[____] [____] [_____] [____] [__] [Index] [Root]
Index M
macwilliams
The MacWilliams Transform (ERROR-CORRECTING CODES)
MacWilliamsTransform
MacWilliamsTransform(n, k, q, W) : RngIntElt, RngIntElt, RngIntElt, [ <RngIntElt, RngIntElt> ] -> [ <RngIntElt, RngIntElt> ]
Magma
MAGMA
Magma Updates (OVERVIEW)
The Magma System (OVERVIEW)
magma
Constructing a General Matrix Algebra (MATRIX ALGEBRAS)
Construction of a Vector Space (VECTOR SPACES)
Construction of the Complete Matrix Algebra (MATRIX ALGEBRAS)
Construction of the General Linear Group (MATRIX GROUPS)
Construction of the Symmetric Group (PERMUTATION GROUPS)
Creation of General Number Fields (NUMBER FIELDS AND THEIR ORDERS)
Creation of Polynomial Rings (MULTIVARIATE POLYNOMIAL RINGS)
Creation of Structures (RATIONAL FIELD)
Creation of Structures (REAL AND COMPLEX FIELDS)
Creation of Structures (UNIVARIATE POLYNOMIAL RINGS)
Magmas (or Structures) (OVERVIEW)
Presentations (FINITELY PRESENTED SEMIGROUPS)
Related Structures (RATIONAL FUNCTION FIELDS)
Specification of a Power-conjugate Presentation (SOLUBLE GROUPS)
The General Group Constructors (GROUPS)
The General Matrix Group Constructor (MATRIX GROUPS)
The General Permutation Group Constructor (PERMUTATION GROUPS)
MAGMA_LIBRARIES
MAGMA_LIBRARIES
MAGMA_LIBRARY_ROOT
MAGMA_LIBRARY_ROOT
MAGMA_MEMORY_LIMIT
MAGMA_MEMORY_LIMIT
MAGMA_PATH
MAGMA_PATH
MAGMA_STARTUP_FILE
MAGMA_STARTUP_FILE
MAGMA_SYSTEM_SPEC
MAGMA_SYSTEM_SPEC
MAGMA_USER_SPEC
MAGMA_USER_SPEC
magmahelp
Overview (OVERVIEW)
mail
Magma Updates (OVERVIEW)
MakeMatgpTup
MakeMatgpTup(~MGT,X) : SetCartElt, GrpMat ->
MantissaExponent
MantissaExponent(r) : FldReElt -> FldReElt, RngIntElt
manual
Documentation (OVERVIEW)
map
Functions, Procedures, and Mappings (OVERVIEW)
Maps (OVERVIEW)
map< A -> B | G > : Struct, Struct -> Map
mapping
Creation of Maps (MAPPINGS)
Creation of Partial Maps (MAPPINGS)
Functions, Procedures, and Mappings (OVERVIEW)
Mappings (OVERVIEW)
Maps (OVERVIEW)
Match
Match(u, v, f) : GrpFPElt, GrpFPElt, RngIntElt -> BoolElt, RngIntElt
Match(u, v, f) : SgpFPElt, SgpFPElt, RngIntElt -> BoolElt, RngIntElt
matgps
Database of Matrix Groups (OVERVIEW)
matgptup
Matrix Group Tuples (MATRIX GROUPS)
Matrices
GrpMat_Matrices (Example H21E2)
KMod_Matrices (Example H40E4)
MatricesTup
MatricesTup(MGT) : SetCartElt -> [ GrpMatElt ]
Matrix
HMod_Matrix (Example H42E6)
matrix
Database of Matrix Groups (OVERVIEW)
General Constructions (MATRIX GROUPS)
Matrices and Vector Spaces Associated with a Graph or Digraph (GRAPHS)
Matrix Action on Forms (QUADRATIC FIELDS)
MATRIX ALGEBRAS
Matrix Group Actions on Polynomials (INVARIANT RINGS OF FINITE GROUPS)
Matrix Group Predicates (MATRIX GROUPS)
MATRIX GROUPS
Rings, Fields, and Algebras (OVERVIEW)
Soluble Matrix Groups (MATRIX GROUPS)
