Index O

O

BigO(x^n) : RngSerElt -> RngIntElt

Omega

Omega(G, i) : GrpPC, RngIntElt -> GrpPC

One

One(B) : MagForm -> MagFormElt

One(R) : Rng -> RngElt

online

operation

Arithmetic with Elements (ABELIAN GROUPS)

Basic Operations (FINITELY PRESENTED GROUPS)

Basic Operations (GROUPS)

Basic Operations (MATRIX GROUPS)

Basic Operations (PERMUTATION GROUPS)

Basic Operations (VECTOR SPACES)

Basic Operations on Ideals (MULTIVARIATE POLYNOMIAL RINGS)

Boolean Operators (MAGMA LANGUAGE)

Constructing New Codes from Old (ERROR-CORRECTING CODES)

Coset Spaces: Elementary Operations (FINITELY PRESENTED GROUPS)

Element Operations (FINITE FIELDS)

Element Operations (MULTIVARIATE POLYNOMIAL RINGS)

Element Operations (NUMBER FIELDS AND THEIR ORDERS)

Element Operations (POWER SERIES AND LAURENT SERIES)

Element Operations (REAL AND COMPLEX FIELDS)

Element Operations (RING OF INTEGERS)

Element Operations (SOLUBLE GROUPS)

Element Operations (THE MODULES Hom_(R)(M, N) AND End(M))

Element Operations (UNIVARIATE POLYNOMIAL RINGS)

Elementary Functions for Words (FINITELY PRESENTED GROUPS)

Elementary Operations on Codewords and Vectors (ERROR-CORRECTING CODES)

Elementary Operators for Words (FINITELY PRESENTED SEMIGROUPS)

Elements Operations (RESIDUE CLASS RINGS)

Functions for Working with a Base and Strong Generating Set (PERMUTATION GROUPS)

Functions on Booleans (MAGMA LANGUAGE)

Functions on p-Adic Structures (LOCAL FIELDS)

General Graph Theoretic Constructions (GRAPHS)

General Subgroup Constructions (SOLUBLE GROUPS)

Matrix Operations (MATRIX GROUPS)

Operation on Points (ELLIPTIC CURVES)

Operations on Edges and Vertices (GRAPHS)

Operations on Elements (ABELIAN GROUPS)

Operations on Elements of Ideals (MULTIVARIATE POLYNOMIAL RINGS)

Operations on Mappings (MAPPINGS)

Operations on p-adic Elements (LOCAL FIELDS)

Operations on Sets (SETS)

Operations on Subgroup Class Posets (GROUPS)

Operations on Submodules (GENERAL MODULES)

Operations on Subspaces (VECTOR SPACES)

Operations on the Elements of a Module (GENERAL MODULES)

Operators for Elements (SOLUBLE GROUPS)

Operators on Sequences (SEQUENCES)

Properties of the Form (VECTOR SPACES)

Set Operations (ABELIAN GROUPS)

Set Operations (SOLUBLE GROUPS)

Soluble Group Functions (MATRIX GROUPS)

Standard Constructions for Modules (GENERAL MODULES)

Standard Subgroup Constructions (GROUPS)

Standard Subgroup Constructions (MATRIX GROUPS)

Standard Subgroup Constructions (PERMUTATION GROUPS)

String Operations on Words (FINITELY PRESENTED SEMIGROUPS)

Structure Operations (FINITE FIELDS)

Structure Operations (MULTIVARIATE POLYNOMIAL RINGS)

Structure Operations (NUMBER FIELDS AND THEIR ORDERS)

Structure Operations (POWER SERIES AND LAURENT SERIES)

Structure Operations (QUADRATIC FIELDS)

Structure Operations (RATIONAL FIELD)

Structure Operations (RATIONAL FUNCTION FIELDS)

Structure Operations (REAL AND COMPLEX FIELDS)

Structure Operations (RESIDUE CLASS RINGS)

Structure Operations (RING OF INTEGERS)

Structure Operations (SOLUBLE GROUPS)

Structure Operations (UNIVARIATE POLYNOMIAL RINGS)

Subgroup Constructions (FINITELY PRESENTED GROUPS)

operation-Boolean

operation-element

Boolean Operators (MAGMA LANGUAGE)

Element Operations (FINITE FIELDS)

Element Operations (MULTIVARIATE POLYNOMIAL RINGS)

Element Operations (NUMBER FIELDS AND THEIR ORDERS)

Element Operations (POWER SERIES AND LAURENT SERIES)

Element Operations (REAL AND COMPLEX FIELDS)

Element Operations (RING OF INTEGERS)

Element Operations (SOLUBLE GROUPS)

Element Operations (THE MODULES Hom_(R)(M, N) AND End(M))

Element Operations (UNIVARIATE POLYNOMIAL RINGS)

Elementary Functions for Words (FINITELY PRESENTED GROUPS)

Elements Operations (RESIDUE CLASS RINGS)

Matrix Operations (MATRIX GROUPS)

Operations on Elements (ABELIAN GROUPS)

