|  | Index Entry | Section | 
|---|
| 
 | 
| M |  |  | 
|---|
|  | M, ordering | B.2.6 Matrix orderings | 
|  | m_merkle_hellman_decryption | D.12.3.50 m_merkle_hellman_decryption | 
|  | m_merkle_hellman_encryption | D.12.3.49 m_merkle_hellman_encryption | 
|  | m_merkle_hellman_transformation | D.12.3.48 m_merkle_hellman_transformation | 
|  | Macdonald's formula | D.15.16 goettsche_lib | 
|  | MacdonaldF | D.15.16.7 MacdonaldF | 
|  | Macintosh installation | E.8 Macintosh installation instructions | 
|  | magnitude | D.11.4.7 magnitude | 
|  | makeDivisor | D.15.13.1 makeDivisor | 
|  | makeFormalDivisor | D.15.13.11 makeFormalDivisor | 
|  | makeGraph | D.4.6.1 makeGraph | 
|  | makeGraphVE | D.15.33.21 makeGraphVE | 
|  | makeHeisenberg | 7.5.19.0. makeHeisenberg | 
|  | makeIdeal | D.15.23.5 makeIdeal | 
|  | makeLetterplaceRing | 7.10.4.8 makeLetterplaceRing | 
|  | makeMalgrange | 7.5.7.0. makeMalgrange | 
|  | makeMatrix | D.15.23.4 makeMatrix | 
|  | makeModElimRing | 7.5.19.0. makeModElimRing | 
|  | makePDivisor | D.15.13.17 makePDivisor | 
|  | makeQsl2 | 7.5.10.0. makeQsl2 | 
|  | makeQsl3 | 7.5.10.0. makeQsl3 | 
|  | makeQso3 | 7.5.10.0. makeQso3 | 
|  | makeSheaf | D.15.33.9 makeSheaf | 
|  | makeUe6 | 7.5.10.0. makeUe6 | 
|  | makeUe7 | 7.5.10.0. makeUe7 | 
|  | makeUe8 | 7.5.10.0. makeUe8 | 
|  | makeUf4 | 7.5.10.0. makeUf4 | 
|  | makeUg2 | 7.5.10.0. makeUg2 | 
|  | makeUgl | 7.5.10.0. makeUgl | 
|  | makeUsl | 7.5.10.0. makeUsl | 
|  | makeUsl2 | 7.5.10.0. makeUsl2 | 
|  | makeUso10 | 7.5.10.0. makeUso10 | 
|  | makeUso11 | 7.5.10.0. makeUso11 | 
|  | makeUso12 | 7.5.10.0. makeUso12 | 
|  | makeUso5 | 7.5.10.0. makeUso5 | 
|  | makeUso6 | 7.5.10.0. makeUso6 | 
|  | makeUso7 | 7.5.10.0. makeUso7 | 
|  | makeUso8 | 7.5.10.0. makeUso8 | 
|  | makeUso9 | 7.5.10.0. makeUso9 | 
|  | makeUsp1 | 7.5.10.0. makeUsp1 | 
|  | makeUsp2 | 7.5.10.0. makeUsp2 | 
|  | makeUsp3 | 7.5.10.0. makeUsp3 | 
|  | makeUsp4 | 7.5.10.0. makeUsp4 | 
|  | makeUsp5 | 7.5.10.0. makeUsp5 | 
|  | makeVariety | D.15.33.1 makeVariety | 
|  | makeVector | D.15.23.33 makeVector | 
|  | makeWeyl | 7.5.19.0. makeWeyl | 
|  | map | 4.11 map | 
|  | map (plural) | 7.2.2 map (plural) | 
|  | map declarations | 4.11.1 map declarations | 
|  | map declarations (plural) | 7.2.2.1 map declarations (plural) | 
|  | map expressions | 4.11.2 map expressions | 
|  | map expressions (plural) | 7.2.2.2 map expressions (plural) | 
|  | map operations | 4.11.3 map operations | 
|  | map operations (plural) | 7.2.2.3 map (plural) operations | 
|  | map related functions | 4.11.4 map related functions | 
|  | map related functions  (plural) | 7.2.2.4 map related functions (plural) | 
|  | mapall | D.2.11.10 mapall | 
|  | mapIsFinite | D.4.2.10 mapIsFinite | 
|  | mappingcone | D.15.20.29 mappingcone | 
|  | mappingcone3 | D.15.20.31 mappingcone3 | 
|  | mapToRatNormCurve | D.5.4.6 mapToRatNormCurve | 
|  | markov4ti2 | D.4.28.1 markov4ti2 | 
|  | mat2arr | D.14.1.3 mat2arr | 
|  | mat2carr | D.14.1.4 mat2carr | 
|  | mat_rk | D.3.2.14 mat_rk | 
|  | matbil | D.12.7.5 matbil | 
