Index N

Nagens

NumberOfActionGenerators(M) : ModTupRng -> RngIntElt

NaiveHeight

Name

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

Name(K, 1) : 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

Expression (OVERVIEW)

Identifier names (OVERVIEW)

Names

names

NameSimple

NaturalActionGenerator

NaturalGroup

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

A ne B : AlgGen, AlgGen -> BoolElt

a ne b : AlgGenElt, AlgGenElt -> BoolElt

R ne T : AlgMat, AlgMat -> BoolElt

a ne b : AlgMatElt, AlgMatElt -> BoolElt

C ne D : Code, Code -> BoolElt

C_1 ne C_2 : Elt, Elt -> BoolElt

x ne y : 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

u ne v : GrpBBElt, GrpBBElt -> 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

S ne T : GrphVertSet, GrphVertSet -> 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

u ne v : SgpFPElt, SgpFPElt -> BoolElt

T ne U : Tup, Tup -> BoolElt

NearLinearSpace

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

NegationMap

negative

Neighbors

Neighbour

Lat_Neighbour (Example H45E20)

Lat_Neighbour (Example H45E6)

Neighbours

NestedExists

NestedIteration

nesting

new

new-construction

next

The continue statement (OVERVIEW)

next-previous

NextClass

NextExtension

Extension(P, Q) : Process -> GrpFP

NextPrime

NextSubgroup

NextVector

Ngens

NumberOfGenerators(R) : AlgMat -> { AlgMatElt }

NumberOfGenerators(C) : Code -> RngIntElt

NumberOfGenerators(G) : Grp -> RngIntElt

NumberOfGenerators(A) : GrpAb -> RngIntElt

NumberOfGenerators(G) : GrpBB -> RngIntElt

NumberOfGenerators(G) : GrpFP -> RngIntElt

NumberOfGenerators(G) : GrpMat -> RngIntElt

NumberOfGenerators(G) : GrpPC -> RngIntElt

NumberOfGenerators(G) : GrpPerm -> RngIntElt

NumberOfGenerators(M) : ModTupFld -> 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

NilRadical

NonNilpotentElement

AlgLie_NonNilpotentElement (Example H49E10)

NonsolvableSubgroups

Norm

Norm(c) : FldComElt -> FldReElt

Norm(a) : FldCycElt -> FldRatElt

Norm(a) : FldFinElt -> FldFinElt

Norm(a) : FldFunElt -> RngElt

Norm(a) : FldNumElt -> FldNumElt

Norm(a) : FldQuadElt -> FldRatElt

Norm(q) : FldRatElt -> FldRatElt

Norm(v) : LatElt -> RngElt

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, Trace, and More (FUNCTION FIELDS AND THEIR ORDERS)

norm-equation

RngInt_norm-equation (Example H24E7)

norm-trace

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

Norm, Trace, and More (FUNCTION FIELDS AND THEIR ORDERS)

norm_equation

NormAbs

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)

Normal Structure of a Primitive Group (PERMUTATION GROUPS)

Special Elements (FINITE FIELDS)

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

NormalForm(f, I) : RngMPolElt, RngMPol -> RngMPolElt

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(f) : ModMPolElt -> ModMPolElt

Normalize(u) : ModTupElt -> ModTupElt

Normalize(u) : ModTupFldElt -> ModTupFldElt

Normalizer

Normalizer(L, K) : AlgLie, AlgLie -> AlgLie

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 : GrphVert, GrphVert -> BoolElt

notation

Notation for Database of Simple Groups (OVERVIEW)

Notations (GENERAL MODULES)

notin

a notin A : AlgGenElt, AlgGen -> BoolElt

x notin R : AlgMatElt, AlgMat -> BoolElt

x notin S : Elt, Seq -> BoolElt

x notin R : Elt, Set -> BoolElt

g notin G : GrpAbElt, GrpAb -> BoolElt

g notin G : GrpBBElt, GrpBB -> BoolElt

g notin G : GrpFinElt, GrpFin -> BoolElt

u notin H : GrpFPElt, GrpFP -> BoolElt

g notin C : GrpFPElt, GrpFPCosElt -> BoolElt

u notin e : GrphVert, GrphEdge -> 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

notsubset

A notsubset B : AlgGen, AlgGen -> 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 G : { GrpAbElt } , GrpAb -> BoolElt

S notsubset G : { GrpBBElt } , GrpBB -> 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 B : { IncPt }, IncBlk -> 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

NumberOfStrongGenerators(G) : GrpPerm -> RngIntElt

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

NumberOfActionGenerators

NumberOfActionGenerators(M) : ModTupRng -> RngIntElt

NumberOfAntisymmetricForms

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

NumberOfComponents

NumberOfConstantWords

NumberOfDivisors

NumberOfGenerators

NumberOfGenerators(R) : AlgMat -> { AlgMatElt }

NumberOfGenerators(C) : Code -> RngIntElt

NumberOfGenerators(G) : Grp -> RngIntElt

NumberOfGenerators(A) : GrpAb -> RngIntElt

NumberOfGenerators(G) : GrpBB -> RngIntElt

NumberOfGenerators(G) : GrpFP -> RngIntElt

NumberOfGenerators(G) : GrpMat -> RngIntElt

NumberOfGenerators(G) : GrpPC -> RngIntElt

NumberOfGenerators(G) : GrpPerm -> RngIntElt

NumberOfGenerators(M) : ModTupFld -> RngIntElt

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

NumberOfGenerators(S) : SgpFP -> RngIntElt

NumberOfInclusions

NumberOfInvariantForms

NumberOfLines

NumberOfPartitions

NumberOfPartitions(n) : RngIntElt -> RngIntElt

NumberOfPCGenerators

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

NumberOfPermutations

NumberOfPoints

NumberOfPoints(P) : Plane -> RngIntElt

NumberOfPrimitiveGroups

NumberOfRelations

NumberOfRows

NumberOfRows(a) : AlgMatElt -> RngIntElt

NumberOfRows(a) : ModMatRngElt -> RngIntElt

NumberOfRows(u) : ModTupFldElt -> RngIntElt

NumberOfRows(v) : ModTupRngElt -> RngIntElt

NumberOfSmallGroups

NumberOfStrongGenerators

NumberOfStrongGenerators(G) : GrpPerm -> RngIntElt

NumberOfSymmetricForms

NumberOfTransitiveGroups

NumberOfWords

Numerator

Numerator(q) : FldRatElt -> RngIntElt

numerator

Numerator and Denominator (RATIONAL FUNCTION FIELDS)

FldRat_numerator (Example H26E3)

numerator-denominator

Numerator and Denominator (RATIONAL FUNCTION FIELDS)

numerical