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

Index N


Nagata

NagataAutomorphism(A) : Aff -> MapSch

NagataAutomorphism

NagataAutomorphism(A) : Aff -> MapSch

Nagens

Nagens(L) : Lat -> RngIntElt
NumberOfActionGenerators(L) : Lat -> RngIntElt
NumberOfActionGenerators(M) : ModTupRng -> RngIntElt

Naive

NaiveHeight(P) : JacHypPt -> FldPrElt
NaiveHeight(P) : PtEll -> FldPrElt

NaiveHeight

NaiveHeight(P) : JacHypPt -> FldPrElt
NaiveHeight(P) : PtEll -> FldPrElt

Name

Name(C, d) : Code, RngIntElt -> ModTupRngElt
C . i : Code, RngIntElt -> ModTupRngElt
F . i : FldOrd, RngIntElt -> FldOrdElt
A . i : Sch,RngIntElt -> RngMPolElt
X . i : Sch,RngIntElt -> RngMPolElt
AssignNamePrefix(A, S) : FldAC, MonStgElt ->
CartanName( C ) : AlgMatElt -> List
CartanName( G ) : GrpLie -> MonStgElt
LatticeName(D, i): DB, RngIntElt -> MonStgElt, RngIntElt
Name(F, 1) : FldFin, RngIntElt -> FldFinElt
Name(F, i) : FldFun, RngIntElt -> FldFunElt
Name(F, i) : FldFunRat, RngIntElt -> FldFunRatElt
Name(K, i) : FldNum, RngIntElt -> FldNumElt
Name(C, 1) : FldPr, RngIntElt -> FldComElt
Name(F, 1) : FldQuad, RngIntElt -> FldQuadElt
Name(R, 1) : RngGal, RngIntElt -> RngGalElt
Name(L, k) : RngLoc, RngIntElt -> RngLocElt
Name(P, k) : RngLoc, RngIntElt -> RngLocElt
Name(P, i) : RngMPol, RngIntElt -> RngMPolElt
Name(S, 1) : RngSer, RngIntElt -> RngSerElt
Name(P, i) : RngUPol, RngIntElt -> RngPolElt
NameSimple(G) : GrpPerm -> <RngIntElt, RngIntElt, RngIntElt>

name

Creating Names (INPUT AND OUTPUT)
Expression (OVERVIEW)
Identifier names (OVERVIEW)

Names

AssignNames(~A,S) : AlgQuat, [MonStgElt] ->
AssignNames(~D, s) : DivFunElt, [ MonStgElt ] ->
AssignNames(~F, [f]) : FldFin, [ MonStgElt ]) ->
AssignNames(~F, s) : FldFun, [ MonStgElt ] ->
AssignNames(~F, s) : FldFunRat, [ MonStgElt ]) ->
AssignNames(~K, s) : FldNum, [ MonStgElt ] ->
AssignNames(~F, s) : FldOrd, [ MonStgElt ] ->
AssignNames(~C, [s]) : FldPr, [ MonStgElt ]) ->
AssignNames(~F, [s]) : FldQuad, [ MonStgElt ]) ->
AssignNames( G, S) : GrpDrch, [MonStgElt] ->
AssignNames(~P, s) : PlcFunElt, [ MonStgElt ] ->
AssignNames(~R, [f]) : RngGal, [ MonStgElt ]) ->
AssignNames(~L, S) : RngLoc, SeqEnum ->
AssignNames(~P, S) : RngLoc, SeqEnum ->
AssignNames(~P, s) : RngMPol, [ MonStgElt ]) ->
AssignNames(~S, ["x"]) : RngSer, [ MonStgElt ] ->
AssignNames(~P, s) : RngUPol, [ MonStgElt ]) ->
AssignNames(~X,N) : Sch,SeqEnum ->
AssignNames(~A,N) : Sch,[MonStgElt] ->
AssignNames(~S, [s_1, ... s_n] ) : Struct, [ MonStgElt ] ->
Names(r) : Rec -> [ MonStgElt ]
Names(F) : RecFormat -> [ MonStgElt ]

names

Names (GALOIS RINGS)
Names (RATIONAL FUNCTION FIELDS)

NameSimple

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

Natural

NaturalActionGenerator(L, i) : Lat, RngIntElt -> GrpMat
NaturalGroup(L) : Lat -> GrpMat

natural

Action on the Natural G-Module (MATRIX GROUPS)
Natural K[G]-Modules (MODULES OVER A MATRIX ALGEBRA)

natural-K[G]-module

Natural K[G]-Modules (MODULES OVER A MATRIX ALGEBRA)

natural-module

Action on the Natural G-Module (MATRIX GROUPS)

NaturalActionGenerator

NaturalActionGenerator(L, i) : Lat, RngIntElt -> GrpMat

NaturalGroup

NaturalGroup(L) : Lat -> GrpMat

Nauty

TestNautyInvariant(G: parameters) : Grph -> BoolElt

nauty

nauty Invariants (GRAPHS)

nauty-invariants

nauty Invariants (GRAPHS)

ncl

Constructor (OVERVIEW)
H ^ G : GrpAb, GrpAb -> GrpAb
H ^ G : GrpGPC, GrpGPC -> GrpGPC
ncl<G | L> : Grp, List -> Grp
ncl<G | f> : GrpFP, Hom(Grp) -> GrpFP
ncl<G | L> : GrpGPC, List -> GrpGPC, Map
ncl<G | L> : GrpMat, List -> GrpMat
ncl<G | L> : GrpPC, List -> GrpPC, Map
ncl<G | L> : GrpPerm, List -> GrpPerm
ncl< G | L > : GrpFP, List -> GrpFP