|  | Mathematical background | C. Mathematical background | 
|  | Mathematical background (letterplace) | 7.9 Mathematical background (letterplace) | 
|  | Mathematical background (plural) | 7.4 Mathematical background (plural) | 
|  | mathematical objects | B.1 Representation of mathematical objects | 
|  | mathinit | D.9.1.2 mathinit | 
|  | matmult | D.12.7.6 matmult | 
|  | matrix | 4.12 matrix | 
|  | matrix | D.14.1.3 mat2arr | 
|  | matrix | D.14.1.4 mat2carr | 
|  | matrix | D.14.1.5 arrPrintMatrix | 
|  | matrix declarations | 4.12.1 matrix declarations | 
|  | matrix diagonalization | D.11.3 jacobson_lib | 
|  | matrix expressions | 4.12.2 matrix expressions | 
|  | matrix operations | 4.12.4 matrix operations | 
|  | Matrix orderings | B.2.6 Matrix orderings | 
|  | matrix related functions | 4.12.5 matrix related functions | 
|  | matrix type cast | 4.12.3 matrix type cast | 
|  | matrix.lib | D.3.1 matrix_lib | 
|  | matrix_lib | D.3.1 matrix_lib | 
|  | matrixExp | D.5.3.2 matrixExp | 
|  | matrixLog | D.5.3.3 matrixLog | 
|  | matrixpres | D.15.20.34 matrixpres | 
|  | matrixsystem | D.15.15.15 matrixsystem | 
|  | matrixT1 | D.6.16.3 matrixT1 | 
|  | max | 5.1.87 max | 
|  | Max | D.6.14.8 Max | 
|  | maxabs | D.12.8.8 maxabs | 
|  | maxcoef | D.2.8.7 maxcoef | 
|  | maxdeg | D.2.8.8 maxdeg | 
|  | maxdeg1 | D.2.8.9 maxdeg1 | 
|  | maxEord | D.5.5.9 maxEord | 
|  | maxExp | 5.1.2 attrib | 
|  | maxideal | 5.1.88 maxideal | 
|  | maximalFace | D.13.2.41 maximalFace | 
|  | maximalGroebnerCone | D.13.4.37 maximalGroebnerCone | 
|  | maximalValue | D.13.2.42 maximalValue | 
|  | maximum | D.12.2.6 maximum | 
|  | maximum number of zeroes | D.5.3.5 maxZeros | 
|  | Maximus | D.5.11.2 Maximus | 
|  | maxIntRoot | 7.5.13.0. maxIntRoot | 
|  | Maxord | D.5.5.16 Maxord | 
|  | maxZeros | D.5.3.5 maxZeros | 
|  | mdouble | 3.8.7.1 mdouble | 
|  | mem, option | 5.1.110 option | 
|  | member | D.15.9.3 member | 
|  | membershipMon | D.4.15.5 membershipMon | 
|  | memory | 5.1.89 memory | 
|  | memory management | 5.1.89 memory | 
|  | merkle_hellman_decryption | D.12.3.52 merkle_hellman_decryption | 
|  | merkle_hellman_encryption | D.12.3.51 merkle_hellman_encryption | 
|  | methods, hashtables | D.15.22 methods_lib | 
|  | methods.lib | D.15.22 methods_lib | 
|  | methods_lib | D.15.22 methods_lib | 
|  | midpoint | D.15.15.11 midpoint | 
|  | MillerRabin | D.12.3.16 MillerRabin | 
|  | milnor | D.6.15.10 milnor | 
|  | Milnor code | D.15.1 arnoldclassify_lib | 
|  | Milnor number | A.4.1 Milnor and Tjurina number | 
|  | Milnor number | D.15.29.3 milnornumber | 
|  | milnorcode | D.6.3.7 milnorcode | 
|  | milnornumber | D.15.29.3 milnornumber | 
|  | Min | D.6.14.9 Min | 
|  | min | 5.1.90 min | 
|  | minAssChar | D.4.22.8 minAssChar | 
|  | minAssCharE | D.4.22.9 minAssCharE | 
|  | minAssGTZ | D.4.22.6 minAssGTZ | 
|  | minAssGTZE | D.4.22.7 minAssGTZE | 
|  | minAssZ | D.4.23.3 minAssZ | 
|  | minbase | 5.1.91 minbase | 
|  | minbaseMon | D.4.15.2 minbaseMon | 
|  | mindeg | D.2.8.10 mindeg | 
|  | mindeg1 | D.2.8.11 mindeg1 | 
|  | mindist | D.10.2.12 mindist | 
