[____] [____] [_____] [____] [__] [Index] [Root]
Index O
O(x) : RngLocElt -> RngLocElt
BigO(x) : RngLocElt -> RngLocElt
BigO(x) : RngLocElt -> RngLocElt
BigO(x) : RngLocElt -> RngLocElt
BigO(f) : RngSerElt -> RngIntElt
ObjectiveFunction(L) : LP -> Mtrx
SetObjectiveFunction(L, F) : LP, Mtrx ->
ObjectiveFunction(L) : LP -> Mtrx
HasOddDegreeModel(C) : CrvHyp -> BoolElt, CrvHyp, MapCrvHyp
IsOdd(x) : GrpDrchElt -> BoolElt
IsOdd(n) : RngIntElt -> BoolElt
LRatioOddPart(M, j) : ModSym, RngIntElt -> FldRatElt
OddGraph(n) : RngIntElt -> GrphUnd
OddGraph(n) : RngIntElt -> GrphUnd
EnumComb_OddGraph (Example H92E1)
Structure of congruence subgroups (SUBGROUPS OF PSL_2(R))
RngLoc_ofe (Example H59E10)
RngPad_ofe (Example H42E8)
IsogenyMapOmega(I) : Map -> RngMPolElt
Omega(arguments)
Omega(G, i) : GrpAb, RngIntElt -> GrpAb
Omega(G, i) : GrpPC, RngIntElt -> GrpPC
OmegaMinus(arguments)
OmegaPlus(arguments)
ProjectiveOmega(arguments)
ProjectiveOmegaMinus(arguments)
ProjectiveOmegaPlus(arguments)
OmegaMinus(arguments)
OmegaPlus(arguments)
Multiple Assignment (OVERVIEW)
InducedMapOnHomology(f,n) : MapChn, RngIntElt -> ModTupFldElt
LongExactSequenceOnHomology(f,g) : MapChn, MapChn -> ModCpx
NumberOfTableauxOnAlphabet(P, m) : SeqEnum,RngIntElt -> RngIntElt
SetQuitOnError(b) : BoolElt ->
WordOnRoot( W, r, w ) : GrpCox, RngIntElt, . -> RngIntElt
WordOnRootSpace( W, v, w ) : GrpCox, ., . -> .
One(A) : AlgQuat -> AlgQuatElt
A ! 1 : AlgQuat, RngIntElt -> AlgQuatElt
DegreeOnePrimeIdeals(O, B) : RngOrd, RngIntElt -> [ RngOrdIdl ]
DivisorOfDegreeOne(F) : FldFun -> DivFunElt
Id(R) : AlgChtr -> AlgChtrElt
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
IsOne(a) : AlgGenElt -> BoolElt
IsOne(a) : AlgMatElt -> BoolElt
IsOne(a) : FldACElt -> BoolElt
IsOne(u) : MonFPElt -> BoolElt
IsOne(A) : Mtrx -> BoolElt
IsOne(a) : RngElt -> BoolElt
IsOne(I) : RngFunOrdIdl -> BoolElt
IsOne(x) : RngLocElt -> BoolElt
IsOne(a) : RngOrdResElt -> BoolElt
MaximalZeroOneSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
MinimalZeroOneSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
NumberOfPlacesOfDegreeOne(F) : FldFun -> RngIntElt
NumberOfPlacesOfDegreeOne(F, m) : FldFun, RngIntElt -> RngIntElt
NumberOfPlacesOfDegreeOne(F, m) : FldFun, RngIntElt -> RngIntElt
NumberOfPlacesOfDegreeOneBound(F) : FldFun -> RngIntElt
NumberOfPlacesOfDegreeOneBound(F, m) : FldFun, RngIntElt -> RngIntElt
One(A) : AlgGen -> AlgGenElt
One(R) : Rng -> RngElt
One(L) : RngLoc -> RngLocElt
Overview (OVERVIEW)
Operations on FP Coxeter groups (COXETER GROUPS)
Operations on words (COXETER GROUPS)
Open(S, T) : MonStgElt, MonStgElt -> File
OpenGraphFile(s, f, p): MonStgElt, RngIntElt, RngIntElt -> File
Opening Files (INPUT AND OUTPUT)
Opening Files (INPUT AND OUTPUT)
OpenGraphFile(s, f, p): MonStgElt, RngIntElt, RngIntElt -> File
Operations on Structure Constant Algebras (STRUCTURE CONSTANT ALGEBRAS)
SteenrodOperation(f, i) : RngMPolElt, RngIntElt -> RngMPolElt
Accessing and Modifying a Matrix (MATRIX ALGEBRAS)
Action of the Algebra on the Module (MODULES OVER A MATRIX ALGEBRA)
Arithmetic Operations on Codewords (LINEAR CODES OVER FINITE FIELDS)
Arithmetic with Elements (ABELIAN GROUPS)
Arithmetic with Elements (GENERIC ABELIAN GROUPS)
Arithmetic with Elements (GROUPS WHOSE ELEMENTS ARE STRAIGHT-LINE PROGRAMS)
Arithmetic with Module Elements (MODULES OVER A MATRIX ALGEBRA)
Basic Element Operations (POWER, LAURENT AND PUISEUX SERIES)
Basic Operations (AUTOMATIC GROUPS)
Basic Operations (GROUPS DEFINED BY REWRITE SYSTEMS)
Basic Operations (GROUPS)
Basic Operations (MONOIDS GIVEN BY REWRITE SYSTEMS)
Basic Operations (VECTOR SPACES)
Basic Operations on Ideals (IDEAL THEORY AND GRÖBNER BASES)
Boolean Operators (STATEMENTS AND EXPRESSIONS)
Constructing New Codes from Old (LINEAR CODES OVER FINITE RINGS)
Coset Spaces: Elementary Operations (FINITELY PRESENTED GROUPS)
Element Operations (ALGEBRAIC FUNCTION FIELDS)
Element Operations (ALGEBRAIC FUNCTION FIELDS)
Element Operations (ALGEBRAIC FUNCTION FIELDS)
Element Operations (ALGEBRAIC FUNCTION FIELDS)
Element Operations (ALGEBRAICALLY CLOSED FIELDS)