Nclasses

Nclasses(G) : GrpAb -> RngIntElt
NumberOfClasses(G) : GrpAb -> RngIntElt
NumberOfClasses(G) : GrpFin -> RngIntElt
NumberOfClasses(G) : GrpMat -> RngIntElt
NumberOfClasses(G) : GrpPC -> RngIntElt
NumberOfClasses(G) : GrpPerm -> RngIntElt

Ncols

Ncols(a) : AlgMatElt -> RngIntElt
NumberOfColumns(a) : AlgMatElt -> RngIntElt
NumberOfColumns(u) : ModTupFldElt -> RngIntElt
NumberOfColumns(A) : Mtrx -> RngIntElt

ne

Comparison (OVERVIEW)
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
x ne y : AlgQuatElt, AlgQuatElt -> BoolElt
C ne D : Code, Code -> BoolElt
C ne D : Code, Code -> BoolElt
E ne F : CrvEll, CrvEll -> BoolElt
C_1 ne C_2 : Elt, Elt -> BoolElt
x ne y : Elt, Elt -> BoolElt
x ne y : Elt, Elt -> BoolElt
G ne H : GrpAb, GrpAb -> BoolElt
u ne v : GrpAbElt, GrpAbElt -> BoolElt
A ne B : GrpAbGen, GrpAbGen -> BoolElt
g ne d : GrpAbGenElt, GrpAbGenElt -> BoolElt
u ne v : GrpAtcElt, GrpAtcElt -> BoolElt
g ne h : GrpAutoElt, GrpAutoElt -> BoolElt
g ne h : GrpElt, GrpElt -> BoolElt
H ne G : GrpFin, GrpFin -> BoolElt
C1 ne C2 : GrpFPCosElt, GrpFPCosElt -> BoolElt
u ne v : GrpFPElt, GrpFPElt -> BoolElt
G ne H : GrpGPC, GrpGPC -> BoolElt
g ne h : GrpGPCElt, GrpGPCElt -> BoolElt
s ne t : GrphVert, GrphVert -> 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
u ne v : GrpRWSElt, GrpRWSElt -> BoolElt
u ne v : GrpSLPElt, GrpSLPElt -> BoolElt
D ne E : Inc, Inc -> BoolElt
P ne Q : JacHypPt, JacHypPt -> BoolElt
L ne M : Lat, Lat -> BoolElt
v ne w : LatElt, LatElt -> BoolElt
U ne V : ModTupFld, ModTupFld -> BoolElt
N ne M : ModTupRng, ModTupRng -> BoolElt
u ne v : ModTupRngElt, ModTupRngElt -> BoolElt
u ne v : MonRWSElt, MonRWSElt -> BoolElt
s ne t : MonStgElt, MonStgElt -> BoolElt
H ne K : GrpFP, GrpFP -> BoolElt
P ne Q : Plane, Plane -> BoolElt
l ne m : PlaneLn, PlaneLn -> BoolElt
p ne q : PlanePt, PlanePt -> BoolElt
P ne Q : PtEll, PtEll -> BoolElt
P ne Q : PtHyp, PtHyp -> 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
L ne K : RngLoc, RngLoc -> BoolElt
P1 ne P2 : RngLoc, RngLoc -> BoolElt
x ne y : RngLocElt, RngLocElt -> BoolElt
I ne J : RngMPol, RngMPol -> BoolElt
I ne J : RngUPol, RngUPol -> BoolElt
G1 ne G2 : SchGrpEll, SchGrpEll -> BoolElt
S ne T : SeqEnum, SeqEnum -> BoolElt
R ne S : Set, Set -> BoolElt
H1 ne H2 : SetPtEll, SetPtEll -> BoolElt
u ne v : SgpFPElt, SgpFPElt -> BoolElt
P ne Q : SrfKumPt, SrfKumPt -> BoolElt
h ne k : SymKod, SymKod -> BoolElt
T ne U : Tup, Tup -> BoolElt

Near

IsNearLinearSpace(D) : Inc -> BoolElt
NearLinearSpace(I) : Inc -> IncNsp
NearLinearSpace< v | X : parameters > : RngIntElt, List -> IncNsp

NearLinearSpace

NearLinearSpace(I) : Inc -> IncNsp
NearLinearSpace< v | X : parameters > : RngIntElt, List -> IncNsp

Nearly

IsNearlyPerfect(C) : Code -> BoolElt

Negation

NegationMap(E) : CrvEll -> Map

NegationMap

NegationMap(E) : CrvEll -> Map

Negative

IsNegative( RD, r ) : RootDtm, RngIntElt -> BoolElt
IsNegativeDefinite(F) : ModMatRngElt -> BoolElt
IsNegativeSemiDefinite(F) : ModMatRngElt -> BoolElt
Negative( RD, r ) : RootDtm, RngIntElt -> RngIntElt

negative

Operators (OVERVIEW)

