Index N

Name

Name(P, i) : FldFun, RngIntElt -> FldFunElt

Name(K, i) : FldNum, RngIntElt -> FldNumElt

Name(R, 1) : FldPow, RngIntElt -> FldPowElt

Name(C, 1) : FldPr, RngIntElt -> FldComElt

Name(F, 1) : FldQuad, RngIntElt -> FldQuadElt

Name(P, i) : RngMPol, RngIntElt -> RngMPolElt

Name(P, i) : RngUPol, RngIntElt -> RngPolElt

name

Names

NameSimple

NameSimple(G) : GrpPerm -> <RngIntElt, RngIntElt, RngIntElt>

ncl

H ^ g : GrpAb, GrpAbElt -> GrpAb

H ^ g : GrpPC, GrpPCElt -> GrpPC

ncl<G | L> : Grp, List -> Grp

ncl< G | L > : GrpFP, List -> GrpFP

ncl<G | L> : GrpMat, List -> GrpMat

ncl<G | L> : GrpPC, List -> GrpPC, Map

ncl<G | L> : GrpPerm, List -> GrpPerm

Nclasses

NumberOfClasses(G) : GrpFin -> RngIntElt

NumberOfClasses(G) : GrpMat -> RngIntElt

NumberOfClasses(G) : GrpPC -> RngIntElt

NumberOfClasses(G) : GrpPerm -> RngIntElt

Ncols

NumberOfColumns(a) : AlgMatElt -> RngIntElt

NumberOfColumns(a) : ModMatRngElt -> RngIntElt

NumberOfColumns(u) : ModTupFldElt -> RngIntElt

NumberOfColumns(v) : ModTupRngElt -> RngIntElt

ne

u ne v : AlgFPElt, AlgFPElt -> BoolElt

R ne T : AlgMat, AlgMat -> BoolElt

a ne b : AlgMatElt, AlgMatElt -> BoolElt

x ne y : BoolElt, BoolElt -> BoolElt

C ne D : Code, Code -> BoolElt

C_1 ne C_2 : Elt, Elt -> BoolElt

C_1 ne C_2 : Elt, Elt -> BoolElt

x ne y : Elt, Elt -> BoolElt

[Future release] C_1 ne C_2 : Elt, Elt -> BoolElt

G ne H : GrpAb, GrpAb -> BoolElt

u ne v : GrpAbElt, GrpAbElt -> BoolElt

g ne h : GrpElt, GrpElt -> BoolElt

H ne G : GrpFin, GrpFin -> BoolElt

H ne K : GrpFP, GrpFP -> BoolElt

C1 ne C2 : GrpFPCosElt, GrpFPCosElt -> BoolElt

u ne v : GrpFPElt, GrpFPElt -> BoolElt

H ne G : GrpMat, GrpMat -> BoolElt

g ne h : GrpMatElt, GrpMatElt -> BoolElt

G ne H : GrpPC, GrpPC -> BoolElt

g ne h : GrpPCElt, GrpPCElt -> BoolElt

H ne G : GrpPerm, GrpPerm -> BoolElt

g ne h : GrpPermElt, GrpPermElt -> BoolElt

D ne E : Inc, Inc -> BoolElt

U ne V : ModTupFld, ModTupFld -> BoolElt

N ne M : ModTupRng, ModTupRng -> BoolElt

s ne t : MonStgElt, MonStgElt -> BoolElt

P ne Q : Plane, Plane -> BoolElt

l ne m : PlaneLn, PlaneLn -> BoolElt

p ne q : PlanePt, PlanePt -> BoolElt

R ne S : Rng, Rng -> BoolElt

R ne S : Rng, Rng -> Rng

a ne b : RngElt, RngElt -> BoolElt

I ne J : RngIdl, RngIdl -> BoolElt

I ne J : RngMPol, RngMPol -> BoolElt

I ne J : RngUPol, RngUPol -> BoolElt

S ne T : SeqEnum, SeqEnum -> BoolElt

R ne S : Set, Set -> BoolElt

T ne U : SetCartElt, SetCartElt -> BoolElt

u ne v : SgpFPElt, SgpFPElt -> BoolElt

S ne T : VertSet, VertSet -> BoolElt

NearLinearSpace

NearLinearSpace< v | X : parameters > : RngIntElt, List -> IncNsp

negative

Neighbors

Neighbours

NestedExists

NestedIteration

nesting

next

Primes and Primality Testing (RING OF INTEGERS)

