[____] [____] [_____] [____] [__] [Index] [Root]
Index L
AGammaL(arguments)
AffineGammaLinearGroup(arguments)
AffineSigmaLinearGroup(arguments)
ProjectiveGammaLinearGroup(arguments)
ProjectiveSigmaLinearGroup(arguments)
Special Values of L-functions (MODULAR SYMBOLS)
L
l
L
l
Special Values of L-functions (MODULAR SYMBOLS)
GrpFP_1_L372 (Example H19E58)
AssignLabel(G, i, l) : Grph, RngIntElt, . ->
AssignLabel(G, i, j, l) : Grph, RngIntElt, RngIntElt, . ->
AssignLabel(t, l) : GrphVert, . ->
CurrentLabel(p) : Process -> RngIntElt, RngIntElt
CurrentLabel(p) : Process -> RngIntElt, RngIntElt
CurrentLabel(p) : Process -> RngIntElt, RngIntElt, RngIntElt
DeleteLabel(G, i) : Grph, RngIntElt ->
DeleteLabel(G, i, j) : Grph, RngIntElt, RngIntElt ->
DeleteLabel(t) : GrphVert ->
EdgeLabel(G, i, j) : Grph, RngIntElt, RngIntElt -> .
Label(t) : GrphVert -> .
VertexLabel(G, i) : Grph, RngIntElt -> .
IsLabelled(t) : GrphVert -> BoolElt
IsLabelledEdge(G, i, j) : Grph, RngIntElt, RngIntElt -> BoolElt
IsLabelledVertex(G, i) : Grph, RngIntElt -> BoolElt
Labelling(G) : GrpPerm -> SetIndx
AssignLabels(G, S, L) : Grph, SeqEnum, SeqEnum ->
AssignLabels(G, S, L) : Grph, [RngIntElt], SeqEnum ->
AssignLabels(T, L) : GrphVertSet, SeqEnum ->
AssignLabels(S, L) : [GrphVert], SeqEnum ->
DeleteLabels(G, S) : Grph, SeqEnum ->
DeleteLabels(G, S) : Grph, [RngIntElt] ->
DeleteLabels(T) : GrphVertSet ->
DeleteLabels(S) : [GrphVert] ->
EdgeLabels(G) : Grph -> SeqEnum
EdgeLabels(G, S) : Grph, SeqEnum -> SeqEnum
EdgeLabels(s) : GrphSpl -> SeqEnum
Labels(T) : GrphVertSet -> SeqEnum
Labels(FS) : SymFry-> SeqEnum
Labels(S) : [GrphVert] -> SeqEnum
VertexLabels(G) : Grph -> SeqEnum
VertexLabels(G, S) : Grph, [RngIntElt] -> SeqEnum
VertexLabels(s) : GrphSpl -> SeqEnum
Graph_Labels (Example H97E8)
Labelled Graphs (GRAPHS)
Labels (MODULAR FORMS)
IsSimplyLaced( G ) : GrpLie-> BoolElt
IsSimplyLaced( RD ) : RootDtm-> BoolElt
LaguerrePolynomial(n) : RngIntElt -> RngUPolElt
LaguerrePolynomial(n) : RngIntElt -> RngUPolElt
CarmichaelLambda(n) : RngIntElt -> RngIntElt
FactoredCarmichaelLambda(n) : RngIntElt -> RngIntEltFact
Language (OVERVIEW)
Laplace(f) : RngSerElt -> RngSerElt
Matrix Groups of Large Degree (MATRIX GROUPS)
Orbit and Stabilizer Functions for Large Groups (MATRIX GROUPS)
Matrix Groups of Large Degree (MATRIX GROUPS)
WriteOverLargerField(G) : GrpMat -> GrpMat, GrpMat, GrpAb, SeqEnum
LargestConductor(D) : DB -> RngIntElt
LargestDimension(D) : DB -> RngIntElt
LargestDimension(D) : DB -> RngIntElt
LargestDimension(D): DB -> RngIntElt
LargestConductor(D) : DB -> RngIntElt
LargestDimension(D) : DB -> RngIntElt
LargestDimension(D) : DB -> RngIntElt
LargestDimension(D): DB -> RngIntElt
ColumnLength(t, j): Tbl,RngIntElt -> RnfIntElt
LastIndexOfColumn(t, j) : Tbl,RngIntElt -> RngIntElt
LastIndexOfRow(t, i) : Tbl,RngIntElt -> RngIntElt
ColumnLength(t, j): Tbl,RngIntElt -> RnfIntElt
LastIndexOfColumn(t, j) : Tbl,RngIntElt -> RngIntElt
RowLength(t, i) : Tbl,RngIntElt -> RngIntElt
LastIndexOfRow(t, i) : Tbl,RngIntElt -> RngIntElt
Modules (OVERVIEW)
Database of Lattices (LATTICES)
Lat_latdb (Example H64E24)
Lat_latdb-names (Example H64E23)
CoordinateLattice(L) : Lat -> Lat
DualBasisLattice(L) : Lat -> Lat
IsReverseLatticeWord(w) : MonOrdElt -> BoolElt
Lattice(C, "A") : Code -> Lat
Lattice(C, "B") : Code -> Lat
Lattice(D, i): DB, RngIntElt -> Lat
Lattice(D, i): DB, RngIntElt -> Lat, SeqEnum
Lattice(D, d, i): DB, RngIntElt, RngIntElt -> GrpMat
Lattice(D, d, i): DB, RngIntElt, RngIntElt -> GrpMat
Lattice(G) : GrpMat -> Lat
Lattice(X) : ModMatRngElt -> Lat
Lattice(X, M) : ModMatRngElt, AlgMatElt -> Lat
Lattice(M) : ModSym -> Lat
Lattice(X, n) : MonStgElt, RngIntElt -> Lat
Lattice(D, i: parameters): DB, RngIntElt -> Lattice
Lattice(f) : QuadBinElt -> Lat
Lattice(O) : RngOrd -> Lat, Map
Lattice(I) : RngOrdIdl -> Lat, Map
LatticeData(D, i): DB, RngIntElt -> Rec
LatticeDatabase() : -> DB
LatticeName(D, i): DB, RngIntElt -> MonStgElt, RngIntElt
LatticeWithBasis(G, B) : GrpMat, ModMatRngElt -> Lat
LatticeWithBasis(G, B, M) : GrpMat, ModMatRngElt, AlgMatElt -> Lat
LatticeWithBasis(B) : ModMatRngElt -> Lat
LatticeWithBasis(B, M) : ModMatRngElt, AlgMatElt -> Lat
LatticeWithGram(F) : AlgMatElt -> Lat
LatticeWithGram(G, F) : GrpMat, AlgMatElt -> Lat
MinkowskiLattice(O) : RngOrd -> Lat, Map
MinkowskiLattice(I) : RngOrdIdl -> Lat, Map
NormalLattice(G) : GrpFin -> NormalLattice
NormalLattice(G) : GrpPC -> SubGrpLat
NormalLattice(G) : GrpPerm -> SubGrpLat
PureLattice(L) : Lat -> Lat
ScaledLattice(L,n) : Lat, RngIntElt -> Lat
SquareLatticeGraph(n) : RngIntElt -> GrphUnd
StandardLattice(n) : RngIntElt -> Lat
SubfieldLattice(K) : FldNum -> SubFldLat
SubgroupLattice(G) : GrpFin -> SubGrpLat
SubgroupLattice(G) : GrpPC -> SubGrpLat
SubmoduleLattice(M) : ModRng -> SubModLat, BoolElt
SubmoduleLatticeAbort(M, n) : ModRng, RngIntElt -> BoolElt, SubModLat
WeightLattice( G ) : RootDtm -> Lat
WeightLattice( RD ) : RootDtm -> Lat
WeightLattice( W ) : RootDtm -> Lat
WindingLattice(M, j : parameters) : ModSym, RngIntElt -> Lat
Attributes of Lattices (LATTICES)
Lattice of Submodules (MODULES OVER A MATRIX ALGEBRA)
LATTICES
Modules (OVERVIEW)
Operations on Lattice Elements (MODULES OVER A MATRIX ALGEBRA)
Predicates and Booleans on Lattices (LATTICES)
Properties of Lattice Elements (MODULES OVER A MATRIX ALGEBRA)
Properties of Lattices (LATTICES)
The Subfield Lattice (ORDERS AND ALGEBRAIC FIELDS)
Attributes of Lattices (LATTICES)
Operations on Lattice Elements (MODULES OVER A MATRIX ALGEBRA)
Properties of Lattice Elements (MODULES OVER A MATRIX ALGEBRA)
Predicates and Booleans on Lattices (LATTICES)
BaseChange(L, S) : Lat, Rng -> Lat, Map
BaseExtend(L, S) : Lat, Rng -> Lat, Map
Properties of Lattices (LATTICES)
