Index I

[____] [____] [_____] [____] [__] [Index] [Root]

Index I

I-key

I

i-key

i

Id

Id(R) : AlgChtr -> AlgChtrElt

Id(M) : MonFP -> MonFPElt

Identity(E) : GeomEC -> GeomECElt

Identity(G) : Grp -> GrpElt

Identity(G) : Grp -> GrpPermElt

Identity(A) : GrpAb -> GrpAbElt

Identity(G) : GrpBB -> GrpBBElt

Identity(G) : GrpFP -> GrpFPElt

Identity(G) : GrpMat -> GrpMatElt

Identity(G) : GrpPC -> GrpPCElt

One(R) : Rng -> RngElt

Ideal

Ideal(Q) : [ RngMPolElt ] -> RngMPol

ideal

Basic Operations on Ideals (MULTIVARIATE POLYNOMIAL RINGS)

Construction of Elimination Ideals (MULTIVARIATE POLYNOMIAL RINGS)

Construction of New Ideals (MULTIVARIATE POLYNOMIAL RINGS)

Construction of Subalgebras, Ideals and Quotient Rings (MATRIX ALGEBRAS)

Constructor (OVERVIEW)

Creation of Ideals and Computation of Gröbner Bases (MULTIVARIATE POLYNOMIAL RINGS)

Creation of Ideals in Orders (NUMBER FIELDS AND THEIR ORDERS)

Elementary Operations on Subalgebras and Ideals (MATRIX ALGEBRAS)

Ideal Arithmetic (NUMBER FIELDS AND THEIR ORDERS)

Ideal Class Groups (NUMBER FIELDS AND THEIR ORDERS)

Ideal Creation (NUMBER FIELDS AND THEIR ORDERS)

Ideal Operations (RESIDUE CLASS RINGS)

Ideals and Quotient Rings (INTRODUCTION [RINGS AND FIELDS])

Ideals and Quotient Rings (UNIVARIATE POLYNOMIAL RINGS)

Ideals and Quotients (NUMBER FIELDS AND THEIR ORDERS)

Other Functions on Ideals (UNIVARIATE POLYNOMIAL RINGS)

Other Ideal Operations (NUMBER FIELDS AND THEIR ORDERS)

Predicates on Ideals (NUMBER FIELDS AND THEIR ORDERS)

Subsemigroups and Ideals (FINITELY PRESENTED SEMIGROUPS)

Subsemigroups, Ideals and Quotients (FINITELY PRESENTED SEMIGROUPS)

Univariate Elimination Ideal Generators (MULTIVARIATE POLYNOMIAL RINGS)

ideal<A | L_1, ..., L_r> : AlgFP, AlgFPElt, ..., AlgFPElt -> AlgFP

ideal<R | L> : AlgMat, List -> AlgMatIdeal

ideal< R | a_1, ..., a_r > : Rng, RngElt, ..., RngElt -> RngIdl

ideal<P | L> : RngMPol, List -> RngMPol

ideal< O | a_1, a_2, ... , a_m > : RngOrd, FldNumElt, ..., FldNumElt -> RngOrdIdl

ideal< R | a_1, ..., a_r > : RngUPol, RngUPolElt, ..., RngUPolElt -> RngUPol

ideal<S | L_1, ..., L_r> : SgpFP, SgpFPElt, ..., SgpFPElt -> SgpFPIdl

ideal-arithmetic

Ideal Arithmetic (NUMBER FIELDS AND THEIR ORDERS)

ideal-Boolean

Predicates on Ideals (NUMBER FIELDS AND THEIR ORDERS)

ideal-class-group

Ideal Class Groups (NUMBER FIELDS AND THEIR ORDERS)

ideal-creation

Ideal Creation (NUMBER FIELDS AND THEIR ORDERS)

ideal-groebner

Creation of Ideals and Computation of Gröbner Bases (MULTIVARIATE POLYNOMIAL RINGS)

ideal-operation

Basic Operations on Ideals (MULTIVARIATE POLYNOMIAL RINGS)

ideal-other

Other Ideal Operations (NUMBER FIELDS AND THEIR ORDERS)

ideal-quotient

Ideals and Quotient Rings (INTRODUCTION [RINGS AND FIELDS])

Ideals and Quotient Rings (UNIVARIATE POLYNOMIAL RINGS)

IdealArithmetic

RngMPol_IdealArithmetic (Example H29E13)

IdealFactorization

FldNum_IdealFactorization (Example H35E14)

IdealQuotient

ColonIdeal(I, J) : RngMPol, RngMPol -> RngMPol

Ideals

FldNum_Ideals (Example H35E8)

Idempotent

Idempotent(C) : Code -> RngUPolElt

identifier

Identifier Classes (MAGMA SEMANTICS)

Identifier names (OVERVIEW)

Identifiers (STATEMENTS AND EXPRESSIONS)

Identifiers and variables (OVERVIEW)

Uninitialized Identifiers (MAGMA SEMANTICS)

identifier-class

Identifier Classes (MAGMA SEMANTICS)

Identifiers

State_Identifiers (Example H1E3)

Identity

Id(R) : AlgChtr -> AlgChtrElt

Identity(E) : GeomEC -> GeomECElt

Identity(G) : Grp -> GrpElt

Identity(G) : Grp -> GrpPermElt

Identity(A) : GrpAb -> GrpAbElt

Identity(G) : GrpBB -> GrpBBElt

Identity(G) : GrpFP -> GrpFPElt

Identity(G) : GrpMat -> GrpMatElt

Identity(G) : GrpPC -> GrpPCElt

identity

Groups (OVERVIEW)

Rings, Fields, and Algebras (OVERVIEW)

IdentityHomomorphism

IdentityHomomorphism(G) : Grp -> Map

if

error statement (OVERVIEW)

The if statement (OVERVIEW)

if boolexpr_1 then statements_1 else statements_2 end if : ->

State_if (Example H1E10)

ignore

Multiple Assignment (OVERVIEW)

Ilog2

Ilog2(n) : RngIntElt -> RngIntElt

Im

Imaginary(c) : FldComElt -> FldReElt

Image

Image(a) : AlgMatElt -> ModTup

Image(a, Y, y) : GrpPermElt, GSet, Elt -> Elt

Image(g, Y, y) : GrpPermElt, GSet, Elt -> Elt

Image(g, Y, y) : GrpPermElt, GSet, Elt -> Elt

Image(g, Y, y) : GrpPermElt, GSet, Elt -> Elt

Image(f) : Map -> Elt

Image(a) : ModMatElt -> ModTupFld

Image(a) : ModMatRngElt -> ModTupRng

image

Images and Preimages (MAPPINGS)

Images, Orbits and Stabilizers (MATRIX GROUPS)

Images, Orbits and Stabilizers (PERMUTATION GROUPS)

image-orbit-stabilizer

Images, Orbits and Stabilizers (MATRIX GROUPS)

Images, Orbits and Stabilizers (PERMUTATION GROUPS)

image-preimage

Images and Preimages (MAPPINGS)