Element Operations (FINITE FIELDS)
Element Operations (FINITE SOLUBLE GROUPS)
Element Operations (FREE MODULES)
Element Operations (GALOIS RINGS)
Element Operations (MULTIVARIATE POLYNOMIAL RINGS)
Element Operations (ORDERS AND ALGEBRAIC FIELDS)
Element Operations (REAL AND COMPLEX FIELDS)
Element Operations (RING OF INTEGERS)
Element Operations (UNIVARIATE POLYNOMIAL RINGS)
Elementary Operators for Words (FINITELY PRESENTED SEMIGROUPS)
Elementary Properties of a Group (PERMUTATION GROUPS)
General Design Constructions (INCIDENCE STRUCTURES AND DESIGNS)
General Subgroup Constructions (POLYCYCLIC GROUPS)
Ideal Operations (ALGEBRAIC FUNCTION FIELDS)
New Codes from Old (LINEAR CODES OVER FINITE FIELDS)
Operations on Codewords and Vectors (LINEAR CODES OVER FINITE RINGS)
Operations on Edges and Vertices (GRAPHS)
Operations on Elements (ABELIAN GROUPS)
Operations on Elements (GENERIC ABELIAN GROUPS)
Operations on Elements (GROUPS WHOSE ELEMENTS ARE STRAIGHT-LINE PROGRAMS)
Operations on Elements (LOCAL RINGS AND FIELDS)
Operations on Elements (p-ADIC RINGS AND FIELDS)
Operations on Elements of Ideals (IDEAL THEORY AND GRÖBNER BASES)
Operations on G-Lattices (LATTICES)
Operations on Lattice Elements (LATTICES)
Operations on Mappings (MAPPINGS)
Operations on Matrices (MATRIX GROUPS)
Operations on Matrix Algebras (MATRIX ALGEBRAS)
Operations on Module Elements (FREE MODULES)
Operations on Points and Blocks (INCIDENCE STRUCTURES AND DESIGNS)
Operations on Points and Lines (FINITE PLANES)
Operations on Sets (SETS)
Operations on Subgroup Class Posets (GROUPS)
Operations on Submodules (FREE MODULES)
Operations on Submodules (MODULES OVER A MATRIX ALGEBRA)
Operations on Subspaces (VECTOR SPACES)
Operators for Elements (POLYCYCLIC GROUPS)
Operators on Sequences (SEQUENCES)
Predicates and Boolean Operations (LATTICES)
Related Structures (ALGEBRAIC FUNCTION FIELDS)
Related Structures (ALGEBRAIC FUNCTION FIELDS)
Related Structures (ALGEBRAIC FUNCTION FIELDS)
Related Structures (ALGEBRAIC FUNCTION FIELDS)
Set Operations (ABELIAN GROUPS)
Set Operations (GROUPS WHOSE ELEMENTS ARE STRAIGHT-LINE PROGRAMS)
Set Operations (POLYCYCLIC GROUPS)
Soluble Group Functions (MATRIX GROUPS)
Standard Constructions (FREE MODULES)
Standard Constructions (MODULES OVER A MATRIX ALGEBRA)
Standard Constructions for Graphs (GRAPHS)
Standard Subgroup Constructions (GROUPS)
String Operations on Words (FINITELY PRESENTED SEMIGROUPS)
Structure Operations (FINITE FIELDS)
Structure Operations (FINITE SOLUBLE GROUPS)
Structure Operations (GALOIS RINGS)
Structure Operations (MULTIVARIATE POLYNOMIAL RINGS)
Structure Operations (ORDERS AND ALGEBRAIC FIELDS)
Structure Operations (POWER, LAURENT AND PUISEUX SERIES)
Structure Operations (RATIONAL FIELD)
Structure Operations (RATIONAL FUNCTION FIELDS)
Structure Operations (REAL AND COMPLEX FIELDS)
Structure Operations (RING OF INTEGERS)
Structure Operations (RING OF INTEGERS)
Structure Operations (UNIVARIATE POLYNOMIAL RINGS)
Subgroup Constructions (FINITELY PRESENTED GROUPS)
Subgroup Constructions Requiring a Nil-po-tent Covering Group (POLYCYCLIC GROUPS)
Working with a Base and Strong Generating Set (PERMUTATION GROUPS)
Accessing and Modifying a Matrix (MATRIX ALGEBRAS)
Basic Element Operations (POWER, LAURENT AND PUISEUX SERIES)
Boolean Operators (STATEMENTS AND EXPRESSIONS)
Element Operations (ALGEBRAIC FUNCTION FIELDS)
Element Operations (ALGEBRAIC FUNCTION FIELDS)
Element Operations (ALGEBRAIC FUNCTION FIELDS)
Element Operations (ALGEBRAIC FUNCTION FIELDS)
Element Operations (ALGEBRAICALLY CLOSED FIELDS)
Element Operations (FINITE FIELDS)
Element Operations (FINITE SOLUBLE GROUPS)
Element Operations (FREE MODULES)
Element Operations (GALOIS RINGS)
Element Operations (MULTIVARIATE POLYNOMIAL RINGS)
Element Operations (ORDERS AND ALGEBRAIC FIELDS)
Element Operations (REAL AND COMPLEX FIELDS)
Element Operations (RING OF INTEGERS)
Element Operations (UNIVARIATE POLYNOMIAL RINGS)
Operations on Elements (ABELIAN GROUPS)
Operations on Elements (GENERIC ABELIAN GROUPS)
Operations on Elements (GROUPS WHOSE ELEMENTS ARE STRAIGHT-LINE PROGRAMS)