matrix-group
Matrix Group Predicates (MATRIX GROUPS)
matrix-vector-space
Matrices and Vector Spaces Associated with a Graph or Digraph (GRAPHS)
MatrixAlgebra
MatrixAlgebra(F, E) : FldFin, FldFin -> AlgMat, Map
MatrixAlgebra(S, n) : Rng, RngIntElt -> AlgMat
MatrixAlgebra<S, n | L> : Rng, RngIntElt, List -> AlgMat
MatrixAlgebra(Q) : RngQPol -> AlgMat, Map
MatrixGroup
MatrixGroup(M) : ModGrp -> GrpMat
MatrixGroup< n, R | L > : RngIntElt, Rng, List -> GrpMat
PermutationGroup< X | L > : Set, List -> GrpPerm, Hom
MatrixRing
MatrixAlgebra(S, n) : Rng, RngIntElt -> AlgMat
MatrixAlgebra<S, n | L> : Rng, RngIntElt, List -> AlgMat
MatrixUnit
MatrixUnit(R, i, j) : AlgMat, RngIntElt, RngIntElt -> AlgMatElt
mattson
Mattson-Solomon Transforms (ERROR-CORRECTING CODES)
mattson-solomon
Mattson-Solomon Transforms (ERROR-CORRECTING CODES)
MattsonSolomonTransform
MattsonSolomonTransform(f, n) : RngUPolElt, RngIntElt -> RngUPolElt
Code_MattsonSolomonTransform (Example H51E18)
Max
Maximum(S) : SeqEnum -> Elt, RngIntElt
Maximum(S) : SetIndx -> Elt, RngIntElt
Maxdeg
MaximumDegree(G) : GrphDir -> RngIntElt, GrphVert
MaximumDegree(G) : GrphUnd -> RngIntElt, GrphVert
MaximalIsotropicSubspace
[Future release] MaximalIsotropicSubspace(V) : ModTupFld -> ModTupFld
MaximalNormalSubgroup
MaximalNormalSubgroup(G) : GrpPerm -> GrpPerm
MaximalOrder
MaximalOrder(K) : FldNum -> RngOrd
MaximalOrder(F) : FldQuad -> RngQuad
MaximalOvergroup
MaximalOvergroup(G, H) : GrpFP, GrpFP -> GrpFP
MaximalPartition
MaximalPartition(G) : GrpPerm -> GSet
MaximalSubgroups
MaximalSubgroups(G) : GrpAb -> [GrpAb]
MaximalSubgroups(G) : GrpPC -> [GrpPC]
MaximalSubgroups(e) : SubGrpLatElt -> { SubGrpLatElt }
MaximalSubmodules
MaximalSubmodules(M) : ModRng -> [ ModRng ], BoolElt
MaximalSubmodules(e) : SubModLatElt -> { SubModLatElt }
Maximum
Comparison (OVERVIEW)
Maximum(a, b) : RngElt, RngElt -> RngElt
Maximum(S) : SeqEnum -> Elt, RngIntElt
Maximum(S) : SetIndx -> Elt, RngIntElt
MaximumDegree
MaximumDegree(G) : GrphDir -> RngIntElt, GrphVert
MaximumDegree(G) : GrphUnd -> RngIntElt, GrphVert
MaximumInDegree
MaximumInDegree(G) : GrphDir -> RngIntElt, GrphVert
MaximumOutDegree
MaximumOutDegree(G) : GrphDir -> RngIntElt, GrphVert
Maxindeg
MaximumInDegree(G) : GrphDir -> RngIntElt, GrphVert
MaxNorm
MaxNorm(f) : RngMPolElt -> RngIntElt
MaxNorm(p) : RngUPolElt -> RngIntElt
Maxoutdeg
MaximumOutDegree(G) : GrphDir -> RngIntElt, GrphVert
McElieceEtAlAsymptoticBound
McElieceEtAlAsymptoticBound(delta) : FldPrElt -> FldPrElt
Meataxe
Meataxe(M) : ModRng -> ModRng, ModRng, AlgMatElt
RMod_Meataxe (Example H41E17)
meet
R meet T : AlgMat, AlgMat -> AlgMat
C meet D : Code, Code -> Code
F meet G : FldFin, FldFin -> FldFin
H meet K : GrpAb, GrpAb -> GrpAb
H meet K : GrpFin, GrpFin -> GrpFin
