[____] [____] [_____] [____] [__] [Index] [Root]

Index L


L

AGammaL(arguments)
AffineGammaLinearGroup(arguments)
AffineSigmaLinearGroup(arguments)
ProjectiveGammaLinearGroup(arguments)
ProjectiveSigmaLinearGroup(arguments)

l

Special Values of L-functions (MODULAR SYMBOLS)

L-key

L
l

l-key

L
l

l-series

Special Values of L-functions (MODULAR SYMBOLS)

L372

GrpFP_1_L372 (Example H22E58)

Label

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 -> .

Labelled

IsLabelled(t) : GrphVert -> BoolElt
IsLabelledEdge(G, i, j) : Grph, RngIntElt, RngIntElt -> BoolElt
IsLabelledVertex(G, i) : Grph, RngIntElt -> BoolElt

Labelling

Labelling(G) : GrpPerm -> SetIndx

Labels

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 H93E7)
Graph_Labels (Example H93E9)

labels

Labelled Graphs (GRAPHS)
Labels (MODULAR FORMS)

Laced

IsSimplyLaced( G ) : GrpLie-> BoolElt
IsSimplyLaced( RD ) : RootDtm-> BoolElt

Laguerre

LaguerrePolynomial(n) : RngIntElt -> RngUPolElt

LaguerrePolynomial

LaguerrePolynomial(n) : RngIntElt -> RngUPolElt

Lambda

CarmichaelLambda(n) : RngIntElt -> RngIntElt
FactoredCarmichaelLambda(n) : RngIntElt -> RngIntEltFact

language

Language (OVERVIEW)

Laplace

Laplace(f) : RngSerElt -> RngSerElt

large

Matrix Groups of Large Degree (MATRIX GROUPS)
Orbit and Stabilizer Functions for Large Groups (MATRIX GROUPS)

large-degree

Matrix Groups of Large Degree (MATRIX GROUPS)

Larger

WriteOverLargerField(G) : GrpMat -> GrpMat, GrpMat, GrpAb, SeqEnum

Largest

LargestConductor(D) : DB -> RngIntElt
LargestDimension(D) : DB -> RngIntElt
LargestDimension(D) : DB -> RngIntElt
LargestDimension(D): DB -> RngIntElt

LargestConductor

LargestConductor(D) : DB -> RngIntElt

LargestDimension

LargestDimension(D) : DB -> RngIntElt
LargestDimension(D) : DB -> RngIntElt
LargestDimension(D): DB -> RngIntElt

Last

ColumnLength(t, j): Tableau,RngIntElt -> RnfIntElt
LastColumnEntry(t, j) : Tableau,RngIntElt -> RngIntElt
LastRowEntry(t, i) : Tableau,RngIntElt -> RngIntElt

LastColumnEntry

ColumnLength(t, j): Tableau,RngIntElt -> RnfIntElt
LastColumnEntry(t, j) : Tableau,RngIntElt -> RngIntElt

LastRowEntry

RowLength(t, i) : Tableau,RngIntElt -> RngIntElt
LastRowEntry(t, i) : Tableau,RngIntElt -> RngIntElt

Lat

Modules (OVERVIEW)

latdb

Database of Lattices (LATTICES)
Lat_latdb (Example H66E24)

latdb-names

Lat_latdb-names (Example H66E23)

Lattice

CoordinateLattice(L) : Lat -> Lat
DualBasisLattice(L) : Lat -> Lat
IsReverseLatticeWord(w) : SeqEnum -> 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

lattice

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)

lattice-attributes

Attributes of Lattices (LATTICES)

lattice-element

Operations on Lattice Elements (MODULES OVER A MATRIX ALGEBRA)
Properties of Lattice Elements (MODULES OVER A MATRIX ALGEBRA)

lattice-predicates

Predicates and Booleans on Lattices (LATTICES)

lattice-properties

BaseChange(L, S) : Lat, Rng -> Lat, Map
BaseExtend(L, S) : Lat, Rng -> Lat, Map
Properties of Lattices (LATTICES)

LatticeCreate

Lat_LatticeCreate (Example H66E1)

LatticeData

LatticeData(D, i): DB, RngIntElt -> Rec

LatticeDatabase

LatticeDatabase() : -> DB

LatticeFunctions

Lat_LatticeFunctions (Example H66E4)