Operations on Elements (LOCAL RINGS AND FIELDS)
Operations on Elements (p-ADIC RINGS AND FIELDS)
Operations on Elements of Ideals (IDEAL THEORY AND GRÖBNER BASES)
Operations on Matrices (MATRIX GROUPS)
String Operations on Words (FINITELY PRESENTED SEMIGROUPS)
Structure Operations (FINITE SOLUBLE GROUPS)
Ideal Operations (ALGEBRAIC FUNCTION FIELDS)
Operations on Points and Blocks (INCIDENCE STRUCTURES AND DESIGNS)
Related Structures (ALGEBRAIC FUNCTION FIELDS)
Related Structures (ALGEBRAIC FUNCTION FIELDS)
Related Structures (ALGEBRAIC FUNCTION FIELDS)
Related Structures (ALGEBRAIC FUNCTION FIELDS)
Structure Operations (POWER, LAURENT AND PUISEUX SERIES)
Structure Operations (REAL AND COMPLEX FIELDS)
General Subgroup Constructions (POLYCYCLIC GROUPS)
Standard Subgroup Constructions (GROUPS)
Subgroup Constructions (FINITELY PRESENTED GROUPS)
Normalizer(G, H) : GrpGPC, GrpGPC -> GrpGPC
Subgroup Constructions Requiring a Nil-po-tent Covering Group (POLYCYCLIC GROUPS)
Operations on Submodules (FREE MODULES)
Operations on Subspaces (VECTOR SPACES)
AlgLie_Operations (Example H75E3)
ModRng_Operations (Example H64E11)
ModRng_Operations (Example H64E3)
Boolean Operations (BINARY QUADRATIC FORMS)
Homogeneous Modules (MODULES OVER AFFINE ALGEBRAS)
Module Operations (MODULES OVER AFFINE ALGEBRAS)
Operations (COXETER GROUPS)
Operations for Polynomials (LOCAL RINGS AND FIELDS)
Operations for Polynomials (p-ADIC RINGS AND FIELDS)
Operations on Affine Algebras (AFFINE ALGEBRAS)
Operations on Coxeter groups and elements (COXETER GROUPS)
Operations on Differentials (PLANE ALGEBRAIC CURVES)
Operations on File Objects (INPUT AND OUTPUT)
Operations on Forms (BINARY QUADRATIC FORMS)
Operations on groups of Lie type (GROUPS OF LIE TYPE)
Operations on Lie Algebras (LIE ALGEBRAS)
Operations on LP objects (LINEAR PROGRAMMING)
Operations on Structures (LOCAL RINGS AND FIELDS)
Operations on Structures (p-ADIC RINGS AND FIELDS)
CoefficientRing(E) : CrvEll -> Rng
Associated Structures (ELLIPTIC CURVES)
Elementary Invariants (ELLIPTIC CURVES)
Operations on Curves (ELLIPTIC CURVES)
Predicates on Elliptic Curves (ELLIPTIC CURVES)
CoefficientRing(E) : CrvEll -> Rng
Associated Structures (ELLIPTIC CURVES)
Elementary Invariants (ELLIPTIC CURVES)
Predicates on Elliptic Curves (ELLIPTIC CURVES)
AtkinLehnerOperator(M, p) : ModBrdt, RngIntElt -> AlgMatElt
DualHeckeOperator(M, n) : ModSym, RngIntElt -> AlgMatElt
HeckeOperator(M, n) : ModBrdt, RngIntElt -> AlgMatElt
HeckeOperator(M, n) : ModFrm, RngIntElt -> AlgMatElt
HeckeOperator(M, n) : ModSym, RngIntElt -> AlgMatElt
IntegralHeckeOperator(M, n) : ModSym, RngIntElt -> AlgMatElt
ReynoldsOperator(f, G) : RngMPolElt, GrpMat -> RngMPolElt
ThetaOperator(M1, M2) : ModSym, ModSym -> Map
Operators (OVERVIEW)
x o:= expression;
ModSym_Operators (Example H88E15)
Equality Operators (STATEMENTS AND EXPRESSIONS)
Hecke Operators (BRANDT MODULES)
Operations on elements (GROUPS OF LIE TYPE)
Operators (MODULAR FORMS)
Operators (MODULAR SYMBOLS)
Operators on root data (ROOT DATA FOR LIE THEORY)
Operators on root data (ROOT DATA FOR LIE THEORY)
OppositeAlgebra(B) : AlgBas -> AlgBas
AlgBas_Opposite (Example H79E4)
Opposite Algebras (BASIC ALGEBRAS)
Opposite Algebras (BASIC ALGEBRAS)
OppositeAlgebra(B) : AlgBas -> AlgBas
Arithmetic of Elements (QUATERNION ALGEBRAS)
Creation of Elements (QUATERNION ALGEBRAS)
Decomposition of an Algebra (ALGEBRAS)
Elementary Operations (FINITE PLANES)
Functions on Elements (ALGEBRAIC FUNCTION FIELDS)
Functions related to Orders and Integrality (ALGEBRAIC FUNCTION FIELDS)
Functions related to Places and Divisors (ALGEBRAIC FUNCTION FIELDS)
Functions related to Places and Divisors (ALGEBRAIC FUNCTION FIELDS)
Further Ideal Operations (ALGEBRAIC FUNCTION FIELDS)
Operations and properties for (co)roots (ROOT DATA FOR LIE THEORY)
Operations at a Point (PLANE ALGEBRAIC CURVES)
Operations not associated with Duval's Algorithm (NEWTON POLYGONS)
Operations on Algebras and Subalgebras (ALGEBRAS)
Operations on Associative Algebras (ASSOCIATIVE ALGEBRAS)
