# The GAP 4 Reference Manual - Index M

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m_N 18.4
Macintosh 73.12
MacOS 73.12
Magma 33.2.1
Magma Categories 33.1
Magma Generation 33.2
Magma Homomorphisms 31.7
Magma Rings 63.0
Magma Rings modulo Relations 63.4
Magma Rings modulo the Span of a Zero Element 63.5
MagmaByGenerators 33.2.4
MagmaByMultiplicationTable 33.3.1
MagmaElement 33.3.4
MagmaHomomorphismByFunctionNC 31.7.2
MagmaRingModuloSpanOfZero 63.5.3
Magmas 33.0
Magmas Defined by Multiplication Tables 33.3
MagmaWithInverses 33.2.3
MagmaWithInversesByGenerators 33.2.6
MagmaWithInversesByMultiplicationTable 33.3.3
MagmaWithOne 33.2.2
MagmaWithOneByGenerators 33.2.5
MagmaWithOneByMultiplicationTable 33.3.2
Main Loop 6.1
Main Loop and Break Loop 6.0
MakeConfluent 36.1.11
MakeImmutable 12.6.4
MAKElb11 69.21.1
MakeReadOnlyGlobal 4.9.2
MakeReadWriteGlobal 4.9.3
Making transformation semigroups 49.1
Manual Conventions 1.1
map, parametrized 71.3
MappedWord 34.3.1
MappingByFunction 31.1.2
MappingPermListList 40.4.3
Mappings 31.0
Mappings that Respect Addition 31.9
Mappings that Respect Multiplication 31.8
Mappings which are Compatible with Algebraic Structures 31.6
maps 71.0
Maps Concerning Character Tables 71.0
MarksTom 68.7.1
MatAlgebra 60.4.4
MatClassMultCoeffsCharTable 69.10.8
MathieuGroup 48.1.9
MatLieAlgebra 61.2.4
Matrices 24.0
Matrices as Basis of a Row Space 24.10
Matrices as Linear Mappings 24.12
Matrices over Finite Fields 24.13
Matrices Representing Linear Equations and the Gaussian Algorithm 24.6
matrices, commutator 24.2.11
matrix automorphisms 71.1
Matrix Constructions 24.4
Matrix Groups 42.0
Matrix Groups in Characteristic 0 42.5
matrix spaces 59.8
MatrixAlgebra 60.4.4
MatrixAutomorphisms 69.19.1
MatrixByBlockMatrix 24.14.3
MatrixLieAlgebra 61.2.4
MatrixOfAction 60.10.15
MatScalarProducts 70.8.6
MatTom 68.7.10
MaximalAbelianQuotient 37.17.4
MaximalBlocks 39.10.2
MaximalNormalSubgroups 37.18.8
MaximalSubgroupClassReps 37.18.5
MaximalSubgroups 37.18.6
MaximalSubgroups, for groups with pcgs 43.16
MaximalSubgroupsLattice 37.19.3
MaximalSubgroupsTom 68.9.12
Maximum 21.20.11
MaximumList 21.20.13
MeatAxe Modules 67.1
MeetEquivalenceRelations 32.6.3
MeetMaps 71.3.8
Membership Test for Collections 28.5
Membership Test for Lists 21.8
Minimal Nonmonomial Groups 72.4
Minimal Polynomials 64.8
MinimalElementCosetStabChain 41.9.12
MinimalGeneratingSet 37.21.3
MinimalGeneratingSet, for groups with pcgs 43.16
MinimalNonmonomialGroup 72.4.2
MinimalPolynomial 64.8.1
MinimalPolynomial, over a field 56.3.2
MinimalPolynomial, over a ring 64.8
MinimalStabChain 41.7.5
MinimalSupergroupsLattice 37.19.4
MinimalSupergroupsTom 68.9.13
MinimizedBombieriNorm 64.11.3
Minimum 21.20.12
MinimumList 21.20.13
MinusCharacter 71.4.5
Miscellaneous 15.5
MOCChars 69.21.6
MOCString 69.21.3
MOCTable 69.21.2
mod 4.12.1
mod, arithmetic operators 4.12
mod, for character tables 69.7
mod, Integers 14.4
mod, Laurent polynomials 64.2.2
mod, lists 21.14
mod, rationals 4.12
mod, residue class rings 14.4
modular inverse 4.12
modular remainder 4.12
modular roots 15.3