LatticeName

LatticeName(D, i): DB, RngIntElt -> MonStgElt, RngIntElt

LatticeOperations

Grp_LatticeOperations (Example H19E17)

LatticeOps

ModAlg_LatticeOps (Example H76E20)

Lattices

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

Lattices from Matrix Groups (LATTICES)
Operations on Lattices (MODULES OVER A MATRIX ALGEBRA)
Special Lattices (LATTICES)

LatticeWithBasis

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

LatticeWithGram(F) : AlgMatElt -> Lat
LatticeWithGram(G, F) : GrpMat, AlgMatElt -> Lat

Laurent

POWER, LAURENT AND PUISEUX SERIES
Rings, Fields, and Algebras (OVERVIEW)
LaurentSeriesRing(R) : Rng -> RngSerLaur

LaurentSeriesRing

LaurentSeriesRing(R) : Rng -> RngSerLaur

Law

ExponentLaw(~P : parameters) : Proc(pQuot) ->

Layer

LayerBoundary(G,i,j,k) : GrpPC, RngIntElt, RngIntElt, RngIntElt -> RngIntElt
LayerLength(G,i,j) : GrpPC, RngIntElt, RngIntElt -> RngIntElt

LayerBoundary

LayerBoundary(G,i,j,k) : GrpPC, RngIntElt, RngIntElt, RngIntElt -> RngIntElt

LayerLength

LayerLength(G,i,j) : GrpPC, RngIntElt, RngIntElt -> RngIntElt

LCM

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

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

lcm

Common Divisors and Common Multiples (MULTIVARIATE POLYNOMIAL RINGS)
Common Divisors and Common Multiples (RING OF INTEGERS)
Common Divisors and Common Multiples (UNIVARIATE POLYNOMIAL RINGS)

LCS

HasComputableLCS(G) : GrpGPC -> BoolElt

le

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

leader

Coset Leaders (LINEAR CODES OVER FINITE FIELDS)

Leaders

CosetLeaders(C) : Code -> {@ ModTupFldElt @}, Map

Leading

LSeriesLeadingCoefficient(M, j, prec) : ModSym, RngIntElt, RngIntElt -> FldPrElt, RngIntElt
LeadingCoefficient(u) : AlgFPElt -> RngElt
LeadingCoefficient(f) : RngMPolElt -> RngElt
LeadingCoefficient(f, i) : RngMPolElt, RngIntElt -> RngElt
LeadingCoefficient(f) : RngSerElt -> RngElt
LeadingCoefficient(f) : RngUPolElt -> RngElt
LeadingExponent(x) : GrpGPCElt -> RngIntElt
LeadingExponent(x) : GrpPCElt -> RngIntElt
LeadingGenerator(x) : GrpGPCElt -> GrpGPCElt
LeadingGenerator(x) : GrpPCElt -> GrpPCElt
LeadingGenerator(w) : GrpFPElt -> GrpFPElt
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(f) : RngSerElt -> RngElt
LeadingTerm(p) : RngUPolElt -> RngUPolElt
LeadingTotalDegree(f) : RngMPolElt -> RngIntElt
LeadingWeightedDegree(f) : RngMPolElt -> RngIntElt

LeadingCoefficient

LeadingCoefficient(u) : AlgFPElt -> RngElt
LeadingCoefficient(f) : RngMPolElt -> RngElt
LeadingCoefficient(f, i) : RngMPolElt, RngIntElt -> RngElt
LeadingCoefficient(f) : RngSerElt -> RngElt
LeadingCoefficient(f) : RngUPolElt -> RngElt

LeadingExponent

LeadingExponent(x) : GrpGPCElt -> RngIntElt
LeadingExponent(x) : GrpPCElt -> RngIntElt

LeadingGenerator

LeadingGenerator(x) : GrpGPCElt -> GrpGPCElt
LeadingGenerator(x) : GrpPCElt -> GrpPCElt
LeadingGenerator(w) : GrpFPElt -> GrpFPElt

LeadingMonomial

LeadingMonomial(f) : RngMPolElt -> RngMPolElt

LeadingMonomialIdeal

LeadingMonomialIdeal(I) : RngMPol -> RngMPol

LeadingTerm

LeadingTerm(x) : GrpGPCElt -> GrpGPCElt
LeadingTerm(x) : GrpPCElt -> GrpPCElt
LeadingTerm(f) : RngMPolElt -> RngMPolElt
LeadingTerm(f, i) : RngMPolElt, RngIntElt -> RngMPolElt
LeadingTerm(f) : RngSerElt -> RngElt
LeadingTerm(p) : RngUPolElt -> RngUPolElt