Operations on Associative Algebras and their Elements (ASSOCIATIVE ALGEBRAS)
Operations on Elements (ALGEBRAIC FUNCTION FIELDS)
Operations on Elements (ALGEBRAS)
Operations on Elements (ASSOCIATIVE ALGEBRAS)
Operations on Elements (GROUP ALGEBRAS)
Operations on Elements of an Algebra (ALGEBRAS)
Operations on Group Algebras (GROUP ALGEBRAS)
Operations on Group Algebras and their Subalgebras (GROUP ALGEBRAS)
Operations on Ideals (QUATERNION ALGEBRAS)
Operations on Modules (MODULES OVER ORDERS)
Operations on Polynomials which use Newton Polygons (NEWTON POLYGONS)
Operations on Subalgebras (ALGEBRAS)
Other Element Operations (ALGEBRAIC FUNCTION FIELDS)
Other Element Operations (ALGEBRAIC FUNCTION FIELDS)
Representations of Associative Algebras (ASSOCIATIVE ALGEBRAS)
Set Operations (FINITE SOLUBLE GROUPS)
Operations and properties for (co)roots (ROOT DATA FOR LIE THEORY)
LINEAR PROGRAMMING
RngOrd_opt-rep (Example H53E3)
OptimalEdgeColouring(G) : GrphUnd -> SeqEnum
OptimalSkewness(F) : RngMPolElt -> FldReElt, FldReElt
OptimalVertexColouring(G) : GrphUnd -> SeqEnum
OptimalEdgeColouring(G) : GrphUnd -> SeqEnum
OptimalSkewness(F) : RngMPolElt -> FldReElt, FldReElt
OptimalVertexColouring(G) : GrphUnd -> SeqEnum
OptimisedRepresentation(F) : FldAlg -> FldAlg, map
OptimizedRepresentation(F) : FldAlg -> FldAlg, map
OptimizedRepresentation(O) : RngOrd -> BoolElt, RngOrd, Map
OptimisedRepresentation(F) : FldAlg -> FldAlg, map
OptimizedRepresentation(F) : FldAlg -> FldAlg, map
OptimizedRepresentation(O) : RngOrd -> BoolElt, RngOrd, Map
Optimizing Magma Code (FINITE SOLUBLE GROUPS)
OptimisedRepresentation(F) : FldAlg -> FldAlg, map
OptimizedRepresentation(F) : FldAlg -> FldAlg, map
OptimizedRepresentation(O) : RngOrd -> BoolElt, RngOrd, Map
OptimisedRepresentation(F) : FldAlg -> FldAlg, map
OptimizedRepresentation(F) : FldAlg -> FldAlg, map
OptimizedRepresentation(O) : RngOrd -> BoolElt, RngOrd, Map
Print Options (MODULES OVER AFFINE ALGEBRAS)
Print Options (UNIVARIATE POLYNOMIAL RINGS)
Special Options (FINITE FIELDS)
Special Options (ORDERS AND ALGEBRAIC FIELDS)
SetOptions(~P : parameters) : Process(Tietze) ->
ShowOptions(~P : parameters) : Process(Tietze) ->
Command Line Options (ENVIRONMENT AND OPTIONS)
ENVIRONMENT AND OPTIONS
Special Options (POWER, LAURENT AND PUISEUX SERIES)
Expression (OVERVIEW)
x or y: BoolElt, BoolElt -> BoolElt
BasicOrbit(G, i) : GrpMat, RngIntElt -> SetIndx
BasicOrbit(G, i) : GrpPerm, RngIntElt -> SetIndx
BasicOrbitLength(G, i) : GrpMat, RngIntElt -> RngIntElt
BasicOrbitLength(G, i) : GrpPerm, RngIntElt -> RngIntElt
BasicOrbitLengths(G) : GrpMat -> [RngIntElt]
BasicOrbitLengths(G) : GrpPerm -> [RngIntElt]
EstimateOrbit(G, U: parameters) : GrpMat, ModTupFld -> RngIntElt, RngIntElt, RngIntElt
ExceptionalUnitOrbit(u) : RngOrdElt -> [ RngOrdElt ]
GaloisOrbit(x) : AlgChtrElt -> { AlgChtrElt }
IsMemberBasicOrbit(G, i, a) : GrpPerm, RngIntElt, Elt -> BoolElt
IsOrbit(G, S) : GrpPerm, { Elt } -> BoolElt
Orbit(A, Y, y) : GrpPerm, GSet, Elt -> GSet
Orbit(G, Y, y) : GrpPerm, GSet, Elt -> GSet
Orbit(G, Y, y) : GrpPerm, GSet, Elt -> GSet
Orbit(G, Y, y) : GrpPerm, GSet, Elt -> GSet
OrbitAction(G, T) : GrpMat, Elt -> Hom(Grp), GrpPerm, GrpMat
OrbitAction(G, T) : GrpPerm, GSet -> Hom(Grp), GrpPerm, GrpPerm
OrbitActionBounded(G, T, b) : GrpMat, Elt, RngIntElt -> BoolElt, Hom(Grp), GrpPerm, GrpMat
OrbitBounded(G, y, b) : GrpMat, Elt, RngIntElt -> BoolElt, SetEnum
OrbitClosure(G, S) : GrpMat, { Elt } -> GSet
OrbitClosure(G, Y, S) : GrpPerm, GSet, { Elt } -> GSet
OrbitImage(G, T) : GrpMat, Set -> GrpPerm
OrbitImage(G, T) : GrpPerm, GSet -> GrpPerm
OrbitImageBounded(G, T, b) : GrpMat, Set, RngIntElt -> BoolElt, GrpPerm
OrbitKernel(G, T) : GrpMat, Set -> GrpMat
OrbitKernel(G, T) : GrpPerm, GSet -> GrpPerm
OrbitKernelBounded(G, T, b) : GrpMat, Set, RngIntElt -> BoolElt, GrpMat
OrbitRepresentatives(G) : GrpPerm -> SeqEnum
ReductionOrbit(f) : QuadBinElt -> SeqEnum[QuadBinElt]
WeightOrbit( W, v ) : GrpCox, . -> @ @
y ^ G : Elt, GrpMat -> SetEnum
Action on Orbits (MATRIX GROUPS)
Action on Orbits (PERMUTATION GROUPS)
