[____] [____] [_____] [____] [__] [Index] [Root]
Index M
MacWilliamsTransform(n, k, K, W) : RngIntElt, RngIntElt, FldFin, RngMPol -> RngMPol
MacWilliamsTransform(n, k, q, W) : RngIntElt, RngIntElt, RngIntElt, [ <RngIntElt, RngIntElt> ] -> [ <RngIntElt, RngIntElt> ]
IsCohenMacaulay(R) : RngInvar -> BoolElt
CodeFld_MacWilliams (Example H101E22)
The MacWilliams Transform (LINEAR CODES OVER FINITE FIELDS)
MacWilliamsTransform(n, k, K, W) : RngIntElt, RngIntElt, FldFin, RngMPol -> RngMPol
MacWilliamsTransform(n, k, q, W) : RngIntElt, RngIntElt, RngIntElt, [ <RngIntElt, RngIntElt> ] -> [ <RngIntElt, RngIntElt> ]
MAGMA
Magma Updates (OVERVIEW)
The Magma System (OVERVIEW)
PrintFileMagma(F, x) : MonStgElt, Var ->
Constructing a General Matrix Algebra (MATRIX ALGEBRAS)
Construction of a Group Algebra (GROUP ALGEBRAS)
Construction of a Rewrite Group (GROUPS DEFINED BY REWRITE SYSTEMS)
Construction of a Vector Space (VECTOR SPACES)
Construction of an Automatic Group (AUTOMATIC GROUPS)
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 Algebraic Fields (ORDERS AND ALGEBRAIC FIELDS)
Creation of Structures (RATIONAL FIELD)
Creation of Structures (REAL AND COMPLEX FIELDS)
Creation of Structures (UNIVARIATE POLYNOMIAL RINGS)
Magma (CLASS FIELD THEORY)
Magmas (or Structures) (OVERVIEW)
Planes in Magma (FINITE PLANES)
Presentations (FINITELY PRESENTED SEMIGROUPS)
Related Structures (RATIONAL FUNCTION FIELDS)
Specification of a Polycyclic Presentation (POLYCYCLIC GROUPS)
The General Group Constructors (GROUPS)
MAGMA_HELP_DIR
MAGMA_LIBRARIES
MAGMA_LIBRARY_ROOT
MAGMA_MEMORY_LIMIT
MAGMA_PATH
MAGMA_STARTUP_FILE
MAGMA_SYSTEM_SPEC
MAGMA_USER_SPEC
MAGMA_HELP_DIR
MAGMA_LIBRARIES
MAGMA_LIBRARY_ROOT
MAGMA_MEMORY_LIMIT
MAGMA_PATH
MAGMA_STARTUP_FILE
MAGMA_SYSTEM_SPEC
MAGMA_USER_SPEC
Overview (OVERVIEW)
Magma Updates (OVERVIEW)
MakePCMap(A, P, S) : Aff, Prj, SeqEnum ->
MakeProjectiveClosureMap(A, P, S) : Aff,Prj,SeqEnum ->
MakeResolutionGraph(g,s,t) : GrphDir,SeqEnum,SeqEnum -> GrphRes
MakeResolutionGraph(N) : NewtonPgon -> GrphRes
MakeSpliceDiagram(g,e,a) : GrphDir,SeqEnum,SeqEnum -> GrphSpl
MakeSpliceDiagram(e,l,a) : SeqEnum,SeqEnum,SeqEnum -> GrphSpl
MakeType(S) : MonStgElt -> Cat
CodeFld_Make12-8-4Code (Example H101E31)
MakePCMap(A, P, S) : Aff, Prj, SeqEnum ->
MakeProjectiveClosureMap(A, P, S) : Aff,Prj,SeqEnum ->
MakePCMap(A, P, S) : Aff, Prj, SeqEnum ->
MakeProjectiveClosureMap(A, P, S) : Aff,Prj,SeqEnum ->
MakeResolutionGraph(g,s,t) : GrphDir,SeqEnum,SeqEnum -> GrphRes
MakeResolutionGraph(N) : NewtonPgon -> GrphRes
MakeSpliceDiagram(g,e,a) : GrphDir,SeqEnum,SeqEnum -> GrphSpl
MakeSpliceDiagram(e,l,a) : SeqEnum,SeqEnum,SeqEnum -> GrphSpl
MakeType(S) : MonStgElt -> Cat
ManhattanForm(M) : Mtrx -> Mtrx, AlgMatElt
ManhattanForm(M) : Mtrx -> Mtrx, AlgMatElt
ManhattanForm(M) : Mtrx -> Mtrx, AlgMatElt
ManhattanForm(M) : Mtrx -> Mtrx, AlgMatElt
ConvertFromManinSymbol(M, x) : ModSym, Tup -> ModSymElt
ManinSymbol(x) : ModSymElt -> SeqEnum
ManinSymbol(x) : ModSymElt -> SeqEnum
MantissaExponent(r) : FldReElt -> FldReElt, RngIntElt
MantissaExponent(r) : FldReElt -> FldReElt, RngIntElt
Documentation (OVERVIEW)
AlgebraMap(f) : MapSch -> Map
ArtinMap(A) : FldAb -> Map
AugmentationMap(A) : AlgGrp -> Map
BoundaryMap(C, n) : ModCpx, RngIntElt -> ModMatFldElt
BoundaryMap(M) : ModSym -> ModMatFldElt
CanonicalMap(C) : Crv -> MapSch
ChainMap(Q, C, D, n) : SeqEnum, ModCpx, ModCpx, RngIntElt -> ModMatCpxElt
ClassMap(G) : GrpAb -> Map
ClassMap(G) : GrpMat -> Map
ClassMap(G) : GrpPC -> Map
ClassMap(G: parameters) : GrpFin -> Map
ClassMap(G: parameters) : GrpPerm -> Map
CoefficientMap(L) : LinSys -> ModTupFldElt
CohomologyGeneratorToChainMap(P,Q,C,n) : ModCpx, ModCpx, Tup, RngIntElt -> MapChn
CohomologyGeneratorToChainMap(P,C,n) : ModCpx, Tup, RngIntElt -> MapChn
ConstantMap(X,Y,p) : Sch,Sch,Pt -> MapSch
DegeneracyMap(M1, M2, d) : ModSym, ModSym, RngIntElt -> Map
DivisorMap(D) : DivCrvElt -> MapSch
EmbeddingMap(F, L): FldAlg, FldAlg -> Map
EmbeddingMap(e) : SubFldLatElt -> Map
FrobeniusMap(E) : CrvEll -> Map
FrobeniusMap(E, i) : CrvEll, RngIntElt -> Map
GrayMap(C) : Code -> Map
GrayMapImage(C) : Code -> [ ModTupRngElt ]
HasDefinedModuleMap(C,n) : ModCpx, RngIntElt -> BoolElt
HasLinearGrayMapImage(C) : Code -> BoolElt, Code
IdentityAutomorphism(X) : Sch -> MapAutSch
IdentityMap(E) : CrvEll -> Map
IdentityMap(E) : CrvEll -> Map
IdentityMap(X) : Sch -> MapSch
InclusionMap(G, H) : GrpGPC, GrpGPC -> Map
InclusionMap(G, H) : GrpPC, GrpPC -> Map
InducedMap(m1, m2, h, c) : Map, Map, Map, RngIntElt -> Map
InducedMapOnHomology(f,n) : MapChn, RngIntElt -> ModTupFldElt
InverseWordMap(G) : GrpMat -> Map
InverseWordMap(G) : GrpPerm -> Map
IsChainMap(L, C, D, n) : List, ModCpx, ModCpx, RngIntElt -> BoolElt
IsChainMap(f) : MapChn -> BoolElt
IsProperChainMap(f) : MapChn -> BoolElt
IsZeroMap(C, n) : ModCpx, RngIntElt -> BoolElt
IsogenyMapOmega(I) : Map -> RngMPolElt
IsogenyMapPhi(I) : Map -> RngUPolElt
IsogenyMapPhiMulti(I) : Map -> RngUPolElt
IsogenyMapPsi(I) : Map -> RngUPolElt
IsogenyMapPsiMulti(I) : Map -> RngUPolElt
IsogenyMapPsiSquared(I) : Map -> RngUPolElt
MakeProjectiveClosureMap(A, P, S) : Aff,Prj,SeqEnum ->
ModuleMap(f, n) : ModMatCpxElt, RngIntElt -> ModMatFldElt
NegationMap(E) : CrvEll -> Map
NumberingMap(G) : GrpAb -> Map
NumberingMap(G) : GrpFin -> Map
NumberingMap(G) : GrpMat -> Map
NumberingMap(G) : GrpPC -> Map
NumberingMap(G) : GrpPerm -> Map
PolyMapKernel(f) : Map -> RngMPol
PolynomialMap(L) : LinSys -> RngMPolElt
PowerMap(G) : GrpAb -> Map
PowerMap(G) : GrpFin -> Map
PowerMap(G) : GrpMat -> Map
PowerMap(G) : GrpPC -> Map
PowerMap(G) : GrpPerm -> Map
PrincipalDivisorMap(F) : FldFun -> Map
PrincipalIdealMap(O) : RngFunOrd -> Map
ProjectiveClosureMap(A) : Aff -> MapSch
QuotientMap(Q1, Q2) : QuadBin, QuadBin -> Map
RationalMap(i, t) : Map, Map -> Map
SPrincipalDivisorMap(S) : SetEnum[PlcFunElt] -> Map
TranslationMap(E, P) : CrvEll, PtEll -> Map
UniversalMap(C, S, [ n_1, ..., n_m ]) : Cop, Str, [ Map ] -> Map
ZeroChainMap(C, D) : ModCpx -> ModMatCpxElt
ZeroMap(M, N) : ModAlg, ModAlg -> ModMatFld
CrvEll_Map (Example H87E36)
Functions, Procedures, and Mappings (OVERVIEW)
Maps (OVERVIEW)
Maps (SCHEMES)
The Gray Map (LINEAR CODES OVER FINITE RINGS)
The Period Map (MODULAR SYMBOLS)
ConstantMap(X,Y,p) : Sch,Sch,Pt -> MapSch
map< A -> B | x : -> e(x) > : Struct, Struct -> Map
map< A -> B | x : -> e(x), y : -> i(y) > : Struct, Struct -> Map
map< X -> Y | F > : Sch,Sch,SeqEnum -> MapSch
map< A -> B | G > : Struct, Struct -> Map
Scheme_map-base-points (Example H83E18)
Scheme_map-creation (Example H83E11)
Scheme_map-error (Example H83E13)
Scheme_map-frobenius (Example H83E12)
Scheme_map-image1 (Example H83E16)
Scheme_map-image2 (Example H83E17)
Scheme_map-patches (Example H83E20)
GB_Map1 (Example H66E25)
IntegralMapping(M) : ModSym -> Map
PeriodMapping(M, prec) : ModSym, RngIntElt -> Map
RationalMapping(M) : ModSym -> Map
Creation of Maps (MAPPINGS)
Creation of Partial Maps (MAPPINGS)
Functions, Procedures, and Mappings (OVERVIEW)
Mappings (OVERVIEW)
Maps (OVERVIEW)
BoundaryMaps(C) : ModCpx -> List
EFAModuleMaps(G) : GrpGPC -> [ModGrp]
Maps(D, C) : Str, Str -> PowMap
SemisimpleEFAModuleMaps(G) : GrpGPC -> [ModGrp]
Automorphisms (SCHEMES)
Basic Attributes (SCHEMES)
Basic Tests (SCHEMES)
Creation of Maps (SCHEMES)
Linear Systems and Maps (SCHEMES)
Maps (CLASS FIELD THEORY)
Maps and Closure (SCHEMES)
Maps and Curves (PLANE ALGEBRAIC CURVES)
Maps and Points (SCHEMES)
Maps and Schemes (SCHEMES)
Maps between Polynomial Rings (IDEAL THEORY AND GRÖBNER BASES)
Maps between Schemes (SCHEMES)
Trivial Attributes (SCHEMES)
Basic Attributes (SCHEMES)
Automorphisms (SCHEMES)
Maps and Closure (SCHEMES)
Creation of Maps (SCHEMES)
Maps and Curves (PLANE ALGEBRAIC CURVES)
RngLaz_maps-multi (Example H57E5)
Scheme_maps-point-image (Example H83E15)
Maps and Points (SCHEMES)
Maps and Schemes (SCHEMES)
Basic Tests (SCHEMES)
Trivial Attributes (SCHEMES)
RngLaz_maps-uni (Example H57E4)
MarkGroebner(I) : RngMPol ->
MarkGroebner(I) : RngMPol ->
ConnectionPolynomial(S) : SeqEnum -> RngUPolElt, RngIntElt