|  | minEcart | D.12.5.7 minEcart | 
|  | minimal display time, setting the | 5.1.153 system | 
|  | minimal representations | 7.10.6 ncrat_lib | 
|  | minimalAfaceOrbits | D.15.18.13 minimalAfaceOrbits | 
|  | minimalAfaces | D.15.18.4 minimalAfaces | 
|  | MinimalDecomposition | D.7.3.10 MinimalDecomposition | 
|  | minimalFace | D.13.2.43 minimalFace | 
|  | minimalOrbitConeOrbits | D.15.18.15 minimalOrbitConeOrbits | 
|  | minimalValue | D.13.2.44 minimalValue | 
|  | Minimum distance | D.10.2 decodegb_lib | 
|  | Minimus | D.5.11.1 Minimus | 
|  | minIntRoot | 7.5.4.0. minIntRoot | 
|  | minIntRoot2 | 7.5.13.0. minIntRoot2 | 
|  | minipoly | D.3.2.19 minipoly | 
|  | minkowskiSum | D.13.2.45 minkowskiSum | 
|  | minMult | D.4.4.1 minMult | 
|  | MinMult | D.15.5.2 MinMult | 
|  | minor | 5.1.92 minor | 
|  | minpoly | 5.3.3 minpoly | 
|  | minres | 5.1.93 minres | 
|  | minres (plural) | 7.3.13 minres (plural) | 
|  | minus | D.15.12.15 difformSub | 
|  | minus | D.15.12.16 difformNeg | 
|  | minus | D.15.12.37 derivationSub | 
|  | minus | D.15.12.38 derivationNeg | 
|  | mirror symmetry | D.4.6 ellipticcovers_lib | 
|  | Miscellaneous libraries | D.14 Miscellaneous libraries | 
|  | mixed Hodge structure | D.6.9 gmssing_lib | 
|  | mixed Hodge structure | D.6.9.6 spectrum | 
|  | mixed Hodge structure | D.6.9.7 sppairs | 
|  | mixed Hodge structure | D.6.9.8 vfilt | 
|  | mixed Hodge structure | D.6.9.9 vwfilt | 
|  | mixed Hodge structure | D.6.9.10 tmatrix | 
|  | mixed Hodge structure | D.6.9.11 endvfilt | 
|  | mixed Hodge structure | D.6.10 gmspoly_lib | 
|  | mixed Hodge structure | D.6.10.2 goodBasis | 
|  | mod | 4.2.3 bigint operations | 
|  | mod | 4.6.3 int operations | 
|  | mod | 4.14.3 number operations | 
|  | mod | 4.16.3 poly operations | 
|  | mod2id | D.2.8.15 mod2id | 
|  | mod_versal | D.6.7.2 mod_versal | 
|  | modality | D.6.3.15 modality | 
|  | modberlekampMassey | D.15.14.5 modberlekampMassey | 
|  | modBorder | D.15.31.2 modBorder | 
|  | modDec | D.4.16.4 modDec | 
|  | moddiq.lib | D.4.12 moddiq_lib | 
|  | moddiq_lib | D.4.12 moddiq_lib | 
|  | ModEqn | D.6.14.2 ModEqn | 
|  | modfrWalk | D.15.24.4 modfrWalk | 
|  | modfWalk | D.15.24.3 modfWalk | 
|  | modIntersect | D.4.14.3 modIntersect | 
|  | modJanet | D.15.31.4 modJanet | 
|  | modNormal | D.4.13.1 modNormal | 
|  | modnormal.lib | D.4.13 modnormal_lib | 
|  | modnormal_lib | D.4.13 modnormal_lib | 
|  | modNPos | D.4.18.4 modNPos | 
|  | modNpos_test | D.4.18.2 modNpos_test | 
|  | modQuotient | D.4.12.1 modQuotient | 
|  | modrationalInterpolation | D.15.14.3 modrationalInterpolation | 
|  | modregCM | D.4.18.8 modregCM | 
|  | modrWalk | D.15.24.2 modrWalk | 
|  | modSagbiAlg | D.15.7.8 modSagbiAlg | 
|  | modSat | D.4.12.2 modSat | 
|  | modsatiety | D.4.18.6 modsatiety | 
|  | modStd | D.4.14.1 modStd | 
|  | modstd.lib | D.4.14 modstd_lib | 
|  | modstd_lib | D.4.14 modstd_lib | 
|  | modSyz | D.4.14.2 modSyz | 
|  | modular | D.2.6.1 modular | 
|  | modular methods | D.4.11 locnormal_lib | 
|  | modular methods | D.4.13 modnormal_lib | 
|  | modular methods. | D.4.11.1 locNormal | 