Images, Orbits and Stabilizers (PERMUTATION GROUPS)
Orbit and Stabilizer Functions for Large Groups (MATRIX GROUPS)
Orbits and Stabilizers (MATRIX GROUPS)
Action on Orbits (MATRIX GROUPS)
Action on Orbits (PERMUTATION GROUPS)
OrbitAction(G, T) : GrpMat, Elt -> Hom(Grp), GrpPerm, GrpMat
OrbitAction(G, T) : GrpPerm, GSet -> Hom(Grp), GrpPerm, GrpPerm
OrbitActionBounded(G, T, b) : GrpMat, Elt, RngIntElt -> BoolElt, Hom(Grp), GrpPerm, GrpMat
GrpPerm_OrbitActions (Example H20E21)
OrbitalGraph(P, u, T) : GrpPerm, RngIntElt, { RngIntElt } -> GrphUnd
OrbitalGraph(P, u, T) : GrpPerm, RngIntElt, { RngIntElt } -> GrphUnd
OrbitBounded(G, y, b) : GrpMat, Elt, RngIntElt -> BoolElt, SetEnum
OrbitClosure(G, S) : GrpMat, { Elt } -> GSet
OrbitClosure(G, Y, S) : GrpPerm, GSet, { Elt } -> GSet
OrbitImage(G, T) : GrpMat, Set -> GrpPerm
OrbitImage(G, T) : GrpPerm, GSet -> GrpPerm
OrbitImageBounded(G, T, b) : GrpMat, Set, RngIntElt -> BoolElt, GrpPerm
OrbitKernel(G, T) : GrpMat, Set -> GrpMat
OrbitKernel(G, T) : GrpPerm, GSet -> GrpPerm
OrbitKernelBounded(G, T, b) : GrpMat, Set, RngIntElt -> BoolElt, GrpMat
OrbitRepresentatives(G) : GrpPerm -> SeqEnum
BasicOrbits(G) : GrpPerm -> [SetIndx]
LineOrbits(G) : GrpMat -> [ GSet ]
Orbits(G) : GrpMat -> [ GSet ]
Orbits(A, Y) : GrpPerm, GSet -> [ GSet ]
Orbits(G, Y) : GrpPerm, GSet -> [ GSet ]
Orbits(G, Y) : GrpPerm, GSet -> [ GSet ]
Orbits(G, Y) : GrpPerm, GSet -> [ GSet ]
OrbitsOfSpaces(G, k) : GrpMat, RngIntElt -> SeqEnum
OrbitsPartition(G : parameters ) : GrphUnd -> [ { GrphVert } ]
ReducedOrbits(Q) : QuadBin -> [ {@ QuadBinElt @} ]
GrpMat_Orbits (Example H21E19)
OrbitsOfSpaces(G, k) : GrpMat, RngIntElt -> SeqEnum
GrpMat_OrbitsOfSpaces (Example H21E20)
GrpMat_OrbitsOfSpaces (Example H21E21)
OrbitsPartition(G : parameters ) : GrphUnd -> [ { GrphVert } ]
Operations on Ideals (QUATERNION ALGEBRAS)
Operations on Ideals (QUATERNION ALGEBRAS)
Order(J) : JacHyp -> RngIntElt
# J : JacHyp -> RngIntElt
# G: SchGrpEll -> RngIntElt
# H: SetPtEll -> RngIntElt
AbsoluteOrder(O) : RngOrd -> RngOrd
AdditiveOrder( W ) : GrpCox -> SeqEnum
AdditiveOrder( F ) : GrpFP -> SeqEnum
ChangeOrder(I, order) : RngMPol, ..., -> RngMPol, Map
ChangeOrder(I, Q) : RngMPol, RngMPol -> RngMPol, Map
ComponentGroupOrder(M, p) : ModSym, RngIntElt -> RngIntElt
CyclotomicOrder(K) : FldCyc -> RngIntElt
EquationOrder(E) : CrvEll -> RngOrdFun
EquationOrder(C) : CrvHyp -> RngFunOrd
EquationOrder(A) : FldAb -> RngOrd
EquationOrder(K) : FldNum -> RngOrd
EquationOrder(F) : FldQuad -> RngQuad
EquationOrder(O) : RngOrd -> RngOrd
EquationOrder(f) : RngUPolElt -> RngOrd
EquationOrderFinite(F) : FldFun -> RngFunOrd
EquationOrderFinite(F) : FldFun -> RngFunOrd
MaximalOrderFinite(F) : FldFun -> RngFunOrd
MaximalOrderInfinite(F) : FldFun -> RngFunOrd
EquationOrderInfinite(F) : FldFun -> RngFunOrd
FactoredOrder(A) : AlgMatElt -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(a) : AlgMatElt -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(a) : FldFinElt -> RngIntElt
FactoredOrder(G) : GrpAb -> [<RngIntElt, RngIntElt>]
FactoredOrder(A) : GrpAuto -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(G) : GrpFin -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(G) : GrpGPC -> [<RngIntElt, RngIntElt>]
FactoredOrder(G) : GrpMat -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(g) : GrpMatElt -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(G) : GrpPC -> [<RngIntElt, RngIntElt>]
FactoredOrder(G) : GrpPerm -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(J) : JacHyp -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(P) : Process(pQuot) -> [ <RngIntElt, RngIntElt> ]
FactoredOrder(P) : PtEll -> RngIntElt
FactoredOrder(G) : SchGrpEll -> RngIntElt
FactoredOrder(H) : SetPtEll -> RngIntElt
FactoredProjectiveOrder(a) : AlgMatElt -> [ <RngIntElt, RngIntElt> ]
FactoredProjectiveOrder(A) : AlgMatElt -> [ <RngIntElt, RngIntElt> ], RngElt
HasFiniteOrder(g) : GrpMatElt -> BoolElt, RngIntElt
HasFiniteOrder(A) : Mtrx -> BoolElt
HasOrder(P, n) : JacHypPt, RngIntElt -> BoolElt
IsAbsoluteOrder(O) : RngOrd -> BoolElt
IsEquationOrder(O) : RngFunOrd -> BoolElt
