[____] [____] [_____] [____] [__] [Index] [Root]
Index I
I
i
Id(J) : JacHyp -> JacHypPt
Identity(J) : JacHyp -> JacHypPt
J ! 0 : JacHyp, RngIntElt -> JacHypPt
Id(R) : AlgChtr -> AlgChtrElt
Id(M) : MonFP -> MonFPElt
Id(O) : MonOrd -> MonOrdElt
Id(P) : MonPlc -> MonPlcElt
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(B) : GrpBrd -> GrpBrdElt
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(u) : GrpBrdElt -> BoolElt
IsIdentity(g) : GrpGPCElt -> BoolElt
IsIdentity(g) : GrpMatElt -> BoolElt
IsIdentity(g) : GrpPCElt -> BoolElt
One(R) : Rng -> RngElt
AugmentationIdeal(A) : AlgGrp -> AlgGrpSub
ColonIdeal(I, J) : RngMPol, RngMPol -> RngMPol
ColonIdeal(I, f) : RngMPol, RngMPolElt -> RngMPol, RngIntElt
ColonIdeal(I, J) : RngOrdIdl, RngOrdIdl -> RngOrdIdl
CommutatorIdeal(A, B) : AlgAss, AlgAss -> AlgAss
CommutatorIdeal(S) : AlgQuatOrd -> AlgQuatOrd
DefiningIdeal(C) : Crv -> RngMPol
DefiningIdeal(C) : Sch -> RngMPol
DefiningIdeal(X) : Sch -> RngMPol
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(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 ]
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 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 (ORDERS AND ALGEBRAIC FIELDS)
RngOrd_ideal-basis (Example H48E30)
Predicates on Ideals (ORDERS AND ALGEBRAIC FIELDS)
Ideal Class Groups (ORDERS AND ALGEBRAIC FIELDS)
Creation of Ideals in Orders (ORDERS AND ALGEBRAIC FIELDS)
IDEAL THEORY AND GRÖBNER BASES
RngOrd_ideal-invar (Example H48E29)
Basic Operations on Ideals (IDEAL THEORY AND GRÖBNER BASES)
Further Ideal Operations (ALGEBRAIC FUNCTION FIELDS)
Other Ideal Operations (ORDERS AND ALGEBRAIC FIELDS)
Ideals and Quotient Rings (INTRODUCTION [BASIC RINGS])
Ideals and Quotient Rings (UNIVARIATE POLYNOMIAL RINGS)
FldAb_ideal-ray (Example H51E2)
Ideal Theory of Orders (QUATERNION ALGEBRAS)
RngOrd_ideal-two (Example H48E31)
AlgQuat_Ideal_Arithmetic (Example H72E10)
AlgQuat_Ideal_Bases (Example H72E7)
AlgQuat_Ideal_Enumeration (Example H72E9)
GB_IdealArithmetic (Example H66E8)
Idealizer(S) : AlgGrpSub -> AlgGrpSub
Idealiser(S) : AlgGrpSub -> AlgGrpSub
Idealizer(A, B: parameters) : AlgAss, AlgAss -> AlgAss
Idealizer(S) : AlgGrpSub -> AlgGrpSub
Idealiser(S) : AlgGrpSub -> AlgGrpSub
Idealizer(A, B: parameters) : AlgAss, AlgAss -> AlgAss
IdealQuotient(I, J) : RngMPol, RngMPol -> RngMPol
ColonIdeal(I, J) : RngMPol, RngMPol -> RngMPol
ColonIdeal(I, f) : RngMPol, RngMPolElt -> RngMPol, RngIntElt
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 H48E28)
Creation of Ideals (ALGEBRAIC FUNCTION FIELDS)
Creation of Ideals and Accessing their Bases (IDEAL THEORY AND GRÖBNER BASES)
Ideals (ALGEBRAIC FUNCTION FIELDS)
Ideals (RING OF INTEGERS)
Special Functions for Ideals (QUADRATIC FIELDS)
FldFunG_ideals (Example H53E15)
Creation of Ideals (ALGEBRAIC FUNCTION FIELDS)
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(B, i) : AlgBas, RngIntElt -> SeqEnum
IdempotentGenerators(B) : AlgBas -> SeqEnum
IdempotentPositions(B) : AlgBas -> SeqEnum
AreIdentical(u, v) : GrpBrdElt, GrpBrdElt -> BoolElt
IsIdentical(f, g) : RngSerElt, RngSerElt -> BoolElt
IsIdenticalPresentation(G, H) : GrpGPC, GrpGPC -> BoolElt
IsIdenticalPresentation(G, H) : GrpPC, GrpPC -> BoolElt
IdentificationNumber(D, i): DB, RngIntElt -> RngIntElt
TransitiveGroupIdentification(G) : GrpPerm -> RngIntElt, RngIntElt
TwoTransitiveGroupIdentification(G) : GrpPerm -> Tup
Identification (PERMUTATION GROUPS)
Identification as a Permutation Group (PERMUTATION GROUPS)
Identification as an Abstract Group (PERMUTATION GROUPS)
Small Group Identification (FINITELY PRESENTED GROUPS)
Identification as an Abstract Group (PERMUTATION GROUPS)
Identification as a Permutation Group (PERMUTATION GROUPS)
IdentificationNumber(D, i): DB, RngIntElt -> RngIntElt
Identifier(X) : VSrfK3 -> RngIntElt
Number(X) : VSrfK3 -> RngIntElt
Identifier Classes (MAGMA SEMANTICS)
Identifier names (OVERVIEW)
Identifiers (STATEMENTS AND EXPRESSIONS)
Identifiers and variables (OVERVIEW)
Uninitialized Identifiers (MAGMA SEMANTICS)
Identifier Classes (MAGMA SEMANTICS)
ShowIdentifiers() : ->
State_Identifiers (Example H1E1)
IdentifyAlmostSimpleGroup(G) : GrpPerm -> Map, GrpPerm
IdentifyGroup(G): Grp -> Tup
IdentifyGroup(G): GrpFP -> Tup
Small Group Identification (DATABASES OF GROUPS)
IdentifyAlmostSimpleGroup(G) : GrpPerm -> Map, GrpPerm
IdentifyGroup(G): Grp -> Tup
IdentifyGroup(G): GrpFP -> Tup
GrpFP_1_IdentifyGroup (Example H19E61)
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(B) : GrpBrd -> GrpBrdElt
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(u) : GrpBrdElt -> BoolElt
IsIdentity(g) : GrpGPCElt -> BoolElt
IsIdentity(g) : GrpMatElt -> BoolElt
IsIdentity(g) : GrpPCElt -> BoolElt
IsIdentity(f) : QuadBinElt -> BoolElt
IsZero(P) : JacHypPt -> BoolElt
Groups (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
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(G) : Grp -> Map
IdentityHomomorphism(G) : GrpPC -> Map
IdentityIsogeny(E) : CrvEll -> Map
IdentityMap(X) : Sch -> MapAutSch
IdentityAutomorphism(X) : Sch -> MapAutSch
IdentityMap(E) : CrvEll -> Map
IdentityMap(E) : CrvEll -> Map
IdentityMap(X) : Sch -> MapSch
error statement (OVERVIEW)
The if statement (OVERVIEW)
if boolexpr_1 then statements_1 else statements_2 end if : ->
State_if (Example H1E10)
GetIgnorePrompt() : -> BoolElt
SetIgnorePrompt(b) : BoolElt ->
SetIgnoreSpaces(b) : BoolElt ->
Multiple Assignment (OVERVIEW)
ClebschToIgusaClebsch(Q) : SeqEnum -> SeqEnum
HyperellipticCurveFromIgusaClebsch(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 (HYPERELLIPTIC CURVES)
IgusaClebschInvariants(C: parameters) : CrvHyp -> SeqEnum
IgusaClebschInvariants(f: parameters) : RngUPolElt -> SeqEnum
IgusaClebschInvariants(h, f) : RngUPolElt, RngUPolElt -> SeqEnum
IgusaClebschToIgusa(S) : SeqEnum -> SeqEnum
JInvariants(f: parameters) : RngUPolElt -> SeqEnum
IgusaInvariants(f: parameters) : RngUPolElt -> SeqEnum
IgusaInvariants(C: parameters): CrvHyp -> SeqEnum
IgusaInvariants(h, f): RngUPolElt, RngUPolElt -> SeqEnum
IharaBound(F) : FldFun -> RngIntElt
IharaBound(F) : FldFun -> RngIntElt
iload "filename";
Ilog(b, n) : RngIntElt, RngIntElt -> RngIntElt
Ilog2(n) : RngIntElt -> RngIntElt
Im(c) : FldComElt -> FldReElt
Imaginary(c) : FldComElt -> FldReElt
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) : 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) : GrpGPC, GrpGPC -> 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) : 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
Images and Preimages (MAPPINGS)
Images, Orbits and Stabilizers (PERMUTATION GROUPS)
Orbit and Stabilizer Functions for Large Groups (MATRIX GROUPS)
Orbits and Stabilizers (MATRIX GROUPS)
Scheme_image-finder (Example H83E30)
Images, Orbits and Stabilizers (PERMUTATION GROUPS)
Orbits and Stabilizers (MATRIX GROUPS)
Orbit and Stabilizer Functions for Large Groups (MATRIX GROUPS)
Images and Preimages (MAPPINGS)
ImageSystem(f,S,d) : AmbProjMap,SchProj,RngIntElt -> LinSys
ImageWithBasis(X, M) : ModMatRngElt, ModRng -> ModRng
Im(c) : FldComElt -> FldReElt
Imaginary(c) : FldComElt -> FldReElt
Imaginary(z) : SpcHypElt -> FldPrElt
ImplicitFunction(f, d, n) : RngUPolElt, RngIntElt, RngIntElt -> RngSerElt
GrpFP_1_ImplicitCosetEnumeration (Example H19E34)
ImplicitFunction(f, d, n) : RngUPolElt, RngIntElt, RngIntElt -> RngSerElt
Implicitization(f) : Map -> RngMPol
Importing Constants (FUNCTIONS, PROCEDURES AND PACKAGES)
import "filename": ident_list;
Func_import (Example H2E7)
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 Unitary Reflection Groups (REFLECTION GROUPS)
Imprimitive Unitary Reflection Groups (REFLECTION GROUPS)
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
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, ModDed -> 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
u in B : GrpBrdElt, GrpBrd -> BoolElt
g in G : GrpFinElt, GrpFin -> BoolElt