|  | Modular techniques | D.2.6 modular_lib | 
|  | modular techniques. | D.4.13.1 modNormal | 
|  | modular.lib | D.2.6 modular_lib | 
|  | modular_lib | D.2.6 modular_lib | 
|  | modular_lib | D.2.6 modular_lib | 
|  | module | 4.13 module | 
|  | module (plural) | 7.2.3 module (plural) | 
|  | module declarations | 4.13.1 module declarations | 
|  | module declarations (plural) | 7.2.3.1 module declarations (plural) | 
|  | module expressions | 4.13.2 module expressions | 
|  | module expressions (plural) | 7.2.3.2 module expressions (plural) | 
|  | module operations | 4.13.3 module operations | 
|  | module operations (plural) | 7.2.3.3 module operations (plural) | 
|  | module ordering C | B.2.5 Module orderings | 
|  | module ordering c | B.2.5 Module orderings | 
|  | Module orderings | B.2.5 Module orderings | 
|  | module related functions | 4.13.4 module related functions | 
|  | module related functions (plural) | 7.2.3.4 module related functions (plural) | 
|  | module_containment | D.4.2.2 module_containment | 
|  | Modules and and their annihilator | 2.3.5 Modules and their annihilator | 
|  | modules.lib | D.15.23 modules_lib | 
|  | modules_lib | D.15.23 modules_lib | 
|  | moduliSpace | D.15.33.23 moduliSpace | 
|  | modulo | 5.1.94 modulo | 
|  | modulo (plural) | 7.3.14 modulo (plural) | 
|  | moduloSlim | 7.5.19.0. moduloSlim | 
|  | modVStd | D.15.8.4 modVStd | 
|  | modVStd0 | D.15.8.5 modVStd0 | 
|  | modWalk | D.15.24.1 modWalk | 
|  | modwalk.lib | D.15.24 modwalk_lib | 
|  | modwalk_lib | D.15.24 modwalk_lib | 
|  | moebius | D.14.1.39 moebius | 
|  | moebius function | D.14.1.39 moebius | 
|  | molien | D.7.1.9 molien | 
|  | mondromy.lib | D.6.13 mondromy_lib | 
|  | mondromy_lib | D.6.13 mondromy_lib | 
|  | monitor | 5.1.95 monitor | 
|  | Monodromy | D.6.13 mondromy_lib | 
|  | monodromy | D.6.9 gmssing_lib | 
|  | monodromy | D.6.9.5 monodromy | 
|  | monodromy | D.6.9.5 monodromy | 
|  | monodromy | D.6.9.10 tmatrix | 
|  | monodromy | D.6.10 gmspoly_lib | 
|  | monodromy | D.6.10.2 goodBasis | 
|  | monodromyB | D.6.13.4 monodromyB | 
|  | monomial | 5.1.96 monomial | 
|  | monomial ordering | D.2.11.19 hasGlobalOrdering | 
|  | Monomial orderings | B.2 Monomial orderings | 
|  | monomial orderings | A.1.3 Rings associated to monomial orderings | 
|  | monomial orderings | B.2.2 General definitions for orderings | 
|  | monomial orderings introduction | B.2.1 Introduction to orderings | 
|  | Monomial orderings on free algebras | 7.9.2 Monomial orderings on free algebras | 
|  | Monomial orderings, Term orderings | 3.3.3 Term orderings | 
|  | monomial output | 5.3.7 short | 
|  | monomial, write | 5.3.7 short | 
|  | monomialabortstd | D.14.2.1 monomialabortstd | 
|  | monomialideal.lib | D.4.15 monomialideal_lib | 
|  | monomialideal_lib | D.4.15 monomialideal_lib | 
|  | monomialInIdeal | 7.5.13.0. monomialInIdeal | 
|  | monomialLcm | D.12.5.5 monomialLcm | 
|  | monomials and precedence | 6.4 Miscellaneous oddities | 
|  | mons2intmat | D.4.20.24 mons2intmat | 
|  | Mori dream spaces | D.15.2 autgradalg_lib | 
