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Index L


L-key

l

l-key

l

L0

L0(O) : RngFunOrd -> SeqEnum

Label

Label(t) : GrphVert -> .

Labelling

Labelling(G) : GrpPerm -> SetIndx

Labels

Labels(S) : [GrphVert] -> SeqEnum

Graph_Labels (Example H55E7)

Graph_Labels (Example H55E9)

labels

Labelled Graphs (GRAPHS)

language

Language (OVERVIEW)

Laplace

Laplace(f) : RngPowElt -> RngPowElt

LargestClique

LargestClique(G) : GrphUnd -> { GrphVert }

LargestIndependentSet

LargestIndependentSet(G) : GrphUnd -> { GrphVert }

Lat

Modules (OVERVIEW)

Lattice

Lattice(C, "A") : Code -> Lat

Lattice(G) : GrpMat -> Lat

Lattice(X, M) : ModMatRngElt, AlgMatElt -> Lat

Lattice(X, n) : MonStgElt, RngIntElt -> Lat

Lattice(O) : RngOrd -> Lat

Lattice(O) : RngOrd -> ModLat

lattice

LATTICES

Modules (OVERVIEW)

Operations on Lattice Elements (GENERAL MODULES)

Submodule Lattices (GENERAL MODULES)

lattice-element

Operations on Lattice Elements (GENERAL MODULES)

LatticeCreate

Lat_LatticeCreate (Example H45E1)

LatticeFunctions

Lat_LatticeFunctions (Example H45E4)

LatticeOperations

Grp_LatticeOperations (Example H15E16)

LatticeOps

RMod_LatticeOps (Example H42E22)

lattices

Lattices from Matrix Groups (LATTICES)

Operations on Lattices (GENERAL MODULES)

Special Lattices (LATTICES)

LatticeWithBasis

LatticeWithBasis(G, B) : GrpMat, ModMatRngElt -> Lat

LatticeWithBasis(B, M) : ModMatRngElt, AlgMatElt -> Lat

LatticeWithGram

LatticeWithGram(F) : AlgMatElt -> Lat

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

Laurent

POWER SERIES AND LAURENT SERIES

Rings, Fields, and Algebras (OVERVIEW)

LaurentSeriesAlgebra

LaurentSeriesRing(R) : Rng -> AlgPowSer

LaurentSeriesRing

LaurentSeriesRing(R) : Rng -> AlgPowSer

LCM

LCM(I, J) : RngFunOrdIdl, RngFunOrdIdl -> RngFunOrdIdl

LCM(I, J) : RngOrdIdl, RngOrdIdl -> RngOrdIdl

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

LeastCommonMultiple(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt

LeastCommonMultiple(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt

LeastCommonMultiple(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt

Lcm

LCM(I, J) : RngFunOrdIdl, RngFunOrdIdl -> RngFunOrdIdl

LCM(I, J) : RngOrdIdl, RngOrdIdl -> RngOrdIdl

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

LeastCommonMultiple(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt

LeastCommonMultiple(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt

LeastCommonMultiple(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt

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)

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 (ERROR-CORRECTING CODES)

LeadingCoefficient

LeadingCoefficient(u) : AlgFPElt -> RngElt

LeadingCoefficient(f) : RngMPolElt -> RngElt

LeadingCoefficient(f) : RngUPolElt -> RngElt

LeadingExponent

LeadingExponent(x) : GrpPCElt -> RngIntElt

LeadingGenerator

LeadingGenerator(x) : GrpPCElt -> GrpPCElt

LeadingMonomial

LeadingMonomial(f) : RngMPolElt -> RngMPolElt

LeadingMonomialIdeal

LeadingMonomialIdeal(I) : RngMPol -> RngMPol

LeadingTerm

LeadingTerm(x) : GrpPCElt -> GrpPCElt

LeadingTerm(f) : RngMPolElt -> RngMPolElt

LeadingTerm(p) : RngUPolElt -> RngUPolElt

LeadingTotalDegree

LeadingTotalDegree(f) : RngMPolElt -> RngIntElt

LeadingWeightedDegree

LeadingWeightedDegree(f) : RngMPolElt -> RngIntElt

LeastCommonMultiple

LCM(I, J) : RngFunOrdIdl, RngFunOrdIdl -> RngFunOrdIdl

LCM(I, J) : RngOrdIdl, RngOrdIdl -> RngOrdIdl

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

LeastCommonMultiple(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt

LeastCommonMultiple(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt

LeastCommonMultiple(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt

Leech

Lat_Leech (Example H45E7)