Lat_LatticeCreate (Example H64E1)
LatticeData(D, i): DB, RngIntElt -> Rec
LatticeDatabase() : -> DB
Lat_LatticeFunctions (Example H64E4)
LatticeName(D, i): DB, RngIntElt -> MonStgElt, RngIntElt
Grp_LatticeOperations (Example H16E17)
ModAlg_LatticeOps (Example H77E10)
NumberOfGroups(D) : DB -> RngIntElt
NumberOfLattices(D) : DB -> RngIntElt
# D : DB -> RngIntElt
# D : DB -> RngIntElt
# D: DB -> RngIntElt
NumberOfGroups(D, d) : DB, RngIntElt -> RngIntElt
NumberOfGroups(D, d) : DB, RngIntElt -> RngIntElt
NumberOfLattices(D, N): DB, MonStgElt -> RngIntElt
NumberOfLattices(D, d): DB, RngIntElt -> RngIntElt
Lattices from Matrix Groups (LATTICES)
Operations on Lattices (MODULES OVER A MATRIX ALGEBRA)
Special Lattices (LATTICES)
LatticeWithBasis(G, B) : GrpMat, ModMatRngElt -> Lat
LatticeWithBasis(G, B, M) : GrpMat, ModMatRngElt, AlgMatElt -> Lat
LatticeWithBasis(B) : ModMatRngElt -> Lat
LatticeWithBasis(B, M) : ModMatRngElt, AlgMatElt -> Lat
LatticeWithGram(F) : AlgMatElt -> Lat
LatticeWithGram(G, F) : GrpMat, AlgMatElt -> Lat
POWER, LAURENT AND PUISEUX SERIES
Rings, Fields, and Algebras (OVERVIEW)
LaurentSeriesRing(R) : Rng -> RngSerLaur
LaurentSeriesRing(R) : Rng -> RngSerLaur
ExponentLaw(~P : parameters) : Proc(pQuot) ->
LayerBoundary(G,i,j,k) : GrpPC, RngIntElt, RngIntElt, RngIntElt -> RngIntElt
LayerLength(G,i,j) : GrpPC, RngIntElt, RngIntElt -> RngIntElt
LayerBoundary(G,i,j,k) : GrpPC, RngIntElt, RngIntElt, RngIntElt -> RngIntElt
LayerLength(G,i,j) : GrpPC, RngIntElt, RngIntElt -> RngIntElt
LazyPowerSeriesRing(C, n) : Rng, RngIntElt -> RngPowLaz
LazySeries(R, f) : RngPowLaz, RngMPolElt -> RngPowLazElt
LAZY POWER SERIES RINGS
LazyPowerSeriesRing(C, n) : Rng, RngIntElt -> RngPowLaz
LazySeries(R, f) : RngPowLaz, RngMPolElt -> RngPowLazElt
Lcm(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
LeastCommonMultiple(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
LCM(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
LeastCommonMultiple(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
LCM(I, J) : RngOrdFracIdl, RngOrdFracIdl -> RngOrdFracIdl
LeastCommonMultiple(I, J) : RngOrdFracIdl, RngOrdFracIdl -> RngOrdFracIdl
LCM(Q) : [ RngMPolElt ] -> RngMPolElt
Lcm(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
LeastCommonMultiple(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
LeastCommonMultiple(m, n) : RngIntElt, RngIntElt -> RngIntElt
LCM(m, n) : RngIntElt, RngIntElt -> RngIntElt
LeastCommonMultiple(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
LCM(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
LeastCommonMultiple(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt
LCM(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt
LeastCommonMultiple(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
LCM(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
LeastCommonMultiple(Q) : Seq(RngIntResElt) -> RngIntResElt
LCM(Q) : Seq(RngIntResElt) -> RngIntResElt
LeastCommonMultiple(s) : [RngIntElt] -> RngIntElt
LCM(s) : [RngIntElt] -> RngIntElt
Lcm(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
LeastCommonMultiple(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
LCM(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
LCM(I, J) : RngOrdFracIdl, RngOrdFracIdl -> RngOrdFracIdl
Lcm(I, J) : RngFunOrdIdl, RngFunOrdIdl -> RngFunOrdIdl
Lcm(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
LeastCommonMultiple(m, n) : RngIntElt, RngIntElt -> RngIntElt
LeastCommonMultiple(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
LeastCommonMultiple(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt
LeastCommonMultiple(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
LeastCommonMultiple(Q) : Seq(RngIntResElt) -> RngIntResElt
LeastCommonMultiple(s) : [RngIntElt] -> RngIntElt
Common Divisors and Common Multiples (MULTIVARIATE POLYNOMIAL RINGS)
Common Divisors and Common Multiples (RING OF INTEGERS)
Common Divisors and Common Multiples (UNIVARIATE POLYNOMIAL RINGS)
HasComputableLCS(G) : GrpGPC -> BoolElt
Comparison (OVERVIEW)
u le v : AlgFPElt, AlgFPElt -> BoolElt
u le v : GrpFPElt, GrpFPElt -> BoolElt
s le t : MonStgElt, MonStgElt -> BoolElt
a le b : RngElt, RngElt -> BoolElt
S le T : SeqEnum, SeqEnum -> BoolElt
u le v : SgpFPElt, SgpFPElt -> BoolElt
e le f : SubGrpLatElt, SubGrpLatElt -> BoolElt
Coset Leaders (LINEAR CODES OVER FINITE FIELDS)
CosetLeaders(C) : Code -> {@ ModTupFldElt @}, Map
LSeriesLeadingCoefficient(M, j, prec) : ModSym, RngIntElt, RngIntElt -> FldPrElt, RngIntElt
LeadingCoefficient(u) : AlgFPElt -> RngElt
LeadingCoefficient(f) : RngMPolElt -> RngElt
LeadingCoefficient(f, i) : RngMPolElt, RngIntElt -> RngElt
LeadingCoefficient(s) : RngPowLazElt -> RngElt
LeadingCoefficient(f) : RngSerElt -> RngElt
LeadingCoefficient(f) : RngUPolElt -> RngElt
LeadingExponent(x) : GrpGPCElt -> RngIntElt
LeadingExponent(x) : GrpPCElt -> RngIntElt
LeadingGenerator(w) : GrpFPElt -> GrpFPElt
LeadingGenerator(x) : GrpGPCElt -> GrpGPCElt
LeadingGenerator(x) : GrpPCElt -> GrpPCElt
LeadingMonomial(f) : RngMPolElt -> RngMPolElt
LeadingMonomialIdeal(I) : RngMPol -> RngMPol
LeadingTerm(x) : GrpGPCElt -> GrpGPCElt
LeadingTerm(x) : GrpPCElt -> GrpPCElt
LeadingTerm(f) : RngMPolElt -> RngMPolElt
LeadingTerm(f, i) : RngMPolElt, RngIntElt -> RngMPolElt
LeadingTerm(s) : RngPowLazElt -> RngPowLazElt
LeadingTerm(f) : RngSerElt -> RngElt
LeadingTerm(p) : RngUPolElt -> RngUPolElt
LeadingTotalDegree(f) : RngMPolElt -> RngIntElt
LeadingWeightedDegree(f) : RngMPolElt -> RngIntElt
LeadingCoefficient(u) : AlgFPElt -> RngElt
LeadingCoefficient(f) : RngMPolElt -> RngElt
LeadingCoefficient(f, i) : RngMPolElt, RngIntElt -> RngElt
LeadingCoefficient(s) : RngPowLazElt -> RngElt