LeadingTotalDegree

LeadingTotalDegree(f) : RngMPolElt -> RngIntElt

LeadingWeightedDegree

LeadingWeightedDegree(f) : RngMPolElt -> RngIntElt

Least

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

LeastCommonMultiple

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

Lee

LeeDistance(u, v) : ModTupRngElt, ModTupRngElt -> RngIntElt
LeeWeight(u) : ModTupRngElt -> RngIntElt
LeeWeight(v) : ModTupRngElt -> RngIntElt
LeeWeightEnumerator(C): Code -> RngMPolElt

lee

Lee Weights (LINEAR CODES OVER FINITE RINGS)

Leech

Lat_Leech (Example H66E6)

LeeDistance

LeeDistance(u, v) : ModTupRngElt, ModTupRngElt -> RngIntElt

LeeWeight

LeeWeight(u) : ModTupRngElt -> RngIntElt
LeeWeight(v) : ModTupRngElt -> RngIntElt

LeeWeightEnumerator

LeeWeightEnumerator(C): Code -> RngMPolElt

Left

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
LeftDescentSet( W, w ) : GrpCox, GrpPermElt -> {}
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

Left_Right_Isomorphisms

AlgQuat_Left_Right_Isomorphisms (Example H71E12)

LeftAnnihilator

LeftAnnihilator(A, B) : AlgAss, AlgAss -> AlgAss, AlgAss
LeftAnnihilator(S) : AlgGrpSub -> AlgGrpSub

LeftCosetSpace

LeftCosetSpace(P) : GrpFPCosetEnumProc -> GrpFPCos
RightCosetSpace(P) : GrpFPCosetEnumProc -> GrpFPCos
RightCosetSpace(G, H: parameters) : GrpFP, GrpFP -> GrpFPCos

LeftDescentSet

LeftDescentSet( W, w ) : GrpCox, GrpPermElt -> {}

LeftExactExtension

LeftExactExtension(C) : ModCpx -> ModCpx

LeftIdeal

lideal<S | X> : AlgQuatOrd, [AlgQuatOrdElt] -> AlgQuatOrd
LeftIdeal(S,X) : AlgQuatOrd, [AlgQuatOrdElt] -> AlgQuatOrd

LeftIdealClasses

LeftIdealClasses(S) : AlgQuatOrd -> [AlgQuatOrd]

LeftIsomorphism

LeftIsomorphism(I,J) : AlgQuatOrd, AlgQuatOrd -> Map, AlgQuatElt

LeftOrder

LeftOrder(I) : AlgQuatOrd -> AlgQuatOrd

LeftString

LeftString( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt

LeftStringLength

LieConstant_p( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LeftStringLength( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt

LeftZeroExtension

LeftZeroExtension(C) : ModCpx -> ModCpx

Legendre

DiagonalForm(C) : CrvCon -> RngMPolElt, ModMatRngElt
LegendreEquation(C) : CrvCon -> RngMPolElt, ModMatRngElt
LegendrePolynomial(n) : RngIntElt -> RngUPolElt
LegendreSymbol(n, m) : RngIntElt, RngIntElt -> RngIntElt

LegendreEquation

DiagonalForm(C) : CrvCon -> RngMPolElt, ModMatRngElt
LegendreEquation(C) : CrvCon -> RngMPolElt, ModMatRngElt

LegendrePolynomial

LegendrePolynomial(n) : RngIntElt -> RngUPolElt

LegendreSymbol

LegendreSymbol(n, m) : RngIntElt, RngIntElt -> RngIntElt

Lehner

AtkinLehner(M, q) : ModSym, RngIntElt -> AlgMatElt
AtkinLehnerOperator(M, p) : ModBrdt, RngIntElt -> AlgMatElt
CanonicalInvolution(X) : CrvMod -> MapSch
DualAtkinLehner(M, q) : ModSym, RngIntElt -> AlgMatElt