Neighbor

Neighbor(L, v, p) : Lat, LatElt, RngIntElt -> Lat
Neighbour(L, v, p) : Lat, LatElt, RngIntElt -> Lat
NeighbourClosure(L, p) : Lat, RngIntElt -> Lat

NeighborClosure

NeighborClosure(L, p) : Lat, RngIntElt -> Lat
NeighbourClosure(L, p) : Lat, RngIntElt -> Lat

Neighbors

InNeighbors(u) : GrphVert -> { GrphVert }
InNeighbours(u) : GrphVert -> { GrphVert }
Neighbours(u) : GrphVert -> { GrphVert }
Neighbours(L, p) : Lat, RngIntElt -> Lat
OutNeighbours(u) : GrphVert -> { GrphVert }

Neighbour

Neighbor(L, v, p) : Lat, LatElt, RngIntElt -> Lat
Neighbour(L, v, p) : Lat, LatElt, RngIntElt -> Lat
NeighbourClosure(L, p) : Lat, RngIntElt -> Lat
Lat_Neighbour (Example H66E19)

NeighbourClosure

NeighborClosure(L, p) : Lat, RngIntElt -> Lat
NeighbourClosure(L, p) : Lat, RngIntElt -> Lat

Neighbours

InNeighbors(u) : GrphVert -> { GrphVert }
InNeighbours(u) : GrphVert -> { GrphVert }
Neighbours(u) : GrphVert -> { GrphVert }
Neighbours(L, p) : Lat, RngIntElt -> Lat
OutNeighbours(u) : GrphVert -> { GrphVert }

neighbours

Neighbour relations and graphs (LATTICES)

NestedExists

Set_NestedExists (Example H7E13)

NestedIteration

Seq_NestedIteration (Example H8E6)

nesting

Nested Aggregates (INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS])

New

AssociatedNewSpace(M) : ModSym -> ModSym
AutomorphismGroupNew(D) : IncGeom -> GrpPerm
DimensionNewCuspFormsGamma0(N, k) : RngIntElt, RngIntElt -> RngIntElt
DimensionNewCuspFormsGamma1(N, k) : RngIntElt, RngIntElt -> RngIntElt
IsNew(M) : ModFrm -> BoolElt
IsNew(M) : ModSym -> BoolElt
NewSubspace(M) : ModFrm-> ModFrm
NewSubspace(M, p) : ModSym, RngIntElt -> ModSym
NewSubspace(M) : ModSym-> ModSym
StartNewClass (~P: parameters) : Process(pQuot) ->

new

Construction of New Lattices (LATTICES)
Creating new root data from old (ROOT DATA FOR LIE THEORY)

new-construction

Construction of New Lattices (LATTICES)

Newform

IsNewform(f) : ModFrmElt -> BoolElt
Newform(M, i : parameters) : ModFrm, RngIntElt -> ModFrmElt
Newform(M, i, j : parameters) : ModFrm, RngIntElt, RngIntElt -> ModFrmElt
NewformDecomposition(M : parameters) : ModSym -> SeqEnum
NumberOfNewformClasses(M : parameters) : ModFrm -> RngIntElt

NewformDecomposition

NewformDecomposition(M : parameters) : ModSym -> SeqEnum

NewformLabeling

ModForm_NewformLabeling (Example H90E15)

Newforms

Newforms(label) : MonStgElt -> ModFrmElt
Newforms(M : parameters) : ModFrm -> List
Newforms(I, M) : [Tup], ModFrm -> ModFrm
ModForm_Newforms (Example H90E14)

newforms

Newforms (MODULAR FORMS)

NewSubspace

NewSubspace(M) : ModFrm-> ModFrm
NewSubspace(M, p) : ModSym, RngIntElt -> ModSym
NewSubspace(M) : ModSym-> ModSym

Newton

NewtonPolygon(C) : Crv -> NwtnPgon
NewtonPolygon(f) : RngMPolElt -> NwtnPgon
NewtonPolygon(f) : RngUPolElt -> NwtnPgon
NewtonPolygon(g) : RngUPolElt -> NwtnPgon
NewtonPolygon(g) : RngUPolElt -> NwtnPgon
NewtonPolygon(V) : SeqEnum -> NwtnPgon

newton

Creation of Newton Polygons (NEWTON POLYGONS)
NEWTON POLYGONS
Newton Polygons (NEWTON POLYGONS)
Polynomials Associated with Newton Polygons (NEWTON POLYGONS)
Tests for Points and Faces (NEWTON POLYGONS)
Vertices and Faces of polygons (NEWTON POLYGONS)

newton-creation

Creation of Newton Polygons (NEWTON POLYGONS)

newton-polygon

NEWTON POLYGONS
RngLoc_newton-polygon (Example H59E14)
RngPad_newton-polygon (Example H42E12)

newton-polynomials

Polynomials Associated with Newton Polygons (NEWTON POLYGONS)

newton-ptbools

Tests for Points and Faces (NEWTON POLYGONS)

newton-vf

Vertices and Faces of polygons (NEWTON POLYGONS)