u in H : GrpFPElt, GrpFP -> 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
p in B : IncPt, IncBlk -> BoolElt
v in L : LatElt, Lat -> BoolElt
f in M : MapIsoSch, PowIsoSch -> 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
Combinatorial and Geometrical Structures (OVERVIEW)
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
Combinatorial and Geometrical Structures (OVERVIEW)
Construction of an Incidence Geometry (INCIDENCE GEOMETRY)
INCIDENCE GEOMETRY
INCIDENCE STRUCTURES AND DESIGNS
INCIDENCE GEOMETRY
INCIDENCE STRUCTURES AND DESIGNS
IncidenceDigraph(A) : ModHomElt -> GrphDir
Combinatorial and Geometrical Structures (OVERVIEW)
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
IncidentEdges(u) : GrphVert -> { GrphEdge }
IncidentEdges(u) : GrphVert -> { GrphEdge }
Include(~S, x) : SeqEnum, Elt ->
Include(~S, x) : SetEnum, Elt ->
Set_Include (Example H7E10)
InclusionMap(G, H) : GrpGPC, GrpGPC -> Map
InclusionMap(G, H) : GrpPC, GrpPC -> Map
Inclusion and Equality (FINITE SOLUBLE GROUPS)
Inclusion and Equality (FINITE SOLUBLE GROUPS)
InclusionMap(G, H) : GrpGPC, GrpGPC -> Map
InclusionMap(G, H) : GrpPC, GrpPC -> Map
NumberOfInclusions(e, f) : SubGrpLatElt, SubGrpLatElt -> RngIntElt
MaximalIncreasingSequence(w) : MonOrdElt -> RngIntElt
MaximalIncreasingSequences(w, k) : SeqEnum,RngIntElt -> RngIntElt
IndecomposableSummands(M) : ModGrp -> [ ModGrp ]
IsIndecomposable(M,B) : ModBrdt, RngIntElt -> BoolElt
Indecomposable Projective Modules (BASIC ALGEBRAS)
Indecomposable Projective Modules (BASIC ALGEBRAS)
IndecomposableSummands(M) : ModGrp -> [ ModGrp ]
IsIndefinite(A) : AlgQuat -> BoolElt
InDegree(u) : GrphVert -> RngIntElt
IndentPop() : ->
IndentPush() : ->
SetIndent(n) : RngIntElt ->
Indentation (INPUT AND OUTPUT)
IndentPop() : ->
IndentPush() : ->
IndependenceNumber(G: parameters) : GrphUnd -> RngIntElt
IndependenceNumber(G: parameters) : GrphUnd -> RngIntElt
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 }
Cliques, Independent Sets (GRAPHS)
IndependentUnits(O) : RngFunOrd -> SeqEnum[RngFunOrdElt]
IndependentUnits(O) : RngOrd -> GrpAb, Map
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> ]
FirstIndexOfColumn(t, j) : Tbl,RngIntElt -> RngIntElt
FirstIndexOfRow(t, i) : Tbl,RngIntElt -> RngIntElt
HasValidIndex(P) : GrpFPCosetEnumProc -> BoolElt
Index(x) : CopElt -> RngIntElt
Index(G, H) : GrpAb, GrpAb -> RngIntElt
Index(G, H) : GrpFin, GrpFin -> RngIntElt
Index(P) : GrpFPCosetEnumProc -> 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(L, S): Lat, Lat -> RngInt
Index(s, t) : MonStgElt, MonStgElt -> RngIntElt
Index(G, H: parameters) : GrpFP, GrpFP -> 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, i, n) : RngPowLazElt, [RngIntElt], [RngIntElt] -> 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
LastIndexOfColumn(t, j) : Tbl,RngIntElt -> RngIntElt
LastIndexOfRow(t, i) : Tbl,RngIntElt -> 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
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 Equations (ORDERS AND ALGEBRAIC FIELDS)
RngOrd_index-form (Example H48E27)
Index of a Subgroup: The Todd-Coxeter Algorithm (FINITELY PRESENTED GROUPS)
GrpFP_1_Index1 (Example H19E30)
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 Assignment (STATEMENTS AND EXPRESSIONS)
Indexed Sets (SETS)
Multisets (SETS)
Sets (OVERVIEW)
The Indexed Set Constructor (SETS)
Indexed Assignment (STATEMENTS AND EXPRESSIONS)
IndexedCoset(V, C) : GrpFPCos, GrpFPCosElt -> GrpFPCosElt
IndexedCoset(V, w) : GrpFPCos, GrpFPElt -> GrpFPCosElt
Isetseq(S) : SetIndx -> SeqEnum
IndexedSetToSequence(S) : SetIndx -> SeqEnum
Isetset(S) : SetIndx -> SetEnum
IndexedSetToSet(S) : SetIndx -> SetEnum
IndexFormEquation(O, k) : RngOrd, RngIntElt -> [ RngOrdElt ]
Mat_Indexing (Example H59E4)
ModFld_Indexing (Example H61E7)
SMat_Indexing (Example H60E2)
State_Indexing (Example H1E3)
Indexing (FREE MODULES)
Indexing (MODULES OVER A MATRIX ALGEBRA)
Indexing Elements (STRUCTURE CONSTANT ALGEBRAS)
Multi-indexing (INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS])
IndexOfPartition(P) : SeqEnum -> RngIntElt
IndexOfSpeciality(D) : DivCrvElt -> RngIntElt
IndexOfSpeciality(D) : DivFunElt -> RngIntElt
Indices(X) : CrvMod -> SeqEnum
Indices(X) : VSrfK3 -> SeqEnum
Implicit Invocation of the Todd-Coxeter Algorithm (FINITELY PRESENTED GROUPS)
Implicit Invocation of the Todd-Coxeter Algorithm (FINITELY PRESENTED GROUPS)
Lifting a Quotient by Choosing an Individual Cocycle (FP GROUPS - ADVANCED FEATURES)
Lifting a Quotient by Choosing an Individual Cocycle (FP GROUPS - ADVANCED FEATURES)
InducedAutomorphism(r, h, c) : Map, Map, RngIntElt -> Map
InducedMap(m1, m2, h, c) : Map, Map, Map, RngIntElt -> Map
InducedMapOnHomology(f,n) : MapChn, RngIntElt -> ModTupFldElt
IsTensorInduced(G : parameters) : GrpMat -> BoolElt
TensorInducedBasis(G) : GrpMat -> GrpMatElt
TensorInducedPermutations(G) : GrpMat -> SeqEnum
Action on a G-Space (PERMUTATION GROUPS)
Coset Spaces: Induced Homomorphism (FINITELY PRESENTED GROUPS)
Action on a G-Space (PERMUTATION GROUPS)
Coset Spaces: Induced Homomorphism (FINITELY PRESENTED GROUPS)
InducedAutomorphism(r, h, c) : Map, Map, RngIntElt -> Map
InducedMap(m1, m2, h, c) : Map, Map, Map, RngIntElt -> Map
FldAb_inducedMap (Example H51E4)
InducedMapOnHomology(f,n) : MapChn, RngIntElt -> ModTupFldElt
Induction(x, G) : AlgChtrElt, Grp -> AlgChtrElt
Induction(R, G) : Map, Grp -> Map
Induction(M, G) : ModGrp, Grp -> ModGrp
Induction and Restriction (K[G]-MODULES AND GROUP REPRESENTATIONS)
Induction, Restriction, Extension (CHARACTERS OF FINITE GROUPS)
Tensor-induced Groups (MATRIX GROUPS)
Induction and Restriction (K[G]-MODULES AND GROUP REPRESENTATIONS)
Induction, Restriction, Extension (CHARACTERS OF FINITE GROUPS)
Comparison (OVERVIEW)
IsInert(P) : RngOrdIdl -> BoolElt
IsInert(P, O) : RngOrdIdl, RngOrd -> BoolElt
LocseqInert(x) : RngLoc -> [ RngLocElt ]
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(I) : RngFunOrdIdl -> RngIntElt
ResidueClassDegree(I) : RngFunOrdIdl -> RngIntElt
Degree(I) : RngFunOrdIdl -> RngIntElt
Degree(I) : RngOrdIdl -> RngIntElt
InertiaDegree(P) : PlcFunElt -> RngIntElt
InertiaDegree(L) : RngLoc -> RngIntElt
L . 2 : RngLoc -> RngLocElt
InertiaElement(L) : RngLoc -> RngLocElt
InertiaField(L) : FldLoc -> FldLoc
InertiaField(p) : RngOrdIdl -> FldNum, Map
InertiaGroup(p) : RngOrdIdl -> GrpPerm
InertialPolynomial(L) : RngLoc -> RngUPolElt
IsInertial(g) : RngUPolElt -> BoolElt
InertialPolynomial(L) : RngLoc -> RngUPolElt
InertiaRing(L) : RngLoc -> RngLoc
InertseqpAdic(x) : RngLoc -> [ RngLocElt ]
InertseqpAdic(x) : RngLoc -> [ RngLocElt ]
Local Rings and Fields with Infinite Precision (LOCAL RINGS AND FIELDS)
p-adic Rings and Fields with Infinite Precision (p-ADIC RINGS AND FIELDS)
EquationOrderInfinite(F) : FldFun -> RngFunOrd
HasInfiniteComputableAbelianQuotient(G) : GrpFP -> BoolElt, GrpAb, Map
InfiniteSum(m, i) : Map, RngIntElt -> FldPrElt
MaximalOrderInfinite(F) : FldFun -> RngFunOrd
Summation of Infinite Series (REAL AND COMPLEX FIELDS)
Summation of Infinite Series (REAL AND COMPLEX FIELDS)
InfiniteSum(m, i) : Map, RngIntElt -> FldPrElt
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
Infinities (RING OF INTEGERS)
Operators (OVERVIEW)
InflectionPoints(C) : Sch -> SeqEnum
Flexes(C) : Sch -> SeqEnum
IsInflectionPoint(p) : Sch,Pt -> BoolElt,RngIntElt
InflectionPoints(C) : Sch -> SeqEnum
Flexes(C) : Sch -> SeqEnum
IsolInfo(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> MonStgElt
ListTypes() : ->
Other Information Procedures (ENVIRONMENT AND OPTIONS)
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 ]
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)
The Information Space and Information Sets (LINEAR CODES OVER FINITE FIELDS)
InformationRate(C) : Code -> FldPrElt
InformationRate(C) : Code -> RngPrElt
InformationSet(C) : Code -> [ RngIntElt ]
InformationSpace(C) : Code -> ModTupFld
