNormal : FldAb -> Bool
A`DefiningGroup : FldAb -> Rec
A`Components : FldAb -> [Rec]
A
a
Construction of an A-Module (MODULES OVER A MATRIX ALGEBRA)
Chtr_A5 (Example H79E1)
AbelianBasis(G) : GrpFin -> [ GrpFinElt ], [ RngIntElt ]
AbelianBasis(G) : GrpPC -> [ GrpPCElt ], [ RngIntElt ]
AbelianExtension(K) : FldOrd -> FldAb
AbelianExtension(I) : RngOrdIdl -> FldAb
AbelianExtension(I, P) : RngOrdIdl, [RngIntElt] -> FldAb
AbelianGroup(GrpAb, Q) : Cat, [ RngIntElt ] -> GrpAb
AbelianGroup(C, Q) : Cat, [ RngIntElt ] -> GrpFin
AbelianGroup(GrpFP, [n_1,...,n_r]): Cat, [ RngIntElt ] -> GrpFP
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) : GrpGPC -> GrpAb, Map
AbelianGroup(G) : GrpPC -> GrpAb, Map
AbelianGroup(J) : JacHyp -> GrpAb, Map
AbelianGroup< X | R > : List(Var), List(GrpAbRel) -> GrpAb, Hom(GrpAb)
AbelianGroup(A: parameters) : GrpAbGen -> GrpAb, Map
AbelianGroup(H: parameters) : SetPtEll -> GrpAb, Map
AbelianGroup(H) : SetPtEll -> GrpAb, Map
AbelianInvariants(G) : GrpFin -> [ RngIntElt ]
AbelianInvariants(G) : GrpMat -> [ RngIntElt ]
AbelianInvariants(G) : GrpPC -> [RngIntElt]
AbelianNormalQuotient(G, H) : GrpPerm -> GrpPerm, Hom(GrpPerm), GrpPerm
AbelianNormalSubgroup(G) : GrpPerm -> GrpPerm
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(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
AbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
AbelianSubgroups(G) : GrpPC -> SeqEnum
ElementaryAbelianSubgroups(G) : GrpPC -> SeqEnum
AbelianSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
AbelianSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
ClassGroupAbelianInvariants(F : parameters) : FldFun -> SeqEnum
ClassGroupAbelianInvariants(F : parameters) : FldFun -> SeqEnum
ClassGroupAbelianInvariants(O) : RngFunOrd -> SeqEnum
ElementaryAbelianGroup(GrpGPC, p, n) : Cat, RngIntElt, RngIntElt -> GrpGPC
ElementaryAbelianNormalSubgroup(G) : GrpPerm -> GrpPerm
ElementaryAbelianQuotient(G, p) : GrpAb, RngIntElt -> GrpAb, Map
ElementaryAbelianQuotient(G, p) : GrpFP, RngIntElt -> GrpAb, Map
ElementaryAbelianQuotient(G, p) : GrpGPC, RngIntElt -> GrpAb, Map
ElementaryAbelianQuotient(G, p) : GrpMat, RngIntElt -> GrpAb, Map
ElementaryAbelianQuotient(G, p) : GrpPC, RngIntElt -> GrpAb, Map
ElementaryAbelianQuotient(G, p) : GrpPerm, RngIntElt -> GrpAb, Map
ElementaryAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
ElementaryAbelianSeries(G) : GrpAb -> [GrpAb]
ElementaryAbelianSeries(G) : GrpPC -> [GrpPC]
ElementaryAbelianSeries(G: parameters) : GrpPerm -> [ GrpPerm ]
ElementaryAbelianSeries(G: parameters) : GrpPerm -> [ GrpPerm ]
ElementaryAbelianSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
ElementaryAbelianSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
FreeAbelianGroup(GrpGPC, n) : Cat, RngIntElt -> GrpGPC
FreeAbelianGroup(n) : RngIntElt -> GrpAb
FreeAbelianQuotient(G) : GrpAb -> GrpAb, Map
FreeAbelianQuotient(G) : GrpGPC -> GrpAb, Map
GenericAbelianGroup(U: parameters) : . -> GrpAbGen
Group< X | R > : List(Identifiers), List(GrpFPRel) -> GrpFP, Hom(Grp)
HasComputableAbelianQuotient(G) : GrpFP -> BoolElt, GrpAb, Map
HasInfiniteComputableAbelianQuotient(G) : GrpFP -> BoolElt, GrpAb, Map
IsAbelian(A) : FldAb -> BoolElt
IsAbelian(F) : FldAlg -> BoolElt
IsAbelian(G) : GrpAb -> BoolElt
IsAbelian(G) : GrpFin -> BoolElt
IsAbelian(G) : GrpGPC -> BoolElt
IsAbelian(G) : GrpMat -> BoolElt
IsAbelian(G) : GrpPC -> BoolElt
IsAbelian(G) : GrpPerm -> BoolElt
IsElementaryAbelian(G) : GrpAb -> BoolElt
IsElementaryAbelian(G) : GrpFin -> BoolElt
IsElementaryAbelian(G) : GrpGPC -> BoolElt
IsElementaryAbelian(G) : GrpMat -> BoolElt
IsElementaryAbelian(G) : GrpPC -> BoolElt
IsElementaryAbelian(G) : GrpPerm -> BoolElt
KeepAbelian(SQG, SQH) : SQProc, SQProc -> SeqEnum
KeepElementaryAbelian(SQG, SQH) : SQProc, SQProc -> SeqEnum
KeepSplitAbelian(SQG, SQH) : SQProc, SQProc -> SeqEnum
KeepSplitElementaryAbelian(SQG, SQH) : SQProc, SQProc -> SeqEnum
MaximalAbelianSubfield(M) : RngOrd -> FldAb
NonsplitSection(SQP: parameter) : SQProc -> BoolElt, SQProc
NonsplitElementaryAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
NumberOfSubgroupsAbelianPGroup (A) : SeqEnum -> SeqEnum
OrderAutomorphismGroupAbelianPGroup (A) : SeqEnum -> RngIntElt
RayClassField(m) : Map -> FldAb
SClassGroupAbelianInvariants(S) : SetEnum[PlcFunElt] -> SeqEnum
SplitAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
SplitElementaryAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
pElementaryAbelianNormalSubgroup(G, p) : GrpPerm, RngIntElt -> GrpPerm
Abelian Extensions (CLASS FIELD THEORY)
Abelian Extensions (CLASS FIELD THEORY)
Abelian Group Functions (MATRIX GROUPS)
ABELIAN GROUPS
Abelian Quotient (FINITELY PRESENTED GROUPS)
CLASS FIELD THEORY
Elliptic Curves (MODULAR FORMS)
The Abelian Quotient Structure of a Group (POLYCYCLIC GROUPS)
CLASS FIELD THEORY
FldAb_abelian-extension-attributes (Example H51E9)
Abelian Extensions (CLASS FIELD THEORY)
Abelian Extensions (CLASS FIELD THEORY)
Invariants(G) : GrpMat -> [ RngIntElt ]
Abelian Group Functions (MATRIX GROUPS)
The Abelian Quotient Structure of a Group (POLYCYCLIC GROUPS)
Elliptic Curves (MODULAR FORMS)
Abelian Group Structure (ELLIPTIC CURVES)
Abelian Group Structure (HYPERELLIPTIC CURVES)
AbelianBasis(G) : GrpFin -> [ GrpFinElt ], [ RngIntElt ]
AbelianBasis(G) : GrpPC -> [ GrpPCElt ], [ RngIntElt ]
AbelianExtension(K) : FldOrd -> FldAb
AbelianExtension(I) : RngOrdIdl -> FldAb
AbelianExtension(I, P) : RngOrdIdl, [RngIntElt] -> FldAb
RayClassField(m) : Map -> FldAb
AbelianGroup(GrpAb, Q) : Cat, [ RngIntElt ] -> GrpAb
AbelianGroup(C, Q) : Cat, [ RngIntElt ] -> GrpFin
AbelianGroup(GrpFP, [n_1,...,n_r]): Cat, [ RngIntElt ] -> GrpFP
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) : GrpGPC -> GrpAb, Map
AbelianGroup(G) : GrpPC -> GrpAb, Map
AbelianGroup(J) : JacHyp -> GrpAb, Map
AbelianGroup< X | R > : List(Var), List(GrpAbRel) -> GrpAb, Hom(GrpAb)
AbelianGroup(A: parameters) : GrpAbGen -> GrpAb, Map
AbelianGroup(H: parameters) : SetPtEll -> GrpAb, Map
AbelianGroup(H) : SetPtEll -> GrpAb, Map
Group< X | R > : List(Identifiers), List(GrpFPRel) -> GrpFP, Hom(Grp)
CrvEll_AbelianGroup (Example H87E31)
GrpAb_AbelianGroup (Example H18E3)
Invariants(G) : GrpFin -> [ RngIntElt ]
AbelianInvariants(G) : GrpFin -> [ RngIntElt ]
AbelianInvariants(G) : GrpMat -> [ RngIntElt ]
AbelianInvariants(G) : GrpPC -> [RngIntElt]
AbelianNormalQuotient(G, H) : GrpPerm -> GrpPerm, Hom(GrpPerm), GrpPerm
AbelianNormalSubgroup(G) : GrpPerm -> GrpPerm
AbelianpExtension(m, p) : Map, RngIntElt -> FldAb
AbelianpExtension(m, p) : Map, RngIntElt -> FldAb
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
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
AbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
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> ]
SubmoduleLatticeAbort(M, n) : ModRng, RngIntElt -> BoolElt, SubModLat
NormAbs(a) : FldAlgElt -> FldRatElt
AbsoluteNorm(a) : FldAlgElt -> FldRatElt
AbsoluteNorm(a) : FldFinElt -> FldFinElt
AbsoluteTrace(a) : FldAlgElt -> FldRatElt
AbsoluteTrace(a) : FldFinElt -> FldFinElt
AbsoluteValue(s) : FldPrElt-> FldPrElt
AbsoluteValue(q) : FldRatElt -> FldRatElt
AbsoluteValue(n) : RngIntElt -> RngIntElt
AbsoluteValue(f) : RngMPolElt -> RngMPolElt
AbsoluteValue(p) : RngUPolElt -> RngUPolElt
Absolute Value and Sign (RATIONAL FIELD)
Absolute Value and Sign (RATIONAL FIELD)
AbsoluteQuotientRing(A) : FldAC -> RngUPolRes
AbsoluteAffineAlgebra(A) : FldAC -> RngUPolRes
AbsoluteBasis(K) : FldAlg -> [FldAlgElt]
AbsoluteCharacteristicPolynomial(a) : FldAlgElt -> RngUPolElt
AbsoluteDegree(A) : FldAb -> RngIntElt
AbsoluteDegree(F) : FldFun -> RngIntElt
AbsoluteDegree(O) : RngOrd -> RngIntElt
AbsoluteDiscriminant(K) : FldAlg -> FldRatElt
AbsoluteDiscriminant(O) : RngOrd -> RngIntElt
AbsoluteField(F) : FldAlg -> FldAlg
AbsoluteInvariants(C) : CrvHyp -> SeqEnum
AbsoluteLogarithmicHeight(a) : FldAlgElt -> FldPrElt
AbsoluteMinimalPolynomial(a) : FldAlgElt -> RngUPolElt
AbsoluteModuleOverMinimalField(M, F) : ModGrp, FldFin -> ModGrp
AbsoluteModulesOverMinimalField(Q, K) : [ ModGrp ], FldFin -> [ ModGrp ]
AbsoluteNorm(a) : FldAlgElt -> FldRatElt
AbsoluteNorm(a) : FldFinElt -> FldFinElt
AbsoluteNorm(I) : RngOrdIdl -> RngIntElt
AbsoluteOrder(O) : RngOrd -> RngOrd
AbsolutePolynomial(A) : FldAC ->
AbsolutePrecision(x) : RngLocElt -> RngIntElt
AbsolutePrecision(f) : RngSerElt -> RngIntElt
AbsoluteRationalScroll(k,N) : Rng,SeqEnum -> PrjScrl
AbsoluteRepresentation(M) : GrpMat -> GrpMat
AbsoluteRepresentationMatrix(a) : FldAlgElt -> AlgMatElt
AbsoluteTrace(a) : FldAlgElt -> FldRatElt
AbsoluteTrace(a) : FldFinElt -> FldFinElt
AbsoluteValue(s) : FldPrElt-> FldPrElt
AbsoluteValue(q) : FldRatElt -> FldRatElt
AbsoluteValue(n) : RngIntElt -> RngIntElt
AbsoluteValue(f) : RngMPolElt -> RngMPolElt
AbsoluteValue(p) : RngUPolElt -> RngUPolElt
