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

Index I


I-key

I

i-key

i

Id

Id(J) : JacHyp -> JacHypPt
Identity(J) : JacHyp -> JacHypPt
J ! 0 : JacHyp, RngIntElt -> JacHypPt
Id(R) : AlgChtr -> AlgChtrElt
Id(M) : MonFP -> MonFPElt
Identity(D) : DiffFun -> DiffFunElt
Identity(G) : DivFun -> DivFunElt
Identity(G) : Grp -> GrpElt
Identity(G) : Grp -> GrpPermElt
Identity(A) : GrpAb -> GrpAbElt
Identity(A) : GrpAbGen -> GrpAbGenElt
Identity(G) : GrpAtc -> GrpAtcElt
Identity(A) : GrpAuto -> GrpAutoElt
Identity(G) : GrpFP -> GrpFPElt
Identity(G) : GrpGPC -> GrpGPCElt
Identity( G ) : GrpLie -> GrpLieElt
Identity(G) : GrpMat -> GrpMatElt
Identity(G) : GrpPC -> GrpPCElt
Identity(G) : GrpRWS -> GrpRWSElt
Identity(G) : GrpSLP -> GrpSLPElt
Identity(M) : MonRWS -> MonRWSElt
IsId(w) : GrpAtcElt -> BoolElt
IsId(g) : GrpElt -> BoolElt
IsId(g) : GrpPermElt -> BoolElt
IsId(w) : GrpRWSElt -> BoolElt
IsId(w) : MonRWSElt -> BoolElt
IsId(P) : PtEll -> BoolElt
IsIdentity(u) : GrpAbElt -> BoolElt
IsIdentity(g) : GrpAbGenElt -> BoolElt
IsIdentity(g) : GrpGPCElt -> BoolElt
IsIdentity(g) : GrpMatElt -> BoolElt
IsIdentity(g) : GrpPCElt -> BoolElt
One(R) : Rng -> RngElt

Ideal

AugmentationIdeal(A) : AlgGrp -> AlgGrpSub
ColonIdeal(I, J) : RngMPol, RngMPol -> RngMPol
ColonIdeal(I, f) : RngMPol, RngMPolElt -> RngMPol, RngIntElt
ColonIdeal(I, J) : RngMPolRes, RngMPolRes -> RngMPolRes
ColonIdeal(I, J) : RngOrdIdl, RngOrdIdl -> RngOrdIdl
CommutatorIdeal(A, B) : AlgAss, AlgAss -> AlgAss
CommutatorIdeal(S) : AlgQuatOrd -> AlgQuatOrd
DivisorIdeal(I) : RngMPolRes -> RngMPol
EasyIdeal(I) : RngMPol -> RngMPol
EliminationIdeal(I, k: parameters) : RngMPol, RngIntElt -> RngMPol
EliminationIdeal(I, S) : RngMPol, { RngIntElt } -> RngMPol
Ideal(A) : FldAC -> RngMPol
Ideal(P) : PlcFunElt -> RngFunOrdIdl
Ideal(P) : PlcFunElt -> RngFunOrdIdl
Ideal(f) : QuadBinElt -> RngQuadIdl
Ideal(f) : QuadBinElt -> RngQuadIdl
Ideal(C) : Sch -> RngMPol
Ideal(X) : Sch -> RngMPol
Ideal(Q) : [ RngMPolElt ] -> RngMPol
IsIdeal(S) : AlgGrpSub -> BoolElt
IsLeftIdeal(S) : AlgGrpSub -> BoolElt
IsPID(R) : Rng -> BoolElt
IsPIR(R) : Rng -> BoolElt
IsPrincipalIdealRing(F) : FldAlg -> BoolElt
IsPrincipalIdealRing(O) : RngOrd -> BoolElt
IsRightIdeal(S) : AlgGrpSub -> BoolElt
JacobianIdeal(f) : RngMPolElt -> RngMPol
JacobianIdeal(C) : Sch -> RngMPol
JacobianIdeal(X) : Sch -> RngMPol
LeadingMonomialIdeal(I) : RngMPol -> RngMPol
LeftIdeal(S,X) : AlgQuatOrd, [AlgQuatOrdElt] -> AlgQuatOrd
LeftIdealClasses(S) : AlgQuatOrd -> [AlgQuatOrd]
PreimageIdeal(I) : RngMPolRes -> RngMPol
PrimaryIdeal(R) : RngInvar -> RngMPol
PrimeIdeal(S,p) : AlgQuatOrd, RngIntElt -> AlgQuatOrd
PrincipalIdealMap(O) : RngFunOrd -> Map
RelationIdeal(R) : RngInvar -> RngMPol
RelationIdeal(Q) : [ RngMPol ] -> RngMPol
RightIdeal(S,X) : AlgQuatOrd, [AlgQuatOrdElt] -> AlgQuatOrd
RightIdealClasses(S) : AlgQuatOrd -> [AlgQuatOrd]
TwoSidedIdealClasses(S) : AlgQuatOrd -> [AlgQuatOrd]
UnivariateEliminationIdealGenerator(I, i) : RngMPol, RngIntElt -> RngMPolElt
UnivariateEliminationIdealGenerators(I) : RngMPol -> [ RngMPolElt ]

ideal

Basic Operations on Ideals (IDEAL THEORY AND GRÖBNER BASES)
Construction of Elimination Ideals (IDEAL THEORY AND GRÖBNER BASES)
Construction of New Ideals (IDEAL THEORY AND GRÖBNER BASES)
Construction of Subalgebras, Ideals and Quotient Algebras (GROUP ALGEBRAS)
Construction of Subalgebras, Ideals and Quotient Rings (MATRIX ALGEBRAS)
Constructor (OVERVIEW)
Creation of Ideals (ALGEBRAIC FUNCTION FIELDS)
Creation of Ideals in Orders (ORDERS AND ALGEBRAIC FIELDS)
Elementary Operations on Subalgebras and Ideals (MATRIX ALGEBRAS)
Further Ideal Operations (ALGEBRAIC FUNCTION FIELDS)
Ideal Arithmetic (ORDERS AND ALGEBRAIC FIELDS)
Ideal Class Groups (ORDERS AND ALGEBRAIC FIELDS)
Ideal Operations (ALGEBRAIC FUNCTION FIELDS)
Ideal Operations (RING OF INTEGERS)
IDEAL THEORY AND GRÖBNER BASES
Ideal Theory of Orders (QUATERNION ALGEBRAS)
Ideals and Quotient Rings (INTRODUCTION [BASIC RINGS])
Ideals and Quotient Rings (UNIVARIATE POLYNOMIAL RINGS)
Ideals and Quotients (ORDERS AND ALGEBRAIC FIELDS)
Other Functions on Ideals (UNIVARIATE POLYNOMIAL RINGS)
Other Ideal Operations (ORDERS AND ALGEBRAIC FIELDS)
Predicates on Ideals (ORDERS AND ALGEBRAIC FIELDS)
Subsemigroups and Ideals (FINITELY PRESENTED SEMIGROUPS)
Subsemigroups, Ideals and Quotients (FINITELY PRESENTED SEMIGROUPS)
Univariate Elimination Ideal Generators (IDEAL THEORY AND GRÖBNER BASES)
ideal< cat : A | L> : Cat, AlgGrp, List -> AlgGrp, Map
ideal<A | L_1, ..., L_r> : AlgFP, AlgFPElt, ..., AlgFPElt -> AlgFP
ideal< A | L > : AlgGen, List -> AlgGen, Map
ideal<R | L> : AlgMat, List -> AlgMatIdeal
ideal<S | X> : AlgQuatOrd, [AlgQuatOrdElt] -> AlgQuatOrd
ideal< R | a_1, ..., a_r > : Rng, RngElt, ..., RngElt -> RngIdl
ideal< O | a_1, a_2, ... , a_m > : RngFunOrd, RngElt, ..., RngElt -> RngFunOrdIdl
ideal<P | L> : RngMPol, List -> RngMPol
ideal< O | a_1, a_2, ... , a_m > : RngOrd, RngElt, ..., RngElt -> RngOrdFracIdl
ideal< R | a_1, ..., a_r > : RngUPol, RngUPolElt, ..., RngUPolElt -> RngUPol
ideal<S | L_1, ..., L_r> : SgpFP, SgpFPElt, ..., SgpFPElt -> SgpFPIdl

ideal-arithmetic

Ideal Arithmetic (ORDERS AND ALGEBRAIC FIELDS)

ideal-basis

RngOrd_ideal-basis (Example H53E32)

ideal-Boolean

Predicates on Ideals (ORDERS AND ALGEBRAIC FIELDS)

ideal-class-group

Ideal Class Groups (ORDERS AND ALGEBRAIC FIELDS)

ideal-creation

Creation of Ideals in Orders (ORDERS AND ALGEBRAIC FIELDS)

ideal-groebner

IDEAL THEORY AND GRÖBNER BASES

ideal-invar

RngOrd_ideal-invar (Example H53E31)

ideal-operation

Basic Operations on Ideals (IDEAL THEORY AND GRÖBNER BASES)

ideal-ops-further

Further Ideal Operations (ALGEBRAIC FUNCTION FIELDS)

ideal-other

Other Ideal Operations (ORDERS AND ALGEBRAIC FIELDS)

ideal-quotient

Ideals and Quotient Rings (INTRODUCTION [BASIC RINGS])
Ideals and Quotient Rings (UNIVARIATE POLYNOMIAL RINGS)

ideal-ray

RngOrd_ideal-ray (Example H53E24)

ideal-theory

Ideal Theory of Orders (QUATERNION ALGEBRAS)

ideal-two

RngOrd_ideal-two (Example H53E33)

Ideal_Arithmetic

AlgQuat_Ideal_Arithmetic (Example H71E10)

Ideal_Bases

AlgQuat_Ideal_Bases (Example H71E7)

Ideal_Enumeration

AlgQuat_Ideal_Enumeration (Example H71E9)

IdealArithmetic

GB_IdealArithmetic (Example H50E8)

Idealiser

Idealizer(S) : AlgGrpSub -> AlgGrpSub
Idealiser(S) : AlgGrpSub -> AlgGrpSub
Idealizer(A, B: parameters) : AlgAss, AlgAss -> AlgAss

Idealizer

Idealizer(S) : AlgGrpSub -> AlgGrpSub
Idealiser(S) : AlgGrpSub -> AlgGrpSub
Idealizer(A, B: parameters) : AlgAss, AlgAss -> AlgAss

IdealQuotient

IdealQuotient(I, J) : RngMPol, RngMPol -> RngMPol
ColonIdeal(I, J) : RngMPol, RngMPol -> RngMPol
ColonIdeal(I, f) : RngMPol, RngMPolElt -> RngMPol, RngIntElt

Ideals

DegreeOnePrimeIdeals(O, B) : RngOrd, RngIntElt -> [ RngOrdIdl ]
Ideals(D) : DivFunElt -> RngFunOrdIdl, RngFunOrdIdl
Ideals(D) : DivFunElt -> RngFunOrdIdl, RngFunOrdIdl
MaximalLeftIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MaximalIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MinimalLeftIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MinimalIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
RngOrd_Ideals (Example H53E30)

ideals

Creation of Ideals and Accessing their Bases (IDEAL THEORY AND GRÖBNER BASES)
Ideals (RING OF INTEGERS)
Special Functions for Ideals (QUADRATIC FIELDS)

Idempotent

Idempotent(C) : Code -> RngUPolElt
IdempotentActionGenerators(B, i) : AlgBas, RngIntElt -> SeqEnum
IdempotentGenerators(B) : AlgBas -> SeqEnum
IdempotentPositions(B) : AlgBas -> SeqEnum
IsIdempotent(a) : AlgGenElt -> BoolElt
IsIdempotent(x) : RngElt -> BoolElt
NonIdempotentActionGenerators(B, i) : AlgBas, RngIntElt -> SeqEnum
NonIdempotentGenerators(B) : AlgBas -> SeqEnum

IdempotentActionGenerators

IdempotentActionGenerators(B, i) : AlgBas, RngIntElt -> SeqEnum

IdempotentGenerators

IdempotentGenerators(B) : AlgBas -> SeqEnum

IdempotentPositions

IdempotentPositions(B) : AlgBas -> SeqEnum

Identical

IsIdentical(f, g) : RngSerElt, RngSerElt -> BoolElt
IsIdenticalPresentation(G, H) : GrpPC, GrpPC -> BoolElt

Identification

IdentificationNumber(D, i): DB, RngIntElt -> RngIntElt
TransitiveGroupIdentification(G) : GrpPerm -> RngIntElt, RngIntElt
TwoTransitiveGroupIdentification(G) : GrpPerm -> Tup

identification

Identification (PERMUTATION GROUPS)
Identification as a Permutation Group (PERMUTATION GROUPS)
Identification as an Abstract Group (PERMUTATION GROUPS)

identification-abstract

Identification as an Abstract Group (PERMUTATION GROUPS)

identification-permutation

Identification as a Permutation Group (PERMUTATION GROUPS)

IdentificationNumber

IdentificationNumber(D, i): DB, RngIntElt -> RngIntElt

Identifier

Identifier(X) : VSrfK3 -> RngIntElt
Number(X) : VSrfK3 -> RngIntElt

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

ShowIdentifiers() : ->
State_Identifiers (Example H1E1)

Identify

IdentifyAlmostSimpleGroup(G) : GrpPerm -> Map, GrpPerm
IdentifyGroup(G): Grp -> Tup

identify

Small Group Identification (DATABASES OF GROUPS)

IdentifyAlmostSimpleGroup

IdentifyAlmostSimpleGroup(G) : GrpPerm -> Map, GrpPerm

IdentifyGroup

IdentifyGroup(G): Grp -> Tup

Identity

Id(J) : JacHyp -> JacHypPt
Identity(J) : JacHyp -> JacHypPt
J ! 0 : JacHyp, RngIntElt -> JacHypPt
Id(R) : AlgChtr -> AlgChtrElt
Identity(D) : DiffFun -> DiffFunElt
Identity(S) : DiffFun -> DiffFunElt
Identity(G) : DivFun -> DivFunElt
Identity(G) : Grp -> GrpElt
Identity(G) : Grp -> GrpPermElt
Identity(A) : GrpAb -> GrpAbElt
Identity(A) : GrpAbGen -> GrpAbGenElt
Identity(G) : GrpAtc -> GrpAtcElt
Identity(A) : GrpAuto -> GrpAutoElt
Identity(G) : GrpFP -> GrpFPElt
Identity(G) : GrpGPC -> GrpGPCElt
Identity( G ) : GrpLie -> GrpLieElt
Identity(G) : GrpMat -> GrpMatElt
Identity(G) : GrpPC -> GrpPCElt
Identity(G) : GrpPSL2 -> GrpPSL2Elt
Identity(G) : GrpRWS -> GrpRWSElt
Identity(G) : GrpSLP -> GrpSLPElt
Identity(M) : MonRWS -> MonRWSElt
Identity(Q) : QuadBin -> QuadBinElt
IdentityAutomorphism(A) : Sch -> AutSch
IdentityAutomorphism(X) : Sch -> MapAutSch
IdentityHomomorphism(G) : Grp -> Map
IdentityHomomorphism(G) : GrpPC -> Map
IdentityIsogeny(E) : CrvEll -> Map
IdentityMap(E) : CrvEll -> Map
IdentityMap(E) : CrvEll -> Map
IdentityMap(X) : Sch -> MapSch
IsId(w) : GrpAtcElt -> BoolElt
IsId(g) : GrpElt -> BoolElt
IsId(g) : GrpPermElt -> BoolElt
IsId(w) : GrpRWSElt -> BoolElt
IsId(w) : MonRWSElt -> BoolElt
IsId(P) : PtEll -> BoolElt
IsIdentity(u) : GrpAbElt -> BoolElt
IsIdentity(g) : GrpAbGenElt -> BoolElt
IsIdentity(g) : GrpGPCElt -> BoolElt
IsIdentity(g) : GrpMatElt -> BoolElt
IsIdentity(g) : GrpPCElt -> BoolElt
IsIdentity(f) : QuadBinElt -> BoolElt
IsZero(P) : JacHypPt -> BoolElt

identity

Groups (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)

IdentityAutomorphism

Translation(A,p) : Sch,Pt -> AutSch
FlipCoordinates(A) : Sch -> AutSch
Automorphism(A,q) : Sch,RngMPolElt -> AutSch
IdentityAutomorphism(A) : Sch -> AutSch
IdentityAutomorphism(X) : Sch -> MapAutSch

IdentityHomomorphism

IdentityHomomorphism(G) : Grp -> Map
IdentityHomomorphism(G) : GrpPC -> Map

IdentityIsogeny

IdentityIsogeny(E) : CrvEll -> Map

IdentityMap

IdentityMap(X) : Sch -> MapAutSch
IdentityAutomorphism(X) : Sch -> MapAutSch
IdentityMap(E) : CrvEll -> Map
IdentityMap(E) : CrvEll -> Map
IdentityMap(X) : Sch -> MapSch

if

error statement (OVERVIEW)
The if statement (OVERVIEW)
if boolexpr_1 then statements_1 else statements_2 end if : ->
State_if (Example H1E10)

Ignore

GetIgnorePrompt() : -> BoolElt
SetIgnorePrompt(b) : BoolElt ->
SetIgnoreSpaces(b) : BoolElt ->

ignore

Multiple Assignment (OVERVIEW)

Igusa

ClebschToIgusaClebsch(Q) : SeqEnum -> SeqEnum
HyperellipticCurveFromIgusa(S) : SeqEnum -> CrvHyp
IgusaClebschInvariants(C: parameters) : CrvHyp -> SeqEnum
IgusaClebschInvariants(f: parameters) : RngUPolElt -> SeqEnum
IgusaClebschInvariants(h, f) : RngUPolElt, RngUPolElt -> SeqEnum
IgusaClebschToIgusa(S) : SeqEnum -> SeqEnum
IgusaInvariants(f: parameters) : RngUPolElt -> SeqEnum
IgusaInvariants(C: parameters): CrvHyp -> SeqEnum
IgusaInvariants(h, f): RngUPolElt, RngUPolElt -> SeqEnum
ScaledIgusaInvariants(f): RngUPolElt -> SeqEnum
ScaledIgusaInvariants(h, f): RngUPolElt, RngUPolElt -> SeqEnum

igusa_invariants

Igusa Invariants (HYPERELLIPTIC CURVES)

IgusaClebschInvariants

IgusaClebschInvariants(C: parameters) : CrvHyp -> SeqEnum
IgusaClebschInvariants(f: parameters) : RngUPolElt -> SeqEnum
IgusaClebschInvariants(h, f) : RngUPolElt, RngUPolElt -> SeqEnum

IgusaClebschToIgusa

IgusaClebschToIgusa(S) : SeqEnum -> SeqEnum

IgusaInvariants

JInvariants(f: parameters) : RngUPolElt -> SeqEnum
IgusaInvariants(f: parameters) : RngUPolElt -> SeqEnum
IgusaInvariants(C: parameters): CrvHyp -> SeqEnum
IgusaInvariants(h, f): RngUPolElt, RngUPolElt -> SeqEnum

Ihara

IharaBound(F) : FldFun -> RngIntElt

IharaBound

IharaBound(F) : FldFun -> RngIntElt

iload

iload "filename";

