[____] [____] [_____] [____] [__] [Index] [Root]
Index I
I-key
I
i-key
i
Id
Id(R) : AlgChtr -> AlgChtrElt
Id(M) : MonFP -> MonFPElt
Identity(E) : CurveEll -> CurveEllPt
Identity(G) : Grp -> GrpElt
Identity(G) : Grp -> GrpPermElt
Identity(A) : GrpAb -> GrpAbElt
Identity(G) : GrpBB -> GrpBBElt
Identity(G) : GrpFP -> GrpFPElt
Identity(G) : GrpMat -> GrpMatElt
Identity(G) : GrpPC -> GrpPCElt
One(R) : Rng -> RngElt
Ideal
Ideal(Q) : [ RngMPolElt ] -> RngMPol
ideal
Basic Operations on Ideals (MULTIVARIATE POLYNOMIAL RINGS)
Construction of Elimination Ideals (MULTIVARIATE POLYNOMIAL RINGS)
Construction of New Ideals (MULTIVARIATE POLYNOMIAL RINGS)
Construction of Subalgebras, Ideals and Quotient Algebras (GROUP ALGEBRAS)
Construction of Subalgebras, Ideals and Quotient Rings (MATRIX ALGEBRAS)
Constructor (OVERVIEW)
Creation of Ideals and Computation of Gröbner Bases (MULTIVARIATE POLYNOMIAL RINGS)
Creation of Ideals in Orders (FUNCTION FIELDS AND THEIR ORDERS)
Creation of Ideals in Orders (NUMBER FIELDS AND THEIR ORDERS)
Elementary Operations on Subalgebras and Ideals (MATRIX ALGEBRAS)
Ideal Arithmetic (FUNCTION FIELDS AND THEIR ORDERS)
Ideal Arithmetic (NUMBER FIELDS AND THEIR ORDERS)
Ideal Class Groups (NUMBER FIELDS AND THEIR ORDERS)
Ideal Creation (FUNCTION FIELDS AND THEIR ORDERS)
Ideal Creation (NUMBER FIELDS AND THEIR ORDERS)
Ideal Factorization (FUNCTION FIELDS AND THEIR ORDERS)
Ideal Operations (RESIDUE CLASS RINGS)
Ideals (FUNCTION FIELDS AND THEIR ORDERS)
Ideals and Quotient Rings (INTRODUCTION [RINGS AND FIELDS])
Ideals and Quotient Rings (UNIVARIATE POLYNOMIAL RINGS)
Ideals and Quotients (NUMBER FIELDS AND THEIR ORDERS)
Other Functions on Ideals (UNIVARIATE POLYNOMIAL RINGS)
Other Ideal Functions (FUNCTION FIELDS AND THEIR ORDERS)
Other Ideal Operations (NUMBER FIELDS AND THEIR ORDERS)
Predicates on Ideals (FUNCTION FIELDS AND THEIR ORDERS)
Predicates on Ideals (NUMBER FIELDS AND THEIR ORDERS)
Subsemigroups and Ideals (FINITELY PRESENTED SEMIGROUPS)
Subsemigroups, Ideals and Quotients (FINITELY PRESENTED SEMIGROUPS)
Univariate Elimination Ideal Generators (MULTIVARIATE POLYNOMIAL RINGS)
ideal< 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< R | a_1, ..., a_r > : Rng, RngElt, ..., RngElt -> RngIdl
ideal< O | a_1, a_2, ... , a_m > : RngFunOrd, FldFunElt, ..., FldFunElt -> RngFunOrdIdl
ideal<P | L> : RngMPol, List -> RngMPol
ideal< Q | a_1, ..., a_r > : RngMPol, RngMPolElt, ..., RngMPolElt -> RngMPolRes, Map
ideal< O | a_1, a_2, ... , a_m > : RngOrd, FldNumElt, ..., FldNumElt -> RngOrdIdl
ideal< R | a_1, ..., a_r > : RngUPol, RngUPolElt, ..., RngUPolElt -> RngUPol
ideal<S | L_1, ..., L_r> : SgpFP, SgpFPElt, ..., SgpFPElt -> SgpFPIdl
ideal-arithmetic
Ideal Arithmetic (FUNCTION FIELDS AND THEIR ORDERS)
Ideal Arithmetic (NUMBER FIELDS AND THEIR ORDERS)
ideal-Boolean
Predicates on Ideals (FUNCTION FIELDS AND THEIR ORDERS)
Predicates on Ideals (NUMBER FIELDS AND THEIR ORDERS)
ideal-class-group
Ideal Class Groups (NUMBER FIELDS AND THEIR ORDERS)
ideal-creation
Ideal Creation (FUNCTION FIELDS AND THEIR ORDERS)
Ideal Creation (NUMBER FIELDS AND THEIR ORDERS)
ideal-factorization
Ideal Factorization (FUNCTION FIELDS AND THEIR ORDERS)
ideal-groebner
Creation of Ideals and Computation of Gröbner Bases (MULTIVARIATE POLYNOMIAL RINGS)
ideal-operation
Basic Operations on Ideals (MULTIVARIATE POLYNOMIAL RINGS)
ideal-other
Other Ideal Functions (FUNCTION FIELDS AND THEIR ORDERS)
Other Ideal Operations (NUMBER FIELDS AND THEIR ORDERS)
ideal-quotient
Ideals and Quotient Rings (INTRODUCTION [RINGS AND FIELDS])
Ideals and Quotient Rings (UNIVARIATE POLYNOMIAL RINGS)
IdealArithmetic
RngMPol_IdealArithmetic (Example H29E14)
IdealFactorization
FldNum_IdealFactorization (Example H36E14)
Idealiser
Idealiser(S) : AlgGrpSub -> AlgGrpSub
Idealizer(A, B: parameters) : AlgAss, AlgAss -> AlgAss
Idealizer
Idealiser(S) : AlgGrpSub -> AlgGrpSub
Idealizer(A, B: parameters) : AlgAss, AlgAss -> AlgAss
IdealQuotient
ColonIdeal(I, J) : RngMPol, RngMPol -> RngMPol
Ideals
FldFunG_Ideals (Example H32E4)
FldNum_Ideals (Example H36E8)
Idempotent
Idempotent(C) : Code -> RngUPolElt
identifier
Identifier Classes (MAGMA SEMANTICS)
Identifier names (OVERVIEW)
Identifiers (STATEMENTS AND EXPRESSIONS)
Identifiers and variables (OVERVIEW)
Uninitialized Identifiers (MAGMA SEMANTICS)
identifier-class
Identifier Classes (MAGMA SEMANTICS)
Identifiers
State_Identifiers (Example H1E1)
Identity
Id(R) : AlgChtr -> AlgChtrElt
Identity(E) : CurveEll -> CurveEllPt
Identity(G) : Grp -> GrpElt
Identity(G) : Grp -> GrpPermElt
Identity(A) : GrpAb -> GrpAbElt
Identity(G) : GrpBB -> GrpBBElt
Identity(G) : GrpFP -> GrpFPElt
Identity(G) : GrpMat -> GrpMatElt
Identity(G) : GrpPC -> GrpPCElt
identity
Groups (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
IdentityHomomorphism
IdentityHomomorphism(G) : Grp -> Map
IdentityIsogeny
IdentityIsogeny(E) : CurveEll -> Map
IdentityMap
IdentityMap(E) : CurveEll -> Map
IdentityMap(E) : CurveEll -> Map
if
error statement (OVERVIEW)
The if statement (OVERVIEW)
if boolexpr_1 then statements_1 else statements_2 end if : ->
State_if (Example H1E10)
ignore
Multiple Assignment (OVERVIEW)
Ilog
Ilog(b, n) : RngIntElt, RngIntElt -> RngIntElt
Ilog2
Ilog2(n) : RngIntElt -> RngIntElt
Im
Imaginary(c) : FldComElt -> FldReElt
Image
Image(a) : AlgMatElt -> ModTup
Image(a, Y, y) : GrpPermElt, GSet, Elt -> Elt
Image(g, Y, y) : GrpPermElt, GSet, Elt -> Elt
Image(g, Y, y) : GrpPermElt, GSet, Elt -> Elt