AbsoluteValues(a) : FldAlgElt -> [FldPrElt]
Basis(Q) : FldRat -> [FldRatElt]
Degree(Q) : FldRat -> RngIntElt
Discriminant(Q) : FldRat -> RngIntElt
IsAbsoluteField(K) : FldAlg -> BoolElt
IsAbsoluteOrder(O) : RngOrd -> BoolElt
Absolute Field (ALGEBRAICALLY CLOSED FIELDS)
AbsoluteQuotientRing(A) : FldAC -> RngUPolRes
AbsoluteAffineAlgebra(A) : FldAC -> RngUPolRes
AbsoluteBasis(K) : FldAlg -> [FldAlgElt]
Basis(Q) : FldRat -> [FldRatElt]
AbsoluteCharacteristicPolynomial(a) : FldAlgElt -> RngUPolElt
AbsoluteDegree(A) : FldAb -> RngIntElt
AbsoluteDegree(F) : FldFun -> RngIntElt
AbsoluteDegree(O) : RngOrd -> RngIntElt
Degree(Q) : FldRat -> RngIntElt
AbsoluteDiscriminant(K) : FldAlg -> FldRatElt
AbsoluteDiscriminant(O) : RngOrd -> RngIntElt
Discriminant(Q) : FldRat -> RngIntElt
AbsoluteField(F) : FldAlg -> FldAlg
AbsoluteInvariants(C) : CrvHyp -> SeqEnum
AbsoluteLogarithmicHeight(a) : FldAlgElt -> FldPrElt
AbsolutelyIrreducibleConstituents(M) : ModGrp -> [ ModGrp ]
AbsolutelyIrreducibleModule(M) : ModRng -> ModRng
AbsolutelyIrreducibleModulesBurnside(G, K : parameters ) : Grp, FldFin -> [ ModGrp ]
AbsolutelyIrreducibleModulesSchur(G, K: parameters) : GrpPC, Rng -> List[GModule]
AbsolutelyIrreducibleRepresentationProcessDelete( P) : SolRepProc ->
AbsolutelyIrreducibleRepresentationsInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
IrreducibleRepresentationsInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
AbsolutelyIrreducibleRepresentationsSchur(G, k: parameters) : GrpPC, Rng -> List[Map]
IrreducibleModules(G, K : parameters) : Grp, Fld -> Seqenum
IsAbsolutelyIrreducible(G) : GrpMat -> BoolElt
IsAbsolutelyIrreducible(M) : ModRng -> BoolElt, AlgMatElt, RngIntElt
AbsolutelyIrreducibleConstituents(M) : ModGrp -> [ ModGrp ]
AbsolutelyIrreducibleModule(M) : ModRng -> ModRng
AbsolutelyIrreducibleModules(G, K : parameters) : Grp, Fld -> SeqEnum
IrreducibleModules(G, K : parameters) : Grp, Fld -> Seqenum
AbsolutelyIrreducibleModulesBurnside(G, K : parameters ) : Grp, FldFin -> [ ModGrp ]
AbsolutelyIrreducibleModulesInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
IrreducibleRepresentationsInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
IrreducibleModulesInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
AbsolutelyIrreducibleRepresentationsInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
AbsolutelyIrreducibleModulesSchur(G, K: parameters) : GrpPC, Rng -> List[GModule]
AbsolutelyIrreducibleRepresentationsSchur(G, k: parameters) : GrpPC, Rng -> List[Map]
AbsolutelyIrreducibleRepresentationProcessDelete( P) : SolRepProc ->
AbsolutelyIrreducibleModulesInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
IrreducibleRepresentationsInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
IrreducibleModulesInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
AbsolutelyIrreducibleRepresentationsInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
AbsolutelyIrreducibleModulesSchur(G, k: parameters) : GrpPC, Rng -> List[GModule]
AbsolutelyIrreducibleRepresentationsSchur(G, k: parameters) : GrpPC, Rng -> List[Map]
AbsoluteMinimalPolynomial(a) : FldAlgElt -> RngUPolElt
AbsoluteModuleOverMinimalField(M, F) : ModGrp, FldFin -> ModGrp
AbsoluteModulesOverMinimalField(Q, K) : [ ModGrp ], FldFin -> [ ModGrp ]
NormAbs(a) : FldAlgElt -> FldRatElt
AbsoluteNorm(a) : FldAlgElt -> FldRatElt
AbsoluteNorm(a) : FldFinElt -> FldFinElt
AbsoluteNorm(I) : RngOrdIdl -> RngIntElt
AbsoluteOrder(O) : RngOrd -> RngOrd
AbsolutePolynomial(A) : FldAC ->
AbsolutePrecision(x) : RngLocElt -> RngIntElt
AbsolutePrecision(f) : RngSerElt -> RngIntElt
AbsoluteQuotientRing(A) : FldAC -> RngUPolRes
AbsoluteAffineAlgebra(A) : FldAC -> RngUPolRes
AbsoluteRationalScroll(k,N) : Rng,SeqEnum -> PrjScrl
AbsoluteRepresentation(M) : GrpMat -> GrpMat
AbsoluteRepresentationMatrix(a) : FldAlgElt -> AlgMatElt
TraceAbs(a) : FldAlgElt -> FldRatElt
AbsoluteTrace(a) : FldAlgElt -> FldRatElt
AbsoluteTrace(a) : FldFinElt -> FldFinElt
Abs(s) : FldPrElt-> FldPrElt
AbsoluteValue(s) : FldPrElt-> FldPrElt
AbsoluteValue(q) : FldRatElt -> FldRatElt
AbsoluteValue(n) : RngIntElt -> RngIntElt
AbsoluteValue(f) : RngMPolElt -> RngMPolElt
AbsoluteValue(p) : RngUPolElt -> RngUPolElt
AbsoluteValues(a) : FldAlgElt -> [FldPrElt]
Absolutize(A) : FldAC ->
AlgFP_Abstract (Example H75E2)
Abstract Group Predicates (GROUPS)
Abstract Group Predicates (MATRIX GROUPS)
Abstract Properties of a Group (PERMUTATION GROUPS)
Identification as an Abstract Group (PERMUTATION GROUPS)
The Abstract Structure of a Group (GROUPS)
Abstract Group Predicates (GROUPS)
Abstract Group Predicates (MATRIX GROUPS)
Abstract Properties of a Group (PERMUTATION GROUPS)
The Abstract Structure of a Group (GROUPS)
Modular Abelian Varieties (MODULAR SYMBOLS)
Modular Degree and Torsion (MODULAR SYMBOLS)
Projection Mappings (MODULAR SYMBOLS)
Tamagawa Numbers and Orders of Component Groups (MODULAR SYMBOLS)
GrpBrd_Access (Example H30E2)
ModAlg_Access (Example H77E2)
A General Facility (GRAPHS)
Access (MODULES OVER AFFINE ALGEBRAS)
Access and Modification Functions (RECORDS)
Access Functions (BASIC ALGEBRAS)
Access Functions (BASIC ALGEBRAS)
Access Functions (BASIC ALGEBRAS)
Access Functions (CHAIN COMPLEXES)
Access Functions (CHAIN COMPLEXES)
Access Functions (FP GROUPS - ADVANCED FEATURES)
Access Functions (GENERIC ABELIAN GROUPS)
Access Functions (LINEAR CODES OVER FINITE FIELDS)
Access Functions (LISTS)
Access Functions (SEQUENCES)
Access Functions for Automorphism Groups (AUTOMORPHISM GROUPS OF GROUPS)
Access Functions for Elements (POLYCYCLIC GROUPS)
Access Functions for Groups (POLYCYCLIC GROUPS)
Access Functions for Words (FINITELY PRESENTED GROUPS)
Access Operations (ELLIPTIC CURVES)
Access Operations (LATTICES)
Accessing (co)roots (ROOT DATA FOR LIE THEORY)
Accessing a Group (MATRIX GROUPS)
Accessing and Modifying Sets (SETS)
Accessing Attributes (FUNCTIONS, PROCEDURES AND PACKAGES)
Accessing Class Functions (CHARACTERS OF FINITE GROUPS)
Accessing Components of a Codeword (LINEAR CODES OVER FINITE FIELDS)
Accessing Components of a Codeword (LINEAR CODES OVER FINITE RINGS)
Accessing functions (COPRODUCTS)
Accessing Group Information (AUTOMATIC GROUPS)
Accessing Group Information (GROUPS DEFINED BY REWRITE SYSTEMS)
Accessing Group Information (GROUPS)
Accessing Group Information (PERMUTATION GROUPS)
Accessing Information (BRAID GROUPS)
Accessing Information (FINITELY PRESENTED GROUPS)
Accessing Information (FP GROUPS - ADVANCED FEATURES)
Accessing Invariant Rings (INVARIANT RINGS OF FINITE GROUPS)
Accessing Module Information (FREE MODULES)
Accessing Module Information (MODULES OVER A MATRIX ALGEBRA)
Accessing Monoid Information (MONOIDS GIVEN BY REWRITE SYSTEMS)
Accessing Sets and their Associated Structures (SETS)
Accessing Sparse Matrices (SPARSE MATRICES)
Accessing the Base and Strong Generating Set (MATRIX GROUPS)
Accessing the Base and Strong Generating Set (PERMUTATION GROUPS)
Accessing the Database (DATABASES OF GROUPS)
Accessing the Database (DATABASES OF GROUPS)
Accessing the Database (LATTICES)
Accessing the Databases (DATABASES OF GROUPS)
Accessing the Defining Generators and Relations (ABELIAN GROUPS)
Accessing the Defining Generators and Relations (FINITELY PRESENTED ALGEBRAS)
Accessing the Defining Generators and Relations (FINITELY PRESENTED GROUPS)
Accessing the Defining Generators and Relations (FINITELY PRESENTED SEMIGROUPS)
Accessing the Defining Generators and Relations (GROUPS OF STRAIGHT-LINE PROGRAMS)
Accessing Vector Space Invariants (VECTOR SPACES)
Alternative defining polynomials (RATIONAL CURVES AND CONICS)
Basic Access Functions (PARTITIONS, WORDS AND YOUNG TABLEAUX)
Creation and Access Functions (QUATERNION ALGEBRAS)
Elementary Invariants (INCIDENCE GEOMETRY)
Elementary Invariants (MATRICES)
Invariants of a Code (LINEAR CODES OVER FINITE FIELDS)
Invariants of Codes (LINEAR CODES OVER FINITE RINGS)
Module Access (MODULES OVER AFFINE ALGEBRAS)
Module Element Access and Operations (MODULES OVER AFFINE ALGEBRAS)
Predicates for Codewords (LINEAR CODES OVER FINITE FIELDS)
Structures Associated with a Plane (FINITE PLANES)
The Algebra (MODULES OVER A MATRIX ALGEBRA)
The Underlying Vector Space (MODULES OVER A MATRIX ALGEBRA)
Tuple Access Functions (TUPLES AND CARTESIAN PRODUCTS)
The Algebra (MODULES OVER A MATRIX ALGEBRA)
Access and Modification Functions (RECORDS)
Accessing and Modifying Sets (SETS)
The Underlying Vector Space (MODULES OVER A MATRIX ALGEBRA)
GrpFP_2_ACEProc1 (Example H32E3)
GrpFP_2_ACEProc2 (Example H32E4)
GrpFP_2_ACEProc3 (Example H32E5)
GrpFP_2_ACEProc4 (Example H32E6)
GrpFP_2_ACEProcCosetSpace (Example H32E8)
GrpFP_2_ACEProcTransversal (Example H32E7)
ActingWord(G, x, y) : GrpPerm, Elt, Elt -> GrpFPElt
ActingWord(G, x, y) : GrpPerm, Elt, Elt -> GrpFPElt
Action( F ) : GrpFP -> Map
Action(V) : GrpFPCos -> Map