LeadingCoefficient(f) : RngSerElt -> RngElt
LeadingCoefficient(f) : RngUPolElt -> RngElt
LeadingExponent(x) : GrpGPCElt -> RngIntElt
LeadingExponent(x) : GrpPCElt -> RngIntElt
LeadingGenerator(w) : GrpFPElt -> GrpFPElt
LeadingGenerator(x) : GrpGPCElt -> GrpGPCElt
LeadingGenerator(x) : GrpPCElt -> GrpPCElt
LeadingMonomial(f) : RngMPolElt -> RngMPolElt
LeadingMonomialIdeal(I) : RngMPol -> RngMPol
LeadingTerm(x) : GrpGPCElt -> GrpGPCElt
LeadingTerm(x) : GrpPCElt -> GrpPCElt
LeadingTerm(f) : RngMPolElt -> RngMPolElt
LeadingTerm(f, i) : RngMPolElt, RngIntElt -> RngMPolElt
LeadingTerm(s) : RngPowLazElt -> RngPowLazElt
LeadingTerm(f) : RngSerElt -> RngElt
LeadingTerm(p) : RngUPolElt -> RngUPolElt
LeadingTotalDegree(f) : RngMPolElt -> RngIntElt
LeadingWeightedDegree(f) : RngMPolElt -> RngIntElt
Lcm(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
LeastCommonMultiple(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
LCM(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
LCM(I, J) : RngOrdFracIdl, RngOrdFracIdl -> RngOrdFracIdl
Lcm(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
LeastCommonMultiple(m, n) : RngIntElt, RngIntElt -> RngIntElt
LeastCommonMultiple(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
LeastCommonMultiple(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt
LeastCommonMultiple(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
LeastCommonMultiple(Q) : Seq(RngIntResElt) -> RngIntResElt
LeastCommonMultiple(s) : [RngIntElt] -> RngIntElt
Lcm(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
LeastCommonMultiple(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
LCM(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
LCM(I, J) : RngOrdFracIdl, RngOrdFracIdl -> RngOrdFracIdl
Lcm(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
LeastCommonMultiple(m, n) : RngIntElt, RngIntElt -> RngIntElt
LeastCommonMultiple(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
LeastCommonMultiple(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt
LeastCommonMultiple(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
LeastCommonMultiple(Q) : Seq(RngIntResElt) -> RngIntResElt
LeastCommonMultiple(s) : [RngIntElt] -> RngIntElt
LeeDistance(u, v) : ModTupRngElt, ModTupRngElt -> RngIntElt
LeeWeight(u) : ModTupRngElt -> RngIntElt
LeeWeight(v) : ModTupRngElt -> RngIntElt
LeeWeightEnumerator(C): Code -> RngMPolElt
Lee Weights (LINEAR CODES OVER FINITE RINGS)
Lat_Leech (Example H64E6)
LeeDistance(u, v) : ModTupRngElt, ModTupRngElt -> RngIntElt
LeeWeight(u) : ModTupRngElt -> RngIntElt
LeeWeight(v) : ModTupRngElt -> RngIntElt
LeeWeightEnumerator(C): Code -> RngMPolElt
CohomologyLeftModuleGenerators(P, CP, Q) : Tup, Tup, Tup -> Tup
IsLeftIdeal(S) : AlgGrpSub -> BoolElt
IsLeftIsomorphic(I,J) : AlgQuatOrd, AlgQuatOrd -> BoolElt, Map, AlgQuatElt
LeftAnnihilator(A, B) : AlgAss, AlgAss -> AlgAss, AlgAss
LeftAnnihilator(S) : AlgGrpSub -> AlgGrpSub
LeftConjugate(u, v) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
LeftConjugate(~u, v) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
LeftDescentSet( W, w ) : GrpCox, GrpPermElt -> { }
LeftDiv(u, v) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
LeftDiv(u, ~v) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
LeftExactExtension(C) : ModCpx -> ModCpx
LeftIdeal(S,X) : AlgQuatOrd, [AlgQuatOrdElt] -> AlgQuatOrd
LeftIdealClasses(S) : AlgQuatOrd -> [AlgQuatOrd]
LeftIsomorphism(I,J) : AlgQuatOrd, AlgQuatOrd -> Map, AlgQuatElt
LeftOrder(I) : AlgQuatOrd -> AlgQuatOrd
LeftString( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LeftStringLength( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LeftZeroExtension(C) : ModCpx -> ModCpx
MaximalLeftIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MinimalLeftIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
RightCosetSpace(P) : GrpFPCosetEnumProc -> GrpFPCos
RightCosetSpace(G, H: parameters) : GrpFP, GrpFP -> GrpFPCos
AlgQuat_Left_Right_Isomorphisms (Example H72E12)
LeftAnnihilator(A, B) : AlgAss, AlgAss -> AlgAss, AlgAss
LeftAnnihilator(S) : AlgGrpSub -> AlgGrpSub
LeftConjugate(u, v) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
LeftConjugate(~u, v) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
LeftCosetSpace(P) : GrpFPCosetEnumProc -> GrpFPCos
RightCosetSpace(P) : GrpFPCosetEnumProc -> GrpFPCos
RightCosetSpace(G, H: parameters) : GrpFP, GrpFP -> GrpFPCos
LeftDescentSet( W, w ) : GrpCox, GrpPermElt -> { }
LeftDiv(u, v) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
LeftDiv(u, ~v) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
LeftExactExtension(C) : ModCpx -> ModCpx
lideal<S | X> : AlgQuatOrd, [AlgQuatOrdElt] -> AlgQuatOrd
LeftIdeal(S,X) : AlgQuatOrd, [AlgQuatOrdElt] -> AlgQuatOrd
LeftIdealClasses(S) : AlgQuatOrd -> [AlgQuatOrd]
LeftIsomorphism(I,J) : AlgQuatOrd, AlgQuatOrd -> Map, AlgQuatElt
LeftOrder(I) : AlgQuatOrd -> AlgQuatOrd
LeftString( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LieConstant_p( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LeftStringLength( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LeftZeroExtension(C) : ModCpx -> ModCpx
LegendreModel(C) : CrvCon -> CrvCon, MapIsoSch
LegendrePolynomial(C) : CrvCon -> RngMPolElt, ModMatRngElt
LegendrePolynomial(n) : RngIntElt -> RngUPolElt
LegendreSymbol(n, m) : RngIntElt, RngIntElt -> RngIntElt
ReducedLegendreModel(C) : CrvCon -> CrvCon, MapIsoSch
ReducedLegendrePolynomial(C) : CrvCon -> RngMPolElt, ModMatRngElt
LegendreModel(C) : CrvCon -> CrvCon, MapIsoSch
LegendrePolynomial(C) : CrvCon -> RngMPolElt, ModMatRngElt
LegendrePolynomial(n) : RngIntElt -> RngUPolElt
LegendreSymbol(n, m) : RngIntElt, RngIntElt -> RngIntElt
AtkinLehner(M, q) : ModSym, RngIntElt -> AlgMatElt