Module Homomorphisms 67.7
ModuleByRestriction 60.10.21
ModuleOfExtension 44.8.7
Modules 55.0
Modules over Lie Algebras and Their Cohomology 61.12
Modules over Semisimple Lie Algebras 61.13
modulo 4.12
modulo, arithmetic operators 4.12
modulo, for pcgs 43.9.5
modulo, residue class rings 14.4.1
ModuloPcgs 43.9.1
MoebiusMu 15.4.3
MoebiusTom 68.7.11
Molien Series 70.12
MolienSeries 70.12.1
MolienSeriesInfo 70.12.2
MolienSeriesWithGivenDenominator 70.12.4
Monoid 50.0 50.0 50.0
MonoidByGenerators 50.0 50.0
MonoidByMultiplicationTable 50.0
MonoidOfRewritingSystem 51.5.4
Monoids 50.0
Monomiality Questions 72.0
MonomialRevLexicoLess 64.16.3
MonomialTotalDegreeLess 64.16.2
monomorphisms, find all 38.9
MorClassLoop 38.9.4
More about Boolean Lists 22.4
More About Global Variables 4.9
More about Tables of Marks 68.1
MostFrequentGeneratorFpGroup 45.5.8
Moved Points of Permutations 40.2
MovedPoints 40.2.3
MTX.BasesCompositionSeries 67.5.9
MTX.BasesMaximalSubmodules 67.5.5
MTX.BasesMinimalSubmodules 67.5.4
MTX.BasesMinimalSupermodules 67.5.8
MTX.BasesSubmodules 67.5.3
MTX.BasisRadical 67.5.6
MTX.BasisSocle 67.5.7
MTX.CollectedFactors 67.5.11
MTX.CompositionFactors 67.5.10
MTX.DegreeSplittingField 67.4.3
MTX.Dimension 67.3.2
MTX.Distinguish 67.7.5
MTX.Field 67.3.3
MTX.Generators 67.3.1
MTX.Homomorphism 67.7.3
MTX.Homomorphisms 67.7.4
MTX.InducedAction 67.6.5
MTX.InducedActionFactorMatrix 67.6.4
MTX.InducedActionFactorModule 67.6.3
MTX.InducedActionMatrix 67.6.4
MTX.InducedActionMatrixNB 67.6.4
MTX.InducedActionSubmodule 67.6.2
MTX.InducedActionSubmoduleNB 67.6.2
MTX.IsAbsolutelyIrreducible 67.4.2
MTX.IsEquivalent 67.7.1
MTX.IsIrreducible 67.4.1
MTX.Isomorphism 67.7.2
MTX.NormedBasisAndBaseChange 67.6.1
MTX.ProperSubmoduleBasis 67.5.2
MTX.SubmoduleGModule 67.5.1
multiplication 4.12.1
multiplication, matrices 24.2.7
multiplication, matrix and matrix list 24.2.13
multiplication, matrix and scalar 24.2.4
multiplication, matrix and vector 24.2.6
multiplication, operation 30.12.1
multiplication, scalar and matrix 24.2.4
multiplication, scalar and matrix list 24.2.12
multiplication, scalar and vector 23.1.4
multiplication, vector and matrix 24.2.5
multiplication, vector and matrix list 24.2.15
multiplication, vector and scalar 23.1.4
multiplication, vectors 23.1.5
MultiplicationTable 33.3.5
Multiplicative Arithmetic for Lists 21.14
Multiplicative Arithmetic Functions 15.4
multiplicative order of an integer 15.2
MultiplicativeNeutralElement 33.4.10
MultiplicativeZero 33.4.11
MultiplicativeZeroOp 30.10.4
multiplicity, of constituents of a group character 70.8
Multiplier 37.23
multisets 21.19
Multivariate Polynomials 64.7
MultRowVector 23.3.3
Murnaghan components 70.11
Mutability and Copyability 12.6
Mutability Status and List Arithmetic 21.15
Mutable Bases 59.7
MutableBasis 59.7.2
MutableBasisOfClosureUnderAction 60.8.11
MutableBasisOfIdealInNonassociativeAlgebra 60.8.13
MutableBasisOfNonassociativeAlgebra 60.8.12
MutableIdentityMat 24.4.11
MutableNullMat 24.4.12

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GAP 4 manual
May 2002