IsEquationOrder(O) : RngOrd -> BoolElt
IsFiniteOrder(O) : RngFunOrd -> BoolElt
IsOrder(P, m) : PtEll, RngIntElt -> BoolElt
IsolOrder(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
KeepGeneratorOrder(SQG, SQH) : SQProc, SQProc -> SeqEnum
LeftOrder(I) : AlgQuatOrd -> AlgQuatOrd
MaximalOrder(A) : AlgQuat -> AlgQuatOrd
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
Order(x) : AlgChtrElt -> RngIntElt
Order(A) : AlgMatElt -> RngIntElt
Order(a) : AlgMatElt -> RngIntElt
Order(D) : Dsgn -> RngIntElt
Order(a) : FldFinElt -> RngIntElt
Order(F) : FldOrd -> RngOrd
Order(G) : GrpAb -> RngIntElt
Order(x) : GrpAbElt -> RngIntElt
Order(A) : GrpAbGen -> RngIntElt
Order(G) : GrpAtc -> RngIntElt
Order(A) : GrpAuto -> RngIntElt
Order(f) : GrpAutoElt -> RngIntElt
Order(g) : GrpElt -> RngIntElt
Order(G) : GrpFin -> RngIntElt
Order(G) : GrpGPC -> RngIntElt
Order(x) : GrpGPCElt -> RngIntElt
Order(G) : Grph -> RngIntElt
Order(G) : GrpMat -> RngIntElt
Order(g) : GrpMatElt -> RngIntElt
Order(G) : GrpPC -> RngIntElt
Order(x) : GrpPCElt -> RngIntElt
Order(G) : GrpPerm -> RngIntElt
Order(g) : GrpPermElt -> RngIntElt
Order(G) : GrpRWS -> RngIntElt
Order(P) : JacHypPt -> RngIntElt
Order(P, l, u, n, m) : JacHypPt, RngIntElt, RngIntElt ,RngIntElt, RngIntElt -> RngIntElt
Order(P, l, u) : JacHypPt, RngIntElt, RngIntElt -> RngIntElt
Order(M) : MonRWS -> RngIntElt
Order(G: parameters) : GrpFP -> RngIntElt
Order(g: parameters) : GrpAbGenElt -> RngIntElt
Order(g, l, u, n, m: parameters) : GrpAbGenElt, RngIntElt, RngIntElt ,RngIntElt, RngIntElt -> RngIntElt
Order(g, l, u: parameters) : GrpAbGenElt, RngIntElt, RngIntElt -> RngIntElt
Order(P) : Plane -> RngIntElt
Order(P) : Process(pQuot) -> RngIntElt
Order(P) : PtEll -> RngIntElt
Order(f) : QuadBinElt -> RngIntElt
Order(I) : RngFunOrdIdl -> RngFunOrd
Order(a) : RngIntResElt -> RngIntElt
Order(O, T, d) : RngOrd, AlgMatElt, RngIntElt -> RngOrd
Order(I) : RngOrdFracIdl -> RngOrd
Order(H, r) : SetPtEll, RngIntElt -> RngIntElt
Order(e) : SubGrpLatElt -> RngIntElt
Order( [ e_1, ... e_n ] ): [FldAlgElt] -> RngOrd
OrderAutomorphismGroupAbelianPGroup (A) : SeqEnum -> RngIntElt
OuterOrder(A) : GrpAuto -> RngIntElt
ProjectiveOrder(a) : AlgMatElt -> RngIntElt
ProjectiveOrder(A) : AlgMatElt -> RngIntElt, RngElt
QuadraticOrder(Q) : QuadBin -> RngQuad
QuaternionOrder(A,M) : AlgQuat, RngIntElt -> AlgQuatOrd
QuaternionOrder(R,S) : Rng, [AlgQuatElt] -> AlgQuatOrd
QuaternionOrder(N) : RngIntElt -> AlgQuatOrd
QuaternionOrder(D1, D2, T) : RngIntElt, RngIntElt, RngIntElt -> AlgQuat
QuaternionOrder(S) : [AlgQuatElt] -> AlgQuatOrd
RightOrder(I) : AlgQuatOrd -> AlgQuatOrd
SetOrderMaximal(O, b) : RngOrd, BoolElt ->
SetOrderTorsionUnit(O, e, r) : RngOrd, RngOrdElt, RngIntElt ->
SetOrderUnitsAreFundamental(O) : RngOrd ->
SubOrder(O) : RngOrd -> RngOrd
pMaximalOrder(O, p) : RngOrd, RngIntElt -> RngOrd
CrvEll_Order (Example H85E27)
GB_Order (Example H50E1)
GrpAtc_Order (Example H31E5)
GrpMat_Order (Example H21E5)
GrpMat_Order (Example H21E6)
GrpRWS_Order (Example H30E5)
Grp_Order (Example H19E12)
MonRWS_Order (Example H18E5)
Attributes of Orders and Ideals (QUATERNION ALGEBRAS)
Changing Monomial Order (IDEAL THEORY AND GRÖBNER BASES)
Creation of Orders and Fields from Orders (ORDERS AND ALGEBRAIC FIELDS)
Creation of Quaternion Orders (QUATERNION ALGEBRAS)
Functions Relating to Group Order (ABELIAN GROUPS)
Functions Relating to Group Order (POLYCYCLIC GROUPS)
Group Order (MATRIX GROUPS)
Group Order (PERMUTATION GROUPS)
Log, Order and Roots (FINITE FIELDS)
MODULES OVER ORDERS
Order and Index Functions (GROUPS)
Order Functions (AUTOMATIC GROUPS)
Order Functions (AUTOMORPHISM GROUPS OF GROUPS)
Order Functions (GROUPS DEFINED BY REWRITE SYSTEMS)
Order Functions (MONOIDS GIVEN BY REWRITE SYSTEMS)
Order of an Element (ABELIAN GROUPS)
Orders of Invertible Matrices (MATRICES)
Point Order (ELLIPTIC CURVES)
Representation and Monomial Orders (IDEAL THEORY AND GRÖBNER BASES)
Testing Order Relations (SEQUENCES)
Attributes of Orders and Ideals (QUATERNION ALGEBRAS)
Creation of Quaternion Orders (QUATERNION ALGEBRAS)