Image(g, Y, y) : GrpPermElt, GSet, Elt -> Elt
Image(f) : Map -> Elt
Image(a) : ModMatElt -> ModTupFld
Image(a) : ModMatRngElt -> ModTupRng
image
Images and Preimages (MAPPINGS)
Images, Orbits and Stabilizers (MATRIX GROUPS)
Images, Orbits and Stabilizers (PERMUTATION GROUPS)
image-orbit-stabilizer
Images, Orbits and Stabilizers (MATRIX GROUPS)
Images, Orbits and Stabilizers (PERMUTATION GROUPS)
image-preimage
Images and Preimages (MAPPINGS)
ImageWithBasis
ImageWithBasis(X, M) : ModMatRngElt, ModRng -> ModRng
Imaginary
Imaginary(c) : FldComElt -> FldReElt
Implicitization
Implicitization(f) : Map -> RngMPol
import
Importing Constants (FUNCTIONS, PROCEDURES AND PACKAGES)
import "filename": ident_list;
Func_import (Example H2E6)
in
Planes in Magma (FINITE PLANES)
Sequences (OVERVIEW)
Sets (OVERVIEW)
The for statement (OVERVIEW)
x in S
x in y : AlgChtrElt, AlgChtrElt -> BoolElt
a in A : AlgGenElt, AlgGen -> BoolElt
x in R : AlgMatElt, AlgMat -> BoolElt
x in S : Elt, Seq -> BoolElt
x in R : Elt, Set -> BoolElt
g in G : GrpAbElt, GrpAb -> BoolElt
g in G : GrpBBElt, GrpBB -> BoolElt
g in G : GrpFinElt, GrpFin -> BoolElt
u in H : GrpFPElt, GrpFP -> BoolElt
g in C : GrpFPElt, GrpFPCosElt -> BoolElt
u in e : GrphVert, GrphEdge -> BoolElt
u in e : GrphVert, GrphEdge -> BoolElt
[Future release] x in C : GrpMatElt, Elt -> BoolElt
g in G : GrpMatElt, GrpMat -> BoolElt
g in G : GrpPCElt, GrpPC -> BoolElt
x in C : GrpPermElt, Elt -> BoolElt
g in G : GrpPermElt, GrpPerm -> BoolElt
p in B : IncPt, IncBlk -> BoolElt
v in L : LatElt, Lat -> BoolElt
f in M : ModMPolElt, ModMPol -> BoolElt
u in C : ModTupFldElt, Code -> BoolElt
v in V : ModTupFldElt, ModTupFld -> BoolElt
u in M : ModTupRngElt, ModTupRng -> BoolElt
s in t : MonStgElt, MonStgElt -> BoolElt
p in l : PlanePt, PlaneLn -> BoolElt
a in R : RngElt, Rng -> BoolElt
a in I : RngElt, RngIdl -> BoolElt
f in R : RngMPol, RngInvar -> FldFunUElt, ModMPolElt
f in I : RngMPolElt, RngMPol -> BoolElt
a in I : RngUPolElt, RngUPol -> BoolElt
S in P : SeqEnum, PowSeqEnum -> BoolElt
S in P : SetEnum, PowSetEnum -> BoolElt
Inc
Combinatorial and Geometrical Structures (OVERVIEW)
incidence
Combinatorial and Geometrical Structures (OVERVIEW)
INCIDENCE STRUCTURES AND DESIGNS
incidence-structure-design
INCIDENCE STRUCTURES AND DESIGNS
IncidenceDigraph
IncidenceDigraph(A) : ModHomElt -> GrphDir
IncidenceGraph
IncidenceGraph(D) : Inc -> Grph
IncidenceGraph(D) : Inc -> GrphUnd
IncidenceGraph(A) : ModHomElt -> GrphUnd
IncidenceGraph(P) : Plane -> Grph
IncidenceGraph(P) : Plane -> GrphUnd;
IncidenceMatrix
IncidenceMatrix(G) : Grph -> ModHomElt
IncidenceMatrix(D) : Inc -> ModMatRngElt
IncidenceMatrix(P) : Plane -> AlgMatElt
IncidenceStructure
IncidenceStructure(G) : Grph -> Inc
IncidenceStructure(I) : Inc -> Inc
IncidenceStructure< v | X > : RngIntElt, List -> Inc
IncidentEdges
IncidentEdges(u) : GrphVert -> { GrphEdge }
Include
Include(W, v) : ModTupRng, ModTupRngElt -> ModTupRng, BoolElt
Include(~S, x) : SeqEnum, Elt ->
Include(~S, x) : SetEnum, Elt ->
Set_Include (Example H7E10)
InclusionMap
InclusionMap(G, H) : GrpPC, GrpPC -> Map
InclusionMap(G, H) : GrpPC, GrpPC -> Map
IndecomposableSummands
IndecomposableSummands(M) : ModRng -> [ ModRng ]
InDegree
InDegree(u) : GrphVert -> RngIntElt
indent
Indentation (INPUT AND OUTPUT)
IndentPop
IndentPop() : ->
IndentPush
IndentPush() : ->
IndependenceNumber
IndependenceNumber(G) : GrphUnd -> RngIntElt
independent
Independent Sets, Cliques, Colourings (GRAPHS)
independent-set-clique-colouring
Independent Sets, Cliques, Colourings (GRAPHS)
IndependentSet
IndependentSet(G, n) : GrphUnd, RngIntElt -> { GrphVert }
IndependentUnits
IndependentUnits(O) : RngOrd -> GrpAb, Map
Index
Sequences (OVERVIEW)
Sets (OVERVIEW)
Index(x) : CopElt -> RngIntElt
Index(G, H) : GrpAb, GrpAb -> RngIntElt
Index(G, H) : GrpFin, GrpFin -> RngIntElt
Index(v) : GrphVert -> RngIntElt
Index(G, H) : GrpMat, GrpMat -> RngIntElt
Index(G, H) : GrpPC, GrpPC -> RngIntElt
Index(G, H) : GrpPerm, GrpPerm -> RngIntElt
Index(L, S): Lat, Lat -> RngInt
Index(s, t) : MonStgElt, MonStgElt -> RngIntElt
Index(G, H: parameters) : GrpFP, GrpFP -> RngIntElt, Map, RngIntElt, RngIntElt
Index(P, p) : PlanePt -> RngIntElt
Index(O, E) : RngOrd, RngOrd -> RngIntElt
Index(O, I) : RngOrdIdl -> RngIntElt
Index(S, x) : SeqEnum, Elt -> RngIntElt
Index(S, x) : SetIndx, Elt -> RngIntElt
index
Index of a Subgroup: The Todd-Coxeter Algorithm (FINITELY PRESENTED GROUPS)
Indexing (MATRIX ALGEBRAS)
Indexing (THE MODULES Hom_(R)(M, N) AND End(M))
Indexing Vectors and Matrices (VECTOR SPACES)
Integer-Valued Functions (INPUT AND OUTPUT)
Low Index Subgroups (FINITELY PRESENTED GROUPS)
Order and Index Functions (GROUPS)
Order and Index Functions (MATRIX GROUPS)
Order and Index Functions (PERMUTATION GROUPS)
index-Todd-Coxeter
Index of a Subgroup: The Todd-Coxeter Algorithm (FINITELY PRESENTED GROUPS)
indexed
Indexed Assignment (STATEMENTS AND EXPRESSIONS)
Indexed Sets (SETS)
Multisets (SETS)
Sets (OVERVIEW)
The Indexed Set Constructor (SETS)
indexed-assignment
Indexed Assignment (STATEMENTS AND EXPRESSIONS)
IndexedCoset
IndexedCoset(V, w) : GrpFPCos, GrpFPElt -> GrpFPCosElt
IndexedSetToSequence
IndexedSetToSequence(S) : SetIndx -> SeqEnum
IndexedSetToSet
IndexedSetToSet(S) : SetIndx -> SetEnum
Indexing
HMod_Indexing (Example H43E8)
KMod_Indexing (Example H41E6)
State_Indexing (Example H1E3)
indexing
Indexing Elements (STRUCTURE CONSTANT ALGEBRAS)
Multi-indexing (INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS])