Action(A, Y) : GrpPerm, GSet -> Hom(Grp), GrpPerm, GrpPerm
Action(G, Y) : GrpPerm, GSet -> Hom(Grp), GrpPerm, GrpPerm
Action(G, Y) : GrpPerm, GSet -> Hom(Grp), GrpPerm, GrpPerm
Action(G, Y) : GrpPerm, GSet -> Hom(Grp), GrpPerm, GrpPerm
Action(Y) : GSet -> Map
Action(M) : ModAlg -> AlgMat
Action(M) : ModTupRng -> AlgMat
ActionGenerator(B, i) : AlgBas, RngIntElt -> SeqEnum
ActionGenerator(L, i) : Lat, RngIntElt -> GrpMat
ActionGenerator(M, i) : ModGrp, RngIntElt -> AlgMatElt
ActionGenerator(M, i) : ModTupRng, RngIntElt -> AlgMatElt
ActionGenerators(M) : ModGrp -> [ AlgMatElt ]
ActionImage(A, Y) : GrpPerm, GSet -> GrpPerm
ActionImage(G, Y) : GrpPerm, GSet -> GrpPerm
ActionImage(G, Y) : GrpPerm, GSet -> GrpPerm
ActionImage(G, Y) : GrpPerm, GSet -> GrpPerm
ActionKernel(A, Y) : GrpPerm, GSet -> GrpPerm
ActionKernel(G, Y) : GrpPerm, GSet -> GrpPerm
ActionKernel(G, Y) : GrpPerm, GSet -> GrpPerm
ActionKernel(G, Y) : GrpPerm, GSet -> GrpPerm
AffineAction(G) : GrpPerm -> Hom, GrpPerm, GrpPerm
BlocksAction(G, P) : GrpPerm, GSet -> Hom(GrpPerm), GrpPerm, GrpPerm
CosetAction(G, H) : Grp, Grp -> Hom(Grp), Grp, Grp
CosetAction(G, H) : Grp, Grp -> Hom(Grp), GrpPerm, Grp
CosetAction(G, H) : Grp, Grp -> Hom(Grp), GrpPerm, Grp
CosetAction(G, H) : Grp, Grp -> Hom(Grp), GrpPerm, GrpPC
CosetAction(V) : GrpFPCos, Grp -> Hom(Grp), GrpPerm
CosetAction(P) : GrpFPCosetEnumProc -> Map, GrpPerm, GrpFP
CosetAction(G, H) : GrpGPC, GrpGPC -> Map, GrpPerm, GrpGPC
CosetAction(G, H) : GrpMat, GrpMat -> Hom(Grp), GrpPerm, GrpMat
CosetAction(G, H: parameters) : Grp, Grp -> Hom(Grp), GrpPerm, GrpPerm
GModuleAction(M) : ModGrp -> Map(Hom)
IdempotentActionGenerators(B, i) : AlgBas, RngIntElt -> SeqEnum
KeepGeneratorAction(SQG, SQH) : SQProc, SQProc -> SeqEnum
NaturalActionGenerator(L, i) : Lat, RngIntElt -> GrpMat
NonIdempotentActionGenerators(B, i) : AlgBas, RngIntElt -> SeqEnum
NumberOfActionGenerators(L) : Lat -> RngIntElt
NumberOfActionGenerators(M) : ModGrp -> RngIntElt
NumberOfActionGenerators(M) : ModTupRng -> RngIntElt
OrbitAction(G, T) : GrpMat, Elt -> Hom(Grp), GrpPerm, GrpMat
OrbitAction(G, T) : GrpPerm, GSet -> Hom(Grp), GrpPerm, GrpPerm
OrbitActionBounded(G, T, b) : GrpMat, Elt, RngIntElt -> BoolElt, Hom(Grp), GrpPerm, GrpMat
PermutationRepresentation(A) : GrpAuto -> Map, GrpPerm, SetIndx
QuotientModuleAction(G, S) : GrpMat -> Map, GrpMat
RootAction( W ) : GrpCox -> Map
RootAction( F ) : GrpFP -> Map
SocleAction(G) : GrpPerm -> Hom, GrpPerm, GrpPerm
StandardAction( W ) : GrpCox -> Map
StandardActionGroup( W ) : GrpCox -> GrpPerm, Map
SubmoduleAction(G, S) : GrpMat -> Map, GrpMat
RootDtm_Action (Example H33E11)
Action of (co)roots (ROOT DATA FOR LIE THEORY)
Action of Automorphisms (GRAPHS)
Action of Automorphisms (INCIDENCE STRUCTURES AND DESIGNS)
Action of PSL_2(R) on the upper half plane (SUBGROUPS OF PSL_2(R))
Action on a Coset Space (FINITE SOLUBLE GROUPS)
Action on a Coset Space (GROUPS)
Action on a Coset Space (MATRIX GROUPS)
Action on a Coset Space (PERMUTATION GROUPS)
Action on a G-invariant Partition (PERMUTATION GROUPS)
Action on a Polynomial Ring (K[G]-MODULES AND GROUP REPRESENTATIONS)
Action on Orbits (MATRIX GROUPS)
Action on Orbits (PERMUTATION GROUPS)
Actions (COXETER GROUPS)
Actions on Roots and Coroots (COXETER GROUPS)
Automorphism Groups (LINEAR CODES OVER FINITE FIELDS)
General Action of Collineations (FINITE PLANES)
Group Actions on Polynomials (INVARIANT RINGS OF FINITE GROUPS)
Matrix Action on Forms (BINARY QUADRATIC FORMS)
Reduced Permutation Actions (PERMUTATION GROUPS)
Action on a Coset Space (MATRIX GROUPS)
Reduced Permutation Actions (PERMUTATION GROUPS)
Actions on Roots and Coroots (COXETER GROUPS)
ActionGenerator(B, i) : AlgBas, RngIntElt -> SeqEnum
ActionGenerator(L, i) : Lat, RngIntElt -> GrpMat
ActionGenerator(M, i) : ModGrp, RngIntElt -> AlgMatElt
ActionGenerator(M, i) : ModTupRng, RngIntElt -> AlgMatElt
ActionGenerators(M) : ModGrp -> [ AlgMatElt ]
ActionImage(A, Y) : GrpPerm, GSet -> GrpPerm
ActionImage(G, Y) : GrpPerm, GSet -> GrpPerm
ActionImage(G, Y) : GrpPerm, GSet -> GrpPerm
ActionImage(G, Y) : GrpPerm, GSet -> GrpPerm
ActionKernel(A, Y) : GrpPerm, GSet -> GrpPerm
ActionKernel(G, Y) : GrpPerm, GSet -> GrpPerm
ActionKernel(G, Y) : GrpPerm, GSet -> GrpPerm
ActionKernel(G, Y) : GrpPerm, GSet -> GrpPerm
GrpCox_Actions (Example H34E16)
GrpMat_Actions (Example H21E24)
GrpPerm_Actions (Example H20E20)
Action on an Elementary Abelian Section (K[G]-MODULES AND GROUP REPRESENTATIONS)
Group Actions (LINEAR CODES OVER FINITE FIELDS)
Matrix Group Actions (MATRIX GROUPS)
Permutation Group Actions (PERMUTATION GROUPS)
AddAttribute(C, F) : Cat, MonStgElt -> ;
AddColumn(~a, u, i, j) : AlgMatElt, RngElt, RngIntElt, RngIntElt ->
AddColumn(A, c, i, j) : Mtrx, RngElt, RngIntElt, RngIntElt -> Mtrx
AddConstraints(L, lhs, rhs) : LP, Mtrx, Mtrx ->
AddEdge(~G, i, j) : Grph, RngIntElt, RngIntElt ->
AddEdge(~G, i, j, l) : Grph, RngIntElt, RngIntElt, . ->
AddEdges(~G, S) : Grph, SeqEnum ->
AddEdges(~G, S, L) : Grph, SeqEnum, SeqEnum ->
AddGenerator(G) : GrpFP -> GrpFP
AddGenerator(G, x) : GrpFp, . -> BoolElt, GrpFP, Map
AddGenerator(G, w) : GrpFP, GrpFPElt -> GrpFP
AddGenerator(S) : SgpFP -> SgpFP
AddGenerator(S, w) : SgpFP, SgpFPElt -> SgpFP
AddLocalGenerators(X) : VSrfK3 -> VSrfK3
AddNormalizingGenerator(~H, x) : GrpPerm, GrpPermElt ->
AddPrimes(SQP, p): SQProc, RngIntElt ->
AddRedundantGenerators(G, Q) : GrpSLP, [ GrpSLPElt ] -> GrpSLP
AddRelation(G, g) : GrpFP, GrpFPElt -> GrpFP
AddRelation(G, g, i) : GrpFP, GrpFPElt, RngIntElt -> GrpFP
AddRelation(G, r) : GrpFP, GrpFPRel -> GrpFP
AddRelation(G, r, i) : GrpFP, GrpFPRel, RngIntElt -> GrpFP
AddRelation(S, r) : SgpFP, Rel -> SgpFP
AddRelator(~P, w) : GrpFPCosetEnumProc, GrpFPElt ->
AddRow(~a, u, i, j) : AlgMatElt, RngElt, RngIntElt, RngIntElt ->
AddRow(A, c, i, j) : Mtrx, RngElt, RngIntElt, RngIntElt -> Mtrx
AddSubgroupGenerator(~P, w) : GrpFPCosetEnumProc, GrpFPElt ->
AddVertex(~G) : Grph ->
AddVertex(~G, l) : Grph, . ->
AddVertices(~G, n) : Grph, RngIntElt ->
AddVertices(~G, n, L) : Grph, RngIntElt, SeqEnum ->
AddWeight(X,w) : VSrfK3,RngIntElt -> VSrfK3
PseudoAdd(P1, P2, P3) : SrfKumPt, SrfKumPt, SrfKumPt -> SrfKumPt
PseudoAddMultiple(P1, P2, P3, n) : SrfKumPt, SrfKumPt, SrfKumPt, RngIntElt -> SrfKumPt
AddAttribute(C, F) : Cat, MonStgElt -> ;
AddColumn(~a, u, i, j) : AlgMatElt, RngElt, RngIntElt, RngIntElt ->
AddColumn(A, c, i, j) : Mtrx, RngElt, RngIntElt, RngIntElt -> Mtrx
AddConstraints(L, lhs, rhs) : LP, Mtrx, Mtrx ->
G +:= i, j : GrphUnd, { RngIntElt, RngIntElt } ->
AddEdge(~G, i, j) : Grph, RngIntElt, RngIntElt ->
AddEdge(~G, i, j, l) : Grph, RngIntElt, RngIntElt, . ->
AddEdges(~G, S) : Grph, SeqEnum ->
AddEdges(~G, S, L) : Grph, SeqEnum, SeqEnum ->
AddGenerator(G) : GrpFP -> GrpFP
AddGenerator(G, x) : GrpFp, . -> BoolElt, GrpFP, Map
AddGenerator(G, w) : GrpFP, GrpFPElt -> GrpFP
AddGenerator(S) : SgpFP -> SgpFP
AddGenerator(S, w) : SgpFP, SgpFPElt -> SgpFP
Operators (OVERVIEW)
AdditiveGroup(F) : FldFin -> GrpAb, Map
AdditiveGroup(Z) : RngInt -> GrpAb, Map
AdditiveGroup(R) : RngIntRes -> GrpAb, Map
AdditiveOrder( W ) : GrpCox -> SeqEnum
AdditiveOrder( F ) : GrpFP -> SeqEnum
AdditiveGroup(F) : FldFin -> GrpAb, Map
AdditiveGroup(Z) : RngInt -> GrpAb, Map
AdditiveGroup(R) : RngIntRes -> GrpAb, Map
AdditiveOrder( W ) : GrpCox -> SeqEnum
AdditiveOrder( F ) : GrpFP -> SeqEnum
GrpCox_AdditiveOrder (Example H34E7)
AddLocalGenerators(X) : VSrfK3 -> VSrfK3
AddNormalizingGenerator(~H, x) : GrpPerm, GrpPermElt ->
AddPrimes(SQP, p): SQProc, RngIntElt ->
AddRedundantGenerators(G, Q) : GrpSLP, [ GrpSLPElt ] -> GrpSLP
AddRelation(G, g) : GrpFP, GrpFPElt -> GrpFP
AddRelation(G, g, i) : GrpFP, GrpFPElt, RngIntElt -> GrpFP
AddRelation(G, r) : GrpFP, GrpFPRel -> GrpFP
AddRelation(G, r, i) : GrpFP, GrpFPRel, RngIntElt -> GrpFP
AddRelation(S, r) : SgpFP, Rel -> SgpFP
AddRelator(~P, w) : GrpFPCosetEnumProc, GrpFPElt ->
Magma Updates (OVERVIEW)
AddRow(~a, u, i, j) : AlgMatElt, RngElt, RngIntElt, RngIntElt ->
AddRow(A, c, i, j) : Mtrx, RngElt, RngIntElt, RngIntElt -> Mtrx
AddSubgroupGenerator(~P, w) : GrpFPCosetEnumProc, GrpFPElt ->
AddVertex(~G) : Grph ->
AddVertex(~G, l) : Grph, . ->
G +:= n : Grph, RngIntElt ->
AddVertices(~G, n) : Grph, RngIntElt ->
AddVertices(~G, n, L) : Grph, RngIntElt, SeqEnum ->
RemoveWeight(X,w) : VSrfK3,RngIntElt -> VSrfK3
AddWeight(X,w) : VSrfK3,RngIntElt -> VSrfK3
RngInvar_AdemMilgram (Example H80E6)
InertseqpAdic(x) : RngLoc -> [ RngLocElt ]
e adj f : GrphEdge, GrphEdge -> BoolElt
e adj f : GrphEdge, GrphEdge -> BoolElt
u adj v : GrphVert, GrphVert -> BoolElt
u adj v : GrphVert, GrphVert -> BoolElt
AdjacencyMatrix(G) : Grph -> AlgMatElt
AdjacencyMatrix(G,p) : SymGen, RngIntElt -> AlgMatElt
OutNeighbors(u) : GrphVert -> { GrphVert }
Adjacency, Degree and Distance (GRAPHS)
OutNeighbors(u) : GrphVert -> { GrphVert }