Ilog

Ilog(b, n) : RngIntElt, RngIntElt -> RngIntElt

Ilog2

Ilog2(n) : RngIntElt -> RngIntElt

Im

Im(c) : FldComElt -> FldReElt
Imaginary(c) : FldComElt -> FldReElt

Image

ActionImage(A, Y) : GrpPerm, GSet -> GrpPerm
ActionImage(G, Y) : GrpPerm, GSet -> GrpPerm
ActionImage(G, Y) : GrpPerm, GSet -> GrpPerm
ActionImage(G, Y) : GrpPerm, GSet -> GrpPerm
AffineImage(G) : GrpPerm -> GrpPerm
BaseImage(x) : GrpPermElt -> [Elt]
BlocksImage(G) : GrpMat -> GrpPerm
BlocksImage(G, P) : GrpPerm, GSet -> GrpPerm
ClassImage(A) : GrpAuto -> GrpPerm
CosetImage(G, H) : GrpGPC, GrpGPC -> GrpPerm
CosetImage(G, H) : Grp, Grp -> Grp
CosetImage(G, H) : Grp, Grp -> GrpPerm
CosetImage(G, H) : Grp, Grp -> GrpPerm
CosetImage(G, H) : Grp, Grp -> GrpPerm
CosetImage(G, H) : Grp, Grp -> GrpPerm
CosetImage(V) : GrpFPCos, Grp -> GrpPerm
CosetImage(P) : GrpFPCosetEnumProc -> GrpPerm
CosetImage(G, H) : GrpMat, GrpMat -> GrpPerm
GaloisImage(x, i) : RngLocElt, RngIntElt -> RngLocElt
GrayMapImage(C) : Code -> [ ModTupRngElt ]
HasLinearGrayMapImage(C) : Code -> BoolElt, Code
Image(a) : AlgMatElt -> ModTup
Image(f,X,d) : AmbProjMap,SchProj,RngIntElt -> []
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(f) : Map -> Grp
Image(f) : Map -> Grp
Image(f) : Map -> Grp
Image(f) : MapSch -> Sch
Image(f) : ModMatCpxElt -> ModCpx, ModMatCpxElt, ModMatCpxElt
Image(a) : ModMatElt -> ModTupFld
Image(a) : ModMatRngElt -> ModTupRng
ImageSystem(f,S,d) : AmbProjMap,SchProj,RngIntElt -> LinSys
ImageWithBasis(X, M) : ModMatRngElt, ModRng -> ModRng
IsInImage(f, p) : Map, RngMPolElt -> [ BoolElt ]
OrbitImage(G, T) : GrpMat, Set -> GrpPerm
OrbitImage(G, T) : GrpPerm, GSet -> GrpPerm
OrbitImageBounded(G, T, b) : GrpMat, Set, RngIntElt -> BoolElt, GrpPerm
QuotientModuleImage(G, S) : GrpMat -> GrpMat
SocleImage(G) : GrpPerm -> GrpPerm
SubmoduleImage(G, S) : GrpMat -> GrpMat

image

Images and Preimages (MAPPINGS)
Images, Orbits and Stabilizers (PERMUTATION GROUPS)
Orbit and Stabilizer Functions for Large Groups (MATRIX GROUPS)
Orbits and Stabilizers (MATRIX GROUPS)

image-finder

Scheme_image-finder (Example H81E30)

image-orbit-stabilizer

Images, Orbits and Stabilizers (PERMUTATION GROUPS)
Orbits and Stabilizers (MATRIX GROUPS)

image-orbit-stabilizer-large

Orbit and Stabilizer Functions for Large Groups (MATRIX GROUPS)

image-preimage

Images and Preimages (MAPPINGS)

ImageSystem

ImageSystem(f,S,d) : AmbProjMap,SchProj,RngIntElt -> LinSys

ImageWithBasis

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

Imaginary

Im(c) : FldComElt -> FldReElt
Imaginary(c) : FldComElt -> FldReElt
Imaginary(z) : SpcHypElt -> FldPrElt

Implicit

ImplicitFunction(f, d, n) : RngUPolElt, RngIntElt, RngIntElt -> RngSerElt

ImplicitCosetEnumeration

GrpFP_1_ImplicitCosetEnumeration (Example H22E34)

ImplicitFunction

ImplicitFunction(f, d, n) : RngUPolElt, RngIntElt, RngIntElt -> RngSerElt

Implicitization

Implicitization(f) : Map -> RngMPol

import

Importing Constants (FUNCTIONS, PROCEDURES AND PACKAGES)
import "filename": ident_list;
Func_import (Example H2E7)

Imprimitive

ImprimitiveReflectionGroup(GrpFP,{ m, p, n}) : Cat, RngIntElt, RngIntElt, RngIntElt -> GrpFP
ImprimitiveReflectionGroup(GrpFP,{ m, p, n}) : Cat, RngIntElt, RngIntElt, RngIntElt -> GrpFP
ImprimitiveReflectionGroup(m, p, n) : RngIntElt, RngIntElt, RngIntElt -> GrpMat, Fld

imprimitive

Imprimitive Unitary Reflection Groups (REFLECTION GROUPS)

imprimitive-unitary-reflection-groups

Imprimitive Unitary Reflection Groups (REFLECTION GROUPS)

ImprimitiveReflectionGroup

ImprimitiveReflectionGroup(GrpFP,{ m, p, n}) : Cat, RngIntElt, RngIntElt, RngIntElt -> GrpFP
ImprimitiveReflectionGroup(GrpFP,{ m, p, n}) : Cat, RngIntElt, RngIntElt, RngIntElt -> GrpFP
ImprimitiveReflectionGroup(m, p, n) : RngIntElt, RngIntElt, RngIntElt -> GrpMat, Fld

in

Equality and Membership (LOCAL RINGS AND FIELDS)
Equality and Membership (p-ADIC RINGS AND FIELDS)
Planes in Magma (FINITE PLANES)
Sequences (OVERVIEW)
Sets (OVERVIEW)
The for statement (OVERVIEW)
x in S
x in L : ., RngLoc -> BoolElt
x in y : AlgChtrElt, AlgChtrElt -> BoolElt
a in A : AlgGenElt, AlgGen -> BoolElt
x in R : AlgMatElt, AlgMat -> BoolElt
x in A : AlgQuatElt, AlgQuat -> BoolElt
x in D : Any, DiffFun -> BoolElt
x in M : Any, ModOrd -> BoolElt
x in S : Elt, Seq -> BoolElt
x in R : Elt, Set -> BoolElt
g in G : GrpAbElt, GrpAb -> BoolElt
g in A : GrpAbGenElt, GrpAbGen -> BoolElt
w in G : GrpAtcElt, GrpAtc -> BoolElt
g in G : GrpFinElt, GrpFin -> BoolElt
g in C : GrpFPElt, GrpFPCosElt -> BoolElt
g in G : GrpGPCElt, GrpGPC -> BoolElt
u in e : GrphVert, GrphEdge -> BoolElt
u in e : GrphVert, GrphEdge -> 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
g in G : GrpPSL2Elt, GrpPSL2 -> BoolElt
w in G : GrpRWSElt, GrpRWS -> BoolElt
g in G : GrpSLPElt, GrpSLP -> BoolElt
u in H : GrpFPElt, GrpFP -> BoolElt
p in B : IncPt, IncBlk -> BoolElt
v in L : LatElt, Lat -> BoolElt
f in M : MapCrvHyp, HomCrvHyp -> BoolElt
x in M : ModBrdtElt, ModBrdt -> BoolElt
f in M : ModMPolElt, ModMPol -> BoolElt
v in V : ModTupFldElt, ModTupFld -> BoolElt
u in C : ModTupRngElt, Code -> BoolElt
u in C : ModTupRngElt, Code -> BoolElt
u in M : ModTupRngElt, ModTupRng -> BoolElt
u in M : ModTupRngElt, ModTupRng -> BoolElt
w in M : MonRWSElt, MonRWS -> BoolElt
s in t : MonStgElt, MonStgElt -> BoolElt
p in l : PlanePt, PlaneLn -> BoolElt
p in C : Pt,Sch -> BoolElt
p in X : Pt,Sch -> BoolElt
P in E : PtEll, CrvEll -> BoolElt
P in H : PtEll, SetPtEll -> BoolElt
f in Q : QuadBinElt, QuadBin -> BoolElt
a in R : RngElt, Rng -> BoolElt
a in I : RngElt, RngIdl -> BoolElt
a in S : RngElt,DiffFun -> BoolElt
N in D: RngIntElt, DB -> BoolElt
f in R : RngMPol, RngInvar -> FldFunUElt, ModMPolElt
f in I : RngMPolElt, RngMPol -> BoolElt
f in L : RngMPolElt,LinSys -> BoolElt
a in I : RngUPolElt, RngUPol -> BoolElt
X in L : Sch,LinSys -> BoolElt
S in P : SeqEnum, PowSeqEnum -> BoolElt
Q in X : SeqEnum,Sch -> BoolElt
S in P : SetEnum, PowSetEnum -> BoolElt
S in P : SetIndx, PowSetIndx -> BoolElt
S in P : SetMulti, PowSetMulti -> BoolElt

Inc

Combinatorial and Geometrical Structures (OVERVIEW)

Incidence

IncidenceDigraph(A) : ModHomElt -> GrphDir
IncidenceGeometry(C) : CosetGeom -> IncGeom
IncidenceGeometry(G) : GrphUnd -> IncGeom
IncidenceGraph(D) : Inc -> Grph
IncidenceGraph(D) : Inc -> GrphUnd
IncidenceGraph(D) : IncGeom -> GrphUnd, GrphVertSet, GrphEdgeSet
IncidenceGraph(A) : ModHomElt -> GrphUnd
IncidenceGraph(P) : Plane -> Grph
IncidenceGraph(P) : Plane -> GrphUnd;
IncidenceMatrix(G) : Grph -> ModHomElt
IncidenceMatrix(D) : Inc -> ModMatRngElt
IncidenceMatrix(P) : Plane -> AlgMatElt
IncidenceStructure(G) : Grph -> Inc
IncidenceStructure(I) : Inc -> Inc
IncidenceStructure< v | X > : RngIntElt, List -> Inc

incidence

Combinatorial and Geometrical Structures (OVERVIEW)
Construction of an Incidence Geometry (INCIDENCE GEOMETRY)
INCIDENCE GEOMETRY
INCIDENCE STRUCTURES AND DESIGNS

incidence-geometry

INCIDENCE GEOMETRY

incidence-structure-design

INCIDENCE STRUCTURES AND DESIGNS

IncidenceDigraph

IncidenceDigraph(A) : ModHomElt -> GrphDir

IncidenceGeometry

Combinatorial and Geometrical Structures (OVERVIEW)
IncidenceGeometry(C) : CosetGeom -> IncGeom
IncidenceGeometry(G) : GrphUnd -> IncGeom

IncidenceGraph

IncidenceGraph(D) : Inc -> Grph
IncidenceGraph(D) : Inc -> GrphUnd
IncidenceGraph(D) : IncGeom -> GrphUnd, GrphVertSet, GrphEdgeSet
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

Incident

IncidentEdges(u) : GrphVert -> { GrphEdge }

IncidentEdges

IncidentEdges(u) : GrphVert -> { GrphEdge }

Include

Include(~S, x) : SeqEnum, Elt ->
Include(~S, x) : SetEnum, Elt ->
Set_Include (Example H7E10)

Inclusion

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

inclusion

Inclusion and Equality (FINITE SOLUBLE GROUPS)

inclusion-equality

Inclusion and Equality (FINITE SOLUBLE GROUPS)

InclusionMap

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

Inclusions

NumberOfInclusions(e, f) : SubGrpLatElt, SubGrpLatElt -> RngIntElt

Increasing

LongestIncreasingSequence(w) : SeqEnum -> RngIntElt
LongestIncreasingSequences(w, k) : SeqEnum,RngIntElt -> RngIntElt

Indecomposable

IndecomposableSummands(M) : ModGrp -> [ ModGrp ]
IsIndecomposable(M,B) : ModBrdt, RngIntElt -> BoolElt

indecomposable

Indecomposable Projective Modules (BASIC ALGEBRAS)

indecomposable-projective-modules

Indecomposable Projective Modules (BASIC ALGEBRAS)

IndecomposableSummands

IndecomposableSummands(M) : ModGrp -> [ ModGrp ]

Indefinite

IsIndefinite(A) : AlgQuat -> BoolElt

InDegree

InDegree(u) : GrphVert -> RngIntElt

Indent

IndentPop() : ->
IndentPush() : ->
SetIndent(n) : RngIntElt ->

indent

Indentation (INPUT AND OUTPUT)

IndentPop

IndentPop() : ->

IndentPush

IndentPush() : ->

Independence

IndependenceNumber(G: parameters) : GrphUnd -> RngIntElt

IndependenceNumber

IndependenceNumber(G: parameters) : GrphUnd -> RngIntElt

Independent

IndependentUnits(O) : RngFunOrd -> SeqEnum[RngFunOrdElt]
IndependentUnits(O) : RngOrd -> GrpAb, Map
IsIndependent(Q) : [ AlgGen ] -> BoolElt
IsIndependent(Q) : [ ModTupFldElt ] -> BoolElt
IsIndependent(S) : { ModTupFldElt } -> BoolElt
IsLinearlyIndependent(P, Q) : PtEll, PtEll -> BoolElt, ModTupElt
IsLinearlyIndependent(P, Q, n) : PtEll, PtEll, RngIntElt -> BoolElt
IsLinearlyIndependent(S) : [ PtEll ] -> BoolElt, ModTupElt
IsLinearlyIndependent(S, n) : [ PtEll ], RngIntElt -> BoolElt
MaximumIndependentSet(G: parameters) : GrphUnd -> { GrphVert }

independent

Cliques, Independent Sets (GRAPHS)

IndependentUnits

IndependentUnits(O) : RngFunOrd -> SeqEnum[RngFunOrdElt]
IndependentUnits(O) : RngOrd -> GrpAb, Map

Index

Sequences (OVERVIEW)
Sets (OVERVIEW)
ChromaticIndex(G) : GrphUnd -> RngIntElt
FactoredIndex(G, H) : GrpAb, GrpAb -> [<RngIntElt, RngIntElt>]
FactoredIndex(G, H) : GrpFin, GrpFin -> [ <RngIntElt, RngIntElt> ]
FactoredIndex(G, H) : GrpGPC, GrpGPC -> [<RngIntElt, RngIntElt>]
FactoredIndex(G, H) : GrpMat, GrpMat -> [ <RngIntElt, RngIntElt> ]
FactoredIndex(G, H) : GrpPC, GrpPC -> [<RngIntElt, RngIntElt>]
FactoredIndex(G, H) : GrpPerm, GrpPerm -> [ <RngIntElt, RngIntElt> ]
HasValidIndex(P) : GrpFPCosetEnumProc -> BoolElt
Index(x) : CopElt -> RngIntElt
Index(G, H) : GrpAb, GrpAb -> RngIntElt
Index(G, H) : GrpFin, GrpFin -> RngIntElt
Index(G, H) : GrpGPC, GrpGPC -> RngIntElt
Index(v) : GrphResVert -> RngIntElt
Index(v) : GrphSplVert -> RngIntElt
Index(v) : GrphVert -> RngIntElt
Index(G, H) : GrpMat, GrpMat -> RngIntElt
Index(G, H) : GrpPC, GrpPC -> RngIntElt
Index(G, H) : GrpPerm, GrpPerm -> RngIntElt
Index(G) : GrpPSL2 -> RngIntElt
Index(G,H) : GrpPSL2, GrpPSL2 -> RngIntElt
Index(G, H: parameters) : GrpFP, GrpFP -> RngIntElt
Index(P) : GrpFPCosetEnumProc -> RngIntElt
Index(L, S): Lat, Lat -> RngInt
Index(s, t) : MonStgElt, MonStgElt -> RngIntElt
Index(P, l) : PlaneLn -> RngIntElt
Index(P, p) : PlanePt -> RngIntElt
Index(O, S) : RngOrd, RngOrd -> RngIntElt
Index(O, I) : RngOrd, RngOrdIdl -> RngIntElt
Index(a) : RngOrdElt -> RngIntElt
Index(S, x) : SeqEnum, Elt -> RngIntElt
Index(S, x) : SetIndx, Elt -> RngIntElt
Index(FS) : SymFry -> RngIntElt
IndexFormEquation(O, k) : RngOrd, RngIntElt -> [ RngOrdElt ]
IndexOfPartition(P) : SeqEnum -> RngIntElt
IndexOfSpeciality(D) : DivCrvElt -> RngIntElt
IndexOfSpeciality(D) : DivFunElt -> RngIntElt
LowIndexProcess(G, R : parameters) : GrpFP, RngIntElt -> Process(Lix)
LowIndexSubgroups(G, R : parameters) : GrpFP, RngIntElt -> [ GrpFP ]
LowIndexSubgroups(G, R : parameters) : GrpMat, RngIntElt -> [ GrpMat ]
LowIndexSubgroups(G, n: parameters) : GrpPerm, RngIntElt -> SeqEnum
RamificationIndex(P) : PlcFunElt -> RngIntElt
RamificationIndex(I) : RngFunOrdIdl -> RngIntElt
RamificationIndex(I, p) : RngInt, RngIntElt -> RngIntElt
RamificationIndex(I) : RngOrdIdl -> RngIntElt

index

Extracting and Inserting Blocks (MATRICES)
Index Form Equations (ORDERS AND ALGEBRAIC FIELDS)
Index of a Subgroup: The Todd-Coxeter Algorithm (FINITELY PRESENTED GROUPS)
Indexing (MATRICES)
Indexing (MATRIX ALGEBRAS)
Indexing Vectors and Matrices (VECTOR SPACES)
Integer-Valued Functions (INPUT AND OUTPUT)
Low Index Subgroups (FINITELY PRESENTED GROUPS)
Order and Index Functions (GROUPS)

index-form

Index Form Equations (ORDERS AND ALGEBRAIC FIELDS)
RngOrd_index-form (Example H53E29)

index-Todd-Coxeter

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

Index1

GrpFP_1_Index1 (Example H22E30)

Indexed

GSetFromIndexed(G, Y) : GrpPerm, SetIndx -> GSet
IndexedCoset(V, C) : GrpFPCos, GrpFPCosElt -> GrpFPCosElt
IndexedCoset(V, w) : GrpFPCos, GrpFPElt -> GrpFPCosElt
IndexedSetToSequence(S) : SetIndx -> SeqEnum
IndexedSetToSet(S) : SetIndx -> SetEnum
PowerIndexedSet(R) : Struct -> PowSetIndx
SetToIndexedSet(E) : SetEnum -> SetIndx

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

IndexedSetToSequence

Isetseq(S) : SetIndx -> SeqEnum
IndexedSetToSequence(S) : SetIndx -> SeqEnum

IndexedSetToSet

Isetset(S) : SetIndx -> SetEnum
IndexedSetToSet(S) : SetIndx -> SetEnum

IndexFormEquation

IndexFormEquation(O, k) : RngOrd, RngIntElt -> [ RngOrdElt ]

Indexing

Mat_Indexing (Example H62E4)
ModFld_Indexing (Example H63E7)
State_Indexing (Example H1E3)

indexing

Indexing (FREE MODULES)
Indexing (MODULES OVER A MATRIX ALGEBRA)
Indexing Elements (STRUCTURE CONSTANT ALGEBRAS)
Multi-indexing (INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS])

IndexOfPartition

IndexOfPartition(P) : SeqEnum -> RngIntElt

IndexOfSpeciality

IndexOfSpeciality(D) : DivCrvElt -> RngIntElt
IndexOfSpeciality(D) : DivFunElt -> RngIntElt

Indices

Indices(X) : CrvMod -> SeqEnum
Indices(X) : VSrfK3 -> SeqEnum

indirect

Implicit Invocation of the Todd-Coxeter Algorithm (FINITELY PRESENTED GROUPS)

indirect-Todd-Coxeter

Implicit Invocation of the Todd-Coxeter Algorithm (FINITELY PRESENTED GROUPS)

individual

Lifting a Quotient by Choosing an Individual Cocycle (FP GROUPS - ADVANCED FEATURES)

individual-cocycle

Lifting a Quotient by Choosing an Individual Cocycle (FP GROUPS - ADVANCED FEATURES)

