# The GAP 4 Manual - Full Index M

_ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

m_N R 18.4
Macintosh R 73.14 R 73.15
MacOS R 73.15
Magma R 33.2.1
Magma Categories R 33.1
Magma Generation R 33.2
Magma Homomorphisms R 31.7
Magma Rings R 63.0
Magma Rings modulo Relations R 63.4
Magma Rings modulo the Span of a Zero Element R 63.5
MagmaByGenerators R 33.2.4
MagmaByMultiplicationTable R 33.3.1
MagmaElement R 33.3.4
MagmaHomomorphismByFunctionNC R 31.7.2
MagmaRingModuloSpanOfZero R 63.5.3
Magmas R 33.0
Magmas Defined by Multiplication Tables R 33.3
MagmaWithInverses R 33.2.3
MagmaWithInversesByGenerators R 33.2.6
MagmaWithInversesByMultiplicationTable R 33.3.3
MagmaWithOne R 33.2.2
MagmaWithOneByGenerators R 33.2.5
MagmaWithOneByMultiplicationTable R 33.3.2
Main Loop R 6.1
Main Loop and Break Loop R 6.0
MakeConfluent R 36.1.11
MakeHomChain N 5.2.5
MakeImmutable R 12.6.4
makeindex E 2.13
MakeReadOnlyGlobal R 4.9.2
MakeReadWriteGlobal R 4.9.3
Making transformation semigroups R 49.1
Manual Conventions R 1.1
manual.bbl E 2.13
manual.bib E 2.13
manual.dvi E 2.13
manual.lab E 2.13
manual.mst E 2.13
manual.six E 2.13
manual.tex E 2.13
manualindex E 2.13
map, parametrized R 71.3
MappedWord R 34.3.1
MappingByFunction R 31.1.2
MappingPermListList R 40.4.3
Mappings R 31.0
Mappings that Respect Addition R 31.9
Mappings that Respect Multiplication R 31.8
Mappings which are Compatible with Algebraic Structures R 31.6
maps R 71.0
Maps Concerning Character Tables R 71.0
maps-to operator T 2.7
MarksTom R 68.7.1
MatAlgebra R 60.4.4
MatClassMultCoeffsCharTable R 69.10.8
mathematics alignments E 2.8
mathematics displays E 2.8
MathieuGroup R 48.1.9
MatLieAlgebra R 61.2.4
Matrices R 24.0
matrices, commutator R 24.2.11
matrices T 3.8
Matrices as Basis of a Row Space R 24.10
Matrices as Linear Mappings R 24.12
Matrices over Finite Fields R 24.13
Matrices Representing Linear Equations and the Gaussian Algorithm R 24.6
matrix automorphisms R 71.1
Matrix Constructions R 24.4
Matrix Groups R 42.0
Matrix Groups in Characteristic 0 R 42.5
matrix spaces R 59.8
MatrixAlgebra R 60.4.4
MatrixAutomorphisms R 69.20.1
MatrixByBlockMatrix R 24.15.3
MatrixLieAlgebra R 61.2.4
MatrixOfAction R 60.10.15
MatScalarProducts R 70.8.6
MatTom R 68.7.10
MaximalAbelianQuotient R 37.18.4
MaximalBlocks R 39.10.2
MaximalNormalSubgroups R 37.19.8
MaximalSubgroupClassReps R 37.19.5
MaximalSubgroups R 37.19.6
MaximalSubgroups, for groups with pcgs R 43.16
MaximalSubgroupsLattice R 37.20.3
MaximalSubgroupsTom R 68.9.12
Maximum R 21.20.12
MaximumList R 21.20.14
MeatAxe Modules R 67.1
meet strategy E 8.2
MeetEquivalenceRelations R 32.6.3
MeetMaps R 71.3.8
MeetPartitionStrat E 8.2.1
Membership Test for Collections R 28.5
Membership Test for Lists R 21.8
method P 2.0
Method Installation P 2.2
Method Selection P 2.0
methods T 8.1
methods, immediate T 8.3
methods, selection T 8.2
methods, true T 8.3
Migrating to GAP 4 T 9.0
Minimal Nonmonomial Groups R 72.4
Minimal Polynomials R 64.8
MinimalElementCosetStabChain R 41.9.12
MinimalGeneratingSet R 37.22.3
MinimalGeneratingSet, for groups with pcgs R 43.16
MinimalNonmonomialGroup R 72.4.2
MinimalNormalSubgroups R 37.19.9
MinimalPolynomial R 64.8.1
MinimalPolynomial, over a field R 56.3.2
MinimalPolynomial, over a ring R 64.8
MinimalStabChain R 41.7.5
MinimalSupergroupsLattice R 37.20.4
MinimalSupergroupsTom R 68.9.13
MinimizedBombieriNorm R 64.11.6
Minimum R 21.20.13
MinimumList R 21.20.14
MinusCharacter R 71.4.5
Miscellaneous R 15.6
Miscellaneous Name Changes or Removed Names R 75.4
mod R 4.12.1
mod, arithmetic operators R 4.12
mod, for character tables R 69.7
mod, Integers R 14.4
mod, Laurent polynomials R 64.2.2
mod, lists R 21.14
mod, rationals R 4.12
mod, residue class rings R 14.4