H meet K : GrpFP, GrpFP -> GrpFP
H meet K : GrpMat, GrpMat -> GrpMat
H meet K : GrpPC, GrpPC -> GrpPC
H meet K : GrpPerm, GrpPerm -> GrpPerm
U meet V : ModTupFld, ModTupFld -> ModTupFld
M meet N : ModTupRng, ModTupRng -> ModTupRng
l meet m : PlaneLn, PlaneLn -> PlanePt
I meet J : RngIdl, RngIdl -> RngIdl
I meet J : RngMPol, RngMPol -> RngMPol
I meet J : RngUPol, RngUPol -> RngUPol
R meet S : SetEnum, SetEnum -> SetEnum
e meet f : SubModLatElt, SubModLatElt -> SubModLatElt
meet:=
H meet:= K : GrpAb, GrpAb -> GrpAb
H meet:= K : GrpPC, GrpPC -> GrpPC
U meet:= V : ModTupFld, ModTupFld -> ModTupFld
membership
Equality and Membership (CYCLOTOMIC FIELDS)
Equality and Membership (MULTIVARIATE POLYNOMIAL RINGS)
Equality and Membership (NUMBER FIELDS AND THEIR ORDERS)
Equality and Membership (POWER SERIES AND LAURENT SERIES)
Equality and Membership (QUADRATIC FIELDS)
Equality and Membership (RATIONAL FUNCTION FIELDS)
Equality and Membership (UNIVARIATE POLYNOMIAL RINGS)
Equality and Membership (VALUATION RINGS)
Membership Testing (SEQUENCES)
MergeUnits
MergeUnits(K, a) : FldNum, FldNumElt -> Boolelt
Meta-B-key
<Meta>-b
Meta-b-key
<Meta>-b
Meta-F-key
<Meta>-f
Meta-f-key
<Meta>-f
Min
Minimum(S) : SeqEnum -> Elt, RngIntElt
Minimum(S) : SetIndx -> Elt, RngIntElt
Mindeg
MinimumDegree(G) : GrphDir -> RngIntElt, GrphVert
MinimumDegree(G) : GrphUnd -> RngIntElt, GrphVert
minimal
Minimal and Characteristic Polynomial (FINITE FIELDS)
Minimal Submodules and Socle Series (GENERAL MODULES)
minimal-characteristic-polynomial
Minimal and Characteristic Polynomial (FINITE FIELDS)
minimal-submodule-socle-series
Minimal Submodules and Socle Series (GENERAL MODULES)
MinimalBasis
MinimalBasis(M) : ModMPol -> [ ModMPolElt ]
MinimalField
MinimalField(a) : FldCycElt -> FldCyc
MinimalField(q) : FldRatElt -> FldRat
MinimalField(G) : GrpMat -> FldFin
MinimalField(M) : ModRng -> FldFin
MinimalInteger
MinimalInteger(I) : RngOrdIdl -> RngIntElt
MinimalModel
MinimalModel(E) : GeomEC -> GeomEC, Map
MinimalNormalSubgroup
MinimalNormalSubgroup(G) : GrpPC -> GrpPC
MinimalNormalSubgroups
MinimalNormalSubgroups(G) : GrpPerm -> [ GrpPerm ]
MinimalOvergroup
MinimalOvergroup(G, H) : GrpFP, GrpFP -> GrpFP
MinimalOvergroups
MinimalOvergroups(e) : SubGrpLatElt -> { SubGrpLatElt }
MinimalPartition
MinimalPartition(G: parameters) : GrpPerm -> GSet
MinimalPartitions
MinimalPartitions(G: parameters) : GrpPerm -> [ GSet ]
MinimalPolynomial
MinimalPolynomial(a) : AlgMatElt -> RngUPolElt
MinimalPolynomial(a) : FldCycElt -> AlgPolElt
MinimalPolynomial(a) : FldFinElt -> RngPolElt
MinimalPolynomial(a) : FldNumElt -> RngUPolElt
MinimalPolynomial(a) : FldQuadElt -> AlgPolElt
MinimalPolynomial(q) : FldRatElt -> RngUPolElt
MinimalPolynomial(g) : GrpMatElt -> RngPolElt