induced
Coset Spaces: Induced Homomorphism (FINITELY PRESENTED GROUPS)
The Homomorphism Induced by a G-Set Action (PERMUTATION GROUPS)
induced-homomorphism
Coset Spaces: Induced Homomorphism (FINITELY PRESENTED GROUPS)
The Homomorphism Induced by a G-Set Action (PERMUTATION GROUPS)
Induction
Induction(x, G) : AlgChtrElt, Grp -> AlgChtrElt
Induction(M, G) : ModGrp, Grp -> ModGrp
induction
Induction, Restriction, Extension (CHARACTERS OF FINITE GROUPS)
induction-restriction-extension
Induction, Restriction, Extension (CHARACTERS OF FINITE GROUPS)
inequality
Comparison (OVERVIEW)
InertiaDegree
InertiaDegree(I) : RngOrdIdl -> RngIntElt
infinite
Summation of Infinite Series (REAL AND COMPLEX FIELDS)
infinite-summation
Summation of Infinite Series (REAL AND COMPLEX FIELDS)
InfiniteSum
InfiniteSum(m, i) : Map, RngIntElt -> FldPrElt
Infinity
Infinity() : -> Infty
infinity
Infinities (RING OF INTEGERS)
infix
Operators (OVERVIEW)
info
Other Information Procedures (ENVIRONMENT AND OPTIONS)
information
Class Information from a Conjugacy Class Poset (GROUPS)
Upper Asymptotic Bounds on the Information Rate (ERROR-CORRECTING CODES)
InformationSet
InformationSet(C) : Code -> [ RngIntElt ]
InformationSpace
InformationSpace(C) : Code -> ModTupFld
initial
The Initial Context (MAGMA SEMANTICS)
initial-context
The Initial Context (MAGMA SEMANTICS)
Injections
Injections(C) : Cop -> [ Map ]
InLineConditional
State_InLineConditional (Example H1E11)
InNeighbors
InNeighbours(u) : GrphVert -> { GrphVert }
InNeighbours
InNeighbours(u) : GrphVert -> { GrphVert }
InnerProduct
(u, v) : ModTupFldElt, ModTupFldElt -> FldElt
(u, v) : ModTupFldElt, ModTupFldElt : -> RngElt
InnerProduct(x, y) : AlgChtrElt, AlgChtrElt -> FldCycElt
InnerProduct(a, b) : AlgGenElt, AlgGenElt -> RngElt
InnerProduct(v, w) : LatElt, LatElt -> RngElt
InnerProductMatrix
InnerProductMatrix(L) : Lat -> AlgMatElt
input
Interactive Input (INPUT AND OUTPUT)
Loading files (OVERVIEW)
InseparableDegree
InseparableDegree(I) : Map -> RngIntElt
Insert
Insert(~S, i, x) : SeqEnum, RngIntElt, Elt ->
InsertBlock
InsertBlock(~a, b, i, j) : AlgMatElt, ModHomElt, RngIntElt, RngIntElt -> AlgMatElt
InsertBlock(~a, b, i, j) : ModMatRngElt, AlgMatElt, RngIntElt, RngIntElt -> ModMatRngElt
InsertVertex
InsertVertex(e) : GrphEdge -> Grph
integer
Polynomials over the Integers (MULTIVARIATE POLYNOMIAL RINGS)
Polynomials over the Integers (UNIVARIATE POLYNOMIAL RINGS)
RING OF INTEGERS
Rings, Fields, and Algebras (OVERVIEW)
IntegerRing
IntegerRing(F) : FldFun -> RngPol
IntegerRing(Q) : FldRat -> RngInt
IntegerRing() : Null -> RngInt
MaximalOrder(K) : FldNum -> RngOrd
MaximalOrder(F) : FldQuad -> RngQuad
ResidueClassRing(m) : RngIntElt -> RngIntRes
pAdicRing(p) : RngIntElt -> RngAdic
Integers
IntegerRing(Q) : FldRat -> RngInt
IntegerRing() : Null -> RngInt
MaximalOrder(K) : FldNum -> RngOrd
ResidueClassRing(m) : RngIntElt -> RngIntRes
RngInt_Integers (Example H24E2)
IntegerToSequence
IntegerToSequence(n, b) : RngIntElt, RngIntElt -> [RngIntElt]
IntegerToString
IntegerToString(n) : RngIntElt -> ModStgElt
IntegerToString(n) : RngIntElt -> MonStgElt
Integral
Integral(m, a, b) : Map, FldPrElt, FldPRElt -> FldPrElt
Integral(f, i) : RngMPolElt, RngIntElt -> RngMPolElt
Integral(f) : RngSerElt -> RngSerElt
Integral(p) : RngUPolElt -> RngUPolElt
FldRe_Integral (Example H37E7)
integral
Derivative, Integral (MULTIVARIATE POLYNOMIAL RINGS)
Derivative, Integral (UNIVARIATE POLYNOMIAL RINGS)
IntegralBasis
IntegralBasis(K) : FldCyc -> [ FldCycElt ]
IntegralBasis(K) : FldNum -> [ FldNumElt ]
IntegralBasis(K) : FldQuad -> [ FldQuadElt ]
IntegralBasis(Q) : FldRat -> [ FldRatElt ]
IntegralGroup
IntegralGroup(G) : GrpMat -> GrpMat, AlgMatElt
IntegralModel
IntegralModel(E) : CurveEll -> CurveEll, Map
integration
Integration (REAL AND COMPLEX FIELDS)
Interactive
GrpPC_Interactive (Example H19E7)
interactive
Interactive Input (INPUT AND OUTPUT)
Using p-Quotient Interactively (FINITELY PRESENTED GROUPS)
interactive-input
Interactive Input (INPUT AND OUTPUT)
InteractiveUserAttributes
Func_InteractiveUserAttributes (Example H2E11)
Func_InteractiveUserAttributes (Example H2E12)
Interior
Interior(P, C) : Plane, { PlanePt } -> { PlanePt }
Interpolate
RngMPol_Interpolate (Example H29E5)
Interpolation
Interpolation(I, V) : [ RngElt ], [ RngElt ] -> RngUPolElt
Interpolation(I, V, i) : [ RngElt ], [ RngMPolElt ], RngIntElt -> RngMPolElt
interpolation
Evaluation, Interpolation (MULTIVARIATE POLYNOMIAL RINGS)
Evaluation, Interpolation (UNIVARIATE POLYNOMIAL RINGS)
interpolation-evaluation
Evaluation, Interpolation (UNIVARIATE POLYNOMIAL RINGS)
interrupt
Control-C key (OVERVIEW)
Starting, Interrupting and Terminating (STATEMENTS AND EXPRESSIONS)
intersection
Groups (OVERVIEW)
Intersection of Subalgebras (MATRIX ALGEBRAS)
Sets (OVERVIEW)
Sum, Intersection and Dual (ERROR-CORRECTING CODES)
IntersectionArray
IntersectionArray(G) : GrphUnd -> [RngIntElt]
IntersectionMatrix
IntersectionMatrix(G, P) : GrphUnd, { { GrphVert } } -> AlgMatElt
IntersectionNumber
IntersectionNumber(D, i, j) : Dsgn, RngIntElt, RngIntElt -> RngIntElt
intrinsic
Intrinsics (FUNCTIONS, PROCEDURES AND PACKAGES)
Intrinsics (OVERVIEW)
Func_intrinsic (Example H2E5)
intro
Introduction (INPUT AND OUTPUT)
introduction
Introduction (ABELIAN GROUPS)
Introduction (ALGEBRAS)
Introduction (ASSOCIATIVE ALGEBRAS)
Introduction (BLACKBOX GROUPS)
Introduction (COPRODUCTS)
Introduction (CYCLOTOMIC FIELDS)
Introduction (ELLIPTIC CURVES)
Introduction (ENUMERATIVE COMBINATORICS)