NewtonPolygon

NewtonPolygon(C) : Crv -> NwtnPgon
NewtonPolygon(f) : RngMPolElt -> NwtnPgon
NewtonPolygon(f) : RngUPolElt -> NwtnPgon
NewtonPolygon(g) : RngUPolElt -> NwtnPgon
NewtonPolygon(g) : RngUPolElt -> NwtnPgon
NewtonPolygon(V) : SeqEnum -> NwtnPgon

Next

[Future release] NextExtension(P) : Process -> GrpFinFP
Extension(P, Q) : Process -> GrpFinFP
Extension(P, Q) : Process -> GrpFP
NextClass(~P : parameters) : Process(pQuot) ->
NextExtension (P) : Proc -> GrpPC
NextGraph(F) : File -> BoolElt, GrphUnd
NextPrime(n) : RngIntElt -> RngIntElt
NextSubgroup(~P) : Process(Lix) ->
NextVector(P) : LatEnumProc -> LatElt, RngElt
TransversalProcessNext(P) : GrpPermTransProc -> GrpPermElt

next

PrimeDivisors(n) : RngIntElt -> [RngIntElt]
Other Functions Relating to Primes (RING OF INTEGERS)
The continue statement (OVERVIEW)

next-previous

PrimeDivisors(n) : RngIntElt -> [RngIntElt]
Other Functions Relating to Primes (RING OF INTEGERS)

NextClass

NextClass(~P : parameters) : Process(pQuot) ->

NextExtension

[Future release] NextExtension(P) : Process -> GrpFinFP
Extension(P, Q) : Process -> GrpFinFP
Extension(P, Q) : Process -> GrpFP
NextExtension (P) : Proc -> GrpPC

NextGraph

NextGraph(F) : File -> BoolElt, GrphUnd

NextPrime

NextPrime(n) : RngIntElt -> RngIntElt

NextSubgroup

NextSubgroup(~P) : Process(Lix) ->

NextVector

NextVector(P) : LatEnumProc -> LatElt, RngElt

NFS

NFS(n, F, m1, m2) : RngIntElt, RngMPolElt, RngIntElt, RngIntElt -> RngIntElt

nfs

Advanced Factorization Techniques: The Number Field Sieve (RING OF INTEGERS)
The Number Field Sieve (RING OF INTEGERS)

nfs-proper

The Number Field Sieve (RING OF INTEGERS)

NFSCharacter

NFSCharacterColumns(n, F, tuple) : RngIntElt, RngMPolElt, Tup -> .

NFSCharacterColumns

NFSCharacterColumns(n, F, tuple) : RngIntElt, RngMPolElt, Tup -> .

NFSClear

NFSClear(n, F, tuple) : RngIntElt, RngMPolElt, Tup -> .

NFSCWIFormat

NFSCWIFormat(n, F, T, pb) : RngIntElt, RngMPolElt, Tup, RngIntElt -> .;

NFSCycle

NFSCycleCount(n, F, tuple) : RngIntElt, RngMPolElt, Tup -> RngIntElt
NFSCycleFile(n, F, tuple) : RngIntElt, RngMPolElt, Tup -> .

NFSCycleCount

NFSCycleCount(n, F, tuple) : RngIntElt, RngMPolElt, Tup -> RngIntElt

NFSCycleFile

NFSCycleFile(n, F, tuple) : RngIntElt, RngMPolElt, Tup -> .

NFSDependencies

NFSDependencies(n, F, tuple) : RngIntElt, RngMPolElt, Tup -> .

NFSFactor

NFSFactor(n, F, tuple) : RngIntElt, RngMPolElt, Tup -> RngIntElt

NFSMerge

NFSMerge(T, fn) : Tup, MonStgElt -> .

nfspoly

Tools for Finding a Suitable Polynomial (RING OF INTEGERS)

NFSRelations

NFSRelations(n, F, tuple) : RngIntElt, RngMPolElt, Tup -> RngIntElt

Ngens

NumberOfGenerators(A) : GrpAuto -> RngIntElt
Ngens(A) : GrpAuto -> RngIntElt
Ngens(G) : GrpDrch -> RngIntElt
Ngens(M) : ModOrd -> RngIntElt
NumberOfGenerators(B) : AlgBas -> RngIntElt
NumberOfGenerators(A) : AlgFP -> RngIntElt
NumberOfGenerators(R) : AlgMat -> { AlgMatElt }
NumberOfGenerators(C) : Code -> RngIntElt
NumberOfGenerators(G) : Grp -> RngIntElt
NumberOfGenerators(A) : GrpAb -> RngIntElt
NumberOfGenerators(A) : GrpAbGen -> RngIntElt
NumberOfGenerators(G) : GrpAtc -> RngIntElt
NumberOfGenerators(G) : GrpFP -> RngIntElt
NumberOfGenerators(G) : GrpGPC -> RngIntElt
NumberOfGenerators(G) : GrpMat -> RngIntElt
NumberOfGenerators(G) : GrpPC -> RngIntElt
NumberOfGenerators(G) : GrpPerm -> RngIntElt
NumberOfGenerators(G) : GrpRWS -> RngIntElt
NumberOfGenerators(G) : GrpSLP -> RngIntElt
NumberOfGenerators(M) : ModTupFld -> RngIntElt
NumberOfGenerators(M) : MonRWS -> RngIntElt
NumberOfGenerators(P) : Process(Tietze) -> RngIntElt
NumberOfGenerators(H) : SetPtEll -> RngIntElt
NumberOfGenerators(H) : SetPtEll -> RngIntElt
NumberOfGenerators(S) : SgpFP -> RngIntElt