NPCGenerators(G) : GrpPC -> RngIntElt
NPCgens(G) : GrpPC -> RngIntElt
Infrastructure (FINITE SOLUBLE GROUPS)
AbsolutelyIrreducibleModulesInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
IrreducibleRepresentationsInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
IrreducibleModulesInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
AbsolutelyIrreducibleRepresentationsInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
IrreducibleRepresentationsInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
IrreducibleModulesInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
The Initial Context (MAGMA SEMANTICS)
The Initial Context (MAGMA SEMANTICS)
Initialisation (FP GROUPS - ADVANCED FEATURES)
Initialisation (FP GROUPS - ADVANCED FEATURES)
Initialize(F) : GrpFP -> SQProc
Initialize(e) : Map -> SQProc
Injection(B, i, v) : AlgBas, RngIntElt, ModRngElt -> AlgBasElt
Injections(C) : Cop -> [ Map ]
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 Modules (BASIC ALGEBRAS)
Injective Modules (BASIC ALGEBRAS)
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
State_InLineConditional (Example H1E11)
InNeighbors(u) : GrphVert -> { GrphVert }
InNeighbours(u) : GrphVert -> { GrphVert }
InNeighbors(u) : GrphVert -> { GrphVert }
InNeighbours(u) : GrphVert -> { GrphVert }
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
SkewShape(t) : Tbl -> SeqEnum[RngIntElt]
KSpace(K, n, F) : Fld, RngIntElt, Mtrx -> ModTupFld
Construction of a Vector Space with Inner Product Matrix (VECTOR SPACES)
Inner Products (FREE MODULES)
Inner Products (FREE MODULES)
InnerFaces(N) : NwtnPgon -> SeqEnum
InnerGenerators(A) : GrpAuto -> SeqEnum
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 H61E6)
InnerProductMatrix(L) : Lat -> AlgMatElt
InnerProductMatrix(M) : ModBrdt -> AlgMatElt
InnerShape(t) : Tbl -> SeqEnum[RngIntElt]
SkewShape(t) : Tbl -> SeqEnum[RngIntElt]
InnerVertices(N) : NwtnPgon -> SeqEnum
SetEchoInput(b) : BoolElt ->
SetEchoInput(b) : BoolElt ->
readi identifier, prompt;
Interactive Input (INPUT AND OUTPUT)
Loading files (OVERVIEW)
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
InverseRowInsert(~t, i, j) : Tbl, RngIntElt, RngIntElt ->
RowInsert(~t, w) : Tbl, MonOrdElt ->
RowInsert(~t, x) : Tbl, RngIntElt ->
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
SmallGroupIsInsolvable(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupIsInsoluble(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupIsInsolvable(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupIsInsoluble(o, n) : RngIntElt, RngIntElt -> Grp
Explicit LP Solving Functions (LINEAR PROGRAMMING)
Explicit LP Solving Functions (LINEAR PROGRAMMING)
FldFunG_int_cl (Example H53E5)
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
OrderedIntegerMonoid() : -> MonOrd
PlacticIntegerMonoid() : -> MonOrd
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 ]
TableauIntegerMonoid() : -> MonTbl
Polynomials over the Integers (MULTIVARIATE POLYNOMIAL RINGS)
Polynomials over the Integers (UNIVARIATE POLYNOMIAL RINGS)
RING OF INTEGERS
Rings, Fields, and Algebras (OVERVIEW)
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
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 H38E2)
IntegerSolutionVariables(L) : LP -> SeqEnum
Intseq(n, b) : RngIntElt, RngIntElt -> [RngIntElt]
IntegerToSequence(n, b) : RngIntElt, RngIntElt -> [RngIntElt]
IntegerToString(n) : RngIntElt -> ModStgElt
IntegerToString(n) : RngIntElt -> MonStgElt
IntegerToString(n, b) : RngIntElt, RngIntElt -> MonStgElt
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(s) : RngPowLazElt -> RngPowLazElt
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
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, MapIsoSch
IntegralPoints(E) : CrvEll -> [ PtEll ], [ Tup ]
IntegralQuarticPoints(Q) : [ RngIntElt ] -> [ SeqEnum ]
IntegralQuarticPoints(Q, P) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]
IntegralSplit(a, O) : FldFunElt, 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 H41E9)
Derivative, Integral (MULTIVARIATE POLYNOMIAL RINGS)
Derivative, Integral (UNIVARIATE POLYNOMIAL RINGS)
Integral Points (ELLIPTIC CURVES)
Integral and S-integral Points (ELLIPTIC CURVES)
Integral Points (ELLIPTIC CURVES)
S-integral Points (ELLIPTIC CURVES)
Integral Points (ELLIPTIC CURVES)
S-integral Points (ELLIPTIC CURVES)
IntegralBasis(F) : FldAlg -> [ FldAlgElt ]
IntegralBasis(Q) : FldRat -> [ FldRatElt ]
IntegralBasis(M) : ModSym -> Lat
ModSym_IntegralBasis (Example H90E8)
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, MapIsoSch
IntegralPoints(E) : CrvEll -> [ PtEll ], [ Tup ]
CrvEll_IntegralPoints (Example H87E21)
CrvEll_IntegralPointsSequence (Example H87E22)
IntegralQuarticPoints(Q) : [ RngIntElt ] -> [ SeqEnum ]
IntegralQuarticPoints(Q, P) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]
IntegralSplit(a, O) : FldFunElt, RngFunOrd -> RngFunOrdElt, RngElt
IntegralSplit(I) : RngFunOrdIdl -> RngFunOrdIdl, RngElt
Integration (REAL AND COMPLEX FIELDS)
readi identifier, prompt;
Interactive Input (INPUT AND OUTPUT)
Using p-Quotient Interactively (FP GROUPS - ADVANCED FEATURES)
readi identifier, prompt;
Interactive Input (INPUT AND OUTPUT)
Func_InteractiveUserAttributes (Example H2E12)
Interior(P, C) : Plane, { PlanePt } -> { PlanePt }
IsInterior(N,p) : NwtnPgon,Tup -> BoolElt
InternalEdges(FS) : SymFry -> SeqEnum
Accessing Internal Data (DATABASES OF GROUPS)
Internal Help Browser (ENVIRONMENT AND OPTIONS)
Internal Help Browser (ENVIRONMENT AND OPTIONS)
InternalEdges(FS) : SymFry -> SeqEnum
RngMPol_Interpolate (Example H43E5)
Interpolation(I, V) : [ RngElt ], [ RngElt ] -> RngUPolElt
Interpolation(I, V, i) : [ RngElt ], [ RngMPolElt ], RngIntElt -> RngMPolElt
Interpolation(P, V, x) : [FldPrElt], [FldPrElt], FldPrElt -> FldPrElt, FldPrElt
Evaluation, Interpolation (MULTIVARIATE POLYNOMIAL RINGS)
Evaluation, Interpolation (UNIVARIATE POLYNOMIAL RINGS)
Evaluation, Interpolation (UNIVARIATE POLYNOMIAL RINGS)
Control-C key (OVERVIEW)
Starting, Interrupting and Terminating (STATEMENTS AND EXPRESSIONS)
IntersectKernels(SQP, SQR) : SQProc, SQProc -> SQProc, Map, Map
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
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)
The Intersection Pairing (MODULAR SYMBOLS)
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
ModSym_IntersectionPairing (Example H90E18)
CalculateTransverseIntersections(~g) : GrphRes ->
SelfIntersections(g) : GrphRes -> SeqEnum
TransverseIntersections(g) : GrphRes -> SeqEnum
IntersectKernels(SQP, SQR) : SQProc, SQProc -> SQProc, Map, Map
IsIntrinsic(S) : MonStgElt -> Bool, Intrinsic
Intrinsics (FUNCTIONS, PROCEDURES AND PACKAGES)
Intrinsics (OVERVIEW)
Func_intrinsic (Example H2E6)
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)
Projective Closure (PLANE ALGEBRAIC CURVES)
Projective Closure (SCHEMES)
Rational Points (SCHEMES)
Schemes (SCHEMES)
Ambient Spaces (SCHEMES)
Projective Closure (PLANE ALGEBRAIC CURVES)
Projective Closure (SCHEMES)
Choosing Coordinates (PLANE ALGEBRAIC CURVES)
Function Fields and Divisors (PLANE ALGEBRAIC CURVES)
Linear Systems (SCHEMES)
Maps (SCHEMES)
Points (PLANE ALGEBRAIC CURVES)
Rational Points (SCHEMES)
Schemes (SCHEMES)
Aside: Types of Schemes (SCHEMES)
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 (BRAID GROUPS)
Introduction (CLASS FIELD THEORY)
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 OF 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 (K[G]-MODULES AND GROUP REPRESENTATIONS)
Introduction (LATTICES)
Introduction (LAZY POWER SERIES RINGS)
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 DEDEKIND DOMAINS)
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 (PARTITIONS, WORDS AND YOUNG TABLEAUX)
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 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 (SPARSE MATRICES)
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 ({THE MODULE OF}{SUPERSINGULAR POINTS})