Introduction (ERROR-CORRECTING CODES)
Introduction (FINITE FIELDS)
Introduction (FINITE PLANES)
Introduction (FINITELY PRESENTED ALGEBRAS)
Introduction (FINITELY PRESENTED GROUPS)
Introduction (FINITELY PRESENTED GROUPS)
Introduction (FINITELY PRESENTED SEMIGROUPS)
Introduction (FUNCTION FIELDS AND THEIR ORDERS)
Introduction (FUNCTIONS, PROCEDURES AND PACKAGES)
Introduction (FUNCTIONS, PROCEDURES AND PACKAGES)
Introduction (GENERAL MODULES)
Introduction (GRAPHS)
Introduction (GROUP ALGEBRAS)
Introduction (GROUPS)
Introduction (INCIDENCE STRUCTURES AND DESIGNS)
Introduction (INVARIANT RINGS OF FINITE GROUPS)
Introduction (LATTICES)
Introduction (LIE ALGEBRAS)
Introduction (LISTS)
Introduction (LOCAL FIELDS)
Introduction (MAGMA SEMANTICS)
Introduction (MAPPINGS)
Introduction (MATRIX ALGEBRAS)
Introduction (MATRIX GROUPS)
Introduction (MATRIX GROUPS)
Introduction (MATRIX GROUPS)
Introduction (MODULES OVER AFFINE ALGEBRAS)
Introduction (MULTIVARIATE POLYNOMIAL RINGS)
Introduction (NUMBER FIELDS AND THEIR ORDERS)
Introduction (PERMUTATION GROUPS)
Introduction (PERMUTATION GROUPS)
Introduction (POWER SERIES AND LAURENT SERIES)
Introduction (QUADRATIC FIELDS)
Introduction (RATIONAL FIELD)
Introduction (RATIONAL FUNCTION FIELDS)
Introduction (REAL AND COMPLEX FIELDS)
Introduction (RECORDS)
Introduction (RESIDUE CLASS RINGS)
Introduction (RING OF INTEGERS)
Introduction (SEQUENCES)
Introduction (SETS)
Introduction (STATEMENTS AND EXPRESSIONS)
Introduction (STRUCTURE CONSTANT ALGEBRAS)
Introduction (THE MODULES Hom_(R)(M, N) AND End(M))
Introduction (TUPLES AND CARTESIAN PRODUCTS)
Introduction (UNIVARIATE POLYNOMIAL RINGS)
Introduction (VALUATION RINGS)
Introduction (VECTOR SPACES)
Overview (OVERVIEW)
Power-conjugate Presentations (SOLUBLE GROUPS)
Intseq
IntegerToSequence(n, b) : RngIntElt, RngIntElt -> [RngIntElt]
invar
Invariants of an Algebra (ALGEBRAS)
Plane_invar (Example H57E6)
invariant
Creation of Invariant Rings (INVARIANT RINGS OF FINITE GROUPS)
Elementary Invariants of a Design (INCIDENCE STRUCTURES AND DESIGNS)
Elementary Invariants of a Graph (GRAPHS)
Elementary Invariants of an Incidence Structure (INCIDENCE STRUCTURES AND DESIGNS)
INVARIANT RINGS OF FINITE GROUPS
Invariants (CYCLOTOMIC FIELDS)
Invariants (ELLIPTIC CURVES)
Invariants (FUNCTION FIELDS AND THEIR ORDERS)
Invariants (NUMBER FIELDS AND THEIR ORDERS)
Invariants (NUMBER FIELDS AND THEIR ORDERS)
Invariants (POWER SERIES AND LAURENT SERIES)
Invariants (RATIONAL FUNCTION FIELDS)
Invariants of an Abelian Group (ABELIAN GROUPS)
Matrix Invariants (MATRIX GROUPS)
Numerical Invariants (CHARACTERS OF FINITE GROUPS)
Numerical Invariants (FINITE FIELDS)
Numerical Invariants (INTRODUCTION [RINGS AND FIELDS])
Numerical Invariants (MULTIVARIATE POLYNOMIAL RINGS)
Numerical Invariants (QUADRATIC FIELDS)
Numerical Invariants (RATIONAL FIELD)
Numerical Invariants (REAL AND COMPLEX FIELDS)
Numerical Invariants (RESIDUE CLASS RINGS)
Numerical Invariants (RING OF INTEGERS)
Numerical Invariants (UNIVARIATE POLYNOMIAL RINGS)
Numerical Invariants (VALUATION RINGS)
Numerical Invariants of a Plane (FINITE PLANES)
Rings, Fields, and Algebras (OVERVIEW)
The Invariants of a Matrix Algebra (MATRIX ALGEBRAS)
invariant-ring
Creation of Invariant Rings (INVARIANT RINGS OF FINITE GROUPS)
INVARIANT RINGS OF FINITE GROUPS
InvariantFactors
InvariantFactors(a) : AlgMatElt -> [ AlgPolElt ]
InvariantFactors(g) : GrpMatElt -> [ RngUPolElt ]
InvariantForms
InvariantForms(G) : GrpMat -> [ AlgMatElt ]
InvariantRing
InvariantRing(G) : GrpMat -> RngInvar
Invariants
AbelianInvariants(G) : GrpFin -> [ RngIntElt ]
AbelianInvariants(G) : GrpMat -> [ RngIntElt ]
Invariants(A) : GrpAb -> [ RngIntElt ]
AlgMat_Invariants (Example H51E3)
Elcu_Invariants (Example H53E6)
GrpMat_Invariants (Example H21E4)
invariants
Construction of Invariants of Specified Degree (INVARIANT RINGS OF FINITE GROUPS)
InvariantsOfDegree
InvariantsOfDegree(R, d) : RngInvar, RngIntElt -> [ RngMPolElt ]
RngInvar_InvariantsOfDegree (Example H30E3)
RngInvar_InvariantsOfDegree (Example H30E4)
invblock
Inverse Block: invblock (MULTIVARIATE POLYNOMIAL RINGS)
inverse
Groups (OVERVIEW)
Inverse Hyperbolic Functions (REAL AND COMPLEX FIELDS)
Inverse Trigonometric Functions (REAL AND COMPLEX FIELDS)
Rings, Fields, and Algebras (OVERVIEW)
inverse-hyperbolic
Inverse Hyperbolic Functions (REAL AND COMPLEX FIELDS)
inverse-trigonometric
Inverse Trigonometric Functions (REAL AND COMPLEX FIELDS)
InverseKrawchouk
InverseKrawchouk(A, K, n) : RngUPolElt, FldFin, RngIntElt -> RngUPolElt
InverseMattsonSolomonTransform
InverseMattsonSolomonTransform(A, n) : RngUPolElt, RngIntElt -> RngUPolElt
InverseWordMap
InverseWordMap(G) : GrpMat -> Map
InverseWordMap(G) : GrpPerm -> Map
invocation
Functions (OVERVIEW)
Functions, Procedures, and Mappings (OVERVIEW)
Involution
Involution(a) : AlgGrpElt -> AlgGrpElt
IO
INPUT AND OUTPUT
Iroot
Iroot(a, n) : RngIntElt, RngIntElt -> RngIntElt
irredsol
Database of Irreducible Soluble Subgroups of GL(n,p) for n > 1 and p^n < 256 (OVERVIEW)
irreducibility
Factorization and Irreducibility (MULTIVARIATE POLYNOMIAL RINGS)
Factorization and Irreducibility (UNIVARIATE POLYNOMIAL RINGS)
irreducible
Database of Irreducible Soluble Subgroups of GL(n,p) for n > 1 and p^n < 256 (OVERVIEW)
The Table of Irreducible Characters (CHARACTERS OF FINITE GROUPS)
IrreduciblePolynomial
IrreduciblePolynomial(F, m) : FldFin, RngIntElt -> RngPolElt
irreducibles
Finding Irreducibles (CHARACTERS OF FINITE GROUPS)