ImageWithBasis

ImageWithBasis(X, M) : ModMatRngElt, ModRng -> ModRng

Imaginary

Imaginary(c) : FldComElt -> FldReElt

import

Importing Constants (FUNCTIONS AND PROCEDURES)

import "filename": ident_list;

Func_import (Example H2E6)

ImprimitiveTup

ImprimitiveTup(MGT) : SetCartElt -> MonStgElt

imprimitivity

Testing for Semilinearity and Imprimitivity (MATRIX GROUPS)

in

Sequences (OVERVIEW)

Sets (OVERVIEW)

The for statement (OVERVIEW)

x in y : AlgChtrElt, AlgChtrElt -> BoolElt

x in R : AlgMatElt, AlgMat -> BoolElt

[Future release] x in I : AlgMatElt, AlgMatIdl -> BoolElt

x in S : Elt, Seq -> BoolElt

x in R : Elt, Set -> BoolElt

g in G : GrpAbElt, GrpAb -> BoolElt

g in G : GrpBBElt, GrpBB -> BoolElt

g in G : GrpFinElt, GrpFin -> BoolElt

u in H : GrpFPElt, GrpFP -> BoolElt

g in C : GrpFPElt, GrpFPCosElt -> BoolElt

u in e : GrphVert, GrphEdge -> BoolElt

u in e : GrphVert, GrphEdge -> BoolElt

[Future release] x in C : GrpMatElt, Elt -> BoolElt

g in G : GrpMatElt, GrpMat -> BoolElt

g in G : GrpPCElt, GrpPC -> BoolElt

x in C : GrpPermElt, Elt -> BoolElt

g in G : GrpPermElt, GrpPerm -> BoolElt

p in B : IncPt, IncBlk -> BoolElt

f in M : ModMPolElt, ModMPol -> BoolElt

u in C : ModTupFldElt, Code -> BoolElt

v in V : ModTupFldElt, ModTupFld -> BoolElt

u in M : ModTupRngElt, ModTupRng -> BoolElt

s in t : MonStgElt, MonStgElt -> BoolElt

p in l : PlanePt, PlaneLn -> BoolElt

a in R : RngElt, Rng -> BoolElt

a in I : RngElt, RngIdl -> BoolElt

f in R : RngMPol, RngInvar -> FldFunUElt, ModMPolElt

f in I : RngMPolElt, RngMPol -> BoolElt

a in I : RngUPolElt, RngUPol -> BoolElt

S in P : SeqEnum, PowSeqEnum -> BoolElt

S in P : SetEnum, PowSetEnum -> BoolElt

Inc

Combinatorial and Geometrical Structures (OVERVIEW)

incidence

Combinatorial and Geometrical Structures (OVERVIEW)

INCIDENCE STRUCTURES AND DESIGNS

incidence-structure-design

INCIDENCE STRUCTURES AND DESIGNS

IncidenceDigraph

IncidenceDigraph(A) : ModHomElt -> GrphDir

IncidenceGraph

IncidenceGraph(D) : Inc -> Grph

IncidenceGraph(D) : Inc -> GrphUnd

IncidenceGraph(A) : ModHomElt -> GrphUnd

IncidenceGraph(P) : Plane -> Grph

IncidenceGraph(P) : Plane -> GrphUnd;

IncidenceMatrix

IncidenceMatrix(G) : Grph -> ModHomElt

IncidenceMatrix(D) : Inc -> ModMatRngElt

IncidenceMatrix(P) : Plane -> AlgMatElt

IncidenceStructure

IncidenceStructure(G) : Grph -> Inc

IncidenceStructure(I) : Inc -> Inc

IncidenceStructure< v | X > : RngIntElt, List -> Inc

IncidentEdges

IncidentEdges(u) : GrphVert -> { GrphEdge }

Include

Include(W, v) : ModTupRng, ModTupRngElt -> ModTupRng, BoolElt

Include(~S, x) : SeqEnum, Elt ->

Include(~S, x) : SetEnum, Elt ->

Set_Include (Example H7E10)

InclusionMap

InclusionMap(G, H) : GrpPC, GrpPC -> Map

InclusionMap(G, H) : GrpPC, GrpPC -> Map

IndecomposableSummands

IndecomposableSummands(M) : ModRng -> [ ModRng ]

InDegree

InDegree(u) : GrphVert -> RngIntElt

IndependenceNumber

IndependenceNumber(G) : GrphUnd -> RngIntElt

independent

Independent Sets, Cliques, Colourings (GRAPHS)

independent-set-clique-colouring

Independent Sets, Cliques, Colourings (GRAPHS)

IndependentSet

IndependentSet(G, n) : GrphUnd, RngIntElt -> { GrphVert }

IndependentUnits

IndependentUnits(O) : RngOrd -> GrpAb, Map

Index

Sequences (OVERVIEW)

Sets (OVERVIEW)

Index(x) : CopElt -> RngIntElt

Index(G, H) : GrpAb, GrpAb -> RngIntElt

Index(G, H) : GrpFin, GrpFin -> RngIntElt

Index(v) : GrphVert -> RngIntElt

Index(G, H) : GrpMat, GrpMat -> RngIntElt

Index(G, H) : GrpPC, GrpPC -> RngIntElt

Index(G, H) : GrpPerm, GrpPerm -> RngIntElt

Index(s, t) : MonStgElt, MonStgElt -> RngIntElt

Index(G, H: parameters) : GrpFP, GrpFP -> RngIntElt, Map, RngIntElt, RngIntElt

Index(l) : PlaneLn -> RngIntElt

Index(p) : PlanePt -> RngIntElt

Index(O, E) : RngOrd, RngOrd -> RngIntElt

Index(O, I) : RngOrdIdl -> RngIntElt

Index(S, x) : SeqEnum, Elt -> RngIntElt

Index(S, x) : SetIndx, Elt -> RngIntElt

index

Index of a Subgroup: The Todd-Coxeter Algorithm (FINITELY PRESENTED GROUPS)

Indexing (MATRIX ALGEBRAS)

Indexing (THE MODULES Hom_(R)(M, N) AND End(M))

Indexing Vectors and Matrices (VECTOR SPACES)

Integer-Valued Functions (INPUT AND OUTPUT)

Low Index Subgroups (FINITELY PRESENTED GROUPS)

Order and Index Functions (GROUPS)

Order and Index Functions (MATRIX GROUPS)

Order and Index Functions (PERMUTATION GROUPS)

index-Todd-Coxeter

Index of a Subgroup: The Todd-Coxeter Algorithm (FINITELY PRESENTED GROUPS)

indexed

Indexed Assignment (STATEMENTS AND EXPRESSIONS)

Indexed Sets (SETS)

Multisets (SETS)

Sets (OVERVIEW)

The Indexed Set Constructor (SETS)

indexed-assignment

Indexed Assignment (STATEMENTS AND EXPRESSIONS)

IndexedCoset

IndexedCoset(V, w) : GrpFPCos, GrpFPElt -> GrpFPCosElt

IndexedSetToSequence

IndexedSetToSequence(S) : SetIndx -> SeqEnum

IndexedSetToSet

IndexedSetToSet(S) : SetIndx -> SetEnum

Indexing

HMod_Indexing (Example H42E8)