AtkinLehnerOperator(M, p) : ModBrdt, RngIntElt -> AlgMatElt
AtkinLehnerOperator(M, q) : ModFrm, RngIntElt -> AlgMatElt
AtkinLehnerOperator(M, q) : ModSS, RngIntElt -> AlgMatElt
CanonicalInvolution(X) : CrvMod -> MapSch
DualAtkinLehner(M, q) : ModSym, RngIntElt -> AlgMatElt
BestLengthLinearCode(K, k, d) : FldFin,RngIntElt,RngIntElt -> Code, BoolElt
BLLC(K, k, d) : FldFin,RngIntElt,RngIntElt -> Code, BoolElt
BasicOrbitLength(G, i) : GrpMat, RngIntElt -> RngIntElt
BasicOrbitLength(G, i) : GrpPerm, RngIntElt -> RngIntElt
ColumnSkewLength(t, j) : Tbl,RngIntElt -> RngIntElt
DerivedLength(G) : GrpAb -> RngIntElt
DerivedLength(G) : GrpFin -> RngIntElt
DerivedLength(G) : GrpGPC -> RngIntElt
DerivedLength(G) : GrpMat -> RngIntElt
DerivedLength(G) : GrpPC -> RngIntElt
DerivedLength(G) : GrpPerm -> RngIntElt
FittingLength(G) : GrpGPC -> RngIntElt
GriesmerLengthBound(K, k, d) : FldFin,RngIntEt,RngIntElt -> RngIntElt
HookLength(t, i, j) : Tbl, RngIntElt, RngIntElt -> RngIntElt
LastIndexOfColumn(t, j) : Tbl,RngIntElt -> RngIntElt
LastIndexOfRow(t, i) : Tbl,RngIntElt -> RngIntElt
LayerLength(G,i,j) : GrpPC, RngIntElt, RngIntElt -> RngIntElt
LeftStringLength( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
Length(C) : Code -> RngIntElt
Length(C) : Code -> RngIntElt
Length(a) : FldAlgElt -> FldPrElt
Length( W, w ) : GrpCox, GrpPermElt -> RngIntElt
Length(v, K) : LatElt, Fld -> FldReElt
Length(w) : MonOrdElt -> RngIntElt
Length(u) : MonPlcElt -> RngIntElt
Length(f) : RngMPolElt -> RngIntElt
Length(e) : SubGrpLatElt -> RngIntElt
MinorLength(G,i) : GrpPC, RngIntElt -> RngIntElt
NilpotentLength(G) : GrpPC -> RngIntElt
NumberOfCoordinates(X) : Sch -> RngIntElt
PresentationLength(G) : GrpFP -> RngIntElt
PresentationLength(P) : Process(Tietze) -> RngIntElt
RightStringLength( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
RowSkewLength(t, i) : Tbl,RngIntElt -> RngIntElt
SimplifyLength(G: parameters) : GrpFP -> GrpFP
SimplifyLength(~P : parameters) : Process(Tietze) ->
Position(s, t) : MonStgElt, MonStgElt -> RngIntElt
Integer-Valued Functions (INPUT AND OUTPUT)
Sequences (OVERVIEW)
The Length of a Word (FINITELY PRESENTED SEMIGROUPS)
Position(s, t) : MonStgElt, MonStgElt -> RngIntElt
Integer-Valued Functions (INPUT AND OUTPUT)
LengthenCode(C) : Code -> Code
LengthenCode(C) : Code -> Code
BasicOrbitLengths(G) : GrpMat -> [RngIntElt]
BasicOrbitLengths(G) : GrpPerm -> [RngIntElt]
Lengths(X) : Sch -> [RngIntElt]
Comparison (OVERVIEW)
AuxiliaryLevel(M) : ModSS -> RngIntElt
Level(S) : AlgQuatOrd -> RngIntElt
Level(X) : CrvMod -> RngIntElt
Level(G) : GrpPSL2 -> RngIntElt
Level(M) : ModBrdt -> RngIntElt
Level(M) : ModFrm -> RngIntElt
Level(f) : ModFrmElt -> RngIntElt
Level(M) : ModSS -> RngIntElt
SetDisplayLevel(~P, Level) : Process(pQuot), RngIntElt ->
SetPrintLevel(l) : MonStgElt ->
Degeneracy Maps (MODULAR SYMBOLS)
Low Level Operations on Presentations and Words (FP GROUPS - ADVANCED FEATURES)
Low Level Operations on Words (FP GROUPS - ADVANCED FEATURES)
LevenshteinBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
LevenshteinBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
HasLeviSubalgebra(L) : AlgLie -> BoolElt
LexProduct(G, H) : GrphDir, GrphDir -> GrphDir
Lexicographical: lex (IDEAL THEORY AND GRÖBNER BASES)
LexicographicalOrdering(~w1, ~w2) : MonOrdElt, MonOrdElt ->
IsLexicographicallyOrdered(w1, w2) : MonOrdElt, MonOrdElt -> boolean
LexicographicalOrdering(~w1, ~w2) : MonOrdElt, MonOrdElt ->
LexProduct(G, H) : GrphDir, GrphDir -> GrphDir
Linear Feedback Shift Registers (PSEUDO-RANDOM BIT SEQUENCES)
LFSRSequence(C, S, t) : RngUPolElt, SeqEnum, RngIntElt -> SeqEnum
LFSRStep(C, S) : RngUPolElt, SeqEnum -> SeqEnum
LHS(r) : Rel -> AlgFPElt
LHS(r) : Rel -> SgpFPElt
r[1] : GrpAbRel, RngIntElt -> GrpAbElt
r[1] : GrpFPRel, RngIntElt -> GrpFPElt
MAGMA_LIBRARIES
GetLibraries() : -> MonStgElt
SetLibraries(s) : MonStgElt ->
Databases of Structure Definitions (OVERVIEW)
Libraries of Functions in the Magma Language (OVERVIEW)
GetLibraryRoot() : -> MonStgElt
SetLibraryRoot(s) : MonStgElt ->
Databases of Structure Definitions (OVERVIEW)
Libraries of Functions in the Magma Language (OVERVIEW)
MAGMA_LIBRARY_ROOT
TateLichtenbaumPairing(D1, D2, m) : DivFunElt, DivFunElt, RngIntElt -> RngElt
Constructor (OVERVIEW)
LeftIdeal(S,X) : AlgQuatOrd, [AlgQuatOrdElt] -> AlgQuatOrd
lideal< cat : A | L> : Cat, AlgGrp, List -> AlgGrp, Map
lideal<A | L_1, ..., L_r> : AlgFP, AlgFPElt, ..., AlgFPElt -> AlgFP
lideal< A | L > : AlgGen, List -> AlgGen, Map
lideal<R | L> : AlgMat, List -> AlgMatIdeal
lideal<G | L_1, ..., L_r> : SgpFP, SgpFPElt, ..., SgpFPElt -> SgpFPIdl
LieConstant_A( RD, r, s) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
CartanInteger( RD, r, s) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
GroupOfLieType( C, R ) : AlgMatElt, Rng -> AlgMatElt
GroupOfLieType( W, R ) : GrpCox, Rng -> AlgMatElt
GroupOfLieType( n, R ) : MonStgElt, Rng -> AlgMatElt
GroupOfLieType( RD, R ) : RootDtm, Rng -> AlgMatElt
GroupOfLieType( RD, k ) : RootDtm, Rng -> GrpLie
GroupOfLieType( W, R ) : RootDtm, Rng -> GrpLie
IsLie(A) : AlgGen -> BoolElt
IsRestrictedLieAlgebra(L) : AlgLie -> BoolElt
LeftStringLength( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
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
LieBracket(a, b) : AlgAssElt, AlgAssElt -> AlgAssElt
LieConstant_epsilon( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LieConstant_eta( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LieConstant_N( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LieConstant_M( RD, r, s, i ) : RootDtm, RngIntElt, RngIntElt, RngIntElt -> RngIntElt
LieConstant_C( RD, i, j, r, s ) : RootDtm, RngIntElt, RngIntElt, RngIntElt, RngIntElt -> RngIntElt