Length

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) : Tableau,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(P, i, j) : Tableau,RngIntElt,RngIntElt -> RngIntElt
LastColumnEntry(t, j) : Tableau,RngIntElt -> RngIntElt
LastRowEntry(t, i) : Tableau,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(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) : Tableau,RngIntElt -> RngIntElt
SimplifyLength(~P : parameters) : Process(Tietze) ->
SimplifyLength(G: parameters) : GrpFP -> GrpFP

length

Position(s, t) : MonStgElt, MonStgElt -> RngIntElt
Integer-Valued Functions (INPUT AND OUTPUT)
Sequences (OVERVIEW)
The Length of a Word (FINITELY PRESENTED SEMIGROUPS)

length-index

Position(s, t) : MonStgElt, MonStgElt -> RngIntElt
Integer-Valued Functions (INPUT AND OUTPUT)

Lengthen

LengthenCode(C) : Code -> Code

LengthenCode

LengthenCode(C) : Code -> Code

Lengths

BasicOrbitLengths(G) : GrpMat -> [RngIntElt]
BasicOrbitLengths(G) : GrpPerm -> [RngIntElt]
Lengths(X) : Sch -> [RngIntElt]

less

Comparison (OVERVIEW)

Level

Level(S) : AlgQuatOrd -> RngIntElt
Level(X) : CrvMod -> RngIntElt
Level(G) : GrpPSL2 -> RngIntElt
Level(M) : ModBrdt -> RngIntElt
Level(M) : ModFrm -> RngIntElt
Level(f) : ModFrmElt -> RngIntElt
SetDisplayLevel(~P, Level) : Process(pQuot), RngIntElt ->
SetPrintLevel(l) : MonStgElt ->

level

Degeneracy Maps (MODULAR SYMBOLS)
Low Level Operations on Presentations and Words (FP GROUPS - ADVANCED FEATURES)
Low Level Operations on Words (FP GROUPS - ADVANCED FEATURES)

Levenshtein

LevenshteinBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt

LevenshteinBound

LevenshteinBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt

Levi

HasLeviSubalgebra(L) : AlgLie -> BoolElt

Lex

LexProduct(G, H) : GrphDir, GrphDir -> GrphDir

lex

Lexicographical: lex (IDEAL THEORY AND GRÖBNER BASES)

LexProduct

LexProduct(G, H) : GrphDir, GrphDir -> GrphDir

lfsr

Linear Feedback Shift Registers (PSEUDO-RANDOM BIT SEQUENCES)

LFSRSequence

LFSRSequence(C, S, t) : RngUPolElt, SeqEnum, RngIntElt -> SeqEnum

LFSRStep

LFSRStep(C, S) : RngUPolElt, SeqEnum -> SeqEnum

LHS

LHS(r) : Rel -> AlgFPElt
LHS(r) : Rel -> SgpFPElt
r[1] : GrpAbRel, RngIntElt -> GrpAbElt
r[1] : GrpFPRel, RngIntElt -> GrpFPElt

LIBRARIES

MAGMA_LIBRARIES

Libraries

GetLibraries() : -> MonStgElt
SetLibraries(s) : MonStgElt ->

libraries

Databases of Structure Definitions (OVERVIEW)
Libraries of Functions in the Magma Language (OVERVIEW)

Library

GetLibraryRoot() : -> MonStgElt
SetLibraryRoot(s) : MonStgElt ->

library

Databases of Structure Definitions (OVERVIEW)
Libraries of Functions in the Magma Language (OVERVIEW)

LIBRARY_

MAGMA_LIBRARY_ROOT

lideal

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

Lie

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
SimpleLieAlgebra(X, n, F) : MonStgElt, RngIntElt, Fld -> AlgLie

lie

GROUPS OF LIE TYPE

liealg

AlgAss_liealg (Example H70E1)

LieAlgebra

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 H75E11)

LieBracket

(a, b) : AlgAssElt, AlgAssElt -> AlgAssElt
LieBracket(a, b) : AlgAssElt, AlgAssElt -> AlgAssElt

LieConstant

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

Lift

HenselLift(g, r) : RngUPolElt, RngLocElt -> RngLocElt
HenselLift(g, r) : RngUPolElt, RngLocElt -> RngLocElt
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 ], RngRes -> [ RngUPolElt ]
Lift(a, P) : RngElt, PlcFunElt -> FldFunElt
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