IrreducibleSecondaryInvariants
IrreducibleSecondaryInvariants(R) : RngInvar -> [ RngMPolElt ]
is
The where ... is Construction (STATEMENTS AND EXPRESSIONS)
IsAbelian
IsAbelian(G) : GrpAb -> BoolElt
IsAbelian(G) : GrpFin -> BoolElt
IsAbelian(G) : GrpMat -> BoolElt
IsAbelian(G) : GrpPC -> BoolElt
IsAbelian(G) : GrpPerm -> BoolElt
IsAbsolutelyIrreducible
IsAbsolutelyIrreducible(G) : GrpMat -> BoolElt
IsAbsolutelyIrreducible(M) : ModRng -> BoolElt, AlgMatElt, RngIntElt
IsAlternating
IsAlternating(G) : GrpPerm -> BoolElt
IsAltsym
IsAltsym(G) : GrpPerm -> BoolElt
IsArc
IsArc(P, A) : Plane, { PlanePt } -> BoolElt
IsArcTransitive
[Future release] IsArcTransitive(G, t) : GrphUnd, RngIntElt -> BoolElt
IsAssociative
IsAssociative(A) : AlgGen -> BoolElt
IsBalanced
IsBalanced(D, t: parameters) : Inc, RngIntElt -> BoolElt, RngIntElt
IsBijective
IsBijective(a) : ModMatRngElt -> BoolElt
IsBipartite
IsBipartite(G) : GrphUnd -> BoolElt
IsBlock
IsBlock(G, S) : GrpPerm, { Elt } -> BoolElt
IsBlock(D, S) : Inc, IncBlk -> BoolElt, IncBlk
IsBlockTransitive
IsBlockTransitive(D) : Inc -> BoolElt
IsCentral
IsCentral(G, H) : GrpAb, GrpAb -> BoolElt
IsCentral(G, H) : GrpFin -> BoolElt
IsCentral(G, H) : GrpMat -> BoolElt
IsCentral(G, H) : GrpPC, GrpPC -> BoolElt
IsCentral(G, H) : GrpPerm -> BoolElt
IsCentralCollineation
IsCentralCollineation(P, g) : Plane, GrpPermElt -> BoolElt, PlanePt, PlaneLn
IsCharacter
IsCharacter(x) : AlgChtrElt -> BoolElt
IsCohenMacaulay
IsCohenMacaulay(R) : RngInvar -> BoolElt
IsCollinear
IsCollinear(P, S) : Plane, { PlanePt } -> BoolElt, PlaneLn
IsCommutative
IsCommutative(A) : AlgGen -> BoolElt
IsCommutative(R) : Rng -> BoolElt
IsComplete
IsComplete(V) : GrpFPCos -> BoolElt
IsComplete(G) : Grph -> BoolElt
IsComplete(D) : Inc -> BoolElt
IsComplete(P, A) : Plane, { PlanePt } -> BoolElt
IsComplete(S) : SeqEnum -> BoolElt
IsConcurrent
IsConcurrent(P, R) : Plane, { PlaneLn } -> BoolElt, PlanePt
IsConditioned
IsConditioned(G) : GrpPC -> BoolElt
IsConditioned(G) : GrpPC -> BoolElt
IsConjugate
IsConjugate(G, H, K) : GrpAb, GrpAb, GrpAb -> BoolElt, GrpAbElt
IsConjugate(G, g, h) : GrpAb, GrpAbElt, GrpAbElt -> BoolElt, GrpAbElt
IsConjugate(G, g, h) : GrpFin, GrpFinElt, GrpFinElt -> BoolElt, GrpFinElt
IsConjugate(G, g, h) : GrpFin, GrpFinElt, GrpFinElt -> BoolElt, GrpFinElt
IsConjugate(G, H, K) : GrpFP, GrpFP, GrpFP -> BoolElt, GrpFPElt
IsConjugate(G, g, h) : GrpMat, GrpMatElt, GrpMatElt -> BoolElt, GrpMatElt | Unass
IsConjugate(G, g, h) : GrpMat, GrpMatElt, GrpMatElt -> BoolElt, GrpMatElt | Unass
IsConjugate(G, H, K) : GrpPC, GrpPC, GrpPC -> BoolElt, GrpPCElt
IsConjugate(G, g, h) : GrpPC, GrpPCElt, GrpPCElt -> BoolElt, GrpPCElt
IsConjugate(G, g, h) : GrpPerm, GrpPermElt, GrpPermElt -> BoolElt, GrpPermElt
IsConjugate(G, g, h) : GrpPerm, GrpPermElt, GrpPermElt -> BoolElt, GrpPermElt
IsConjugate(G, Y, y, z) : GrpPerm, GSet, Elt, Elt -> BoolElt, GrpPermElt
IsConnected
IsConnected(G) : GrphUnd -> BoolElt
IsConsistent
IsConsistent(G) : GrpPC -> BoolElt
IsConsistent(a, v) : ModMatFldElt, ModTupFld -> BoolElt, ModTupFldElt, ModTupFld
IsConsistent(A, w) : ModMatRngElt, ModTupRng -> BoolElt, ModTupRngElt, ModTupRng
IsConsistent(A, w) : ModMatRngElt, ModTupRng -> BoolElt, ModTupRngElt, ModTupRng
IsConstant
IsZero(I) : Map -> Bool
IsConway
IsConway(F) : FldFin -> BoolElt
IsCyclic
IsCyclic(C) : Code -> BoolElt
IsCyclic(G) : GrpAb -> BoolElt
IsCyclic(G) : GrpFin -> BoolElt
IsCyclic(G) : GrpMat -> BoolElt
IsCyclic(G) : GrpPC -> BoolElt
IsCyclic(G) : GrpPerm -> BoolElt
IsDecomposable
IsDecomposable(M) : ModRng -> BoolElt, ModRng, ModRng
IsDefined
IsDefined(S, i) : SeqEnum, RngIntElt -> BoolElt
IsDesarguesian
IsDesarguesian(P) : Plane -> BoolElt
IsDesign
IsDesign(D, t: parameters) : Inc, RngIntElt -> BoolElt, RngIntElt
IsDiagonal
IsDiagonal(a) : AlgMatElt -> BoolElt
IsDifferenceSet
IsDifferenceSet(B) : SetEnum -> BoolElt, RngIntElt
IsDirectSummand
HasComplement(M, S) : ModGrp, ModGrp -> BoolElt, ModGrp
IsDiscriminant
IsDiscriminant(d) : RngIntElt -> BoolElt
IsDisjoint
IsDisjoint(R, S) : SetEnum, SetEnum -> BoolElt
IsDistanceRegular
IsDistanceRegular(G) : GrphUnd -> BoolElt
IsDistanceTransitive
IsDistanceTransitive(G) : GrphUnd -> BoolElt
IsDivisibleBy
IsDivisibleBy(n, d) : RngIntElt, RngIntElt -> BoolElt, RngIntElt
IsDivisibleBy(a, b) : RngMPolElt, RngMPolElt -> BoolElt, RngMPolElt
IsDivisionRing
IsDivisionRing(R) : Rng -> BoolElt
IsDomain
IsDomain(R) : Rng -> BoolElt
IsEdgeTransitive
IsEdgeTransitive(G) : GrphUnd -> BoolElt
IsElementaryAbelian
IsElementaryAbelian(G) : GrpAb -> BoolElt
IsElementaryAbelian(G) : GrpFin -> BoolElt
IsElementaryAbelian(G) : GrpMat -> BoolElt
IsElementaryAbelian(G) : GrpPC -> BoolElt
IsElementaryAbelian(G) : GrpPerm -> BoolElt
IsEllipticCurve
IsEllipticCurve([a, b]) : [ RngElt ] -> BoolElt, CurveEll
IsEmpty
IsEmpty(G) : Grph -> BoolElt
IsEmpty(P) : LatEnumProc -> BoolElt
IsEmpty(S) : List -> BoolElt
IsEmpty(p) : Process -> BoolElt
IsEmpty(p) : Process -> BoolElt
IsEmpty(P) : Process(Lix) -> BoolElt
IsEmpty(S) : SeqEnum -> BoolElt
IsEmpty(R) : SetEnum -> BoolElt
IsEof
IsEof(S) : MonStgElt -> BoolElt
IsEquationOrder
IsEquationOrder(O) : RngOrd -> BoolElt
IsEquationOrder(O) : RngQuad -> BoolElt
IsEquidistant
IsEquidistant(C) : Code -> BoolElt
IsEquitable
IsEquitable(G, P) : GrphUnd, { { GrphVert } } -> BoolElt
Isetseq
IndexedSetToSequence(S) : SetIndx -> SeqEnum
Isetset
IndexedSetToSet(S) : SetIndx -> SetEnum
IsEuclideanDomain
IsEuclideanDomain(R) : Rng -> BoolElt
IsEuclideanRing