Introduction and First Examples (SCHEMES)
Overview (OVERVIEW)
Intseq(n, b) : RngIntElt, RngIntElt -> [RngIntElt]
IntegerToSequence(n, b) : RngIntElt, RngIntElt -> [RngIntElt]
Class Invariants (BINARY QUADRATIC FORMS)
Elliptic and Modular Invariants (BINARY QUADRATIC FORMS)
General Structure Invariants (ALGEBRAIC FUNCTION FIELDS)
Invariants of an Algebra (ALGEBRAS)
FldFunG_invar (Example H53E7)
Plane_invar (Example H99E6)
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> ]
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)
Creation of Invariant Rings (INVARIANT RINGS OF FINITE GROUPS)
INVARIANT RINGS OF FINITE GROUPS
InvariantFactors(a) : AlgMatElt -> [ AlgPolElt ]
InvariantFactors(A) : Mtrx -> [ RngUPolElt ]
InvariantForms(G) : GrpMat -> [ AlgMatElt ]
InvariantForms(G, n) : GrpMat, RngIntElt -> [ AlgMatElt ]
InvariantRing(G) : GrpMat -> RngInvar
Elementary Invariants (BRANDT MODULES)
AbelianInvariants(G) : GrpFin -> [ RngIntElt ]
AbelianInvariants(G) : GrpMat -> [ RngIntElt ]
AbelianInvariants(G) : GrpPC -> [RngIntElt]
AbelianQuotientInvariants(G) : GrpFP -> [ RngIntElt ]
AbelianQuotientInvariants(H) : GrpFP -> [ RngIntElt ]
AbelianQuotientInvariants(G, n) : GrpFP, RngIntElt -> [ 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 H73E3)
CrvEll_Invariants (Example H87E6)
GrpMat_Invariants (Example H21E12)
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)
Elementary Invariants (SPARSE MATRICES)
Invariants (CLASS FIELD THEORY)
Invariants of Isomorphisms (HYPERELLIPTIC CURVES)
Numerical Invariants (FINITE SOLUBLE GROUPS)
CrvEll_Invariants to Read (Example H87E30)
Invariants of Isomorphisms (HYPERELLIPTIC CURVES)
InvariantsOfDegree(R, d) : RngInvar, RngIntElt -> [ RngMPolElt ]
InvariantsOfDegree(R, d, k) : RngInvar, RngIntElt, RngIntElt -> [ RngMPolElt ]
RngInvar_InvariantsOfDegree (Example H80E3)
RngInvar_InvariantsOfDegree (Example H80E4)
Inverse Block: invblock (IDEAL THEORY AND GRÖBNER BASES)
EulerPhiInverse(m) : RngIntElt -> RngIntElt
FactoredEulerPhiInverse(n) : RngIntElt -> RngIntEltFact
FactoredInverseDefiningPolynomials(f) : MapSch -> SeqEnum
Inverse(w) : GrpAtcElt -> GrpAtcElt
Inverse(~u) : GrpBrdElt ->
Inverse(u) : GrpBrdElt -> GrpBrdElt
Inverse( F, w ) : GrpFP, GrpFPElt -> GrpFPElt
Inverse( g ) : GrpLieElt -> GrpLieElt
Inverse(w) : GrpRWSElt -> GrpRWSElt
Inverse(f) : MapIsoSch -> MapIsoSch
Inverse(f) : MapSch -> MapSch
InverseDefiningPolynomials(f) : MapSch -> SeqEnum
InverseJeuDeTaquin(~t, i, j) : Tbl, RngIntElt, RngIntElt ->
InverseKrawchouk(A, K, n) : RngUPolElt, FldFin, RngIntElt -> RngUPolElt
InverseMattsonSolomonTransform(A, n) : RngUPolElt, RngIntElt -> RngUPolElt
InverseMod(E, M) : RngOrdElt, RngIntElt -> RngOrdElt
InverseRSKCorrespondenceDoubleWord(t1, t2) : Tbl, Tbl -> MonOrdElt, MonOrdElt
InverseRSKCorrespondenceMatrix(t1, t2) : Tbl, Tbl -> Mat
InverseRSKCorrespondenceSingleWord(t1, t2) : Tbl, Tbl -> MonOrdElt
InverseRowInsert(~t, i, j) : Tbl, RngIntElt, RngIntElt ->
InverseWordMap(G) : GrpMat -> Map
InverseWordMap(G) : GrpPerm -> Map
Modinv(n, m) : RngIntElt, RngIntElt -> RngIntElt
Groups (OVERVIEW)
Inverse Hyperbolic Functions (REAL AND COMPLEX FIELDS)
Inverse Trigonometric Functions (REAL AND COMPLEX FIELDS)
Rings, Fields, and Algebras (OVERVIEW)
Inverse Hyperbolic Functions (REAL AND COMPLEX FIELDS)
Inverse Trigonometric Functions (REAL AND COMPLEX FIELDS)
InverseDefiningPolynomials(f) : MapSch -> SeqEnum
InverseJeuDeTaquin(~t, i, j) : Tbl, RngIntElt, RngIntElt ->
InverseKrawchouk(A, K, n) : RngUPolElt, FldFin, RngIntElt -> RngUPolElt
InverseMattsonSolomonTransform(A, n) : RngUPolElt, RngIntElt -> RngUPolElt
Modinv(E, M) : RngOrdElt, RngOrdIdl -> RngOrdElt
InverseMod(E, M) : RngOrdElt, RngIntElt -> RngOrdElt
Modinv(n, m) : RngIntElt, RngIntElt -> RngIntElt
InverseRowInsert(~t, i, j) : Tbl, RngIntElt, RngIntElt ->
InverseRSKCorrespondenceDoubleWord(t1, t2) : Tbl, Tbl -> MonOrdElt, MonOrdElt
InverseRSKCorrespondenceMatrix(t1, t2) : Tbl, Tbl -> Mat
InverseRSKCorrespondenceSingleWord(t1, t2) : Tbl, Tbl -> MonOrdElt
InverseWordMap(G) : GrpMat -> Map
InverseWordMap(G) : GrpPerm -> Map
Functions (OVERVIEW)
Functions, Procedures, and Mappings (OVERVIEW)
Involution(P) : PtHyp -> PtHyp
- P : PtHyp -> PtHyp
CanonicalInvolution(X) : CrvMod -> MapSch
DualStarInvolution(M) : ModSym -> AlgMatElt
Involution(a) : AlgGrpElt -> AlgGrpElt
StarInvolution(M) : ModSym -> AlgMatElt
INPUT AND OUTPUT
Iroot(a, n) : RngIntElt, RngIntElt -> RngIntElt
Database of Irreducible Soluble Subgroups of GL(n,p) for n > 1 and p^n < 256 (OVERVIEW)
Factorization and Irreducibility (MULTIVARIATE POLYNOMIAL RINGS)
Factorization and Irreducibility (UNIVARIATE POLYNOMIAL RINGS)
AbsolutelyIrreducibleConstituents(M) : ModGrp -> [ ModGrp ]
AbsolutelyIrreducibleModule(M) : ModRng -> ModRng
AbsolutelyIrreducibleModulesBurnside(G, K : parameters ) : Grp, FldFin -> [ ModGrp ]
AbsolutelyIrreducibleModulesSchur(G, K: parameters) : GrpPC, Rng -> List[GModule]
AbsolutelyIrreducibleRepresentationProcessDelete( P) : SolRepProc ->
AbsolutelyIrreducibleRepresentationsInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
IrreducibleRepresentationsInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
IrreducibleModulesInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
AbsolutelyIrreducibleRepresentationsSchur(G, k: parameters) : GrpPC, Rng -> List[Map]
AllIrreduciblePolynomials(F, m) : FldFin, RngIntElt -> { RngPolElt }
IrreducibleModule(B, i) : AlgBas, RngIntElt -> ModAlg
IrreducibleModules(G, K : parameters) : Grp, Fld -> Seqenum
IrreducibleModulesBurnside(G, K : parameters ) : Grp, FldFin -> [ ModGrp ]
IrreducibleModulesSchur(G, K: parameters) : GrpPC, Rng -> List[GModule]
IrreduciblePolynomial(F, m) : FldFin, RngIntElt -> RngPolElt
IrreducibleRepresentationsSchur(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
Database of Irreducible Soluble Subgroups of GL(n,p) for n > 1 and p^n < 256 (OVERVIEW)
Generic Functions for Finding Irreducible Modules (K[G]-MODULES AND GROUP REPRESENTATIONS)
Irreducible Modules (FP GROUPS - ADVANCED FEATURES)
The Burnside Algorithm for General Groups (K[G]-MODULES AND GROUP REPRESENTATIONS)
The Construction of all Irreducible Modules (K[G]-MODULES AND GROUP REPRESENTATIONS)
The Schur Algorithm for Soluble Groups (K[G]-MODULES AND GROUP REPRESENTATIONS)
The Table of Irreducible Characters (CHARACTERS OF FINITE GROUPS)
Generic Functions for Finding Irreducible Modules (K[G]-MODULES AND GROUP REPRESENTATIONS)
Irreducible Modules (FP GROUPS - ADVANCED FEATURES)
The Construction of all Irreducible Modules (K[G]-MODULES AND GROUP REPRESENTATIONS)
The Burnside Algorithm for General Groups (K[G]-MODULES AND GROUP REPRESENTATIONS)
The Schur Algorithm for Soluble Groups (K[G]-MODULES AND GROUP REPRESENTATIONS)
SimpleModule(B, i) : AlgBas, RngIntElt -> ModAlg
IrreducibleModule(B, i) : AlgBas, RngIntElt -> ModAlg
AbsolutelyIrreducibleModules(G, K : parameters) : Grp, Fld -> SeqEnum
IrreducibleModules(G, K : parameters) : Grp, Fld -> Seqenum
ModGrp_IrreducibleModules (Example H78E12)
IrreducibleModulesBurnside(G, K : parameters ) : Grp, FldFin -> [ ModGrp ]
AbsolutelyIrreducibleModulesInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
IrreducibleRepresentationsInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
IrreducibleModulesInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
AbsolutelyIrreducibleRepresentationsInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
IrreducibleModulesSchur(G, K: parameters) : GrpPC, Rng -> List[GModule]
IrreducibleRepresentationsSchur(G, k: parameters) : GrpPC, Rng -> List[Map]
IrreduciblePolynomial(F, m) : FldFin, RngIntElt -> RngPolElt
AbsolutelyIrreducibleModulesInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
IrreducibleRepresentationsInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
IrreducibleModulesInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
AbsolutelyIrreducibleRepresentationsInit(G, F : parameters) : GrpPC, Fld -> SolRepProc
IrreducibleModulesSchur(G, k: parameters) : GrpPC, Rng -> List[GModule]
IrreducibleRepresentationsSchur(G, k: parameters) : GrpPC, Rng -> List[Map]
KnownIrreducibles(R) : AlgChtr -> SeqEnum
RemoveIrreducibles(I, C) : [ AlgChtrElt ], [ AlgChtrElt ] -> [ AlgChtrElt ], [ AlgChtrElt ]
Finding Irreducibles (CHARACTERS OF FINITE GROUPS)
IrreducibleSecondaryInvariants(R) : RngInvar -> [ RngMPolElt ]
HasIrregularFibres(s) : GrphSpl -> BoolElt
The where ... is Construction (STATEMENTS AND EXPRESSIONS)
ISA(T, U) : Cat, Cat -> BoolElt
IsAbelian(A) : FldAb -> BoolElt
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(K) : FldAlg -> BoolElt
IsAbsolutelyIrreducible(G) : GrpMat -> BoolElt
IsAbsolutelyIrreducible(M) : ModRng -> BoolElt, AlgMatElt, RngIntElt
IsAbsoluteOrder(O) : RngOrd -> BoolElt
IsAdjoint( G ) : GrpLie-> BoolElt
IsAdjoint( RD ) : RootDtm-> BoolElt
IsAffine(X) : Sch -> BoolElt
IsAffineLinear(f) : MapSch -> BoolElt
IsAffineSpace(X) : Sch -> BoolElt
IsAlgebraicallyIsomorphic( G, H ) : GrpLie, GrpLie -> BoolElt
IsAlgebraicGeometric(C) : Code -> BoolElt
IsAlternating(G) : GrpPerm -> BoolElt
IsAltsym(G) : GrpPerm -> BoolElt
IsAmbient(M) : ModBrdt -> BoolElt
IsAmbientFunction(A,f) : Sch,RngElt -> BoolElt, RngElt
IsAmbientRationalFunction(A,f) : Sch,RngElt -> BoolElt
IsAmbientSpace(M) : ModFrm -> BoolElt
IsAmbientSpace(M) : ModSS -> BoolElt
IsAnalyticallyIrreducible(p) : Crv,Pt -> BoolElt
IsArc(P, A) : Plane, { PlanePt } -> BoolElt
[Future release] IsArcTransitive(G, t) : GrphUnd, RngIntElt -> BoolElt
IsAssociative(A) : AlgGen -> BoolElt
IsAutomorphism(f) : MapSch -> BoolElt,AutSch
IsBalanced(D, t: parameters) : Inc, RngIntElt -> BoolElt, RngIntElt
IsFree(L) : LinSys -> BoolElt
IsBasePointFree(L) : LinSys -> BoolElt
IsBiconnected(G) : GrphUnd -> BoolElt
IsBijective(a) : ModMatRngElt -> BoolElt
IsBipartite(G) : GrphUnd -> BoolElt
IsBlock(G, S) : GrpPerm, { Elt } -> BoolElt
IsBlock(D, S) : Inc, IncBlk -> BoolElt, IncBlk
IsBlockTransitive(D) : Inc -> BoolElt
IsBoundary(N, p) : NwtnPgon,Tup -> BoolElt
IsCanonical(D) : DivCrvElt -> BoolElt,DiffFunElt
IsCanonical(D) : DivFunElt -> BoolElt, DiffFunElt
IsCanonical(D) : DivFunElt -> BoolElt, DiffFunElt
IsCartanIrreducible( C ) : AlgMatElt -> BoolElt
IsCartanMatrix( M ) : AlgMatElt -> BoolElt
IsCentral(A) : FldAb -> BoolElt
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(P, g) : Plane, GrpPermElt -> BoolElt, PlanePt, PlaneLn
IsChainMap(L, C, D, n) : List, ModCpx, ModCpx, RngIntElt -> BoolElt
IsChainMap(f) : MapChn -> BoolElt
IsCharacter(x) : AlgChtrElt -> BoolElt
IsCluster(X) : Sch -> BoolElt,Clstr
IsCoercible(X,Q) : Sch,SeqEnum -> BoolElt,Pt
IsCoercible(S, x) : Str, Elt -> Bool, Elt
IsCohenMacaulay(R) : RngInvar -> BoolElt
IsCollinear(P, S) : Plane, { PlanePt } -> BoolElt, PlaneLn
IsCommutative(A) : AlgGen -> BoolElt
IsCommutative(R) : Rng -> BoolElt
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(P, R) : Plane, { PlaneLn } -> BoolElt, PlanePt
IsConditioned(G) : GrpPC -> BoolElt
IsConfluent(G) : GrpAtc -> BoolElt
IsConfluent(G) : GrpRWS -> BoolElt
IsConfluent(M) : MonRWS -> BoolElt
GrpAtc_IsConfluent (Example H28E7)
GrpRWS_IsConfluent (Example H27E7)
MonRWS_IsConfluent (Example H15E7)
IsCongruence(G) : GrpPSL2 -> BoolElt
IsConic(C) : Sch -> BoolElt, CrvCon
IsConic(X) : Sch -> BoolElt,CrvCon
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) : GrpFP, GrpFP, GrpFP -> BoolElt, GrpFPElt
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
IsConnected(G) : GrphUnd -> BoolElt
IsConsistent(G) : GrpGPC -> BoolElt
IsConsistent(G) : GrpPC -> 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 H24E3)
Possibly Inconsistent Presentations (FINITE SOLUBLE GROUPS)
IsConstant(a) : FldFunElt -> BoolElt, RngElt
IsZero(I) : Map -> BoolElt
IsConway(F) : FldFin -> BoolElt
IsCrystallographic( C ) : AlgMatElt -> BoolElt
IsCrystallographic( W ) : GrpCox -> BoolElt
IsCrystallographic( RD ) : RootDtm -> BoolElt
IsCurve(X) : Sch -> BoolElt,Crv
IsCusp(p) : Crv,Pt -> BoolElt
IsCusp(z) : SpcHypElt -> BoolElt
IsCuspidal(M) : ModBrdt -> BoolElt
IsCuspidal(M) : ModFrm -> BoolElt
IsCuspidal(M) : ModSym -> BoolElt
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(M) : ModRng -> BoolElt, ModRng, ModRng
IsDeficient(C, p) : CrvHyp, RngIntElt -> BoolElt
IsDefined(S, i) : SeqEnum, RngIntElt -> BoolElt
IsDefinite(A) : AlgQuat -> BoolElt
[Future release] IsDegenerate(N) : NwtnPgon -> BoolElt
[Future release] IsDegenerate(F) : NwtnPgon,Tup -> BoolElt
IsDesarguesian(P) : Plane -> BoolElt
IsDesign(D, t: parameters) : Inc, RngIntElt -> BoolElt, RngIntElt
IsDiagonal(a) : AlgMatElt -> BoolElt
IsDiagonal(A) : Mtrx -> BoolElt
IsDifferenceSet(B) : SetEnum -> BoolElt, RngIntElt
IsDirectSummand(M, S) : ModGrp, ModGrp -> BoolElt, ModGrp
HasComplement(M, S) : ModGrp, ModGrp -> BoolElt, ModGrp
IsDiscriminant(D) : RngIntElt -> BoolElt
IsDisjoint(R, S) : SetEnum, SetEnum -> BoolElt
IsDistanceRegular(G) : GrphUnd -> BoolElt
IsDistanceTransitive(G) : GrphUnd -> BoolElt
IsDivisibleBy(a, b) : FldFunElt, FldFunElt -> BoolElt, FldFunElt
IsDivisibleBy(n, d) : RngIntElt, RngIntElt -> BoolElt, RngIntElt
IsDivisibleBy(a, b) : RngMPolElt, RngMPolElt -> BoolElt, RngMPolElt
IsDivisionRing(R) : Rng -> BoolElt
IsIntegralDomain(R): Rng -> BoolElt
IsDomain(R) : Rng -> BoolElt
IsDominant(f) : AmbMap -> BoolElt
IsDoublePoint(p) : Crv,Pt -> BoolElt
IsDoublyEven(C) : Code -> BoolElt
IsEdgeTransitive(G) : GrphUnd -> BoolElt
IsPositive(D) : DivCrvElt -> BoolElt
IsEffective(D) : DivCrvElt -> BoolElt
IsEisenstein(M) : ModBrdt -> BoolElt
IsEisenstein(M) : ModFrm -> BoolElt
IsEisenstein(M) : ModSym -> BoolElt
IsEisenstein(g) : RngUPolElt -> BoolElt
IsEisensteinSeries(f) : ModFrmElt -> BoolElt
IsEisensteinSeries(f) : ModFrmElt -> BoolElt
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(C) : CrvHyp -> BoolElt, CrvEll, MapIsoSch, MapIsoSch
IsEllipticCurve(C) : CrvHyp -> BoolElt, CrvEll, MapIsoSch, MapIsoSch
IsEllipticCurve([a,b]) : [ RngElt ] -> BoolElt, CrvEll
IsEllipticWeierstrass(C) : Crv -> BoolElt
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
IsEmptyWord(u) : GrpBrdElt -> BoolElt
IsEndomorphism(f) : MapSch -> BoolElt
IsEof(S) : MonStgElt -> BoolElt
IsEqual( F, w1, w2 ) : GrpFP, GrpFPElt, GrpFPElt -> BoolElt
IsEquationOrder(O) : RngFunOrd -> BoolElt
IsEquationOrder(O) : RngOrd -> BoolElt
IsEquidistant(C) : Code -> BoolElt
IsEquitable(G, P) : GrphUnd, { { GrphVert } } -> BoolElt
IsEquivalent(G,a,b) : GrpPSL2, SpcHypElt, SpcHypElt -> BoolElt, GrpPSL2Elt
IsEquivalent(g,h,G) : GrpPSL2Elt, GrpPSL2Elt, GrpPSL2 -> BoolElt
IsEquivalent(C, D: parameters) : Code, Code -> BoolElt, Map
IsEquivalent(f, g) : QuadBinElt, QuadBinElt -> BoolElt, AlgMatElt
Isetseq(S) : SetIndx -> SeqEnum
IndexedSetToSequence(S) : SetIndx -> SeqEnum
Isetset(S) : SetIndx -> SetEnum
IndexedSetToSet(S) : SetIndx -> SetEnum
IsEuclideanDomain(F) : FldAlg -> BoolElt
IsEuclideanDomain(R) : Rng -> BoolElt
IsEuclideanRing(R) : Rng -> BoolElt
IsEulerian(G) : Grph -> BoolElt
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(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(u) : RngOrdElt -> BoolElt
IsExtension(G, H, f) : GrpPC, GrpPC, [Map] -> BoolElt, GrpPC
IsExtraSpecial(G) : GrpFin -> BoolElt
IsExtraSpecial(G) : GrpMat -> BoolElt
IsExtraSpecial(G) : GrpPC -> BoolElt
IsExtraSpecial(G) : GrpPerm -> BoolElt
IsExtraSpecialNormalise(G) : GrpMat -> BoolElt
IsFace(N, F) : NwtnPgon,Tup -> BoolElt
IsFaithful(G, Y) : : GrpPerm, GSet -> BoolElt
IsFaithful(x) : AlgChtrElt -> BoolElt
IsField(R) : Rng -> BoolElt
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(O) : RngFunOrd -> BoolElt
IsFirm(C) : CosetGeom -> BoolElt
IsFirm(D) : IncGeom -> BoolElt
IsFlex(C,p) : Sch,Pt -> BoolElt,RngIntElt
IsInflectionPoint(p) : Sch,Pt -> BoolElt,RngIntElt