LiftCharacter

Extension(x, f, G) : AlgChtrElt, MapHom, Grp -> AlgChtrElt
LiftCharacter(x, f, G) : AlgChtrElt, MapHom, Grp -> AlgChtrElt

LiftCharacters

Extension(T, f, G) : AlgChtrElt, MapHom, Grp -> AlgChtrElt
LiftCharacters(T, f, G) : AlgChtrElt, MapHom, Grp -> AlgChtrElt

LiftHomomorphism

LiftHomomorphism(x, n) : ModAlgElt, RngIntElt -> ModMatFldElt
LiftHomomorphism(X, S) : SeqEnum[ModAlgElt], SeqEnum[RngIntElt] -> ModMatFldElt

lifting

Lifting a Quotient (FP GROUPS - ADVANCED FEATURES)

lifting-quotient

Lifting a Quotient (FP GROUPS - ADVANCED FEATURES)

LiftNonsplitExtension

LiftNonsplitExtension (SQP, p, i, k : parameters) : SQProc, RngIntElt, RngIntElt, RngIntElt -> RngIntElt, SQProc

LiftNonsplitExtensionRow

LiftNonsplitExtensionRow (SQP, p, l) : SQProc, RngIntElt, RngIntElt -> RngIntElt, SQProc

LiftSplitExtension

LiftSplitExtension (SQP, p, i, k : parameters) : SQProc, RngIntElt, RngIntElt, RngIntElt -> RngIntElt, SQProc

LiftSplitExtensionRow

LiftSplitExtensionRow (SQP): SQProc -> RngIntElt, SQProc

like

Q as a Number Field (RING OF INTEGERS)

LIMIT

MAGMA_MEMORY_LIMIT

Limit

GetMemoryLimit() : -> RngIntElt
SetMemoryLimit(n) : RngIntElt ->
SmallGroupDatabaseLimit() : -> RngIntElt
TransitiveGroupDatabaseLimit() : -> RngIntElt

limit

Limits (FINITELY PRESENTED ALGEBRAS)

lin

Linear Algebra (LOCAL RINGS AND FIELDS)
Linear Algebra (p-ADIC RINGS AND FIELDS)
LINEAR PROGRAMMING

lin-alg

Linear Algebra (LOCAL RINGS AND FIELDS)
Linear Algebra (p-ADIC RINGS AND FIELDS)

lin-opt

LINEAR PROGRAMMING

linalg

IsSubsystem(L,K) : LinSys,LinSys -> BoolElt
Basic Algebra of Linear Systems (SCHEMES)

Line

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 -> [ GSet ]
LineSet(P) : Plane -> PlaneLnSet
SetLineEditor(b) : BoolElt ->
TangentLine(p) : Crv,Pt -> Crv

line

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)

line-editor

The Magma Line Editor (ENVIRONMENT AND OPTIONS)

Linear

AGammaL(arguments)
AffineGammaLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineGeneralLinearGroup(arguments)
AffineSigmaLinearGroup(arguments)
AffineSpecialLinearGroup(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)

linear

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

linear-algebra

IsSubsystem(L,K) : LinSys,LinSys -> BoolElt
Linear Algebra (SCHEMES)

linear-equivalence

Linear Equivalence of Divisors (PLANE ALGEBRAIC CURVES)

linear-group

PSz(arguments)
Permutation Representations of Linear Groups (PERMUTATION GROUPS)

linear-transformation

Modules (OVERVIEW)
Operations with Linear Transformations (VECTOR SPACES)

LinearCharacters

LinearCharacters(G): Grp -> SeqEnum
LinearCharacters(G) : GrpMat -> [ Chtr ]

LinearCode

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

LinearIndependence

CrvEll_LinearIndependence (Example H85E19)

Linearly

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

LinearRelation(q: parameters) : [ FldPrElt ] -> [ RngIntElt ]

LinearSpace

LinearSpace(I) : Inc -> IncLsp
LinearSpace< v | X : parameters > : RngIntElt, List -> IncLsp

LinearSystem

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

LinearSystemTrace(L,X) : LinearSys,Sch -> LinearSys

LinearTrans

ModFld_LinearTrans (Example H63E14)

LineAtInfinity

LineAtInfinity(A) : Aff -> Crv

LineCount

IO_LineCount (Example H3E9)

LineGraph

LineGraph(G) : Grph -> Grph
LineGraph(P) : Plane -> Grph
LineGraph(P) : Plane -> GrphUnd