The continue statement (OVERVIEW)

next-previous

next-previous-Boolean

NextClass

NextExtension

Extension(P, Q) : Process -> GrpFP

NextPrime

NextSubgroup

Ngens

NumberOfGenerators(R) : AlgMat -> { AlgMatElt }

NumberOfGenerators(C) : Code -> RngIntElt

NumberOfGenerators(G) : Grp -> RngIntElt

NumberOfGenerators(A) : GrpAb -> RngIntElt

NumberOfGenerators(G) : GrpFP -> RngIntElt

NumberOfGenerators(G) : GrpMat -> RngIntElt

NumberOfGenerators(G) : GrpPC -> RngIntElt

NumberOfGenerators(G) : GrpPerm -> RngIntElt

NumberOfGenerators(M) : ModTupFld -> RngIntElt

NumberOfGenerators(M) : ModTupRng -> RngIntElt

NumberOfGenerators(P) : Process(Tietze) -> RngIntElt

NumberOfGenerators(S) : SgpFP -> RngIntElt

NilpotencyClass

NilpotencyClass(G) : GrpFin -> RngIntElt

NilpotencyClass(G) : GrpMat -> RngIntElt

NilpotencyClass(G) : GrpPC -> RngIntElt

NilpotencyClass(G) : GrpPerm -> RngIntElt

NilpotentSubgroups

Norm

Norm(c) : FldComElt -> FldReElt

Norm(a) : FldCycElt -> FldRatElt

Norm(a) : FldFinElt -> FldFinElt

Norm(a) : FldNumElt -> FldRatElt

Norm(a) : FldQuadElt -> FldRatElt

Norm(q) : FldRatElt -> FldRatElt

Norm(n) : RngIntElt -> RngIntElt

Norm(I) : RngOrdIdl -> FldRatElt

norm

Conjugates, Norm and Trace (RATIONAL FIELD)

Conjugates, Norm and Trace (RING OF INTEGERS)

Norm and Trace (FINITE FIELDS)

Norm, Trace, and Minimal Polynomial (NUMBER FIELDS AND THEIR ORDERS)

norm-equation

RngInt_norm-equation (Example H21E8)

norm-trace

Norm, Trace, and Minimal Polynomial (NUMBER FIELDS AND THEIR ORDERS)

norm_equation

normal

Characteristic Subgroups and Normal Structure (MATRIX GROUPS)

Characteristic Subgroups and Normal Structure (PERMUTATION GROUPS)

Constructor (OVERVIEW)

Normal Structure and Characteristic Subgroups (ABELIAN GROUPS)

Normal Structure and Characteristic Subgroups (SOLUBLE GROUPS)

Special Elements (FINITE FIELDS)

The Normal Structure of a Primitive Group (PERMUTATION GROUPS)