KMod_Indexing (Example H40E6)

State_Indexing (Example H1E5)

indexing

Multi-indexing (INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS])

induced

Coset Spaces: Induced Homomorphism (FINITELY PRESENTED GROUPS)

The Homomorphism Induced by a G-Set Action (PERMUTATION GROUPS)

induced-homomorphism

Coset Spaces: Induced Homomorphism (FINITELY PRESENTED GROUPS)

The Homomorphism Induced by a G-Set Action (PERMUTATION GROUPS)

Induction

Induction(x, G) : AlgChtrElt, Grp -> AlgChtrElt

Induction(M, G) : ModGrp, Grp -> ModGrp

induction

Induction, Restriction, Extension (CHARACTERS OF FINITE GROUPS)

induction-restriction-extension

Induction, Restriction, Extension (CHARACTERS OF FINITE GROUPS)

inequality

Comparison (OVERVIEW)

infinite

Summation of Infinite Series (REAL AND COMPLEX FIELDS)

infinite-summation

Summation of Infinite Series (REAL AND COMPLEX FIELDS)

InfiniteSum

InfiniteSum(m, i) : Map, RngIntElt -> FldPrElt

infix

Operators (OVERVIEW)

info

Other Information Procedures (ENVIRONMENT AND OPTIONS)

information

Class Information from a Conjugacy Class Poset (GROUPS)

Upper Asymptotic Bounds on the Information Rate (ERROR-CORRECTING CODES)

InformationSet

InformationSet(C) : Code -> [ RngIntElt ]

InformationSpace

InformationSpace(C) : Code -> ModTupFld

initial

The Initial Context (MAGMA SEMANTICS)

initial-context

The Initial Context (MAGMA SEMANTICS)

Injections

Injections(C) : Cop -> [ Map ]

InLineConditional

State_InLineConditional (Example H1E11)

InNeighbors

InNeighbours(u) : GrphVert -> { GrphVert }

InNeighbours

InNeighbours(u) : GrphVert -> { GrphVert }

inner

Quadratic Forms and Inner Products (VECTOR SPACES)

Structure of Inner Product Spaces (VECTOR SPACES)

inner-product-space

Structure of Inner Product Spaces (VECTOR SPACES)

InnerProduct

InnerProduct(x, y) : AlgChtrElt, AlgChtrElt -> FldCycElt

InnerProduct(u, v) : ModTupFldElt, ModTupFldElt -> FldElt

InnerProduct(u, v) : ModTupFldElt, ModTupFldElt : -> RngElt

input

Interactive Input (INPUT AND OUTPUT)

Loading files (OVERVIEW)

Insert

Insert(~S, i, x) : SeqEnum, RngIntElt, Elt ->

InsertBlock

InsertBlock(~a, b, i, j) : AlgMatElt, AlgMatElt, RngIntElt, RngIntElt -> AlgMatElt

InsertBlock(~a, b, i, j) : ModMatRngElt, AlgMatElt, RngIntElt, RngIntElt -> ModMatRngElt

InsertVertex

InsertVertex(e) : GrphEdge -> Grph

integer

Polynomials over the Integers (MULTIVARIATE POLYNOMIAL RINGS)

Polynomials over the Integers (UNIVARIATE POLYNOMIAL RINGS)

RING OF INTEGERS

Rings, Fields, and Algebras (OVERVIEW)

IntegerRing

IntegerRing(F) : FldFun -> RngPol

IntegerRing(Q) : FldRat -> RngInt

IntegerRing() : Null -> RngInt

MaximalOrder(K) : FldNum -> RngOrd

MaximalOrder(F) : FldQuad -> RngQuad

ResidueClassRing(m) : RngIntElt -> RngIntRes

pAdicRing(p) : RngIntElt -> RngAdic

Integers

IntegerRing(Q) : FldRat -> RngInt

IntegerRing() : Null -> RngInt

MaximalOrder(K) : FldNum -> RngOrd

ResidueClassRing(m) : RngIntElt -> RngIntRes

RngInt_Integers (Example H24E2)

IntegerToSequence

IntegerToSequence(n, b) : RngIntElt, RngIntElt -> [RngIntElt]

IntegerToString

IntegerToString(n) : RngIntElt -> ModStgElt

IntegerToString(n) : RngIntElt -> MonStgElt

Integral

Integral(m, a, b) : Map, FldPrElt, FldPRElt -> FldPrElt

Integral(f, i) : RngMPolElt, RngIntElt -> RngMPolElt

Integral(f) : RngSerElt -> RngSerElt

Integral(p) : RngUPolElt -> RngUPolElt

FldRe_Integral (Example H36E7)

integral

Derivative, Integral (MULTIVARIATE POLYNOMIAL RINGS)

Derivative, Integral (UNIVARIATE POLYNOMIAL RINGS)

IntegralBasis

IntegralBasis(K) : FldCyc -> [ FldCycElt ]

IntegralBasis(K) : FldNum -> [ FldNumElt ]

IntegralBasis(K) : FldQuad -> [ FldQuadElt ]

IntegralBasis(Q) : FldRat -> [ FldRatElt ]

IntegralModel

IntegralModel(E) : GeomEC -> GeomEC, Map

integration

Integration (REAL AND COMPLEX FIELDS)

Interactive

GrpPC_Interactive (Example H19E7)

interactive

Interactive Input (INPUT AND OUTPUT)

Using p-Quotient Interactively (FINITELY PRESENTED GROUPS)

interactive-input

Interactive Input (INPUT AND OUTPUT)

Interior

Interior(C) : { PlanePt } -> { PlanePt }

Interpolate

RngMPol_Interpolate (Example H29E5)

Interpolation

Interpolation(I, V) : [ RngElt ], [ RngElt ] -> RngUPolElt

Interpolation(I, V, i) : [ RngElt ], [ RngMPolElt ], RngIntElt -> RngMPolElt

interpolation

Evaluation, Interpolation (MULTIVARIATE POLYNOMIAL RINGS)

Evaluation, Interpolation (UNIVARIATE POLYNOMIAL RINGS)

interpolation-evaluation

Evaluation, Interpolation (UNIVARIATE POLYNOMIAL RINGS)

interrupt

Control-C key (OVERVIEW)

Starting, Interrupting and Terminating (STATEMENTS AND EXPRESSIONS)

intersection

Groups (OVERVIEW)

Intersection of Subalgebras (MATRIX ALGEBRAS)

Sets (OVERVIEW)

Sum, Intersection and Dual (ERROR-CORRECTING CODES)

IntersectionArray

IntersectionArray(G) : GrphUnd -> [RngIntElt]

IntersectionMatrix

IntersectionMatrix(G, P) : GrphUnd, { { GrphVert } } -> AlgMatElt

IntersectionNumber

IntersectionNumber(D, i, j) : Dsgn, RngIntElt, RngIntElt -> RngIntElt

intrinsic

Intrinsics (FUNCTIONS AND PROCEDURES)

Intrinsics (OVERVIEW)