FldFunG_order-ideals (Example H57E10)
Order and Index Functions (GROUPS)
Eltseq(a) : ModOrdElt -> SeqEnum
MODULES OVER ORDERS
GrpFP_1_Order11 (Example H22E31)
OrderAutomorphismGroupAbelianPGroup (A) : SeqEnum -> RngIntElt
IsOrdered(R) : Rng -> BoolElt
Ordering(G) : GrpAtc -> String
Ordering(G) : GrpRWS -> String
Ordering(M) : MonRWS -> String
Lat_OrderLattice (Example H66E3)
Order and Discrete Logarithm (GENERIC ABELIAN GROUPS)
ElementToSequence(a) : RngOrdResElt -> []
Elements of Quotients (ORDERS AND ALGEBRAIC FIELDS)
Operations on Quotient Rings (ORDERS AND ALGEBRAIC FIELDS)
ElementToSequence(a) : RngOrdResElt -> []
Elements of Quotients (ORDERS AND ALGEBRAIC FIELDS)
WronskianOrders(D) : DivCrvElt -> SeqEnum
WronskianOrders(F) : FldFunG -> [RngIntElt]
WronskianOrders(D) : DivFunElt -> [RngIntElt]
RngOrd_Orders (Example H53E4)
Functions related to Orders and Integrality (ALGEBRAIC FUNCTION FIELDS)
Orders (ALGEBRAIC FUNCTION FIELDS)
FldFunG_orders (Example H57E9)
Orders and Ideals (ORDERS AND ALGEBRAIC FIELDS)
IsOrdinary(E) : CrvEll -> BoolElt
IsOrdinaryProjective(X) : Sch -> BoolElt
IsOrdinaryProjectiveSpace(X) : Sch -> BoolElt
IsOrdinarySingularity(p) : Sch,Pt -> BoolElt
IsOrdinarySingularity(p) : Sch,Pt -> BoolElt
IsOrdinarySingularity(p) : Sch,Pt -> BoolElt
OrientatedGraph(G) : GrphUnd -> GrphDir
OrientatedGraph(G) : GrphUnd -> GrphDir
Origin(A) : Aff -> Pt
Origin(A) : Aff -> Pt
OriginalRing(Q) : RngMPolRes -> Rng
OriginalRing(Q) : RngMPolRes -> Rng
Orthogonalization (LATTICES)
OrthogonalSum(L, M) : Lat, Lat -> Lat
DirectSum(L, M) : Lat, Lat -> Lat
GeneralOrthogonalGroup(arguments)
GeneralOrthogonalGroupMinus(arguments)
GeneralOrthogonalGroupPlus(arguments)
IsOrthogonalGroup(G) : GrpMat ->BoolElt
IsSelfDual(C) : Code -> BoolElt
IsSelfDual(C) : Code -> BoolElt
IsWeaklySelfDual(C) : Code -> BoolElt
IsWeaklySelfDual(C) : Code -> BoolElt
OrthogonalComplement(M) : ModBrdt -> ModBrdt
OrthogonalComponent(x, p) : AlgChtrElt, [ RngIntElt ] -> AlgChtrElt
OrthogonalComponents(x, n) : AlgChtrElt, RngIntElt -> SetEnum
OrthogonalDecomposition(L) : Lat -> [Lat]
PGO(arguments)
PGOMinus(arguments)
PGOPlus(arguments)
PSO(arguments)
PSOMinus(arguments)
PSOPlus(arguments)
SpecialOrthogonalGroup(arguments)
SpecialOrthogonalGroupMinus(arguments)
SpecialOrthogonalGroupPlus(arguments)
Orthogonal Groups (MATRIX GROUPS)
Orthogonal Polynomials (UNIVARIATE POLYNOMIAL RINGS)
Orthogonal Polynomials (UNIVARIATE POLYNOMIAL RINGS)
OrthogonalComplement(M) : ModBrdt -> ModBrdt
OrthogonalComponent(x, p) : AlgChtrElt, [ RngIntElt ] -> AlgChtrElt
OrthogonalComponents(x, n) : AlgChtrElt, RngIntElt -> SetEnum
OrthogonalDecomposition(L) : Lat -> [Lat]
OrthogonalizeGram(M) : MtrxSpcElt -> MtrxSpcElt, AlgMatElt, RngIntElt
Diagonalization(M) : MtrxSpcElt -> MtrxSpcElt, AlgMatElt, RngIntElt
Orthogonalize(L) : Lat -> Lat, AlgMatElt
Orthogonalize(M) : MtrxSpcElt -> MtrxSpcElt, AlgMatElt, RngIntElt
Lat_Orthogonalize (Example H66E14)
OrthogonalizeGram(M) : MtrxSpcElt -> MtrxSpcElt, AlgMatElt, RngIntElt
Diagonalization(M) : MtrxSpcElt -> MtrxSpcElt, AlgMatElt, RngIntElt
OrthogonalSum(L, M) : Lat, Lat -> Lat
DirectSum(L, M) : Lat, Lat -> Lat
Cholesky(L) : Lat -> AlgMatElt
Orthonormalize(L) : Lat -> AlgMatElt
Orthonormalize(M, K) : MtrxSpcElt, Fld -> AlgMatElt
AlgLie_Other (Example H75E9)
Covering Radius and Diameter (LINEAR CODES OVER FINITE FIELDS)
Creating New Enumerated Sequences from Old Ones (SEQUENCES)
Elementary Functions for Elements (FINITELY PRESENTED ALGEBRAS)
General function fields (ALGEBRAIC FUNCTION FIELDS)
General Structure Invariants (ALGEBRAIC FUNCTION FIELDS)
Global Function Fields (ALGEBRAIC FUNCTION FIELDS)
Global Function Fields (ALGEBRAIC FUNCTION FIELDS)
Operations on Submodules (FREE MODULES)
Other (ALGEBRAIC FUNCTION FIELDS)
Other Bounds (LINEAR CODES OVER FINITE FIELDS)
Other Element Functions (QUADRATIC FIELDS)
Other Element Functions (VALUATION RINGS)
Other Element Operations (ALGEBRAIC FUNCTION FIELDS)
Other Element Operations (ALGEBRAIC FUNCTION FIELDS)
Other Functions (ORDERS AND ALGEBRAIC FIELDS)
Other Functions on Elements (MODULES OVER ORDERS)