IsEuclideanRing(R) : Rng -> BoolElt
IsEulerian
IsEulerian(G) : Grph -> BoolElt
IsEven
IsEven(g) : GrpPermElt -> BoolElt
IsEven(L) : Lat -> BoolElt
IsEven(n) : RngIntElt -> BoolElt
IsExceptionalUnit
IsExceptionalUnit(u) : RngOrdElt -> Boolelt
IsExtraSpecial
IsExtraSpecial(G) : GrpFin -> BoolElt
IsExtraSpecial(G) : GrpMat -> BoolElt
IsExtraSpecial(G) : GrpPC -> BoolElt
IsExtraSpecial(G) : GrpPerm -> BoolElt
IsExtraSpecialNormaliser
IsExtraSpecialNormaliser (G) : GrpMat -> BoolElt
IsFaithful
IsFaithful(G, Y) : : GrpPerm, GSet -> BoolElt
IsFaithful(x) : AlgChtrElt -> BoolElt
IsField
IsField(R) : Rng -> BoolElt
IsFinite
IsFinite(G) : GrpAb -> BoolElt
IsFinite(G) : GrpMat -> Bool, RngIntElt
IsFinite(x) : Infty -> BoolElt
IsFinite(R) : Rng -> BoolElt
IsFinitePointWithThisX
IsFinitePointWithThisX(x) : FldElt -> BoolElt, FldElt, CurveEllPt
IsForest
IsForest(G) : GrphUnd -> BoolElt
IsFrobenius
IsFrobenius(G) : GrpPerm -> BoolElt
IsFundamental
IsFundamental(d) : RngIntElt -> BoolElt
IsGeneralizedCharacter
IsGeneralizedCharacter(x) : AlgChtrElt -> BoolElt
IsGeneralLinear
[Future release] IsGeneralLinear(G) : GrpMat -> BoolElt
IsGHom
IsGHom(X) : ModMatElt -> BoolElt
IsGood
GrpPC_IsGood (Example H19E11)
IsGroebner
IsGroebner(S) : { RngMPolElt } -> BoolElt
IsHadamard
IsHadamard(H) : AlgMatElt -> BoolElt
IsHadamardEquivalent
IsHadamardEquivalent(H, J) : AlgMatElt, AlgMatElt -> BoolElt
IsHomogeneous
IsHomogeneous(M) : ModMPol -> BoolElt
IsHomogeneous(f) : RngMPolElt -> BoolElt
IsId
IsId(P) : CurveEllPt -> BoolElt
IsId(g) : GrpElt -> BoolElt
IsId(g) : GrpPermElt -> BoolElt
IsIdentity(u) : GrpAbElt -> BoolElt
IsIdentity(g) : GrpMatElt -> BoolElt
IsIdentity(g) : GrpPCElt -> BoolElt
IsIdeal
IsIdeal(S) : AlgGrpSub -> BoolElt
IsIdempotent
IsIdempotent(a) : AlgGenElt -> BoolElt
IsIdempotent(x) : RngElt -> BoolElt
IsIdenticalPresentation
IsIdenticalPresentation(G, H) : GrpPC, GrpPC -> BoolElt
IsIdentity
IsId(P) : CurveEllPt -> BoolElt
IsId(g) : GrpElt -> BoolElt
IsId(g) : GrpPermElt -> BoolElt
IsIdentity(u) : GrpAbElt -> BoolElt
IsIdentity(g) : GrpMatElt -> BoolElt
IsIdentity(g) : GrpPCElt -> BoolElt
IsIndependent
IsIndependent(Q) : [ AlgGen ] -> BoolElt
IsIndependent(S) : { ModTupFldElt } -> BoolElt
IsIndependent(S) : { ModTupRngElt } -> BoolElt
IsInImage
IsInImage(f, p) : Map, RngMPolElt -> [ BoolElt ]
IsInjective
IsInjective(a) : ModMatRngElt -> BoolElt
IsInRadical
IsInRadical(f, I) : RngMPolElt, RngMPol -> BoolElt
IsInseparable
IsInseparable(I) : Map -> Bool
IsIntegral
IsIntegral(P) : CurveEllPt -> BoolElt
IsIntegral(a) : FldNumElt -> BoolElt
IsIntegral(c) : FldPrElt -> BoolElt
IsIntegral(q) : FldRatElt -> BoolElt
IsIntegral(L) : Lat -> BoolElt
IsIntegral(I) : RngFunOrdIdl -> BoolElt
IsIntegral(n) : RngIntElt -> BoolElt
IsIntegral(I) : RngOrdIdl -> BoolElt
IsIntegralDomain
IsDomain(R) : Rng -> BoolElt
IsIrreducible
IsIrreducible(x) : AlgChtrElt -> BoolElt
IsIrreducible(G) : GrpMat -> BoolElt
IsIrreducible(G) : GrpMat -> BoolElt, ModGrp
IsIrreducible(M) : ModRng -> BoolElt, ModRng, ModRng
IsIrreducible(x) : RngElt -> BoolElt
IsIrreducible(f) : RngMPolElt -> BoolElt
IsIrreducible(p) : RngUPolElt -> BoolElt
IsIsogenous
IsIsogenous(E, F) : CurveEll, CurveEll -> BoolElt
IsIsometric
IsIsometric(L, M) : Lat, Lat -> BoolElt, AlgMatElt
IsIsomorphic
IsIsometric(L, M) : Lat, Lat -> BoolElt, AlgMatElt
IsIsomorphic(E, F) : CurveEll, CurveEll -> BoolElt, Map
IsIsomorphic(K, L) : FldNum, FldNum -> 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(D, E: parameters) : Inc, Inc -> BoolElt, Map
IsIsomorphic(P, Q: parameters) : Plane, Plane -> BoolElt, Map
IsIsomorphism
IsIsomorphism(I) : BoolElt, Map -> Map
IsLabelled
IsLabelled(t) : GrphVert -> BoolElt
IsLabelledEdge
IsLabelledEdge(G, i, j) : Grph, RngIntElt, RngIntElt -> BoolElt
IsLabelledVertex
IsLabelledVertex(G, i) : Grph, RngIntElt -> BoolElt
IsLeftIdeal
IsLeftIdeal(S) : AlgGrpSub -> BoolElt
IsLie
IsLie(A) : AlgGen -> BoolElt
IsLinear
IsLinear(x) : AlgChtrElt -> BoolElt
IsLinearSpace
IsLinearSpace(D) : Inc -> BoolElt
IsLineRegular
IsLineRegular(D) : IncNsp -> BoolElt, RngIntElt
IsLineTransitive
IsLineTransitive(P) : Plane -> BoolElt
IsMaximal
IsMaximal(G, H) : GrpAb, GrpAb -> BoolElt
IsMaximal(G, H) : GrpFin, GrpFin -> BoolElt
IsMaximal(G, H) : GrpFP, GrpFP -> BoolElt
IsMaximal(G, H) : GrpMat, GrpMat -> BoolElt
IsMaximal(G, H) : GrpPC, GrpPC -> BoolElt
IsMaximal(G, H) : GrpPerm, GrpPerm -> BoolElt
IsMaximal(I) : RngMPol -> BoolElt
IsMaximal(O) : RngOrd -> BoolElt
IsMaximal(O) : RngQuad -> BoolElt
IsMaximumDistanceSeparable
IsMaximumDistanceSeparable(C) : Code -> BoolElt
IsMDS
IsMaximumDistanceSeparable(C) : Code -> BoolElt
IsMemberBasicOrbit
IsMemberBasicOrbit(G, i, a) : GrpPerm, RngIntElt, Elt -> BoolElt
IsMinusOne
IsMinusOne(a) : AlgGenElt -> BoolElt
IsMinusOne(a) : AlgMatElt -> BoolElt
IsMinusOne(a) : RngElt -> BoolElt
IsMinusOne(a) : RngOrdResElt -> Boolelt
IsNearLinearSpace
IsNearLinearSpace(D) : Inc -> BoolElt
IsNearlyPerfect
IsNearlyPerfect(C) : Code -> BoolElt
IsNegativeDefinite
IsNegativeDefinite(F) : ModMatRngElt -> BoolElt
IsNegativeSemiDefinite
IsNegativeSemiDefinite(F) : ModMatRngElt -> BoolElt
IsNilpotent
IsNilpotent(a) : AlgGenElt -> BoolElt, RngIntElt
IsNilpotent(L) : AlgLie -> BoolElt
IsNilpotent(G) : GrpAb -> BoolElt
IsNilpotent(G) : GrpFin -> BoolElt
IsNilpotent(G) : GrpMat -> BoolElt
IsNilpotent(G) : GrpPC -> BoolElt
IsNilpotent(G) : GrpPerm -> BoolElt
IsNilpotent(x) : RngElt -> BoolElt
IsNilpotent(f) : RngMPolResElt -> BoolElt, RngIntElt