Func_intrinsic (Example H2E5)

intro

Introduction (INPUT AND OUTPUT)

introduction

Introduction (ABELIAN GROUPS)

Introduction (BLACKBOX GROUPS)

Introduction (COPRODUCTS)

Introduction (CYCLOTOMIC FIELDS)

Introduction (ELLIPTIC CURVES)

Introduction (ENUMERATIVE COMBINATORICS)

Introduction (ERROR-CORRECTING CODES)

Introduction (FINITE FIELDS)

Introduction (FINITE PLANES)

Introduction (FINITELY PRESENTED ALGEBRAS)

Introduction (FINITELY PRESENTED GROUPS)

Introduction (FINITELY PRESENTED GROUPS)

Introduction (FINITELY PRESENTED SEMIGROUPS)

Introduction (FUNCTIONS AND PROCEDURES)

Introduction (FUNCTIONS AND PROCEDURES)

Introduction (GENERAL MODULES)

Introduction (GRAPHS)

Introduction (GROUPS)

Introduction (INCIDENCE STRUCTURES AND DESIGNS)

Introduction (INVARIANT RINGS OF FINITE GROUPS)

Introduction (LISTS)

Introduction (LOCAL FIELDS)

Introduction (MAGMA SEMANTICS)

Introduction (MAPPINGS)

Introduction (MATRIX ALGEBRAS)

Introduction (MATRIX GROUPS)

Introduction (MATRIX GROUPS)

Introduction (MATRIX GROUPS)

Introduction (MODULES OVER K[x_1, ..., x_n])

Introduction (MULTIVARIATE POLYNOMIAL RINGS)

Introduction (NUMBER FIELDS AND THEIR ORDERS)

Introduction (PERMUTATION GROUPS)

Introduction (PERMUTATION GROUPS)

Introduction (POWER SERIES AND LAURENT SERIES)

Introduction (QUADRATIC FIELDS)

Introduction (RATIONAL FIELD)

Introduction (RATIONAL FUNCTION FIELDS)

Introduction (REAL AND COMPLEX FIELDS)

Introduction (RECORDS)

Introduction (RESIDUE CLASS RINGS)

Introduction (RING OF INTEGERS)

Introduction (SEQUENCES)

Introduction (SETS)

Introduction (STATEMENTS AND EXPRESSIONS)

Introduction (THE MODULES Hom_(R)(M, N) AND End(M))

Introduction (TUPLES AND CARTESIAN PRODUCTS)

Introduction (UNIVARIATE POLYNOMIAL RINGS)

Introduction (VALUATION RINGS)

Introduction (VECTOR SPACES)

Overview (OVERVIEW)

Power-conjugate Presentations (SOLUBLE GROUPS)

Intseq

IntegerToSequence(n, b) : RngIntElt, RngIntElt -> [RngIntElt]

invariant

Creation of Invariant Rings (INVARIANT RINGS OF FINITE GROUPS)

Elementary Invariants of a Design (INCIDENCE STRUCTURES AND DESIGNS)

Elementary Invariants of a Graph (GRAPHS)

Elementary Invariants of an Incidence Structure (INCIDENCE STRUCTURES AND DESIGNS)

INVARIANT RINGS OF FINITE GROUPS

Invariants (CYCLOTOMIC FIELDS)

Invariants (ELLIPTIC CURVES)

Invariants (NUMBER FIELDS AND THEIR ORDERS)

Invariants (NUMBER FIELDS AND THEIR ORDERS)

Invariants (POWER SERIES AND LAURENT SERIES)

Invariants (RATIONAL FUNCTION FIELDS)

Invariants of an Abelian Group (ABELIAN GROUPS)

Matrix Invariants (MATRIX GROUPS)

Numerical Invariants (CHARACTERS OF FINITE GROUPS)

Numerical Invariants (FINITE FIELDS)

Numerical Invariants (INTRODUCTION [RINGS AND FIELDS])

Numerical Invariants (MULTIVARIATE POLYNOMIAL RINGS)

Numerical Invariants (QUADRATIC FIELDS)

Numerical Invariants (QUADRATIC FIELDS)

Numerical Invariants (RATIONAL FIELD)

Numerical Invariants (REAL AND COMPLEX FIELDS)

Numerical Invariants (RESIDUE CLASS RINGS)

Numerical Invariants (RING OF INTEGERS)

Numerical Invariants (UNIVARIATE POLYNOMIAL RINGS)

Numerical Invariants (VALUATION RINGS)

Numerical Invariants of a Plane (FINITE PLANES)

Rings, Fields, and Algebras (OVERVIEW)

The Invariants of a Matrix Algebra (MATRIX ALGEBRAS)

invariant-ring

Creation of Invariant Rings (INVARIANT RINGS OF FINITE GROUPS)

INVARIANT RINGS OF FINITE GROUPS

InvariantFactors

InvariantFactors(a) : AlgMatElt -> [ AlgPolElt ]

InvariantFactors(g) : GrpMatElt -> [ RngUPolElt ]

InvariantRing

InvariantRing(G) : GrpMat -> RngInvar

Invariants

AbelianInvariants(G) : GrpFin -> [ RngIntElt ]

AbelianInvariants(G) : GrpMat -> [ RngIntElt ]

Invariants(A) : GrpAb -> [ RngIntElt ]

AlgMat_Invariants (Example H44E3)

GrpMat_Invariants (Example H21E4)

invariants

Construction of Invariants of Specified Degree (INVARIANT RINGS OF FINITE GROUPS)

InvariantsOfDegree

InvariantsOfDegree(R, d) : RngInvar, RngIntElt -> [ RngMPolElt ]

RngInvar_InvariantsOfDegree (Example H30E3)

invblock

Inverse Block Order (invblock) (MULTIVARIATE POLYNOMIAL RINGS)

inverse

Groups (OVERVIEW)

Inverse Hyperbolic Functions (REAL AND COMPLEX FIELDS)

Inverse Trigonometric Functions (REAL AND COMPLEX FIELDS)

Rings, Fields, and Algebras (OVERVIEW)

inverse-hyperbolic

Inverse Hyperbolic Functions (REAL AND COMPLEX FIELDS)

inverse-trigonometric

Inverse Trigonometric Functions (REAL AND COMPLEX FIELDS)

InverseKrawchouk

InverseKrawchouk(A, K, n) : RngUPolElt, FldFin, RngIntElt -> RngUPolElt

InverseMattsonSolomonTransform

InverseMattsonSolomonTransform(A, n) : RngUPolElt, RngIntElt -> RngUPolElt

InverseMod

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

InverseWordMap

InverseWordMap(G) : GrpMat -> Map

InverseWordMap(G) : GrpPerm -> Map

invocation

Functions (OVERVIEW)

Functions, Procedures, and Mappings (OVERVIEW)

IO

INPUT AND OUTPUT

Iroot

Iroot(a, n) : RngIntElt, RngIntElt -> RngIntElt

irredsol

Database of Irreducible Soluble Subgroups of GL(n,p) for n > 1 and p^n < 256 (OVERVIEW)

irreducibility

Factorization and Irreducibility (MULTIVARIATE POLYNOMIAL RINGS)