NGrad

NGrad(X) : Sch -> RngIntElt
NumberOfGradings(X) : Sch -> RngIntElt

Nil

NilRadical(L) : AlgLie -> AlgLie

Nilpotency

NilpotencyClass(G) : GrpAb -> RngIntElt
NilpotencyClass(G) : GrpFin -> RngIntElt
NilpotencyClass(G) : GrpMat -> RngIntElt
NilpotencyClass(G) : GrpPC -> RngIntElt
NilpotencyClass(G) : GrpPerm -> RngIntElt
NilpotencyClass(G) : GrpGPC -> RngIntElt

NilpotencyClass

NilpotencyClass(G) : GrpAb -> RngIntElt
NilpotencyClass(G) : GrpFin -> RngIntElt
NilpotencyClass(G) : GrpMat -> RngIntElt
NilpotencyClass(G) : GrpPC -> RngIntElt
NilpotencyClass(G) : GrpPerm -> RngIntElt
NilpotencyClass(G) : GrpGPC -> RngIntElt

Nilpotent

CyclicSubgroups(G) : GrpPC -> SeqEnum
ElementaryAbelianSubgroups(G) : GrpPC -> SeqEnum
NilpotentSubgroups(G) : GrpPC -> SeqEnum
AbelianSubgroups(G) : GrpPC -> SeqEnum
FreeNilpotentGroup(r, e) : RngIntElt, RngIntElt -> GrpGPC
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
NilpotentBoundary(G,i) : GrpPC, RngIntElt -> RngIntElt
NilpotentLength(G) : GrpPC -> RngIntElt
NilpotentPresentation(G) : GrpGPC -> GrpGPC, Map
[Future release] NilpotentQuotient(G, c) : GrpMat, RngIntElt -> GrpGPC, Map
NilpotentQuotient(G, c) : GrpPerm, RngIntElt -> GrpGPC, Map
NilpotentQuotient(G, c: parameters) : GrpFP, RngIntElt -> GrpGPC, Map
NilpotentSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
NilpotentSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
NonNilpotentElement(L) : AlgLie -> AlgLieElt
PGroupSection(SQP, p: parameter) : SQProc, RngIntElt -> BoolElt, SQProc

nilpotent

Nilpotent Quotient (FINITELY PRESENTED GROUPS)
Properties of Subgroups Requiring a Nil-po-tent Covering Group (POLYCYCLIC GROUPS)
Subgroup Constructions Requiring a Nil-po-tent Covering Group (POLYCYCLIC GROUPS)

nilpotent-quotient

Nilpotent Quotient (FINITELY PRESENTED GROUPS)

NilpotentBoundary

NilpotentBoundary(G,i) : GrpPC, RngIntElt -> RngIntElt

NilpotentLength

NilpotentLength(G) : GrpPC -> RngIntElt

NilpotentPresentation

NilpotentPresentation(G) : GrpGPC -> GrpGPC, Map

NilpotentQuotient

[Future release] NilpotentQuotient(G, c) : GrpMat, RngIntElt -> GrpGPC, Map
NilpotentQuotient(G, c) : GrpPerm, RngIntElt -> GrpGPC, Map
NilpotentQuotient(G, c: parameters) : GrpFP, RngIntElt -> GrpGPC, Map

NilpotentQuotient1

GrpFP_1_NilpotentQuotient1 (Example H22E24)

NilpotentQuotient2

GrpFP_1_NilpotentQuotient2 (Example H22E25)

NilpotentSection

NilpotentSection(SQP: parameter) : SQProc -> BoolElt, SQProc
PGroupSection(SQP, p: parameter) : SQProc, RngIntElt -> BoolElt, SQProc

NilpotentSubgroups

CyclicSubgroups(G) : GrpPC -> SeqEnum
ElementaryAbelianSubgroups(G) : GrpPC -> SeqEnum
NilpotentSubgroups(G) : GrpPC -> SeqEnum
AbelianSubgroups(G) : GrpPC -> SeqEnum
NilpotentSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
NilpotentSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]

NilRadical

NilRadical(L) : AlgLie -> AlgLie

no-reduced-affine-solution

CrvCon_no-reduced-affine-solution (Example H84E8)

Node

IsNode(p) : Crv,Pt -> BoolElt

Noether

EnriquesForm(X) : VSrfK3 -> SeqEnum
NoetherForm(X) : VSrfK3 -> SeqEnum
HilbertForm(X) : VSrfK3 -> SeqEnum

NoetherForm

EnriquesForm(X) : VSrfK3 -> SeqEnum
NoetherForm(X) : VSrfK3 -> SeqEnum
HilbertForm(X) : VSrfK3 -> SeqEnum