LeeWeight

LeeWeight(u) : ModTupFldElt -> RngIntElt

LeftAnnihilator

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

LeftAnnihilator(S) : AlgGrpSub -> AlgGrpSub

LeftCosetSpace

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

LegendreSymbol

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

Length

Length(C) : Code -> RngIntElt

Length(a) : FldNumElt -> FldPrElt

Length(v, K) : LatElt, Fld -> FldReElt

Length(f) : RngMPolElt -> RngIntElt

Length(e) : SubGrpLatElt -> RngIntElt

length

Integer-Valued Functions (INPUT AND OUTPUT)

Sequences (OVERVIEW)

The Length of a Word (FINITELY PRESENTED SEMIGROUPS)

length-index

Integer-Valued Functions (INPUT AND OUTPUT)

LengthenCode

LengthenCode(C) : Code -> Code

less

Comparison (OVERVIEW)

LevenshteinBound

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

lex

Lexicographical: lex (MULTIVARIATE POLYNOMIAL RINGS)

LexProduct

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

LHS

LHS(r) : Rel -> AlgFPElt

LHS(r) : Rel -> SgpFPElt

r[1] : GrpAbRel, RngIntElt -> GrpAbElt

r[1] : GrpFPRel, RngIntElt -> GrpFPElt

libraries

Databases of Structure Definitions (OVERVIEW)

Libraries of Functions in the Magma Language (OVERVIEW)

library

Databases of Structure Definitions (OVERVIEW)

Libraries of Functions in the Magma Language (OVERVIEW)

lideal

Constructor (OVERVIEW)

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

liealg

AlgAss_liealg (Example H48E1)

LieAlgebra

LieAlgebra(A) : AlgAss -> AlgGen, Map

LieAlgebra< R, n | Q : parameters > : Rng, RngIntElt, SeqEnum -> AlgLie

LieAlgebra< R, n | Q > : Rng, RngIntElt, SeqEnum -> AlgLie

AlgLie_LieAlgebra (Example H49E11)

LieBracket

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

Lift

Lift(E, K, h) : CurveEll, Rng, Map -> CurveEll

LiftCharacter

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

LiftCharacters

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

LiftIsogeny

LiftIsogeny(I, K) : Map, Rng -> Map

LiftIsomorphism

LiftIsomorphism(I, K) : Map, Rng -> Map

limit

Limits (FINITELY PRESENTED ALGEBRAS)

Line

Line(D, p, q) : Inc, IncPt, IncPt -> IncBlk

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

Creation of the General Linear Group and its Elements (MATRIX GROUPS)

ERROR-CORRECTING CODES

General and Special Linear Groups (MATRIX GROUPS)

Modules (OVERVIEW)

Operations with Linear Transformations (VECTOR SPACES)

Permutation Representations of Linear Groups (PERMUTATION GROUPS)

VECTOR SPACES

linear-group

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<K, n | L> : FldFin, RngIntElt, List -> Code

LinearCode(D, K) : Inc, FldFin -> Code

LinearCode(P, K) : Plane, FldFin -> Code

LinearRelation

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

LinearSpace

LinearSpace(I) : Inc -> IncLsp

LinearSpace< v | X : parameters > : RngIntElt, List -> IncLsp

LinearTrans

KMod_LinearTrans (Example H41E13)