Factorization and Irreducibility (UNIVARIATE POLYNOMIAL RINGS)

irreducible

Database of Irreducible Soluble Subgroups of GL(n,p) for n > 1 and p^n < 256 (OVERVIEW)

The Table of Irreducible Characters (CHARACTERS OF FINITE GROUPS)

IrreduciblePolynomial

IrreduciblePolynomial(F, m) : FldFin, RngIntElt -> RngPolElt

irreducibles

Finding Irreducibles (CHARACTERS OF FINITE GROUPS)

is

The where ... is Construction (STATEMENTS AND EXPRESSIONS)

IsAbelian

IsAbelian(G) : GrpAb -> BoolElt

IsAbelian(G) : GrpFin -> BoolElt

IsAbelian(G) : GrpMat -> BoolElt

IsAbelian(G) : GrpPC -> BoolElt

IsAbelian(G) : GrpPerm -> BoolElt

IsAbsolutelyIrreducible

IsAbsolutelyIrreducible(G) : GrpMat -> BoolElt

IsAbsolutelyIrreducible(M) : ModRng -> BoolElt

IsAlternating

IsAlternating(G) : GrpPerm -> BoolElt

IsAltsym

IsAltsym(G) : GrpPerm -> BoolElt

IsArc

IsArc(C) : { PlanePt } -> BoolElt

IsArcTransitive

[Future release] IsArcTransitive(G, t) : GrphUnd, RngIntElt -> BoolElt

IsBalanced

IsBalanced(D, t: parameters) : Inc, RngIntElt -> BoolElt, RngIntElt

IsBijective

IsBijective(a) : ModMatRngElt -> BoolElt

IsBipartite

IsBipartite(G) : GrphUnd -> BoolElt

IsBlock

IsBlock(G, S) : GrpPerm, { Elt } -> BoolElt

IsBlock(S, D) : IncBlk, Inc -> BoolElt, IncBlk

IsBlockTransitive

IsBlockTransitive(D) : Inc -> BoolElt

IsCentral

IsCentral(G, H) : GrpAb, GrpAb -> BoolElt

IsCentral(G, H) : GrpFin -> BoolElt

IsCentral(G, H) : GrpMat -> BoolElt

IsCentral(G, H) : GrpPC, GrpPC -> BoolElt

IsCentral(G, H) : GrpPerm -> BoolElt

IsCentralCollineation

IsCentralCollineation(P, g) : Plane, GrpPermElt -> BoolElt, PlanePt, PlaneLn

IsCharacter

IsCharacter(x) : AlgChtrElt -> BoolElt

IsCohenMacaulay

IsCohenMacaulay(R) : RngInvar -> BoolElt

IsCollinear

IsCollinear(S) : { PlanePt } -> BoolElt, PlaneLn

IsCommutative

IsCommutative(R) : Rng -> BoolElt

IsComplete

IsComplete(V) : GrpFPCos -> BoolElt

IsComplete(G) : Grph -> BoolElt

IsComplete(D) : Inc -> BoolElt

IsComplete(S) : SeqEnum -> BoolElt

IsComplete(C) : { PlanePt } -> BoolElt

IsConcurrent

IsConcurrent(R) : { PlaneLn } -> BoolElt, PlanePt

IsConditioned

IsConditioned(G) : GrpPC -> BoolElt

IsConditioned(G) : GrpPC -> BoolElt

IsConjugate

IsConjugate(G, H, K) : GrpAb, GrpAb, GrpAb -> BoolElt, GrpAbElt

IsConjugate(G, g, h) : GrpAb, GrpAbElt, GrpAbElt -> BoolElt, GrpAbElt

IsConjugate(G, g, h) : GrpFin, GrpFinElt, GrpFinElt -> BoolElt, GrpFinElt

IsConjugate(G, g, h) : GrpFin, GrpFinElt, GrpFinElt -> BoolElt, GrpFinElt

IsConjugate(G, H, K) : GrpFP, GrpFP, GrpFP -> BoolElt, GrpFPElt

IsConjugate(G, g, h) : GrpMat, GrpMatElt, GrpMatElt -> BoolElt, GrpMatElt | Unass

IsConjugate(G, g, h) : GrpMat, GrpMatElt, GrpMatElt -> BoolElt, GrpMatElt | Unass