LineGroup

LineGroup(P) : Plane -> GrpPerm, PowMap, Map

LineOrbits

LineOrbits(G) : GrpMat -> [ GSet ]

Lines

AllPassants(P, A) : Plane, { PlanePt } -> { PlaneLn }
ExternalLines(P, A) : Plane, { PlanePt } -> { PlaneLn }
Lines(P) : PlaneLnSet -> { PlaneLn }
NumberOfLines(P) : Plane -> RngIntElt

LineSet

LineSet(P) : Plane -> PlaneLnSet

Linking

Linking(u,v) : GrphSplVert,GrphSplVert -> RngIntElt
LinkingNumbers(s) : GrphSpl -> SeqEnum
TotalLinking(v) : GrphSplVert -> RngIntElt

LinkingNumbers

LinkingNumbers(s) : GrphSpl -> SeqEnum

linsys

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)

linsys-construction

Scheme_linsys-construction (Example H81E29)

linsys-creation

Creation of Linear Systems (SCHEMES)

linsys-linalg

IsSubsystem(L,K) : LinSys,LinSys -> BoolElt
Basic Algebra of Linear Systems (SCHEMES)

linsys-maps

Linear Systems and Maps (SCHEMES)

Lint

VanLintBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt

List

ListAttributes(C) : Cat ->
ListCategories() : ->
ListSignatures(C) : Cat ->
ListVerbose() : ->
SequenceToList(Q) : SeqEnum -> List
TupleToList(T) : Tup -> List
TupleToList(T) : Tup -> List

list

Elimination List: elim (IDEAL THEORY AND GRÖBNER BASES)
LISTS

ListAttributes

ListAttributes(C) : Cat ->

ListCategories

ListTypes() : ->
ListCategories() : ->

ListSignatures

ListSignatures(C) : Cat ->

ListTypes

ListTypes() : ->
ListCategories() : ->

ListVerbose

ListVerbose() : ->

literal

Literal Sequences (SEQUENCES)
a_1a_2...a_r : RngIntElt, ..., RngIntElt -> RngIntElt

Little

IsLittleWoodRichardsonSkew(t) : Tableau -> BoolElt

Lix1

GrpFP_1_Lix1 (Example H22E36)

Lix2

GrpFP_1_Lix2 (Example H22E37)

Lix3

GrpFP_1_Lix3 (Example H22E38)

Lix4

GrpFP_1_Lix4 (Example H22E39)

Lix5

GrpFP_1_Lix5 (Example H22E40)

Ljunggren

SIntegralLjunggrenPoints(Q, S) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]

LLL

LLL Reduction (LATTICES)
LLL(L) : Lat -> Lat, AlgMatElt
LLL(X) : ModMatRngElt -> ModMatRngElt, AlgMatElt, RngIntElt
LLL(O) : RngOrd -> RngOrd, AlgMatElt

lll

RngOrd_lll (Example H53E10)

LLLBasis

LLLBasisMatrix(L) : Lat -> ModMatElt, AlgMatElt

LLLBasisMatrix

LLLBasisMatrix(L) : Lat -> ModMatElt, AlgMatElt

LLLGram

LLLGram(F) : ModMatRngElt -> ModMatRngElt, AlgMatElt, RngIntElt
LLLGramMatrix(L) : Lat -> AlgMatElt, AlgMatElt

LLLGramMatrix

LLLGramMatrix(L) : Lat -> AlgMatElt, AlgMatElt

LLLXGCD

Lat_LLLXGCD (Example H66E12)

load

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

loc< R | a_1, ..., a_r > : Rng, RngElt, ..., RngElt -> Rng, Map

Local

AddLocalGenerators(X) : VSrfK3 -> VSrfK3
Completion(P, n) : RngOrdIdl, RngIntElt -> RngLoc, Map
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

local

Creation of Points on Curves (PLANE ALGEBRAIC CURVES)
Invariants of Rational Curves (ELLIPTIC CURVES)
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
Operations at a Point (PLANE ALGEBRAIC CURVES)

local-curve

Local Geometry (PLANE ALGEBRAIC CURVES)

local-declaration

Local Declarations (MAGMA SEMANTICS)

local-fields

Local Fields (LOCAL RINGS AND FIELDS)

local-intersection

Local Intersection Theory (PLANE ALGEBRAIC CURVES)

local-intersection-example

Crv_local-intersection-example (Example H82E6)

local-ops

Operations at a Point (PLANE ALGEBRAIC CURVES)

local-points

Creation of Points on Curves (PLANE ALGEBRAIC CURVES)

local-rings

Local Rings (LOCAL RINGS AND FIELDS)

local_genus_invariants

Invariants of p-adic genera (LATTICES)