normal-structure

NormalClosure

NormalClosure(G, H) : GrpFP, GrpFP -> GrpFP

NormalClosure(G, H) : GrpPC, GrpPC -> GrpPC

H ^ G : GrpFin -> GrpFin

H ^ G : GrpFin, GrpFin -> GrpFin

H ^ G : GrpMat -> GrpMat

H ^ G : GrpMat, GrpMat -> GrpMat

H ^ G : GrpPerm -> GrpPerm

H ^ G : GrpPerm, GrpPerm -> GrpPerm

NormalElement

NormalForm

Normalise

Normalize(u) : ModTupElt -> ModTupElt

Normaliser

Normalizer(G, H) : GrpAb, GrpAb -> GrpAb

Normalizer(G, H) : GrpFin, GrpFin -> GrpFin

Normalizer(G, H) : GrpPC, GrpPC -> GrpPC

Normalizer(G, H) : GrpPerm, GrpPerm -> GrpPerm

Normalize

Normalize(u) : ModTupElt -> ModTupElt

Normalize(u) : ModTupFldElt -> ModTupFldElt

Normalizer

Normalizer(G, H) : GrpAb, GrpAb -> GrpAb

Normalizer(G, H) : GrpFin, GrpFin -> GrpFin

Normalizer(G, H) : GrpFP, GrpFP -> GrpFP

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

Normalizer(G, H) : GrpPC, GrpPC -> GrpPC

Normalizer(G, H) : GrpPerm, GrpPerm -> GrpPerm

NormalLattice

NormalLattice(G) : GrpPerm -> NormalLattice

NormalSubgroups

[Future release] NormalSubgroups(G) : GrpMat -> [ <GrpMat> ]

NormalSubgroups(G) : GrpPerm -> [ Rec ]

NormEquation

NormEquation(d, m) : RngIntElt, RngIntElt -> BoolElt, RngIntElt, RngIntElt

NormEquation(O, m) : RngOrd, RngIntElt -> BoolElt, RngOrdElt

normequation

NormsEtc

not

not x : BoolElt -> BoolElt

notadj

u notadj v : Vert, Vert -> BoolElt

notation

Notation for Database of Simple Groups (OVERVIEW)

Notations (GENERAL MODULES)