IsConjugate(G, H, K) : GrpPC, GrpPC, GrpPC -> BoolElt, GrpPCElt

IsConjugate(G, g, h) : GrpPC, GrpPCElt, GrpPCElt -> BoolElt, GrpPCElt

IsConjugate(G, g, h) : GrpPerm, GrpPermElt, GrpPermElt -> BoolElt, GrpPermElt

IsConjugate(G, g, h) : GrpPerm, GrpPermElt, GrpPermElt -> BoolElt, GrpPermElt

IsConjugate(G, Y, y, z) : GrpPerm, GSet, Elt, Elt -> BoolElt, GrpPermElt

IsConnected

IsConnected(G) : GrphUnd -> BoolElt

IsConsistent

IsConsistent(G) : GrpPC -> BoolElt

IsConsistent(a, v) : ModMatFldElt, ModTupFld -> BoolElt, ModTupFldElt, ModTupFld

IsConsistent(A, w) : ModMatRngElt, ModTupRng -> BoolElt, ModTupRngElt, ModTupRng

IsConsistent(A, w) : ModMatRngElt, ModTupRng -> BoolElt, ModTupRngElt, ModTupRng

IsConway

IsConway(F) : FldFin -> BoolElt

IsCyclic

IsCyclic(C) : Code -> BoolElt

IsCyclic(G) : GrpAb -> BoolElt

IsCyclic(G) : GrpFin -> BoolElt

IsCyclic(G) : GrpMat -> BoolElt

IsCyclic(G) : GrpPC -> BoolElt

IsCyclic(G) : GrpPerm -> BoolElt

IsDecomposable

IsDecomposable(M) : ModRng -> BoolElt, ModRng, ModRng

IsDefined

IsDefined(S, i) : SeqEnum, RngIntElt -> BoolElt

IsDesarguesian

IsDesarguesian(P) : Plane -> BoolElt

IsDesign

IsDesign(D, t: parameters) : Inc, RngIntElt -> BoolElt, RngIntElt

IsDiagonal

IsDiagonal(a) : AlgMatElt -> BoolElt

IsDifferenceSet

IsDifferenceSet(B) : SetEnum -> BoolElt, RngIntElt

IsDisjoint

IsDisjoint(R, S) : SetEnum, SetEnum -> BoolElt

IsDistanceRegular

IsDistanceRegular(G) : GrphUnd -> BoolElt

IsDistanceTransitive

IsDistanceTransitive(G) : GrphUnd -> BoolElt

IsDivisible

IsDivisible(a, b) : RngMPolElt, RngMPolElt -> BoolElt, RngMPolElt

IsDivisionRing

IsDivisionRing(R) : Rng -> BoolElt

IsDomain

IsDomain(R) : Rng -> BoolElt

IsEdgeTransitive

IsEdgeTransitive(G) : GrphUnd -> BoolElt

IsElementaryAbelian

IsElementaryAbelian(G) : GrpAb -> BoolElt

IsElementaryAbelian(G) : GrpFin -> BoolElt

IsElementaryAbelian(G) : GrpMat -> BoolElt

IsElementaryAbelian(G) : GrpPC -> BoolElt

IsElementaryAbelian(G) : GrpPerm -> BoolElt

IsEllipticCurve

IsEllipticCurve([a, b]) : [ RngElt ] -> BoolElt, GeomEC

IsEmpty

IsEmpty(G) : Grph -> BoolElt

IsEmpty(S) : List -> BoolElt

IsEmpty(P) : Process(Lix) -> BoolElt

IsEmpty(S) : SeqEnum -> BoolElt

IsEmpty(R) : SetEnum -> BoolElt

IsEof

IsEof(S) : MonStgElt -> BoolElt

IsEquationOrder

IsEquationOrder(O) : RngOrd -> Boolelt

IsEquationOrder(O) : RngQuad -> BoolElt

IsEquidistant

IsEquidistant(C) : Code -> BoolElt

IsEquitable

IsEquitable(G, P) : GrphUnd, { { GrphVert } } -> BoolElt

Isetseq

IndexedSetToSequence(S) : SetIndx -> SeqEnum

Isetset

IndexedSetToSet(S) : SetIndx -> SetEnum

IsEuclideanDomain

IsEuclideanDomain(R) : Rng -> BoolElt

IsEuclideanRing

IsEuclideanRing(R) : Rng -> BoolElt

IsEulerian

IsEulerian(G) : Grph -> BoolElt

IsEven

IsEven(g) : GrpPermElt -> BoolElt

IsEven(n) : RngIntElt -> BoolElt

IsExceptionalUnit

IsExceptionalUnit(u) : RngOrdElt -> Boolelt

IsExtraSpecial

IsExtraSpecial(G) : GrpFin -> BoolElt

IsExtraSpecial(G) : GrpMat -> BoolElt

IsExtraSpecial(G) : GrpPC -> BoolElt

IsExtraSpecial(G) : GrpPerm -> BoolElt

IsFaithful

IsFaithful(G, Y) : : GrpPerm, GSet -> BoolElt

IsFaithful(x) : AlgChtrElt -> BoolElt

IsField

IsField(R) : Rng -> BoolElt

IsFinite

IsFinite(G) : GrpAb -> BoolElt

IsFinite(R) : Rng -> BoolElt

IsForest

IsForest(G) : GrphUnd -> BoolElt

IsFrobenius

IsFrobenius(G) : GrpPerm -> BoolElt

IsGeneralizedCharacter

IsGeneralizedCharacter(x) : AlgChtrElt -> BoolElt

IsGeneralLinear

[Future release] IsGeneralLinear(G) : GrpMat -> BoolElt

IsGHom

IsGHom(X) : ModMatElt -> BoolElt

IsGood

GrpPC_IsGood (Example H19E11)