IsForest(G) : GrphUnd -> BoolElt
IsFree(L) : LinSys -> BoolElt
IsBasePointFree(L) : LinSys -> BoolElt
IsFrobenius(G) : GrpPerm -> BoolElt
IsFTGeometry(C) : CosetGeom -> BoolElt
IsFTGeometry(D) : IncGeom -> BoolElt
IsFundamentalDiscriminant(D) : RngIntElt -> BoolElt
IsGamma0(G) : GrpPSL2 -> BoolElt
IsGamma0(M) : ModFrm -> BoolElt
IsGamma1(G) : GrpPSL2 -> BoolElt
IsGamma1(M) : ModFrm -> BoolElt
IsGeneralizedCharacter(x) : AlgChtrElt -> BoolElt
IsGenus(G) : SymGen -> BoolElt
IsGL2Equivalent(f, g, n) : RngUPolElt, RngUPolElt, RngIntElt -> BoolElt, SeqEnum
IsGLattice(L) : Lat -> GrpMat
IsGlobal(F) : FldFun -> BoolElt
IsGlobalUnit(a) : FldFunElt -> BoolElt
IsGlobalUnit(a) : FldFunElt -> BoolElt
IsGlobalUnitWithPreimage(a) : FldFunElt -> BoolElt, GrpAbElt
IsGlobalUnitWithPreimage(a) : FldFunElt -> BoolElt, GrpAbElt
GrpPGp_IsGood (Example H25E3)
IsGraph(C) : CosetGeom -> GrphUnd
IsGraph(D) : IncGeom -> GrphUnd
IsGroebner(S) : { RngMPolElt } -> BoolElt
IsHadamard(H) : AlgMatElt -> BoolElt
IsHadamardEquivalent(H, J) : AlgMatElt, AlgMatElt -> BoolElt
IsHomeomorphic(G: parameters) : GraphUnd -> BoolElt
IsHomogeneous(M) : ModMPol -> BoolElt
IsHomogeneous(I) : RngMPol -> BoolElt
IsHomogeneous(f) : RngMPolElt -> BoolElt
IsHomogeneous(X,f) : Sch,RngMPolElt -> BoolElt
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([h, g]) : [ RngUPolElt ] -> BoolElt, CrvHyp
IsHyperellipticCurveOfGenus(g, [h, f]) : RngIntElt, [RngUPolElt] -> BoolElt, CrvHyp
IsHyperellipticWeierstrass(C) : Crv -> BoolElt
IsHypersurface(X) : Sch -> BoolElt, RngMPolElt
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(u) : GrpBrdElt -> BoolElt
IsIdentity(g) : GrpGPCElt -> BoolElt
IsIdentity(g) : GrpMatElt -> BoolElt
IsIdentity(g) : GrpPCElt -> BoolElt
IsIdeal(S) : AlgGrpSub -> BoolElt
IsIdempotent(a) : AlgGenElt -> BoolElt
IsIdempotent(x) : RngElt -> BoolElt
IsIdentical(f, g) : RngSerElt, RngSerElt -> BoolElt
IsIdenticalPresentation(G, H) : GrpGPC, GrpGPC -> BoolElt
IsIdenticalPresentation(G, H) : GrpPC, GrpPC -> BoolElt
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(u) : GrpBrdElt -> BoolElt
IsIdentity(g) : GrpGPCElt -> BoolElt
IsIdentity(g) : GrpMatElt -> BoolElt
IsIdentity(g) : GrpPCElt -> BoolElt
IsIdentity(f) : QuadBinElt -> BoolElt
IsZero(P) : JacHypPt -> BoolElt
IsIndecomposable(M,B) : ModBrdt, RngIntElt -> BoolElt
IsIndefinite(A) : AlgQuat -> BoolElt
IsIndependent(Q) : [ AlgGen ] -> BoolElt
IsIndependent(Q) : [ ModTupFldElt ] -> BoolElt
IsIndependent(S) : { ModTupFldElt } -> BoolElt
IsInert(P) : RngOrdIdl -> BoolElt
IsInert(P, O) : RngOrdIdl, RngOrd -> BoolElt
IsInertial(g) : RngUPolElt -> BoolElt
IsFlex(C,p) : Sch,Pt -> BoolElt,RngIntElt
IsInflectionPoint(p) : Sch,Pt -> BoolElt,RngIntElt
IsInImage(f, p) : Map, RngMPolElt -> [ BoolElt ]
IsInjective(M) : ModAlg -> BoolElt, SeqEnum
IsInjective(a) : ModMatRngElt -> BoolElt
IsInjective(f) : MotMatCpxElt -> BoolElt
IsInner(f) : GrpAutoElt -> BoolElt, GrpElt
IsInRadical(f, I) : RngMPolElt, RngMPol -> BoolElt
IsInSmallGroupDatabase(o) : RngIntElt -> RngIntElt
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(R): Rng -> BoolElt
IsDomain(R) : Rng -> BoolElt
IsIntegralModel(E) : CrvEll -> BoolElt
IsInterior(N,p) : NwtnPgon,Tup -> BoolElt
IsIntersection(C,D,p) : Sch,Sch,Pt -> BoolElt
IsIntrinsic(S) : MonStgElt -> Bool, Intrinsic
State_IsIntrinsic (Example H1E19)
State_IsIntrinsic (Example H1E20)
IsInvariant(f, G) : RngMPolElt, Grp -> BoolElt
IsInvariant(f, g) : RngMPolElt, GrpElt -> 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
IsIsogenous(E, F) : CrvEll, CrvEll -> BoolElt
IsIsogenous( G, H ) : GrpLie, GrpLie -> BoolElt
IsIsogenous( RD1, RD2 ) : RootDtm, RootDtm -> BoolElt
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(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(C,D) : CrvCon, CrvCon -> BoolElt, MapIsoSch
IsIsomorphic(E, F) : CrvEll, CrvEll -> BoolElt, Map
IsIsomorphic(C1, C2) : CrvHyp, CrvHyp -> BoolElt, MapIsoSch
IsIsomorphic(F, L) : FldAlg, FldAlg -> BoolElt, Map
IsIsomorphic(G, H) : GrphDir, GrphDir -> BoolElt, Map
IsIsomorphic(G, H) : GrpPC, GrpPC -> BoolElt, Map
IsIsomorphic(M, N) : ModRng, ModRng -> BoolElt, AlgMatElt
IsIsomorphic(C, D: parameters) : Code, Code -> BoolElt, Map
IsIsomorphic(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(I) : Map -> BoolElt, Map
IsIsomorphism(f) : MapSch -> BoolElt, IsoSch
IsIsomorphism(f) : MotMatCpxElt -> BoolElt
IsKnuthEquivalent(w1, w2) : MonOrdElt, MonOrdElt -> BoolElt
IsLabelled(t) : GrphVert -> BoolElt
IsLabelledEdge(G, i, j) : Grph, RngIntElt, RngIntElt -> BoolElt
IsLabelledVertex(G, i) : Grph, RngIntElt -> BoolElt
IsLeftIdeal(S) : AlgGrpSub -> BoolElt
IsLeftIsomorphic(I,J) : AlgQuatOrd, AlgQuatOrd -> BoolElt, Map, AlgQuatElt
IsLexicographicallyOrdered(w1, w2) : MonOrdElt, MonOrdElt -> boolean
IsLie(A) : AlgGen -> BoolElt
IsLinear(x) : AlgChtrElt -> BoolElt
IsLinear(f) : MapSch -> BoolElt
IsLinearGroup(G) : GrpMat -> BoolElt
IsLinearlyEquivalent(D1,D2) : DivCrvElt,DivCrvElt -> 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
IsLinearSpace(D) : Inc -> BoolElt
IsLineRegular(D) : IncNsp -> BoolElt, RngIntElt
IsLineTransitive(P) : Plane -> BoolElt
IsLittlewoodRichardson(t) : Tbl -> BoolElt
IsLocalNorm(A, x) : FldAb, RngOrdElt -> BoolElt
IsLocalNorm(A, x, p) : FldAb, RngOrdElt, PlcNumElt -> BoolElt
IsLocalNorm(A, x, i) : FldAb, RngOrdElt, RngIntElt -> BoolElt
IsLocalNorm(A, x, p) : FldAb, RngOrdElt, RngOrdIdl -> BoolElt
IsLongRoot( RD, r ) : RootDtm, RngIntElt -> BoolElt
IsMaximal(G, H) : GrpAb, GrpAb -> BoolElt
IsMaximal(G, H) : GrpFin, GrpFin -> BoolElt
IsMaximal(G, H) : GrpFP, GrpFP -> BoolElt
IsMaximal(G, H) : GrpMat, GrpMat -> BoolElt
IsMaximal(G, H) : GrpPC, GrpPC -> BoolElt
IsMaximal(G, H) : GrpPerm, GrpPerm -> BoolElt
IsMaximal(O) : RngFunOrd -> BoolElt
IsMaximal(I) : RngMPol -> BoolElt
IsMaximal(O) : RngOrd -> BoolElt
IsMaximisingFunction(L) : LP -> BoolElt
IsMDS(C) : Code -> BoolElt
IsMaximumDistanceSeparable(C) : Code -> BoolElt
IsMDS(C) : Code -> BoolElt
IsMaximumDistanceSeparable(C) : Code -> BoolElt
IsMemberBasicOrbit(G, i, a) : GrpPerm, RngIntElt, Elt -> BoolElt
IsMinimalModel(E) : CrvEll -> BoolElt
IsMinusOne(a) : AlgGenElt -> BoolElt
IsMinusOne(a) : AlgMatElt -> BoolElt
IsMinusOne(a) : FldACElt -> BoolElt
IsMinusOne(A) : Mtrx -> BoolElt
IsMinusOne(a) : RngElt -> BoolElt
IsMinusOne(x) : RngLocElt -> BoolElt
IsMinusOne(a) : RngOrdResElt -> BoolElt
IsMinusOne(s) : RngPowLazElt -> BoolElt
IsModuleHomomorphism(X) : ModMatElt -> BoolElt
IsModuleHomomorphism(f) : ModMatFldElt -> BoolElt
IsNearLinearSpace(D) : Inc -> BoolElt
IsNearlyPerfect(C) : Code -> BoolElt
IsNegative( RD, r ) : RootDtm, RngIntElt -> BoolElt
IsNegativeDefinite(F) : ModMatRngElt -> BoolElt
IsNegativeSemiDefinite(F) : ModMatRngElt -> BoolElt
IsNew(M) : ModFrm -> BoolElt
IsNew(M) : ModSym -> BoolElt
IsNewform(f) : ModFrmElt -> BoolElt
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(p) : Crv,Pt -> BoolElt
IsNonsingular(C) : Sch -> BoolElt
IsNonsingular(X) : Sch -> BoolElt
IsNonsingular(p) : Sch,Pt -> BoolElt
IsNonsingular(p) : Sch,Pt -> BoolElt
IsNorm(A, x) : FldAb, RngOrdElt -> BoolElt
IsNormal(A) : FldAb -> BoolElt
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) : GrpFP, GrpFP -> 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
IsNormalising( G ) : GrpLie -> BoolElt
IsNull(S) : SeqEnum -> BoolElt
IsNull(R) : SetEnum -> BoolElt
Iso(C1,C2) : CrvHyp, CrvHyp -> PowIsoSch
Maps(D, C) : Str, Str -> PowMap
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(x) : GrpDrchElt -> BoolElt
IsOdd(n) : RngIntElt -> BoolElt
IsogeniesAreEqual(I, J) : Map, Map -> BoolElt
IsogeniesAreEqual(I, J) : Map, Map -> BoolElt
IsIsogenous(E, F) : CrvEll, CrvEll -> BoolElt
IsIsogenous( G, H ) : GrpLie, GrpLie -> BoolElt
IsIsogenous( RD1, RD2 ) : RootDtm, RootDtm -> BoolElt
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
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 H87E33)