notin

x notin R : AlgMatElt, AlgMat -> BoolElt

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

x notin B : BoolElt, Bool -> BoolElt

x notin S : Elt, Seq -> BoolElt

x notin R : Elt, Set -> BoolElt

g notin G : GrpAbElt, GrpAb -> BoolElt

x notin C : GrpFinElt, Elt -> BoolElt

g notin G : GrpFinElt, GrpFin -> BoolElt

u notin H : GrpFPElt, GrpFP -> BoolElt

g notin C : GrpFPElt, GrpFPCosElt -> BoolElt

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

g notin G : GrpMatElt, GrpMat -> BoolElt

g notin G : GrpPCElt, GrpPC -> BoolElt

x notin C : GrpPermElt, Elt -> BoolElt

g notin G : GrpPermElt, GrpPerm -> BoolElt

p notin B : IncPt, IncBlk -> BoolElt

u notin C : ModTupFldElt, Code -> BoolElt

v notin V : ModTupFldElt, ModTupFld -> BoolElt

u notin M : ModTupRngElt, ModTupRng -> BoolElt

s notin t : MonStgElt, MonStgElt -> BoolElt

p notin l : PlanePt, PlaneLn -> BoolElt

a notin R : RngElt, Rng -> BoolElt

a notin I : RngElt, RngIdl -> BoolElt

f notin I : RngMPolElt, RngMPol -> BoolElt

a notin I : RngUPolElt, RngUPol -> BoolElt

u notin e : Vert, Edge -> BoolElt

s notin S : Vert, VertSet -> BoolElt

S notin B : { IncPt }, IncBlk -> BoolElt

notsubset

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

C notsubset D : Code, Code -> BoolElt

H notsubset G : GrpAb, GrpAb -> BoolElt

H notsubset G : GrpFin, GrpFin -> BoolElt

H notsubset K : GrpFP, GrpFP -> BoolElt

H notsubset G : GrpPC, GrpPC -> BoolElt

H notsubset G : GrpPerm, GrpPerm -> BoolElt

U notsubset V : ModTupFld, ModTupFld -> BoolElt

N notsubset M : ModTupRng, ModTupRng -> BoolElt

I notsubset J : RngIdl, RngIdl -> BoolElt

I notsubset J : RngMPol, RngMPol -> BoolElt

I notsubset J : RngUPol, RngUPol -> BoolElt

R notsubset S : SetEnum, Set -> BoolElt

S notsubset T : VertSet, VertSet -> BoolElt

S notsubset G : { GrpAbElt } , GrpAb -> BoolElt

S notsubset G : { GrpFinElt }, GrpFin -> BoolElt

S notsubset G : { GrpMatElt }, GrpMat -> BoolElt

S notsubset G : { GrpPCElt } , GrpPC -> BoolElt

S notsubset G : { GrpPermElt }, GrpPerm -> BoolElt

S notsubset l : { PlanePt }, PlaneLn -> BoolElt

NPCgens

Nrels

Nrows

NumberOfRows(a) : AlgMatElt -> RngIntElt

NumberOfRows(a) : ModMatRngElt -> RngIntElt

NumberOfRows(u) : ModTupFldElt -> RngIntElt

NumberOfRows(v) : ModTupRngElt -> RngIntElt

Nsgens

NuclearRank

NuclearRank(P) : Process(pgaProc) -> RngIntElt

null

Sets (OVERVIEW)

NullSpace

Kernel(a) : ModMatElt -> ModTupFld

Kernel(a) : ModMatRngElt -> ModTupRng

number

Rings, Fields, and Algebras (OVERVIEW)

number-field

NumberField

NumberingMap

NumberingMap(G) : GrpFin -> Map

NumberingMap(G) : GrpMat -> Map

NumberingMap(G) : GrpPC -> Map

NumberingMap(G) : GrpPerm -> Map

NumberOfBlocks

NumberOfClasses

NumberOfClasses(G) : GrpFin -> RngIntElt

NumberOfClasses(G) : GrpMat -> RngIntElt

NumberOfClasses(G) : GrpPC -> RngIntElt

NumberOfClasses(G) : GrpPerm -> RngIntElt

NumberOfColumns

NumberOfColumns(a) : AlgMatElt -> RngIntElt

NumberOfColumns(a) : ModMatRngElt -> RngIntElt

NumberOfColumns(u) : ModTupFldElt -> RngIntElt

NumberOfColumns(v) : ModTupRngElt -> RngIntElt

NumberOfGenerators

NumberOfGenerators(R) : AlgMat -> { AlgMatElt }

NumberOfGenerators(C) : Code -> RngIntElt

NumberOfGenerators(G) : Grp -> RngIntElt

NumberOfGenerators(A) : GrpAb -> RngIntElt

NumberOfGenerators(G) : GrpFP -> RngIntElt

NumberOfGenerators(G) : GrpMat -> RngIntElt

NumberOfGenerators(G) : GrpPC -> RngIntElt

NumberOfGenerators(G) : GrpPerm -> RngIntElt

NumberOfGenerators(M) : ModTupFld -> RngIntElt

NumberOfGenerators(M) : ModTupRng -> RngIntElt

NumberOfGenerators(P) : Process(Tietze) -> RngIntElt

NumberOfGenerators(S) : SgpFP -> RngIntElt

NumberOfInclusions

NumberOfPartitions

NumberOfPCGenerators

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

NumberOfPoints

NumberOfPoints(P) : Plane -> RngIntElt

NumberOfRelations

NumberOfRows

NumberOfRows(a) : AlgMatElt -> RngIntElt

NumberOfRows(a) : ModMatRngElt -> RngIntElt

NumberOfRows(u) : ModTupFldElt -> RngIntElt

NumberOfRows(v) : ModTupRngElt -> RngIntElt

NumberOfStrongGenerators

NumberOfStrongGenerators(G) : GrpPerm -> RngIntElt

NumberOfWords

Numerator

Numerator(q) : FldRatElt -> RngIntElt

numerator

Numerator and Denominator (RATIONAL FUNCTION FIELDS)

FldRat_numerator (Example H20E3)

numerator-denominator

Numerator and Denominator (RATIONAL FUNCTION FIELDS)

numerical