Adjacency, Degree and Distance (GRAPHS)
AdjacencyMatrix(G) : Grph -> AlgMatElt
AdjacencyMatrix(G,p) : SymGen, RngIntElt -> AlgMatElt
Adjoint(a) : AlgMatElt -> AlgMatElt
Adjoint(A) : Mtrx -> AlgMatElt
AdjointMatrix(L, x) : AlgLie, AlgLieElt -> AlgMatElt
IsAdjoint( G ) : GrpLie-> BoolElt
IsAdjoint( RD ) : RootDtm-> BoolElt
AdjointMatrix(L, x) : AlgLie, AlgLieElt -> AlgMatElt
Advance(~p) : Process ->
Advance(~p) : Process ->
Advance(~p) : Process ->
A Pair of Twisted Cubics (SCHEMES)
Advanced Examples (SCHEMES)
Curves in Space (SCHEMES)
FP GROUPS - ADVANCED FEATURES
AbsoluteQuotientRing(A) : FldAC -> RngUPolRes
AbsoluteAffineAlgebra(A) : FldAC -> RngUPolRes
AffineAction(G) : GrpPerm -> Hom, GrpPerm, GrpPerm
AffineAlgebra< R, X | L > : Fld, List, List -> RngMPolRes
AffineAlgebra(A) : FldAC -> RngMPolRes
AffineDecomposition(f) : MapSch -> MapSch,MapSch
AffineDecomposition(P) : Prj -> [MapSch],Pt
AffineGammaLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineImage(G) : GrpPerm -> GrpPerm
AffineKernel(G) : GrpPerm -> GrpPerm
AffinePatch(C,i) : Crv,RngIntElt -> SeqEnum
AffinePatch(X,p) : Sch,Pt -> Sch,Pt
AffinePatch(X,i) : Sch,RngIntElt -> Sch
AffineSigmaLinearGroup(arguments)
AffineSpace(k,2) : Rng, RngIntElt -> Aff
AffineSpace(k,n) : Rng,RngIntElt -> Aff
AffineSpace(R) : RngMPol -> Aff
AffineSpecialLinearGroup(arguments)
AffineSpecialLinearGroup(arguments)
AffineSpecialLinearGroup(arguments)
AffineSpecialLinearGroup(arguments)
AffineSpecialLinearGroup(arguments)
CentredAffinePatch(S, p) : Sch, Pt -> Sch, MapSch
FiniteAffinePlane(D) : Inc -> Plane, PlanePtSet, PlaneLnSet
FiniteAffinePlane(W) : ModFld -> PlaneAff
FiniteAffinePlane< v | X : parameters > : RngIntElt, List -> PlaneAff
FiniteAffinePlane(P, l) : PlaneProj, PlaneLn -> PlaneAff, PlanePtSet, PlaneLnSet, Map
IsAffine(X) : Sch -> BoolElt
IsAffineLinear(f) : MapSch -> BoolElt
IsAffineSpace(X) : Sch -> BoolElt
AFFINE ALGEBRAS
Affine Automorphisms (SCHEMES)
Combinatorial and Geometrical Structures (OVERVIEW)
MODULES OVER AFFINE ALGEBRAS
The Connection between Projective and Affine Planes (FINITE PLANES)
AFFINE ALGEBRAS
Affine Automorphisms (SCHEMES)
Scheme_affine-space-names (Example H83E1)
AffineAction(G) : GrpPerm -> Hom, GrpPerm, GrpPerm
AffineAlgebra< R, X | L > : Fld, List, List -> RngMPolRes
AffineAlgebra(A) : FldAC -> RngMPolRes
AffineDecomposition(f) : MapSch -> MapSch,MapSch
AffineDecomposition(P) : Prj -> [MapSch],Pt
AGammaL(arguments)
AffineGammaLinearGroup(arguments)
AGL(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineImage(G) : GrpPerm -> GrpPerm
AffineKernel(G) : GrpPerm -> GrpPerm
AffinePatch(C,i) : Crv,RngIntElt -> SeqEnum
AffinePatch(X,p) : Sch,Pt -> Sch,Pt
AffinePatch(X,i) : Sch,RngIntElt -> Sch
AffinePlane(k) : Rng -> Aff
AffineSpace(k,2) : Rng, RngIntElt -> Aff
ASigmaL(arguments)
AffineSigmaLinearGroup(arguments)
AffinePlane(k) : Rng -> Aff
AffineSpace(k,2) : Rng, RngIntElt -> Aff
AffineSpace(k,n) : Rng,RngIntElt -> Aff
AffineSpace(R) : RngMPol -> Aff
ASL(arguments)
AffineSpecialLinearGroup(arguments)
AffineSpecialLinearGroup(arguments)
Combinatorial and Geometrical Structures (OVERVIEW)
K3SurfaceFromAFR(DB,c,n) : SeqEnum,RngIntElt,RngIntElt -> VSrfK3
SetAFR(~DB) : SeqEnum ->
ReidNumber(X) : VSrfK3 -> RngIntElt
FletcherNumber(X) : VSrfK3 -> RngIntElt
AltinokNumber(X) : VSrfK3 -> RngIntElt
AFRNumber(X) : VSrfK3 -> RngIntElt
FletcherNumber(X) : VSrfK3 -> RngIntElt
IsStronglyAG(C) : Code -> BoolElt
IsWeaklyAG(C) : Code -> BoolElt
AGammaL(arguments)
AffineGammaLinearGroup(arguments)
AGammaL(arguments)
AffineGammaLinearGroup(arguments)
Agemo(G, i) : GrpAb, RngIntElt -> GrpAb
Agemo(G, i) : GrpPC, RngIntElt -> GrpPC
Aggregate (OVERVIEW)
AGL(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AGM(x, y) : FldPrElt, FldPrElt -> FldPrElt
ArithmeticGeometricMean(x, y) : FldPrElt, FldPrElt -> FldPrElt
ArithmeticGeometricMean(x, y) : FldPrElt, FldPrElt -> FldPrElt
ArithmeticGeometricMean(x, y) : FldPrElt, FldPrElt -> FldPrElt
ArithmeticGeometricMean(x, y) : FldPrElt, FldPrElt -> FldPrElt
AHom(M, N) : ModAlg, ModAlg -> ModMatFld
AHom(M, N) : ModGrp, ModGrp -> ModMatGrp
Coefficients(E) : CrvEll -> [ RngElt ]
ElementToSequence(E) : CrvEll -> [ RngElt ]
Eltseq(E) : CrvEll -> [ RngElt ]
aInvariants(E) : CrvEll -> [ RngElt ]
McElieceEtAlAsymptoticBound(delta) : FldPrElt -> FldPrElt
Alarm(s)
Decomposition of an Algebra (ALGEBRAS)
Homomorphisms (STRUCTURE CONSTANT ALGEBRAS)
Linear Algebra (LOCAL RINGS AND FIELDS)
Linear Algebra (p-ADIC RINGS AND FIELDS)
Operations on Associative Algebras (ASSOCIATIVE ALGEBRAS)
Operations on Elements (ALGEBRAS)
Operations on Elements (ASSOCIATIVE ALGEBRAS)
Operations on Group Algebras (GROUP ALGEBRAS)
Operations on Group Algebras and their Subalgebras (GROUP ALGEBRAS)
Operations on Structure Constant Algebras (STRUCTURE CONSTANT ALGEBRAS)
Operations on Subalgebras (ALGEBRAS)
Representations of Associative Algebras (ASSOCIATIVE ALGEBRAS)
The Module structure of a Structure Constant Algebra (STRUCTURE CONSTANT ALGEBRAS)
Homomorphisms (STRUCTURE CONSTANT ALGEBRAS)
The Module structure of a Structure Constant Algebra (STRUCTURE CONSTANT ALGEBRAS)
Operations on Structure Constant Algebras (STRUCTURE CONSTANT ALGEBRAS)
Decomposition of an Algebra (ALGEBRAS)
Operations on Associative Algebras (ASSOCIATIVE ALGEBRAS)
Operations on Elements (ALGEBRAS)
Operations on Elements (ASSOCIATIVE ALGEBRAS)
Operations on Subalgebras (ALGEBRAS)
Representations of Associative Algebras (ASSOCIATIVE ALGEBRAS)
GROUP ALGEBRAS
QUATERNION ALGEBRAS
Rings, Fields, and Algebras (OVERVIEW)
AbsoluteQuotientRing(A) : FldAC -> RngUPolRes
AbsoluteAffineAlgebra(A) : FldAC -> RngUPolRes
AffineAlgebra< R, X | L > : Fld, List, List -> RngMPolRes
AffineAlgebra(A) : FldAC -> RngMPolRes
Algebra(A) : AlgGrp -> AlgAss, Map
Algebra(A) : AlgGrp -> AlgAss, Map
Algebra(K, J) : FldCyc, Fld -> AlgAss, Map
Algebra(F, E) : FldFin, FldFin -> AlgAss, Map;
Algebra(M) : ModAlg -> AlgBas
Algebra(C) : ModCpx -> AlgBas
Algebra(M) : ModTupRng -> Rng
Algebra< R, n | Q : parameters > : Rng, RngIntElt, SeqEnum -> AlgGen
Algebra< R, n | T : parameters > : Rng, RngIntElt, SeqEnum -> AlgGen
Algebra< R, n | Q > : Rng, RngIntElt, SeqEnum -> AlgGen
Algebra(R) : RngInvar -> RngMPol, [ RngMPolElt ]
AlgebraMap(f) : MapSch -> Map
AssociativeAlgebra(A) : AlgGen -> AlgAss
AssociativeAlgebra< R, n | Q : parameters > : Rng, RngIntElt, SeqEnum -> AlgAss
AssociativeAlgebra< R, n | T : parameters > : Rng, RngIntElt, SeqEnum -> AlgAss
AssociativeAlgebra< R, n | Q > : Rng, RngIntElt, SeqEnum -> AlgAss
BasicAlgebra(FA, N, LR, R) : AlgFP, RngIntElt, SeqEnum, SeqEnum -> AlgBas
BasicAlgebra(G, k) : GrpPerm, FldFin -> AlgBas
BasicAlgebra(Q) : SeqEnum[Tup] -> AlgBas
DiscriminantOfHeckeAlgebra(M : Bound) : ModSym -> RngIntElt
EndomorphismAlgebra(M) : ModRng -> AlgMat
EndomorphismAlgebra(M) : ModTupRng -> AlgMat
FreeAlgebra(R, M) : Rng, MonFP -> AlgFP
GroupAlgebra(S) : AlgGrpSub -> AlgGrp
GroupAlgebra( R, G: parameters ) : Rng, Grp -> AlgGrp
GroupAlgebra(R, G) : Rng, Grp -> AlgGrp
HeckeAlgebra(M : Bound) : ModSym -> AlgMat
IsRestrictedLieAlgebra(L) : AlgLie -> BoolElt
LieAlgebra(A) : AlgAss -> AlgGen, Map
LieAlgebra(A) : AlgAss -> AlgLie
LieAlgebra(A) : AlgAss -> AlgLie
LieAlgebra( W, R ) : GrpCox, Rng -> AlgLie
LieAlgebra< R, n | Q : parameters > : Rng, RngIntElt, SeqEnum -> AlgLie
LieAlgebra< R, n | T : parameters > : Rng, RngIntElt, SeqEnum -> AlgLie
LieAlgebra< R, n | Q > : Rng, RngIntElt, SeqEnum -> AlgLie
LieAlgebra( RD, k ) : RootDtm, Rng -> AlgLie
MatrixAlgebra(A) : AlgAss -> AlgMat
MatrixAlgebra(A, E) : AlgMat, FldFin -> AlgMat, Map
MatrixAlgebra(F, E) : FldFin, FldFin -> AlgMat, Map
MatrixAlgebra(R, n) : Rng, RngInt -> AlgMat
MatrixAlgebra(S, n) : Rng, RngIntElt -> AlgMat
MatrixAlgebra<S, n | L> : Rng, RngIntElt, List -> AlgMat
MatrixAlgebra(Q) : RngMPolRes -> AlgMat, Map
MinimalAlgebraGenerators(L) : [ RngMPol ] -> [ RngMPol ]
MinimalAlgebraGenerators(L) : [ RngMPol ] -> [ RngMPol ]
MinimalAlgebraGenerators(L) : [ RngMPol ] -> [ RngMPol ]
MinimalAlgebraGenerators(L) : [ RngMPol ] -> [ RngMPol ]
OppositeAlgebra(B) : AlgBas -> AlgBas
PolynomialAlgebra(R) : Rng -> RngUPol
PolynomialRing(R, n) : Rng, RngIntElt -> RngMPol
PolynomialRing(R, n) : Rng, RngIntElt -> RngMPol
PolynomialRing(R, n, order) : Rng, RngIntElt, MonStgElt, ... -> RngMPol
PolynomialRing(R, n, order) : Rng, RngIntElt, MonStgElt, ... -> RngMPol
PolynomialRing(R, Q) : Rng, [ RngIntElt ] -> RngMPol
PrimaryAlgebra(R) : RngInvar -> RngMPol
QuaternionAlgebra(S) : AlgQuatOrd -> AlgQuat
QuaternionAlgebra(C) : CrvCon-> AlgQuat
QuaternionAlgebra< K | a, b > : Rng, RngElt, RngElt -> AlgQuat
QuaternionAlgebra< K | a, b > : Rng, RngElt, RngElt -> AlgQuat
QuaternionAlgebra(N) : RngIntElt -> AlgQuat
QuaternionAlgebra(D1, D2, T) : RngIntElt, RngIntElt, RngIntElt -> AlgQuat
SemiSimpleLieAlgebra(X, F) : MonStgElt, Fld -> AlgLie