Induced

InducedMapOnHomology(f,n) : MapChn, RngIntElt -> ModTupFldElt
IsTensorInduced(G : parameters) : GrpMat -> BoolElt
TensorInducedBasis(G) : GrpMat -> GrpMatElt
TensorInducedPermutations(G) : GrpMat -> SeqEnum

induced

Action on a G-Space (PERMUTATION GROUPS)
Coset Spaces: Induced Homomorphism (FINITELY PRESENTED GROUPS)

induced-homomorphism

Action on a G-Space (PERMUTATION GROUPS)
Coset Spaces: Induced Homomorphism (FINITELY PRESENTED GROUPS)

InducedMapOnHomology

InducedMapOnHomology(f,n) : MapChn, RngIntElt -> ModTupFldElt

Induction

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

induction

Induction and Restriction (MODULES OVER A MATRIX ALGEBRA)
Induction, Restriction, Extension (CHARACTERS OF FINITE GROUPS)
Tensor-induced Groups (MATRIX GROUPS)

induction-restriction

Induction and Restriction (MODULES OVER A MATRIX ALGEBRA)

induction-restriction-extension

Induction, Restriction, Extension (CHARACTERS OF FINITE GROUPS)

inequality

Comparison (OVERVIEW)

Inert

IsInert(P) : RngOrdIdl -> BoolElt
IsInert(P, O) : RngOrdIdl, RngOrd -> BoolElt
LocseqInert(x) : RngLoc -> [ RngLocElt ]

Inertia

InertiaDegree(I) : RngFunOrdIdl -> RngIntElt
ResidueClassDegree(I) : RngFunOrdIdl -> RngIntElt
Degree(I) : RngFunOrdIdl -> RngIntElt
Degree(I) : RngOrdIdl -> RngIntElt
InertiaDegree(P) : PlcFunElt -> RngIntElt
InertiaDegree(L) : RngLoc -> RngIntElt
InertiaElement(L) : RngLoc -> RngLocElt
InertiaField(L) : FldLoc -> FldLoc
InertiaField(p) : RngOrdIdl -> FldNum, Map
InertiaGroup(p) : RngOrdIdl -> GrpPerm
InertiaRing(L) : RngLoc -> RngLoc

InertiaDegree

InertiaDegree(I) : RngFunOrdIdl -> RngIntElt
ResidueClassDegree(I) : RngFunOrdIdl -> RngIntElt
Degree(I) : RngFunOrdIdl -> RngIntElt
Degree(I) : RngOrdIdl -> RngIntElt
InertiaDegree(P) : PlcFunElt -> RngIntElt
InertiaDegree(L) : RngLoc -> RngIntElt

InertiaElement

L . 2 : RngLoc -> RngLocElt
InertiaElement(L) : RngLoc -> RngLocElt

InertiaField

InertiaField(L) : FldLoc -> FldLoc
InertiaField(p) : RngOrdIdl -> FldNum, Map

InertiaGroup

InertiaGroup(p) : RngOrdIdl -> GrpPerm

Inertial

InertialPolynomial(L) : RngLoc -> RngUPolElt
IsInertial(g) : RngUPolElt -> BoolElt

InertialPolynomial

InertialPolynomial(L) : RngLoc -> RngUPolElt

InertiaRing

InertiaRing(L) : RngLoc -> RngLoc

Inertseqp

InertseqpAdic(x) : RngLoc -> [ RngLocElt ]

InertseqpAdic

InertseqpAdic(x) : RngLoc -> [ RngLocElt ]

inf

Local Rings and Fields with Infinite Precision (LOCAL RINGS AND FIELDS)
p-adic Rings and Fields with Infinite Precision (p-ADIC RINGS AND FIELDS)

Infinite

EquationOrderInfinite(F) : FldFun -> RngFunOrd
MaximalOrderFinite(F) : FldFun -> RngFunOrd
MaximalOrderInfinite(F) : FldFun -> RngFunOrd
EquationOrderFinite(F) : FldFun -> RngFunOrd
MaximalOrderFinite(F) : FldFun -> RngFunOrd
EquationOrderInfinite(F) : FldFun -> RngFunOrd
InfiniteSum(m, i) : Map, RngIntElt -> FldPrElt
MaximalOrderInfinite(F) : FldFun -> RngFunOrd

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

Infinity

HyperplaneAtInfinity(X) : Sch -> Sch
Infinity() : -> Infty
LineAtInfinity(A) : Aff -> Crv
MinusInfinity() : -> Infty
PointsAtInfinity(C) : Crv -> SetEnum
PointsAtInfinity(C) : CrvHyp -> SetIndx
PointsAtInfinity(H) : SetPtEll -> @ PtEll @
TranslationToInfinity(C,p) : Crv,Pt -> Crv,AutSch

infinity

Infinities (RING OF INTEGERS)

infix

Operators (OVERVIEW)

Inflection

InflectionPoints(C) : Sch -> SeqEnum
Flexes(C) : Sch -> SeqEnum
IsInflectionPoint(p) : Sch,Pt -> BoolElt,RngIntElt

InflectionPoints

InflectionPoints(C) : Sch -> SeqEnum
Flexes(C) : Sch -> SeqEnum

Info

IsolInfo(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> MonStgElt

info

ListTypes() : ->
Other Information Procedures (ENVIRONMENT AND OPTIONS)

Information

AllInformationSets(C) : Code -> [ [ RngIntElt ] ]
InformationRate(C) : Code -> FldPrElt
InformationRate(C) : Code -> RngPrElt
InformationSet(C) : Code -> [ RngIntElt ]
InformationSpace(C) : Code -> ModTupFld
LocalInformation(E, p) : CrvEll, RngIntElt -> <RngIntElt, RngIntElt, RngIntElt, RngIntElt, SymKod>
LocalInformation(E) : CrvEll, RngIntElt -> [ Tup ]

information

Asymptotic Bounds on the Information Rate (LINEAR CODES OVER FINITE FIELDS)
Class Information from a Conjugacy Class Poset (GROUPS)
Database Information (LATTICES)
The Information Space and Information Sets (LINEAR CODES OVER FINITE FIELDS)

information-set

The Information Space and Information Sets (LINEAR CODES OVER FINITE FIELDS)

InformationRate

InformationRate(C) : Code -> FldPrElt
InformationRate(C) : Code -> RngPrElt

InformationSet

InformationSet(C) : Code -> [ RngIntElt ]

InformationSpace

InformationSpace(C) : Code -> ModTupFld

infrastructure

NPCGenerators(G) : GrpPC -> RngIntElt
NPCgens(G) : GrpPC -> RngIntElt
Infrastructure (FINITE SOLUBLE GROUPS)

initial

The Initial Context (MAGMA SEMANTICS)

initial-context

The Initial Context (MAGMA SEMANTICS)

initialising

Initialisation (FP GROUPS - ADVANCED FEATURES)

initialising-soluble-quotient-process

Initialisation (FP GROUPS - ADVANCED FEATURES)

Initialize

Initialize(F) : GrpFP -> SQProc
Initialize(e) : Map -> SQProc

Injection

Injection(B, i, v) : AlgBas, RngIntElt, ModRngElt -> AlgBasElt

Injections

Injections(C) : Cop -> [ Map ]

Injective

CompactInjectiveResolution(M, n) : ModAlg, RngIntElt -> List, ModMatFldElt
DimensionsOfInjectiveModules(B) : AlgBas -> SeqEnum
InjectiveHull(M) : ModAlg -> ModAlg, ModMatFldElt, SeqEnum[ModMatFldElt], SeqEnum[ModMatFldElt], SeqEnum[RngIntElt]
InjectiveModule(B, i) : AlgBas, RngIntElt -> ModAlg
InjectiveResolution(M, n) : ModAlg, RngIntElt -> ModCpx, ModMatFldElt
InjectiveSyzygyModule(M, n) : ModAlg, RngIntElt -> ModAlg
IsInjective(M) : ModAlg -> BoolElt, SeqEnum
IsInjective(a) : ModMatRngElt -> BoolElt
IsInjective(f) : MotMatCpxElt -> BoolElt

injective

Injective Modules (BASIC ALGEBRAS)

injective-modules

Injective Modules (BASIC ALGEBRAS)

InjectiveHull

InjectiveHull(M) : ModAlg -> ModAlg, ModMatFldElt, SeqEnum[ModMatFldElt], SeqEnum[ModMatFldElt], SeqEnum[RngIntElt]

InjectiveModule

InjectiveModule(B, i) : AlgBas, RngIntElt -> ModAlg

InjectiveResolution

InjectiveResolution(M, n) : ModAlg, RngIntElt -> ModCpx, ModMatFldElt

InjectiveSyzygyModule

InjectiveSyzygyModule(M, n) : ModAlg, RngIntElt -> ModAlg

InLineConditional

State_InLineConditional (Example H1E11)

InNeighbors

InNeighbors(u) : GrphVert -> { GrphVert }
InNeighbours(u) : GrphVert -> { GrphVert }

InNeighbours

InNeighbors(u) : GrphVert -> { GrphVert }
InNeighbours(u) : GrphVert -> { GrphVert }

Inner

InnerProduct(u, v) : ModTupFldElt, ModTupFldElt -> FldElt
(u, v) : ModTupFldElt, ModTupFldElt -> FldElt
(u, v) : ModTupRngElt, ModTupRngElt -> RngElt
(u, v) : ModTupRngElt, ModTupRngElt : -> RngElt
(u, v) : ModTupRngElt, ModTupRngElt : -> RngElt
InnerFaces(N) : NwtnPgon -> SeqEnum
InnerGenerators(A) : GrpAuto -> SeqEnum
InnerProduct(x, y) : AlgChtrElt, AlgChtrElt -> FldCycElt
InnerProduct(a, b) : AlgGenElt, AlgGenElt -> RngElt
InnerProduct(v, w) : LatElt, LatElt -> RngElt
InnerProduct(x,y) : ModBrdtElt, ModBrdtElt -> RngElt
InnerProductMatrix(L) : Lat -> AlgMatElt
InnerProductMatrix(M) : ModBrdt -> AlgMatElt
InnerVertices(N) : NwtnPgon -> SeqEnum
IsInner(f) : GrpAutoElt -> BoolElt, GrpElt

inner

KSpace(K, n, F) : Fld, RngIntElt, Mtrx -> ModTupFld
Construction of a Vector Space with Inner Product Matrix (VECTOR SPACES)
Inner Products (FREE MODULES)

inner-product

Inner Products (FREE MODULES)

InnerFaces

InnerFaces(N) : NwtnPgon -> SeqEnum

InnerGenerators

InnerGenerators(A) : GrpAuto -> SeqEnum

InnerProduct

InnerProduct(u, v) : ModTupFldElt, ModTupFldElt -> FldElt
(u, v) : ModTupFldElt, ModTupFldElt -> FldElt
(u, v) : ModTupRngElt, ModTupRngElt -> RngElt
(u, v) : ModTupRngElt, ModTupRngElt : -> RngElt
(u, v) : ModTupRngElt, ModTupRngElt : -> RngElt
InnerProduct(x, y) : AlgChtrElt, AlgChtrElt -> FldCycElt
InnerProduct(a, b) : AlgGenElt, AlgGenElt -> RngElt
InnerProduct(v, w) : LatElt, LatElt -> RngElt
InnerProduct(x,y) : ModBrdtElt, ModBrdtElt -> RngElt
ModFld_InnerProduct (Example H63E6)

InnerProductMatrix

InnerProductMatrix(L) : Lat -> AlgMatElt
InnerProductMatrix(M) : ModBrdt -> AlgMatElt

InnerVertices

InnerVertices(N) : NwtnPgon -> SeqEnum

Input

SetEchoInput(b) : BoolElt ->
SetEchoInput(b) : BoolElt ->

input

readi identifier, prompt;
Interactive Input (INPUT AND OUTPUT)
Loading files (OVERVIEW)

Insert

Insert(~S, i, x) : SeqEnum, RngIntElt, Elt ->
Insert(~S, k, m, T) : SeqEnum, RngIntElt, RngIntElt, SeqEnum ->
InsertBlock(~a, b, i, j) : AlgMatElt, ModHomElt, RngIntElt, RngIntElt -> AlgMatElt
InsertBlock(A, B, i, j) : Mtrx, Mtrx, RngIntElt, RngIntElt -> Mtrx
InsertVertex(e) : GrphEdge -> Grph
InsertVertex(T) : { GrphEdge } -> Grph
RowInsert(~t, i) : Tableau,RngIntElt ->
RowInsert(~t, w) : Tableau,SeqEnum ->

InsertBlock

InsertBlock(~a, b, i, j) : AlgMatElt, ModHomElt, RngIntElt, RngIntElt -> AlgMatElt
InsertBlock(A, B, i, j) : Mtrx, Mtrx, RngIntElt, RngIntElt -> Mtrx

InsertVertex

InsertVertex(e) : GrphEdge -> Grph
InsertVertex(T) : { GrphEdge } -> Grph

Insoluble

SmallGroupIsInsoluble(o, n) : RngIntElt, RngIntElt -> Grp

instant

Explicit LP Solving Functions (LINEAR PROGRAMMING)

instant-lp

Explicit LP Solving Functions (LINEAR PROGRAMMING)

Integer

LieConstant_A( RD, r, s) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
CartanInteger( RD, r, s) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
Facint(f) : RngIntEltFact -> RngIntElt
FactorizationToInteger(s) : [ <RngIntElt, RngIntElt> ] -> RngIntElt
Facint(s) : [ <RngIntElt, RngIntElt> ] -> RngIntElt
IntegerRing(F) : FldFunRat -> RngPol
IntegerRing(L) : FldLoc -> RngLoc
IntegerRing(P) : FldLoc -> RngLoc
IntegerRing() : Null -> RngInt
RingOfIntegers(Q) : Fldrat -> RngInt
IntegerSolutionVariables(L) : LP -> SeqEnum
IntegerToSequence(n, b) : RngIntElt, RngIntElt -> [RngIntElt]
IntegerToString(n) : RngIntElt -> ModStgElt
IntegerToString(n) : RngIntElt -> MonStgElt
IntegerToString(n, b) : RngIntElt, RngIntElt -> MonStgElt
MaximalIntegerSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
MaximalOrder(F) : FldAlg -> RngOrd
MaximalOrder(F) : FldQuad -> RngQuad
MaximalOrder(Q) : FldRat -> RngInt
Integers() : Null -> RngInt
MinimalInteger(I) : RngInt -> RngIntElt
MinimalIntegerSolution(LHS, relations, RHS, objective) : Mtrx, Mtrx, Mtrx, Mtrx -> Mtrx, RngIntElt
ResidueClassRing(m) : RngIntElt -> RngIntRes
ResidueClassRing(Q) : RngIntEltFact -> RngIntRes
SequenceToInteger(s, b) : [RngIntElt], RngIntElt -> RngIntElt
SetIntegerSolutionVariables(L, I, m) : LP, SeqEnum[RngIntElt], BoolElt ->
StringToInteger(s) : MonStgElt -> RngIntElt
StringToInteger(s, b) : MonStgElt, MonStgElt -> RngIntElt
StringToIntegerSequence(s) : MonStgElt -> [ RngIntElt ]

integer

Polynomials over the Integers (MULTIVARIATE POLYNOMIAL RINGS)
Polynomials over the Integers (UNIVARIATE POLYNOMIAL RINGS)
RING OF INTEGERS
Rings, Fields, and Algebras (OVERVIEW)

IntegerRing

RingOfIntegers(F) : FldFunRat -> RngPol
IntegerRing(F) : FldFunRat -> RngPol
IntegerRing(L) : FldLoc -> RngLoc
IntegerRing(P) : FldLoc -> RngLoc
IntegerRing() : Null -> RngInt
MaximalOrder(F) : FldAlg -> RngOrd
MaximalOrder(F) : FldQuad -> RngQuad
MaximalOrder(Q) : FldRat -> RngInt
ResidueClassRing(m) : RngIntElt -> RngIntRes
ResidueClassRing(Q) : RngIntEltFact -> RngIntRes

Integers

RingOfIntegers(F) : FldFunRat -> RngPol
IntegerRing(F) : FldFunRat -> RngPol
IntegerRing(L) : FldLoc -> RngLoc
RingOfIntegers(L) : FldLoc -> RngLoc
IntegerRing(P) : FldLoc -> RngLoc
RingOfIntegers(P) : FldLoc -> RngLoc
IntegerRing() : Null -> RngInt
RingOfIntegers(Q) : Fldrat -> RngInt
MaximalOrder(F) : FldAlg -> RngOrd
Integers(F) : FldAlg -> RngOrd
MaximalOrder(F) : FldQuad -> RngQuad
MaximalOrder(Q) : FldRat -> RngInt
Integers() : Null -> RngInt
ResidueClassRing(m) : RngIntElt -> RngIntRes
Integers(m) : RngIntElt -> RngIntRes
ResidueClassRing(Q) : RngIntEltFact -> RngIntRes
RngInt_Integers (Example H40E2)

IntegerSolutionVariables

IntegerSolutionVariables(L) : LP -> SeqEnum

IntegerToSequence

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

IntegerToString

IntegerToString(n) : RngIntElt -> ModStgElt
IntegerToString(n) : RngIntElt -> MonStgElt
IntegerToString(n, b) : RngIntElt, RngIntElt -> MonStgElt

Integral

DawsonIntegral(r) : FldReElt -> FldReElt
ExponentialIntegral(r) : FldReElt -> FldReElt
ExponentialIntegralE1(r) : FldReElt -> FldReElt
Integral(m, a, b) : Map, FldPrElt, FldPRElt -> FldPrElt
Integral(f, i) : RngMPolElt, RngIntElt -> RngMPolElt
Integral(f) : RngSerElt -> RngSerElt
Integral(p) : RngUPolElt -> RngUPolElt
IntegralBasis(F) : FldAlg -> [ FldAlgElt ]
IntegralBasis(Q) : FldRat -> [ FldRatElt ]
IntegralBasis(M) : ModSym -> Lat
IntegralClosure(R, F) : Rng, FldFun -> RngFunOrd
IntegralClosure(R, F) : Rng, FldFun -> RngFunOrd
IntegralGroup(G) : GrpMat -> GrpMat, AlgMatElt
IntegralHeckeOperator(M, n) : ModSym, RngIntElt -> AlgMatElt
IntegralMapping(M) : ModSym -> Map
IntegralModel(E) : CrvEll -> CrvEll, Map, Map
IntegralModel(C) : CrvHyp -> CrvHyp, MapCrvHyp
IntegralPoints(E) : CrvEll -> [ PtEll ], [ Tup ]
IntegralQuarticPoints(Q) : [ RngIntElt ] -> [ SeqEnum ]
IntegralQuarticPoints(Q, P) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]
IntegralSplit(a, O) : FldFunElt, RngFunOrd -> RngFunOrdElt, RngElt
IntegralSplit(a, O) : RngFunOrdElt, RngFunOrd -> RngFunOrdElt, RngElt
IntegralSplit(I) : RngFunOrdIdl -> RngFunOrdIdl, RngElt
IsDomain(R) : Rng -> BoolElt
IsIntegral(C) : CrvHyp -> BoolElt
IsIntegral(a) : FldAlgElt -> BoolElt
IsIntegral(c) : FldPrElt -> BoolElt
IsIntegral(q) : FldRatElt -> BoolElt
IsIntegral(L) : Lat -> BoolElt
IsIntegral(P) : PtEll -> BoolElt
IsIntegral(I) : RngFunOrdIdl -> BoolElt
IsIntegral(n) : RngIntElt -> BoolElt
IsIntegral(x) : RngLocElt -> BoolElt
IsIntegral(I) : RngOrdFracIdl -> BoolElt
IsIntegralModel(E) : CrvEll -> BoolElt
IspIntegral(C, p) : CrvHyp, RngIntElt -> BoolElt
LogIntegral(s) : FldPrElt -> FldPrElt
qIntegralBasis(M, prec : parameters: Al) : ModSym, RngIntElt -> SeqEnum
FldRe_Integral (Example H43E9)

integral

Derivative, Integral (MULTIVARIATE POLYNOMIAL RINGS)
Derivative, Integral (UNIVARIATE POLYNOMIAL RINGS)
Integral Points (ELLIPTIC CURVES)

integral_points

Integral and S-integral Points (ELLIPTIC CURVES)
Integral Points (ELLIPTIC CURVES)
S-integral Points (ELLIPTIC CURVES)

integral_points-integral

Integral Points (ELLIPTIC CURVES)

integral_points-sintegral

S-integral Points (ELLIPTIC CURVES)