MinimalPolynomial(n) : RngIntElt -> RngUPolElt
MinimalPolynomial(f) : RngQPolElt -> RngUPol
RngMPol_MinimalPolynomial (Example H29E26)
Minimals
RMod_Minimals (Example H41E19)
MinimalSubmodules
MinimalSubmodules(M) : ModRng -> [ ModRng ], BoolElt
MinimalSupermodules
MinimalSupermodules(e) : SubModLatElt -> { SubModLatElt }
MinimalSyzygyModule
MinimalSyzygyModule(M) : ModMPol -> [ ModMPolElt ]
Minimise
Minimise(~a) : FldCycElt ->
Minimize
Minimise(~a) : FldCycElt ->
Minimum
Comparison (OVERVIEW)
Minimum(a, b) : RngElt, RngElt -> RngElt
Minimum(S) : SeqEnum -> Elt, RngIntElt
Minimum(S) : SetIndx -> Elt, RngIntElt
minimum
The Minimum Distance and Weight (ERROR-CORRECTING CODES)
minimum-weight
The Minimum Distance and Weight (ERROR-CORRECTING CODES)
MinimumDegree
MinimumDegree(G) : GrphDir -> RngIntElt, GrphVert
MinimumDegree(G) : GrphUnd -> RngIntElt, GrphVert
MinimumDistance
MinimumDistance(C) : Code -> RngIntElt
MinimumInDegree
MinimumInDegree(G) : GrphDir -> RngIntElt, GrphVert
MinimumOutDegree
MinimumOutDegree(G) : GrphDir -> RngIntElt, GrphVert
MinimumWeight
MinimumWeight(C) : Code -> RngIntElt
MinimumWords
MinimumWords(C) : Code -> { ModTupFldElt }
Minindeg
MinimumInDegree(G) : GrphDir -> RngIntElt, GrphVert
MinkowskiBound
MinkowskiBound(K) : FldNum -> RngIntElt
Minoutdeg
MinimumOutDegree(G) : GrphDir -> RngIntElt, GrphVert
minus
Operators (OVERVIEW)
MinusOne
One(B) : MagForm -> MagFormElt
Miscellaneous
Set_Miscellaneous (Example H7E7)
miscellaneous
Miscellaneous (FINITELY PRESENTED ALGEBRAS)
mod
Rings, Fields, and Algebras (OVERVIEW)
n mod m : RngIntElt, RngIntElt -> RngIntElt
n mod m : RngIntElt, RngIntElt -> RngIntElt
a mod I : RngOrdElt, RngOrdIdl -> RngOrdElt
f mod g : RngUPolElt, RngUPolElt -> RngUPolElt
model
Alternative Models (ELLIPTIC CURVES)
Models
Elcu_Models (Example H46E2)
Modexp
Modexp(n, k, m) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
Modexp(f, n, g) : RngUPolElt, RngIntElt, RngUPolElt -> RngUPolElt
ModGrp
Modules (OVERVIEW)
modification
Access and Modification Functions (RECORDS)
Accessing and Modifying a Matrix (THE MODULES Hom_(R)(M, N) AND End(M))
Accessing and Modifying Sets (SETS)
Change Ground Ring (ELLIPTIC CURVES)
Changing the Alphabet of a Code (ERROR-CORRECTING CODES)
Changing the Coefficient Field (VECTOR SPACES)
Changing the Coefficient Ring (GENERAL MODULES)
Editing Defining Relations (FINITELY PRESENTED ALGEBRAS)
Elementary Tietze Transformations (FINITELY PRESENTED SEMIGROUPS)
Modification of a Presentation (FINITELY PRESENTED GROUPS)
Modifying a Base and Strong Generating Set (PERMUTATION GROUPS)
Modifying Enumerated Sequences (SEQUENCES)
Modifying Sets (SETS)
Modifying the Universe of a Set or Sequence (INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS])
modification-alphabet