Non

NonIdempotentActionGenerators(B, i) : AlgBas, RngIntElt -> SeqEnum
NonIdempotentGenerators(B) : AlgBas -> SeqEnum
NonNilpotentElement(L) : AlgLie -> AlgLieElt
NonPrimitiveAlternantCode(n,m,r) : RngIntElt,RngIntElt,RngIntElt->Code
RootsNonExact(p) : RngUPolElt -> [ FldPrElt ], [ FldPrElt ]

non

Operations not associated with Duval's Algorithm (NEWTON POLYGONS)

non-duval-ops

Operations not associated with Duval's Algorithm (NEWTON POLYGONS)

NonIdempotentActionGenerators

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

NonIdempotentGenerators

NonIdempotentGenerators(B) : AlgBas -> SeqEnum

NonNilpotentElement

NonNilpotentElement(L) : AlgLie -> AlgLieElt
AlgLie_NonNilpotentElement (Example H75E10)

NonPrimitiveAlternantCode

NonPrimitiveAlternantCode(n,m,r) : RngIntElt,RngIntElt,RngIntElt->Code

Nonsingular

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

Nonsolvable

NonsolvableSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
NonsolvableSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]

NonsolvableSubgroups

NonsolvableSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
NonsolvableSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]

Nonsplit

DeleteSplitCollector (SQP) : SQProc, RngIntElt ->
DeleteNonsplitCollector (SQP) : SQProc, RngIntElt ->
DeleteCollector (SQP) : SQProc, RngIntElt ->
DeleteCollector (SQP, p) : SQProc, RngIntElt ->
DeleteSplitSolutionspace(SQP, p, i, k): SQProc, RngIntElt, RngIntElt, RngIntElt ->
LiftNonsplitExtension (SQP, p, i, k : parameters) : SQProc, RngIntElt, RngIntElt, RngIntElt -> RngIntElt, SQProc
LiftNonsplitExtensionRow (SQP, p, l) : SQProc, RngIntElt, RngIntElt -> RngIntElt, SQProc
NonsplitCollector(SQP, p) : SQProc, RngIntElt ->
NonsplitSection(SQP: parameter) : SQProc -> BoolElt, SQProc
NonsplitElementaryAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
SplitExtensionSpace (SQP): SQProc -> SeqEnum

NonsplitAbelianSection

NonsplitAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
NonsplitElementaryAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
NonsplitSection(SQP: parameter) : SQProc -> BoolElt, SQProc

NonsplitCollector

SplitCollector(SQP, p) : SQProc, RngIntElt ->
NonsplitCollector(SQP, p) : SQProc, RngIntElt ->

NonsplitElementaryAbelianSection

NonsplitAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
NonsplitElementaryAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
NonsplitSection(SQP: parameter) : SQProc -> BoolElt, SQProc

NonsplitExtensionSpace

NonsplitExtensionSpace (SQP): SQProc -> SeqEnum
SplitExtensionSpace (SQP): SQProc -> SeqEnum

NonsplitSection

NonsplitAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
NonsplitElementaryAbelianSection(SQP: parameter) : SQProc -> BoolElt, SQProc
NonsplitSection(SQP: parameter) : SQProc -> BoolElt, SQProc

Norm

NormAbs(a) : FldAlgElt -> FldRatElt
AbsoluteNorm(a) : FldAlgElt -> FldRatElt
AbsoluteNorm(a) : FldFinElt -> FldFinElt
AbsoluteNorm(I) : RngOrdIdl -> RngIntElt
EuclideanNorm(n) : RngIntElt -> RngIntElt
EuclideanNorm(p) : RngUPol -> RngIntElt
EuclideanNorm(v) : RngValElt -> RngIntElt
IsSpinorNorm(G,p) : SymGen, RngIntElt -> RngIntElt
MaxNorm(f) : RngMPolElt -> RngIntElt
MaxNorm(p) : RngUPolElt -> RngIntElt
Norm(x) : AlgChtrElt -> FldCycElt
Norm(x) : AlgQuatElt -> FldElt
Norm(I) : AlgQuatOrd -> RngIntElt
Norm(a) : FldACElt -> FldACElt
Norm(a) : FldAlgElt -> FldAlgElt
Norm(c) : FldComElt -> FldReElt
Norm(a) : FldFinElt -> FldFinElt
Norm(a, E) : FldFinElt, FldFin -> FldFinElt
Norm(q) : FldRatElt -> FldRatElt
Norm(v) : LatElt -> RngElt
Norm(x) : ModBrdtElt -> RngElt
Norm(u) : ModTupFldElt -> FldElt
Norm(u) : ModTupRngElt -> RngElt
Norm(I) : RngFunOrdIdl -> RngElt
Norm(n) : RngIntElt -> RngIntElt
Norm(x) : RngLocElt -> RngLocElt
Norm(I) : RngOrdIdl -> RngIntElt
NormEquation(K, y) : FldFin, FldFin -> BoolElt, FldFinElt
NormEquation(F, m) : FldQuad, RngIntElt -> BoolElt, SeqEnum
NormEquation(d, m) : RngIntElt, RngIntElt -> BoolElt, RngIntElt, RngIntElt
NormEquation(O, m) : RngOrd, RngIntElt -> BoolElt, [ RngOrdElt ]
NormSpace(A) : AlgQuat -> ModTupFld
RootNorm( RD, r ) : RootDtm, RngIntElt -> RngIntElt
SumNorm(f) : RngMPolElt -> RngIntElt
SumNorm(p) : RngUPolElt -> RngIntElt