LocalCoxeterGroup

LocalCoxeterGroup( H ) : GrpCox -> GrpCox, Map

LocalField

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

LocalGenera(G) : SymGen -> Lat

LocalHeight

LocalHeight(P, p) : PtEll, RngIntElt -> FldPrElt

LocalInformation

LocalInformation(E, p) : CrvEll, RngIntElt -> <RngIntElt, RngIntElt, RngIntElt, RngIntElt, SymKod>
LocalInformation(E) : CrvEll, RngIntElt -> [ Tup ]

Localization

Localization(R, P) : Rng, Rng -> Rng, Map

localization

Localization (INTRODUCTION [BASIC RINGS])

LocalRing

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

LocalUniformizer

UniformizingElement(P) : PlcFunElt -> FldFunGElt
LocalUniformizer(P) : PlcFunElt -> FldFunGElt

lock

Related Files (FUNCTIONS, PROCEDURES AND PACKAGES)

Locseq

Locseq(x) : RngLoc -> [ [ RngLocElt ] ]
LocseqInert(x) : RngLoc -> [ RngLocElt ]

LocseqInert

LocseqInert(x) : RngLoc -> [ RngLocElt ]

Log

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 ->
UnsetLogFile() : ->

log

Discrete Logarithms (BINARY QUADRATIC FORMS)
Log, Order and Roots (FINITE FIELDS)
Logarithms and Exponentials (LOCAL RINGS AND FIELDS)
Logarithms and Exponentials (p-ADIC RINGS AND FIELDS)
RngLoc_log (Example H59E11)
RngPad_log (Example H42E9)

log-exp

Logarithms and Exponentials (LOCAL RINGS AND FIELDS)
Logarithms and Exponentials (p-ADIC RINGS AND FIELDS)

log-order-root

Log, Order and Roots (FINITE FIELDS)

Logarithm

EllipticLogarithm(P: parameters): PtEll -> FldPrElt
pAdicEllipticLogarithm(P, p: parameters): PtEll, RngIntElt -> FldLocElt

logarithm

Exponential and Logarithmic Functions (POWER, LAURENT AND PUISEUX SERIES)
Exponential, Logarithmic and Polylogarithmic Functions (REAL AND COMPLEX FIELDS)

logarithm-exponential

Exponential and Logarithmic Functions (POWER, LAURENT AND PUISEUX SERIES)
Exponential, Logarithmic and Polylogarithmic Functions (REAL AND COMPLEX FIELDS)

Logarithmic

AbsoluteLogarithmicHeight(a) : FldAlgElt -> FldPrElt

LogDerivative

Psi(s) : FldPrElt -> FldPrElt
LogDerivative(s) : FldPrElt -> FldPrElt

LogGamma

LogGamma(s) : FldPrElt -> FldPrElt
LogGamma(f) : RngSerElt -> RngSerElt

logging

Logging (FINITELY PRESENTED ALGEBRAS)
Logging a Session (INPUT AND OUTPUT)

logical

Booleans (OVERVIEW)

LogIntegral

LogIntegral(s) : FldPrElt -> FldPrElt

logout

Control-C key (OVERVIEW)
Quitting (OVERVIEW)

Logs

Logs(a) : FldAlgElt -> [FldPrElt]

Long

HighestLongRoot( RD ) : RootDtm -> .
HighestRoot( RD ) : RootDtm -> .
IsLongRoot( RD, r ) : RootDtm, RngIntElt -> BoolElt
LongExactSequenceOnHomology(f,g) : MapChn, MapChn -> ModCpx

Longest

LongestElement( W ) : GrpCox -> GrpPermElt
LongestElement( F ) : GrpFP -> SeqEnum
LongestIncreasingSequence(w) : SeqEnum -> RngIntElt
LongestIncreasingSequences(w, k) : SeqEnum,RngIntElt -> RngIntElt

LongestCoxeterElements

GrpCox_LongestCoxeterElements (Example H36E5)