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

Lines(P) : PlaneLnSet -> { PlaneLn }

LineSet

LineSet(P) : Plane -> PlaneLnSet

list

Elimination List: elim (MULTIVARIATE POLYNOMIAL RINGS)

LISTS

ListCategories

ListCategories() : ->

ListSignatures

ListSignatures(C) : Cat ->

ListTypes

ListCategories() : ->

ListVerbose

ListVerbose() : ->

literal

Literal Sequences (SEQUENCES)

a_1a_2...a_r : RngIntElt, ..., RngIntElt -> RngIntElt

Lix1

GrpFP_Lix1 (Example H16E38)

Lix2

GrpFP_Lix2 (Example H16E39)

Lix3

GrpFP_Lix3 (Example H16E40)

Lix4

GrpFP_Lix4 (Example H16E41)

LLL

LLL Reduction (LATTICES)

LLL(L) : Lat -> Lat, AlgMatElt

LLL(X) : ModMatRngElt -> ModMatRngElt, AlgMatElt, RngIntElt

LLL(O) : RngOrd -> RngOrd, AlgMatElt

LLLBasisMatrix

LLLBasisMatrix(L) : Lat -> ModMatElt, AlgMatElt

LLLGram

LLLGram(F) : ModMatRngElt -> ModMatRngElt, AlgMatElt, RngIntElt

LLLGramMatrix

LLLGramMatrix(L) : Lat -> AlgMatElt, AlgMatElt

LLLXGCD

Lat_LLLXGCD (Example H45E13)

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

Local Declarations (MAGMA SEMANTICS)

LOCAL FIELDS

Special Invariants for Rational Curves (ELLIPTIC CURVES)

local-declaration

Local Declarations (MAGMA SEMANTICS)

LocalHeight

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

LocalInformation

LocalInformation(E, p) : CurveEll, RgIntElt -> < RngIntElt, RngIntElt, RngIntElt, RngIntElt, KodSym>

Localization

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

localization

Localization (INTRODUCTION [RINGS AND FIELDS])

lock

Related Files (FUNCTIONS, PROCEDURES AND PACKAGES)

Log

Log(a) : FldFinElt -> RngIntElt

Log(a) : FldLocElt -> RngIntElt

Log(s) : FldPrElt -> FldPrElt

Log(f) : RngSerElt -> RngSerElt

log

Log, Order and Roots (FINITE FIELDS)

log-order-root

Log, Order and Roots (FINITE FIELDS)

logarithm

Exponential, Logarithmic and Polylogarithmic Functions (REAL AND COMPLEX FIELDS)

logarithm-exponential

Exponential, Logarithmic and Polylogarithmic Functions (REAL AND COMPLEX FIELDS)

LogDerivative

LogDerivative(s) : FldPrElt -> FldPrElt

LogGamma

LogGamma(s) : FldPrElt -> FldPrElt

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) : FldNumElt -> [FldPrElt]

loop

Iteration (OVERVIEW)

low

Low Index Subgroups (FINITELY PRESENTED GROUPS)

low-index-subgroup

Low Index Subgroups (FINITELY PRESENTED GROUPS)

lower

Lower Bounds on the Cardinality of a Largest Code (ERROR-CORRECTING CODES)

LowerCentralSeries

LowerCentralSeries(L) : AlgLie -> [ AlgLie ]

LowerCentralSeries(G) : GrpFin -> [ GrpFin ]

LowerCentralSeries(G) : GrpMat -> [ GrpMat ]

LowerCentralSeries(G) : GrpPC -> [GrpPC]

LowerCentralSeries(G) : GrpPerm -> [ GrpPerm ]

LowIndexProcess

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

LowIndexSubgroups

LowIndexSubgroups(G, R : parameters) : GrpFP, RngIntElt -> [ GrpFP ]

LSeries

LSeries(E) : CurveEll -> RngPow

lt

Comparison (OVERVIEW)

u lt v : AlgFPElt, AlgFPElt -> BoolElt

u lt v : GrpFPElt, GrpFPElt -> 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


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