IntegralBasis

IntegralBasis(F) : FldAlg -> [ FldAlgElt ]
IntegralBasis(Q) : FldRat -> [ FldRatElt ]
IntegralBasis(M) : ModSym -> Lat
ModSym_IntegralBasis (Example H88E8)

IntegralClosure

IntegralClosure(R, F) : Rng, FldFun -> RngFunOrd
IntegralClosure(R, F) : Rng, FldFun -> RngFunOrd

IntegralGroup

IntegralGroup(G) : GrpMat -> GrpMat, AlgMatElt

IntegralHeckeOperator

IntegralHeckeOperator(M, n) : ModSym, RngIntElt -> AlgMatElt

IntegralMapping

IntegralMapping(M) : ModSym -> Map

IntegralModel

IntegralModel(E) : CrvEll -> CrvEll, Map, Map
IntegralModel(C) : CrvHyp -> CrvHyp, MapCrvHyp

IntegralPoints

IntegralPoints(E) : CrvEll -> [ PtEll ], [ Tup ]
CrvEll_IntegralPoints (Example H85E20)

IntegralPointsSequence

CrvEll_IntegralPointsSequence (Example H85E21)

IntegralQuarticPoints

IntegralQuarticPoints(Q) : [ RngIntElt ] -> [ SeqEnum ]
IntegralQuarticPoints(Q, P) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]

IntegralSplit

IntegralSplit(a, O) : FldFunElt, RngFunOrd -> RngFunOrdElt, RngElt
IntegralSplit(a, O) : RngFunOrdElt, RngFunOrd -> RngFunOrdElt, RngElt
IntegralSplit(I) : RngFunOrdIdl -> RngFunOrdIdl, RngElt

integration

Integration (REAL AND COMPLEX FIELDS)

interactive

readi identifier, prompt;
Interactive Input (INPUT AND OUTPUT)
Using p-Quotient Interactively (FP GROUPS - ADVANCED FEATURES)

interactive-input

readi identifier, prompt;
Interactive Input (INPUT AND OUTPUT)

InteractiveUserAttributes

Func_InteractiveUserAttributes (Example H2E12)

Interior

Interior(P, C) : Plane, { PlanePt } -> { PlanePt }
IsInterior(N,p) : NwtnPgon,Tup -> BoolElt

Internal

InternalEdges(FS) : SymFry -> SeqEnum

internal

Internal Help Browser (ENVIRONMENT AND OPTIONS)

internal-help-browser

Internal Help Browser (ENVIRONMENT AND OPTIONS)

InternalEdges

InternalEdges(FS) : SymFry -> SeqEnum

Interpolate

RngMPol_Interpolate (Example H45E5)

Interpolation

Interpolation(I, V) : [ RngElt ], [ RngElt ] -> RngUPolElt
Interpolation(I, V, i) : [ RngElt ], [ RngMPolElt ], RngIntElt -> RngMPolElt
Interpolation(P, V, x) : [FldPrElt], [FldPrElt], FldPrElt -> FldPrElt, FldPrElt

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)

Intersect

IntersectKernels(SQP, SQR) : SQProc, SQProc -> SQProc, Map, Map

Intersection

GeodesicsIntersection(x,y) : [SpcHypElt],[SpcHypElt] -> SpcHypElt
Intersection(G,H) : GrpPSL2, GrpPSL2 -> GrpPSL2
IntersectionArray(G) : GrphUnd -> [RngIntElt]
IntersectionGroup(M1, M2) : ModSym, ModSym -> GrpAb
IntersectionGroup(S) : SeqEnum -> GrpAb
IntersectionMatrix(G, P) : GrphUnd, { { GrphVert } } -> AlgMatElt
IntersectionNumber(D, i, j) : Dsgn, RngIntElt, RngIntElt -> RngIntElt
IntersectionNumber(C,D,p) : Sch,Sch,Pt -> RngIntElt
IntersectionPairing(x, y) : ModSymElt, ModSymElt -> FldRatElt
IsIntersection(C,D,p) : Sch,Sch,Pt -> BoolElt
ModifyTransverseIntersection(~v,n) : GrphResVert,RngIntElt ->
L meet K : LinSys,LinSys -> LinSys
X meet Y : Sch,Sch -> Sch

intersection

Groups (OVERVIEW)
Intersection of Subalgebras (MATRIX ALGEBRAS)
Local Intersection Theory (PLANE ALGEBRAIC CURVES)
Sets (OVERVIEW)
Sum, Intersection and Dual (LINEAR CODES OVER FINITE FIELDS)
Sum, Intersection and Dual (LINEAR CODES OVER FINITE RINGS)

intersection_pairing

The Intersection Pairing (MODULAR SYMBOLS)

IntersectionArray

IntersectionArray(G) : GrphUnd -> [RngIntElt]

IntersectionGroup

IntersectionGroup(M1, M2) : ModSym, ModSym -> GrpAb
IntersectionGroup(S) : SeqEnum -> GrpAb

IntersectionMatrix

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

IntersectionNumber

IntersectionNumber(D, i, j) : Dsgn, RngIntElt, RngIntElt -> RngIntElt
IntersectionNumber(C,D,p) : Sch,Sch,Pt -> RngIntElt

IntersectionPairing

IntersectionPairing(x, y) : ModSymElt, ModSymElt -> FldRatElt
ModSym_IntersectionPairing (Example H88E18)

Intersections

CalculateTransverseIntersections(~g) : GrphRes ->
SelfIntersections(g) : GrphRes -> SeqEnum
TransverseIntersections(g) : GrphRes -> SeqEnum

IntersectKernels

IntersectKernels(SQP, SQR) : SQProc, SQProc -> SQProc, Map, Map

Intrinsic

IsIntrinsic(S) : MonStgElt -> Bool, Intrinsic

intrinsic

Intrinsics (FUNCTIONS, PROCEDURES AND PACKAGES)
Intrinsics (OVERVIEW)
Func_intrinsic (Example H2E6)

intro

Ambient Spaces (SCHEMES)
Aside: Types of Schemes (SCHEMES)
Choosing Coordinates (PLANE ALGEBRAIC CURVES)
Function Fields and Divisors (PLANE ALGEBRAIC CURVES)
Introduction (INPUT AND OUTPUT)
Linear Systems (SCHEMES)
Maps (SCHEMES)
Points (PLANE ALGEBRAIC CURVES)
Points (SCHEMES)
Projective Closure (PLANE ALGEBRAIC CURVES)
Projective Closure (SCHEMES)
Schemes (SCHEMES)

intro-ambient

Ambient Spaces (SCHEMES)

intro-closure

Projective Closure (PLANE ALGEBRAIC CURVES)
Projective Closure (SCHEMES)

intro-coords

Choosing Coordinates (PLANE ALGEBRAIC CURVES)
Function Fields and Divisors (PLANE ALGEBRAIC CURVES)

intro-linsys

Linear Systems (SCHEMES)

intro-map

Maps (SCHEMES)

intro-point

Points (PLANE ALGEBRAIC CURVES)

intro-points

Points (SCHEMES)

intro-schemes

Schemes (SCHEMES)

intro-types

Aside: Types of Schemes (SCHEMES)

introduction

Basics (MODULAR SYMBOLS)
Introduction (ABELIAN GROUPS)
Introduction (AFFINE ALGEBRAS)
Introduction (ALGEBRAIC FUNCTION FIELDS)
Introduction (ALGEBRAICALLY CLOSED FIELDS)
Introduction (ALGEBRAS)
Introduction (ASSOCIATIVE ALGEBRAS)
Introduction (AUTOMATIC GROUPS)
Introduction (AUTOMORPHISM GROUPS OF GROUPS)
Introduction (BASIC ALGEBRAS)
Introduction (BINARY QUADRATIC FORMS)
Introduction (COPRODUCTS)
Introduction (COXETER GROUPS)
Introduction (CYCLOTOMIC FIELDS)
Introduction (DATABASES OF GROUPS)
Introduction (ELLIPTIC CURVES)
Introduction (ENUMERATIVE COMBINATORICS)
Introduction (ENVIRONMENT AND OPTIONS)
Introduction (FINITE FIELDS)
Introduction (FINITE PLANES)
Introduction (FINITE SOLUBLE GROUPS)
Introduction (FINITELY PRESENTED ALGEBRAS)
Introduction (FINITELY PRESENTED GROUPS)
Introduction (FINITELY PRESENTED GROUPS)
Introduction (FINITELY PRESENTED SEMIGROUPS)
Introduction (FP GROUPS - ADVANCED FEATURES)
Introduction (FP GROUPS - ADVANCED FEATURES)
Introduction (FP GROUPS - ADVANCED FEATURES)
Introduction (FREE MODULES)
Introduction (FUNCTIONS, PROCEDURES AND PACKAGES)
Introduction (FUNCTIONS, PROCEDURES AND PACKAGES)
Introduction (GALOIS RINGS)
Introduction (GENERIC ABELIAN GROUPS)
Introduction (GRAPHS)
Introduction (GROUP ALGEBRAS)
Introduction (GROUPS DEFINED BY REWRITE SYSTEMS)
Introduction (GROUPS OF LIE TYPE)
Introduction (GROUPS WHOSE ELEMENTS ARE STRAIGHT-LINE PROGRAMS)
Introduction (GROUPS)
Introduction (HYPERELLIPTIC CURVES)
Introduction (IDEAL THEORY AND GRÖBNER BASES)
Introduction (INCIDENCE GEOMETRY)
Introduction (INCIDENCE STRUCTURES AND DESIGNS)
Introduction (INVARIANT RINGS OF FINITE GROUPS)
Introduction (LATTICES)
Introduction (LIE ALGEBRAS)
Introduction (LINEAR CODES OVER FINITE FIELDS)
Introduction (LINEAR CODES OVER FINITE FIELDS)
Introduction (LINEAR CODES OVER FINITE FIELDS)
Introduction (LINEAR CODES OVER FINITE RINGS)
Introduction (LINEAR PROGRAMMING)
Introduction (LISTS)
Introduction (LOCAL RINGS AND FIELDS)
Introduction (MAGMA SEMANTICS)
Introduction (MAPPINGS)
Introduction (MATRICES)
Introduction (MATRIX ALGEBRAS)
Introduction (MATRIX GROUPS)
Introduction (MATRIX GROUPS)
Introduction (MATRIX GROUPS)
Introduction (MODULAR CURVES)
Introduction (MODULAR FORMS)
Introduction (MODULAR SYMBOLS)
Introduction (MODULES OVER A MATRIX ALGEBRA)
Introduction (MODULES OVER AFFINE ALGEBRAS)
Introduction (MODULES OVER ORDERS)
Introduction (MONOIDS GIVEN BY REWRITE SYSTEMS)
Introduction (MULTIVARIATE POLYNOMIAL RINGS)
Introduction (NEWTON POLYGONS)
Introduction (ORDERS AND ALGEBRAIC FIELDS)
Introduction (p-ADIC RINGS AND FIELDS)
Introduction (p-GROUPS)
Introduction (PERMUTATION GROUPS)
Introduction (POLYCYCLIC GROUPS)
Introduction (POLYCYCLIC GROUPS)
Introduction (POWER, LAURENT AND PUISEUX SERIES)
Introduction (PSEUDO-RANDOM BIT SEQUENCES)
Introduction (QUADRATIC FIELDS)
Introduction (QUATERNION ALGEBRAS)
Introduction (RATIONAL CURVES AND CONICS)
Introduction (RATIONAL FIELD)
Introduction (RATIONAL FUNCTION FIELDS)
Introduction (REAL AND COMPLEX FIELDS)
Introduction (RECORDS)
Introduction (REFLECTION GROUPS)
Introduction (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Introduction (RING OF INTEGERS)
Introduction (ROOT DATA FOR LIE THEORY)
Introduction (SEQUENCES)
Introduction (SETS)
Introduction (STATEMENTS AND EXPRESSIONS)
Introduction (STRUCTURE CONSTANT ALGEBRAS)
Introduction (SUBGROUPS OF PSL_2(R))
Introduction (THE K3 DATABASE)
Introduction (TUPLES AND CARTESIAN PRODUCTS)
Introduction (UNIVARIATE POLYNOMIAL RINGS)
Introduction (VALUATION RINGS)
Introduction (VECTOR SPACES)
Introduction and First Examples (SCHEMES)
Overview (OVERVIEW)

Intseq

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

invar

Class Invariants (BINARY QUADRATIC FORMS)
Elliptic and Modular Invariants (BINARY QUADRATIC FORMS)
Invariants of an Algebra (ALGEBRAS)
Plane_invar (Example H95E6)

Invariant

HasseWittInvariant(F) : FldFunG -> RngIntElt
HasseWittInvariant(F) : FldFunG -> RngIntElt
InvariantFactors(a) : AlgMatElt -> [ AlgPolElt ]
InvariantFactors(A) : Mtrx -> [ RngUPolElt ]
InvariantForms(G) : GrpMat -> [ AlgMatElt ]
InvariantForms(G, n) : GrpMat, RngIntElt -> [ AlgMatElt ]
InvariantRing(G) : GrpMat -> RngInvar
IsInvariant(f, G) : RngMPolElt, Grp -> BoolElt
IsInvariant(f, g) : RngMPolElt, GrpElt -> BoolElt
NumberOfInvariantForms(G) : GrpMat -> RngIntElt, RngIntElt
PrimaryInvariantFactors(a) : AlgMatElt -> [ <RngUPolElt, RngIntElt ]
PrimaryInvariantFactors(A) : Mtrx -> [ <RngUPolElt, RngIntElt> ]
TestNautyInvariant(G: parameters) : Grph -> BoolElt

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 (ORDERS AND ALGEBRAIC FIELDS)
Invariants (ORDERS AND ALGEBRAIC FIELDS)
Invariants (POWER, LAURENT AND PUISEUX 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 (GALOIS RINGS)
Numerical Invariants (INTRODUCTION [BASIC RINGS])
Numerical Invariants (MULTIVARIATE POLYNOMIAL RINGS)
Numerical Invariants (RATIONAL FIELD)
Numerical Invariants (REAL AND COMPLEX FIELDS)
Numerical Invariants (RING OF INTEGERS)
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(A) : Mtrx -> [ RngUPolElt ]

InvariantForms

InvariantForms(G) : GrpMat -> [ AlgMatElt ]
InvariantForms(G, n) : GrpMat, RngIntElt -> [ AlgMatElt ]

InvariantRing

InvariantRing(G) : GrpMat -> RngInvar

Invariants

Elementary Invariants (BRANDT MODULES)
AbelianInvariants(G) : GrpFin -> [ RngIntElt ]
AbelianInvariants(G) : GrpMat -> [ RngIntElt ]
AbelianInvariants(G) : GrpPC -> [RngIntElt]
AbelianQuotientInvariants(G) : GrpFP -> [ RngIntElt ]
AbelianQuotientInvariants(G, n) : GrpFP, RngIntElt -> [ RngIntElt ]
AbelianQuotientInvariants(H) : GrpFP -> [ RngIntElt ]
AbelianQuotientInvariants(H, n) : GrpFP, RngIntElt -> [ RngIntElt ]
AbelianQuotientInvariants(G) : GrpGPC -> [ RngIntElt ]
AbelianQuotientInvariants(G) : GrpPC -> SeqEnum
AbsoluteInvariants(C) : CrvHyp -> SeqEnum
ClassGroupAbelianInvariants(F : parameters) : FldFun -> SeqEnum
ClassGroupAbelianInvariants(F : parameters) : FldFun -> SeqEnum
ClassGroupAbelianInvariants(O) : RngFunOrd -> SeqEnum
ClebschInvariants(C) : CrvHyp -> SeqEnum
ClebschInvariants(f) : RngUPolElt -> SeqEnum
FundamentalInvariants(R) : RngInvar -> [ RngMPolElt ]
IgusaClebschInvariants(C: parameters) : CrvHyp -> SeqEnum
IgusaClebschInvariants(f: parameters) : RngUPolElt -> SeqEnum
IgusaClebschInvariants(h, f) : RngUPolElt, RngUPolElt -> SeqEnum
IgusaInvariants(f: parameters) : RngUPolElt -> SeqEnum
IgusaInvariants(C: parameters): CrvHyp -> SeqEnum
IgusaInvariants(h, f): RngUPolElt, RngUPolElt -> SeqEnum
Invariants(A) : GrpAb -> [ RngIntElt ]
Invariants(A) : GrpAbGen -> [ RngIntElt ]
InvariantsOfDegree(R, d) : RngInvar, RngIntElt -> [ RngMPolElt ]
InvariantsOfDegree(R, d, k) : RngInvar, RngIntElt, RngIntElt -> [ RngMPolElt ]
IrreducibleSecondaryInvariants(R) : RngInvar -> [ RngMPolElt ]
R`PrimaryInvariants
PrimaryInvariants(A) : GrpAb -> [ RngIntElt ]
PrimaryInvariants(R) : RngInvar -> [ RngMPolElt ]
SClassGroupAbelianInvariants(S) : SetEnum[PlcFunElt] -> SeqEnum
ScaledIgusaInvariants(f): RngUPolElt -> SeqEnum
ScaledIgusaInvariants(h, f): RngUPolElt, RngUPolElt -> SeqEnum
R`SecondaryInvariants
SecondaryInvariants(R) : RngInvar -> [ RngMPolElt ]
SecondaryInvariants(R, H) : RngInvar, Grp -> [ RngMPolElt ]
SetAllInvariantsOfDegree(R, d, Q) : RngInvar, RngIntElt, [ RngMPolElt ] ->
TorsionInvariants(A) : GrpAb -> [ RngIntElt ]
pPrimaryInvariants(A, p) : GrpAb, RngIntElt -> [ RngIntElt ]
AlgMat_Invariants (Example H72E3)
CrvEll_Invariants (Example H85E29)
CrvEll_Invariants (Example H85E5)
GrpMat_Invariants (Example H21E12)

invariants

nauty Invariants (GRAPHS)
Basic Invariants (BINARY QUADRATIC FORMS)
Basic Invariants (PLANE ALGEBRAIC CURVES)
Basic Numerical Invariants (LINEAR CODES OVER FINITE FIELDS)
Construction of Invariants of Specified Degree (INVARIANT RINGS OF FINITE GROUPS)
Elementary Invariants (ELLIPTIC CURVES)
Elementary Invariants (LOCAL RINGS AND FIELDS)
Elementary Invariants (p-ADIC RINGS AND FIELDS)
Invariants of Isomorphisms (HYPERELLIPTIC CURVES)
Numerical Invariants (FINITE SOLUBLE GROUPS)

invariants-isomorphisms

Invariants of Isomorphisms (HYPERELLIPTIC CURVES)

InvariantsOfDegree

InvariantsOfDegree(R, d) : RngInvar, RngIntElt -> [ RngMPolElt ]
InvariantsOfDegree(R, d, k) : RngInvar, RngIntElt, RngIntElt -> [ RngMPolElt ]
RngInvar_InvariantsOfDegree (Example H78E3)
RngInvar_InvariantsOfDegree (Example H78E4)

invblock

Inverse Block: invblock (IDEAL THEORY AND GRÖBNER BASES)

