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