CharacteristicPolynomial(S) : SeqEnum -> RngUPolElt, RngIntElt
BerlekampMassey(S) : SeqEnum -> RngUPolElt, RngIntElt
MATRICES
The Burnside Algorithm for General Groups (K[G]-MODULES AND GROUP REPRESENTATIONS)
Match(u, v, f) : GrpFPElt, GrpFPElt, RngIntElt -> BoolElt, RngIntElt
Match(u, v, f) : SgpFPElt, SgpFPElt, RngIntElt -> BoolElt, RngIntElt
Database of Matrix Groups (OVERVIEW)
CoreflectionMatrices( RD ) : RootDtm -> []
ReflectionMatrices( RD ) : RootDtm -> []
SimpleReflectionMatrices( RD ) : RootDtm -> []
GrpMat_Matrices (Example H21E2)
ModFld_Matrices (Example H61E4)
Cartan Matrices (ROOT DATA FOR LIE THEORY)
Matrices as Words (MATRIX GROUPS)
Matrices as Words (MATRIX GROUPS)
AbsoluteRepresentationMatrix(a) : FldAlgElt -> AlgMatElt
AdjacencyMatrix(G) : Grph -> AlgMatElt
AdjacencyMatrix(G,p) : SymGen, RngIntElt -> AlgMatElt
AdjointMatrix(L, x) : AlgLie, AlgLieElt -> AlgMatElt
AntisymmetricMatrix(R, Q) : Rng, [ RngElt ] -> Mtrx
AntisymmetricMatrix(Q) : [ RngElt ] -> Mtrx
BaseChangeMatrix(A) : AlgBas -> ModAlg
BasisMatrix(S) : AlgGrpSub -> ModMatRngElt
BasisMatrix(L) : Lat -> ModMatRngElt
BasisMatrix(M) : ModMPol -> ModMatRngElt
BasisMatrix(V) : ModTupFld -> ModMatElt
BasisMatrix(I) : RngFunOrdIdl -> AlgMatElt
BasisMatrix(O) : RngOrd -> AlgMatElt
BasisMatrix(I) : RngOrdFracIdl -> MtrxSpcElt
BurnsideMatrix(G) : GrpPC -> AlgMatElt
CambridgeMatrix(t, K, n, Q) : RngIntElt, FldFint, RngIntElt, [ ] -> AlgMatElt
CartanMatrix( W ) : GrpCox -> AlgMatElt
CartanMatrix(g) : GrphRes -> Mtrx
CartanMatrix( G ) : GrpLie -> AlgMatElt
CartanMatrix( t ) : MonStgElt -> AlgMatElt
CartanMatrix( RD ) : RootDtm -> AlgMatElt
CentralisingMatrix(G) : GrpMat -> AlgMatElt
ChangeRing(A, R) : Mtrx, Ring -> Mtrx
ChangeRing(A, R) : MtrxSprs, Ring -> MtrxSprs
ClassMatrix(G, i) : GrpAb, RngIntElt -> AlgMatElt
CloseVectorsMatrix(L, w, u) : Lat, ModTupRngElt, RngElt -> ModMatRngElt
ClosestVectorsMatrix(L, w) : Lat, ModTupRngElt -> ModMatRngElt, RngElt
CompanionMatrix(p) : RngPolElt -> AlgMatElt
CompanionMatrix(f) : RngUPolElt -> AlgMatElt
DegeneracyMatrix(M1, M2, d) : ModSym, ModSym, RngIntElt -> AlgMatElt
DiagonalMatrix(R, Q) : AlgMat, [ RngElt ] -> AlgMatElt
DiagonalMatrix(R, n, Q) : Rng, RngIntElt, [ RngElt ] -> Mtrx
DiagonalMatrix(R, Q) : Rng, [ RngElt ] -> Mtrx
DiagonalMatrix(Q) : [ RngElt ] -> Mtrx
DisplayBurnsideMatrix(G) : GrpPC ->
DistanceMatrix(G) : Grph -> AlgMatElt
EmbeddingMatrix(S) : AlgQuatOrd -> AlgMatElt
GeneratorMatrix(C) : Code -> ModMatFldElt
GeneratorMatrix(C) : Code -> ModMatRngElt
GramMatrix(S) : AlgQuatOrd -> AlgMat
GramMatrix(L) : Lat -> AlgMatElt
GramMatrix(M) : ModBrdt -> AlgMatElt
GramMatrix(X) : ModMatRngElt : -> AlgMatElt
GramMatrix(f) : QuadBinElt -> AlgMatElt
HeightPairingMatrix(S: Precision) : [JacHypPt] -> AlgMat
HessianMatrix(X) : Sch -> ModMatRngElt
HessianMatrix(C) : Sch -> Mtrx
IncidenceMatrix(G) : Grph -> ModHomElt
IncidenceMatrix(D) : Inc -> ModMatRngElt
IncidenceMatrix(P) : Plane -> AlgMatElt
InnerProductMatrix(L) : Lat -> AlgMatElt
InnerProductMatrix(M) : ModBrdt -> AlgMatElt
IntersectionMatrix(G, P) : GrphUnd, { { GrphVert } } -> AlgMatElt
InverseRSKCorrespondenceMatrix(t1, t2) : Tbl, Tbl -> Mat
IsCartanMatrix( M ) : AlgMatElt -> BoolElt
JacobianMatrix(C) : Sch -> ModMatRngElt
JacobianMatrix(X) : Sch -> ModMatRngElt
JacobianMatrix( [ f ] ) : [ RngMPolElt ] -> RngMPol
KillingMatrix(L) : AlgLie -> AlgMatElt
LLLBasisMatrix(L) : Lat -> ModMatElt, AlgMatElt
LLLGramMatrix(L) : Lat -> AlgMatElt, AlgMatElt
LowerTriangularMatrix(R, Q) : Rng, [ RngElt ] -> Mtrx
LowerTriangularMatrix(Q) : [ RngElt ] -> Mtrx
Matrix(f) : MapSch -> Mtrx
Matrix(A) : Mtrx -> Mtrx
Matrix(A) : MtrxSprs -> Mtrx
Matrix(R, m, n, Q) : Rng, RngIntElt, RngIntElt, [ RngElt ] -> Mtrx
Matrix(R, n, Q) : Rng, RngIntElt, [ RngElt ] -> Mtrx
Matrix(Q) : Rng, [ [ RngElt ] ] -> Mtrx
Matrix(R, Q) : Rng, [ [ RngElt ] ] -> Mtrx
Matrix(m, n, Q) : RngIntElt, RngIntElt, [ RngElt ] -> Mtrx
Matrix(m, n, Q) : RngIntElt, RngIntElt, [ [ RngElt ] ] -> Mtrx
Matrix(n, Q) : RngIntElt, [ RngElt ] -> Mtrx
Matrix(Q) : [ Mtrx ] -> Mtrx
MatrixAlgebra(A) : AlgAss -> AlgMat
MatrixAlgebra(A, E) : AlgMat, FldFin -> AlgMat, Map
MatrixAlgebra(F, E) : FldFin, FldFin -> AlgMat, Map
MatrixAlgebra(R, n) : Rng, RngInt -> AlgMat
MatrixAlgebra(S, n) : Rng, RngIntElt -> AlgMat
MatrixAlgebra<S, n | L> : Rng, RngIntElt, List -> AlgMat
MatrixAlgebra(Q) : RngMPolRes -> AlgMat, Map
MatrixGroup(M) : ModGrp -> GrpMat
MatrixGroup< n, R | L > : RngIntElt, Rng, List -> GrpMat
MatrixToPerm( W, M ) : GrpCox, AlgMatElt -> GrpPermElt
MatrixToWord( W, M ) : GrpCox, AlgMatElt -> SeqEnum
MatrixUnit(R, i, j) : AlgMat, RngIntElt, RngIntElt -> AlgMatElt
NullspaceMatrix(A) : Mtrx -> ModTupRng
NullspaceMatrix(A) : MtrxSprs -> Mtrx
ParametrizationMatrix(C) : CrvCon -> ModMatRngElt
ParityCheckMatrix(C) : Code -> ModMatFldElt
ParityCheckMatrix(C) : Code -> ModMatRngElt
PermToMatrix( W, M ) : GrpCox, GrpPermElt -> AlgMatElt
PermutationGroup< X | L > : Set, List -> GrpPerm, Hom
QuaternionicMatrixGroupDatabase() : -> DB
RationalMatrixGroupDatabase() : -> DB
ReducedGramMatrix(S) : AlgQuatOrd -> AlgMat
ReflectionMatrix( RD, r ) : RootDtm, RngIntElt -> []
RelationMatrix(K, B) : FldNum, RngIntElt -> ModHomElt
RelationMatrix(O) : RngOrd -> ModHomElt
RepresentationMatrix(a) : FldAlgElt -> AlgMatElt
RepresentationMatrix(a) : FldFunGElt -> AlgMatElt
RepresentationMatrix(f) : RngMPolResElt -> AlgMatElt
RootSystemMatrix(t, n) : MonStgElt, RngIntElt -> AlgMatElt
ScalarMatrix(R, t) : AlgMat, RngElt -> AlgMatElt
ScalarMatrix(R, n, s) : Rng, RngIntElt, RngElt -> Mtrx
ScalarMatrix(n, s) : RngIntElt, RngElt -> Mtrx
ShortVectorsMatrix(L, u) : Lat, RngElt -> ModMatRngElt
ShortestVectorsMatrix(L) : Lat -> ModMatRngElt
SparseMatrix(A) : Mtrx -> MtrxSprs
SparseMatrix(R) : Rng -> MtrxSprs
SparseMatrix(R, m, n) : Rng, RngIntElt, RngIntElt -> MtrxSprs
SparseMatrix(R, m, n, Q) : Rng, RngIntElt, RngIntElt, [ <RngIntElt, RngIntElt, RngElt> ] -> MtrxSprs
SparseMatrix(m, n) : RngIntElt, RngIntElt -> MtrxSprs
SymmetricMatrix(R, Q) : Rng, [ RngElt ] -> Mtrx
SymmetricMatrix(Q) : [ RngElt ] -> Mtrx
SyzygyMatrix(Q) : [ RngMPolElt ] -> ModMatRngElt
TraceMatrix(O) : RngOrd -> AlgMatElt
TransformationMatrix(I) : RngFunOrdIdl -> AlgMatElt, RngElt
TransformationMatrix(O, P) : RngOrd -> AlgMatElt, RngIntElt
TransformationMatrix(I) : RngOrdFracIdl -> MtrxSpcElt, RngIntElt
UpperTriangularMatrix(R, Q) : Rng, [ RngElt ] -> Mtrx
UpperTriangularMatrix(Q) : [ RngElt ] -> Mtrx
WordToMatrix( W, w ) : GrpCox, [] -> AlgMatElt
ModRng_Matrix (Example H62E10)
Construction of a General Matrix Group (MATRIX GROUPS)
Construction of Initialized Sparse Matrices (SPARSE MATRICES)
Construction of Modules of m x n Matrices (FREE MODULES)
Construction of Trivial Sparse Matrices (SPARSE MATRICES)
Database of Matrix Groups (OVERVIEW)
General Matrix Construction (MATRICES)
Matrices and Vector Spaces Associated with a Graph or Digraph (GRAPHS)
Matrix Action on Forms (BINARY QUADRATIC FORMS)
MATRIX ALGEBRAS
Matrix Group Actions on Polynomials (INVARIANT RINGS OF FINITE GROUPS)
MATRIX GROUPS
Rings, Fields, and Algebras (OVERVIEW)
Soluble Matrix Groups (MATRIX GROUPS)
Construction of Modules of m x n Matrices (FREE MODULES)
Matrices and Vector Spaces Associated with a Graph or Digraph (GRAPHS)
MatrixAlgebra(A) : AlgAss -> AlgMat
MatrixAlgebra(A, E) : AlgMat, FldFin -> AlgMat, Map
MatrixAlgebra(F, E) : FldFin, FldFin -> AlgMat, Map
MatrixAlgebra(R, n) : Rng, RngInt -> AlgMat
MatrixAlgebra(S, n) : Rng, RngIntElt -> AlgMat
MatrixAlgebra<S, n | L> : Rng, RngIntElt, List -> AlgMat
MatrixAlgebra(Q) : RngMPolRes -> AlgMat, Map
MatrixGroup(M) : ModGrp -> GrpMat
MatrixGroup< n, R | L > : RngIntElt, Rng, List -> GrpMat
PermutationGroup< X | L > : Set, List -> GrpPerm, Hom
MatrixRing(S, n) : Rng, RngIntElt -> AlgMat
MatrixAlgebra(S, n) : Rng, RngIntElt -> AlgMat
MatrixAlgebra<S, n | L> : Rng, RngIntElt, List -> AlgMat
DualMatrixToPerm( W, M ) : GrpCox, AlgMatElt -> GrpPermElt
MatrixToPerm( W, M ) : GrpCox, AlgMatElt -> GrpPermElt
DualMatrixToWord( W, M ) : GrpCox, AlgMatElt -> SeqEnum