Inverse

Inverse(w) : GrpAtcElt -> GrpAtcElt
Inverse( F, w ) : GrpFP, GrpFPElt -> GrpFPElt
Inverse( g ) : GrpLieElt -> GrpLieElt
Inverse(w) : GrpRWSElt -> GrpRWSElt
Inverse(f) : MapCrvHyp -> MapCrvHyp
Inverse(f) : MapSch -> MapSch
InverseDefiningEquations(f) : MapSch -> SeqEnum
InverseKrawchouk(A, K, n) : RngUPolElt, FldFin, RngIntElt -> RngUPolElt
InverseMattsonSolomonTransform(A, n) : RngUPolElt, RngIntElt -> RngUPolElt
InverseMod(E, M) : RngOrdElt, RngIntElt -> RngOrdElt
InverseWordMap(G) : GrpMat -> Map
InverseWordMap(G) : GrpPerm -> Map
Modinv(n, m) : RngIntElt, RngIntElt -> RngIntElt

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)

InverseDefiningEquations

InverseDefiningEquations(f) : MapSch -> SeqEnum

InverseKrawchouk

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

InverseMattsonSolomonTransform

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

InverseMod

Modinv(E, M) : RngOrdElt, RngOrdIdl -> RngOrdElt
InverseMod(E, M) : RngOrdElt, RngIntElt -> RngOrdElt
Modinv(n, m) : RngIntElt, RngIntElt -> RngIntElt

InverseWordMap

InverseWordMap(G) : GrpMat -> Map
InverseWordMap(G) : GrpPerm -> Map

Invertible

IsInvertible(I) : RngFunOrdIdl -> BoolElt

invocation

Functions (OVERVIEW)
Functions, Procedures, and Mappings (OVERVIEW)

Involution

Involution(P) : PtHyp -> PtHyp
- P : PtHyp -> PtHyp
CanonicalInvolution(X) : CrvMod -> MapSch
DualStarInvolution(M) : ModSym -> AlgMatElt
Involution(a) : AlgGrpElt -> AlgGrpElt
StarInvolution(M) : ModSym -> AlgMatElt

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

AbsolutelyIrreducibleModule(M) : ModRng -> ModRng
AbsolutelyIrreducibleRepresentations(G, k: parameters) : GrpPC, Rng -> List[Map]
AllIrreduciblePolynomials(F, m) : FldFin, RngIntElt -> { RngPolElt }
IrreducibleModule(B, i) : AlgBas, RngIntElt -> ModAlg
IrreduciblePolynomial(F, m) : FldFin, RngIntElt -> RngPolElt
IrreducibleRepresentations(G, k: parameters) : GrpPC, Rng -> List[Map]
IrreducibleSecondaryInvariants(R) : RngInvar -> [ RngMPolElt ]
IsAbsolutelyIrreducible(G) : GrpMat -> BoolElt
IsAbsolutelyIrreducible(M) : ModRng -> BoolElt, AlgMatElt, RngIntElt
IsAnalyticallyIrreducible(p) : Crv,Pt -> BoolElt
IsCartanIrreducible( C ) : AlgMatElt -> BoolElt
IsIrreducible(x) : AlgChtrElt -> BoolElt
IsIrreducible( W ) : GrpCox -> BoolElt
IsIrreducible(G) : GrpMat -> BoolElt, ModGrp
IsIrreducible(M) : ModRng -> BoolElt, ModRng, ModRng
IsIrreducible(M) : ModSym -> BoolElt
IsIrreducible(x) : RngElt -> BoolElt
IsIrreducible(f) : RngMPolElt -> BoolElt
IsIrreducible(f) : RngUPolElt -> BoolElt
IsIrreducible(g) : RngUPolElt -> BoolElt
IsIrreducible(g) : RngUPolElt -> BoolElt
IsIrreducible( RD ) : RootDtm -> BoolElt
IsIrreducible(C) : Sch -> BoolElt
IsIrreducible(X) : Sch -> BoolElt

irreducible

Database of Irreducible Soluble Subgroups of GL(n,p) for n > 1 and p^n < 256 (OVERVIEW)
Irreducible Modules (FP GROUPS - ADVANCED FEATURES)
The Table of Irreducible Characters (CHARACTERS OF FINITE GROUPS)

irreducible-modules

Irreducible Modules (FP GROUPS - ADVANCED FEATURES)

IrreducibleModule

SimpleModule(B, i) : AlgBas, RngIntElt -> ModAlg
IrreducibleModule(B, i) : AlgBas, RngIntElt -> ModAlg

IrreducibleModules

IrreducibleModules(G, k: parameters) : GrpPC, Rng -> List[GModule]
IrreducibleRepresentations(G, k: parameters) : GrpPC, Rng -> List[Map]

IrreduciblePolynomial

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

IrreducibleRepresentations

IrreducibleModules(G, k: parameters) : GrpPC, Rng -> List[GModule]
IrreducibleRepresentations(G, k: parameters) : GrpPC, Rng -> List[Map]

Irreducibles

KnownIrreducibles(R) : AlgChtr -> SeqEnum
RemoveIrreducibles(I, C) : [ AlgChtrElt ], [ AlgChtrElt ] -> [ AlgChtrElt ], [ AlgChtrElt ]

irreducibles

Finding Irreducibles (CHARACTERS OF FINITE GROUPS)

IrreducibleSecondaryInvariants

IrreducibleSecondaryInvariants(R) : RngInvar -> [ RngMPolElt ]

Irregular

HasIrregularFibres(s) : GrphSpl -> BoolElt

is

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

ISA

ISA(T, U) : Cat, Cat -> BoolElt

IsAbelian

IsAbelian(F) : FldAlg -> BoolElt
IsAbelian(G) : GrpAb -> BoolElt
IsAbelian(G) : GrpFin -> BoolElt
IsAbelian(G) : GrpGPC -> BoolElt
IsAbelian(G) : GrpMat -> BoolElt
IsAbelian(G) : GrpPC -> BoolElt
IsAbelian(G) : GrpPerm -> BoolElt

IsAbsoluteField

IsAbsoluteField(K) : FldAlg -> BoolElt

IsAbsolutelyIrreducible

IsAbsolutelyIrreducible(G) : GrpMat -> BoolElt
IsAbsolutelyIrreducible(M) : ModRng -> BoolElt, AlgMatElt, RngIntElt

IsAbsoluteOrder

IsAbsoluteOrder(O) : RngOrd -> BoolElt

IsAdjoint

IsAdjoint( G ) : GrpLie-> BoolElt
IsAdjoint( RD ) : RootDtm-> BoolElt

IsAffine

IsAffine(X) : Sch -> BoolElt

IsAffineLinear

IsAffineLinear(f) : MapSch -> BoolElt

IsAffineSpace

IsAffineSpace(X) : Sch -> BoolElt

IsAlgebraicallyIsomorphic

IsAlgebraicallyIsomorphic( G, H ) : GrpLie, GrpLie -> BoolElt

IsAlgebraicGeometric

IsAlgebraicGeometric(C) : Code -> BoolElt

IsAlternating

IsAlternating(G) : GrpPerm -> BoolElt

IsAltsym

IsAltsym(G) : GrpPerm -> BoolElt

IsAmbient

IsAmbient(M) : ModBrdt -> BoolElt

IsAmbientFunction

IsAmbientFunction(A,f) : Sch,RngElt -> BoolElt, RngElt

IsAmbientRationalFunction

IsAmbientRationalFunction(A,f) : Sch,RngElt -> BoolElt

IsAmbientSpace

IsAmbientSpace(M) : ModFrm -> BoolElt

IsAnalyticallyIrreducible

IsAnalyticallyIrreducible(p) : Crv,Pt -> BoolElt

IsArc

IsArc(P, A) : Plane, { PlanePt } -> BoolElt

IsArcTransitive

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

IsAssociative

IsAssociative(A) : AlgGen -> BoolElt

IsAutomorphism

IsAutomorphism(f) : MapSch -> BoolElt,AutSch

IsBalanced

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

IsBasePointFree

IsFree(L) : LinSys -> BoolElt
IsBasePointFree(L) : LinSys -> BoolElt

IsBijective

IsBijective(a) : ModMatRngElt -> BoolElt

IsBipartite

IsBipartite(G) : GrphUnd -> BoolElt

IsBlock

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

IsBlockTransitive

IsBlockTransitive(D) : Inc -> BoolElt

IsBoundary

IsBoundary(N, p) : NwtnPgon,Tup -> BoolElt

IsCanonical

IsCanonical(D) : DivCrvElt -> BoolElt,DiffFunElt
IsCanonical(D) : DivFunElt -> BoolElt, DiffFunElt
IsCanonical(D) : DivFunElt -> BoolElt, DiffFunElt

IsCartanIrreducible

IsCartanIrreducible( C ) : AlgMatElt -> BoolElt

IsCartanMatrix

IsCartanMatrix( M ) : AlgMatElt -> BoolElt

IsCentral

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

IsChainMap

IsChainMap(L, C, D, n) : List, ModCpx, ModCpx, RngIntElt -> BoolElt
IsChainMap(f) : MapChn -> BoolElt

IsCharacter

IsCharacter(x) : AlgChtrElt -> BoolElt

IsCluster

IsCluster(X) : Sch -> BoolElt,Clstr

IsCoercible

IsCoercible(X,Q) : Sch,SeqEnum -> BoolElt,Pt
IsCoercible(S, x) : Str, Elt -> Bool, Elt

IsCohenMacaulay

IsCohenMacaulay(R) : RngInvar -> BoolElt

IsCollinear

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

IsCommutative

IsCommutative(A) : AlgGen -> BoolElt
IsCommutative(R) : Rng -> BoolElt

IsComplete

IsComplete(V) : GrpFPCos -> BoolElt
IsComplete(G) : Grph -> BoolElt
IsComplete(D) : Inc -> BoolElt
IsComplete(L) : LinSys -> BoolElt
IsComplete(P, A) : Plane, { PlanePt } -> BoolElt
IsComplete(S) : SeqEnum -> BoolElt

IsConcurrent

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

IsConditioned

IsConditioned(G) : GrpPC -> BoolElt

IsConfluent

IsConfluent(G) : GrpAtc -> BoolElt
IsConfluent(G) : GrpRWS -> BoolElt
IsConfluent(M) : MonRWS -> BoolElt
GrpAtc_IsConfluent (Example H31E7)
GrpRWS_IsConfluent (Example H30E7)
MonRWS_IsConfluent (Example H18E7)

IsCongruence

IsCongruence(G) : GrpPSL2 -> BoolElt

IsConic

IsConic(X) : Sch -> BoolElt, CrvCon
IsConic(X) : Sch -> BoolElt,CrvCon

IsConjugate

IsConjugate(G, H, K) : GrpAb, GrpAb, GrpAb -> BoolElt, GrpAbElt
IsConjugate(G, H, K) : GrpAb, GrpAb, GrpAb -> BoolElt, GrpAbElt
IsConjugate(G, g, h) : GrpAb, GrpAbElt, GrpAbElt -> BoolElt, GrpAbElt
IsConjugate(G, H, K) : GrpFin, GrpFin, GrpFin -> BoolElt, GrpFinElt
IsConjugate(G, H, K) : GrpFin, GrpFin, GrpFin -> BoolElt, GrpFinElt
IsConjugate(G, g, h) : GrpFin, GrpFinElt, GrpFinElt -> BoolElt, GrpFinElt
IsConjugate(G, g, h) : GrpFin, GrpFinElt, GrpFinElt -> BoolElt, GrpFinElt
IsConjugate(G, H, K) : GrpGPC, GrpGPC, GrpGPC -> BoolElt, GrpGPCElt
IsConjugate(G, H, K) : GrpGPC, GrpGPC, GrpGPC -> BoolElt, GrpGPCElt
IsConjugate(G, g, h) : GrpGPC, GrpGPCElt, GrpGPCElt -> BoolElt, GrpGPCElt
[Future release] IsConjugate(G, H, K) : GrpMat, GrpMat, GrpMat -> 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) : GrpPC, GrpPCElt, GrpPCElt -> BoolElt, GrpPCElt
IsConjugate(G, H, K) : GrpPerm, GrpPerm, GrpPerm -> BoolElt, GrpPermElt
IsConjugate(G, g, h) : GrpPerm, GrpPermElt, GrpPermElt -> BoolElt, GrpPermElt
IsConjugate(G, Y, y, z) : GrpPerm, GSet, Elt, Elt -> BoolElt, GrpPermElt
IsConjugate(G, H, K) : GrpFP, GrpFP, GrpFP -> BoolElt, GrpFPElt

IsConnected

IsConnected(G) : GrphUnd -> BoolElt

IsConsistent

IsConsistent(G) : GrpPC -> BoolElt
IsConsistent(G) : GrpGPC -> BoolElt
IsConsistent(A, w) : ModMatRngElt, ModTupRng -> BoolElt, ModTupRngElt, ModTupRng
IsConsistent(A, W) : ModMatRngElt, [ ModTupRng ] -> BoolElt, [ ModTupRngElt ], ModTupRng
IsConsistent(A, W) : Mtrx, Mtrx -> BoolElt, Mtrx, ModTupRng
IsConsistent(A, Q) : Mtrx, [ ModTupRng ] -> BoolElt, [ ModTupRngElt ], ModTupRng
GrpPC_IsConsistent (Example H25E3)

isconsistent

Possibly Inconsistent Presentations (FINITE SOLUBLE GROUPS)

IsConstant

IsConstant(x) : FldFunElt -> BoolElt, RngElt
IsConstant(a) : RngFunOrdElt -> BoolElt, RngElt
IsZero(I) : Map -> BoolElt

IsConway

IsConway(F) : FldFin -> BoolElt

IsCrystallographic

IsCrystallographic( C ) : AlgMatElt -> BoolElt
IsCrystallographic( W ) : GrpCox -> BoolElt
IsCrystallographic( RD ) : RootDtm -> BoolElt

IsCurve

IsCurve(X) : Sch -> BoolElt,Crv

IsCusp

IsCusp(p) : Crv,Pt -> BoolElt
IsCusp(z) : SpcHypElt -> BoolElt

IsCuspidal

IsCuspidal(M) : ModBrdt -> BoolElt
IsCuspidal(M) : ModFrm -> BoolElt
IsCuspidal(M) : ModSym -> BoolElt

IsCyclic

IsCyclic(C) : Code -> BoolElt
IsCyclic(C) : Code -> BoolElt
IsCyclic(G) : GrpAb -> BoolElt
IsCyclic(G) : GrpFin -> BoolElt
IsCyclic(G) : GrpGPC -> BoolElt
IsCyclic(G) : GrpMat -> BoolElt
IsCyclic(G) : GrpPC -> BoolElt
IsCyclic(G) : GrpPerm -> BoolElt

IsDecomposable

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

IsDeficient

IsDeficient(C, p) : CrvHyp, RngIntElt -> BoolElt

IsDefined

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

IsDefinite

IsDefinite(A) : AlgQuat -> BoolElt

IsDegenerate

[Future release] IsDegenerate(N) : NwtnPgon -> BoolElt
[Future release] IsDegenerate(F) : NwtnPgon,Tup -> BoolElt

IsDesarguesian

IsDesarguesian(P) : Plane -> BoolElt

IsDesign

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

IsDiagonal

IsDiagonal(a) : AlgMatElt -> BoolElt
IsDiagonal(A) : Mtrx -> BoolElt

IsDifferenceSet

IsDifferenceSet(B) : SetEnum -> BoolElt, RngIntElt

IsDirectSummand

IsDirectSummand(M, S) : ModGrp, ModGrp -> BoolElt, ModGrp
HasComplement(M, S) : ModGrp, ModGrp -> BoolElt, ModGrp

IsDiscriminant

IsDiscriminant(D) : RngIntElt -> BoolElt

IsDisjoint

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

IsDistanceRegular

IsDistanceRegular(G) : GrphUnd -> BoolElt

IsDistanceTransitive

IsDistanceTransitive(G : parameters) : GrphUnd -> BoolElt

IsDivisibleBy

IsDivisibleBy(a, b) : FldFunElt, FldFunElt -> BoolElt, FldFunElt
IsDivisibleBy(a, b) : RngFunOrdElt, RngFunOrdElt -> BoolElt, RngFunOrdElt
IsDivisibleBy(n, d) : RngIntElt, RngIntElt -> BoolElt, RngIntElt
IsDivisibleBy(a, b) : RngMPolElt, RngMPolElt -> BoolElt, RngMPolElt

IsDivisionRing

IsDivisionRing(R) : Rng -> BoolElt

IsDomain

IsIntegralDomain(R): Rng -> BoolElt
IsDomain(R) : Rng -> BoolElt

IsDominant

IsDominant(f) : AmbMap -> BoolElt

IsDoublePoint

IsDoublePoint(p) : Crv,Pt -> BoolElt

IsDoublyEven

IsDoublyEven(C) : Code -> BoolElt

IsEdgeTransitive

IsEdgeTransitive(G : parameters) : GrphUnd -> BoolElt

IsEffective

IsPositive(D) : DivCrvElt -> BoolElt
IsEffective(D) : DivCrvElt -> BoolElt

IsEisenstein

IsEisenstein(M) : ModBrdt -> BoolElt
IsEisenstein(M) : ModFrm -> BoolElt
IsEisenstein(M) : ModSym -> BoolElt
IsEisenstein(g) : RngUPolElt -> BoolElt

IsEisensteinSeries

IsEisensteinSeries(f) : ModFrmElt -> BoolElt
IsEisensteinSeries(f) : ModFrmElt -> BoolElt

IsElementaryAbelian

IsElementaryAbelian(G) : GrpAb -> BoolElt
IsElementaryAbelian(G) : GrpFin -> BoolElt
IsElementaryAbelian(G) : GrpGPC -> BoolElt
IsElementaryAbelian(G) : GrpMat -> BoolElt
IsElementaryAbelian(G) : GrpPC -> BoolElt
IsElementaryAbelian(G) : GrpPerm -> BoolElt

IsEllipticCurve

IsEllipticCurve(C) : CrvHyp -> BoolElt, CrvEll, Map
IsEllipticCurve(C) : CrvHyp -> BoolElt, CrvEll, Map, Map
IsEllipticCurve([a,b]) : [ RngElt ] -> BoolElt, CrvEll

IsEllipticWeierstrass

IsEllipticWeierstrass(C) : Crv -> BoolElt

IsEmpty

IsEmpty(G) : Grph -> BoolElt
IsEmpty(P) : LatEnumProc -> BoolElt
IsEmpty(S) : List -> BoolElt
IsEmpty (P) : Proc -> BoolElt
IsEmpty(p) : Process -> BoolElt
IsEmpty(p) : Process -> BoolElt
IsEmpty(p) : Process -> BoolElt
IsEmpty(P) : Process(Lix) -> BoolElt
IsEmpty(X) : Sch -> BoolElt
IsEmpty(S) : SeqEnum -> BoolElt
IsEmpty(R) : SetEnum -> BoolElt

IsEndomorphism

IsEndomorphism(f) : MapSch -> BoolElt

IsEof

IsEof(S) : MonStgElt -> BoolElt

IsEqual

IsEqual( F, w1, w2 ) : GrpFP, GrpFPElt, GrpFPElt -> BoolElt

IsEquationOrder

IsEquationOrder(O) : RngFunOrd -> BoolElt
IsEquationOrder(O) : RngOrd -> BoolElt

IsEquidistant

IsEquidistant(C) : Code -> BoolElt

IsEquitable

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

IsEquivalent

IsEquivalent(g,h,G) : GrpPSL2Elt, GrpPSL2Elt, GrpPSL2 -> BoolElt
IsEquivalent(C, D: parameters) : Code, Code -> BoolElt, Map
IsEquivalent(f, g) : QuadBinElt, QuadBinElt -> BoolElt, AlgMatElt
IsEquivalent(a,b,G) : SpcHypElt, SpcHypElt, GrpPSL2 -> BoolElt