Changing the Alphabet of a Code (ERROR-CORRECTING CODES)
modification-coefficient-field
Changing the Coefficient Field (VECTOR SPACES)
modification-coefficient-ring
Changing the Coefficient Ring (GENERAL MODULES)
modification-ground-ring
Change Ground Ring (ELLIPTIC CURVES)
modification-Tietze
Elementary Tietze Transformations (FINITELY PRESENTED SEMIGROUPS)
ModMatFld
Modules (OVERVIEW)
ModMatRng
Modules (OVERVIEW)
ModMPol
Modules (OVERVIEW)
Modsqrt
Modsqrt(n, m) : RngIntElt, RngIntElt -> BoolElt, RngIntElt
ModTupFld
Modules (OVERVIEW)
ModTupRng
Modules (OVERVIEW)
Modular
GrpFP_Modular (Example H16E7)
modular
Elliptic and Modular Functions (REAL AND COMPLEX FIELDS)
Modular Arithmetic (RING OF INTEGERS)
Modular Arithmetic (UNIVARIATE POLYNOMIAL RINGS)
Modular Representations (GROUPS)
modular-representation
Modular Representations (GROUPS)
Module
Module(P, r) : Rng, RngIntElt -> RngMPol
Module(P, W) : Rng, [ RngIntElt ] -> RngMPol
Module(R) : RngInvar -> ModMPol, Map
Module(e) : SubModLatElt -> ModRng
RngInvar_Module (Example H30E8)
module
Construction of a Free Module (GENERAL MODULES)
Construction of an R[G]-Module (GENERAL MODULES)
Definition of a Module (GENERAL MODULES)
Finitely Presented Modules (FINITELY PRESENTED ALGEBRAS)
Modules (OVERVIEW)
MODULES OVER K[x_1, ..., x_n]
Standard Constructions for R[G]-Modules (GENERAL MODULES)
Syzygy Modules (MULTIVARIATE POLYNOMIAL RINGS)
The Module of an Invariant Ring (INVARIANT RINGS OF FINITE GROUPS)
The Natural G-Module (MATRIX GROUPS)
Modules
Grp_Modules (Example H15E17)
modules
Modules (OVERVIEW)
modulo
Rings, Fields, and Algebras (OVERVIEW)
Modulus
Modulus(c) : FldComElt -> FldReElt
Modulus(R) : RngIntRes -> RngInt
Modulus(Q) : RngModPol -> RngUPolElt
MoebiusMu
MoebiusMu(n) : RngIntElt -> RngIntElt
molien
Molien Series (INVARIANT RINGS OF FINITE GROUPS)
MolienSeries
MolienSeries(G) : GrpMat -> FldFunUElt
RngInvar_MolienSeries (Example H30E4)
MonFP
Semigroups (OVERVIEW)
Monoid
Monoid(A) : Alg -> MonFP
Monoid< generators | relations > : MonFPElt, ..., MonFPElt, Rel, ..., Rel -> MonFP
SgpFP_Monoid (Example H14E2)
monoid
Accessing an Algebra (FINITELY PRESENTED ALGEBRAS)
Semigroups (OVERVIEW)
monomial
Coefficients, Monomials and Terms (MULTIVARIATE POLYNOMIAL RINGS)
MonomialCoefficient
MonomialCoefficient(u, m) : AlgFPElt, MonElt -> RngElt
MonomialCoefficient(f, m) : RngMPolElt, RngMPolElt -> RngElt
MonomialCoefficient(p, m) : RngUPolElt, RngUPolElt -> RngElt
MonomialGroup
AutomorphismGroup(C) : Code -> GrpPerm, PowMap, Map
MonomialGroupStabilizer
AutomorphismGroupStabilizer(C, k) : Code, RngIntElt -> GrpPerm, PowMap, Map
Monomials
Monomials(f) : RngMPolElt -> [ RngMPolElt ]
MonomialSubgroup
AutomorphismSubgroup(C) : Code -> GrpPerm, PowMap, Map
Mordell