IsNormal
IsNormal(a) : FldFinElt -> BoolElt
IsNormal(G, H) : GrpAb, GrpAb -> BoolElt
IsNormal(G, H) : GrpFin, GrpFin -> BoolElt
IsNormal(G, H) : GrpFP, GrpFP -> BoolElt
IsNormal(G, H) : GrpMat, GrpMat -> BoolElt
IsNormal(G, H) : GrpPC, GrpPC -> BoolElt
IsNormal(G, H) : GrpPerm, GrpPerm -> BoolElt
IsNull
IsNull(S) : SeqEnum -> BoolElt
IsNull(R) : SetEnum -> BoolElt
IsOdd
IsOdd(n) : RngIntElt -> BoolElt
IsogeniesAreEqual
IsogeniesAreEqual(I, J) : Map, Map -> Bool
Isogeny
Morphism(E, F, psi , phi, omega ) : CurveEll, CurveEll, RngMPolElt, RngMPolElt, RngMPolElt -> Map
Elcu_Isogeny (Example H53E14)
IsogenyFromKernel
IsogenyFromKernel(E, psi) : CurveEll, RngUPolElt -> CurveEll, Map
IsogenyFromKernel(G) : CurveEllSubgroup -> CurveEll, Map
IsogenyFromKernelFactored
IsogenyFromKernelFactored(E, psi) : CurveEllSubgroup -> CurveEll, Map
IsogenyFromKernelFactored(G) : CurveEllSubgroup -> CurveEll, Map
IsogenyMapOmega
IsogenyMapOmega(I) : Map -> RngMPolElt
IsogenyMapPhi
IsogenyMapPhi(I) : Map -> RngUPolElt
IsogenyMapPhiUni
IsogenyMapPhiUni(I) : Map -> RngUPolElt
IsogenyMapPsi
IsogenyMapPsi(I) : Map -> RngUPolElt
IsogenyMapPsiUni
IsogenyMapPsiUni(I) : Map -> RngUPolElt
isolgps
Database of Irreducible Soluble Subgroups of GL(n,p) for n > 1 and p^n < 256 (OVERVIEW)
Isom
Lat_Isom (Example H45E19)
isom
Automorphism Group and Isometry Testing (LATTICES)
Isomorphism
Isomorphism(E, F, [r, s, t, u]) : CurveEll, CurveEll, Seq -> Map
Elcu_Isomorphism (Example H53E15)
isomorphism
Automorphisms and Isomorphisms (SOLUBLE GROUPS)
The Isomorphism (FINITELY PRESENTED ALGEBRAS)
IsomorphismClasses
Elcu_IsomorphismClasses (Example H53E8)
IsomorphismImage
IsomorphismImage(E, [r, s, t, u]) : CurveEll, Seq -> Map, CurveEll
IsomorphismToIsogeny
IsomorphismToIsogeny(I) : Map -> Map
IsomorphismToIsogeny(I) : Map -> Map
IsOne
IsOne(a) : AlgGenElt -> BoolElt
IsOne(a) : AlgMatElt -> BoolElt
IsOne(u) : MonFPElt -> BoolElt
IsOne(a) : RngElt -> BoolElt
IsOne(a) : RngOrdResElt -> Boolelt
IsOrbit
IsOrbit(G, S) : GrpPerm, { Elt } -> BoolElt
IsOrdered
IsOrdered(R) : Rng -> BoolElt
IsOrderOfPoint
IsOrderOfPoint(P, m) : CurveEll -> BoolElt
IsOverSmallerField
IsOverSmallerField(G) : GrpMat -> BoolElt, GrpMat
GrpMat_IsOverSmallerField (Example H21E24)
IsParallel
IsParallel(P, l, m) : Plane, PlaneLn, PlaneLn -> BoolElt
IsParallelClass
IsParallelClass(D, B, C) : Inc, IncBlk, IncBlk -> BoolElt, { IncBlk }
IsPath
IsPath(G) : Grph -> BoolElt
IsPerfect
IsPerfect(C) : Code -> BoolElt
IsPerfect(G) : GrpAb -> BoolElt
IsPerfect(G) : GrpFin -> BoolElt
IsPerfect(G) : GrpMat -> BoolElt
IsPerfect(G) : GrpPC -> BoolElt
IsPerfect(G) : GrpPerm -> BoolElt
IsPID
IsPID(R) : Rng -> BoolElt
IsPlanar
[Future release] IsPlanar(G) : GrphUnd -> BoolElt
IsPoint
IsPoint(S, E) : [RngElt], CurveEll -> BoolElt, CurveEllPt
IsPointRegular
IsPointRegular(D) : IncNsp -> BoolElt, RngIntElt
IsPointTransitive
IsPointTransitive(D) : Inc -> BoolElt
IsPointTransitive(P) : Plane -> BoolElt
IsPolygon
IsPolygon(G) : Grph -> BoolElt
IsPositiveDefinite
IsPositiveDefinite(F) : ModMatRngElt -> BoolElt
IsPositiveSemiDefinite
IsPositiveSemiDefinite(F) : ModMatRngElt -> BoolElt
IsPower
IsPower(a, n) : FldFinElt, RngIntElt -> BoolElt, FldFinElt
IsPower(n) : RngIntElt -> BoolElt
IsPower(w, n) : RngOrdElt, RngIntElt -> BoolElt, RngOrdElt
IsPowerTimesTorsionUnit
IsPowerTimesTorsionUnit(w, n) : RngOrdElt, RngIntElt -> BoolElt, RngOrdElt
IsPowerTimesUnit
IsPowerTimesUnit(w, n) : RngOrdElt, RngIntElt -> BoolElt, RngOrdElt
IsPrimary
IsPrimary(I) : RngMPol -> BoolElt
IsPrimary(I) : RngMPolRes -> BoolElt
IsPrime
IsPrime(x) : RngElt -> BoolElt
IsPrime(I) : RngFunOrdIdl -> BoolElt
IsPrime(n) : RngIntElt -> BoolElt
IsPrime(n) : RngIntElt -> BoolElt
IsPrime(I) : RngMPol -> BoolElt
IsPrime(I) : RngMPolRes -> BoolElt
IsPrime(I) : RngOrdIdl -> BoolElt, RngOrdIdl
RngInt_IsPrime (Example H24E3)
IsPrimePower
IsPrimePower(n) : RngIntElt -> BoolElt, RngIntElt, RngIntElt
IsPrimitive
IsPrimitive(a) : FldFinElt -> BoolElt
IsPrimitive(a) : FldNumElt -> BoolElt
IsPrimitive(G) : GrphUnd -> BoolElt
IsPrimitive(G) : GrpMat -> BoolElt
IsPrimitive(G) : GrpPerm -> BoolElt
IsPrimitive(G) : GrpPerm -> BoolElt
IsPrimitive(G, Y) : GrpPerm, GSet -> BoolElt
IsPrimitive(n, m) : RngIntElt, RngIntElt -> BoolElt
IsPrimitive(n) : RngIntResElt -> BoolElt
GrpMat_IsPrimitive (Example H21E18)
IsPrincipal
IsPrincipal(I) : RngOrdIdl -> BoolElt, FldNumElt
IsPrincipalIdealDomain
IsPID(R) : Rng -> BoolElt
IsPrincipalIdealRing
IsPrincipalIdealRing(R) : Rng -> BoolElt
IsProbablePrime
IsProbablePrime(n) : RngIntElt -> BoolElt
IsProbablyOrdinary
IsProbablyOrdinary(E) : CurveEll -> BoolElt
IsProjective
IsProjective(C) : Code -> BoolElt
IsProper
IsProper(I) : RngMPol -> BoolElt
IsProper(I) : RngMPolRes -> BoolElt
IsProportional
IsProportional (X, k) : Mtrx, RngIntElt -> BoolElt, Tup
IsProvenSupersingular
IsProvenSupersingular(E) : CurveEll -> BoolElt
Isqrt
Isqrt(n) : RngIntElt -> RngIntElt
IsRadical
IsRadical(I) : RngMPol -> BoolElt
IsRadical(I) : RngMPolRes -> BoolElt
IsReal
IsReal(x) : AlgChtrElt -> BoolElt
IsReal(c) : FldComElt -> BoolElt
IsReduced
IsReduced(f) : MagFormElt -> BoolElt
IsRegular
IsRegular(a) : AlgGenElt -> BoolElt
IsRegular(G) : Grph -> BoolElt
IsRegular(G) : GrpPerm -> BoolElt
IsRegular(G, Y) : GrpPerm, GSet -> BoolElt
IsResolvable
IsResolvable(D) : Inc -> BoolElt, { SetEnum }
IsRestrictedLieAlgebra
IsRestrictedLieAlgebra(L) : AlgLie -> BoolElt
IsRightIdeal
IsRightIdeal(S) : AlgGrpSub -> BoolElt
IsSatisfied