MatrixToWord( W, M ) : GrpCox, AlgMatElt -> SeqEnum
MatrixUnit(R, i, j) : AlgMat, RngIntElt, RngIntElt -> AlgMatElt
InverseMattsonSolomonTransform(A, n) : RngUPolElt, RngIntElt -> RngUPolElt
MattsonSolomonTransform(f, n) : RngUPolElt, RngIntElt -> RngUPolElt
Mattson--Solomon Transforms (LINEAR CODES OVER FINITE FIELDS)
Mattson--Solomon Transforms (LINEAR CODES OVER FINITE FIELDS)
MattsonSolomonTransform(f, n) : RngUPolElt, RngIntElt -> RngUPolElt
CodeFld_MattsonSolomonTransform (Example H101E43)
MaxNorm(f) : RngMPolElt -> RngIntElt
MaxNorm(p) : RngUPolElt -> RngIntElt
MaxParabolics(C) : CosetGeom -> SetIndx
Maximum(S) : SeqEnum -> Elt, RngIntElt
Maximum(S) : SetIndx -> Elt, RngIntElt
Maxdeg(G) : GrphDir -> RngIntElt, GrphVert
MaximumDegree(G) : GrphDir -> RngIntElt, GrphVert
MaximumDegree(G) : GrphUnd -> RngIntElt, GrphVert
IsMaximal(G, H) : GrpAb, GrpAb -> BoolElt
IsMaximal(G, H) : GrpFin, GrpFin -> BoolElt
IsMaximal(G, H) : GrpFP, GrpFP -> BoolElt
IsMaximal(G, H) : GrpMat, GrpMat -> BoolElt
IsMaximal(G, H) : GrpPC, GrpPC -> BoolElt
IsMaximal(G, H) : GrpPerm, GrpPerm -> BoolElt
IsMaximal(O) : RngFunOrd -> BoolElt
IsMaximal(I) : RngMPol -> BoolElt
IsMaximal(O) : RngOrd -> BoolElt
IsProbablyMaximal(G, H: parameters) : GrpPerm, GrpPerm -> BoolElt
MaxParabolics(C) : CosetGeom -> SetIndx
MaximalAbelianSubfield(M) : RngOrd -> FldAb
MaximalIncreasingSequence(w) : MonOrdElt -> RngIntElt
MaximalIncreasingSequences(w, k) : SeqEnum,RngIntElt -> RngIntElt
MaximalIntegerSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
MaximalLeftIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MaximalIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MaximalNormalSubgroup(G) : GrpPerm -> GrpPerm
MaximalNumberOfCosets(P) : GrpFPCosetEnumProc -> RngIntElt
MaximalOrder(A) : AlgQuat -> AlgQuatOrd
MaximalOrder(A) : FldAb -> RngOrd
MaximalOrder(F) : FldAlg -> RngOrd
MaximalOrder(F) : FldQuad -> RngQuad
MaximalOrder(Q) : FldRat -> RngInt
MaximalOrder(O) : RngFunOrd -> RngFunOrd
MaximalOrder(O) : RngOrd -> RngOrd
MaximalOrder(f) : RngUPolElt -> RngOrd
MaximalOrderFinite(F) : FldFun -> RngFunOrd
MaximalOrderInfinite(F) : FldFun -> RngFunOrd
MaximalOvergroup(G, H) : GrpFP, GrpFP -> GrpFP
MaximalPartition(G) : GrpPerm -> GSet
MaximalSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
MaximalSubfields(e) : SubFldLatElt -> [ SubFldLatElt ]
MaximalSubgroups(G) : GrpAb -> [GrpAb]
MaximalSubgroups(G) : GrpPC -> [GrpPC]
MaximalSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
MaximalSubgroups(e) : SubGrpLatElt -> { SubGrpLatElt }
MaximalSubmodules(M) : ModRng -> [ ModRng ], BoolElt
MaximalSubmodules(e) : SubModLatElt -> { SubModLatElt }
MaximalZeroOneSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
SetOrderMaximal(O, b) : RngOrd, BoolElt ->
MaximalAbelianSubfield(M) : RngOrd -> FldAb
MaximalRightIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MaximalIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MaximalLeftIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MaximalIncreasingSequence(w) : MonOrdElt -> RngIntElt
MaximalIncreasingSequences(w, k) : SeqEnum,RngIntElt -> RngIntElt
MaximalIntegerSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
MaximalRightIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MaximalIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MaximalLeftIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MaximalNormalSubgroup(G) : GrpPerm -> GrpPerm
MaximalNumberOfCosets(P) : GrpFPCosetEnumProc -> RngIntElt
MaximalOrder(A) : AlgQuat -> AlgQuatOrd
MaximalOrder(A) : FldAb -> RngOrd
MaximalOrder(F) : FldAlg -> RngOrd
MaximalOrder(F) : FldQuad -> RngQuad
MaximalOrder(Q) : FldRat -> RngInt
MaximalOrder(O) : RngFunOrd -> RngFunOrd
MaximalOrder(O) : RngOrd -> RngOrd
MaximalOrder(f) : RngUPolElt -> RngOrd
MaximalOrderFinite(F) : FldFun -> RngFunOrd
MaximalOrderInfinite(F) : FldFun -> RngFunOrd
MaximalOvergroup(G, H) : GrpFP, GrpFP -> GrpFP
MaximalParabolics(C) : CosetGeom -> SetIndx
MaxParabolics(C) : CosetGeom -> SetIndx
MaximalPartition(G) : GrpPerm -> GSet
MaximalRightIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MaximalIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MaximalLeftIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
GrpPerm_Maximals (Example H20E14)
Conjugacy Classes of Subgroups (PERMUTATION GROUPS)
Maximal Subgroups (PERMUTATION GROUPS)
MaximalSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
MaximalSubfields(e) : SubFldLatElt -> [ SubFldLatElt ]
MaximalSubgroups(G) : GrpAb -> [GrpAb]
MaximalSubgroups(G) : GrpPC -> [GrpPC]
MaximalSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
MaximalSubgroups(e) : SubGrpLatElt -> { SubGrpLatElt }
MaximalSubmodules(M) : ModRng -> [ ModRng ], BoolElt
MaximalSubmodules(e) : SubModLatElt -> { SubModLatElt }
MaximalZeroOneSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
SetMaximiseFunction(L, m) : LP, BoolElt ->
IsMaximisingFunction(L) : LP -> BoolElt
Comparison (OVERVIEW)
GetMaximumMemoryUsage() : -> RngIntElt
IsMaximumDistanceSeparable(C) : Code -> BoolElt
Maximum(a, b) : RngElt, RngElt -> RngElt
Maximum(S) : SeqEnum -> Elt, RngIntElt
Maximum(S) : SetIndx -> Elt, RngIntElt
Maximum(Q) : [RngIntElt] -> RngElt
MaximumClique(G: parameters) : GrphUnd -> { GrphVert }
MaximumDegree(G) : GrphDir -> RngIntElt, GrphVert
MaximumDegree(G) : GrphUnd -> RngIntElt, GrphVert
MaximumInDegree(G) : GrphDir -> RngIntElt, GrphVert
MaximumIndependentSet(G: parameters) : GrphUnd -> { GrphVert }
MaximumOutDegree(G) : GrphDir -> RngIntElt, GrphVert
ResetMaximumMemoryUsage() : ->
MaximumClique(G: parameters) : GrphUnd -> { GrphVert }
Maxdeg(G) : GrphDir -> RngIntElt, GrphVert
MaximumDegree(G) : GrphDir -> RngIntElt, GrphVert
MaximumDegree(G) : GrphUnd -> RngIntElt, GrphVert
Maxindeg(G) : GrphDir -> RngIntElt, GrphVert
MaximumInDegree(G) : GrphDir -> RngIntElt, GrphVert
MaximumIndependentSet(G: parameters) : GrphUnd -> { GrphVert }
Maxoutdeg(G) : GrphDir -> RngIntElt, GrphVert
MaximumOutDegree(G) : GrphDir -> RngIntElt, GrphVert
Maxindeg(G) : GrphDir -> RngIntElt, GrphVert
MaximumInDegree(G) : GrphDir -> RngIntElt, GrphVert
MaxNorm(f) : RngMPolElt -> RngIntElt
MaxNorm(p) : RngUPolElt -> RngIntElt
Maxoutdeg(G) : GrphDir -> RngIntElt, GrphVert
MaximumOutDegree(G) : GrphDir -> RngIntElt, GrphVert
MaximalParabolics(C) : CosetGeom -> SetIndx
MaxParabolics(C) : CosetGeom -> SetIndx
McElieceEtAlAsymptoticBound(delta) : FldPrElt -> FldPrElt
McElieceEtAlAsymptoticBound(delta) : FldPrElt -> FldPrElt
FactoredMCPolynomials(A: parameters) : Mtrx -> [<RngUPolElt, RngIntElt>], [<RngUPolElt, RngIntElt>]
FactoredMinimalAndCharacteristicPolynomials(A: parameters) : Mtrx -> [<RngUPolElt, RngIntElt>], [<RngUPolElt, RngIntElt>]
MinimalAndCharacteristicPolynomials(A: parameter) : Mtrx -> RngUPolElt, RngUPolElt
IsMDS(C) : Code -> BoolElt
IsMaximumDistanceSeparable(C) : Code -> BoolElt
Maximum Distance Separable Codes (LINEAR CODES OVER FINITE FIELDS)
Maximum Distance Separable Codes (LINEAR CODES OVER FINITE FIELDS)
MDSCode(K, k) : FldFin,RngIntElt -> Code
AGM(x, y) : FldPrElt, FldPrElt -> FldPrElt
ArithmeticGeometricMean(x, y) : FldPrElt, FldPrElt -> FldPrElt
ArithmeticGeometricMean(x, y) : FldPrElt, FldPrElt -> FldPrElt
MEANS(G) : GrpPerm -> GrpPerm
MEANS(G, N) : GrpPerm, GrpPerm -> GrpPerm
Meataxe(M) : ModRng -> ModRng, ModRng, AlgMatElt
ModAlg_Meataxe (Example H77E5)
G meet H : GrpPSL2, GrpPSL2 -> GrpPSL2
Intersection(G,H) : GrpPSL2, GrpPSL2 -> GrpPSL2
A meet B : AlgGen, AlgGen -> AlgGen
R meet T : AlgMat, AlgMat -> AlgMat
I meet J : AlgQuatOrd, AlgQuatOrd -> AlgQuatOrd
C meet D : Code, Code -> Code
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 : GrpGPC, GrpGPC -> GrpGPC
H meet K : GrpMat, GrpMat -> GrpMat
H meet K : GrpPC, GrpPC -> GrpPC
H meet K : GrpPerm, GrpPerm -> GrpPerm
L meet M : Lat, Lat -> Lat
L meet K : LinSys,LinSys -> LinSys
M meet N : ModBrdt, ModBrdt -> ModBrdt
M1 meet M2 : ModDed, ModDed -> ModDed
M meet N : ModMPol, ModMPol -> ModMPol
M1 meet M2 : ModSS, ModSS -> ModSS
U meet V : ModTupFld, ModTupFld -> ModTupFld