SimpleLieAlgebra(X, n, F) : MonStgElt, RngIntElt, Fld -> AlgLie
AFFINE ALGEBRAS
Attributes of Quaternion Algebras (QUATERNION ALGEBRAS)
Finitely Presented Algebras (FINITELY PRESENTED ALGEBRAS)
Functions for Polynomial Algebra and Module Generators (IDEAL THEORY AND GRÖBNER BASES)
Linear Algebra (SCHEMES)
Magmas (or Structures) (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
S-algebras (FINITELY PRESENTED ALGEBRAS)
The Algebra (MODULES OVER A MATRIX ALGEBRA)
The Algebra of an Invariant Ring and Algebraic Relations (INVARIANT RINGS OF FINITE GROUPS)
The Hecke Algebra (MODULAR SYMBOLS)
Attributes of Quaternion Algebras (QUATERNION ALGEBRAS)
Functions for Polynomial Algebra and Module Generators (IDEAL THEORY AND GRÖBNER BASES)
The Algebra of an Invariant Ring and Algebraic Relations (INVARIANT RINGS OF FINITE GROUPS)
AlgebraicClosure() : -> FldAC
AlgebraicGenerators( G ) : GrpLie ->
AlgebraicGeometricCode(S, D) : [PlcCrvElt], DivCrvElt -> Code
IsAlgebraicGeometric(C) : Code -> BoolElt
VarietySizeOverAlgebraicClosure(I) : RngMPol -> RngIntElt
Algebraic Geometric Codes (LINEAR CODES OVER FINITE FIELDS)
ORDERS AND ALGEBRAIC FIELDS
PLANE ALGEBRAIC CURVES
PLANE ALGEBRAIC CURVES
ORDERS AND ALGEBRAIC FIELDS
Algebraic Geometric Codes (LINEAR CODES OVER FINITE FIELDS)
IsAlgebraicallyIsomorphic( G, H ) : GrpLie, GrpLie -> BoolElt
ALGEBRAICALLY CLOSED FIELDS
ALGEBRAICALLY CLOSED FIELDS
AlgebraicClosure() : -> FldAC
AlgebraicGenerators( G ) : GrpLie ->
AlgebraicGeometricCode(S, D) : [PlcCrvElt], DivCrvElt -> Code
CodeFld_AlgebraicGeometricCode (Example H101E37)
CodeFld_AlgebraicGeometricCode (Example H101E38)
AlgebraMap(f) : MapSch -> Map
Associative Structure Constant Algebras from other Algebras (ASSOCIATIVE ALGEBRAS)
Basic Algebras (BASIC ALGEBRAS)
Construction of a General Algebra (ALGEBRAS)
Construction of a Lie Structure Constant Algebra (LIE ALGEBRAS)
Construction of a Structure Constant Algebra (STRUCTURE CONSTANT ALGEBRAS)
Construction of an Associative Structure Constant Algebra (ASSOCIATIVE ALGEBRAS)
MODULES OVER AFFINE ALGEBRAS
Opposite Algebras (BASIC ALGEBRAS)
Rings, Fields, and Algebras (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Magma's Evaluation Process (MAGMA SEMANTICS)
Overview of Facilities (FINITELY PRESENTED GROUPS)
Sketch of the Algorithm (FINITELY PRESENTED ALGEBRAS)
FldFunG_AlgReln1 (Example H53E19)
FldFunG_AlgReln2 (Example H53E20)
AllCliques(G) : GrphUnd -> SeqEnum
AllCliques(G, k) : GrphUnd, RngIntEl -> SeqEnum
AllCliques(G, k, m: parameters) : GrphUnd, RngIntElt, BoolElt -> SeqEnum
Alldeg(G, n) : GrphDir, RngIntElt -> { GrphVert }
Alldeg(G, n) : GrphUnd, RngIntElt -> { GrphVert }
AllFaces(N) : NwtnPgon -> SeqEnum
AllInformationSets(C) : Code -> [ [ RngIntElt ] ]
AllIrreduciblePolynomials(F, m) : FldFin, RngIntElt -> { RngPolElt }
AllParallelClasses(D) : Inc -> SeqEnum
AllParallelisms(D) : Inc -> SeqEnum
AllPartitions(G) : GrpPerm -> SetEnum
AllPassants(P, A) : Plane, { PlanePt } -> { PlaneLn }
ExternalLines(P, A) : Plane, { PlanePt } -> { PlaneLn }
AllResolutions(D) : Inc -> SeqEnum
AllResolutions(D, lambda) : Inc, RngIntElt -> SeqEnum
AllRoots(a, n) : FldFinElt, RngIntElt -> SeqEnum
AllSecants(P, A) : Plane, { PlanePt } -> { PlaneLn }
AllSqrts(a) : RngIntResElt -> [ RngIntResElt ]
AllSquareRoots(a) : RngIntResElt -> [ RngIntResElt ]
AllSqrts(a) : RngIntResElt -> [ RngIntResElt ]
AllSquareRoots(a) : RngIntResElt -> [ RngIntResElt ]
AllTangents(P, A) : Plane, { PlanePt } -> { PlaneLn }
AllTangents(P, U) : Plane, { PlanePt } -> { PlaneLn }
AllVertices(N) : NwtnPgon -> SeqEnum
AlmostSimpleGroupDatabase() : -> DB
IdentifyAlmostSimpleGroup(G) : GrpPerm -> Map, GrpPerm
Set_AlmostFermat (Example H7E2)
Set_AlmostFermatIndexed (Example H7E3)
AlmostSimpleGroupDatabase() : -> DB
MurphyAlphaApproximation(F, b) : RngMPolElt, RngIntElt -> FldReElt
Alphabet(C) : Code -> Rng
Alphabet(C) : Code -> Rng
NumberOfTableauxOnAlphabet(P, m) : SeqEnum,RngIntElt -> RngIntElt
Changing the Alphabet of a Code (LINEAR CODES OVER FINITE FIELDS)
Alt(C, n) : Cat, RngIntElt -> GrpFin
AlternatingGroup(C, n) : Cat, RngIntElt -> GrpFin
AlternatingGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP
AlternatingGroup(GrpPerm, n) : Cat, RngIntElt -> GrpPerm
AlternantCode(A, Y, r, S) : [ FldFinElt ], [ FldFinElt ], RngIntElt, FldFin -> Code
NonPrimitiveAlternantCode(n,m,r) : RngIntElt,RngIntElt,RngIntElt->Code
AlternantCode(A, Y, r, S) : [ FldFinElt ], [ FldFinElt ], RngIntElt, FldFin -> Code
CodeFld_AlternantCode (Example H101E28)
AlternateDefiningPolynomials(f) : MapSch -> SeqEnum
Creation of Points (HYPERELLIPTIC CURVES)
Models for Hyperelliptic Curves (HYPERELLIPTIC CURVES)
AlternateDefiningPolynomials(f) : MapSch -> SeqEnum
Alt(C, n) : Cat, RngIntElt -> GrpFin
AlternatingGroup(C, n) : Cat, RngIntElt -> GrpFin
AlternatingGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP
AlternatingGroup(GrpPerm, n) : Cat, RngIntElt -> GrpPerm
AlternatingSum(m, i) : Map, RngIntElt -> FldPrElt
IsAlternating(G) : GrpPerm -> BoolElt
Alt(C, n) : Cat, RngIntElt -> GrpFin
AlternatingGroup(C, n) : Cat, RngIntElt -> GrpFin
AlternatingGroup(GrpFP, n) : Cat, RngIntElt -> GrpFP
AlternatingGroup(GrpPerm, n) : Cat, RngIntElt -> GrpPerm
AlternatingSum(m, i) : Map, RngIntElt -> FldPrElt
ReidNumber(X) : VSrfK3 -> RngIntElt
FletcherNumber(X) : VSrfK3 -> RngIntElt
AltinokNumber(X) : VSrfK3 -> RngIntElt
AFRNumber(X) : VSrfK3 -> RngIntElt
ReidNumber(X) : VSrfK3 -> RngIntElt
FletcherNumber(X) : VSrfK3 -> RngIntElt
AltinokNumber(X) : VSrfK3 -> RngIntElt
AFRNumber(X) : VSrfK3 -> RngIntElt
IsAltsym(G) : GrpPerm -> BoolElt
AmbientSpace(L) : LinSys -> Prj
Ambient(L) : LinSys -> Prj
AmbientModule(M) : ModBrdt -> ModBrdt
AmbientSpace(C) : Code -> ModTupRng
AmbientSpace(C) : Code -> ModTupRng
AmbientSpace(L) : Lat -> ModTupFld, Map
AmbientSpace(C) : Sch -> Sch
AmbientSpace(X) : Sch -> Sch
IsAmbient(M) : ModBrdt -> BoolElt
IsAmbientFunction(A,f) : Sch,RngElt -> BoolElt, RngElt
IsAmbientRationalFunction(A,f) : Sch,RngElt -> BoolElt
IsAmbientSpace(M) : ModFrm -> BoolElt
IsAmbientSpace(M) : ModSS -> BoolElt
Ambient Spaces (MODULAR FORMS)
Ambient Spaces (MODULAR SYMBOLS)
Ambient Spaces (SCHEMES)
Ambient Spaces ({THE MODULE OF}{SUPERSINGULAR POINTS})
Functions and Homogeneity on Ambient Spaces (SCHEMES)
Functions of the Ambient Space (SCHEMES)
Introduction (SCHEMES)
Prelude to Points (SCHEMES)
Projective Closure and Affine Patches (SCHEMES)
The Ambient Space and Alphabet (LINEAR CODES OVER FINITE FIELDS)
Field(C) : Code -> Rng
The Ambient Space and Alphabet (LINEAR CODES OVER FINITE FIELDS)
AmbientModule(M) : ModBrdt -> ModBrdt
Ambient Spaces (PLANE ALGEBRAIC CURVES)
AmbientSpace(L) : LinSys -> Prj
Ambient(L) : LinSys -> Prj
AmbientSpace(C) : Code -> ModTupRng
AmbientSpace(C) : Code -> ModTupRng
AmbientSpace(L) : Lat -> ModTupFld, Map
AmbientSpace(C) : Sch -> Sch
AmbientSpace(X) : Sch -> Sch
AmbiguousForms(Q) : QuadBin -> SeqEnum
AmbiguousForms(Q) : QuadBin -> SeqEnum
RngInt_Amicable (Example H38E4)
AModule(B, Q) : AlgBas, SeqEnum[AlgMatElt] -> ModRng
AlgBas_AModules (Example H81E2)
IsAnalyticallyIrreducible(p) : Crv,Pt -> BoolElt
Contpp(f) : RngMPolElt -> RngIntElt, RngMPolElt
ContentAndPrimitivePart(f) : RngMPolElt -> RngIntElt, RngMPolElt
ContentAndPrimitivePart(p) : RngUPolElt -> RngIntElt, RngUPolElt
FactoredMinimalAndCharacteristicPolynomials(A: parameters) : Mtrx -> [<RngUPolElt, RngIntElt>], [<RngUPolElt, RngIntElt>]
HasSparseRep(G) : Grph -> BoolElt
MinimalAndCharacteristicPolynomials(A: parameter) : Mtrx -> RngUPolElt, RngUPolElt
Absolute Value and Sign (RATIONAL FIELD)
Cartan Matrices (ROOT DATA FOR LIE THEORY)
Cusps and elliptic points of congruence subgroups (SUBGROUPS OF PSL_2(R))
Expression (OVERVIEW)
Order and Ideal Isomorphisms (QUATERNION ALGEBRAS)
x and y : BoolElt, BoolElt -> BoolElt
Lattices from Algebraic Number Fields (LATTICES)
Generator Assignment (OVERVIEW)
Generator Assignment (OVERVIEW)
LeftAnnihilator(A, B) : AlgAss, AlgAss -> AlgAss, AlgAss
LeftAnnihilator(S) : AlgGrpSub -> AlgGrpSub
RightAnnihilator(A, B) : AlgAss, AlgAss -> AlgAss, AlgAss
RightAnnihilator(S) : AlgGrpSub -> AlgGrpSub
AntisymmetricForms(G) : GrpMat -> [ AlgMatElt ]
AntisymmetricForms(G, n) : GrpMat, RngIntElt -> [ AlgMatElt ]
AntisymmetricMatrix(R, Q) : Rng, [ RngElt ] -> Mtrx
AntisymmetricMatrix(Q) : [ RngElt ] -> Mtrx
NumberOfAntisymmetricForms(G) : GrpMat -> RngIntElt
AntisymmetricForms(G) : GrpMat -> [ AlgMatElt ]
AntisymmetricForms(G, n) : GrpMat, RngIntElt -> [ AlgMatElt ]
AntisymmetricMatrix(R, Q) : Rng, [ RngElt ] -> Mtrx
AntisymmetricMatrix(Q) : [ RngElt ] -> Mtrx
ApparentCodimension(X) : VSrfK3 -> RngIntElt
ApparentCodimension(X) : VSrfK3 -> RngIntElt
Append(~S, x) : List, Elt ->
Append(S, x) : List, Elt -> List
Append(~S, x) : SeqEnum, Elt ->
Append(~T, x) : Tup, Elt ->