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
RootDtm_IsogenyGroups (Example H33E7)
IsogenyMapOmega(I) : Map -> RngMPolElt
IsogenyMapPhi(I) : Map -> RngUPolElt
IsogenyMapPhiMulti(I) : Map -> RngUPolElt
IsogenyMapPsi(I) : Map -> RngUPolElt
IsogenyMapPsiMulti(I) : Map -> RngUPolElt
IsogenyMapPsiSquared(I) : Map -> RngUPolElt
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
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)
The Database of Irreducible Soluble Matrix Groups (DATABASES OF GROUPS)
Group(D, n, p, i) : DB, RngIntElt, RngIntElt, RngIntElt -> GrpMat
IsolGroup(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> GrpMat
GrpData_IsolGroup (Example H22E12)
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
Lat_Isom (Example H64E18)
Automorphism Group and Isometry Testing (LATTICES)
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
Automorphism Group and Isomorphism Testing (HYPERELLIPTIC CURVES)
Automorphism Group and Isomorphism Testing (HYPERELLIPTIC CURVES)
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(C,D) : CrvCon, CrvCon -> BoolElt, MapIsoSch
IsIsomorphic(E, F) : CrvEll, CrvEll -> BoolElt, Map
IsIsomorphic(C1, C2) : CrvHyp, CrvHyp -> BoolElt, MapIsoSch
IsIsomorphic(F, L) : FldAlg, FldAlg -> BoolElt, Map
IsIsomorphic(G, H) : GrphDir, GrphDir -> BoolElt, Map
IsIsomorphic(G, H) : GrpPC, GrpPC -> BoolElt, Map
IsIsomorphic(M, N) : ModRng, ModRng -> BoolElt, AlgMatElt
IsIsomorphic(C, D: parameters) : Code, Code -> BoolElt, Map
IsIsomorphic(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(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(C,D) : Crv, Crv -> MapIsoSch
Isomorphism(C,D) : CrvCon, CrvCon -> MapIsoSch
Isomorphism(E, F) : CrvEll, CrvEll -> Map
Isomorphism(E, F, [r, s, t, u]) : CrvEll, CrvEll, Seq -> Map
Isomorphism(C,D,S,T) : CrvRat, CrvRat, [Pt], [Pt] -> MapIsoSch
Isomorphism(X,C,p) : Sch, Crv, Pt -> MapIsoSch
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 H87E35)
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)
Arithmetic with Isomorphisms (HYPERELLIPTIC CURVES)
Creation of Isomorphisms (HYPERELLIPTIC CURVES)
Equivalence and Isomorphism of Codes (LINEAR CODES OVER FINITE FIELDS)
IsomorphismData(I) : Map -> [ RngElt ]
RootDtm_IsomorphismIsogeny (Example H33E5)
CrvEll_Isomorphisms (Example H87E34)
Invariants of Isomorphisms (HYPERELLIPTIC CURVES)
Order and Ideal Isomorphisms (QUATERNION ALGEBRAS)
Order and Ideal Isomorphisms (QUATERNION ALGEBRAS)
IsomorphismToIsogeny(I) : Map -> Map
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
IsOne(s) : RngPowLazElt -> BoolElt
IsOrbit(G, S) : GrpPerm, { Elt } -> BoolElt
IsOrder(P, m) : PtEll, RngIntElt -> BoolElt
IsOrdered(R) : Rng -> BoolElt
IsOrdinary(E) : CrvEll -> BoolElt
IsOrdinaryProjective(X) : Sch -> BoolElt
IsOrdinaryProjectiveSpace(X) : Sch -> BoolElt
IsOrdinarySingularity(p) : Sch,Pt -> BoolElt
IsOrdinarySingularity(p) : Sch,Pt -> BoolElt
IsOrthogonalGroup(G) : GrpMat ->BoolElt
IsOverSmallerField(G) : GrpMat -> BoolElt, GrpMat
IsOverSmallerField(G, d) : GrpMat, RngIntElt -> BoolElt, GrpMat
GrpMat_IsOverSmallerField (Example H21E37)
IspIntegral(C, p) : CrvHyp, RngIntElt -> BoolElt
IspMinimal(C, p) : CrvHyp, RngIntElt -> BoolElt, BoolElt
IspNormal(C, p) : CrvHyp, RngIntElt -> BoolElt
IsParallel(P, l, m) : Plane, PlaneLn, PlaneLn -> BoolElt
IsParallelClass(D, B, C) : Inc, IncBlk, IncBlk -> BoolElt, { IncBlk }
IsParallelism(D, P) : Inc, SetEnum[SetEnum] -> BoolElt, RngIntElt
IsPartialRoot(f, c) : RngUPolElt, RngSerElt -> BoolElt
IsPartition(S) : SeqEnum -> BoolElt
IsPartitionRefined(G: parameters) : Grph -> BoolElt
IsPath(G) : Grph -> BoolElt
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
IsPrincipalIdealDomain(R) : Rng -> BoolElt
IsPID(R) : Rng -> BoolElt
IspIntegral(C, p) : CrvHyp, RngIntElt -> BoolElt
IsPrincipalIdealRing(R) : Rng -> BoolElt
IsPIR(R) : Rng -> BoolElt
IsPlanar(G) : GraphUnd -> BoolElt, GrphUnd
IspMinimal(C, p) : CrvHyp, RngIntElt -> BoolElt, BoolElt
IspNormal(C, p) : CrvHyp, RngIntElt -> BoolElt
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(D) : IncNsp -> BoolElt, RngIntElt
IsPointTransitive(D) : Inc -> BoolElt
IsPointTransitive(P) : Plane -> BoolElt
IsPolygon(G) : Grph -> BoolElt
IsPolynomial(f) : MapSch -> BoolElt
IsRegular(f) : MapSch -> BoolElt
IsPositive(D) : DivCrvElt -> BoolElt
IsEffective(D) : DivCrvElt -> BoolElt
IsPositive( RD, r ) : RootDtm, RngIntElt -> BoolElt
IsPositiveDefinite(F) : ModMatRngElt -> BoolElt
IsPositiveSemiDefinite(F) : ModMatRngElt -> BoolElt
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(I) : RngMPol -> BoolElt
IsPrimary(I) : RngMPolRes -> BoolElt
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 H38E3)
IsPrimePower(n) : RngIntElt -> BoolElt, RngIntElt, RngIntElt
IsPrimitive(a) : FldAlgElt -> BoolElt
IsPrimitive(a) : FldFinElt -> BoolElt
IsPrimitive(G) : GrphUnd -> BoolElt
IsPrimitive(G) : GrpPerm -> BoolElt
IsPrimitive(G, Y) : GrpPerm, GSet -> 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(D) : DivCrvElt -> BoolElt,FldFunRatMElt
IsPrincipal(I) : RngFunOrdIdl -> BoolElt, FldFunElt
IsPrincipal(I) : RngMPol -> BoolElt, RngMPolElt
IsPrincipal(I) : RngOrdFracIdl -> BoolElt, FldOrdElt
IsPrincipalIdealDomain(R) : Rng -> BoolElt
IsPID(R) : Rng -> BoolElt
IsPrincipalIdealRing(R) : Rng -> BoolElt
IsPIR(R) : Rng -> BoolElt
IsPrincipalIdealRing(F) : FldAlg -> BoolElt
IsPrincipalIdealRing(O) : RngOrd -> BoolElt
IsProbablyPrime(n: parameter) : RngIntElt -> BoolElt
IsProbablePrime(n: parameter) : RngIntElt -> BoolElt
IsProbablyMaximal(G, H: parameters) : GrpPerm, GrpPerm -> BoolElt
IsProbablyPermutationPolynomial(p) : RngUPolElt -> BoolElt
IsProbablyPrime(n: parameter) : RngIntElt -> BoolElt
IsProbablePrime(n: parameter) : RngIntElt -> BoolElt
IsProbablySupersingular(E) : CrvEll -> BoolElt
IsProjective(C) : Code -> BoolElt
IsProjective(M) : ModAlg -> BoolElt, SeqEnum
IsProjective(X) : Sch -> BoolElt
IsProjectiveSpace(X) : Sch -> BoolElt
IsProper(I) : RngMPol -> BoolElt
IsProper(I) : RngMPolRes -> BoolElt
IsProperChainMap(f) : MapChn -> BoolElt
IsProportional(X, k) : Mtrx, RngIntElt -> BoolElt, Tup
Isqrt(n) : RngIntElt -> RngIntElt
IsQuadratic(K) : FldNum -> BoolElt, FldQuad
IsQuadraticTwist(E,F) : CrvEll -> BoolElt, RngElt
IsQuadraticTwist(C1, C2) : CrvHyp, CrvHyp -> BoolElt, RngElt
IsRadical(I) : RngMPol -> BoolElt
IsRadical(I) : RngMPolRes -> BoolElt
IsRamified(P) : RngOrdIdl -> BoolElt
IsRamified(P, O) : RngOrdIdl, RngOrd -> BoolElt
IsRationalCurve(C) : Sch -> BoolElt, CrvRat
IsRationalCurve(X) : Sch -> BoolElt,CrvRat
IsRC(C) : CosetGeom -> BoolElt
IsResiduallyConnected(C) : CosetGeom -> BoolElt
IsResiduallyConnected(D) : IncGeom -> BoolElt
IsReal(x) : AlgChtrElt -> BoolElt
IsReal(c) : FldComElt -> BoolElt
IsReal(a) : FldCycElt -> BoolElt
IsRealisableOverSmallerField(M) : ModGrp -> BoolElt, ModGrp
IsRealisableOverSubfield(M, F) : ModGrp, FldFin -> BoolElt, ModGrp
IsReduced(s) : GrphSpl -> BoolElt
IsReduced(p) : Pt -> BoolElt
IsReduced(f) : QuadBinElt -> BoolElt
IsReduced(C) : Sch -> BoolElt
IsReduced(X) : Sch -> BoolElt
IsReflectionSubgroup( W, H ) : GrpCox -> GrpCox
IsRegular(a) : AlgGenElt -> BoolElt
IsRegular(G) : Grph -> BoolElt
IsRegular(s) : GrphSpl -> BoolElt
IsRegular(G, Y) : GrpPerm, GSet -> BoolElt
IsRegular(f) : MapSch -> BoolElt
IsRC(C) : CosetGeom -> BoolElt
IsResiduallyConnected(C) : CosetGeom -> BoolElt
IsResiduallyConnected(D) : IncGeom -> BoolElt
IsResolution(D, P) : Inc, SetEnum[SetEnum] -> BoolElt, RngIntElt
IsRestrictedLieAlgebra(L) : AlgLie -> BoolElt
IsReverseLatticeWord(w) : MonOrdElt -> BoolElt
IsRightIdeal(S) : AlgGrpSub -> BoolElt
IsRightIsomorphic(I,J) : AlgQuatOrd, AlgQuatOrd -> BoolElt, Map, AlgQuatElt
IsRingOfAllModularForms(M) : ModFrm -> BoolElt
IsRoot(v) : GrphVert -> BoolElt
IsRootedTree(G) : GrphDir -> BoolElt, GrphVert
IsSatisfied(U, E) : { RelElt }, [ GrpElt ] -> BoolElt
IsScalar(u) : AlgFPElt -> BoolElt