RightStringLength( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
SemiSimpleLieAlgebra(X, F) : MonStgElt, Fld -> AlgLie
SimpleLieAlgebra(X, n, F) : MonStgElt, RngIntElt, Fld -> AlgLie
GROUPS OF LIE TYPE
AlgAss_liealg (Example H71E1)
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
AlgLie_LieAlgebra (Example H76E13)
(a, b) : AlgAssElt, AlgAssElt -> AlgAssElt
LieBracket(a, b) : AlgAssElt, AlgAssElt -> AlgAssElt
LieConstant_A( RD, r, s) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
CartanInteger( RD, r, s) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LeftStringLength( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LieConstant_epsilon( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LieConstant_eta( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LieConstant_N( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LieConstant_M( RD, r, s, i ) : RootDtm, RngIntElt, RngIntElt, RngIntElt -> RngIntElt
LieConstant_C( RD, i, j, r, s ) : RootDtm, RngIntElt, RngIntElt, RngIntElt, RngIntElt -> RngIntElt
RightStringLength( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
HenselLift(g, r) : RngUPolElt, RngLocElt -> RngLocElt
HenselLift(g, r) : RngUPolElt, RngLocElt -> RngLocElt
HenselLift(g, r) : RngUPolElt, RngLocElt -> RngLocElt
HenselLift(f, g, h) : RngUPolElt, RngUPolElt, RngUPolElt -> RngUPolElt, RngUPolElt
HenselLift(f, g, h) : RngUPolElt, RngUPolElt, RngUPolElt -> RngUPolElt, RngUPolElt
HenselLift(f, s, P) : RngUPolElt, [ RngUPolElt ], RngUPol -> [ RngUPolElt ]
Lift(a, P) : RngElt, PlcFunElt -> FldFunElt
Lift(a, P) : RngElt, PlcFunElt -> FldFunElt
LiftCharacter(x, f, G) : AlgChtrElt, MapHom, Grp -> AlgChtrElt
LiftCharacters(T, f, G) : AlgChtrElt, MapHom, Grp -> AlgChtrElt
LiftHomomorphism(x, n) : ModAlgElt, RngIntElt -> ModMatFldElt
LiftHomomorphism(X, S) : SeqEnum[ModAlgElt], SeqEnum[RngIntElt] -> ModMatFldElt
LiftNonsplitExtension(SQP, p, i, k : parameters) : SQProc, RngIntElt, RngIntElt, RngIntElt -> RngIntElt, SQProc
LiftNonsplitExtensionRow(SQP, p, l) : SQProc, RngIntElt, RngIntElt -> RngIntElt, SQProc
LiftSplitExtension(SQP, p, i, k : parameters) : SQProc, RngIntElt, RngIntElt, RngIntElt -> RngIntElt, SQProc
LiftSplitExtensionRow(SQP): SQProc -> RngIntElt, SQProc
SubgroupsLift(G, A, B, Q: parameters) : GrpPerm, GrpPerm, GrpPerm, SeqEnum -> SeqEnum
Extension(x, f, G) : AlgChtrElt, MapHom, Grp -> AlgChtrElt
LiftCharacter(x, f, G) : AlgChtrElt, MapHom, Grp -> AlgChtrElt
Extension(T, f, G) : AlgChtrElt, MapHom, Grp -> AlgChtrElt
LiftCharacters(T, f, G) : AlgChtrElt, MapHom, Grp -> AlgChtrElt
LiftHomomorphism(x, n) : ModAlgElt, RngIntElt -> ModMatFldElt
LiftHomomorphism(X, S) : SeqEnum[ModAlgElt], SeqEnum[RngIntElt] -> ModMatFldElt
Lifting a Quotient (FP GROUPS - ADVANCED FEATURES)
Lifting a Quotient (FP GROUPS - ADVANCED FEATURES)
LiftNonsplitExtension(SQP, p, i, k : parameters) : SQProc, RngIntElt, RngIntElt, RngIntElt -> RngIntElt, SQProc
LiftNonsplitExtensionRow(SQP, p, l) : SQProc, RngIntElt, RngIntElt -> RngIntElt, SQProc
LiftSplitExtension(SQP, p, i, k : parameters) : SQProc, RngIntElt, RngIntElt, RngIntElt -> RngIntElt, SQProc
LiftSplitExtensionRow(SQP): SQProc -> RngIntElt, SQProc
Q as a Number Field (RING OF INTEGERS)
MAGMA_MEMORY_LIMIT
GetMemoryLimit() : -> RngIntElt
SetMemoryLimit(n) : RngIntElt ->
SmallGroupDatabaseLimit() : -> RngIntElt
TransitiveGroupDatabaseLimit() : -> RngIntElt
Limits (FINITELY PRESENTED ALGEBRAS)
Linear Algebra (LOCAL RINGS AND FIELDS)
Linear Algebra (p-ADIC RINGS AND FIELDS)
LINEAR PROGRAMMING
Linear Algebra (LOCAL RINGS AND FIELDS)
Linear Algebra (p-ADIC RINGS AND FIELDS)
LINEAR PROGRAMMING
IsSubsystem(L,K) : LinSys,LinSys -> BoolElt
Basic Algebra of Linear Systems (SCHEMES)
IsLineRegular(D) : IncNsp -> BoolElt, RngIntElt
IsLineTransitive(P) : Plane -> BoolElt
Line(C,p,q) : Crv, Pt,Pt -> Crv
Line(D, p, q) : Inc, IncPt, IncPt -> IncBlk
LineAtInfinity(A) : Aff -> Crv
LineGraph(G) : Grph -> Grph
LineGraph(P) : Plane -> Grph
LineGraph(P) : Plane -> GrphUnd
LineGroup(P) : Plane -> GrpPerm, PowMap, Map
LineOrbits(G) : GrpMat -> [ SetIndx ]
LineSet(P) : Plane -> PlaneLnSet
SetLineEditor(b) : BoolElt ->
TangentLine(p) : Crv,Pt -> Crv
Combinatorial and Geometrical Structures (OVERVIEW)
Constructing Complements, Line Graphs; Contraction, Switching (GRAPHS)
The Magma Line Editor (ENVIRONMENT AND OPTIONS)
The Point-Set and Line-Set of a Plane (FINITE PLANES)
The Set of Points and Set of Lines (FINITE PLANES)
Using the Point-Set and Line-Set to Create Points and Lines (FINITE PLANES)
The Magma Line Editor (ENVIRONMENT AND OPTIONS)
AGammaL(arguments)
AffineGammaLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineSigmaLinearGroup(arguments)
AffineSpecialLinearGroup(arguments)
AffineSpecialLinearGroup(arguments)
AffineSpecialLinearGroup(arguments)
BDLC(K, n, d) : FldFin,RngIntElt,RngIntElt -> Code
BKLC(K, n, k) : FldFin,RngIntElt,RngIntElt -> Code
BLLC(K, k, d) : FldFin,RngIntElt,RngIntElt -> Code, BoolElt
GeneralLinearGroup(arguments)
GeneralLinearGroup(n, R) : RngIntElt, Rng -> GrpMat
GilbertVarshamovLinearBound(K, n, d) : FldFin,RngIntElt,RngIntElt -> RngIntElt
HasLinearGrayMapImage(C) : Code -> BoolElt, Code
IsAffineLinear(f) : MapSch -> BoolElt
IsLinear(x) : AlgChtrElt -> BoolElt
IsLinear(f) : MapSch -> BoolElt
IsLinearGroup(G) : GrpMat -> BoolElt
IsLinearSpace(D) : Inc -> BoolElt
IsNearLinearSpace(D) : Inc -> BoolElt
IsSemiLinear(G) : GrpMat -> BoolElt
LinearCharacters(G): Grp -> SeqEnum
LinearCharacters(G) : GrpMat -> [ Chtr ]
LinearCode(C, S) : Code, FldFin -> Code, Map
LinearCode<R, n | L> : FldFin, RngIntElt, List -> Code
LinearCode(D, K) : Inc, FldFin -> Code
LinearCode(A) : ModMatRngElt -> Code
LinearCode(A) : ModMatRngElt -> Code