Append(T, x) : Tup, Elt -> Tup
Function Application (MAGMA SEMANTICS)
ApproximateStabiliser(G, A, U: parameters) : GrpMat, GrpMat, ModTupFld -> GrpMat, GrpMat, RngIntElt, RngIntElt, RngIntElt
ApproximateStabiliser(G, A, U: parameters) : GrpMat, GrpMat, ModTupFld -> GrpMat, GrpMat, RngIntElt, RngIntElt, RngIntElt
BernoulliApproximation(n) : RngIntElt -> FldPrElt
BernoulliApproximation(n) : RngIntElt -> FldPrElt
BestApproximation(r, n) : FldPrElt, RngIntElt -> FldPrElt
ClassNumberApproximation(F, e) : FldFun, FldPrElt -> FldReElt
ClassNumberApproximationBound(q, g, e) : RngIntElt, RngIntElt, -> RngIntElt
MurphyAlphaApproximation(F, b) : RngMPolElt, RngIntElt -> FldReElt
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
General K[G]-Modules (K[G]-MODULES AND GROUP REPRESENTATIONS)
General K[G]-Modules (K[G]-MODULES AND GROUP REPRESENTATIONS)
FixedArc(g,H) : GrpPSL2Elt, SpcHyp -> SeqEnum
IsArc(P, A) : Plane, { PlanePt } -> BoolElt
[Future release] IsArcTransitive(G, t) : GrphUnd, RngIntElt -> BoolElt
Arcs (FINITE PLANES)
Arccos(s) : FldPrElt -> FldPrElt
Arccos(f) : RngSerElt -> RngSerElt
Arccos(f) : RngSerElt -> RngSerElt
Arccosec(s) : FldPrElt -> FldPrElt
Arccot(s) : FldPrElt -> FldPrElt
Plane_arcs (Example H99E10)
Arcsec(s) : FldPrElt -> FldPrElt
Arcsin(s) : FldPrElt -> FldPrElt
Arcsin(f) : RngSerElt -> RngSerElt
Arcsin(f) : RngSerElt -> RngSerElt
Arctan(s) : FldPrElt -> FldPrElt
Arctan(a, b) : FldPrElt, FldPrElt -> FldPrElt
Arctan(f) : RngSerElt -> RngSerElt
Arctan(f) : RngSerElt -> RngSerElt
Arctan2(a, b) : FldPrElt, FldPrElt -> FldPrElt
Arctan(a, b) : FldPrElt, FldPrElt -> FldPrElt
AreIdentical(u, v) : GrpBrdElt, GrpBrdElt -> BoolElt
IsogeniesAreEqual(I, J) : Map, Map -> BoolElt
SetOrderUnitsAreFundamental(O) : RngOrd ->
AreIdentical(u, v) : GrpBrdElt, GrpBrdElt -> BoolElt
Arg(c) : FldComElt -> FldReElt
Argument(c) : FldComElt -> FldReElt
Argcosech(s) : FldPrElt -> FldPrElt
Argcosh(s) : FldPrElt -> FldPrElt
Argcosh(f) : RngSerElt -> RngSerElt
Argcosh(f) : RngSerElt -> RngSerElt
Argcoth(s) : FldPrElt -> FldPrElt
Argsech(s) : FldPrElt -> FldPrElt
Argsinh(s) : FldPrElt -> FldPrElt
Argsinh(f) : RngSerElt -> RngSerElt
Argsinh(f) : RngSerElt -> RngSerElt
Argtanh(s) : FldPrElt -> FldPrElt
Argtanh(f) : RngSerElt -> RngSerElt
Argtanh(f) : RngSerElt -> RngSerElt
Arg(c) : FldComElt -> FldReElt
Argument(c) : FldComElt -> FldReElt
Intrinsics (OVERVIEW)
Reference Arguments (MAGMA SEMANTICS)
Arithmetic of Points (HYPERELLIPTIC CURVES)
Arithmetic Operators (ALGEBRAIC FUNCTION FIELDS)
Arithmetic with Elements (MODULES OVER DEDEKIND DOMAINS)
Arithmetic with Lazy Series (LAZY POWER SERIES RINGS)
Arithmetic with Modules (MODULES OVER DEDEKIND DOMAINS)
Arithmetic with places and divisors (ORDERS AND ALGEBRAIC FIELDS)
Coefficient Arithmetic (PLANE ALGEBRAIC CURVES)
Modular Degree and Torsion (MODULAR SYMBOLS)
Arithmetic of Points (HYPERELLIPTIC CURVES)
ArithmeticGenus(C) : Crv -> RngIntElt
ArithmeticGeometricMean(x, y) : FldPrElt, FldPrElt -> FldPrElt
ArithmeticGeometricMean(x, y) : FldPrElt, FldPrElt -> FldPrElt
GrpAtc_Arithmetic (Example H28E3)
GrpMat_Arithmetic (Example H21E11)
GrpPerm_Arithmetic (Example H20E9)
GrpRWS_Arithmetic (Example H27E3)
Grp_Arithmetic (Example H16E2)
ModFld_Arithmetic (Example H61E5)
ModForm_Arithmetic (Example H93E9)
ModSS_Arithmetic (Example H92E7)
MonRWS_Arithmetic (Example H15E3)
Addition and Subtraction (ABELIAN GROUPS)
Addition and Subtraction (GENERIC ABELIAN GROUPS)
Arithmetic (BINARY QUADRATIC FORMS)
Arithmetic (CHARACTERS OF FINITE GROUPS)
Arithmetic (ELLIPTIC CURVES)
Arithmetic (FREE MODULES)
Arithmetic (LOCAL RINGS AND FIELDS)
Arithmetic (MATRIX ALGEBRAS)
Arithmetic (MODULAR FORMS)
Arithmetic (MODULES OVER AFFINE ALGEBRAS)
Arithmetic (p-ADIC RINGS AND FIELDS)
Arithmetic (RATIONAL FUNCTION FIELDS)
Arithmetic (REAL AND COMPLEX FIELDS)
Arithmetic (RING OF INTEGERS)
Arithmetic (RING OF INTEGERS)
Arithmetic ({THE MODULE OF}{SUPERSINGULAR POINTS})
Arithmetic Functions (RING OF INTEGERS)
Arithmetic of Divisors (PLANE ALGEBRAIC CURVES)
Arithmetic Operations (INTRODUCTION [BASIC RINGS])
Arithmetic Operations (RING OF INTEGERS)
Arithmetic Operations (RING OF INTEGERS)
Arithmetic Operations (VALUATION RINGS)
Arithmetic Operations on Elements (FINITE SOLUBLE GROUPS)
Arithmetic Operations on Elements (POLYCYCLIC GROUPS)
Arithmetic Operations on Ideals (INTRODUCTION [BASIC RINGS])
Arithmetic Operators (ALGEBRAIC FUNCTION FIELDS)
Arithmetic Operators (ALGEBRAIC FUNCTION FIELDS)
Arithmetic Operators (ALGEBRAIC FUNCTION FIELDS)
Arithmetic Operators (ALGEBRAIC FUNCTION FIELDS)
Arithmetic Operators (ALGEBRAICALLY CLOSED FIELDS)
Arithmetic Operators (FINITE FIELDS)
Arithmetic Operators (GALOIS RINGS)
Arithmetic Operators (MULTIVARIATE POLYNOMIAL RINGS)
Arithmetic Operators (POWER, LAURENT AND PUISEUX SERIES)
Arithmetic Operators (RATIONAL FIELD)
Arithmetic Operators (RING OF INTEGERS)
Arithmetic Operators (UNIVARIATE POLYNOMIAL RINGS)
Arithmetic Operators and Functions for Elements (BRAID GROUPS)
Arithmetic Operators for Words (FINITELY PRESENTED GROUPS)
Arithmetic with Elements (GROUPS)
Arithmetic with Isomorphisms (HYPERELLIPTIC CURVES)
Arithmetic with Matrices (MATRIX GROUPS)
Arithmetic with Permutations (PERMUTATION GROUPS)
Arithmetic with Vectors (VECTOR SPACES)
Arithmetic with Words (AUTOMATIC GROUPS)
Arithmetic with Words (GROUPS DEFINED BY REWRITE SYSTEMS)
Arithmetic with Words (MONOIDS GIVEN BY REWRITE SYSTEMS)
Creation of Vector Spaces and Arithmetic with Vectors (VECTOR SPACES)
Elementary Arithmetic (MATRICES)
Elementary Operations (BASIC ALGEBRAS)
Elementary Operations (BASIC ALGEBRAS)
Elementary Operations (CHAIN COMPLEXES)
Elementary operations (CHAIN COMPLEXES)
Elementary Operators for Elements (FINITELY PRESENTED ALGEBRAS)
Ideal Arithmetic (ORDERS AND ALGEBRAIC FIELDS)
Ideal Arithmetic (UNIVARIATE POLYNOMIAL RINGS)
Modular Arithmetic (QUADRATIC FIELDS)
Multiplication and Exponentiation (FINITELY PRESENTED SEMIGROUPS)
Sequences (OVERVIEW)
Sets (OVERVIEW)
The Arithmetic Progression Constructors (SEQUENCES)
The Arithmetic Progression Constructors (SETS)
Arithmetic Functions (RING OF INTEGERS)
Sequences (OVERVIEW)
Sets (OVERVIEW)
The Arithmetic Progression Constructors (SEQUENCES)
The Arithmetic Progression Constructors (SETS)
Arithmetic of Points (HYPERELLIPTIC CURVES)
ArithmeticGenus(C) : Crv -> RngIntElt
AGM(f, g) : RngSerElt, RngSerElt -> RngSerElt
ArithmeticGeometricMean(x, y) : FldPrElt, FldPrElt -> FldPrElt
ArithmeticGeometricMean(x, y) : FldPrElt, FldPrElt -> FldPrElt
IntersectionArray(G) : GrphUnd -> [RngIntElt]
Arrows(s) : GrphRes -> SeqEnum
ArtinMap(A) : FldAb -> Map
ArtinMap(A) : FldAb -> Map
ASigmaL(arguments)
AffineSigmaLinearGroup(arguments)
ASigmaL(arguments)
AffineSigmaLinearGroup(arguments)
ASL(arguments)
AffineSpecialLinearGroup(arguments)
AffineSpecialLinearGroup(arguments)
AffineSpecialLinearGroup(arguments)
AffineSpecialLinearGroup(arguments)
AffineSpecialLinearGroup(arguments)
AssertAttribute(x, "IsCharacter", b) : AlgChtrElt, MonStgElt, BoolElt ->
AssertAttribute(FldFin, "PowerPrinting", l) : Cat, MonStgElt, BoolElt ->
AssertAttribute(ModMPol, "MatrixPrinting", l) : Cat, MonStgElt, BoolElt ->
AssertAttribute(FldPr, "OutputPrecision", n) : Cat, MonStgElt, RngIntElt ->
AssertAttribute(FldPr, "Precision", n) : Cat, MonStgElt, RngIntElt ->
AssertAttribute(GrpMat, "FirstBasicOrbitBound", n) : Cat, MonStgElt, RngIntElt ->
AssertAttribute(RngInt, "CunninghamStorageLimit", l) : Cat, MonStgElt, RngIntElt ->
AssertAttribute(G, "IsVerified", b) : GrpMat, MonStgElt, BoolElt ->
AssertAttribute(G, "Order", n) : GrpMat, MonStgElt, RngIntElt ->
AssertAttribute(G, "Base", B) : GrpMat, MonStgElt, Tup ->
AssertAttribute(G, "Classes", Q) : GrpMat, MonStgElt, [ GrpMatElt ] ->
[Future release] AssertAttribute(G, "BSGS", S) : GrpPerm, MonStgElt, GrpPermBSGS ->
AssertAttribute(G, "Order", n) : GrpPerm, MonStgElt, RngIntElt ->
AssertAttribute(G, "Classes", Q) : GrpPerm, MonStgElt, [ GrpPermElt ] ->
AssertAttribute(G, "Order", Q) : GrpPerm, MonStgElt, [<RngIntElt, RngIntElt>] ->
AssertAttribute(M, "MatrixPrinting", l) : ModMPol, MonStgElt, BoolElt ->
AssertAttribute(S, "Precision", n) : RngSer, MonStgElt, RngIntElt ->
SetPowerPrinting(F, l) : FldFin, BoolElt ->
assert boolexpr;
AssertAttribute(x, "IsCharacter", b) : AlgChtrElt, MonStgElt, BoolElt ->
AssertAttribute(FldFin, "PowerPrinting", l) : Cat, MonStgElt, BoolElt ->
AssertAttribute(ModMPol, "MatrixPrinting", l) : Cat, MonStgElt, BoolElt ->
AssertAttribute(FldPr, "OutputPrecision", n) : Cat, MonStgElt, RngIntElt ->
AssertAttribute(FldPr, "Precision", n) : Cat, MonStgElt, RngIntElt ->
AssertAttribute(GrpMat, "FirstBasicOrbitBound", n) : Cat, MonStgElt, RngIntElt ->
AssertAttribute(RngInt, "CunninghamStorageLimit", l) : Cat, MonStgElt, RngIntElt ->
AssertAttribute(G, "IsVerified", b) : GrpMat, MonStgElt, BoolElt ->