norm

Conjugates, Norm and Trace (RATIONAL FIELD)
Conjugates, Norm and Trace (RING OF INTEGERS)
Functions related to Norm and Trace (ALGEBRAIC FUNCTION FIELDS)
Functions related to Norm and Trace (ALGEBRAIC FUNCTION FIELDS)
Minimal Polynomial, Norm and Trace (ALGEBRAICALLY CLOSED FIELDS)
Norm and Trace (FINITE FIELDS)
Norm and Trace Functions (LOCAL RINGS AND FIELDS)
Norm Equations (ORDERS AND ALGEBRAIC FIELDS)
Norm Spaces and Basis Reduction (QUATERNION ALGEBRAS)
Norm, Trace, and Minimal Polynomial (ORDERS AND ALGEBRAIC FIELDS)

norm-equation

Norm Equations (ORDERS AND ALGEBRAIC FIELDS)
FldQuad_norm-equation (Example H54E3)
RngInt_norm-equation (Example H40E9)
RngOrd_norm-equation (Example H53E26)

norm-space

Norm Spaces and Basis Reduction (QUATERNION ALGEBRAS)

norm-trace

Norm and Trace (FINITE FIELDS)
Norm and Trace Functions (LOCAL RINGS AND FIELDS)
Norm, Trace, and Minimal Polynomial (ORDERS AND ALGEBRAIC FIELDS)

norm_equation

Norm Equations (QUADRATIC FIELDS)

NormAbs

NormAbs(a) : FldAlgElt -> FldRatElt
AbsoluteNorm(a) : FldAlgElt -> FldRatElt
AbsoluteNorm(a) : FldFinElt -> FldFinElt

Normal

AbelianNormalQuotient(G, H) : GrpPerm -> GrpPerm, Hom(GrpPerm), GrpPerm
AbelianNormalSubgroup(G) : GrpPerm -> GrpPerm
CentralizerOfNormalSubgroup(G, H) : GrpPerm, GrpPerm -> GrpPerm
ElementaryAbelianNormalSubgroup(G) : GrpPerm -> GrpPerm
IsNormal(F) : FldAlg -> BoolElt
IsNormal(a) : FldFinElt -> BoolElt
IsNormal(a, E) : FldFinElt -> BoolElt
IsNormal(G, H) : GrpAb, GrpAb -> BoolElt
IsNormal(G, H) : GrpFin, GrpFin -> BoolElt
IsNormal(G, H) : GrpGPC, GrpGPC -> BoolElt
IsNormal(G, H) : GrpMat, GrpMat -> BoolElt
IsNormal(G, H) : GrpPC, GrpPC -> BoolElt
IsNormal(G, H) : GrpPerm, GrpPerm -> BoolElt
IsNormal(G, H) : GrpFP, GrpFP -> BoolElt
IspNormal(C, p) : CrvHyp, RngIntElt -> BoolElt
MaximalNormalSubgroup(G) : GrpPerm -> GrpPerm
MinimalNormalSubgroup(G) : GrpPC -> GrpPC
MinimalNormalSubgroup(G, N) : GrpPC -> GrpPC
MinimalNormalSubgroups(G) : GrpPerm -> [ GrpPerm ]
NormalClosure(G, H) : GrpAb, GrpAb -> GrpAb
NormalComplements(G, H, N) : GrpPC, GrpPC -> SeqEnum
NormalComplements(G, N) : GrpPC, GrpPC -> SeqEnum
NormalElement(F) : FldFin -> FldFinElt
NormalElement(F, E) : FldFin, FldFin -> FldFinElt
NormalForm(f, M) : ModMPolElt, ModMPol -> ModMPolElt
NormalForm(f, I) : RngMPolElt, RngMPol -> RngMPolElt
NormalForm(f, S) : RngMPolElt, [ RngMPolElt ] -> RngMPolElt
NormalLattice(G) : GrpFin -> NormalLattice
NormalLattice(G) : GrpPC -> SubGrpLat
NormalLattice(G) : GrpPerm -> SubGrpLat
NormalSubgroups(G) : GrpFin -> [ Rec ]
NormalSubgroups(G) : GrpPC -> SeqEnum
NormalSubgroups(G) : GrpPerm -> [ Rec ]
NormalSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
TwoElementNormal(I) : RngInt -> RngIntElt, RngIntElt
TwoElementNormal(I) : RngOrdIdl -> RngOrdElt, RngOrdElt, RngIntElt
H ^ G : GrpFin -> GrpFin
H ^ G : GrpFin, GrpFin -> GrpFin
H ^ G : GrpFP, GrpFP -> GrpFP
H ^ G : GrpGPC, GrpGPC -> GrpGPC
H ^ G : GrpMat -> GrpMat
H ^ G : GrpMat, GrpMat -> GrpMat
H ^ G : GrpPC, GrpPC -> GrpPC
H ^ G : GrpPerm, GrpPerm -> GrpPerm
pElementaryAbelianNormalSubgroup(G, p) : GrpPerm, RngIntElt -> GrpPerm