M meet N : ModTupRng, ModTupRng -> ModTupRng
M meet N : ModTupRng, ModTupRng -> ModTupRng
l meet m : PlaneLn, PlaneLn -> PlanePt
I meet J : RngFunOrdIdl, RngFunOrdIdl -> RngFunOrdIdl
I meet J : RngIdl, RngIdl -> RngIdl
I meet J : RngMPol, RngMPol -> RngMPol
I meet J : RngMPolRes, RngMPolRes -> RngMPolRes
I meet R : RngOrdFracIdl, Rng -> Any
I meet J : RngOrdFracIdl, RngOrdFracIdl -> RngOrdFracIdl
I meet J : RngUPol, RngUPol -> RngUPol
X meet Y : Sch,Sch -> Sch
R meet S : SetEnum, SetEnum -> SetEnum
e meet f : SubFldLatElt, SubFldLatElt -> SubFldLatElt
e meet f : SubModLatElt, SubModLatElt -> SubModLatElt
H meet:= K : GrpAb, GrpAb -> GrpAb
H meet:= K : GrpGPC, GrpGPC -> GrpGPC
H meet:= K : GrpPC, GrpPC -> GrpPC
U meet:= V : ModTupFld, ModTupFld -> ModTupFld
IsMemberBasicOrbit(G, i, a) : GrpPerm, RngIntElt, Elt -> BoolElt
Equality and Membership (ALGEBRAIC FUNCTION FIELDS)
Equality and Membership (ALGEBRAIC FUNCTION FIELDS)
Equality and Membership (ALGEBRAIC FUNCTION FIELDS)
Equality and Membership (MULTIVARIATE POLYNOMIAL RINGS)
Equality and Membership (ORDERS AND ALGEBRAIC FIELDS)
Equality and Membership (POWER, LAURENT AND PUISEUX SERIES)
Equality and Membership (RATIONAL FUNCTION FIELDS)
Equality and Membership (UNIVARIATE POLYNOMIAL RINGS)
Equality and Membership (VALUATION RINGS)
Equality, Comparison and Membership (ALGEBRAIC FUNCTION FIELDS)
Membership and Coercion (FINITE SOLUBLE GROUPS)
Membership and Equality testing (SUBGROUPS OF PSL_2(R))
Membership Testing (SEQUENCES)
Membership and Coercion (FINITE SOLUBLE GROUPS)
Membership and Equality testing (SUBGROUPS OF PSL_2(R))
GetMaximumMemoryUsage() : -> RngIntElt
GetMemoryUsage() : -> RngIntElt
ResetMaximumMemoryUsage() : ->
SetMemoryLimit(n) : RngIntElt ->
ShowMemoryUsage() : ->
MAGMA_MEMORY_LIMIT
CompositeFields(F, L) : FldAlg, FldAlg -> SeqEnum
MergeFields(F, L) : FldAlg, FldAlg -> SeqEnum
MergeUnits(K, a) : FldNum, FldNumElt -> BoolElt
CompositeFields(F, L) : FldAlg, FldAlg -> SeqEnum
MergeFields(F, L) : FldAlg, FldAlg -> SeqEnum
MergeUnits(K, a) : FldNum, FldNumElt -> BoolElt
UsesMestre(M) : ModSS -> BoolElt
<Meta>-B
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Chabauty's Method (HYPERELLIPTIC CURVES)
IsolMinBlockSize(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
MinParabolics(C) : CosetGeom -> SetIndx
Minimum(S) : SeqEnum -> Elt, RngIntElt
Minimum(S) : SetIndx -> Elt, RngIntElt
Mindeg(G) : GrphDir -> RngIntElt, GrphVert
MinimumDegree(G) : GrphDir -> RngIntElt, GrphVert
MinimumDegree(G) : GrphUnd -> RngIntElt, GrphVert
SuccessiveMinima(L) : Lat, RngIntElt -> [ RngIntElt ], [ LatElt ]
Successive Minima and Theta Series (LATTICES)
Successive Minima and Theta Series (LATTICES)
AbsoluteMinimalPolynomial(a) : FldAlgElt -> RngUPolElt
AbsoluteModuleOverMinimalField(M, F) : ModGrp, FldFin -> ModGrp
AbsoluteModulesOverMinimalField(Q, K) : [ ModGrp ], FldFin -> [ ModGrp ]
FactoredMinimalAndCharacteristicPolynomials(A: parameters) : Mtrx -> [<RngUPolElt, RngIntElt>], [<RngUPolElt, RngIntElt>]
FactoredMinimalPolynomial(A: parameter) : Mtrx -> [ <RngUPolElt, RngIntElt>]
IsMinimalModel(E) : CrvEll -> BoolElt
IspMinimal(C, p) : CrvHyp, RngIntElt -> BoolElt, BoolElt
MinParabolics(C) : CosetGeom -> SetIndx
MinimalAlgebraGenerators(L) : [ RngMPol ] -> [ RngMPol ]
MinimalAlgebraGenerators(L) : [ RngMPol ] -> [ RngMPol ]
MinimalAlgebraGenerators(L) : [ RngMPol ] -> [ RngMPol ]
MinimalAlgebraGenerators(L) : [ RngMPol ] -> [ RngMPol ]
MinimalAndCharacteristicPolynomials(A: parameter) : Mtrx -> RngUPolElt, RngUPolElt
MinimalBasis(M) : ModMPol -> [ ModMPolElt ]
MinimalBasis(X) : Sch -> [ RngMPolElt ]
MinimalBasis(S) : [ ModMPolElt ] -> [ ModMPolElt ]
MinimalField(a) : FldCycElt -> FldCyc
MinimalField(q) : FldRatElt -> FldRat
MinimalField(G) : GrpMat -> FldFin
MinimalField(M) : ModRng -> FldFin
MinimalField(S) : SetEnum -> FldRat
MinimalField(S) : [ FldCycElt ] -> FldCyc
MinimalFreeResolution(M) : ModMPol -> [ ModMPol ]
MinimalFreeResolution(M) : ModMPol -> [ ModMPol ]
MinimalInteger(I) : RngInt -> RngIntElt
MinimalIntegerSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
MinimalLeftIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MinimalIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MinimalModel(E) : CrvEll -> CrvEll, Map, Map
MinimalNormalSubgroup(G) : GrpPC -> GrpPC
MinimalNormalSubgroup(G, N) : GrpPC -> GrpPC
MinimalNormalSubgroups(G) : GrpPerm -> [ GrpPerm ]
MinimalOverfields(e) : SubFldLatElt -> [ SubFldLatElt ]
MinimalOvergroup(G, H) : GrpFP, GrpFP -> GrpFP
MinimalOvergroups(e) : SubGrpLatElt -> { SubGrpLatElt }
MinimalPartition(G: parameters) : GrpPerm -> GSet
MinimalPartitions(G: parameters) : GrpPerm -> [ GSet ]
MinimalPolynomial(a) : AlgGenElt -> RngUPolElt
MinimalPolynomial(a) : AlgMatElt -> RngUPolElt
MinimalPolynomial(x) : AlgQuatElt -> RngUPolElt
MinimalPolynomial(a) : FldACElt -> RngPolElt
MinimalPolynomial(a) : FldAlgElt -> RngUPolElt
MinimalPolynomial(a) : FldFinElt -> RngPolElt
MinimalPolynomial(a, E) : FldFinElt, FldFin -> RngPolElt
MinimalPolynomial(q) : FldRatElt -> RngUPolElt
MinimalPolynomial(g) : GrpMatElt -> RngPolElt
MinimalPolynomial(A: parameter) : Mtrx -> RngUPolElt
MinimalPolynomial(n) : RngIntElt -> RngUPolElt
MinimalPolynomial(x) : RngLocElt -> RngUPolElt
MinimalPolynomial(f) : RngMPolResElt -> RngUPol
MinimalSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
MinimalSubmodule(M) : ModRng -> ModRng
MinimalSubmodules(M) : ModRng -> [ ModRng ], BoolElt
MinimalSubmodules(M, F) : ModRng, ModRng -> [ ModRng ], BoolElt
MinimalSupermodules(e) : SubModLatElt -> { SubModLatElt }
MinimalSyzygyModule(M) : ModMPol -> [ ModMPolElt ]
MinimalWeierstrassModel(C) : CrvHyp -> CrvHyp, MapIsoSch
MinimalZeroOneSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
ReducedMinimalWeierstrassModel(C) : CrvHyp -> CrvHyp, MapIsoSch
Minimal and Characteristic Polynomial (FINITE FIELDS)
Minimal Polynomial, Norm and Trace (ALGEBRAICALLY CLOSED FIELDS)
Socle Series (MODULES OVER A MATRIX ALGEBRA)
Minimal and Characteristic Polynomial (FINITE FIELDS)
Minimal Polynomial, Norm and Trace (ALGEBRAICALLY CLOSED FIELDS)
Socle Series (MODULES OVER A MATRIX ALGEBRA)
MinimalAlgebraGenerators(L) : [ RngMPol ] -> [ RngMPol ]
MinimalAlgebraGenerators(L) : [ RngMPol ] -> [ RngMPol ]
RngInvar_MinimalAlgebraGenerators (Example H80E13)
MCPolynomials(A) : Mtrx -> RngUPolElt, RngUPolElt
MinimalAndCharacteristicPolynomials(A: parameter) : Mtrx -> RngUPolElt, RngUPolElt
MinimalBasis(M) : ModMPol -> [ ModMPolElt ]
MinimalBasis(X) : Sch -> [ RngMPolElt ]
MinimalBasis(S) : [ ModMPolElt ] -> [ ModMPolElt ]
MinimalField(a) : FldCycElt -> FldCyc
MinimalField(q) : FldRatElt -> FldRat
MinimalField(G) : GrpMat -> FldFin
MinimalField(M) : ModRng -> FldFin
MinimalField(S) : SetEnum -> FldRat
MinimalField(S) : [ FldCycElt ] -> FldCyc
MinimalFreeResolution(M) : ModMPol -> [ ModMPol ]
MinimalFreeResolution(M) : ModMPol -> [ ModMPol ]
MinimalRightIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MinimalIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MinimalLeftIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MinimalInteger(I) : RngInt -> RngIntElt
MinimalIntegerSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
Minimalization and Homogeneous Module Testing (INVARIANT RINGS OF FINITE GROUPS)
Minimalization and Homogeneous Module Testing (INVARIANT RINGS OF FINITE GROUPS)
MinimalRightIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MinimalIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MinimalLeftIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MinimalModel(E) : CrvEll -> CrvEll, Map, Map
MinimalNormalSubgroup(G) : GrpPC -> GrpPC
MinimalNormalSubgroup(G, N) : GrpPC -> GrpPC
MinimalNormalSubgroups(G) : GrpPerm -> [ GrpPerm ]
MinimalOverfields(e) : SubFldLatElt -> [ SubFldLatElt ]
MinimalOvergroup(G, H) : GrpFP, GrpFP -> GrpFP
MinimalOvergroups(e) : SubGrpLatElt -> { SubGrpLatElt }
MinimalParabolics(C) : CosetGeom -> SetIndx
MinParabolics(C) : CosetGeom -> SetIndx
MinimalPartition(G: parameters) : GrpPerm -> GSet