AssertAttribute(G, "Order", n) : GrpMat, MonStgElt, RngIntElt ->
AssertAttribute(G, "Base", B) : GrpMat, MonStgElt, Tup ->
AssertAttribute(G, "Classes", Q) : GrpMat, MonStgElt, [ GrpMatElt ] ->
[Future release] AssertAttribute(G, "BSGS", S) : GrpPerm, MonStgElt, GrpPermBSGS ->
AssertAttribute(G, "Order", n) : GrpPerm, MonStgElt, RngIntElt ->
AssertAttribute(G, "Classes", Q) : GrpPerm, MonStgElt, [ GrpPermElt ] ->
AssertAttribute(G, "Order", Q) : GrpPerm, MonStgElt, [<RngIntElt, RngIntElt>] ->
AssertAttribute(M, "MatrixPrinting", l) : ModMPol, MonStgElt, BoolElt ->
AssertAttribute(S, "Precision", n) : RngSer, MonStgElt, RngIntElt ->
SetPowerPrinting(F, l) : FldFin, BoolElt ->
GetAssertions() : -> BoolElt
SetAssertions(b) : BoolElt ->
AssignLabel(G, i, l) : Grph, RngIntElt, . ->
AssignLabel(G, i, j, l) : Grph, RngIntElt, RngIntElt, . ->
AssignLabel(t, l) : GrphVert, . ->
AssignLabels(G, S, L) : Grph, SeqEnum, SeqEnum ->
AssignLabels(G, S, L) : Grph, [RngIntElt], SeqEnum ->
AssignLabels(T, L) : GrphVertSet, SeqEnum ->
AssignLabels(S, L) : [GrphVert], SeqEnum ->
AssignNamePrefix(A, S) : FldAC, MonStgElt ->
AssignNames(~A,S) : AlgQuat, [MonStgElt] ->
AssignNames(~D, s) : DivFunElt, [ MonStgElt ] ->
AssignNames(~F, [f]) : FldFin, [ MonStgElt ]) ->
AssignNames(~F, s) : FldFun, [ MonStgElt ] ->
AssignNames(~F, s) : FldFunRat, [ MonStgElt ]) ->
AssignNames(~K, s) : FldNum, [ MonStgElt ] ->
AssignNames(~F, s) : FldOrd, [ MonStgElt ] ->
AssignNames(~C, [s]) : FldPr, [ MonStgElt ]) ->
AssignNames(~F, [s]) : FldQuad, [ MonStgElt ]) ->
AssignNames( G, S) : GrpDrch, [MonStgElt] ->
AssignNames(~P, s) : PlcFunElt, [ MonStgElt ] ->
AssignNames(~R, [f]) : RngGal, [ MonStgElt ]) ->
AssignNames(~L, S) : RngLoc, SeqEnum ->
AssignNames(~P, S) : RngLoc, SeqEnum ->
AssignNames(~P, s) : RngMPol, [ MonStgElt ]) ->
AssignNames(~R, S) : RngPowLaz, [MonStgElt] ->
AssignNames(~S, ["x"]) : RngSer, [ MonStgElt ] ->
AssignNames(~P, s) : RngUPol, [ MonStgElt ]) ->
AssignNames(~X,N) : Sch,SeqEnum ->
AssignNames(~A,N) : Sch,[MonStgElt] ->
AssignNames(~S, [s_1, ... s_n] ) : Struct, [ MonStgElt ] ->
Assignment (OVERVIEW)
Testing whether an identifier is assigned (OVERVIEW)
assigned r`fieldname : Rec, Fieldname -> BoolElt
assigned S`fieldname : Str, Fieldname -> BoolElt
assigned x : Var -> BoolElt
Labelling a Graph (GRAPHS)
AssignLabel(G, i, l) : Grph, RngIntElt, . ->
AssignLabel(G, i, j, l) : Grph, RngIntElt, RngIntElt, . ->
AssignLabel(t, l) : GrphVert, . ->
AssignLabels(G, S, L) : Grph, SeqEnum, SeqEnum ->
AssignLabels(G, S, L) : Grph, [RngIntElt], SeqEnum ->
AssignLabels(T, L) : GrphVertSet, SeqEnum ->
AssignLabels(S, L) : [GrphVert], SeqEnum ->
Assignment (MAGMA SEMANTICS)
Assignment (OVERVIEW)
Assignment (STATEMENTS AND EXPRESSIONS)
Assignment Operator (LISTS)
Function Values Assigned to Identifiers (MAGMA SEMANTICS)
Generator Assignment (OVERVIEW)
Generator Assignment (STATEMENTS AND EXPRESSIONS)
Indexed Assignment (STATEMENTS AND EXPRESSIONS)
Multiple Assignment (OVERVIEW)
Simple Assignment (STATEMENTS AND EXPRESSIONS)
AssignNamePrefix(A, S) : FldAC, MonStgElt ->
AssignNames(~A,S) : AlgQuat, [MonStgElt] ->
AssignNames(~D, s) : DivFunElt, [ MonStgElt ] ->
AssignNames(~F, [f]) : FldFin, [ MonStgElt ]) ->
AssignNames(~F, s) : FldFun, [ MonStgElt ] ->
AssignNames(~F, s) : FldFunRat, [ MonStgElt ]) ->
AssignNames(~K, s) : FldNum, [ MonStgElt ] ->
AssignNames(~F, s) : FldOrd, [ MonStgElt ] ->
AssignNames(~C, [s]) : FldPr, [ MonStgElt ]) ->
AssignNames(~F, [s]) : FldQuad, [ MonStgElt ]) ->
AssignNames( G, S) : GrpDrch, [MonStgElt] ->
AssignNames(~P, s) : PlcFunElt, [ MonStgElt ] ->
AssignNames(~R, [f]) : RngGal, [ MonStgElt ]) ->
AssignNames(~L, S) : RngLoc, SeqEnum ->
AssignNames(~P, S) : RngLoc, SeqEnum ->
AssignNames(~P, s) : RngMPol, [ MonStgElt ]) ->
AssignNames(~R, S) : RngPowLaz, [MonStgElt] ->
AssignNames(~S, ["x"]) : RngSer, [ MonStgElt ] ->
AssignNames(~P, s) : RngUPol, [ MonStgElt ]) ->
AssignNames(~X,N) : Sch,SeqEnum ->
AssignNames(~A,N) : Sch,[MonStgElt] ->
AssignNames(~S, [s_1, ... s_n] ) : Struct, [ MonStgElt ] ->
RngMPol_AssignNames (Example H43E1)
Associated Structures (BRANDT MODULES)
AssociatedNewSpace(M) : ModSym -> ModSym
Associated Functions (DATABASES OF GROUPS)
Associated Spaces ({THE MODULE OF}{SUPERSINGULAR POINTS})
Associated Structures (LATTICES)
ModSS_Associated structures (Example H92E5)
Associated Functions (DATABASES OF GROUPS)
Associated Spaces ({THE MODULE OF}{SUPERSINGULAR POINTS})
Associated Structures (BRANDT MODULES)
Type(L) : Lat -> Cat
Associated Structures (LATTICES)
AssociatedNewSpace(M) : ModSym -> ModSym
AssociativeAlgebra(A) : AlgGen -> AlgAss
AssociativeAlgebra< R, n | Q : parameters > : Rng, RngIntElt, SeqEnum -> AlgAss
AssociativeAlgebra< R, n | T : parameters > : Rng, RngIntElt, SeqEnum -> AlgAss
AssociativeAlgebra< R, n | Q > : Rng, RngIntElt, SeqEnum -> AlgAss
IsAssociative(A) : AlgGen -> BoolElt
AssociativeAlgebra(A) : AlgGen -> AlgAss
AssociativeAlgebra< R, n | Q : parameters > : Rng, RngIntElt, SeqEnum -> AlgAss
AssociativeAlgebra< R, n | T : parameters > : Rng, RngIntElt, SeqEnum -> AlgAss
AssociativeAlgebra< R, n | Q > : Rng, RngIntElt, SeqEnum -> AlgAss
EliasAsymptoticBound(K, delta) : FldFin, FldPrElt -> FldPrElt
GilbertVarshamovAsymptoticBound(K, delta) : FldFin, FldPrElt -> FldPrElt
HammingAsymptoticBound(K, delta) : FldFin, FldPrElt -> FldPrElt
McElieceEtAlAsymptoticBound(delta) : FldPrElt -> FldPrElt
PlotkinAsymptoticBound(K, delta) : FldFin, FldPrElt -> FldPrElt
SingletonAsymptoticBound(delta) : FldPrElt -> FldPrElt
Asymptotic Bounds on the Information Rate (LINEAR CODES OVER FINITE FIELDS)
Asymptotic Bounds on the Information Rate (LINEAR CODES OVER FINITE FIELDS)
EvaluateAt(L, p) : LP, Mtrx -> RngIntElt
HyperplaneAtInfinity(X) : Sch -> Sch
LineAtInfinity(A) : Aff -> Crv
PointsAtInfinity(C) : Crv -> SetEnum
PointsAtInfinity(C) : CrvHyp -> SetIndx
PointsAtInfinity(H) : SetPtEll -> @ PtEll @
AtkinLehner(M, q) : ModSym, RngIntElt -> AlgMatElt
AtkinLehnerOperator(M, p) : ModBrdt, RngIntElt -> AlgMatElt
AtkinLehnerOperator(M, q) : ModFrm, RngIntElt -> AlgMatElt
AtkinLehnerOperator(M, q) : ModSS, RngIntElt -> AlgMatElt
AtkinModularPolynomial(N) : RngIntElt -> RngMPolElt
CanonicalInvolution(X) : CrvMod -> MapSch
DualAtkinLehner(M, q) : ModSym, RngIntElt -> AlgMatElt
AtkinLehner(M, q) : ModSym, RngIntElt -> AlgMatElt
AtkinLehnerInvolution(X,N) : CrvMod, RngIntElt -> MapSch
CanonicalInvolution(X) : CrvMod -> MapSch
AtkinLehnerOperator(M, p) : ModBrdt, RngIntElt -> AlgMatElt
AtkinLehnerOperator(M, q) : ModFrm, RngIntElt -> AlgMatElt
AtkinLehnerOperator(M, q) : ModSS, RngIntElt -> AlgMatElt
AtkinModularPolynomial(N) : RngIntElt -> RngMPolElt
Attach(F); : file ->
AttachSpec(S) : file ->
Attaching and Detaching Package Files (FUNCTIONS, PROCEDURES AND PACKAGES)
Attaching and Detaching Package Files (FUNCTIONS, PROCEDURES AND PACKAGES)
AttachSpec(S) : file ->
Attributes of Local Rings and Fields (LOCAL RINGS AND FIELDS)
Attributes of p-adic Rings and Fields (p-ADIC RINGS AND FIELDS)
AddAttribute(C, F) : Cat, MonStgElt -> ;
AssertAttribute(x, "IsCharacter", b) : AlgChtrElt, MonStgElt, BoolElt ->
AssertAttribute(FldFin, "PowerPrinting", l) : Cat, MonStgElt, BoolElt ->
AssertAttribute(ModMPol, "MatrixPrinting", l) : Cat, MonStgElt, BoolElt ->
AssertAttribute(FldPr, "OutputPrecision", n) : Cat, MonStgElt, RngIntElt ->
AssertAttribute(FldPr, "Precision", n) : Cat, MonStgElt, RngIntElt ->
AssertAttribute(GrpMat, "FirstBasicOrbitBound", n) : Cat, MonStgElt, RngIntElt ->
AssertAttribute(RngInt, "CunninghamStorageLimit", l) : Cat, MonStgElt, RngIntElt ->
AssertAttribute(G, "IsVerified", b) : GrpMat, MonStgElt, BoolElt ->
AssertAttribute(G, "Order", n) : GrpMat, MonStgElt, RngIntElt ->
AssertAttribute(G, "Base", B) : GrpMat, MonStgElt, Tup ->
AssertAttribute(G, "Classes", Q) : GrpMat, MonStgElt, [ GrpMatElt ] ->
[Future release] AssertAttribute(G, "BSGS", S) : GrpPerm, MonStgElt, GrpPermBSGS ->
AssertAttribute(G, "Order", n) : GrpPerm, MonStgElt, RngIntElt ->
AssertAttribute(G, "Classes", Q) : GrpPerm, MonStgElt, [ GrpPermElt ] ->
AssertAttribute(G, "Order", Q) : GrpPerm, MonStgElt, [<RngIntElt, RngIntElt>] ->
AssertAttribute(M, "MatrixPrinting", l) : ModMPol, MonStgElt, BoolElt ->
AssertAttribute(S, "Precision", n) : RngSer, MonStgElt, RngIntElt ->
HasAttribute(FldPr, "OutputPrecision") : Cat, MonStgElt -> BoolElt, RngIntElt
HasAttribute(FldPr, "Precision") : Cat, MonStgElt -> BoolElt, RngIntElt
HasAttribute(GrpMat, "FirstBasicOrbitBound") : Cat, MonStgElt -> BoolElt, RngIntElt
HasAttribute(FldFin, "PowerPrinting", l) : Cat, MonStgElt, BoolElt ->
HasAttribute(ModMPol, "MatrixPrinting", l) : Cat, MonStgElt, BoolElt ->
HasAttribute(F, "PowerPrinting") : FldFin, MonStgElt -> BoolElt, BoolElt
HasAttribute(A, s) : GrpAuto, MonStgElt -> BoolElt, .
