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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 Structures (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 Cartesian Product Constructor (TUPLES AND CARTESIAN PRODUCTS)
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_EXTENSION_SIZE
MAGMA_MEMORY_EXTENSION_SIZE
MAGMA_MEMORY_LIMIT
MAGMA_MEMORY_LIMIT
MAGMA_PATH
MAGMA_PATH
MAGMA_STARTUP_FILE
MAGMA_STARTUP_FILE
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
Functions, Procedures, and Mappings (OVERVIEW)
Mappings (OVERVIEW)
Maps (OVERVIEW)
The Partial Mapping Constructor (MAPPINGS)
Maps
Map_Maps (Example H8E1)
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 H15E2)
KMod_Matrices (Example H33E4)
MatricesTup
MatricesTup(MGT) : SetCartElt -> [ GrpMatElt ]
Matrix
HMod_Matrix (Example H35E2)
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 (MULTIVARIATE POLYNOMIAL RINGS)
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
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
Max
Maximum(S) : SeqEnum -> Elt, RngIntElt
Maximum(S) : SetIndx -> Elt, RngIntElt
Maxdeg
MaximumDegree(G) : GrphDir -> RngIntElt, Vert
MaximumDegree(G) : GrphUnd -> RngIntElt, Vert
MaximalIsotropicSubspace
[Future release] MaximalIsotropicSubspace(V) : ModTupFld -> ModTupFld
MaximalNormalSubgroup
MaximalNormalSubgroup(G) : GrpFin -> GrpFin
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(e) : ModLatElt -> { ModLatElt }
MaximalSubmodules(M) : ModRng -> [ ModRng ], BoolElt
Maximum
Comparison (OVERVIEW)
Maximum(a, b) : RngElt, RngElt -> RngElt
Maximum(S) : SeqEnum -> Elt, RngIntElt
Maximum(S) : SetIndx -> Elt, RngIntElt
MaximumDegree
MaximumDegree(G) : GrphDir -> RngIntElt, Vert
MaximumDegree(G) : GrphUnd -> RngIntElt, Vert
MaximumInDegree
MaximumInDegree(G) : GrphDir -> RngIntElt, Vert
MaximumOutDegree
MaximumOutDegree(G) : GrphDir -> RngIntElt, Vert
Maxindeg
MaximumInDegree(G) : GrphDir -> RngIntElt, Vert
MaxNorm
MaxNorm(p) : RngDPolElt -> RngIntElt
MaxNorm(p) : RngUPolElt -> RngIntElt
Maxoutdeg
MaximumOutDegree(G) : GrphDir -> RngIntElt, Vert
Meataxe
Meataxe(M) : ModRng -> ModRng, ModRng, AlgMatElt
RMod_Meataxe (Example H34E16)
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
e meet f : ModLatElt, ModLatElt -> ModLatElt
U meet V : ModTupFld, ModTupFld -> ModTupFld
M meet N : ModTupRng, ModTupRng -> ModTupRng
I meet J : RngDPol, RngDPol -> RngDPol
I meet J : RngIdl, RngIdl -> RngIdl
I meet J : RngUPol, RngUPol -> RngUPol
R meet S : SetEnum, SetEnum -> SetEnum
meet:=
H meet:= K : GrpAb, GrpAb -> GrpAb
H meet:= K : GrpPC, GrpPC -> GrpPC
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)
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, Vert
MinimumDegree(G) : GrphUnd -> RngIntElt, Vert
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)
MinimalField
MinimalField(a) : FldCycElt -> FldCyc
MinimalField(q) : FldRatElt -> FldRat
MinimalInteger
MinimalInteger(I) : RngOrdIdl -> RngIntElt
MinimalModel
MinimalModel(E) : GeomEC -> GeomEC, Map
MinimalNormalSubgroup
MinimalNormalSubgroup(G) : GrpPC -> GrpPC
MinimalNormalSubgroups
MinimalNormalSubgroups(G) : GrpFin -> [ GrpFin ]
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 -> AlgPolElt
MinimalPolynomial(a) : FldNumElt -> AlgPolElt
MinimalPolynomial(a) : FldQuadElt -> AlgPolElt
MinimalPolynomial(q) : FldRatElt -> RngUPolElt
MinimalPolynomial(g) : GrpMatElt -> RngPolElt
MinimalPolynomial(n) : RngIntElt -> RngUPolElt