Mordell-Weil group (ELLIPTIC CURVES)
Mordell-Weil
Mordell-Weil group (ELLIPTIC CURVES)
MordellWeil
Elcu_MordellWeil (Example H46E3)
MordellWeilGroup
MordellWeilGroup(E) : GeomEC -> GrpAb, Map
MordellWeilRank
MordellWeilRank(E) : GeomEC -> RngIntElt
MordellWeilRankBounds
MordellWeilRankBounds(E) : GeomEC -> RngIntElt, RngIntElt
Morphism
Morphism(H, G) : GrpAb, GrpAb -> Map
Morphism(M, N) : ModRng, ModRng -> ModMatRngElt
Morphism(U, V) : ModTupFld, ModTupFld -> Map
Morphism(M, N) : ModTupRng, ModTupRng -> ModMatRngElt
Morphism(e) : SubModLatElt -> ModMatRngElt
multi
Multi-indexing (INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS])
multi-indexing
Multi-indexing (INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS])
Multinomial
Multinomial(n, [a_1, ... a_n]) : RngIntElt, [RngIntElt] -> RngIntElt
Multinomial(n, [a_1, ... a_n]) : RngIntElt, [RngIntElt] -> RngIntElt
MultipartiteGraph
MultipartiteGraph(Q) : [RngIntElt] -> GrphUnd
multiple
Multiple Assignment (OVERVIEW)
multiple-assignment
Multiple Assignment (OVERVIEW)
MultipleReturns
State_MultipleReturns (Example H1E4)
multiplication
Operators (OVERVIEW)
MultiplicationTable
MultiplicationTable(O) : RngOrd -> [AlgMatElt]
FldNum_MultiplicationTable (Example H35E10)
MultiplicativeGroup
MultiplicativeGroup(F) : FldFin -> GrpAb, Map
MultiplicativeGroup(Z) : RngInt -> GrpAb, Map
MultiplicativeGroup(R) : RngIntRes -> GrpAb, Map
MultiplicatorRing
MultiplicatorRing(I) : RngOrdIdl -> Rng
MultiplicatorRing(I) : RngOrdIdl -> RngOrd
Multiplicity
Multiplicity(S, x) : SetMulti, Elt -> RngIntElt
MultiplyColumn
MultiplyColumn(~a, u, i) : AlgMatElt, RngElt, RngIntElt ->
MultiplyColumn(~a, u, i) : ModMatElt, FldElt, RngIntElt ->
MultiplyColumn(~a, u, i) : ModMatRngElt, RngElt, RngIntElt ->
MultiplyRow
MultiplyRow(~a, u, j) : AlgMatElt, RngElt, RngIntElt ->
MultiplyRow(~a, u, j) : ModMatElt, RngElt, RngIntElt ->
MultiplyRow(~a, u, j) : ModMatRngElt, RngElt, RngIntElt ->
Multiset
Set_Multiset (Example H7E4)
multiset
The Multiset Constructor (SETS)
Multisets
Multisets(S, k) : SetEnum, RngIntElt -> SetEnum
Multisets(S, k) : SetEnum, RngIntElt -> SetEnum
MultisetToSet
MultisetToSet(S) : SetMulti -> SetEnum
multivariate
MODULES OVER K[x_1, ..., x_n]
MULTIVARIATE POLYNOMIAL RINGS
multivariate-polynomial-module
MODULES OVER K[x_1, ..., x_n]
MultivariatePolynomial
MultivariatePolynomial(P, f, i) : RngMPol, RngUPolElt, RngIntElt -> RngMPolElt
mutate
Mutation assignment (OVERVIEW)
mutation
Incremental Construction of Graphs (GRAPHS)
Mutation assignment (OVERVIEW)
Mutation Assignment (STATEMENTS AND EXPRESSIONS)
MutationAssignment
State_MutationAssignment (Example H1E8)
mutual
Recursion and forward (OVERVIEW)
Recursion and Mutual Recursion (MAGMA SEMANTICS)
[____] [____] [_____] [____] [__] [Index] [Root]