Other Functions on Ideals (UNIVARIATE POLYNOMIAL RINGS)
Other Functions on Modules (MODULES OVER ORDERS)
Other Functions on Quotients (UNIVARIATE POLYNOMIAL RINGS)
Other Ideal Operations (ORDERS AND ALGEBRAIC FIELDS)
Other Operations (MODULES OVER AFFINE ALGEBRAS)
Other Operations on Elements (ALGEBRAIC FUNCTION FIELDS)
Other Operations on Elements (ALGEBRAIC FUNCTION FIELDS)
Other Point and Line Functions (FINITE PLANES)
Other Predicates (REAL AND COMPLEX FIELDS)
Other properties of Lie Algebras (LIE ALGEBRAS)
Other Ring Constructions (INTRODUCTION [BASIC RINGS])
Other Set Operations (SETS)
Other Structure Functions (REAL AND COMPLEX FIELDS)
Properties of Elements (MATRIX ALGEBRAS)
Structure Invariants (ALGEBRAIC FUNCTION FIELDS)
Structure Invariants (ALGEBRAIC FUNCTION FIELDS)
Eltseq(a) : ModOrdElt -> SeqEnum
Other Functions on Elements (MODULES OVER ORDERS)
General function fields (ALGEBRAIC FUNCTION FIELDS)
Global Function Fields (ALGEBRAIC FUNCTION FIELDS)
Global Function Fields (ALGEBRAIC FUNCTION FIELDS)
Other Functions on Ideals (UNIVARIATE POLYNOMIAL RINGS)
Other Functions on Quotients (UNIVARIATE POLYNOMIAL RINGS)
General Structure Invariants (ALGEBRAIC FUNCTION FIELDS)
Function Fields over the Rationals (ALGEBRAIC FUNCTION FIELDS)
Global Function Fields (ALGEBRAIC FUNCTION FIELDS)
Maxoutdeg(G) : GrphDir -> RngIntElt, GrphVert
MaximumOutDegree(G) : GrphDir -> RngIntElt, GrphVert
MinimumOutDegree(G) : GrphDir -> RngIntElt, GrphVert
OutDegree(u) : GrphVert -> RngIntElt
OutNeighbours(u) : GrphVert -> { GrphVert }
OutDegree(u) : GrphVert -> RngIntElt
OuterFPGroup(A) : GrpAuto -> GrpFP, Map
OuterFaces(N) : NwtnPgon -> SeqEnum
OuterOrder(A) : GrpAuto -> RngIntElt
OuterVertices(N) : NwtnPgon -> SeqEnum
Shape(t) : Tableau -> SeqEnum
OuterFaces(N) : NwtnPgon -> SeqEnum
OuterFPGroup(A) : GrpAuto -> GrpFP, Map
OuterOrder(A) : GrpAuto -> RngIntElt
OuterShape(t) : Tableau -> SeqEnum
Shape(t) : Tableau -> SeqEnum
OuterVertices(N) : NwtnPgon -> SeqEnum
OutNeighbors(u) : GrphVert -> { GrphVert }
OutNeighbours(u) : GrphVert -> { GrphVert }
OutNeighbors(u) : GrphVert -> { GrphVert }
OutNeighbours(u) : GrphVert -> { GrphVert }
Verbose Output (BRANDT MODULES)
HasOutputFile() : -> BoolElt
SetOutputFile(F) : MonStgElt ->
SetOutputFile(F) : MonStgElt ->
UnsetOutputFile() : ->
Redirecting Output (INPUT AND OUTPUT)
The print statement (OVERVIEW)
OvalDerivation(q: parameters) : RngIntElt -> PlaneAff, PlanePtSet, PlaneLnSet
OvalDerivation(q: parameters) : RngIntElt -> PlaneAff, PlanePtSet, PlaneLnSet
FactorisationOverSplittingField(f) : RngPolElt(FldFin) -> [<RngPolElt, RngIntElt>], FldFin
FactorizationOverSplittingField(f) : RngPolElt(FldFin) -> [<RngPolElt, RngIntElt>], FldFin
GHomOverCentralizingField(M, N) : ModGrp, ModGrp -> ModMatGrp
HasPointsOverExtension(X) : Sch -> BoolElt
HasSingularPointsOverExtension(C) : Sch -> BoolElt
IsOverSmallerField(G) : GrpMat -> BoolElt, GrpMat
IsOverSmallerField(G, d) : GrpMat, RngIntElt -> BoolElt, GrpMat
OverDimension(V) : ModTupFld -> RngIntElt
OverDimension(u) : ModTupFldElt -> RngIntElt
OverDimension(M) : ModTupRng -> RngIntElt
OverDimension(u) : ModTupRngElt -> RngIntElt
SupportOverSplittingField(Z) : Clstr -> SetEnum
VarietySizeOverAlgebraicClosure(I) : RngMPol -> RngIntElt
WriteOverLargerField(G) : GrpMat -> GrpMat, GrpMat, GrpAb, SeqEnum
WriteOverSmallerField(G, F) : GrpMat, FldFin -> GrpMat, Map
Overdatum( H ) : GrpCox -> GrpCox
OverDimension(V) : ModTupFld -> RngIntElt
OverDimension(u) : ModTupFldElt -> RngIntElt
OverDimension(M) : ModTupRng -> RngIntElt
OverDimension(u) : ModTupRngElt -> RngIntElt
MinimalOverfields(e) : SubFldLatElt -> [ SubFldLatElt ]
MaximalOvergroup(G, H) : GrpFP, GrpFP -> GrpFP
MinimalOvergroup(G, H) : GrpFP, GrpFP -> GrpFP
Overgroup( H ) : GrpCox -> GrpCox
MinimalOvergroups(e) : SubGrpLatElt -> { SubGrpLatElt }
ModForm_Overview (Example H90E2)
AUTOMORPHISM GROUPS OF GROUPS
DATABASES OF GROUPS
GROUPS
Overview (INTRODUCTION [BASIC RINGS])
Overview (INTRODUCTION [LINEAR ALGEBRA AND MODULE THEORY])
[____] [____] [_____] [____] [__] [Index] [Root]