IsGroebner

IsGroebner(S) : { RngMPolElt } -> BoolElt

IsHadamard

IsHadamard(H) : AlgMatElt -> BoolElt

IsHadamardEquivalent

IsHadamardEquivalent(H, J) : AlgMatElt, AlgMatElt -> BoolElt

IsHomogeneous

IsHomogeneous(M) : ModMPol -> BoolElt

IsHomogeneous(f) : RngMPolElt -> BoolElt

IsId

IsId(P) : GeomECElt -> BoolElt

IsId(g) : GrpElt -> BoolElt

IsId(g) : GrpPermElt -> BoolElt

IsIdentity(u) : GrpAbElt -> BoolElt

IsIdentity(g) : GrpMatElt -> BoolElt

IsIdentity(g) : GrpPCElt -> BoolElt

IsIdempotent

IsIdempotent(x) : RngElt -> BoolElt

IsIdenticalPresentation

IsIdenticalPresentation(G, H) : GrpPC, GrpPC -> BoolElt

IsIdentity

IsId(P) : GeomECElt -> BoolElt

IsId(g) : GrpElt -> BoolElt

IsId(g) : GrpPermElt -> BoolElt

IsIdentity(u) : GrpAbElt -> BoolElt

IsIdentity(g) : GrpMatElt -> BoolElt

IsIdentity(g) : GrpPCElt -> BoolElt

IsIndependent

IsIndependent(S) : { ModTupFldElt } -> BoolElt

IsIndependent(S) : { ModTupRngElt } -> BoolElt

IsInjective

IsInjective(a) : ModMatRngElt -> BoolElt

IsInRadical

IsInRadical(f, I) : RngMPolElt, RngMPol -> BoolElt

IsIntegral

IsIntegral(a) : FldNumElt -> BoolElt

IsIntegral(c) : FldPrElt -> BoolElt

IsIntegral(q) : FldRatElt -> BoolElt

IsIntegral(P) : GeomECElt -> BoolElt

IsIntegral(n) : RngIntElt -> BoolElt

IsIntegral(I) : RngOrdIdl -> BoolElt

IsIntegralDomain

IsDomain(R) : Rng -> BoolElt

IsIrreducible

IsIrreducible(x) : AlgChtrElt -> BoolElt

IsIrreducible(G) : GrpMat -> BoolElt

IsIrreducible(G) : GrpMat -> BoolElt, ModGrp

IsIrreducible(M) : ModRng -> BoolElt, ModRng, ModRng

IsIrreducible(x) : RngElt -> BoolElt

IsIrreducible(f) : RngMPolElt -> BoolElt

IsIrreducible(p) : RngUPolElt -> BoolElt

IsIsomorphic

IsIsomorphic(K, L) : FldNum, FldNum -> BoolElt, Map

IsIsomorphic(E, F) : GeomEC, GeomEC -> BoolElt

IsIsomorphic(G, H) : GrphDir, GrphDir -> BoolElt, Map

IsIsomorphic(G, H) : GrpPC, GrpPC -> BoolElt, Map

IsIsomorphic(M, N) : ModRng, ModRng -> BoolElt, AlgMatElt

IsIsomorphic(C, D: parameters) : Code, Code -> BoolElt, Map

IsIsomorphic(D, E: parameters) : Inc, Inc -> BoolElt, Map

IsIsomorphic(P, Q: parameters) : Plane, Plane -> BoolElt, Map

IsLabelled

IsLabelled(t) : GrphVert -> BoolElt

IsLabelledEdge

IsLabelledEdge(G, i, j) : Grph, RngIntElt, RngIntElt -> BoolElt

IsLabelledVertex

IsLabelledVertex(G, i) : Grph, RngIntElt -> BoolElt

IsLinear

IsLinear(x) : AlgChtrElt -> BoolElt

IsLinearSpace

IsLinearSpace(D) : Inc -> BoolElt

IsLineRegular

IsLineRegular(D) : IncNsp -> BoolElt, RngIntElt

IsLineTransitive

IsLineTransitive(P) : Plane -> BoolElt

IsMaximal

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(I) : RngMPol -> BoolElt

IsMaximal(O) : RngOrd -> BoolElt

IsMaximal(O) : RngQuad -> BoolElt

IsMaximumDistanceSeparable

IsMaximumDistanceSeparable(C) : Code -> BoolElt

IsMDS

IsMaximumDistanceSeparable(C) : Code -> BoolElt

IsMemberBasicOrbit

IsMemberBasicOrbit(G, i, a) : GrpPerm, RngIntElt, Elt -> BoolElt

IsMinusOne

IsMinusOne(a) : AlgMatElt -> BoolElt

IsMinusOne(a) : RngElt -> BoolElt

IsMinusOne(a) : RngOrdResElt -> Boolelt

IsNearLinearSpace

IsNearLinearSpace(D) : Inc -> BoolElt

IsNearlyPerfect

IsNearlyPerfect(C) : Code -> BoolElt

IsNilpotent

IsNilpotent(G) : GrpAb -> BoolElt

IsNilpotent(G) : GrpFin -> BoolElt

IsNilpotent(G) : GrpMat -> BoolElt

IsNilpotent(G) : GrpPC -> BoolElt

IsNilpotent(G) : GrpPerm -> BoolElt

IsNilpotent(x) : RngElt -> BoolElt

IsNilpotent(f) : RngQPolElt -> BoolElt, RngIntElt

IsNormal

IsNormal(a) : FldFinElt -> BoolElt

IsNormal(G, H) : GrpAb, GrpAb -> BoolElt

IsNormal(G, H) : GrpFin, GrpFin -> BoolElt

IsNormal(G, H) : GrpFP, GrpFP -> BoolElt

IsNormal(G, H) : GrpMat, GrpMat -> BoolElt

IsNormal(G, H) : GrpPC, GrpPC -> BoolElt

IsNormal(G, H) : GrpPerm, GrpPerm -> BoolElt

IsNull

IsNull(S) : SeqEnum -> BoolElt

IsNull(R) : SetEnum -> BoolElt

IsOdd

IsOdd(n) : RngIntElt -> BoolElt

isolgps

Database of Irreducible Soluble Subgroups of GL(n,p) for n > 1 and p^n < 256 (OVERVIEW)

isomorphism

Automorphisms and Isomorphisms (SOLUBLE GROUPS)

The Isomorphism (FINITELY PRESENTED ALGEBRAS)

IsOne

IsOne(a) : AlgMatElt -> BoolElt

IsOne(u) : MonFPElt -> BoolElt

IsOne(a) : RngElt -> BoolElt

IsOne(a) : RngOrdResElt -> Boolelt

IsOrbit

IsOrbit(G, S) : GrpPerm, { Elt } -> BoolElt

IsOrdered

IsOrdered(R) : Rng -> BoolElt

IsotropicVector

[Future release] IsotropicVector(V) : ModTupFld -> ModTupFldElt

IsParallel

IsParallel(l, m) : PlaneLn, PlaneLn -> BoolElt

IsParallelClass

IsParallelClass(B, C) : IncBlk, IncBlk -> BoolElt, { IncBlk }

IsPath

IsPath(G) : Grph -> BoolElt

IsPerfect

IsPerfect(C) : Code -> BoolElt

IsPerfect(G) : GrpAb -> BoolElt

IsPerfect(G) : GrpFin -> BoolElt

IsPerfect(G) : GrpMat -> BoolElt

IsPerfect(G) : GrpPC -> BoolElt

IsPerfect(G) : GrpPerm -> BoolElt

IsPID

IsPID(R) : Rng -> BoolElt

IsPlanar

[Future release] IsPlanar(G) : GrphUnd -> BoolElt

IsPoint

IsPoint(S, E) : [RngElt], GeomEC -> BoolElt, GeomECElt

IsPointRegular

IsPointRegular(D) : IncNsp -> BoolElt, RngIntElt

IsPointTransitive

IsPointTransitive(D) : Inc -> BoolElt

IsPointTransitive(P) : Plane -> BoolElt

IsPolygon

IsPolygon(G) : Grph -> BoolElt

IsPower

IsPower(n) : RngIntElt -> BoolElt

IsPrimary

IsPrimary(I) : RngMPol -> BoolElt

IsPrime

IsPrime(x) : RngElt -> BoolElt

IsPrime(n) : RngIntElt -> BoolElt

IsPrime(n) : RngIntElt -> BoolElt

IsPrime(I) : RngMPol -> BoolElt

IsPrime(I) : RngOrdIdl -> BoolElt, RngOrdIdl

RngInt_IsPrime (Example H24E3)