LinearCode(U) : ModTupRng -> Code
LinearCode(U) : ModTupRng -> Code
LinearCode(P, K) : Plane, FldFin -> Code
LinearCode<R, n | L> : Rng, RngIntElt, List -> Code
LinearRelation(q: parameters) : [ FldPrElt ] -> [ RngIntElt ]
LinearSpace(I) : Inc -> IncLsp
LinearSpace< v | X : parameters > : RngIntElt, List -> IncLsp
LinearSystem(L,V) : LinSys,ModTupFld -> LinSys
LinearSystem(L,p) : LinSys,Pt -> LinSys
LinearSystem(L,p,m) : LinSys,Pt,RngIntElt -> LinSys
LinearSystem(L,X) : LinSys,Sch -> LinSys
LinearSystem(L,F) : LinSys,SeqEnum -> LinSys
LinearSystem(P,d) : Prj,RngIntElt -> LinSys
LinearSystem(P,F) : Prj,SeqEnum -> LinSys
LinearSystemTrace(L,X) : LinearSys,Sch -> LinearSys
NearLinearSpace(I) : Inc -> IncNsp
NearLinearSpace< v | X : parameters > : RngIntElt, List -> IncNsp
ProjectiveGammaLinearGroup(arguments)
ProjectiveGeneralLinearGroup(arguments)
ProjectiveSigmaLinearGroup(arguments)
ProjectiveSpecialLinearGroup(arguments)
RandomLinearCode(K, n, k) : FldFin, RngIntElt, RngIntElt -> Code
SemiLinearGroup(G, S) : GrpMat, FldFin -> GrpMat
SpecialLinearGroup(arguments)
Creation of a Matrix Group (MATRIX GROUPS)
General and Special Linear Groups (MATRIX GROUPS)
Linear Algebra (SCHEMES)
LINEAR CODES OVER FINITE FIELDS
LINEAR CODES OVER FINITE RINGS
Linear Equivalence of Divisors (PLANE ALGEBRAIC CURVES)
Modules (OVERVIEW)
Operations with Linear Transformations (VECTOR SPACES)
Permutation Representations of Linear Groups (PERMUTATION GROUPS)
VECTOR SPACES
IsSubsystem(L,K) : LinSys,LinSys -> BoolElt
Linear Algebra (SCHEMES)
Linear Equivalence of Divisors (PLANE ALGEBRAIC CURVES)
PSz(arguments)
Permutation Representations of Linear Groups (PERMUTATION GROUPS)
Modules (OVERVIEW)
Operations with Linear Transformations (VECTOR SPACES)
LinearCharacters(G): Grp -> SeqEnum
LinearCharacters(G) : GrpMat -> [ Chtr ]
LinearCode(C, S) : Code, FldFin -> Code, Map
LinearCode<R, n | L> : FldFin, RngIntElt, List -> Code
LinearCode(D, K) : Inc, FldFin -> Code
LinearCode(A) : ModMatRngElt -> Code
LinearCode(A) : ModMatRngElt -> Code
LinearCode(U) : ModTupRng -> Code
LinearCode(U) : ModTupRng -> Code
LinearCode(P, K) : Plane, FldFin -> Code
LinearCode<R, n | L> : Rng, RngIntElt, List -> Code
CrvEll_LinearIndependence (Example H87E20)
IsLinearlyEquivalent(D1,D2) : DivCrvElt,DivCrvElt -> BoolElt
IsLinearlyIndependent(P, Q) : PtEll, PtEll -> BoolElt, ModTupElt
IsLinearlyIndependent(P, Q, n) : PtEll, PtEll, RngIntElt -> BoolElt
IsLinearlyIndependent(S) : [ PtEll ] -> BoolElt, ModTupElt
IsLinearlyIndependent(S, n) : [ PtEll ], RngIntElt -> BoolElt
LinearRelation(q: parameters) : [ FldPrElt ] -> [ RngIntElt ]
LinearSpace(I) : Inc -> IncLsp
LinearSpace< v | X : parameters > : RngIntElt, List -> IncLsp
LinearSystem(L,V) : LinSys,ModTupFld -> LinSys
LinearSystem(L,p) : LinSys,Pt -> LinSys
LinearSystem(L,p,m) : LinSys,Pt,RngIntElt -> LinSys
LinearSystem(L,X) : LinSys,Sch -> LinSys
LinearSystem(L,F) : LinSys,SeqEnum -> LinSys
LinearSystem(P,d) : Prj,RngIntElt -> LinSys
LinearSystem(P,F) : Prj,SeqEnum -> LinSys
LinearSystemTrace(L,X) : LinearSys,Sch -> LinearSys
ModFld_LinearTrans (Example H61E14)
LineAtInfinity(A) : Aff -> Crv
IO_LineCount (Example H3E9)
LineGraph(G) : Grph -> Grph
LineGraph(P) : Plane -> Grph
LineGraph(P) : Plane -> GrphUnd
LineGroup(P) : Plane -> GrpPerm, PowMap, Map
LineOrbits(G) : GrpMat -> [ SetIndx ]
AllPassants(P, A) : Plane, { PlanePt } -> { PlaneLn }
ExternalLines(P, A) : Plane, { PlanePt } -> { PlaneLn }
Lines(P) : PlaneLnSet -> { PlaneLn }
NumberOfLines(P) : Plane -> RngIntElt
LineSet(P) : Plane -> PlaneLnSet
Linking(u,v) : GrphSplVert,GrphSplVert -> RngIntElt
LinkingNumbers(s) : GrphSpl -> SeqEnum
TotalLinking(v) : GrphSplVert -> RngIntElt
LinkingNumbers(s) : GrphSpl -> SeqEnum
IsSubsystem(L,K) : LinSys,LinSys -> BoolElt
Basic Algebra of Linear Systems (SCHEMES)
Creation of Linear Systems (SCHEMES)
Linear Systems (SCHEMES)
Linear Systems (SCHEMES)
Linear Systems and Maps (SCHEMES)
Scheme_linsys-construction (Example H83E29)
Creation of Linear Systems (SCHEMES)
IsSubsystem(L,K) : LinSys,LinSys -> BoolElt
Basic Algebra of Linear Systems (SCHEMES)
Linear Systems and Maps (SCHEMES)
VanLintBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
ListAttributes(C) : Cat ->
ListCategories() : ->
ListSignatures(C) : Cat ->
ListVerbose() : ->
SequenceToList(Q) : SeqEnum -> List
TupleToList(T) : Tup -> List
TupleToList(T) : Tup -> List
Elimination List: elim (IDEAL THEORY AND GRÖBNER BASES)
LISTS
ListAttributes(C) : Cat ->
ListTypes() : ->
ListCategories() : ->
ListSignatures(C) : Cat ->
ListTypes() : ->
ListCategories() : ->
ListVerbose() : ->
Literal Sequences (SEQUENCES)
a_1a_2...a_r : RngIntElt, ..., RngIntElt -> RngIntElt
IsLittlewoodRichardson(t) : Tbl -> BoolElt
GrpFP_1_Lix1 (Example H19E36)
GrpFP_1_Lix2 (Example H19E37)
GrpFP_1_Lix3 (Example H19E38)
GrpFP_1_Lix4 (Example H19E39)
GrpFP_1_Lix5 (Example H19E40)
SIntegralLjunggrenPoints(Q, S) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]
LLL Reduction (LATTICES)
LLL(L) : Lat -> Lat, AlgMatElt
LLL(X) : ModMatRngElt -> ModMatRngElt, AlgMatElt, RngIntElt
LLL(O) : RngOrd -> RngOrd, AlgMatElt
RngOrd_lll (Example H48E10)
LLLBasisMatrix(L) : Lat -> ModMatElt, AlgMatElt
LLLBasisMatrix(L) : Lat -> ModMatElt, AlgMatElt
LLLGram(F) : ModMatRngElt -> ModMatRngElt, AlgMatElt, RngIntElt
LLLGramMatrix(L) : Lat -> AlgMatElt, AlgMatElt
LLLGramMatrix(L) : Lat -> AlgMatElt, AlgMatElt
Lat_LLLXGCD (Example H64E12)
Databases of Structure Definitions (OVERVIEW)
Libraries of Functions in the Magma Language (OVERVIEW)
Loading a Program File (INPUT AND OUTPUT)
Loading files (OVERVIEW)
load "filename";
loc< R | a_1, ..., a_r > : Rng, RngElt, ..., RngElt -> Rng, Map