HasAttribute(A, "GenWeights") : GrpAuto, MonStgElt -> BoolElt, [ RngIntElt ]
HasAttribute(A, "WeightSubgroupOrders") : GrpAuto, MonStgElt -> BoolElt, [ RngIntElt ]
HasAttribute(G, "IsVerified") : GrpMat, MonStgElt -> BoolElt
HasAttribute(G, "Base") : GrpMat, MonStgElt -> BoolElt, Tup
HasAttribute(G, "Order") : GrpMat, MonStgElt -> RngIntElt
HasAttribute(M, "MatrixPrinting") : ModMPol, MonStgElt -> BoolElt, BoolElt
HasAttribute(S, "Precision") : RngSer, MonStgElt -> BoolElt, RngIntElt
SetPowerPrinting(F, l) : FldFin, BoolElt ->
Attribute (CHARACTERS OF FINITE GROUPS)
Attribute Access (BINARY QUADRATIC FORMS)
Attributes (FUNCTIONS, PROCEDURES AND PACKAGES)
Attributes (INTRODUCTION [BASIC RINGS])
Class Polynomials (MODULAR CURVES)
Defining Values for Attributes (MATRIX GROUPS)
Defining Values for Attributes (PERMUTATION GROUPS)
Invariants (MODULAR CURVES)
Modular Polynomial Databases (MODULAR CURVES)
GetAttributes(C) : Cat -> [ MonStgElt ]
ListAttributes(C) : Cat ->
RngInvar_Attributes (Example H80E15)
Attributes (CLASS FIELD THEORY)
Attributes of Invariant Rings (INVARIANT RINGS OF FINITE GROUPS)
Attributes of Lattices (LATTICES)
Attributes of Lattices (LATTICES)
Attributes of Orders and Ideals (QUATERNION ALGEBRAS)
Attributes of Quaternion Algebras (QUATERNION ALGEBRAS)
Basic Attributes (PLANE ALGEBRAIC CURVES)
Basic Attributes (SCHEMES)
Stored Attributes of an Automorphism Group (AUTOMORPHISM GROUPS OF GROUPS)
AugmentCode(C) : Code -> Code
Augmentation(a) : AlgGrpElt -> RngElt
AugmentationIdeal(A) : AlgGrp -> AlgGrpSub
AugmentationMap(A) : AlgGrp -> Map
AugmentationIdeal(A) : AlgGrp -> AlgGrpSub
AugmentationMap(A) : AlgGrp -> Map
AugmentCode(C) : Code -> Code
Aut(C) : Code -> Pow, Map
Aut(C, T) : Code, MonStgElt -> Pow, Map
Aut(C) : CrvHyp -> PowAutSch
Aut(D) : Inc -> PowMapAut, Map
Aut(P) : Prj -> PowAutSch
Aut(S) : Str -> PowMapAut
Scheme_aut-aff-jac (Example H83E22)
Scheme_aut-aff-perm (Example H83E23)
AutoCorrelation(S, t) : SeqEnum, RngIntElt -> RngIntElt
SetAutoColumns(b) : BoolElt ->
SetAutoCompact(b) : BoolElt ->
Automatic Printing (INPUT AND OUTPUT)
Automorphism Group and Isometry Testing (LATTICES)
AUTOMORPHISM GROUPS OF GROUPS
Design_auto (Example H98E11)
Automorphism Group and Isometry Testing (LATTICES)
GrpAuto_auto-maximals (Example H26E3)
Automatic Printing (INPUT AND OUTPUT)
IO_auto-print (Example H3E7)
Lat_AutoAction (Example H64E15)
PseudoRandom_autocorr_example (Example H103E3)
AutoCorrelation(S, t) : SeqEnum, RngIntElt -> RngIntElt
Lat_AutoDepth (Example H64E17)
GrpAuto_autogp-elts (Example H26E1)
AutomaticGroup(Q: parameters) : GrpFP -> GrpAtc
Automatic Coercion (INTRODUCTION [BASIC RINGS])
Automatic Group Predicates (AUTOMATIC GROUPS)
AUTOMATIC GROUPS
Magmas (or Structures) (OVERVIEW)
Automatic Group Predicates (AUTOMATIC GROUPS)
AutomaticGroup(Q: parameters) : GrpFP -> GrpAtc
GrpAtc_AutomaticGroup (Example H28E1)
Accessing Automata (AUTOMATIC GROUPS)
Automorphism(A,M) : Aff,Mtrx -> IsoSch
Automorphism(C,a) : CrvCon, AlgQuatElt -> MapIsoSch
Automorphism(E, [r, s, t, u]) : CrvEll, Seq -> Map
Automorphism(C,S,T) : CrvRat, SetIndx, SetIndx -> MapIsoSch
Automorphism(P,F) : Prj, SeqEnum -> MapSch
Automorphism(A,p) : Sch, RngMPolElt -> IsoSch
Automorphism(P,M) : Sch,Mtrx -> MapSch
Automorphism(X,F) : Sch,SeqEnum -> MapAutSch
Automorphism(A,F) : Sch,SeqEnum -> MapSch
AutomorphismGroup(C) : CrvHyp -> GrpPerm, Map, Map
AutomorphismGroup(A) : FldAb -> GrpFP, [Map], Map
AutomorphismGroup(F) : FldAlg -> GrpPerm, PowMap, Map
AutomorphismGroup(G): Grp -> GrpAuto
AutomorphismGroup(G, Q, I): Grp, SeqEnum[GrpElt], SeqEnum[SeqEnum[GrpElt]] -> GrpAuto
AutomorphismGroup(G): GrpPC -> GrpAuto
AutomorphismGroup(G): GrpPC -> GrpAuto
AutomorphismGroup(G): GrpPC -> GrpAuto
AutomorphismGroup(D) : Inc -> GrpPerm, GSet, GSet, PowMap, Map
AutomorphismGroup(D) : IncGeom -> GrpPerm
AutomorphismGroup(L) : Lat -> GrpMat
AutomorphismGroup(L, F) : Lat, [ AlgMatElt ] -> GrpMat
AutomorphismGroup(M) : ModRng -> AlgMat
AutomorphismGroup(P) : P -> GrpMat,Map
AutomorphismGroup(C: parameters) : Code -> GrpPerm, PowMap, Map
AutomorphismGroup( G: parameters) : Grph -> GrpPerm, GSet, GSet, PowMap, Map, Grph
AutomorphismGroup(G: parameters) : GrpPerm -> GrpAuto
AutomorphismGroup(L) : RngLoc -> GrpPerm, Map
AutomorphismGroup(F) : [ AlgMatElt ] -> GrpMat
AutomorphismGroupStabilizer(C, k) : Code, RngIntElt -> GrpPerm, PowMap, Map
AutomorphismGroupStabilizer(D, k) : Inc, RngIntElt -> GrpPerm, PowMap, Map
AutomorphismSubgroup(C) : Code -> GrpPerm, PowMap, Map
AutomorphismSubgroup(D) : Inc -> GrpPerm, PowMap, Map
CollineationGroup(P) : Plane -> GrpPerm, GSet, GSet, PowMap, Map
HadamardAutomorphismGroup(H) : AlgMatElt -> AlgMatElt
IdentityAutomorphism(A) : Sch -> AutSch
FlipCoordinates(A) : Sch -> AutSch
IdentityAutomorphism(X) : Sch -> MapAutSch
InducedAutomorphism(r, h, c) : Map, Map, RngIntElt -> Map
IsAutomorphism(f) : MapSch -> BoolElt,AutSch
NagataAutomorphism(A) : Aff -> MapSch
OrderAutomorphismGroupAbelianPGroup (A) : SeqEnum -> RngIntElt
PermutationAutomorphism(A,g) : Sch,GrpPermElt -> IsoSch
Automorphism Group (FINITE SOLUBLE GROUPS)
Automorphism Group (LINEAR CODES OVER FINITE FIELDS)
Automorphism Group Algorithm (p-GROUPS)
Automorphism Group of a Graph or Digraph (GRAPHS)
Automorphism Groups (ORDERS AND ALGEBRAIC FIELDS)
The Automorphism Group of an Incidence Structure (INCIDENCE STRUCTURES AND DESIGNS)
Design_automorphism (Example H98E12)
Scheme_automorphism-construction (Example H83E21)
Automorphism Group (FINITE SOLUBLE GROUPS)
Automorphism Group (LINEAR CODES OVER FINITE FIELDS)
Automorphism Group Algorithm (p-GROUPS)
The Automorphism Group of an Incidence Structure (INCIDENCE STRUCTURES AND DESIGNS)
Automorphism Group of a Graph or Digraph (GRAPHS)
CrvHyp_Automorphism_Group (Example H88E8)
The Automorphism Group (ELLIPTIC CURVES)
Graph_AutomorphismAction (Example H97E18)
AutomorphismGroup(C) : CrvHyp -> GrpPerm, Map, Map
AutomorphismGroup(A) : FldAb -> GrpFP, [Map], Map
AutomorphismGroup(F) : FldAlg -> GrpPerm, PowMap, Map
AutomorphismGroup(G): Grp -> GrpAuto
AutomorphismGroup(G, Q, I): Grp, SeqEnum[GrpElt], SeqEnum[SeqEnum[GrpElt]] -> GrpAuto
AutomorphismGroup(G): GrpPC -> GrpAuto
AutomorphismGroup(G): GrpPC -> GrpAuto
AutomorphismGroup(D) : Inc -> GrpPerm, GSet, GSet, PowMap, Map
AutomorphismGroup(D) : IncGeom -> GrpPerm
AutomorphismGroup(L) : Lat -> GrpMat
AutomorphismGroup(L, F) : Lat, [ AlgMatElt ] -> GrpMat
AutomorphismGroup(M) : ModRng -> AlgMat
AutomorphismGroup(P) : P -> GrpMat,Map
AutomorphismGroup(C: parameters) : Code -> GrpPerm, PowMap, Map
AutomorphismGroup( G: parameters) : Grph -> GrpPerm, GSet, GSet, PowMap, Map, Grph
AutomorphismGroup(G: parameters) : GrpPerm -> GrpAuto
AutomorphismGroup(L) : RngLoc -> GrpPerm, Map
AutomorphismGroup(F) : [ AlgMatElt ] -> GrpMat
CollineationGroup(P) : Plane -> GrpPerm, GSet, GSet, PowMap, Map
CodeFld_AutomorphismGroup (Example H101E44)
Graph_AutomorphismGroup (Example H97E16)
GrpPC_AutomorphismGroup (Example H24E26)
GrpPGp_AutomorphismGroup (Example H25E5)
MonomialGroupStabilizer(C, k) : Code, RngIntElt -> GrpPerm, PowMap, Map
AutomorphismGroupStabilizer(C, k) : Code, RngIntElt -> GrpPerm, PowMap, Map
AutomorphismGroupStabilizer(D, k) : Inc, RngIntElt -> GrpPerm, PowMap, Map
CodeFld_AutoMorphismGroupWithWeight (Example H101E45)
Automorphisms(F) : FldAlg -> [ Map ]
Automorphisms(L) : RngLoc -> [Map]
FrobeniusAutomorphisms(G) : GrpMat -> SeqEnum
GrpPerm_Automorphisms (Example H20E29)
RngOrd_Automorphisms (Example H48E20)
Affine Automorphisms (SCHEMES)
Automorphism Group and Correlation Group (INCIDENCE GEOMETRY)
Automorphism Groups (PERMUTATION GROUPS)
Automorphisms (CLASS FIELD THEORY)
Automorphisms (MODULAR CURVES)
Automorphisms (SCHEMES)
Endomorphisms and Automorphisms (MODULES OVER A MATRIX ALGEBRA)
Parametrized Structures (MODULAR CURVES)
Projective Automorphisms (SCHEMES)
MonomialSubgroup(C) : Code -> GrpPerm, PowMap, Map
AutomorphismSubgroup(C) : Code -> GrpPerm, PowMap, Map
AutomorphismSubgroup(D) : Inc -> GrpPerm, PowMap, Map
AutomorphousClasses(L,p) : Lat, RngIntElt -> RngIntElt
AutomorphousClasses(L,p) : Lat, RngIntElt -> RngIntElt
FrobeniusAutomosphism(A, p) : FldAb, RngOrdIdl -> Map
Automorphisms of Local Rings and Fields (LOCAL RINGS AND FIELDS)
Lat_AutoStabilizers (Example H64E16)
AuxiliaryLevel(M) : ModSS -> RngIntElt
AuxiliaryLevel(M) : ModSS -> RngIntElt
AlgGrp_average (Example H74E6)
[____] [____] [_____] [____] [__] [Index] [Root]