IsSatisfied(U, E) : { RelElt }, [ GrpElt ] -> BoolElt
IsScalar
IsScalar(u) : AlgFPElt -> BoolElt
IsScalar(a) : AlgMatElt -> BoolElt
IsScalar(g) : GrpMatElt -> BoolElt
IsSelfDual
IsSelfDual(C) : Code -> BoolElt
IsSelfDual(D) : Inc -> BoolElt
IsSelfDual(P) : ProjPl -> BoolElt
IsSelfNormalising
IsSelfNormalizing(G, H) : GrpFin, GrpFin -> BoolElt
IsSelfNormalizing(G, H) : GrpPerm, GrpPerm -> BoolElt
IsSelfNormalizing
IsSelfNormalizing(G, H) : GrpFin, GrpFin -> BoolElt
IsSelfNormalizing(G, H) : GrpFP, GrpFP -> BoolElt
[Future release] IsSelfNormalizing(G, H) : GrpMat, GrpMat -> BoolElt
IsSelfNormalizing(G, H) : GrpPC, GrpPC -> BoolElt
IsSelfNormalizing(G, H) : GrpPerm, GrpPerm -> BoolElt
IsSelfOrthogonal
IsSelfDual(C) : Code -> BoolElt
IsSemiLinear
IsSemiLinear(G) : GrpMat -> BoolElt
IsSemiregular
IsSemiregular(G, S) : GrpPerm, GSet -> BoolElt
IsSemiregular(G, Y) : GrpPerm, GSet -> BoolElt
IsSemisimple
IsSemisimple(A) : AlgGen -> BoolElt
IsSeparable
IsSeparable(G) : Grph -> BoolElt
IsSeparable(I) : Map -> Bool
IsSeparable(p) : RngUPolElt -> BoolElt
IsSharplyTransitive
IsSharplyTransitive(G, Y, k) : GrpPerm, GSet, RngIntElt -> BoolElt
IsSharplyTransitive(G, k) : GrpPerm, RngIntElt -> BoolElt
IsSimilar
IsSimilar(a, b) : AlgMatElt, AlgMatElt -> BoolElt, AlgMatElt
IsSimple
IsSimple(A) : AlgGen -> BoolElt
IsSimple(G) : GrpAb -> BoolElt
IsSimple(G) : GrpFin -> BoolElt
IsSimple(G) : GrpMat -> BoolElt
IsSimple(G) : GrpPC -> BoolElt
IsSimple(G) : GrpPerm -> BoolElt
IsSimple(D) : Inc -> BoolElt
IsSimplifiedModel
IsSimplifiedModel(E) : CurveEll -> BoolElt
IsSinglePrecision
IsSinglePrecision(n) : RngIntElt -> BoolElt
IsSLGL
[Future release] IsSLGL(G) : GrpMat -> BoolElt
IsSoluble
IsSoluble(G) : GrpAb -> BoolElt
IsSoluble(G) : GrpFin -> BoolElt
IsSoluble(G) : GrpMat -> BoolElt
IsSoluble(G) : GrpPC -> BoolElt
IsSoluble(G) : GrpPerm -> BoolElt
IsSolvable
IsSoluble(G) : GrpAb -> BoolElt
IsSoluble(G) : GrpFin -> BoolElt
IsSoluble(G) : GrpMat -> BoolElt
IsSoluble(G) : GrpPC -> BoolElt
IsSoluble(G) : GrpPerm -> BoolElt
IsSolvable(L) : AlgLie -> BoolElt
IsSpecial
IsSpecial(G) : GrpFin -> BoolElt
IsSpecial(G) : GrpMat -> BoolElt
IsSpecial(G) : GrpPC -> BoolElt
IsSpecial(G) : GrpPerm -> BoolElt
IsSpecialLinear
[Future release] IsSpecialLinear(G) : GrpMat -> BoolElt
IsSquare
IsSquare(a) : FldFinElt -> BoolElt
IsSquare(n) : RngIntElt -> BoolElt, RngIntElt
IsSquare(n) : RngIntResElt -> BoolElt, RngIntResElt
IsSquareFree
IsSquareFree(n) : RngIntElt -> BoolElt
IsSteiner
IsSteiner(D, t) : Dsgn -> BoolElt
IsStronglyConnected
IsStronglyConnected(G) : GrphDir -> BoolElt
IsSubfield
IsSubfield(K, L) : FldNum, FldNum -> BoolElt, Map
IsSubgroup
IsSubgroup(Es) : CurveEllSubscheme -> BoolElt
IsSubnormal
IsSubnormal(G, H) : GrpAb, GrpAb -> BoolElt
IsSubnormal(G, H) : GrpFin, GrpFin -> BoolElt
IsSubnormal(G, H) : GrpMat, GrpMat -> BoolElt
IsSubnormal(G, H) : GrpPC, GrpPC -> BoolElt
IsSubnormal(G, H) : GrpPerm, GrpPerm -> BoolElt
IsSubsequence
IsSubsequence(S, T) : SeqEnum, SeqEnum -> BoolElt
IsSurjective
IsSurjective(f) : Map -> [ BoolElt ]
IsSurjective(a) : ModMatRngElt -> BoolElt
IsSymmetric
IsSymmetric(a) : AlgMatElt -> BoolElt
IsSymmetric(D) : Dsgn -> BoolElt
IsSymmetric(G) : GrphUnd -> BoolElt
IsSymmetric(G) : GrpPerm -> BoolElt
IsSymmetric(f) : RngMPolElt -> BoolElt, RngMPolElt
RngMPol_IsSymmetric (Example H29E30)
IsSymmetricTensor
IsSymmetricTensor(G) : GrpMat -> BoolElt
IsTensor
IsTensor(G) : GrpMat -> BoolElt
IsTorsionUnit
IsTorsionUnit(w) : RngOrdElt -> BoolElt
IsTransitive
IsPointTransitive(P) : Plane -> BoolElt
IsTransitive(G) : GrphUnd -> BoolElt
IsTransitive(G) : GrpPerm -> BoolElt
IsTransitive(G, Y) : GrpPerm, GSet -> BoolElt
IsTree
IsTree(G) : Grph -> BoolElt
IsTrivial
IsTrivial(G) : Grp -> BoolElt
IsTrivial(D) : Inc -> BoolElt
IsUFD
IsUFD(R) : Rng -> BoolElt
IsUniform
IsUniform(D) : Inc -> BoolElt, RngIntElt
IsUniqueFactorizationDomain
IsUFD(R) : Rng -> BoolElt
IsUnit
IsUnit(a) : AlgGenElt -> BoolElt, AlgGenElt
IsUnit(a) : AlgMatElt -> BoolElt
IsUnit(a) : RngElt -> BoolElt
IsUnit(f) : RngMPolResElt -> BoolElt
IsUnital
IsUnital(P, U) : Plane, { PlanePt } -> BoolElt
IsUnitary
IsUnitary(R) : Rng -> BoolElt
IsUnivariate
IsUnivariate(f) : RngMPolElt -> BoolElt, RngUPolElt, RngIntElt
IsVerbose
IsVerbose(s) : MonStgElt -> BoolElt
IsVertexTransitive
IsTransitive(G) : GrphUnd -> BoolElt
IsWeaklyConnected
IsWeaklyConnected(G) : GrphDir -> BoolElt
IsWeaklySelfDual
IsWeaklySelfDual(C) : Code -> BoolElt
IsWeaklySelfOrthogonal
IsWeaklySelfDual(C) : Code -> BoolElt
IsZero
IsZero(u) : AlgFPElt -> BoolElt
IsZero(A) : AlgGen -> BoolElt
IsZero(a) : AlgGenElt -> BoolElt
IsZero(a) : AlgMatElt -> BoolElt
IsZero(v) : LatElt -> BoolElt
IsZero(I) : Map -> Bool
IsZero(u) : ModElt -> BoolElt
IsZero(M) : ModMPol -> ModMPol
IsZero(f) : ModMPolElt -> BoolElt
IsZero(u) : ModTupElt -> BoolElt
IsZero(u) : ModTupFldElt -> BoolElt
IsZero(a) : RngElt -> BoolElt
IsZero(I) : RngFunOrdIdl -> BoolElt
IsZero(I) : RngMPol -> BoolElt
IsZero(I) : RngMPolRes -> BoolElt
IsZero(I) : RngOrdIdl -> BoolElt
IsZero(a) : RngOrdResElt -> Boolelt
IsZeroDimensional
IsZeroDimensional(I) : RngMPol -> BoolElt
IsZeroDivisor
IsZeroDivisor(a) : AlgGenElt -> BoolElt
IsZeroDivisor(x) : RngElt -> BoolElt
iteration
Iteration (OVERVIEW)
Iteration (SEQUENCES)
Iteration (STATEMENTS AND EXPRESSIONS)
Iterative Statements (STATEMENTS AND EXPRESSIONS)
Recursion, Reduction, and Iteration (SEQUENCES)
Reduction and Iteration over Sets (SETS)
[____] [____] [_____] [____] [__] [Index] [Root]