MinimalPartitions(G: parameters) : GrpPerm -> [ GSet ]
MinimalPolynomial(a) : AlgGenElt -> RngUPolElt
MinimalPolynomial(a) : AlgMatElt -> RngUPolElt
MinimalPolynomial(x) : AlgQuatElt -> RngUPolElt
MinimalPolynomial(a) : FldACElt -> RngPolElt
MinimalPolynomial(a) : FldAlgElt -> RngUPolElt
MinimalPolynomial(a) : FldFinElt -> RngPolElt
MinimalPolynomial(a, E) : FldFinElt, FldFin -> RngPolElt
MinimalPolynomial(q) : FldRatElt -> RngUPolElt
MinimalPolynomial(g) : GrpMatElt -> RngPolElt
MinimalPolynomial(A: parameter) : Mtrx -> RngUPolElt
MinimalPolynomial(n) : RngIntElt -> RngUPolElt
MinimalPolynomial(x) : RngLocElt -> RngUPolElt
MinimalPolynomial(f) : RngMPolResElt -> RngUPol
AlgAff_MinimalPolynomial (Example H67E2)
MinimalRightIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MinimalIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MinimalLeftIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
ModAlg_Minimals (Example H77E7)
MinimalSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
MinimalSubmodule(M) : ModRng -> ModRng
MinimalSubmodules(M) : ModRng -> [ ModRng ], BoolElt
MinimalSubmodules(M, F) : ModRng, ModRng -> [ ModRng ], BoolElt
MinimalSupermodules(e) : SubModLatElt -> { SubModLatElt }
MinimalSyzygyModule(M) : ModMPol -> [ ModMPolElt ]
MinimalWeierstrassModel(C) : CrvHyp -> CrvHyp, MapIsoSch
MinimalZeroOneSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
Minimize(~a) : FldCycElt ->
Minimise(~a) : FldCycElt ->
Minimise(a) : FldCycElt -> RngElt
Minimise(~s) : [ FldCycElt ] ->
Minimise(s) : { FldCycElt } -> { RngElt }
Minimize(~a) : FldCycElt ->
Minimise(~a) : FldCycElt ->
Minimise(a) : FldCycElt -> RngElt
Minimise(~s) : [ FldCycElt ] ->
Minimise(s) : { FldCycElt } -> { RngElt }
Comparison (OVERVIEW)
GriesmerMinimumWeightBound(K, n, k) : FldFin,RngIntElt,RngIntElt->RngIntElt
Minimum(a, O) : FldFunElt, RngFunOrd -> RngElt, RngElt
Minimum(L) : Lat -> RngElt
Minimum(P) : PlcFunElt -> RngElt
Minimum(a, b) : RngElt, RngElt -> RngElt
Minimum(I) : RngFunOrdIdl -> Any
Minimum(I) : RngOrdFracIdl -> RngElt
Minimum(S) : SeqEnum -> Elt, RngIntElt
Minimum(S) : SetIndx -> Elt, RngIntElt
Minimum(Q) : [RngIntElt] -> RngElt
MinimumDegree(G) : GrphDir -> RngIntElt, GrphVert
MinimumDegree(G) : GrphUnd -> RngIntElt, GrphVert
MinimumDominatingSet(G) : GrphUnd -> SetEnum
MinimumInDegree(G) : GrphDir -> RngIntElt, GrphVert
MinimumOutDegree(G) : GrphDir -> RngIntElt, GrphVert
MinimumWeight(C) : Code -> RngIntElt
MinimumWeight(C: parameters) : Code -> RngIntElt
MinimumWeightBounds(C) : Code -> RngIntElt, RngIntElt
MinimumWord(C) : Code -> ModTupFldElt
MinimumWords(C) : Code -> { ModTupFldElt }
ResetMinimumWeightBounds(C) : Code ->
VerifyMinimumDistanceLowerBound(C, d) : Code, RngIntElt -> BoolElt, RngIntElt, BoolElt
VerifyMinimumDistanceUpperBound(C, d) : Code, RngIntElt -> BoolElt, RngIntElt, BoolElt
Bounds on the Minimum Distance (LINEAR CODES OVER FINITE FIELDS)
Minimum, Density and Kissing Number (LATTICES)
The Minimum Weight (LINEAR CODES OVER FINITE FIELDS)
The Minimum Weight (LINEAR CODES OVER FINITE RINGS)
Bounds on the Minimum Distance (LINEAR CODES OVER FINITE FIELDS)
The Minimum Weight (LINEAR CODES OVER FINITE FIELDS)
The Minimum Weight (LINEAR CODES OVER FINITE RINGS)
Mindeg(G) : GrphDir -> RngIntElt, GrphVert
MinimumDegree(G) : GrphDir -> RngIntElt, GrphVert
MinimumDegree(G) : GrphUnd -> RngIntElt, GrphVert
MinimumDistance(C) : Code -> RngIntElt
MinimumWeight(C) : Code -> RngIntElt
MinimumWeight(C: parameters) : Code -> RngIntElt
MinimumDominatingSet(G) : GrphUnd -> SetEnum
Minindeg(G) : GrphDir -> RngIntElt, GrphVert
MinimumInDegree(G) : GrphDir -> RngIntElt, GrphVert
Minoutdeg(G) : GrphDir -> RngIntElt, GrphVert
MinimumOutDegree(G) : GrphDir -> RngIntElt, GrphVert
MinimumDistance(C) : Code -> RngIntElt
MinimumWeight(C) : Code -> RngIntElt
MinimumWeight(C: parameters) : Code -> RngIntElt
MinimumWeightBounds(C) : Code -> RngIntElt, RngIntElt
MinimumWord(C) : Code -> ModTupFldElt
MinimumWords(C) : Code -> { ModTupFldElt }
Minindeg(G) : GrphDir -> RngIntElt, GrphVert
MinimumInDegree(G) : GrphDir -> RngIntElt, GrphVert
MinkowskiLattice(O) : RngOrd -> Lat, Map
Lattice(O) : RngOrd -> Lat, Map
Lattice(I) : RngOrdIdl -> Lat, Map
MinkowskiBound(K) : FldNum -> RngIntElt
MinkowskiLattice(O) : RngOrd -> Lat, Map
MinkowskiLattice(I) : RngOrdIdl -> Lat, Map
MinkowskiSpace(F) : FldAlg -> Lat, Map
MinkowskiSpace(K) : FldNum -> KModTup, Map
MinkowskiBound(K) : FldNum -> RngIntElt
MinkowskiLattice(O) : RngOrd -> Lat, Map
Lattice(O) : RngOrd -> Lat, Map
Lattice(I) : RngOrdIdl -> Lat, Map
MinkowskiLattice(O) : RngOrd -> Lat, Map
MinkowskiLattice(I) : RngOrdIdl -> Lat, Map
MinkowskiSpace(F) : FldAlg -> Lat, Map
MinkowskiSpace(K) : FldNum -> KModTup, Map
MinorBoundary(G,i,j) : GrpPC, RngIntElt, RngIntElt -> RngIntElt
MinorLength(G,i) : GrpPC, RngIntElt -> RngIntElt
MinorBoundary(G,i,j) : GrpPC, RngIntElt, RngIntElt -> RngIntElt
MinorLength(G,i) : GrpPC, RngIntElt -> RngIntElt
Minoutdeg(G) : GrphDir -> RngIntElt, GrphVert
MinimumOutDegree(G) : GrphDir -> RngIntElt, GrphVert
MinimalParabolics(C) : CosetGeom -> SetIndx
MinParabolics(C) : CosetGeom -> SetIndx
GOMinus(arguments)
GeneralOrthogonalGroupMinus(arguments)
IsMinusOne(a) : AlgGenElt -> BoolElt
IsMinusOne(a) : AlgMatElt -> BoolElt
IsMinusOne(a) : FldACElt -> BoolElt
IsMinusOne(A) : Mtrx -> BoolElt
IsMinusOne(a) : RngElt -> BoolElt
IsMinusOne(x) : RngLocElt -> BoolElt
IsMinusOne(a) : RngOrdResElt -> BoolElt
IsMinusOne(s) : RngPowLazElt -> BoolElt
MinusInfinity() : -> Infty
MinusTamagawaNumber(M) : ModSym -> RngIntElt
MinusVolume(M, prec) : ModSym, RngIntElt) -> FldPrElt
OmegaMinus(arguments)
PGOMinus(arguments)
PSOMinus(arguments)
ProjectiveOmegaMinus(arguments)
SpecialOrthogonalGroupMinus(arguments)
Operators (OVERVIEW)
MinusInfinity() : -> Infty
MinusTamagawaNumber(M) : ModSym -> RngIntElt
MinusVolume(M, prec) : ModSym, RngIntElt) -> FldPrElt
Miscellanous p-group functions (p-GROUPS)
Decimation (PSEUDO-RANDOM BIT SEQUENCES)
Miscellaneous (RING OF INTEGERS)
Miscellaneous (STATEMENTS AND EXPRESSIONS)
Miscellaneous Graph Constructions (GRAPHS)
Set_Miscellaneous (Example H7E7)
Miscellaneous (FINITELY PRESENTED ALGEBRAS)
Miscellaneous Functions (FP GROUPS - ADVANCED FEATURES)
Miscellaneous Functions (FP GROUPS - ADVANCED FEATURES)
MultiplicationByMMap(E, m) : CrvEll, RngIntElt -> Map
EulerFactorModChar(J) : JacHyp -> RngUPolElt
InverseMod(E, M) : RngOrdElt, RngIntElt -> RngOrdElt
Modinv(n, m) : RngIntElt, RngIntElt -> RngIntElt
Rings, Fields, and Algebras (OVERVIEW)
The Module structure of a Structure Constant Algebra (STRUCTURE CONSTANT ALGEBRAS)
n mod m : RngIntElt, RngIntElt -> RngIntElt
n mod m : RngIntElt, RngIntElt -> RngIntElt
a mod I : RngOrdElt, RngOrdIdl -> RngOrdElt
a mod I : RngOrdElt, RngOrdIdl -> RngOrdElt
a mod b : RngQuadElt, RngQuadElt -> RngQuadElt
f mod g : RngUPolElt, RngUPolElt -> RngUPolElt
Combinatorial and Geometrical Structures (OVERVIEW)
Brandt Module Creation (BRANDT MODULES)
Brandt Module Creation (BRANDT MODULES)
ModBrdt_ModBrdt:Constructors (Example H91E1)
ModBrdt_ModBrdt:Decomposition (Example H91E4)
ModBrdt_ModBrdt:Dimension (Example H91E6)
Dimensions of Spaces (BRANDT MODULES)
Dimensions of Spaces (BRANDT MODULES)
ModBrdt_ModBrdt:EisensteinSubspace (Example H91E5)
Introduction (BRANDT MODULES)
ModBrdt_ModBrdt:Module-Creation (Example H91E2)
Boolean Tests on Subspaces (BRANDT MODULES)
Subspaces and Decomposition (BRANDT MODULES)
Boolean Tests on Subspaces (BRANDT MODULES)
ModBrdt_ModBrdt:Verbose-Output (Example H91E3)
Modules (OVERVIEW)
GetViMode() : -> BoolElt
SetViMode(b) : BoolElt ->
HasOddDegreeModel(C) : CrvHyp -> BoolElt, CrvHyp, MapIsoSch
IntegralModel(E) : CrvEll -> CrvEll, Map, Map
IntegralModel(C) : CrvHyp -> CrvHyp, MapIsoSch
IsIntegralModel(E) : CrvEll -> BoolElt
IsMinimalModel(E) : CrvEll -> BoolElt
IsSimplifiedModel(E) : CrvEll -> BoolElt
IsWeierstrassModel(E) : CrvEll -> BoolElt
LegendreModel(C) : CrvCon -> CrvCon, MapIsoSch
MinimalModel(E) : CrvEll -> CrvEll, Map, Map
MinimalWeierstrassModel(C) : CrvHyp -> CrvHyp, MapIsoSch