Isetseq

Isetseq(S) : SetIndx -> SeqEnum
IndexedSetToSequence(S) : SetIndx -> SeqEnum

Isetset

Isetset(S) : SetIndx -> SetEnum
IndexedSetToSet(S) : SetIndx -> SetEnum

IsEuclideanDomain

IsEuclideanDomain(F) : FldAlg -> BoolElt
IsEuclideanDomain(R) : Rng -> BoolElt

IsEuclideanRing

IsEuclideanRing(R) : Rng -> BoolElt

IsEulerian

IsEulerian(G) : Grph -> BoolElt

IsEven

IsEven(C) : Code -> BoolElt
IsEven(x) : GrpDrchElt -> BoolElt
IsEven(g) : GrpPermElt -> BoolElt
IsEven(J) : JacHyp -> BoolElt
IsEven(L) : Lat -> BoolElt
IsEven(n) : RngIntElt -> BoolElt

IsExact

IsExact(a) : DiffFunElt -> BoolElt
IsExact(d) : DiffFunElt -> BoolElt, FldFunGElt
IsExact(L) : Lat -> BoolElt
IsExact(C) : ModComplex -> BoolElt
IsExact(C, n) : ModCpx, RngIntElt -> BoolElt
IsExact(z) : SpcHypElt -> BoolElt

IsExceptionalUnit

IsExceptionalUnit(u) : RngOrdElt -> BoolElt

IsExtension

IsExtension(G, H, f) : GrpPC, GrpPC, [Map] -> BoolElt, GrpPC

IsExtraSpecial

IsExtraSpecial(G) : GrpFin -> BoolElt
IsExtraSpecial(G) : GrpMat -> BoolElt
IsExtraSpecial(G) : GrpPC -> BoolElt
IsExtraSpecial(G) : GrpPerm -> BoolElt

IsExtraSpecialNormalise

IsExtraSpecialNormalise(G) : GrpMat -> BoolElt

IsFace

IsFace(N, F) : NwtnPgon,Tup -> BoolElt

IsFaithful

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

IsField

IsField(R) : Rng -> BoolElt

IsFinite

IsFinite(G) : GrpAb -> BoolElt
IsFinite(G) : GrpAtc -> BoolElt, RngIntElt
IsFinite(G) : GrpGPC -> BoolElt
IsFinite(G) : GrpMat -> Bool, RngIntElt
IsFinite(G) : GrpRWS -> BoolElt, RngIntElt
IsFinite(x) : Infty -> BoolElt
IsFinite(M) : MonRWS -> BoolElt, RngIntElt
IsFinite(P) : PlcFunElt -> BoolElt
IsFinite(R) : Rng -> BoolElt

IsFiniteOrder

IsFiniteOrder(O) : RngFunOrd -> BoolElt

IsFirm

IsFirm(C) : CosetGeom -> BoolElt
IsFirm(D) : IncGeom -> BoolElt

IsFlex

IsFlex(C,p) : Sch,Pt -> BoolElt,RngIntElt
IsInflectionPoint(p) : Sch,Pt -> BoolElt,RngIntElt

IsForest

IsForest(G) : GrphUnd -> BoolElt

IsFree

IsFree(L) : LinSys -> BoolElt
IsBasePointFree(L) : LinSys -> BoolElt

IsFrobenius

IsFrobenius(G) : GrpPerm -> BoolElt

IsFTGeometry

IsFTGeometry(C) : CosetGeom -> BoolElt
IsFTGeometry(D) : IncGeom -> BoolElt

IsFundamentalDiscriminant

IsFundamentalDiscriminant(D) : RngIntElt -> BoolElt

IsGamma0

IsGamma0(G) : GrpPSL2 -> BoolElt
IsGamma0(M) : ModFrm -> BoolElt

IsGamma1

IsGamma1(G) : GrpPSL2 -> BoolElt
IsGamma1(M) : ModFrm -> BoolElt

IsGeneralizedCharacter

IsGeneralizedCharacter(x) : AlgChtrElt -> BoolElt

IsGenus

IsGenus(G) : SymGen -> BoolElt

IsGL2Equivalent

IsGL2Equivalent(f, g, n) : RngUPolElt, RngUPolElt, RngIntElt -> BoolElt, SeqEnum

IsGLattice

IsGLattice(L) : Lat -> GrpMat

IsGlobal

IsGlobal(F) : FldFun -> BoolElt

IsGlobalUnit

IsGlobalUnit(a) : FldFunElt -> BoolElt
IsGlobalUnit(a) : FldFunElt -> BoolElt

IsGlobalUnitWithPreimage

IsGlobalUnitWithPreimage(a) : FldFunElt -> BoolElt, GrpAbElt
IsGlobalUnitWithPreimage(a) : FldFunElt -> BoolElt, GrpAbElt

IsGood

GrpPGp_IsGood (Example H26E3)

IsGroebner

IsGroebner(S) : { RngMPolElt } -> BoolElt

IsHadamard

IsHadamard(H) : AlgMatElt -> BoolElt

IsHadamardEquivalent

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

IsHomogeneous

IsHomogeneous(M) : ModMPol -> BoolElt
IsHomogeneous(I) : RngMPol -> BoolElt
IsHomogeneous(f) : RngMPolElt -> BoolElt
IsHomogeneous(X,f) : Sch,RngMPolElt -> BoolElt

IsHomomorphism

IsHomomorphism(G, H, Q) : GrpMat, GrpMat, SeqEnum[GrpMatElt] -> Bool, Map
IsHomomorphism(G, H, L) : GrpPC, GrpPC, SeqEnum -> BoolElt, Map
IsHomomorphism(G, H, Q) : GrpPerm, GrpPerm, SeqEnum[GrpPermElt] -> Bool, Map

IsHyperellipticCurve

IsHyperellipticCurve([h, g]) : [ RngUPolElt ] -> BoolElt, CrvHyp

IsHyperellipticCurveOfGenus

IsHyperellipticCurveOfGenus(g, [h, f]) : RngIntElt, [RngUPolElt] -> BoolElt, CrvHyp

IsHyperellipticWeierstrass

IsHyperellipticWeierstrass(C) : Crv -> BoolElt

IsHypersurface

IsHypersurface(X) : Sch -> BoolElt, RngMPolElt

IsId

IsIdentity(w) : GrpAtcElt -> BoolElt
IsId(w) : GrpAtcElt -> BoolElt
IsId(g) : GrpElt -> BoolElt
IsId(g) : GrpPermElt -> BoolElt
IsId(w) : GrpRWSElt -> BoolElt
IsId(w) : MonRWSElt -> BoolElt
IsId(P) : PtEll -> BoolElt
IsIdentity(u) : GrpAbElt -> BoolElt
IsIdentity(g) : GrpAbGenElt -> BoolElt
IsIdentity(g) : GrpGPCElt -> BoolElt
IsIdentity(g) : GrpMatElt -> BoolElt
IsIdentity(g) : GrpPCElt -> BoolElt

IsIdeal

IsIdeal(S) : AlgGrpSub -> BoolElt

IsIdempotent

IsIdempotent(a) : AlgGenElt -> BoolElt
IsIdempotent(x) : RngElt -> BoolElt

IsIdentical

IsIdentical(f, g) : RngSerElt, RngSerElt -> BoolElt

IsIdenticalPresentation

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

IsIdentity

IsIdentity(w) : GrpAtcElt -> BoolElt
IsId(w) : GrpAtcElt -> BoolElt
IsId(g) : GrpElt -> BoolElt
IsId(g) : GrpPermElt -> BoolElt
IsId(w) : GrpRWSElt -> BoolElt
IsId(w) : MonRWSElt -> BoolElt
IsId(P) : PtEll -> BoolElt
IsIdentity(u) : GrpAbElt -> BoolElt
IsIdentity(g) : GrpAbGenElt -> BoolElt
IsIdentity(g) : GrpGPCElt -> BoolElt
IsIdentity(g) : GrpMatElt -> BoolElt
IsIdentity(g) : GrpPCElt -> BoolElt
IsIdentity(f) : QuadBinElt -> BoolElt
IsZero(P) : JacHypPt -> BoolElt

IsIndecomposable

IsIndecomposable(M,B) : ModBrdt, RngIntElt -> BoolElt

IsIndefinite

IsIndefinite(A) : AlgQuat -> BoolElt

IsIndependent

IsIndependent(Q) : [ AlgGen ] -> BoolElt
IsIndependent(Q) : [ ModTupFldElt ] -> BoolElt
IsIndependent(S) : { ModTupFldElt } -> BoolElt

IsInert

IsInert(P) : RngOrdIdl -> BoolElt
IsInert(P, O) : RngOrdIdl, RngOrd -> BoolElt

IsInertial

IsInertial(g) : RngUPolElt -> BoolElt

IsInflectionPoint

IsFlex(C,p) : Sch,Pt -> BoolElt,RngIntElt
IsInflectionPoint(p) : Sch,Pt -> BoolElt,RngIntElt

IsInImage

IsInImage(f, p) : Map, RngMPolElt -> [ BoolElt ]

IsInjective

IsInjective(M) : ModAlg -> BoolElt, SeqEnum
IsInjective(a) : ModMatRngElt -> BoolElt
IsInjective(f) : MotMatCpxElt -> BoolElt

IsInner

IsInner(f) : GrpAutoElt -> BoolElt, GrpElt

IsInRadical

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

IsIntegral

IsIntegral(C) : CrvHyp -> BoolElt
IsIntegral(a) : FldAlgElt -> BoolElt
IsIntegral(c) : FldPrElt -> BoolElt
IsIntegral(q) : FldRatElt -> BoolElt
IsIntegral(L) : Lat -> BoolElt
IsIntegral(P) : PtEll -> BoolElt
IsIntegral(I) : RngFunOrdIdl -> BoolElt
IsIntegral(n) : RngIntElt -> BoolElt
IsIntegral(x) : RngLocElt -> BoolElt
IsIntegral(I) : RngOrdFracIdl -> BoolElt

IsIntegralDomain

IsIntegralDomain(R): Rng -> BoolElt
IsDomain(R) : Rng -> BoolElt

IsIntegralModel

IsIntegralModel(E) : CrvEll -> BoolElt

IsInterior

IsInterior(N,p) : NwtnPgon,Tup -> BoolElt

IsIntersection

IsIntersection(C,D,p) : Sch,Sch,Pt -> BoolElt

IsIntrinsic

IsIntrinsic(S) : MonStgElt -> Bool, Intrinsic
State_IsIntrinsic (Example H1E19)
State_IsIntrinsic (Example H1E20)

IsInvariant

IsInvariant(f, G) : RngMPolElt, Grp -> BoolElt
IsInvariant(f, g) : RngMPolElt, GrpElt -> BoolElt

IsInvertible

IsInvertible(I) : RngFunOrdIdl -> BoolElt

IsIrreducible

IsIrreducible(x) : AlgChtrElt -> BoolElt
IsIrreducible( W ) : GrpCox -> BoolElt
IsIrreducible(G) : GrpMat -> BoolElt, ModGrp
IsIrreducible(M) : ModRng -> BoolElt, ModRng, ModRng
IsIrreducible(M) : ModSym -> BoolElt
IsIrreducible(x) : RngElt -> BoolElt
IsIrreducible(f) : RngMPolElt -> BoolElt
IsIrreducible(f) : RngUPolElt -> BoolElt
IsIrreducible(g) : RngUPolElt -> BoolElt
IsIrreducible(g) : RngUPolElt -> BoolElt
IsIrreducible( RD ) : RootDtm -> BoolElt
IsIrreducible(C) : Sch -> BoolElt
IsIrreducible(X) : Sch -> BoolElt

IsIsogenous

IsIsogenous(E, F) : CrvEll, CrvEll -> BoolElt
IsIsogenous( G, H ) : GrpLie, GrpLie -> BoolElt
IsIsogenous( RD1, RD2 ) : RootDtm, RootDtm -> BoolElt

IsIsometric

IsIsomorphic(L, M) : Lat, Lat -> BoolElt, AlgMatElt
IsIsometric(L, M) : Lat, Lat -> BoolElt, AlgMatElt
IsIsometric(L, F_1, M, F()_2) : Lat, [ AlgMatElt ], Lat, [ AlgMatElt ] -> BoolElt, AlgMatElt
IsIsometric(F_1, F()_2) : [ AlgMatElt ], [ AlgMatElt ] -> BoolElt, AlgMatElt

IsIsomorphic

IsIsomorphic(L, M) : Lat, Lat -> BoolElt, AlgMatElt
IsIsometric(L, M) : Lat, Lat -> BoolElt, AlgMatElt
IsIsometric(L, F_1, M, F()_2) : Lat, [ AlgMatElt ], Lat, [ AlgMatElt ] -> BoolElt, AlgMatElt
IsIsometric(F_1, F()_2) : [ AlgMatElt ], [ AlgMatElt ] -> BoolElt, AlgMatElt
IsIsomorphic(I,J) : AlgQuatOrd, AlgQuatOrd -> BoolElt
IsIsomorphic(E, F) : CrvEll, CrvEll -> BoolElt, Map
IsIsomorphic(C1, C2) : CrvHyp, CrvHyp -> BoolElt, MapCrvHyp
IsIsomorphic(F, L) : FldAlg, FldAlg -> BoolElt, Map
IsIsomorphic(G, H) : GrpPC, GrpPC -> BoolElt, Map
IsIsomorphic(M, N) : ModRng, ModRng -> BoolElt, AlgMatElt
IsIsomorphic(G, H : parameters ) : GrphDir, GrphDir -> BoolElt, Map
IsIsomorphic(C, D: parameters) : Code, Code -> BoolElt, Map
IsIsomorphic(G, H: parameters) : GrpPerm, GrpPerm -> BoolElt, Hom(Grp)
IsIsomorphic(D, E: parameters) : Inc, Inc -> BoolElt, Map
IsIsomorphic(P, Q: parameters) : Plane, Plane -> BoolElt, Map
IsIsomorphic( RD1, RD2 ) : RootDtm, RootDtm -> BoolElt

IsIsomorphism

IsIsomorphism(I) : Map -> BoolElt, Map
IsIsomorphism(f) : MapSch -> BoolElt, IsoSch
IsIsomorphism(f) : MotMatCpxElt -> BoolElt

IsLabelled

IsLabelled(t) : GrphVert -> BoolElt

IsLabelledEdge

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

IsLabelledVertex

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

IsLeftIdeal

IsLeftIdeal(S) : AlgGrpSub -> BoolElt

IsLeftIsomorphic

IsLeftIsomorphic(I,J) : AlgQuatOrd, AlgQuatOrd -> BoolElt, Map, AlgQuatElt

IsLie

IsLie(A) : AlgGen -> BoolElt

IsLinear

IsLinear(x) : AlgChtrElt -> BoolElt
IsLinear(f) : MapSch -> BoolElt

IsLinearGroup

IsLinearGroup(G) : GrpMat -> BoolElt

IsLinearlyEquivalent

IsLinearlyEquivalent(D1,D2) : DivCrvElt,DivCrvElt -> BoolElt

IsLinearlyIndependent

IsLinearlyIndependent(P, Q) : PtEll, PtEll -> BoolElt, ModTupElt
IsLinearlyIndependent(P, Q, n) : PtEll, PtEll, RngIntElt -> BoolElt
IsLinearlyIndependent(S) : [ PtEll ] -> BoolElt, ModTupElt
IsLinearlyIndependent(S, n) : [ PtEll ], RngIntElt -> BoolElt

IsLinearSpace

IsLinearSpace(D) : Inc -> BoolElt

IsLineRegular

IsLineRegular(D) : IncNsp -> BoolElt, RngIntElt

IsLineTransitive

IsLineTransitive(P) : Plane -> BoolElt

IsLittleWoodRichardsonSkew

IsLittleWoodRichardsonSkew(t) : Tableau -> BoolElt

IsLongRoot

IsLongRoot( RD, r ) : RootDtm, RngIntElt -> BoolElt

IsMaximal

IsMaximal(G, H) : GrpAb, GrpAb -> BoolElt
IsMaximal(G, H) : GrpFin, GrpFin -> BoolElt
IsMaximal(G, H) : GrpMat, GrpMat -> BoolElt
IsMaximal(G, H) : GrpPC, GrpPC -> BoolElt
IsMaximal(G, H) : GrpPerm, GrpPerm -> BoolElt
IsMaximal(G, H) : GrpFP, GrpFP -> BoolElt
IsMaximal(O) : RngFunOrd -> BoolElt
IsMaximal(I) : RngMPol -> BoolElt
IsMaximal(O) : RngOrd -> BoolElt

IsMaximisingFunction

IsMaximisingFunction(L) : LP -> BoolElt

IsMaximumDistanceSeparable

IsMDS(C) : Code -> BoolElt
IsMaximumDistanceSeparable(C) : Code -> BoolElt

IsMDS

IsMDS(C) : Code -> BoolElt
IsMaximumDistanceSeparable(C) : Code -> BoolElt

IsMemberBasicOrbit

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

IsMinimalModel

IsMinimalModel(E) : CrvEll -> BoolElt

IsMinusOne

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

IsModuleHomomorphism

IsModuleHomomorphism(X) : ModMatElt -> BoolElt
IsModuleHomomorphism(f) : ModMatFldElt -> BoolElt

IsNearLinearSpace

IsNearLinearSpace(D) : Inc -> BoolElt

IsNearlyPerfect

IsNearlyPerfect(C) : Code -> BoolElt

IsNegative

IsNegative( RD, r ) : RootDtm, RngIntElt -> BoolElt

IsNegativeDefinite

IsNegativeDefinite(F) : ModMatRngElt -> BoolElt

IsNegativeSemiDefinite

IsNegativeSemiDefinite(F) : ModMatRngElt -> BoolElt

IsNew

IsNew(M) : ModFrm -> BoolElt
IsNew(M) : ModSym -> BoolElt

IsNewform

IsNewform(f) : ModFrmElt -> BoolElt

IsNilpotent

IsNilpotent(a) : AlgGenElt -> BoolElt, RngIntElt
IsNilpotent(L) : AlgLie -> BoolElt
IsNilpotent(G) : GrpAb -> BoolElt
IsNilpotent(G) : GrpFin -> BoolElt
IsNilpotent(G) : GrpGPC -> BoolElt
IsNilpotent(G) : GrpMat -> BoolElt
IsNilpotent(G) : GrpPC -> BoolElt
IsNilpotent(G) : GrpPerm -> BoolElt
IsNilpotent(x) : RngElt -> BoolElt
IsNilpotent(f) : RngMPolResElt -> BoolElt, RngIntElt

IsNode

IsNode(p) : Crv,Pt -> BoolElt

IsNonsingular

IsNonsingular(C) : Sch -> BoolElt
IsNonsingular(X) : Sch -> BoolElt
IsNonsingular(p) : Sch,Pt -> BoolElt
IsNonsingular(p) : Sch,Pt -> BoolElt

IsNormal

IsNormal(F) : FldAlg -> BoolElt
IsNormal(a) : FldFinElt -> BoolElt
IsNormal(a, E) : FldFinElt -> BoolElt
IsNormal(G, H) : GrpAb, GrpAb -> BoolElt
IsNormal(G, H) : GrpFin, GrpFin -> BoolElt
IsNormal(G, H) : GrpGPC, GrpGPC -> BoolElt
IsNormal(G, H) : GrpMat, GrpMat -> BoolElt
IsNormal(G, H) : GrpPC, GrpPC -> BoolElt
IsNormal(G, H) : GrpPerm, GrpPerm -> BoolElt
IsNormal(G, H) : GrpFP, GrpFP -> BoolElt

IsNormalising

IsNormalising( G ) : GrpLie -> BoolElt

IsNull

IsNull(S) : SeqEnum -> BoolElt
IsNull(R) : SetEnum -> BoolElt

iso

iso< A -> B | L> : Grp, Grp, List -> Map
hom< A -> B | L> : Grp, Grp, List -> Map
iso< X -> Y | F, G > : Sch,Sch,SeqEnum,SeqEnum -> MapAutSch