IsScalar(a) : AlgMatElt -> BoolElt
IsScalar(g) : GrpMatElt -> BoolElt
IsScalar(A) : Mtrx -> BoolElt
IsSelfOrthogonal(C) : Code -> BoolElt
IsSelfDual(C) : Code -> BoolElt
IsSelfDual(C) : Code -> BoolElt
IsSelfDual(D) : Inc -> BoolElt
IsSelfDual(P) : PlaneProj -> BoolElt
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(G, H) : GrpGPC, GrpGPC -> BoolElt
IsSelfNormalising(G, H) : GrpGPC, GrpGPC -> BoolElt
IsSelfNormalizing(G, H) : GrpFin, GrpFin -> BoolElt
IsSelfNormalizing(G, H) : GrpFP, GrpFP -> BoolElt
IsSelfNormalizing(G, H) : GrpPC, GrpPC -> BoolElt
IsSelfNormalizing(G, H) : GrpPerm, GrpPerm -> BoolElt
IsSelfOrthogonal(C) : Code -> BoolElt
IsSelfDual(C) : Code -> BoolElt
IsSelfDual(C) : Code -> BoolElt
IsSemiLinear(G) : GrpMat -> BoolElt
IsSemiregular(G, Y) : GrpPerm, GSet -> BoolElt
IsSemiregular(G, Y, S) : GrpPerm, GSet, SetEnum -> BoolElt
IsSemisimple(A) : AlgGen -> BoolElt
IsSemisimple( G ) : GrpLie-> BoolElt
IsSemisimple(M) : ModAlg -> BoolElt, SeqEnum
IsSemisimple(M) : ModGrp -> BoolElt
IsSemisimple( RD ) : RootDtm-> BoolElt
IsSeparable(G) : GrphUnd -> BoolElt
IsSeparable(f) : RngUPolElt -> BoolElt
IsSeparating(a) : FldFunGElt -> BoolElt
IsSharplyTransitive(G, Y, k) : GrpPerm, GSet, RngIntElt -> BoolElt
IsShortExactSequence(f, g) : MapChn, MapChn -> BoolElt
IsShortExactSequence(C) : ModCpx -> BoolElt, RngIntElt
IsShortRoot( RD, r ) : RootDtm, RngIntElt -> BoolElt
IsSimilar(A, B) : AlgMatElt, AlgMatElt -> BoolElt, AlgMatElt
IsSimilar(a, b) : AlgMatElt, AlgMatElt -> BoolElt, AlgMatElt
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(E) : CrvEll -> BoolElt
IsSimplyConnected( G ) : GrpLie-> BoolElt
IsSimplyConnected( RD ) : RootDtm-> BoolElt
IsSimplyLaced( G ) : GrpLie-> BoolElt
IsSimplyLaced( RD ) : RootDtm-> BoolElt
IsSinglePrecision(n) : RngIntElt -> BoolElt
IsSingular(A) : Mtrx -> BoolElt
IsSingular(C) : Sch -> BoolElt
IsSingular(X) : Sch -> BoolElt
IsSingular(p) : Sch,Pt -> BoolElt
IsSingular(p) : Sch,Pt -> BoolElt
IsSIntegral(P, S) : PtEll, SeqEnum -> BoolElt
IsSkew(t) : Tbl -> BoolElt
IsSolvable(D, o, n) : DB, RngIntElt, RngIntElt -> Grp
SmallGroupIsSoluble(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupIsSolvable(o, n) : RngIntElt, RngIntElt -> Grp
IsSoluble(D, o, n) : DB, RngIntElt, RngIntElt -> Grp
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(D, o, n) : DB, RngIntElt, RngIntElt -> Grp
SmallGroupIsSoluble(o, n) : RngIntElt, RngIntElt -> Grp
SmallGroupIsSolvable(o, n) : RngIntElt, RngIntElt -> Grp
IsSoluble(D, o, n) : DB, RngIntElt, RngIntElt -> Grp
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(D) : DivCrvElt -> BoolElt
IsSpecial(G) : GrpFin -> BoolElt
IsSpecial(G) : GrpMat -> BoolElt
IsSpecial(G) : GrpPC -> BoolElt
IsSpecial(G) : GrpPerm -> BoolElt
IsSpinorGenus(G) : SymGen -> BoolElt
IsSpinorNorm(G,p) : SymGen, RngIntElt -> RngIntElt
IsSplit(P) : RngOrdIdl -> BoolElt
IsSplit(P, O) : RngOrdIdl, RngOrd -> BoolElt
IsSPrincipal(D, S) : DivFunElt, SetEnum[PlcFunElt] -> BoolElt, FldFunElt
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
IsSquare(s) : RngPowLazElt -> BoolElt, RngPowLazElt
IsSquarefree(n) : RngIntElt -> BoolElt
IsStandard(t) : Tbl -> BoolElt
IsStandardParabolicSubgroup( W, H ) : GrpCox -> GrpCox
IsSteiner(D, t) : Dsgn -> BoolElt
IsStronglyAG(C) : Code -> BoolElt
IsStronglyConnected(G) : GrphDir -> BoolElt
IsSubfield(F, L) : FldAlg, FldAlg -> BoolElt, Map
IsSubgraph(G, H) : Grph, Grph -> BoolElt
IsSubgroup(G,H) : GrpPSL2, GrpPSL2 -> BoolElt
IsSubmodule(M, N) : ModDed, ModDed -> BoolElt, Map
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(S, T) : SeqEnum, SeqEnum -> BoolElt
IsSubsystem(L,K) : LinSys,LinSys -> BoolElt
K subset L : LinSys,LinSys -> BoolElt
IsSUnit(a, S) : FldFunElt, SetEnum[PlcFunElt] -> BoolElt
IsSUnitWithPreimage(a, S) : FldFunElt, SetEnum[PlcFunElt] -> BoolElt, GrpAbElt
IsSupersingular(E: parameters) : CrvEll -> BoolElt
IsSurjective(f) : Map -> [ BoolElt ]
IsSurjective(a) : ModMatRngElt -> BoolElt
IsSurjective(f) : MotMatCpxElt -> BoolElt
IsSymmetric(a) : AlgMatElt -> BoolElt
IsSymmetric(D) : Dsgn -> BoolElt
IsSymmetric(G) : GrphUnd -> BoolElt
IsSymmetric(G) : GrpPerm -> BoolElt
IsSymmetric(A) : Mtrx -> BoolElt
IsSymmetric(f) : RngMPolElt -> BoolElt, RngMPolElt
IsSymmetric(f) : RngMPolElt -> BoolElt, RngMPolElt
GB_IsSymmetric (Example H66E26)
RngMPol_IsSymmetric (Example H43E11)
IsSymplecticGroup(G) : GrpMat -> BoolElt
IsTamelyRamified(K) : FldAlg -> BoolElt
IsTamelyRamified(O) : RngOrd -> BoolElt
IsTamelyRamified(P) : RngOrdIdl -> BoolElt
IsTamelyRamified(P, O) : RngOrdIdl, RngOrd -> BoolElt
IsTangent(C,D,p) : Sch,Sch,Pt -> BoolElt
IsTensor(G: parameters) : GrpMat -> BoolElt
IsTensorInduced(G : parameters) : GrpMat -> BoolElt
IsThick(C) : CosetGeom -> BoolElt
IsThick(D) : IncGeom -> BoolElt
IsThin(C) : CosetGeom -> BoolElt
IsThin(D) : IncGeom -> BoolElt
IsTorsionUnit(w) : RngOrdElt -> BoolElt
IsTotallyRamified(P) : RngOrdIdl -> BoolElt
IsTotallyRamified(P, O) : RngOrdIdl, RngOrd -> BoolElt
IsTotallySplit(P) : RngOrdIdl -> BoolElt
IsTotallySplit(P, O) : RngOrdIdl, RngOrd -> BoolElt
IsTransitive(P) : Plane -> BoolElt
IsPointTransitive(P) : Plane -> BoolElt
IsTransitive(G) : GrphUnd -> BoolElt
IsTransitive(G, Y) : GrpPerm, GSet -> BoolElt
IsTransitive(G, Y, k) : GrpPerm, GSet, RngIntElt -> BoolElt
IsTransverse(C,D,p) : Sch,Sch,Pt -> BoolElt
IsTree(G) : Grph -> BoolElt
IsTrivial(G) : Grp -> BoolElt
IsTrivial(x) : GrpDrchElt -> BoolElt
IsTrivial(G) : GrpPC -> BoolElt
IsTrivial(D) : Inc -> BoolElt
IsTwist(E,F) : CrvEll -> BoolElt
IsUniqueFactorizationDomain(R) : Rng -> BoolElt
IsUFD(R) : Rng -> BoolElt
IsUniform(D) : Inc -> BoolElt, RngIntElt
IsUniqueFactorizationDomain(R) : Rng -> BoolElt
IsUFD(R) : Rng -> BoolElt
IsUniquePartialRoot(f, c) : RngUPolElt, RngSerElt -> BoolElt
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
IsUnit(s) : RngPowLazElt -> BoolElt
IsUnital(P, U) : Plane, { PlanePt } -> BoolElt
IsUnitary(R) : Rng -> BoolElt
IsUnitaryGroup(G) : GrpMat -> BoolElt
IsUnitWithPreimage(a) : RngFunOrdElt -> BoolElt, GrpAbElt
IsUnivariate(f) : RngMPolElt -> BoolElt, RngUPolElt, RngIntElt
IsUnivariate(f, i) : RngMPolElt, RngIntElt -> BoolElt, RngUPolElt
IsUnramified(K) : FldAlg -> BoolElt
IsUnramified(O) : RngOrd -> BoolElt
IsUnramified(P) : RngOrdIdl -> BoolElt
IsUnramified(P, O) : RngOrdIdl, RngOrd -> BoolElt
IsVerbose(s) : MonStgElt -> BoolElt
IsVerbose(s, l) : MonStgElt, RngIntElt -> BoolElt
IsVertex(g,v) : GrphRes,GrphResVert -> BoolElt
IsVertex(N, p) : NwtnPgon,Tup -> BoolElt
IsVertexTransitive(G) : GrphUnd -> BoolElt
IsTransitive(G) : GrphUnd -> BoolElt
IsWeaklyAG(C) : Code -> BoolElt
IsWeaklyConnected(G) : GrphDir -> BoolElt
IsWeaklyEqual(s, t, n) : RngPowLazElt, RngPowLazElt, RngIntElt -> BoolElt
IsWeaklyEqual(f, g) : RngSerElt, RngSerElt -> BoolElt
IsWeaklySelfOrthogonal(C) : Code -> BoolElt
IsWeaklySelfDual(C) : Code -> BoolElt
IsWeaklySelfDual(C) : Code -> BoolElt
IsWeaklySelfOrthogonal(C) : Code -> BoolElt
IsWeaklySelfDual(C) : Code -> BoolElt
IsWeaklySelfDual(C) : Code -> BoolElt
IsWeaklyZero(s, n) : RngPowLazElt, RngIntElt -> BoolElt
IsWeaklyZero(f) : RngSerElt -> BoolElt
IsWeierstrassModel(E) : CrvEll -> BoolElt
IsWeierstrassPlace(P) : PlcCrvElt -> BoolElt
IsWeierstrassPlace(P) : PlcFunElt -> BoolElt
IsWildlyRamified(K) : FldAlg -> BoolElt
IsWildlyRamified(O) : RngOrd -> BoolElt
IsWildlyRamified(P) : RngOrdIdl -> BoolElt
IsWildlyRamified(P, O) : RngOrdIdl, RngOrd -> BoolElt
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) : MtrxSprs -> 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
IsZero(s) : RngPowLazElt -> BoolElt
IsZeroComplex(C) : ModCpx -> BoolElt
IsZeroDimensional(I) : RngMPol -> BoolElt
IsZeroDivisor(a) : AlgGenElt -> BoolElt
IsZeroDivisor(x) : RngElt -> BoolElt
IsZeroMap(C, n) : ModCpx, RngIntElt -> BoolElt
IsZeroTerm(C, n) : ModCpx, RngIntElt -> BoolElt
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]