MinimalPolynomial(f) : RngQPolElt -> RngUPol
RngDPol_MinimalPolynomial (Example H23E17)
Minimals
RMod_Minimals (Example H34E18)
MinimalSubmodules
MinimalSubmodules(M) : ModRng -> [ ModRng ], BoolElt
MinimalSupermodules
MinimalSupermodules(e) : ModLatElt -> { ModLatElt }
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 Weight (ERROR-CORRECTING CODES)
minimum-weight
The Minimum Weight (ERROR-CORRECTING CODES)
MinimumDegree
MinimumDegree(G) : GrphDir -> RngIntElt, Vert
MinimumDegree(G) : GrphUnd -> RngIntElt, Vert
MinimumInDegree
MinimumInDegree(G) : GrphDir -> RngIntElt, Vert
MinimumOutDegree
MinimumOutDegree(G) : GrphDir -> RngIntElt, Vert
MinimumWeight
MinimumWeight(C) : Code -> RngIntElt
MinimumWords
MinimumWords(C) : Code -> { ModTupFldElt }
Minindeg
MinimumInDegree(G) : GrphDir -> RngIntElt, Vert
MinkowskiBound
MinkowskiBound(K) : FldNum -> RngIntElt
Minoutdeg
MinimumOutDegree(G) : GrphDir -> RngIntElt, Vert
minus
Operators (OVERVIEW)
MinusOne
One(B) : MagForm -> MagFormElt
Miscellaneous
Set_Miscellaneous (Example H4E6)
miscellaneous
Miscellaneous (FINITELY PRESENTED ALGEBRAS)
mod
Rings, Fields, and Algebras (OVERVIEW)
n mod m : RngIntElt, RngIntElt -> RngIntElt
n mod m : RngIntElt, RngIntElt -> RngIntElt
f mod g : RngUPolElt, RngUPolElt -> RngUPolElt
model
Alternative Models (ELLIPTIC CURVES)
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)
Modsqrt
Modsqrt(n, m) : RngIntElt, RngIntElt -> BoolElt, RngIntElt
ModTupFld
Modules (OVERVIEW)
ModTupRng
Modules (OVERVIEW)
Modular
GrpFP_Modular (Example H12E7)
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(e) : ModLatElt -> ModRng
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)
Standard Constructions for R[G]-Modules (GENERAL MODULES)
Syzygy Modules (MULTIVARIATE POLYNOMIAL RINGS)
Modules
Grp_Modules (Example H9E17)
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
MonFP
Semigroups (OVERVIEW)
Monoid
Monoid(A) : Alg -> MonFP
Monoid< generators | relations > : MonFPElt, ..., MonFPElt, Rel, ..., Rel -> MonFP
SgpFP_Monoid (Example H10E2)
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(p, m) : RngDPolElt, RngDPolElt -> RngElt
MonomialCoefficient(p, m) : RngUPolElt, RngUPolElt -> RngElt
Monomials
Monomials(p) : RngDPolElt -> [ RngDPolElt ]
Morphism
Morphism(H, G) : GrpAb, GrpAb -> Map
Morphism(e) : ModLatElt -> ModMatRngElt
Morphism(M, N) : ModRng, ModRng -> ModMatRngElt
Morphism(U, V) : ModTupFld, ModTupFld -> Map
Morphism(M, N) : ModTupRng, ModTupRng -> ModMatRngElt
Morphism(e) : SubGrpLatElt -> ModMatRngElt
Muller
Construction of Standard Linear Codes (ERROR-CORRECTING CODES)
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
MultipartiteGraph
MultipartiteGraph(Q) : [RngIntElt] -> GrphUnd
multiple
Multiple Assignment (OVERVIEW)
multiple-assignment
Multiple Assignment (OVERVIEW)
MultipleReturns
Lang_MultipleReturns (Example H1E4)
multiplication
Operators (OVERVIEW)
MultiplicationTable
MultiplicationTable(O) : RngOrd -> [AlgMatElt]
FldNum_MultiplicationTable (Example H28E10)
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
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 ->
multivariate
MULTIVARIATE POLYNOMIAL RINGS
mutate
Mutation assignment (OVERVIEW)
mutation
Mutation assignment (OVERVIEW)
MutationAssignment
Lang_MutationAssignment (Example H1E7)
mutual
Recursion and forward (OVERVIEW)
Recursion and Mutual Recursion (MAGMA SEMANTICS)
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