ModelType(X) : CrvMod -> MonStgElt
ReducedLegendreModel(C) : CrvCon -> CrvCon, MapIsoSch
ReducedMinimalWeierstrassModel(C) : CrvHyp -> CrvHyp, MapIsoSch
ReducedModel(C) : CrvHyp -> CrvHyp, MapIsoSch
SimplifiedModel(E): CrvEll -> CrvEll, Map, Map
SimplifiedModel(C) : CrvHyp -> CrvHyp, MapIsoSch
WeierstrassModel(E) : CrvEll -> CrvEll, Map, Map
pMinimalWeierstrassModel(C, p) : CrvHyp, RngIntElt -> CrvHyp, MapIsoSch
pNormalModel(C, p) : CrvHyp, RngIntElt -> CrvHyp, MapIsoSch
Predicates on Curve Models (ELLIPTIC CURVES)
Predicates on Curve Models (HYPERELLIPTIC CURVES)
CrvEll_Models (Example H87E3)
Alternative Models (ELLIPTIC CURVES)
Alternative Models (RATIONAL CURVES AND CONICS)
ModelType(X) : CrvMod -> MonStgElt
Modexp(n, k, m) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
Modexp(a, n, m) : RngOrdElt, RngIntElt, RngIntElt -> RngOrdElt
Modexp(a, e, n) : RngQuadElt, RngInt, RngQuadElt -> RngQuadElt
Modexp(f, n, g) : RngUPolElt, RngIntElt, RngUPolElt -> RngUPolElt
Modules (OVERVIEW)
Access and Modification Functions (RECORDS)
Accessing and Modifying Sets (SETS)
Changing the Alphabet of a Code (LINEAR CODES OVER FINITE FIELDS)
Changing the Coefficient Field (VECTOR SPACES)
Changing the Coefficient Ring (FREE MODULES)
Editing Defining Relations (FINITELY PRESENTED ALGEBRAS)
Elementary Tietze Transformations (FINITELY PRESENTED SEMIGROUPS)
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])
Changing the Alphabet of a Code (LINEAR CODES OVER FINITE FIELDS)
KSpace(V, F) : ModTupFld, Fld -> ModTupFld, Map
KMatrixSpace(V, F) : ModTupFld, Fld -> ModTupFld, Map
KModule(V, F) : ModTupFld, Fld -> ModTupFld, Map
Changing the Coefficient Field (VECTOR SPACES)
Changing the Coefficient Ring (FREE MODULES)
Elementary Tietze Transformations (FINITELY PRESENTED SEMIGROUPS)
Modifying Resolution Graphs (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
ModifySelfintersection(~v,n) : GrphResVert,RngIntElt ->
ModifyTransverseIntersection(~v,n) : GrphResVert,RngIntElt ->
Modifying Presentations (FP GROUPS - ADVANCED FEATURES)
Modifying Presentations (FP GROUPS - ADVANCED FEATURES)
ModifySelfintersection(~v,n) : GrphResVert,RngIntElt ->
ModifyTransverseIntersection(~v,n) : GrphResVert,RngIntElt ->
Modinv(E, M) : RngOrdElt, RngOrdIdl -> RngOrdElt
InverseMod(E, M) : RngOrdElt, RngIntElt -> RngOrdElt
Modinv(n, m) : RngIntElt, RngIntElt -> RngIntElt
Modules (OVERVIEW)
Modules (OVERVIEW)
Modules (OVERVIEW)
Modorder(n, m) : RngIntElt, RngIntElt -> RngIntElt
Modsqrt(n, m) : RngIntElt, RngIntElt -> BoolElt, RngIntElt
Combinatorial and Geometrical Structures (OVERVIEW)
Modules (OVERVIEW)
Modules (OVERVIEW)
AtkinModularPolynomial(N) : RngIntElt -> RngMPolElt
CanonicalModularPolynomial(N) : RngIntElt -> RngMPolElt
ClassicalModularPolynomial(N) : RngIntElt -> RngMPolElt
ExistsModularCurveDatabase(t) : MonStgElt -> BoolElt
IsRingOfAllModularForms(M) : ModFrm -> BoolElt
ModularCurve(D, N) : DB, RngIntElt -> CrvMod
ModularCurve(X,t,N) : Sch, MonStgElt, RngIntElt -> CrvMod
ModularCurveDatabase(t) : MonStgElt -> DB
ModularDegree(M) : ModSym -> RngIntElt
ModularForm(E) : CrvEll -> ModFrm
ModularForm(E) : CrvEll -> ModFrm
ModularForms(G) : -> ModFrm
ModularForms(G, k) : -> ModFrm
ModularForms(N) : RngIntElt -> ModFrm
ModularForms(N, k) : RngIntElt, RngIntElt -> ModFrm
ModularForms(chars, k) : [GrpDrchElt], RngIntElt -> ModFrm
ModularKernel(M) : ModSym -> GrpAb
ModularPolynomial(M) : ModSS -> RngMPolElt
ModularSolution(A, M) : MtrxSprs, RngIntElt -> ModTupRng
ModularSymbols(E) : CurveEll -> ModSym
ModularSymbols(eps, k) : GrpDrchElt, RngIntElt -> ModSym
ModularSymbols(eps, k, sign) : GrpDrchElt, RngIntElt, RngIntElt -> ModSym
ModularSymbols(M) : ModFrm -> SeqEnum
ModularSymbols(M, sign) : ModFrm, RngIntElt -> ModSym
ModularSymbols(M, N') : ModSym, RngIntElt -> ModSym
ModularSymbols(s, sign) : MonStgElt, RngIntElt -> ModSym
ModularSymbols(M : parameters) : ModSS -> ModSym
ModularSymbols(M, sign : parameters) : ModSS, RngIntElt -> ModSym
ModularSymbols(N) : RngIntElt -> ModSym
ModularSymbols(N, k) : RngIntElt, RngIntElt -> ModSym
ModularSymbols(N, k, F) : RngIntElt, RngIntElt, Fld -> ModSym
ModularSymbols(N, k, F, sign) : RngIntElt, RngIntElt, Fld, RngIntElt -> ModSym
ModularSymbols(N, k, sign) : RngIntElt, RngIntElt, RngIntElt -> ModSym
GrpFP_1_Modular (Example H19E7)
An Illustrative Overview (MODULAR FORMS)
Arithmetic Operations (RING OF INTEGERS)
Elliptic and Modular Functions (REAL AND COMPLEX FIELDS)
Modular Abelian Varieties (MODULAR SYMBOLS)
Modular Arithmetic (QUADRATIC FIELDS)
Modular Arithmetic (RING OF INTEGERS)
Modular Arithmetic (UNIVARIATE POLYNOMIAL RINGS)
MODULAR CURVES
Modular Degree and Torsion (MODULAR SYMBOLS)
MODULAR FORMS
Modular Forms (MODULAR FORMS)
MODULAR SYMBOLS
Modular Symbols (MODULAR FORMS)
Modular Symbols (MODULAR SYMBOLS)
Projection Mappings (MODULAR SYMBOLS)
Representation Theory (GROUPS)
Tamagawa Numbers and Orders of Component Groups (MODULAR SYMBOLS)
The j-invariant and the Discriminant (REAL AND COMPLEX FIELDS)
CrvMod_Modular base curve (Example H89E4)
CrvMod_Modular polynomials (Example H89E2)
GrpFP_1_modular-abelian-quotient (Example H19E19)
Modular Abelian Varieties (MODULAR SYMBOLS)
Modular Degree and Torsion (MODULAR SYMBOLS)
Tamagawa Numbers and Orders of Component Groups (MODULAR SYMBOLS)
Projection Mappings (MODULAR SYMBOLS)
Arithmetic Operations (RING OF INTEGERS)
Modular Arithmetic (QUADRATIC FIELDS)
MODULAR CURVES
An Illustrative Overview (MODULAR FORMS)
MODULAR FORMS
Modular Forms (MODULAR FORMS)
Representation Theory (GROUPS)
MODULAR SYMBOLS
Modular Symbols (MODULAR FORMS)
Modular Symbols (MODULAR SYMBOLS)
ModSym_ModularAbVarArithmetic (Example H90E25)
ModSym_ModularAbVarCompGrp (Example H90E26)
ModSym_ModularAbVarRational (Example H90E24)
ModularCurve(D, N) : DB, RngIntElt -> CrvMod
ModularCurve(X,t,N) : Sch, MonStgElt, RngIntElt -> CrvMod
ModularCurveDatabase(t) : MonStgElt -> DB
ModularDegree(M) : ModSym -> RngIntElt
ModularForm(E) : CrvEll -> ModFrm
ModularForm(E) : CrvEll -> ModFrm
ModularForms(G) : -> ModFrm
ModularForms(G, k) : -> ModFrm
ModularForms(N) : RngIntElt -> ModFrm
ModularForms(N, k) : RngIntElt, RngIntElt -> ModFrm
ModularForms(chars, k) : [GrpDrchElt], RngIntElt -> ModFrm
ModularKernel(M) : ModSym -> GrpAb
ModularPolynomial(M) : ModSS -> RngMPolElt
ModularSolution(A, M) : MtrxSprs, RngIntElt -> ModTupRng
ModularSymbols(E) : CurveEll -> ModSym
ModularSymbols(eps, k) : GrpDrchElt, RngIntElt -> ModSym
ModularSymbols(eps, k, sign) : GrpDrchElt, RngIntElt, RngIntElt -> ModSym
ModularSymbols(M) : ModFrm -> SeqEnum
ModularSymbols(M, sign) : ModFrm, RngIntElt -> ModSym
ModularSymbols(M, N') : ModSym, RngIntElt -> ModSym
ModularSymbols(s, sign) : MonStgElt, RngIntElt -> ModSym
ModularSymbols(M : parameters) : ModSS -> ModSym
ModularSymbols(M, sign : parameters) : ModSS, RngIntElt -> ModSym
ModularSymbols(N) : RngIntElt -> ModSym
ModularSymbols(N, k) : RngIntElt, RngIntElt -> ModSym
ModularSymbols(N, k, F) : RngIntElt, RngIntElt, Fld -> ModSym
ModularSymbols(N, k, F, sign) : RngIntElt, RngIntElt, Fld, RngIntElt -> ModSym
ModularSymbols(N, k, sign) : RngIntElt, RngIntElt, RngIntElt -> ModSym
ModForm_ModularSymbols (Example H93E21)
AbsoluteModuleOverMinimalField(M, F) : ModGrp, FldFin -> ModGrp
AbsolutelyIrreducibleModule(M) : ModRng -> ModRng
AmbientModule(M) : ModBrdt -> ModBrdt
BaseModule(R, S) : AlgMat, Rng -> ModTup
BrandtModule(A) : AlgQuatOrd -> ModBrdt
BrandtModule(M) : ModSS -> ModBrdt
BrandtModule(D) : RngIntElt, RngIntElt -> ModBrdt
BrandtModuleDimension(D,N) : RngIntElt, RngIntElt -> RngIntElt
CohomologyLeftModuleGenerators(P, CP, Q) : Tup, Tup, Tup -> Tup
CohomologyRightModuleGenerators(P, Q, CQ) : Tup, Tup, Tup -> Tup
CommutatorModule(A, B) : AlgAss, AlgAss -> ModTupRng
DimensionOfHighestWeightModule(D, w) : RootDtm, [ ] -> RngIntElt
GetModules(SQP, p ) : SQProc, RngIntElt -> List
HasDefinedModuleMap(C,n) : ModCpx, RngIntElt -> BoolElt
HomogeneousModuleTest(P, S, F) : [ RngMPol ], [ RngMPol ], RngMPol -> BoolElt, [ RngMPol ]