IsPrimitive

IsPrimitive(a) : FldFinElt -> BoolElt

IsPrimitive(a) : FldNumElt -> BoolElt

IsPrimitive(G) : GrphUnd -> BoolElt

IsPrimitive (G) : GrpMat -> Boolean, SetCartElt

IsPrimitive(G) : GrpPerm -> BoolElt

IsPrimitive(G) : GrpPerm -> BoolElt

IsPrimitive(G, Y) : GrpPerm, GSet -> BoolElt

IsPrimitive(n, m) : RngIntElt, RngIntElt -> BoolElt

IsPrimitive(n) : RngIntResElt -> BoolElt

IsPrincipal

IsPrincipal(I) : RngOrdIdl -> BoolElt, FldNumElt

IsPrincipalIdealDomain

IsPID(R) : Rng -> BoolElt

IsPrincipalIdealRing

IsPrincipalIdealRing(R) : Rng -> BoolElt

IsProjective

IsProjective(C) : Code -> BoolElt

IsProper

IsProper(I) : RngMPol -> BoolElt

Isqrt

Isqrt(n) : RngIntElt -> RngIntElt

IsRadical

IsRadical(I) : RngMPol -> BoolElt

IsReal

IsReal(x) : AlgChtrElt -> BoolElt

IsReal(c) : FldComElt -> BoolElt

IsRegular

IsRegular(G) : Grph -> BoolElt

IsRegular(G) : GrpPerm -> BoolElt

IsRegular(G, Y) : GrpPerm, GSet -> BoolElt

IsRelative

IsRelative(O) : RngOrd -> Boolelt

IsResolvable

IsResolvable(D) : Inc -> BoolElt, { SetEnum }

IsSatisfied

IsSatisfied(U, E) : { RelElt }, [ GrpElt ] -> BoolElt

IsScalar

IsScalar(u) : AlgFPElt -> BoolElt

IsScalar(a) : AlgMatElt -> BoolElt

IsScalar(g) : GrpMatElt -> BoolElt

IsSelfDual

IsSelfDual(C) : Code -> BoolElt

IsSelfDual(D) : Inc -> BoolElt

IsSelfDual(P) : ProjPl -> BoolElt

IsSelfNormalising

IsSelfNormalizing(G, H) : GrpFin, GrpFin -> BoolElt

IsSelfNormalizing(G, H) : GrpPerm, GrpPerm -> BoolElt

IsSelfNormalizing

IsSelfNormalizing(G, H) : GrpFin, GrpFin -> BoolElt

IsSelfNormalizing(G, H) : GrpFP, GrpFP -> BoolElt

[Future release] IsSelfNormalizing(G, H) : GrpMat, GrpMat -> BoolElt

IsSelfNormalizing(G, H) : GrpPC, GrpPC -> BoolElt

IsSelfNormalizing(G, H) : GrpPerm, GrpPerm -> BoolElt

IsSelfOrthogonal

IsSelfDual(C) : Code -> BoolElt

IsSemiLinear

IsSemiLinear(G) : GrpMat -> Boolean, SetCartElt

IsSemiregular

IsSemiregular(G, S) : GrpPerm, GSet -> BoolElt

IsSemiregular(G, Y) : GrpPerm, GSet -> BoolElt

IsSeparable

IsSeparable(G) : Grph -> BoolElt

IsSharplyTransitive

IsSharplyTransitive(G, Y, k) : GrpPerm, GSet, RngIntElt -> BoolElt

IsSharplyTransitive(G, k) : GrpPerm, RngIntElt -> BoolElt

IsSimilar

IsSimilar(a, b) : AlgMatElt, AlgMatElt -> BoolElt, AlgMatElt

IsSimple

IsSimple(G) : GrpAb -> BoolElt

IsSimple(G) : GrpFin -> BoolElt

IsSimple(G) : GrpMat -> BoolElt

IsSimple(G) : GrpPC -> BoolElt

IsSimple(G) : GrpPerm -> BoolElt

IsSimple(D) : Inc -> BoolElt

IsSinglePrecision

IsSinglePrecision(n) : RngIntElt -> BoolElt

IsSingular

[Future release] IsSingular(F) : AlgMatElt -> BoolElt

IsSLGL

[Future release] IsSLGL(G) : GrpMat -> BoolElt

IsSoluble

IsSoluble(G) : GrpAb -> BoolElt

IsSoluble(G) : GrpFin -> BoolElt

IsSoluble(G) : GrpMat -> BoolElt

IsSoluble(G) : GrpPC -> BoolElt

IsSoluble(G) : GrpPerm -> BoolElt

IsSolvable

IsSoluble(G) : GrpAb -> BoolElt

IsSoluble(G) : GrpFin -> BoolElt

IsSoluble(G) : GrpMat -> BoolElt

IsSoluble(G) : GrpPC -> BoolElt

IsSoluble(G) : GrpPerm -> BoolElt

IsSpecial

IsSpecial(G) : GrpFin -> BoolElt

IsSpecial(G) : GrpMat -> BoolElt

IsSpecial(G) : GrpPC -> BoolElt

IsSpecial(G) : GrpPerm -> BoolElt

IsSpecialLinear

[Future release] IsSpecialLinear(G) : GrpMat -> BoolElt

IsSquare

IsSquare(a) : FldFinElt -> BoolElt

IsSquare(n) : RngIntElt -> BoolElt, RngIntElt

IsSquare(n) : RngIntResElt -> BoolElt, RngIntResElt

IsSquareFree

IsSquareFree(n) : RngIntElt -> BoolElt

IsSteiner

IsSteiner(D, t) : Dsgn -> BoolElt

IsStronglyConnected

IsStronglyConnected(G) : GrphDir -> BoolElt

IsSubfield

IsSubfield(K, L) : FldNum, FldNum -> BoolElt, Map

IsSubnormal

IsSubnormal(G, H) : GrpAb, GrpAb -> BoolElt

IsSubnormal(G, H) : GrpFin, GrpFin -> BoolElt

IsSubnormal(G, H) : GrpMat, GrpMat -> BoolElt

IsSubnormal(G, H) : GrpPC, GrpPC -> BoolElt

IsSubnormal(G, H) : GrpPerm, GrpPerm -> BoolElt

IsSubsequence

IsSubsequence(S, T) : SeqEnum, SeqEnum -> BoolElt

IsSurjective

IsSurjective(a) : ModMatRngElt -> BoolElt

IsSymmetric

IsSymmetric(a) : AlgMatElt -> BoolElt

IsSymmetric(D) : Dsgn -> BoolElt

IsSymmetric(G) : GrphUnd -> BoolElt

IsSymmetric(G) : GrpPerm -> BoolElt

IsSymmetric(f) : RngMPolElt -> BoolElt, RngMPolElt

RngMPol_IsSymmetric (Example H29E27)

IsTorsionUnit

IsTorsionUnit(w) : RngOrdElt -> BoolElt

IsTransitive

IsPointTransitive(P) : Plane -> BoolElt

IsTransitive(G) : GrphUnd -> BoolElt

IsTransitive(G) : GrpPerm -> BoolElt

IsTransitive(G, Y) : GrpPerm, GSet -> BoolElt

IsTree

IsTree(G) : Grph -> BoolElt

IsTrivial

IsTrivial(G) : Grp -> BoolElt

IsTrivial(D) : Inc -> BoolElt

IsUFD

IsUFD(R) : Rng -> BoolElt

IsUniform

IsUniform(D) : Inc -> BoolElt, RngIntElt

IsUniqueFactorizationDomain

IsUFD(R) : Rng -> BoolElt

IsUnit

IsUnit(a) : AlgMatElt -> BoolElt

IsUnit(a) : RngElt -> BoolElt

IsUnit(f) : RngQPolElt -> BoolElt

IsUnital

IsUnital(U) : { PlanePt } -> BoolElt

IsUnitary

IsUnitary(R) : Rng -> BoolElt

IsUnivariate

IsUnivariate(f) : RngMPolElt -> BoolElt, RngUPolElt, RngIntElt

IsVertexTransitive

IsTransitive(G) : GrphUnd -> BoolElt

IsWeaklyConnected

IsWeaklyConnected(G) : GrphDir -> BoolElt

IsWeaklySelfDual

IsWeaklySelfDual(C) : Code -> BoolElt

IsWeaklySelfOrthogonal

IsWeaklySelfDual(C) : Code -> BoolElt

IsZero

IsZero(u) : AlgFPElt -> BoolElt

IsZero(a) : AlgMatElt -> BoolElt

IsZero(u) : ModElt -> BoolElt

IsZero(M) : ModMPol -> ModMPol

IsZero(f) : ModMPolElt -> BoolElt

IsZero(u) : ModTupElt -> BoolElt

IsZero(u) : ModTupFldElt -> BoolElt

IsZero(a) : RngElt -> BoolElt

IsZero(I) : RngMPol -> BoolElt

IsZero(I) : RngOrdIdl -> BoolElt

IsZero(a) : RngOrdResElt -> Boolelt

IsZeroDimensional

IsZeroDimensional(I) : RngMPol -> BoolElt

IsZeroDivisor

IsZeroDivisor(x) : RngElt -> BoolElt

iteration

Iteration (OVERVIEW)

Iteration (SEQUENCES)

Iteration (STATEMENTS AND EXPRESSIONS)

Iterative Statements (STATEMENTS AND EXPRESSIONS)

Recursion, Reduction, and Iteration (SEQUENCES)

Reduction and Iteration over Sets (SETS)

[____] [____] [_____] [____] [__] [Index] [Root]