AddLocalGenerators(X) : VSrfK3 -> VSrfK3
Completion(P, n) : RngOrdIdl, RngIntElt -> RngLoc, Map
IsLocalNorm(A, x) : FldAb, RngOrdElt -> BoolElt
IsLocalNorm(A, x, p) : FldAb, RngOrdElt, PlcNumElt -> BoolElt
IsLocalNorm(A, x, i) : FldAb, RngOrdElt, RngIntElt -> BoolElt
IsLocalNorm(A, x, p) : FldAb, RngOrdElt, RngOrdIdl -> BoolElt
LocalCoxeterGroup( H ) : GrpCox -> GrpCox, Map
LocalGenera(G) : SymGen -> Lat
LocalHeight(P, p) : PtEll, RngIntElt -> FldPrElt
LocalInformation(E, p) : CrvEll, RngIntElt -> <RngIntElt, RngIntElt, RngIntElt, RngIntElt, SymKod>
LocalInformation(E) : CrvEll, RngIntElt -> [ Tup ]
LocalRing(p, f, n) : RngIntElt, RngIntElt, RngIntElt -> RngLoc
LocalRing(p, f, g, n) : RngIntElt, RngIntElt, RngUPolElt, RngIntElt -> RngLoc
LocalRing(p, g, n) : RngIntElt, RngUPolElt, RngIntElt -> RngLoc
LocalRing(L, f, n) : RngLoc, RngIntElt -> RngLoc
LocalRing(L, g, n) : RngLoc, RngUPolElt, RngIntElt -> RngLoc
LocalRing(P, prec) : RngOrdIdl, RngIntElt -> RngLoc, Map
LocalUniformizer(P) : PlcFunElt -> FldFunGElt
Creation of Points on Curves (PLANE ALGEBRAIC CURVES)
Invariants of Curves over Q (ELLIPTIC CURVES)
Local Conditions for Conics (RATIONAL CURVES AND CONICS)
Local Declarations (MAGMA SEMANTICS)
Local Fields (LOCAL RINGS AND FIELDS)
Local Geometry (PLANE ALGEBRAIC CURVES)
Local Geometry of Schemes (SCHEMES)
Local Intersection Theory (PLANE ALGEBRAIC CURVES)
Local Rings (LOCAL RINGS AND FIELDS)
LOCAL RINGS AND FIELDS
Local--Global Correspondence (RATIONAL CURVES AND CONICS)
Norm Residue Symbol (RATIONAL CURVES AND CONICS)
Operations at a Point (PLANE ALGEBRAIC CURVES)
Local Geometry (PLANE ALGEBRAIC CURVES)
Local Declarations (MAGMA SEMANTICS)
Local Fields (LOCAL RINGS AND FIELDS)
Local Conditions for Conics (RATIONAL CURVES AND CONICS)
Local--Global Correspondence (RATIONAL CURVES AND CONICS)
Norm Residue Symbol (RATIONAL CURVES AND CONICS)
Local Intersection Theory (PLANE ALGEBRAIC CURVES)
Crv_local-intersection-example (Example H84E6)
Operations at a Point (PLANE ALGEBRAIC CURVES)
Creation of Points on Curves (PLANE ALGEBRAIC CURVES)
Local Rings (LOCAL RINGS AND FIELDS)
Invariants of p-adic genera (LATTICES)
LocalCoxeterGroup( H ) : GrpCox -> GrpCox, Map
LocalField(p, f, n) : RngIntElt, RngIntElt, RngIntElt -> FldLoc
LocalRing(p, f, n) : RngIntElt, RngIntElt, RngIntElt -> RngLoc
LocalRing(p, f, g, n) : RngIntElt, RngIntElt, RngUPolElt, RngIntElt -> RngLoc
LocalRing(p, g, n) : RngIntElt, RngUPolElt, RngIntElt -> RngLoc
LocalRing(L, f, n) : RngLoc, RngIntElt -> RngLoc
LocalRing(L, g, n) : RngLoc, RngUPolElt, RngIntElt -> RngLoc
LocalGenera(G) : SymGen -> Lat
CrvCon_LocalGlobal (Example H86E4)
LocalHeight(P, p) : PtEll, RngIntElt -> FldPrElt
LocalInformation(E, p) : CrvEll, RngIntElt -> <RngIntElt, RngIntElt, RngIntElt, RngIntElt, SymKod>
LocalInformation(E) : CrvEll, RngIntElt -> [ Tup ]
Localization(R, P) : Rng, Rng -> Rng, Map
Localization (INTRODUCTION [BASIC RINGS])
LocalRing(P, n) : RngOrdIdl, RngIntElt -> RngLoc, Map
Completion(P, n) : RngOrdIdl, RngIntElt -> RngLoc, Map
LocalRing(p, f, n) : RngIntElt, RngIntElt, RngIntElt -> RngLoc
LocalRing(p, f, g, n) : RngIntElt, RngIntElt, RngUPolElt, RngIntElt -> RngLoc
LocalRing(p, g, n) : RngIntElt, RngUPolElt, RngIntElt -> RngLoc
LocalRing(L, f, n) : RngLoc, RngIntElt -> RngLoc
LocalRing(L, g, n) : RngLoc, RngUPolElt, RngIntElt -> RngLoc
LocalRing(P, prec) : RngOrdIdl, RngIntElt -> RngLoc, Map
UniformizingElement(P) : PlcFunElt -> FldFunGElt
LocalUniformizer(P) : PlcFunElt -> FldFunGElt
Related Files (FUNCTIONS, PROCEDURES AND PACKAGES)
Locseq(x) : RngLoc -> [ [ RngLocElt ] ]
LocseqInert(x) : RngLoc -> [ RngLocElt ]
LocseqInert(x) : RngLoc -> [ RngLocElt ]
Log(x) : FldFinElt -> RngIntElt
Log(b, x) : FldFinElt, FldFinElt -> RngIntElt
Log(s) : FldPrElt -> FldPrElt
Log(b, s) : FldPrElt -> FldReElt
Log(g, d: parameters) : GrpAbGenElt, GrpAbGenElt -> RngIntElt
Log(Q, P) : PtEll, PtEll -> RngIntElt
Log(Q, P, t) : PtEll, PtEll, RngIntElt -> RngIntElt
Log(b, x): QuadBinElt, QuadBinElt -> RngIntElt
Log(b, x, t): QuadBinElt, QuadBinElt, RngIntElt -> RngIntElt
Log(x) : RngLocElt -> RngLocElt
Log(x) : RngLocElt -> RngLocElt
Log(f) : RngSerElt -> RngSerElt
Log(f) : RngSerElt -> RngSerElt
LogDerivative(s) : FldPrElt -> FldPrElt
LogGamma(s) : FldPrElt -> FldPrElt
LogGamma(f) : RngSerElt -> RngSerElt
LogIntegral(s) : FldPrElt -> FldPrElt
SetLogFile(F) : MonStgElt ->
SetLogFile(F) : MonStgElt ->
SetLogFile(F) : MonStgElt ->
UnsetLogFile() : ->
FldFin_Log (Example H45E5)
Discrete Logarithms (BINARY QUADRATIC FORMS)
Discrete Logarithms (FINITE FIELDS)
Logarithms and Exponentials (LOCAL RINGS AND FIELDS)
Logarithms and Exponentials (p-ADIC RINGS AND FIELDS)
RngLoc_log (Example H55E11)
RngPad_log (Example H40E9)
Logarithms and Exponentials (LOCAL RINGS AND FIELDS)
Logarithms and Exponentials (p-ADIC RINGS AND FIELDS)
EllipticLogarithm(P: parameters): PtEll -> FldPrElt
pAdicEllipticLogarithm(P, p: parameters): PtEll, RngIntElt -> FldLocElt
Exponential and Logarithmic Functions (POWER, LAURENT AND PUISEUX SERIES)
Exponential, Logarithmic and Polylogarithmic Functions (REAL AND COMPLEX FIELDS)
Exponential and Logarithmic Functions (POWER, LAURENT AND PUISEUX SERIES)
Exponential, Logarithmic and Polylogarithmic Functions (REAL AND COMPLEX FIELDS)
AbsoluteLogarithmicHeight(a) : FldAlgElt -> FldPrElt
Psi(s) : FldPrElt -> FldPrElt
LogDerivative(s) : FldPrElt -> FldPrElt
LogGamma(s) : FldPrElt -> FldPrElt
LogGamma(f) : RngSerElt -> RngSerElt
Logging (FINITELY PRESENTED ALGEBRAS)
Logging a Session (INPUT AND OUTPUT)
Booleans (OVERVIEW)
LogIntegral(s) : FldPrElt -> FldPrElt
Control-C key (OVERVIEW)
Quitting (OVERVIEW)
Logs(a) : FldAlgElt -> [FldPrElt]
HighestLongRoot( RD ) : RootDtm -> .