HomogeneousModuleTest(P, S, F) : [ RngMPol ], [ RngMPol ], RngMPol -> BoolElt, [ RngMPol ]
HomogeneousModuleTest(P, S, L) : [ RngMPol ], [ RngMPol ], [ RngMPol ] -> [ BoolElt ], [ [ RngMPol ] ]
HomogeneousModuleTest(P, S, L) : [ RngMPol ], [ RngMPol ], [ RngMPol ] -> [ BoolElt ], [ [ RngMPol ] ]
HomogeneousModuleTestBasis(P, S, L) : [ RngMPol ], [ RngMPol ], [ RngMPol ] -> [ BoolElt ], [ [ RngMPol ] ]
InjectiveModule(B, i) : AlgBas, RngIntElt -> ModAlg
InjectiveSyzygyModule(M, n) : ModAlg, RngIntElt -> ModAlg
IrreducibleModule(B, i) : AlgBas, RngIntElt -> ModAlg
IsModuleHomomorphism(X) : ModMatElt -> BoolElt
IsModuleHomomorphism(f) : ModMatFldElt -> BoolElt
MinimalSyzygyModule(M) : ModMPol -> [ ModMPolElt ]
Module(A) : AlgGen -> ModTupRng
Module(S) : AlgGrpSub -> ModTupRng, Map
Module(P, r) : Rng, RngIntElt -> RngMPol
Module(P, r, S) : Rng, RngIntElt, MonStgElt -> RngMPol
Module(P, W) : Rng, [ RngIntElt ] -> RngMPol
Module(P, W, S) : Rng, [ RngIntElt ], MonStgElt -> RngMPol
Module(R) : RngInvar -> ModMPol, Map
Module(O) : RngOrd -> ModDed, Map
Module(O, n) : RngOrd, RngIntElt -> ModDed
Module(I) : RngOrdFracIdl -> ModDed, Map
Module(L, R) : SeqEnum[ DiffFunElt ], Rng -> Mod, Map, SeqEnum[ ModElt ]
Module(L, R) : SeqEnum[ FldFunGElt ], Rng -> Mod, Map, SeqEnum[ ModElt ]
Module(S) : SeqEnum[ModElt] -> ModDed, Map
Module(S) : SeqEnum[RngOrdFracIdl] -> ModDed
Module(S) : SeqEnum[Tup] -> ModDed, Map
Module(e) : SubModLatElt -> ModRng
ModuleMap(f, n) : ModMatCpxElt, RngIntElt -> ModMatFldElt
ModuleOverSmallerField(M, F) : ModGrp, FldFin -> ModGrp
NextRepresentation(P) : SolRepProc -> BoolElt, Map
NormSpace(A) : AlgQuat -> ModTupFld
PermutationModule(G, K) : Grp, Fld -> ModGrp
PermutationModule(G, K) : Grp, Fld -> ModGrp
PermutationModule(G, H, K) : Grp, Grp, Fld -> ModGrp
PermutationModule(G, H, R) : Grp, Grp, Rng -> ModGrp
PermutationModule(G, V) : Grp, ModTup -> ModGrp
PermutationModule(G, u) : Grp, ModTupElt -> ModGrp
PermutationModule(G, H, R) : GrpFin, GrpFin, Rng -> ModGrpFin
PermutationModule(G, H, R) : GrpMat, GrpMat, Rng -> ModGrp
PermutationModule(G, R) : GrpPerm, Rng -> ModGrp
PermutationModule(G, R) : GrpPerm, Rng -> ModGrpFin
ProjectiveModule(B, i) : AlgBas, RngIntElt -> ModRng
ProjectiveModule(B, S) : AlgBas, SeqEnum[RngIntElt] -> ModAlg, SeqEnum, SeqEnum
QuotientModule(A, S) : AlgFP, AlgFP -> AlgFP
QuotientModule(A, S) : AlgFP, AlgFP -> AlgFP
QuotientModule(A, S) : AlgFP, AlgFP -> AlgFP
QuotientModule(A, S) : AlgFP, AlgFP -> AlgFP
QuotientModule(A, S) : AlgFP, AlgFP -> AlgFP
QuotientModuleAction(G, S) : GrpMat -> Map, GrpMat
QuotientModuleImage(G, S) : GrpMat -> GrpMat
RightRegularModule(B) : AlgBas -> ModAlg
SupersingularModule(p : parameters) : RngIntElt -> ModSS
SyzygyModule(M, n) : ModAlg, RngIntElt -> ModAlg
SyzygyModule(M) : ModMPol -> [ ModMPolElt ]
SyzygyModule(Q) : [ RngMPolElt ] -> ModTupRng
TrivialModule(G, K) : Grp, Fld -> ModGrp
ZeroModule(B) : AlgBas -> ModAlg
RngInvar_Module (Example H80E9)
Action on the Natural G-Module (MATRIX GROUPS)
Arithmetic with Modules (MODULES OVER DEDEKIND DOMAINS)
Construction of a Module with Specified Basis (FREE MODULES)
Construction of an A-Module (MODULES OVER A MATRIX ALGEBRA)
Construction of K[G]-Modules (K[G]-MODULES AND GROUP REPRESENTATIONS)
Construction of Modules of m x n Matrices (FREE MODULES)
Construction of Modules of n-tuples (FREE MODULES)
Constructions for K[G]-Modules (MODULES OVER A MATRIX ALGEBRA)
Definition of a Module (FREE MODULES)
Finitely Presented Modules (FINITELY PRESENTED ALGEBRAS)
Functions for Polynomial Algebra and Module Generators (IDEAL THEORY AND GRÖBNER BASES)
Galois Module Structure (CLASS FIELD THEORY)
General Constructions (MODULES OVER A MATRIX ALGEBRA)
General K[G]-Modules (K[G]-MODULES AND GROUP REPRESENTATIONS)
Minimalization and Homogeneous Module Testing (INVARIANT RINGS OF FINITE GROUPS)
Modules (OVERVIEW)
Modules Hom_(R)(M, N) with Given Basis (FREE MODULES)
Natural K[G]-Modules (K[G]-MODULES AND GROUP REPRESENTATIONS)
Syzygy Modules (IDEAL THEORY AND GRÖBNER BASES)
The Module of an Invariant Ring (INVARIANT RINGS OF FINITE GROUPS)
{THE MODULE OF}{SUPERSINGULAR POINTS}
FldFunG_module (Example H53E14)
Arithmetic with Modules (MODULES OVER DEDEKIND DOMAINS)
Modules (OVERVIEW)
{THE MODULE OF}{SUPERSINGULAR POINTS}
Construction of a Module with Specified Basis (FREE MODULES)
Modules Hom_(R)(M, N) with Given Basis (FREE MODULES)
ModuleMap(f, n) : ModMatCpxElt, RngIntElt -> ModMatFldElt
GrpGPC_ModuleMaps (Example H23E16)
ModuleOverSmallerField(M, F) : ModGrp, FldFin -> ModGrp
AbsoluteModulesOverMinimalField(Q, K) : [ ModGrp ], FldFin -> [ ModGrp ]
AbsolutelyIrreducibleModulesBurnside(G, K : parameters ) : Grp, FldFin -> [ ModGrp ]
AbsolutelyIrreducibleModulesSchur(G, K: parameters) : GrpPC, Rng -> List[GModule]
AbsolutelyIrreducibleRepresentationsInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
IrreducibleRepresentationsInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
AbsolutelyIrreducibleRepresentationsSchur(G, k: parameters) : GrpPC, Rng -> List[Map]
DimensionsOfInjectiveModules(B) : AlgBas -> SeqEnum
DimensionsOfProjectiveModules(B) : AlgBas -> SeqEnum
GetModules(SQP, p ) : SQProc, RngIntElt -> List
IrreducibleModules(G, K : parameters) : Grp, Fld -> Seqenum
IrreducibleModulesBurnside(G, K : parameters ) : Grp, FldFin -> [ ModGrp ]
IrreducibleModulesSchur(G, K: parameters) : GrpPC, Rng -> List[GModule]
IrreducibleRepresentationsSchur(G, k: parameters) : GrpPC, Rng -> List[Map]
Modules(SQP : parameters): SQProc ->
ModulesOverCommonField(M, N) : ModGrp, ModGrp -> ModGrp, ModGrp
ModulesOverSmallerField(Q, F) : SeqEnum, FldFin -> ModGrp
PrintModules(SQP) : SQProc ->
Grp_Modules (Example H16E18)
Brandt Module Creation (BRANDT MODULES)
BRANDT MODULES
Free Modules (FREE MODULES)
Generic Functions for Finding Irreducible Modules (K[G]-MODULES AND GROUP REPRESENTATIONS)
Indecomposable Projective Modules (BASIC ALGEBRAS)
Injective Modules (BASIC ALGEBRAS)
Irreducible Modules (FP GROUPS - ADVANCED FEATURES)
Modules (OVERVIEW)
MODULES OVER AFFINE ALGEBRAS
Modules over Basic Algebras (BASIC ALGEBRAS)
MODULES OVER DEDEKIND DOMAINS
Permutation Modules (K[G]-MODULES AND GROUP REPRESENTATIONS)
The Burnside Algorithm for General Groups (K[G]-MODULES AND GROUP REPRESENTATIONS)
The Construction of all Irreducible Modules (K[G]-MODULES AND GROUP REPRESENTATIONS)
The Schur Algorithm for Soluble Groups (K[G]-MODULES AND GROUP REPRESENTATIONS)
MODULES OVER AFFINE ALGEBRAS
ModulesOverCommonField(M, N) : ModGrp, ModGrp -> ModGrp, ModGrp
ModulesOverSmallerField(Q, F) : SeqEnum, FldFin -> ModGrp
Moduli(M) : ModTupRng -> [ RngElt ]
ModuliPoints(X,E) : CrvMod, CrvEll -> SeqEnum
CrvMod_Moduli points (Example H89E1)
ModuliPoints(X,E) : CrvMod, CrvEll -> SeqEnum
Rings, Fields, and Algebras (OVERVIEW)
BlumBlumShubModulus(b) : RngIntElt -> RngIntElt
BBSModulus(b) : RngIntElt -> RngIntElt
CongruenceModulus(M : parameters) : ModSym -> RngIntElt
FactoredModulus(R) : RngIntRes -> RngIntEltFact
Modulus(c) : FldComElt -> FldReElt
Modulus(R) : RngIntRes -> RngInt
Modulus(OQ) : RngOrdRes -> RngOrdIdl
Modulus(Q) : RngUPolRes -> RngUPolElt
MoebiusMu(n) : RngIntElt -> RngIntElt
MoebiusMu(n) : RngIntElt -> RngIntElt
MolienSeries(G) : GrpMat -> FldFunUElt
Molien Series (INVARIANT RINGS OF FINITE GROUPS)
MolienSeries(G) : GrpMat -> FldFunUElt
RngInvar_MolienSeries (Example H80E5)
Semigroups (OVERVIEW)
MonodromyPairing(P, Q) : ModSSElt, ModSSElt -> RngIntElt
MonodromyWeights(M) : ModSS -> SeqEnum
The Monodromy Pairing ({THE MODULE OF}{SUPERSINGULAR POINTS})
ModSS_Monodromy pairing (Example H92E9)
The Monodromy Pairing ({THE MODULE OF}{SUPERSINGULAR POINTS})
MonodromyPairing(P, Q) : ModSSElt, ModSSElt -> RngIntElt
MonodromyWeights(M) : ModSS -> SeqEnum
FreeMonoid(n) : RngIntElt -> MonFP
Monoid(A) : Alg -> MonFP
Monoid< generators | relations > : MonFPElt, ..., MonFPElt, Rel, ..., Rel -> MonFP
OrderedIntegerMonoid() : -> MonOrd
OrderedMonoid(P) : MonPlc -> MonOrd
OrderedMonoid(M) : MonPlc -> MonOrd;
OrderedMonoid(n) : RngIntElt -> MonOrd
PlacticIntegerMonoid() : -> MonOrd