|  | Morse lemma | D.15.29.2 realmorsesplit | 
|  | Morse lemma | D.15.29.5 addnondegeneratevariables | 
|  | morsesplit | D.6.3.8 morsesplit | 
|  | movingCone | D.15.18.11 movingCone | 
|  | mp_res_mat | D.8.3.4 mp_res_mat | 
|  | mplot | D.9.1.3 mplot | 
|  | mpresmat | 5.1.97 mpresmat | 
|  | mprimdec.lib | D.4.16 mprimdec_lib | 
|  | mprimdec_lib | D.4.16 mprimdec_lib | 
|  | mregular.lib | D.4.17 mregular_lib | 
|  | mregular_lib | D.4.17 mregular_lib | 
|  | mRes | D.15.23.13 mRes | 
|  | mres | 5.1.98 mres | 
|  | mres (plural) | 7.3.15 mres (plural) | 
|  | mstd | 5.1.99 mstd | 
|  | msum | 3.8.7.3 msum | 
|  | mtriple | 3.8.7.2 mtriple | 
|  | mult | 5.1.100 mult | 
|  | mult | 6.4 Miscellaneous oddities | 
|  | multarr2arr | D.14.1.34 multarr2arr | 
|  | multarrMultRestrict | D.14.1.36 multarrMultRestrict | 
|  | multarrRestrict | D.14.1.35 multarrRestrict | 
|  | multBound | 5.3.4 multBound | 
|  | multcol | D.3.1.18 multcol | 
|  | multdivisor | D.15.13.3 multdivisor | 
|  | multformaldivisor | D.15.13.15 multformaldivisor | 
|  | multi | D.12.4.5 multi | 
|  | multi indices | 3.5.3 Names | 
|  | multi-graded Hilbert series | 7.10.5 ncHilb_lib | 
|  | multiarrangement | D.14.1.30 arrDer | 
|  | multiarrangement | D.14.1.31 arrIsFree | 
|  | multiarrangement | D.14.1.32 arrExponents | 
|  | multiarrangement | D.14.1.33 arr2multarr | 
|  | multiarrangement | D.14.1.34 multarr2arr | 
|  | multiarrangement | D.14.1.35 multarrRestrict | 
|  | multiarrangement | D.14.1.36 multarrMultRestrict | 
|  | multiDeg | D.15.25.30 multiDeg | 
|  | multiDegBasis | D.15.25.31 multiDegBasis | 
|  | multiDegGroebner | D.15.25.39 multiDegGroebner | 
|  | multiDegModulo | D.15.25.41 multiDegModulo | 
|  | multiDegPartition | D.15.25.32 multiDegPartition | 
|  | multiDegResolution | D.15.25.42 multiDegResolution | 
|  | multiDegSyzygy | D.15.25.40 multiDegSyzygy | 
|  | multiDegTensor | D.15.25.43 multiDegTensor | 
|  | multiDegTor | D.15.25.44 multiDegTor | 
|  | multidimensional_knapsack | D.12.3.44 multidimensional_knapsack | 
|  | multigrading, multidegree, multiweights, multigraded-homogeneous, integral linear algebra | D.15.25 multigrading_lib | 
|  | multigrading.lib | D.15.25 multigrading_lib | 
|  | multigrading_lib | D.15.25 multigrading_lib | 
|  | multipleCover | D.15.33.29 multipleCover | 
|  | multiplication | D.15.12.17 difformMul | 
|  | multiplication | D.15.12.39 derivationMul | 
|  | multiplicities, sequence of | D.6.11.6 invariants | 
|  | multiplicity | D.15.10.2 curveConductorMult | 
|  | multiplicity sequence | D.6.1.7 charexp2multseq | 
|  | multiplicity sequence | D.6.1.10 charexp2conductor | 
|  | multiplicity sequence | D.6.11.8 multsequence | 
|  | MultiplicitySequence | D.6.6.6 MultiplicitySequence | 
|  | multiplyLeftFractions | 7.5.20.0. multiplyLeftFractions | 
|  | multiplylist | D.5.5.29 multiplylist | 
|  | multivariate equations | D.8.1 ffsolve_lib | 
|  | multRat | 7.5.13.0. multRat | 
|  | multrow | D.3.1.19 multrow | 
|  | multseq2charexp | D.6.1.6 multseq2charexp | 
|  | multsequence | D.6.11.8 multsequence | 
|  | MVComplex | D.15.11.2 MVComplex | 
| 
 |