IsOdd

IsOdd(x) : GrpDrchElt -> BoolElt
IsOdd(n) : RngIntElt -> BoolElt

Isogenies

IsogeniesAreEqual(I, J) : Map, Map -> BoolElt

IsogeniesAreEqual

IsogeniesAreEqual(I, J) : Map, Map -> BoolElt

Isogenous

IsIsogenous(E, F) : CrvEll, CrvEll -> BoolElt
IsIsogenous( G, H ) : GrpLie, GrpLie -> BoolElt
IsIsogenous( RD1, RD2 ) : RootDtm, RootDtm -> BoolElt

Isogeny

IdentityIsogeny(E) : CrvEll -> Map
Isogeny(E,P) : CrvEll, Pt) -> MapCrvEll
IsogenyFromKernel(E, psi) : CrvEll, RngUPolElt -> CrvEll, Map
IsogenyFromKernel(G) : CrvEllSubgroup -> CrvEll, Map
IsogenyFromKernelFactored(E, psi) : CrvEllSubgroup -> CrvEll, Map
IsogenyFromKernelFactored(G) : CrvEllSubgroup -> CrvEll, Map
IsogenyGroup( G ) : GrpLie -> RootDtm
IsogenyGroup( RD ) : RootDtm -> GrpAb
IsogenyMapOmega(I) : Map -> RngMPolElt
IsogenyMapPhi(I) : Map -> RngUPolElt
IsogenyMapPhiMulti(I) : Map -> RngUPolElt
IsogenyMapPsi(I) : Map -> RngUPolElt
IsogenyMapPsiMulti(I) : Map -> RngUPolElt
IsogenyMapPsiSquared(I) : Map -> RngUPolElt
IsogenyType( W ) : GrpCox -> List
IsogenyType( RD ) : RootDtm -> List
IsomorphismToIsogeny(I) : Map -> Map
Morphism(E, F, psi, phi, omega) : CrvEll, CrvEll, RngMPolElt, RngMPolElt, RngMPolElt -> Map
NumberOfIsogenyClasses(D, N) : DB, RngIntElt -> RngIntElt
PushThroughIsogeny(I, v) : Map, RngUPolElt -> RngUPolElt
CrvEll_Isogeny (Example H85E32)

IsogenyFromKernel

IsogenyFromKernel(E, psi) : CrvEll, RngUPolElt -> CrvEll, Map
IsogenyFromKernel(G) : CrvEllSubgroup -> CrvEll, Map

IsogenyFromKernelFactored

IsogenyFromKernelFactored(E, psi) : CrvEllSubgroup -> CrvEll, Map
IsogenyFromKernelFactored(G) : CrvEllSubgroup -> CrvEll, Map

IsogenyGroup

IsogenyGroup( G ) : GrpLie -> RootDtm
IsogenyGroup( RD ) : RootDtm -> GrpAb

IsogenyGroups

RootDtm_IsogenyGroups (Example H35E7)

IsogenyMapOmega

IsogenyMapOmega(I) : Map -> RngMPolElt

IsogenyMapPhi

IsogenyMapPhi(I) : Map -> RngUPolElt

IsogenyMapPhiMulti

IsogenyMapPhiMulti(I) : Map -> RngUPolElt

IsogenyMapPsi

IsogenyMapPsi(I) : Map -> RngUPolElt

IsogenyMapPsiMulti

IsogenyMapPsiMulti(I) : Map -> RngUPolElt

IsogenyMapPsiSquared

IsogenyMapPsiSquared(I) : Map -> RngUPolElt

IsogenyType

IsogenyType( W ) : GrpCox -> List
IsogenyType( RD ) : RootDtm -> List

Isol

Group(D, n, p, i) : DB, RngIntElt, RngIntElt, RngIntElt -> GrpMat
IsolGroup(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> GrpMat
IsolGroupDatabase() : -> DB
IsolGroupOfDegreeFieldSatisfying(d,{p, f}) : RngIntElt, RngIntElt, Predicate -> GrpMat
IsolGroupOfDegreeSatisfying(d, f) : RngIntElt, Predicate -> GrpMat
IsolGroupSatisfying(f) : Predicate -> GrpMat
IsolGroupsOfDegreeFieldSatisfying(d,{p, f}) : RngIntElt, RngIntElt, Predicate -> SeqEnum
IsolGroupsOfDegreeSatisfying(d, f) : RngIntElt, Predicate -> SeqEnum
IsolGroupsSatisfying(f) : Predicate -> SeqEnum
IsolGuardian(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> GrpMat
IsolInfo(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> MonStgElt
IsolIsPrimitive(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> BoolElt
IsolMinBlockSize(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
IsolNumberOfDegreeField(n, p) : RngIntElt, RngIntElt -> RngIntElt
IsolOrder(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
IsolProcess() : -> Process
IsolProcessOfDegree(d) : . -> Process
IsolProcessOfDegreeField(d, p) : ., . -> Process
IsolProcessOfField(p) : . -> Process

isolgps

Basic Functions (DATABASES OF GROUPS)
Database of Irreducible Soluble Subgroups of GL(n,p) for n > 1 and p^n < 256 (OVERVIEW)
The Database of Irreducible Soluble Matrix Groups (DATABASES OF GROUPS)

isolgps-database

The Database of Irreducible Soluble Matrix Groups (DATABASES OF GROUPS)

IsolGroup

Group(D, n, p, i) : DB, RngIntElt, RngIntElt, RngIntElt -> GrpMat
IsolGroup(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> GrpMat
GrpData_IsolGroup (Example H34E11)

IsolGroupDatabase

IsolGroupDatabase() : -> DB

IsolGroupOfDegreeFieldSatisfying

IsolGroupOfDegreeFieldSatisfying(d,{p, f}) : RngIntElt, RngIntElt, Predicate -> GrpMat

IsolGroupOfDegreeSatisfying

IsolGroupOfDegreeSatisfying(d, f) : RngIntElt, Predicate -> GrpMat

IsolGroupSatisfying

IsolGroupSatisfying(f) : Predicate -> GrpMat

IsolGroupsOfDegreeFieldSatisfying

IsolGroupsOfDegreeFieldSatisfying(d,{p, f}) : RngIntElt, RngIntElt, Predicate -> SeqEnum

IsolGroupsOfDegreeSatisfying

IsolGroupsOfDegreeSatisfying(d, f) : RngIntElt, Predicate -> SeqEnum

IsolGroupsSatisfying

IsolGroupsSatisfying(f) : Predicate -> SeqEnum

IsolGuardian

IsolGuardian(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> GrpMat

IsolInfo

IsolInfo(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> MonStgElt

IsolIsPrimitive

IsolIsPrimitive(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> BoolElt

IsolMinBlockSize

IsolMinBlockSize(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt

IsolNumberOfDegreeField

IsolNumberOfDegreeField(n, p) : RngIntElt, RngIntElt -> RngIntElt

IsolOrder

IsolOrder(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt

IsolProcess

IsolProcess() : -> Process

IsolProcessOfDegree

IsolProcessOfDegree(d) : . -> Process

IsolProcessOfDegreeField

IsolProcessOfDegreeField(d, p) : ., . -> Process

IsolProcessOfField

IsolProcessOfField(p) : . -> Process

Isom

Isom(C1,C2) : CrvHyp, CrvHyp -> HomCrvHyp
Lat_Isom (Example H66E18)

isom

Automorphism Group and Isometry Testing (LATTICES)

Isometric

IsIsomorphic(L, M) : Lat, Lat -> BoolElt, AlgMatElt
IsIsometric(L, M) : Lat, Lat -> BoolElt, AlgMatElt
IsIsometric(L, F_1, M, F()_2) : Lat, [ AlgMatElt ], Lat, [ AlgMatElt ] -> BoolElt, AlgMatElt
IsIsometric(F_1, F()_2) : [ AlgMatElt ], [ AlgMatElt ] -> BoolElt, AlgMatElt

isomor

Automorphism Group and Isomorphism Testing (HYPERELLIPTIC CURVES)

isomor-check

Automorphism Group and Isomorphism Testing (HYPERELLIPTIC CURVES)

Isomorphic

IsAlgebraicallyIsomorphic( G, H ) : GrpLie, GrpLie -> BoolElt
IsIsometric(L, M) : Lat, Lat -> BoolElt, AlgMatElt
IsIsometric(L, F_1, M, F()_2) : Lat, [ AlgMatElt ], Lat, [ AlgMatElt ] -> BoolElt, AlgMatElt
IsIsometric(F_1, F()_2) : [ AlgMatElt ], [ AlgMatElt ] -> BoolElt, AlgMatElt
IsIsomorphic(I,J) : AlgQuatOrd, AlgQuatOrd -> BoolElt
IsIsomorphic(E, F) : CrvEll, CrvEll -> BoolElt, Map
IsIsomorphic(C1, C2) : CrvHyp, CrvHyp -> BoolElt, MapCrvHyp
IsIsomorphic(F, L) : FldAlg, FldAlg -> BoolElt, Map
IsIsomorphic(G, H) : GrpPC, GrpPC -> BoolElt, Map
IsIsomorphic(M, N) : ModRng, ModRng -> BoolElt, AlgMatElt
IsIsomorphic(G, H : parameters ) : GrphDir, GrphDir -> BoolElt, Map
IsIsomorphic(C, D: parameters) : Code, Code -> BoolElt, Map
IsIsomorphic(G, H: parameters) : GrpPerm, GrpPerm -> BoolElt, Hom(Grp)
IsIsomorphic(D, E: parameters) : Inc, Inc -> BoolElt, Map
IsIsomorphic(P, Q: parameters) : Plane, Plane -> BoolElt, Map
IsIsomorphic( RD1, RD2 ) : RootDtm, RootDtm -> BoolElt
IsLeftIsomorphic(I,J) : AlgQuatOrd, AlgQuatOrd -> BoolElt, Map, AlgQuatElt
IsRightIsomorphic(I,J) : AlgQuatOrd, AlgQuatOrd -> BoolElt, Map, AlgQuatElt

Isomorphism

Isomorphism(A, B, gens, images) : Grp, Grp, [ GrpElt ], [ GrpElt ] -> Map
Homomorphism(A, B, gens, images) : Grp, Grp, [ GrpElt ], [ GrpElt ] -> Map
IsIsomorphism(I) : Map -> BoolElt, Map
IsIsomorphism(f) : MapSch -> BoolElt, IsoSch
IsIsomorphism(f) : MotMatCpxElt -> BoolElt
Isomorphism(I,J) : AlgQuatOrd, AlgQuatOrd -> BoolElt
Isomorphism(E, F) : CrvEll, CrvEll -> Map
Isomorphism(E, F, [r, s, t, u]) : CrvEll, CrvEll, Seq -> Map
IsomorphismData(I) : Map -> [ RngElt ]
IsomorphismToIsogeny(I) : Map -> Map
LeftIsomorphism(I,J) : AlgQuatOrd, AlgQuatOrd -> Map, AlgQuatElt
RightIsomorphism(I,J) : AlgQuatOrd, AlgQuatOrd -> Map, AlgQuatElt
CrvEll_Isomorphism (Example H85E34)

isomorphism

Arithmetic with Isomorphisms (HYPERELLIPTIC CURVES)
Creation of Isomorphisms (HYPERELLIPTIC CURVES)
Equivalence and Isomorphism of Codes (LINEAR CODES OVER FINITE FIELDS)
The Isomorphism (FINITELY PRESENTED ALGEBRAS)

isomorphism-arithmetic

Arithmetic with Isomorphisms (HYPERELLIPTIC CURVES)

isomorphism-creation

Creation of Isomorphisms (HYPERELLIPTIC CURVES)

isomorphism-equivalence

Equivalence and Isomorphism of Codes (LINEAR CODES OVER FINITE FIELDS)

IsomorphismData

IsomorphismData(I) : Map -> [ RngElt ]

IsomorphismIsogeny

RootDtm_IsomorphismIsogeny (Example H35E5)

Isomorphisms

CrvEll_Isomorphisms (Example H85E33)

isomorphisms

Invariants of Isomorphisms (HYPERELLIPTIC CURVES)
Order and Ideal Isomorphisms (QUATERNION ALGEBRAS)

isomorphisms-and-units

Order and Ideal Isomorphisms (QUATERNION ALGEBRAS)

IsomorphismToIsogeny

IsomorphismToIsogeny(I) : Map -> Map

IsOne

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

IsOrbit

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

IsOrder

IsOrder(P, m) : PtEll, RngIntElt -> BoolElt

IsOrdered

IsOrdered(R) : Rng -> BoolElt

IsOrdinary

IsOrdinary(E) : CrvEll -> BoolElt

IsOrdinaryProjective

IsOrdinaryProjective(X) : Sch -> BoolElt

IsOrdinaryProjectiveSpace

IsOrdinaryProjectiveSpace(X) : Sch -> BoolElt

IsOrdinarySingularity

IsOrdinarySingularity(p) : Sch,Pt -> BoolElt
IsOrdinarySingularity(p) : Sch,Pt -> BoolElt

IsOrthogonalGroup

IsOrthogonalGroup(G) : GrpMat ->BoolElt

IsOverSmallerField

IsOverSmallerField(G) : GrpMat -> BoolElt, GrpMat
IsOverSmallerField(G, d) : GrpMat, RngIntElt -> BoolElt, GrpMat
GrpMat_IsOverSmallerField (Example H21E37)

Isp

IspIntegral(C, p) : CrvHyp, RngIntElt -> BoolElt
IspMinimal(C, p) : CrvHyp, RngIntElt -> BoolElt, BoolElt
IspNormal(C, p) : CrvHyp, RngIntElt -> BoolElt

IsParallel

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

IsParallelClass

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

IsParallelism

IsParallelism(D, P) : Inc, SetEnum[SetEnum] -> BoolElt, RngIntElt

IsPartialRoot

IsPartialRoot(f, c) : RngUPolElt, RngSerElt -> BoolElt

IsPartition

IsPartition(S) : SeqEnum -> BoolElt

IsPath

IsPath(G) : Grph -> BoolElt

IsPerfect

IsPerfect(C) : Code -> BoolElt
IsPerfect(G) : GrpAb -> BoolElt
IsPerfect(G) : GrpFin -> BoolElt
IsPerfect(G) : GrpGPC -> BoolElt
IsPerfect(G) : GrpMat -> BoolElt
IsPerfect(G) : GrpPC -> BoolElt
IsPerfect(G) : GrpPerm -> BoolElt

IsPID

IsPrincipalIdealDomain(R) : Rng -> BoolElt
IsPID(R) : Rng -> BoolElt

IspIntegral

IspIntegral(C, p) : CrvHyp, RngIntElt -> BoolElt

IsPIR

IsPrincipalIdealRing(R) : Rng -> BoolElt
IsPIR(R) : Rng -> BoolElt

IsPlanar

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

IspMinimal

IspMinimal(C, p) : CrvHyp, RngIntElt -> BoolElt, BoolElt

IspNormal

IspNormal(C, p) : CrvHyp, RngIntElt -> BoolElt

IsPoint

IsPoint(C, S) : CrvHyp, SeqEnum -> BoolElt, PtHyp
IsPoint(N,p) : NwtnPgon,Tup -> BoolElt
IsPoint(H, x) : SetPtEll, RngElt -> BoolElt, PtEll
IsPoint(H, S) : SetPtEll, [ RngElt ] -> BoolElt, PtEll
IsPoint(K, S) : SrfKum, [RngElt] -> BoolElt, SrfKumPt

IsPointRegular

IsPointRegular(D) : IncNsp -> BoolElt, RngIntElt

IsPointTransitive

IsPointTransitive(D) : Inc -> BoolElt
IsPointTransitive(P) : Plane -> BoolElt

IsPolygon

IsPolygon(G) : Grph -> BoolElt

IsPolynomial

IsPolynomial(f) : MapSch -> BoolElt
IsRegular(f) : MapSch -> BoolElt

IsPositive

IsPositive(D) : DivCrvElt -> BoolElt
IsEffective(D) : DivCrvElt -> BoolElt
IsPositive( RD, r ) : RootDtm, RngIntElt -> BoolElt

IsPositiveDefinite

IsPositiveDefinite(F) : ModMatRngElt -> BoolElt

IsPositiveSemiDefinite

IsPositiveSemiDefinite(F) : ModMatRngElt -> BoolElt

IsPower

IsPower(a, n) : FldACElt, RngIntElt -> BoolElt, FldACElt
IsPower(a, k) : FldAlgElt, RngIntElt -> BoolElt, FldAlgElt
IsPower(a, n) : FldFinElt, RngIntElt -> BoolElt, FldFinElt
IsPower(n) : RngIntElt -> BoolElt
IsPower(n, k) : RngIntElt -> BoolElt
IsPower(x, n) : RngLocElt, RngIntElt -> RngLocElt
IsPower(w, n) : RngOrdElt, RngIntElt -> BoolElt, RngOrdElt
IsPower(I, k) : RngOrdFracIdl, RngIntElt -> BoolElt, RngOrdFracIdl

IsPrimary

IsPrimary(I) : RngMPol -> BoolElt
IsPrimary(I) : RngMPolRes -> BoolElt

IsPrime

IsPrime(x) : RngElt -> BoolElt
IsPrime(I) : RngFunOrdIdl -> BoolElt
IsPrime(n) : RngIntElt -> BoolElt
IsPrime(n) : RngIntElt -> BoolElt
IsPrime(I) : RngMPol -> BoolElt
IsPrime(I) : RngMPolRes -> BoolElt
IsPrime(I) : RngOrdIdl -> BoolElt, RngOrdIdl
RngInt_IsPrime (Example H40E3)

IsPrimePower

IsPrimePower(n) : RngIntElt -> BoolElt, RngIntElt, RngIntElt

IsPrimitive

IsPrimitive(a) : FldAlgElt -> BoolElt
IsPrimitive(a) : FldFinElt -> BoolElt
IsPrimitive(G) : GrpPerm -> BoolElt
IsPrimitive(G, Y) : GrpPerm, GSet -> BoolElt
IsPrimitive(G : parameters) : GrphUnd -> BoolElt
IsPrimitive(G: parameters) : GrpMat -> BoolElt
IsPrimitive(n, m) : RngIntElt, RngIntElt -> BoolElt
IsPrimitive(n) : RngIntResElt -> BoolElt
IsPrimitive(f) : RngUPolElt -> BoolElt
GrpMat_IsPrimitive (Example H21E31)

IsPrincipal

IsPrincipal(D) : DivCrvElt -> BoolElt,FldFunRatMElt
IsPrincipal(I) : RngFunOrdIdl -> BoolElt, FldFunElt
IsPrincipal(I) : RngMPol -> BoolElt, RngMPolElt
IsPrincipal(I) : RngOrdFracIdl -> BoolElt, FldOrdElt

IsPrincipalIdealDomain

IsPrincipalIdealDomain(R) : Rng -> BoolElt
IsPID(R) : Rng -> BoolElt

IsPrincipalIdealRing

IsPrincipalIdealRing(R) : Rng -> BoolElt
IsPIR(R) : Rng -> BoolElt
IsPrincipalIdealRing(F) : FldAlg -> BoolElt
IsPrincipalIdealRing(O) : RngOrd -> BoolElt

IsProbablePrime

IsProbablyPrime(n: parameter) : RngIntElt -> BoolElt
IsProbablePrime(n: parameter) : RngIntElt -> BoolElt

IsProbablyMaximal

IsProbablyMaximal(G, H: parameters) : GrpPerm, GrpPerm -> BoolElt

IsProbablyPermutationPolynomial

IsProbablyPermutationPolynomial(p) : RngUPolElt -> BoolElt

IsProbablyPrime

IsProbablyPrime(n: parameter) : RngIntElt -> BoolElt
IsProbablePrime(n: parameter) : RngIntElt -> BoolElt

IsProbablySupersingular

IsProbablySupersingular(E) : CrvEll -> BoolElt

IsProjective

IsProjective(C) : Code -> BoolElt
IsProjective(M) : ModAlg -> BoolElt, SeqEnum
IsProjective(X) : Sch -> BoolElt