Operations on Elements of Ideals (MULTIVARIATE POLYNOMIAL RINGS)

Operations on p-adic Elements (LOCAL FIELDS)

String Operations on Words (FINITELY PRESENTED SEMIGROUPS)

Structure Operations (POWER SERIES AND LAURENT SERIES)

operation-group

operation-point

operation-quadratic-form

operation-structure

operation-subgroup

Standard Subgroup Constructions (GROUPS)

Standard Subgroup Constructions (MATRIX GROUPS)

Standard Subgroup Constructions (PERMUTATION GROUPS)

Subgroup Constructions (FINITELY PRESENTED GROUPS)

operation-submodule

operation-subspace

operation_R[G]

operation_R[G]-module

Operations

RMod_Operations (Example H34E14)

operations

operator

operator:=

optimization

option

Print Options (MULTIVARIATE POLYNOMIAL RINGS)

Print Options (UNIVARIATE POLYNOMIAL RINGS)

Special Options (FINITE FIELDS)

Special Options (NUMBER FIELDS AND THEIR ORDERS)

options

Special Options (QUADRATIC FIELDS)

or

x or y: BoolElt, BoolElt -> BoolElt

Orbit

y ^ g : Elt, GrpMatElt -> Elt

orbit

Images, Orbits and Stabilizers (MATRIX GROUPS)

Images, Orbits and Stabilizers (PERMUTATION GROUPS)

The Homomorphism Induced by G-action on Orbits (MATRIX GROUPS)

orbit-action

The Homomorphism Induced by G-action on Orbits (MATRIX GROUPS)

OrbitAction

OrbitAction(G, T) : GrpPerm, GSet -> Hom(Grp), GrpPerm, GrpPerm

OrbitActionBounded

OrbitActions

OrbitalDigraph

OrbitalGraph

OrbitBounded

OrbitClosure

OrbitClosure(G, Y, S) : GrpPerm, GSet, { Elt } -> GSet

OrbitImage

OrbitImage(G, T) : GrpPerm, GSet -> GrpPerm

OrbitImageBounded

OrbitKernel

OrbitKernel(G, T) : GrpPerm, GSet -> GrpPerm

OrbitKernelBounded

Orbits

Orbits(G, Y) : GrpPerm, GSet -> [ GSet ]

GrpMat_Orbits (Example H15E14)

OrbitsPartition

Order

Order(a) : AlgMatElt -> RngIntElt

Order(a) : FldFinElt -> RngIntElt

Order(G) : GrpAb -> RngIntElt

Order(x) : GrpAbElt -> RngIntElt

Order(g) : GrpElt -> RngIntElt

Order(G) : GrpFin -> RngIntElt

Order(G) : GrpFPElt -> 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: parameters) : GrpFP -> RngIntElt

Order(P) : Process(pQuot) -> RngIntElt

Order(n, m) : RngIntElt, RngIntElt -> RngIntElt

Order(a) : RngIntResElt -> RngIntElt

Order(e) : SubGrpLatElt -> RngIntElt

GrpMat_Order (Example H15E12)

GrpPerm_Order (Example H14E10)

Grp_Order (Example H9E11)

order

Determinant, Trace, Transpose and Order (MATRIX ALGEBRAS)

Functions Relating to Group Order (ABELIAN GROUPS)

Functions Relating to Group Order (SOLUBLE GROUPS)

Log, Order and Roots (FINITE FIELDS)

Order and Index Functions (GROUPS)

Order and Index Functions (MATRIX GROUPS)

Order and Index Functions (PERMUTATION GROUPS)

Order of an Element (ABELIAN GROUPS)

Testing Order Relations (SEQUENCES)

order-index

Order and Index Functions (MATRIX GROUPS)

Order and Index Functions (PERMUTATION GROUPS)

Orders

OrientatedGraph

OrthogonalBasis

OrthogonalComplement

other

Elementary Functions for Elements (FINITELY PRESENTED ALGEBRAS)

Ideal Arithmetic (RESIDUE CLASS RINGS)

Operations on Submodules (GENERAL MODULES)

Other Element Functions (QUADRATIC FIELDS)

Other Element Functions (VALUATION RINGS)

Other Functions (NUMBER FIELDS AND THEIR ORDERS)

Other Functions on Ideals (UNIVARIATE POLYNOMIAL RINGS)

Other Functions on Quotients (UNIVARIATE POLYNOMIAL RINGS)

Other Predicates (REAL AND COMPLEX FIELDS)

Other Structural Properties (ERROR-CORRECTING CODES)

Other Structure Functions (REAL AND COMPLEX FIELDS)

Properties of Elements (MATRIX ALGEBRAS)

other-ideal

other-quotient

OutDegree

OutNeighbors

OutNeighbours

output

The print statement (OVERVIEW)

OverDimension

OverDimension(M) : ModTupRng -> RngIntElt

overview

Overview (INTRODUCTION [MODULES])

Overview (INTRODUCTION [RINGS AND FIELDS])