LongestElement

LongestElement( W ) : GrpCox -> GrpPermElt
LongestElement( F ) : GrpFP -> SeqEnum

LongestIncreasingSequence

LongestIncreasingSequence(w) : SeqEnum -> RngIntElt

LongestIncreasingSequences

LongestIncreasingSequences(w, k) : SeqEnum,RngIntElt -> RngIntElt

LongExactSequence

ModCpx_LongExactSequence (Example H80E3)

LongExactSequenceOnHomology

LongExactSequenceOnHomology(f,g) : MapChn, MapChn -> ModCpx

loop

Iteration (OVERVIEW)

Low

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

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-subgroup

Low Index Subgroups (FINITELY PRESENTED GROUPS)

low-level

Low Level Operations on Presentations and Words (FP GROUPS - ADVANCED FEATURES)

low-level-words

Low Level Operations on Words (FP GROUPS - ADVANCED FEATURES)

Lower

LowerCentralSeries(L) : AlgLie -> [ AlgLie ]
LowerCentralSeries(G) : GrpFin -> [ GrpFin ]
LowerCentralSeries(G) : GrpMat -> [ GrpMat ]
LowerCentralSeries(G) : GrpPC -> [GrpPC]
LowerCentralSeries(G) : GrpPerm -> [ GrpPerm ]
LowerCentralSeries(G) : GrpGPC -> [GrpGPC]
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

lower

Bounds on the Minimum Distance (LINEAR CODES OVER FINITE FIELDS)

LowerCentralSeries

LowerCentralSeries(L) : AlgLie -> [ AlgLie ]
LowerCentralSeries(G) : GrpFin -> [ GrpFin ]
LowerCentralSeries(G) : GrpMat -> [ GrpMat ]
LowerCentralSeries(G) : GrpPC -> [GrpPC]
LowerCentralSeries(G) : GrpPerm -> [ GrpPerm ]
LowerCentralSeries(G) : GrpGPC -> [GrpGPC]

LowerFaces

LowerFaces(N) : NwtnPgon -> SeqEnum

LowerTriangularMatrix

LowerTriangularMatrix(R, Q) : Rng, [ RngElt ] -> Mtrx
LowerTriangularMatrix(Q) : [ RngElt ] -> Mtrx

LowerVertices

LowerVertices(N) : NwtnPgon -> SeqEnum

LowIndexMatrixGroup

GrpMat_LowIndexMatrixGroup (Example H21E16)

LowIndexProcess

LowIndexProcess(G, R : parameters) : GrpFP, RngIntElt -> Process(Lix)

LowIndexSubgroups

LowIndexSubgroups(G, R : parameters) : GrpFP, RngIntElt -> [ GrpFP ]
LowIndexSubgroups(G, R : parameters) : GrpMat, RngIntElt -> [ GrpMat ]
LowIndexSubgroups(G, n: parameters) : GrpPerm, RngIntElt -> SeqEnum

lp

Explicit LP Solving Functions (LINEAR PROGRAMMING)

LPCreation

LP_LPCreation (Example H100E3)

LPolynomial

LPolynomial(F) : FldFun -> RngUPolElt
LPolynomial(F, m) : FldFun, RngIntElt -> RngUPolElt

LPProcess

LPProcess(R, n) : Rng, RngIntElt -> LP

LRatio

LRatio(M, j : parameters) : ModSym, RngIntElt -> FldRatElt
LRatioOddPart(M, j) : ModSym, RngIntElt -> FldRatElt

LRatioOddPart

LRatioOddPart(M, j) : ModSym, RngIntElt -> FldRatElt

ls-reduction

Scheme_ls-reduction (Example H81E33)

LSeries

LSeries(M, j, prec) : ModSym, RngIntElt, RngIntElt -> FldPrElt
LSeriesLeadingCoefficient(M, j, prec) : ModSym, RngIntElt, RngIntElt -> FldPrElt, RngIntElt
ModSym_LSeries (Example H88E19)

LSeriesLeadingCoefficient

LSeriesLeadingCoefficient(M, j, prec) : ModSym, RngIntElt, RngIntElt -> FldPrElt, RngIntElt

lt

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

Lucas(n) : RngIntElt -> RngIntElt
Lucas(n) : RngIntElt -> RngIntElt

[____] [____] [_____] [____] [__] [Index] [Root]