modular inverse R 4.12
modular remainder R 4.12
modular roots R 15.3
Module Constructions R 67.2
Module Homomorphisms R 67.8
ModuleByRestriction R 60.10.21
ModuleOfExtension R 44.8.7
Modules R 55.0
Modules over Lie Algebras and Their Cohomology R 61.12
Modules over Semisimple Lie Algebras R 61.13
modulo R 4.12
modulo, arithmetic operators R 4.12
modulo, for pcgs R 43.9.5
modulo, residue class rings R 14.4.1
ModuloPcgs R 43.9.1
MoebiusMu R 15.4.3
MoebiusTom R 68.7.11
Molien Series R 70.12
MolienSeries R 70.12.1
MolienSeriesInfo R 70.12.2
MolienSeriesWithGivenDenominator R 70.12.4
Monoid R 50.0 R 50.0 R 50.0
MonoidByGenerators R 50.0 R 50.0
MonoidByMultiplicationTable R 50.0
MonoidOfRewritingSystem R 51.5.5
Monoids R 50.0
Monomial Orderings R 64.16
MonomialComparisonFunction R 64.16.5
MonomialExtGrlexLess R 64.16.14
MonomialExtrepComparisonFun R 64.16.6
MonomialGrevlexOrdering R 64.16.9
MonomialGrlexOrdering R 64.16.8
Monomiality Questions R 72.0
MonomialLexOrdering R 64.16.7
MonomialTotalDegreeLess R 75.4
monomorphisms, find all R 38.9
MorClassLoop R 38.9.4
More about Boolean Lists R 22.4
More About Global Variables R 4.9
More about Tables of Marks R 68.1
MostFrequentGeneratorFpGroup R 45.5.8
Moved Points of Permutations R 40.2
MovedPoints R 40.2.3
MTX.BasesCompositionSeries R 67.6.9
MTX.BasesMaximalSubmodules R 67.6.5
MTX.BasesMinimalSubmodules R 67.6.4
MTX.BasesMinimalSupermodules R 67.6.8
MTX.BasesSubmodules R 67.6.3
MTX.BasisInOrbit R 67.9.4
MTX.BasisRadical R 67.6.6
MTX.BasisSocle R 67.6.7
MTX.CollectedFactors R 67.6.11
MTX.CompositionFactors R 67.6.10
MTX.DegreeSplittingField R 67.5.3
MTX.Dimension R 67.4.2
MTX.Distinguish R 67.8.5
MTX.Field R 67.4.3
MTX.Generators R 67.4.1
MTX.Homomorphism R 67.8.3
MTX.Homomorphisms R 67.8.4
MTX.InducedAction R 67.7.5
MTX.InducedActionFactorMatrix R 67.7.4
MTX.InducedActionFactorModule R 67.7.3
MTX.InducedActionMatrix R 67.7.4
MTX.InducedActionMatrixNB R 67.7.4
MTX.InducedActionSubmodule R 67.7.2
MTX.InducedActionSubmoduleNB R 67.7.2
MTX.InvariantBilinearForm R 67.9.1
MTX.InvariantQuadraticForm R 67.9.3
MTX.InvariantSesquilinearForm R 67.9.2
MTX.IsAbsolutelyIrreducible R 67.5.2
MTX.IsEquivalent R 67.8.1
MTX.IsIrreducible R 67.5.1
MTX.Isomorphism R 67.8.2
MTX.NormedBasisAndBaseChange R 67.7.1
MTX.OrthogonalSign R 67.9.5
MTX.ProperSubmoduleBasis R 67.6.2
MTX.SubGModule R 67.6.1
MTX.SubmoduleGModule R 67.6.1
multiplication R 4.12.1
multiplication, matrices R 24.2.7
multiplication, matrix and matrix list R 24.2.13
multiplication, matrix and scalar R 24.2.4
multiplication, matrix and vector R 24.2.6
multiplication, operation R 30.12.1
multiplication, scalar and matrix R 24.2.4
multiplication, scalar and matrix list R 24.2.12
multiplication, scalar and vector R 23.1.4
multiplication, vector and matrix R 24.2.5
multiplication, vector and matrix list R 24.2.15
multiplication, vector and scalar R 23.1.4
multiplication, vectors R 23.1.5
MultiplicationTable R 33.3.5
Multiplicative Arithmetic for Lists R 21.14
Multiplicative Arithmetic Functions R 15.4
multiplicative order of an integer R 15.2
MultiplicativeNeutralElement R 33.4.10
MultiplicativeZero R 33.4.11
MultiplicativeZeroOp R 30.10.4
multiplicity, of constituents of a group character R 70.8
Multiplier R 37.24
multisets R 21.19
Multivariate Polynomials R 64.7
MultRowVector R 23.3.3
Murnaghan components R 70.11
Mutability and Copyability R 12.6
Mutability and Copying P 3.16
Mutability Status and List Arithmetic R 21.15
Mutable Bases R 59.7
MutableBasis R 59.7.2
MutableBasisOfClosureUnderAction R 60.8.11
MutableBasisOfIdealInNonassociativeAlgebra R 60.8.13
MutableBasisOfNonassociativeAlgebra R 60.8.12
MutableIdentityMat R 24.4.11
MutableNullMat R 24.4.12

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