HighestRoot( RD ) : RootDtm -> .
IsLongRoot( RD, r ) : RootDtm, RngIntElt -> BoolElt
LongExactSequenceOnHomology(f,g) : MapChn, MapChn -> ModCpx
LongestElement( W ) : GrpCox -> GrpPermElt
LongestElement( F ) : GrpFP -> SeqEnum
GrpCox_LongestCoxeterElements (Example H34E5)
LongestElement( W ) : GrpCox -> GrpPermElt
LongestElement( F ) : GrpFP -> SeqEnum
ModCpx_LongExactSequence (Example H82E3)
LongExactSequenceOnHomology(f,g) : MapChn, MapChn -> ModCpx
Iteration (OVERVIEW)
LowIndexProcess(G, R : parameters) : GrpFP, RngIntElt -> Process(Lix)
LowIndexSubgroups(G, R : parameters) : GrpFP, RngIntElt -> [ GrpFP ]
LowIndexSubgroups(G, R : parameters) : GrpMat, RngIntElt -> [ GrpMat ]
LowIndexSubgroups(G, n: parameters) : GrpPerm, RngIntElt -> SeqEnum
Low Index Subgroups (FINITELY PRESENTED GROUPS)
Low Level Operations on Presentations and Words (FP GROUPS - ADVANCED FEATURES)
Low Level Operations on Words (FP GROUPS - ADVANCED FEATURES)
Low Index Subgroups (FINITELY PRESENTED GROUPS)
Low Level Operations on Presentations and Words (FP GROUPS - ADVANCED FEATURES)
Low Level Operations on Words (FP GROUPS - ADVANCED FEATURES)
LowerCentralSeries(L) : AlgLie -> [ AlgLie ]
LowerCentralSeries(G) : GrpFin -> [ GrpFin ]
LowerCentralSeries(G) : GrpGPC -> [GrpGPC]
LowerCentralSeries(G) : GrpMat -> [ GrpMat ]
LowerCentralSeries(G) : GrpPC -> [GrpPC]
LowerCentralSeries(G) : GrpPerm -> [ GrpPerm ]
LowerFaces(N) : NwtnPgon -> SeqEnum
LowerTriangularMatrix(R, Q) : Rng, [ RngElt ] -> Mtrx
LowerTriangularMatrix(Q) : [ RngElt ] -> Mtrx
LowerVertices(N) : NwtnPgon -> SeqEnum
RegulatorLowerBound(O) : RngOrd -> FldPrElt
SetLowerBound(L, n, b) : LP, RngIntElt, RngElt ->
VerifyMinimumDistanceLowerBound(C, d) : Code, RngIntElt -> BoolElt, RngIntElt, BoolElt
Bounds on the Minimum Distance (LINEAR CODES OVER FINITE FIELDS)
LowerCentralSeries(L) : AlgLie -> [ AlgLie ]
LowerCentralSeries(G) : GrpFin -> [ GrpFin ]
LowerCentralSeries(G) : GrpGPC -> [GrpGPC]
LowerCentralSeries(G) : GrpMat -> [ GrpMat ]
LowerCentralSeries(G) : GrpPC -> [GrpPC]
LowerCentralSeries(G) : GrpPerm -> [ GrpPerm ]
LowerFaces(N) : NwtnPgon -> SeqEnum
LowerTriangularMatrix(R, Q) : Rng, [ RngElt ] -> Mtrx
LowerTriangularMatrix(Q) : [ RngElt ] -> Mtrx
LowerVertices(N) : NwtnPgon -> SeqEnum
GrpMat_LowIndexMatrixGroup (Example H21E16)
LowIndexProcess(G, R : parameters) : GrpFP, RngIntElt -> Process(Lix)
LowIndexSubgroups(G, R : parameters) : GrpFP, RngIntElt -> [ GrpFP ]
LowIndexSubgroups(G, R : parameters) : GrpMat, RngIntElt -> [ GrpMat ]
LowIndexSubgroups(G, n: parameters) : GrpPerm, RngIntElt -> SeqEnum
Explicit LP Solving Functions (LINEAR PROGRAMMING)
LP_LPCreation (Example H104E3)
LPolynomial(F) : FldFun -> RngUPolElt
LPolynomial(F, m) : FldFun, RngIntElt -> RngUPolElt
LPProcess(R, n) : Rng, RngIntElt -> LP
LRatio(M, j : parameters) : ModSym, RngIntElt -> FldRatElt
LRatioOddPart(M, j) : ModSym, RngIntElt -> FldRatElt
LRatioOddPart(M, j) : ModSym, RngIntElt -> FldRatElt
Scheme_ls-reduction (Example H83E33)
LSeries(M, j, prec) : ModSym, RngIntElt, RngIntElt -> FldPrElt
LSeriesLeadingCoefficient(M, j, prec) : ModSym, RngIntElt, RngIntElt -> FldPrElt, RngIntElt
ModSym_LSeries (Example H90E20)
LSeriesLeadingCoefficient(M, j, prec) : ModSym, RngIntElt, RngIntElt -> FldPrElt, RngIntElt
Comparison (OVERVIEW)
u lt v : AlgFPElt, AlgFPElt -> BoolElt
u lt v : GrpFPElt, GrpFPElt -> BoolElt
M1 lt M2 : ModBrdt, ModBrdt -> BoolElt
M1 lt M2 : ModSym, ModSym -> BoolElt
s lt t : MonStgElt, MonStgElt -> BoolElt
a lt b : RngElt, RngElt -> BoolElt
S lt T : SeqEnum, SeqEnum -> BoolElt
u lt v : SgpFPElt, SgpFPElt -> BoolElt
e lt f : SubGrpLatElt, SubGrpLatElt -> BoolElt
Lucas(n) : RngIntElt -> RngIntElt
Lucas(n) : RngIntElt -> RngIntElt
[____] [____] [_____] [____] [__] [Index] [Root]