IsProjectiveSpace

IsProjectiveSpace(X) : Sch -> BoolElt

IsProper

IsProper(I) : RngMPol -> BoolElt
IsProper(I) : RngMPolRes -> BoolElt

IsProperChainMap

IsProperChainMap(f) : MapChn -> BoolElt

IsProportional

IsProportional(X, k) : Mtrx, RngIntElt -> BoolElt, Tup

Isqrt

Isqrt(n) : RngIntElt -> RngIntElt

IsQuadratic

IsQuadratic(K) : FldNum -> BoolElt, FldQuad

IsQuadraticTwist

IsQuadraticTwist(C1, C2) : CrvHyp, CrvHyp -> BoolElt, RngElt

IsRadical

IsRadical(I) : RngMPol -> BoolElt
IsRadical(I) : RngMPolRes -> BoolElt

IsRamified

IsRamified(P) : RngOrdIdl -> BoolElt
IsRamified(P, O) : RngOrdIdl, RngOrd -> BoolElt

IsRationalCurve

IsRationalCurve(X) : Sch -> BoolElt,CrvRat
IsRationalCurve(X) : Sch -> BoolElt,CrvRat

IsRC

IsRC(C) : CosetGeom -> BoolElt
IsResiduallyConnected(C) : CosetGeom -> BoolElt
IsResiduallyConnected(D) : IncGeom -> BoolElt

IsReal

IsReal(x) : AlgChtrElt -> BoolElt
IsReal(c) : FldComElt -> BoolElt
IsReal(a) : FldCycElt -> BoolElt

IsReduced

IsReduced(s) : GrphSpl -> BoolElt
IsReduced(p) : Pt -> BoolElt
IsReduced(f) : QuadBinElt -> BoolElt
IsReduced(C) : Sch -> BoolElt
IsReduced(X) : Sch -> BoolElt

IsReducible

IsReducible(C) : Sch -> BoolElt
IsReducible(X) : Sch -> BoolElt

IsReflectionSubgroup

IsReflectionSubgroup( W, H ) : GrpCox -> GrpCox

IsRegular

IsRegular(a) : AlgGenElt -> BoolElt
IsRegular(G) : Grph -> BoolElt
IsRegular(s) : GrphSpl -> BoolElt
IsRegular(G, Y) : GrpPerm, GSet -> BoolElt
IsRegular(f) : MapSch -> BoolElt

IsResiduallyConnected

IsRC(C) : CosetGeom -> BoolElt
IsResiduallyConnected(C) : CosetGeom -> BoolElt
IsResiduallyConnected(D) : IncGeom -> BoolElt

IsResolution

IsResolution(D, P) : Inc, SetEnum[SetEnum] -> BoolElt, RngIntElt

IsRestrictedLieAlgebra

IsRestrictedLieAlgebra(L) : AlgLie -> BoolElt

IsReverseLatticeWord

IsReverseLatticeWord(w) : SeqEnum -> BoolElt

IsRightIdeal

IsRightIdeal(S) : AlgGrpSub -> BoolElt

IsRightIsomorphic

IsRightIsomorphic(I,J) : AlgQuatOrd, AlgQuatOrd -> BoolElt, Map, AlgQuatElt

IsRingOfAllModularForms

IsRingOfAllModularForms(M) : ModFrm -> BoolElt

IsRoot

IsRoot(v) : GrphVert -> BoolElt

IsRootedTree

IsRootedTree(g) : GrphDir -> BoolElt,GrphVert

IsSatisfied

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

IsScalar

IsScalar(u) : AlgFPElt -> BoolElt
IsScalar(a) : AlgMatElt -> BoolElt
IsScalar(g) : GrpMatElt -> BoolElt
IsScalar(A) : Mtrx -> BoolElt

IsSelfDual

IsSelfOrthogonal(C) : Code -> BoolElt
IsSelfDual(C) : Code -> BoolElt
IsSelfDual(C) : Code -> BoolElt
IsSelfDual(D) : Inc -> BoolElt
IsSelfDual(P) : PlaneProj -> BoolElt

IsSelfNormalising

IsSelfNormalizing(G, H) : GrpGPC, GrpGPC -> BoolElt
IsSelfNormalising(G, H) : GrpGPC, GrpGPC -> BoolElt
IsSelfNormalizing(G, H) : GrpFin, GrpFin -> BoolElt
IsSelfNormalizing(G, H) : GrpPerm, GrpPerm -> BoolElt

IsSelfNormalizing

IsSelfNormalizing(G, H) : GrpGPC, GrpGPC -> BoolElt
IsSelfNormalising(G, H) : GrpGPC, GrpGPC -> BoolElt
IsSelfNormalizing(G, H) : GrpFin, GrpFin -> BoolElt
IsSelfNormalizing(G, H) : GrpPC, GrpPC -> BoolElt
IsSelfNormalizing(G, H) : GrpPerm, GrpPerm -> BoolElt
IsSelfNormalizing(G, H) : GrpFP, GrpFP -> BoolElt

IsSelfOrthogonal

IsSelfOrthogonal(C) : Code -> BoolElt
IsSelfDual(C) : Code -> BoolElt
IsSelfDual(C) : Code -> BoolElt

IsSemiLinear

IsSemiLinear(G) : GrpMat -> BoolElt

IsSemiregular

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

IsSemisimple

IsSemisimple(A) : AlgGen -> BoolElt
IsSemisimple( G ) : GrpLie-> BoolElt
IsSemisimple(M) : ModAlg -> BoolElt, SeqEnum
IsSemisimple(M) : ModGrp -> BoolElt
IsSemisimple( RD ) : RootDtm-> BoolElt

IsSeparable

IsSeparable(G) : Grph -> BoolElt
IsSeparable(f) : RngUPolElt -> BoolElt

IsSeparating

IsSeparating(x) : FldFunGElt -> BoolElt

IsSharplyTransitive

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

IsShortExactSequence

IsShortExactSequence(f, g) : MapChn, MapChn -> BoolElt
IsShortExactSequence(C) : ModCpx -> BoolElt, RngIntElt

IsShortRoot

IsShortRoot( RD, r ) : RootDtm, RngIntElt -> BoolElt

IsSimilar

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

IsSimple

IsSimple(A) : AlgGen -> BoolElt
IsSimple(F) : FldAlg -> BoolElt
IsSimple(G) : GrpAb -> BoolElt
IsSimple(G) : GrpFin -> BoolElt
IsSimple(G) : GrpGPC -> BoolElt
IsSimple( G ) : GrpLie -> BoolElt
IsSimple(G) : GrpMat -> BoolElt
IsSimple(G) : GrpPC -> BoolElt
IsSimple(G) : GrpPerm -> BoolElt
IsSimple(D) : Inc -> BoolElt

IsSimplifiedModel

IsSimplifiedModel(E) : CrvEll -> BoolElt

IsSimplyConnected

IsSimplyConnected( G ) : GrpLie-> BoolElt
IsSimplyConnected( RD ) : RootDtm-> BoolElt

IsSimplyLaced

IsSimplyLaced( G ) : GrpLie-> BoolElt
IsSimplyLaced( RD ) : RootDtm-> BoolElt

IsSinglePrecision

IsSinglePrecision(n) : RngIntElt -> BoolElt

IsSingular

IsSingular(A) : Mtrx -> BoolElt
IsSingular(C) : Sch -> BoolElt
IsSingular(X) : Sch -> BoolElt
IsSingular(p) : Sch,Pt -> BoolElt
IsSingular(p) : Sch,Pt -> BoolElt

IsSIntegral

IsSIntegral(P, S) : PtEll, SeqEnum -> BoolElt

IsSkew

IsSkew(t) : Tableau -> BoolElt

IsSoluble

IsSolvable(G) : GrpAb -> BoolElt
IsSoluble(G) : GrpAb -> BoolElt
IsSoluble(A) : GrpAuto -> BoolElt
IsSoluble(G) : GrpFin -> BoolElt
IsSoluble(G) : GrpGPC -> BoolElt
IsSoluble(G) : GrpMat -> BoolElt
IsSoluble(G) : GrpPC -> BoolElt
IsSoluble(G) : GrpPerm -> BoolElt

IsSolvable

IsSolvable(G) : GrpAb -> BoolElt
IsSoluble(G) : GrpAb -> BoolElt
IsSoluble(A) : GrpAuto -> BoolElt
IsSoluble(G) : GrpFin -> BoolElt
IsSoluble(G) : GrpGPC -> BoolElt
IsSoluble(G) : GrpMat -> BoolElt
IsSoluble(G) : GrpPC -> BoolElt
IsSoluble(G) : GrpPerm -> BoolElt
IsSolvable(L) : AlgLie -> BoolElt

IsSpecial

IsSpecial(D) : DivCrvElt -> BoolElt
IsSpecial(G) : GrpFin -> BoolElt
IsSpecial(G) : GrpMat -> BoolElt
IsSpecial(G) : GrpPC -> BoolElt
IsSpecial(G) : GrpPerm -> BoolElt

IsSpinorGenus

IsSpinorGenus(G) : SymGen -> BoolElt

IsSpinorNorm

IsSpinorNorm(G,p) : SymGen, RngIntElt -> RngIntElt

IsSplit

IsSplit(P) : RngOrdIdl -> BoolElt
IsSplit(P, O) : RngOrdIdl, RngOrd -> BoolElt

IsSPrincipal

IsSPrincipal(D, S) : DivFunElt, SetEnum[PlcFunElt] -> BoolElt, FldFunElt

IsSquare

IsSquare(a) : FldAlgElt -> BoolElt, FldAlgElt
IsPower(a, k) : FldAlgElt, RngIntElt -> BoolElt, FldAlgElt
IsSquare(a) : FldACElt -> BoolElt
IsSquare(a) : FldFinElt -> BoolElt
IsSquare(n) : RngIntElt -> BoolElt, RngIntElt
IsSquare(n) : RngIntResElt -> BoolElt, RngIntResElt
IsSquare(x) : RngLocElt -> BoolElt
IsSquare(I) : RngOrdFracIdl -> BoolElt, RngOrdFracIdl

IsSquarefree

IsSquarefree(n) : RngIntElt -> BoolElt

IsStandard

IsStandard(t) : Tableau -> BoolElt

IsStandardParabolicSubgroup

IsStandardParabolicSubgroup( W, H ) : GrpCox -> GrpCox

IsSteiner

IsSteiner(D, t) : Dsgn -> BoolElt

IsStronglyAG

IsStronglyAG(C) : Code -> BoolElt

IsStronglyConnected

IsStronglyConnected(G) : GrphDir -> BoolElt

IsSubfield

IsSubfield(F, L) : FldAlg, FldAlg -> BoolElt, Map

IsSubgroup

IsSubgroup(G,H) : GrpPSL2, GrpPSL2 -> BoolElt

IsSubmodule

IsSubmodule(M, N) : ModOrd, ModOrd -> 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

IsSubsystem

IsSubsystem(L,K) : LinSys,LinSys -> BoolElt
K subset L : LinSys,LinSys -> BoolElt

IsSUnit

IsSUnit(a, S) : FldFunElt, SetEnum[PlcFunElt] -> BoolElt

IsSUnitWithPreimage

IsSUnitWithPreimage(a, S) : FldFunElt, SetEnum[PlcFunElt] -> BoolElt, GrpAbElt

IsSupersingular

IsSupersingular(E: parameters) : CrvEll -> BoolElt

IsSurjective

IsSurjective(f) : Map -> [ BoolElt ]
IsSurjective(a) : ModMatRngElt -> BoolElt
IsSurjective(f) : MotMatCpxElt -> BoolElt

IsSymmetric

IsSymmetric(a) : AlgMatElt -> BoolElt
IsSymmetric(D) : Dsgn -> BoolElt
IsSymmetric(G) : GrpPerm -> BoolElt
IsSymmetric(A) : Mtrx -> BoolElt
IsSymmetric(G : parameters) : GrphUnd -> BoolElt
IsSymmetric(f) : RngMPolElt -> BoolElt, RngMPolElt
IsSymmetric(f) : RngMPolElt -> BoolElt, RngMPolElt
GB_IsSymmetric (Example H50E26)
RngMPol_IsSymmetric (Example H45E11)

IsSymplecticGroup

IsSymplecticGroup(G) : GrpMat -> BoolElt

IsTamelyRamified

IsTamelyRamified(K) : FldAlg -> BoolElt
IsTamelyRamified(O) : RngOrd -> BoolElt
IsTamelyRamified(P) : RngOrdIdl -> BoolElt
IsTamelyRamified(P, O) : RngOrdIdl, RngOrd -> BoolElt

IsTangent

IsTangent(C,D,p) : Sch,Sch,Pt -> BoolElt

IsTensor

IsTensor(G: parameters) : GrpMat -> BoolElt

IsTensorInduced

IsTensorInduced(G : parameters) : GrpMat -> BoolElt

IsThick

IsThick(C) : CosetGeom -> BoolElt
IsThick(D) : IncGeom -> BoolElt

IsThin

IsThin(C) : CosetGeom -> BoolElt
IsThin(D) : IncGeom -> BoolElt

IsTorsionUnit

IsTorsionUnit(w) : RngOrdElt -> BoolElt

IsTotallyRamified

IsTotallyRamified(P) : RngOrdIdl -> BoolElt
IsTotallyRamified(P, O) : RngOrdIdl, RngOrd -> BoolElt

IsTotallySplit

IsTotallySplit(P) : RngOrdIdl -> BoolElt
IsTotallySplit(P, O) : RngOrdIdl, RngOrd -> BoolElt

IsTransitive

IsTransitive(P) : Plane -> BoolElt
IsPointTransitive(P) : Plane -> BoolElt
IsTransitive(G, Y) : GrpPerm, GSet -> BoolElt
IsTransitive(G, Y, k) : GrpPerm, GSet, RngIntElt -> BoolElt
IsTransitive(G : parameters) : GrphUnd -> BoolElt

IsTransverse

IsTransverse(C,D,p) : Sch,Sch,Pt -> BoolElt

IsTree

IsTree(G) : Grph -> BoolElt

IsTrivial

IsTrivial(G) : Grp -> BoolElt
IsTrivial(x) : GrpDrchElt -> BoolElt
IsTrivial(G) : GrpPC -> BoolElt
IsTrivial(D) : Inc -> BoolElt

IsUFD

IsUniqueFactorizationDomain(R) : Rng -> BoolElt
IsUFD(R) : Rng -> BoolElt

IsUniform

IsUniform(D) : Inc -> BoolElt, RngIntElt

IsUniqueFactorizationDomain

IsUniqueFactorizationDomain(R) : Rng -> BoolElt
IsUFD(R) : Rng -> BoolElt

IsUniquePartialRoot

IsUniquePartialRoot(f, c) : RngUPolElt, RngSerElt -> BoolElt

IsUnit

IsUnit(a) : AlgGenElt -> BoolElt, AlgGenElt
IsUnit(a) : AlgMatElt -> BoolElt
IsUnit(A) : Mtrx -> BoolElt
IsUnit(a) : RngElt -> BoolElt
IsUnit(x) : RngLocElt -> BoolElt
IsUnit(f) : RngMPolResElt -> BoolElt
IsUnit(a) : RngOrdResElt -> BoolElt

IsUnital

IsUnital(P, U) : Plane, { PlanePt } -> BoolElt

IsUnitary

IsUnitary(R) : Rng -> BoolElt

IsUnitaryGroup

IsUnitaryGroup(G) : GrpMat -> BoolElt

IsUnitWithPreimage

IsUnitWithPreimage(a) : RngFunOrdElt -> BoolElt, GrpAbElt

IsUnivariate

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

IsUnramified

IsUnramified(K) : FldAlg -> BoolElt
IsUnramified(O) : RngOrd -> BoolElt
IsUnramified(P) : RngOrdIdl -> BoolElt
IsUnramified(P, O) : RngOrdIdl, RngOrd -> BoolElt

IsVerbose

IsVerbose(s) : MonStgElt -> BoolElt
IsVerbose(s, l) : MonStgElt, RngIntElt -> BoolElt

IsVertex

IsVertex(g,v) : GrphRes,GrphResVert -> BoolElt
IsVertex(N, p) : NwtnPgon,Tup -> BoolElt

IsVertexTransitive

IsVertexTransitive(G : parameters) : GrphUnd -> BoolElt
IsTransitive(G : parameters) : GrphUnd -> BoolElt

IsWeaklyAG

IsWeaklyAG(C) : Code -> BoolElt

IsWeaklyConnected

IsWeaklyConnected(G) : GrphDir -> BoolElt

IsWeaklyEqual

IsWeaklyEqual(f, g) : RngSerElt, RngSerElt -> BoolElt

IsWeaklySelfDual

IsWeaklySelfOrthogonal(C) : Code -> BoolElt
IsWeaklySelfDual(C) : Code -> BoolElt
IsWeaklySelfDual(C) : Code -> BoolElt

IsWeaklySelfOrthogonal

IsWeaklySelfOrthogonal(C) : Code -> BoolElt
IsWeaklySelfDual(C) : Code -> BoolElt
IsWeaklySelfDual(C) : Code -> BoolElt

IsWeaklyZero

IsWeaklyZero(f) : RngSerElt -> BoolElt

IsWeierstrassModel

IsWeierstrassModel(E) : CrvEll -> BoolElt

IsWeierstrassPlace

IsWeierstrassPlace(P) : PlcCrvElt -> BoolElt
IsWeierstrassPlace(P) : PlcFunElt -> BoolElt

IsWildlyRamified

IsWildlyRamified(K) : FldAlg -> BoolElt
IsWildlyRamified(O) : RngOrd -> BoolElt
IsWildlyRamified(P) : RngOrdIdl -> BoolElt
IsWildlyRamified(P, O) : RngOrdIdl, RngOrd -> BoolElt

IsZero

IsIdentity(P) : PtEll -> BoolElt
IsZero(P) : PtEll -> BoolElt
IsId(P) : PtEll -> BoolElt
IsZero(u) : AlgFPElt -> BoolElt
IsZero(A) : AlgGen -> BoolElt
IsZero(a) : AlgGenElt -> BoolElt
IsZero(a) : AlgMatElt -> BoolElt
IsZero(a) : DiffFunElt -> BoolElt
IsZero(d) : DiffFunElt -> BoolElt
IsZero(D) : DivCrvElt -> BoolElt
IsZero(a) : FldACElt -> BoolElt
IsZero(P) : JacHypPt -> BoolElt
IsZero(v) : LatElt -> BoolElt
IsZero(I) : Map -> BoolElt
IsZero(u) : ModElt -> BoolElt
IsZero(M) : ModMPol -> ModMPol
IsZero(f) : ModMPolElt -> BoolElt
IsZero(u) : ModTupElt -> BoolElt
IsZero(u) : ModTupElt -> BoolElt
IsZero(u) : ModTupRngElt -> BoolElt
IsZero(u) : ModTupRngElt -> BoolElt
IsZero(f) : MotMatCpxElt -> BoolElt
IsZero(A) : Mtrx -> BoolElt
IsZero(a) : RngElt -> BoolElt
IsZero(I) : RngFunOrdIdl -> BoolElt
IsZero(x) : RngLocElt -> BoolElt
IsZero(I) : RngMPol -> BoolElt
IsZero(I) : RngMPolRes -> BoolElt
IsZero(I) : RngOrdFracIdl -> BoolElt
IsZero(a) : RngOrdResElt -> BoolElt

IsZeroComplex

IsZeroComplex(C) : ModCpx -> BoolElt

IsZeroDimensional

IsZeroDimensional(I) : RngMPol -> BoolElt

IsZeroDivisor

IsZeroDivisor(a) : AlgGenElt -> BoolElt
IsZeroDivisor(x) : RngElt -> BoolElt

IsZeroMap

IsZeroMap(C, n) : ModCpx, RngIntElt -> BoolElt

IsZeroTerm

IsZeroTerm(C, n) : ModCpx, RngIntElt -> 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]