PlacticMonoid(O) : MonOrd -> MonOrd
TableauIntegerMonoid() : -> MonTbl
TableauMonoid(O) : MonOrd -> MonTbl
SgpFP_Monoid (Example H14E2)
Accessing an Algebra (FINITELY PRESENTED ALGEBRAS)
Ordered Monoids (PARTITIONS, WORDS AND YOUNG TABLEAUX)
Plactic Monoids (PARTITIONS, WORDS AND YOUNG TABLEAUX)
Rewrite Monoid Predicates (MONOIDS GIVEN BY REWRITE SYSTEMS)
Semigroups (OVERVIEW)
Tableau Monoids (PARTITIONS, WORDS AND YOUNG TABLEAUX)
MonomialGroup(C: parameters) : Code -> GrpPerm, PowMap, Map
AutomorphismGroup(C: parameters) : Code -> GrpPerm, PowMap, Map
AutomorphismGroupStabilizer(C, k) : Code, RngIntElt -> GrpPerm, PowMap, Map
AutomorphismSubgroup(C) : Code -> GrpPerm, PowMap, Map
LeadingMonomial(f) : RngMPolElt -> RngMPolElt
LeadingMonomialIdeal(I) : RngMPol -> RngMPol
Monomial(P, E) : RngMPol, [ RngIntElt ] -> RngMPolElt
MonomialCoefficient(u, m) : AlgFPElt, MonElt -> RngElt
MonomialCoefficient(f, m) : RngMPolElt, RngMPolElt -> RngElt
MonomialCoefficient(p, m) : RngUPolElt, RngUPolElt -> RngElt
Coefficients, Monomials and Terms (MULTIVARIATE POLYNOMIAL RINGS)
MonomialCoefficient(u, m) : AlgFPElt, MonElt -> RngElt
MonomialCoefficient(f, m) : RngMPolElt, RngMPolElt -> RngElt
MonomialCoefficient(p, m) : RngUPolElt, RngUPolElt -> RngElt
MonomialGroup(C: parameters) : Code -> GrpPerm, PowMap, Map
AutomorphismGroup(C: parameters) : Code -> GrpPerm, PowMap, Map
MonomialGroupStabilizer(C, k) : Code, RngIntElt -> GrpPerm, PowMap, Map
AutomorphismGroupStabilizer(C, k) : Code, RngIntElt -> GrpPerm, PowMap, Map
Monomials(f) : RngMPolElt -> [ RngMPolElt ]
MonomialsOfDegree(P) : RngMPolElt -> {@ RngMPolElt @}
MonomialsOfWeightedDegree(P) : RngMPolElt -> {@ RngMPolElt @}
MonomialsOfDegree(P) : RngMPolElt -> {@ RngMPolElt @}
MonomialsOfWeightedDegree(P) : RngMPolElt -> {@ RngMPolElt @}
MonomialSubgroup(C) : Code -> GrpPerm, PowMap, Map
AutomorphismSubgroup(C) : Code -> GrpPerm, PowMap, Map
MordellWeilGroup(H: parameters) : SetPtEll -> GrpAb, Map
AbelianGroup(H: parameters) : SetPtEll -> GrpAb, Map
Rank(H: parameters) : SetPtEll -> RngIntElt
RankBounds(H: parameters) : SetPtEll -> RngIntElt, RngIntElt
Heights and Mordell--Weil Group (HYPERELLIPTIC CURVES)
Heights and Mordell--Weil Group (HYPERELLIPTIC CURVES)
CrvEll_MordellWeil (Example H87E17)
MordellWeilGroup(H: parameters) : SetPtEll -> GrpAb, Map
AbelianGroup(H: parameters) : SetPtEll -> GrpAb, Map
MordellWeilRank(H: parameters) : SetPtEll -> RngIntElt
Rank(H: parameters) : SetPtEll -> RngIntElt
MordellWeilRankBounds(H: parameters) : SetPtEll -> RngIntElt, RngIntElt
RankBounds(H: parameters) : SetPtEll -> RngIntElt, RngIntElt
More About Presentations (FINITE SOLUBLE GROUPS)
More Creation Functions (LOCAL RINGS AND FIELDS)
GrpPSL2_more-graphics (Example H31E9)
More About Presentations (FINITE SOLUBLE GROUPS)
Morphism(A, B) : AlgGen, AlgGen -> Map
Morphism(E, F, psi, phi, omega) : CrvEll, CrvEll, RngMPolElt, RngMPolElt, RngMPolElt -> Map
Morphism(H, G) : GrpAb, GrpAb -> ModMatRngElt
Morphism(M, N) : ModDed, ModDed -> Map
Morphism(M, N) : ModRng, ModRng -> ModMatRngElt
Morphism(M, N) : ModRng, ModRng -> ModMatRngElt
Morphism(U, V) : ModTupFld, ModTupFld -> RModMatElt
Morphism(M, N) : ModTupRng, ModTupRng -> ModMatRngElt
Morphism(e) : SubModLatElt -> ModMatRngElt
Morphisms (ELLIPTIC CURVES)
Creation Functions (ELLIPTIC CURVES)
Structure Operations (ELLIPTIC CURVES)
Predicates on Isogenies (ELLIPTIC CURVES)
BaseMPolynomial(n, m, d) : RngIntElt, RngIntElt, RngIntElt -> RngMPolElt
MPQS(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]
MoebiusMu(n) : RngIntElt -> RngIntElt
ReedMullerCode(r, m) : RngIntElt, RngIntElt -> Code
IsogenyMapPhiMulti(I) : Map -> RngUPolElt
IsogenyMapPsiMulti(I) : Map -> RngUPolElt
Multi-indexing (INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS])
Multi-indexing (INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS])
Multidegree(X,f) : Sch,RngMPolElt -> SeqEnum
AlgAff_MultiExtension (Example H67E5)
Multinomial(n, [a_1, ... a_n]) : RngIntElt, [RngIntElt] -> RngIntElt
Multinomial(n, [a_1, ... a_n]) : RngIntElt, [RngIntElt] -> RngIntElt
MultipartiteGraph(Q) : [RngIntElt] -> GrphUnd
MultipartiteGraph(Q) : [RngIntElt] -> GrphUnd
Lcm(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
LeastCommonMultiple(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
LCM(D1, D2) : DivFunElt, DivFunElt -> DivFunElt
LCM(I, J) : RngOrdFracIdl, RngOrdFracIdl -> RngOrdFracIdl
Lcm(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
LeastCommonMultiple(m, n) : RngIntElt, RngIntElt -> RngIntElt
LeastCommonMultiple(a, b) : RngIntResElt, RngIntResElt -> RngIntResElt
LeastCommonMultiple(f, g) : RngMPolElt, RngMPolElt -> RngMPolElt
LeastCommonMultiple(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
LeastCommonMultiple(Q) : Seq(RngIntResElt) -> RngIntResElt
LeastCommonMultiple(s) : [RngIntElt] -> RngIntElt
PseudoAddMultiple(P1, P2, P3, n) : SrfKumPt, SrfKumPt, SrfKumPt, RngIntElt -> SrfKumPt
Multiple Assignment (OVERVIEW)
Multiple Assignment (OVERVIEW)
State_MultipleReturns (Example H1E2)
MultiplicationByMMap(E, m) : CrvEll, RngIntElt -> Map
MultiplicationTable(O) : RngOrd -> [AlgMatElt]
Operators (OVERVIEW)
MultiplicationByMMap(E, m) : CrvEll, RngIntElt -> Map
MultiplicationTable(O) : RngOrd -> [AlgMatElt]
RngOrd_MultiplicationTable (Example H48E15)
UnitGroup(F) : FldFin -> GrpAb, Map
MultiplicativeGroup(F) : FldFin -> GrpAb, Map
MultiplicativeGroup(Z) : RngInt -> GrpAb, Map
MultiplicativeGroup(R) : RngIntRes -> GrpAb, Map
UnitGroup(O) : RngOrd -> GrpAb, Map
UnitGroup(OQ) : RngOrdRes -> GrpAb, Map
UnitGroup(F) : FldFin -> GrpAb, Map
MultiplicativeGroup(F) : FldFin -> GrpAb, Map
MultiplicativeGroup(Z) : RngInt -> GrpAb, Map
MultiplicativeGroup(R) : RngIntRes -> GrpAb, Map
UnitGroup(O) : RngOrd -> GrpAb, Map
UnitGroup(OQ) : RngOrdRes -> GrpAb, Map
MultiplicatorRing(I) : RngFunOrdIdl -> RngFunOrd
MultiplicatorRing(I) : RngOrdFracIdl -> Rng
MultiplicatorRing(I) : RngFunOrdIdl -> RngFunOrd
MultiplicatorRing(I) : RngOrdFracIdl -> Rng
CalculateMultiplicities(~g) : GrphRes ->
ConstituentsWithMultiplicities(M) : ModRng -> [ <ModRng, RngIntElt> ]
Multiplicities(g) : GrphRes -> SeqEnum
Multiplicity(L,p) : LinSys,Pt -> RngIntElt
Multiplicity(p) : Sch,Pt -> RngIntElt
Multiplicity(p) : Sch,Pt -> RngIntElt
Multiplicity(S, x) : SetMulti, Elt -> RngIntElt
MultiplyByTranspose(v, A) : ModTupRng, MtrxSprs -> ModTupRng
MultiplyColumn(~a, u, i) : AlgMatElt, RngElt, RngIntElt ->
MultiplyColumn(A, c, i) : Mtrx, RngElt, RngIntElt -> Mtrx
MultiplyRow(~a, u, j) : AlgMatElt, RngElt, RngIntElt ->
MultiplyRow(A, c, i) : Mtrx, RngElt, RngIntElt -> Mtrx
Multiplying Vectors or Matrices by Sparse Matrices (SPARSE MATRICES)
MultiplyByTranspose(v, A) : ModTupRng, MtrxSprs -> ModTupRng
MultiplyColumn(~a, u, i) : AlgMatElt, RngElt, RngIntElt ->
MultiplyColumn(A, c, i) : Mtrx, RngElt, RngIntElt -> Mtrx
MultiplyRow(~a, u, j) : AlgMatElt, RngElt, RngIntElt ->
MultiplyRow(A, c, i) : Mtrx, RngElt, RngIntElt -> Mtrx
MultisetToSet(S) : SetMulti -> SetEnum
PowerMultiset(R) : Struct -> PowSetMulti
SequenceToMultiset(Q) : SeqEnum -> SetMulti
SetToMultiset(E) : SetEnum -> SetMulti
Set_Multiset (Example H7E4)
The Multiset Constructor (SETS)
Multisets(S, k) : SetEnum, RngIntElt -> SetEnum
Multisets(S, k) : SetEnum, RngIntElt -> SetEnum
MultisetToSet(S) : SetMulti -> SetEnum
MultivariatePolynomial(P, f, i) : RngMPol, RngUPolElt, RngIntElt -> RngMPolElt
MULTIVARIATE POLYNOMIAL RINGS
MultivariatePolynomial(P, f, i) : RngMPol, RngUPolElt, RngIntElt -> RngMPolElt
Tableau_MultTabcreate-fingen (Example H96E14)
Tableau_MultTabCreate1 (Example H96E13)
MurphyAlphaApproximation(F, b) : RngMPolElt, RngIntElt -> FldReElt
MurphyAlphaApproximation(F, b) : RngMPolElt, RngIntElt -> FldReElt
Mutation assignment (OVERVIEW)
Incremental Construction of Graphs (GRAPHS)
Mutation assignment (OVERVIEW)
Mutation Assignment (STATEMENTS AND EXPRESSIONS)
State_MutationAssignment (Example H1E6)
Recursion and forward (OVERVIEW)
Recursion and Mutual Recursion (MAGMA SEMANTICS)
[____] [____] [_____] [____] [__] [Index] [Root]