normal

Abelian Normal Subgroups (PERMUTATION GROUPS)
Characteristic Subgroups and Normal Structure (GROUPS)
Constructor (OVERVIEW)
Lattice of Normal Subgroups (PERMUTATION GROUPS)
Maximal and Minimal Normal Subgroups (PERMUTATION GROUPS)
Normal and Subnormal Subgroups (MATRIX GROUPS)
Normal and Subnormal Subgroups (PERMUTATION GROUPS)
Normal Structure and Characteristic Subgroups (ABELIAN GROUPS)
Normal Structure and Characteristic Subgroups (POLYCYCLIC GROUPS)
Normal Subgroups and Subgroup Series (FINITE SOLUBLE GROUPS)
Special Elements (FINITE FIELDS)

normal-series

Normal Subgroups and Subgroup Series (FINITE SOLUBLE GROUPS)

normal-subgroups

Abelian Normal Subgroups (PERMUTATION GROUPS)
Lattice of Normal Subgroups (PERMUTATION GROUPS)
Maximal and Minimal Normal Subgroups (PERMUTATION GROUPS)

NormalClosure

NormalClosure(G, H) : GrpAb, GrpAb -> GrpAb
H ^ G : GrpFin -> GrpFin
H ^ G : GrpFin, GrpFin -> GrpFin
H ^ G : GrpFP, GrpFP -> GrpFP
H ^ G : GrpGPC, GrpGPC -> GrpGPC
H ^ G : GrpMat -> GrpMat
H ^ G : GrpMat, GrpMat -> GrpMat
H ^ G : GrpPC, GrpPC -> GrpPC
H ^ G : GrpPerm, GrpPerm -> GrpPerm

NormalComplements

NormalComplements(G, H, N) : GrpPC, GrpPC -> SeqEnum
NormalComplements(G, N) : GrpPC, GrpPC -> SeqEnum
GrpPC_NormalComplements (Example H25E21)

NormalElement

NormalElement(F) : FldFin -> FldFinElt
NormalElement(F, E) : FldFin, FldFin -> FldFinElt

NormalForm

NormalForm(f, M) : ModMPolElt, ModMPol -> ModMPolElt
NormalForm(f, I) : RngMPolElt, RngMPol -> RngMPolElt
NormalForm(f, S) : RngMPolElt, [ RngMPolElt ] -> RngMPolElt

Normalise

IsExtraSpecialNormalise(G) : GrpMat -> BoolElt
Normalise( g ) : GrpLieElt ->
Normalise(u) : ModTupFldElt -> ModTupFldElt
Normalize(u) : ModTupElt -> ModTupElt

Normaliser

Normalizer(G, H) : GrpGPC, GrpGPC -> GrpGPC
Normaliser(G, H) : GrpGPC, GrpGPC -> GrpGPC
Normaliser(G, H) : GrpFP, GrpFP -> GrpFP
Normaliser(e, f) : SubGrpLatElt, SubGrpLatElt -> SubGrpLatElt
Normalizer(G, H) : GrpAb, GrpAb -> GrpAb
Normalizer(G, H) : GrpFin, GrpFin -> GrpFin
Normalizer(G, H) : GrpPC, GrpPC -> GrpPC
Normalizer(G, H) : GrpPerm, GrpPerm -> GrpPerm
SymmetricNormalizer(G) : GrpPerm -> GrpPerm
SystemNormalizer(G) : GrpPC -> GrpPC

Normalising

ExistsNormalizingCoset(P) : GrpFPCosetEnumProc -> BoolElt, GrpFPElt
ExistsNormalisingCoset(P) : GrpFPCosetEnumProc -> BoolElt, GrpFPElt
IsNormalising( G ) : GrpLie -> BoolElt
IsSelfNormalising(G, H) : GrpGPC, GrpGPC -> BoolElt
IsSelfNormalizing(G, H) : GrpFin, GrpFin -> BoolElt
IsSelfNormalizing(G, H) : GrpPerm, GrpPerm -> BoolElt
SetNormalising( G, Normalising ) : GrpLie, BoolElt -> .

normalization

Normalization (FREE MODULES)

Normalize

HadamardNormalize(H) : AlgMatElt -> AlgMatElt
Normalise(u) : ModTupFldElt -> ModTupFldElt
Normalize(f) : ModMPolElt -> ModMPolElt
Normalize(u) : ModTupElt -> ModTupElt
Normalize(u) : ModTupRngElt -> ModTupRngElt
Normalize(u) : ModTupRngElt -> ModTupRngElt
Normalize(f) : RngMPolElt -> RngMPolElt
Normalize(f) : RngUPolElt -> RngUPolElt

Normalizer

Normalizer(G, H) : GrpGPC, GrpGPC -> GrpGPC
Normaliser(G, H) : GrpGPC, GrpGPC -> GrpGPC
Normaliser(G, H) : GrpFP, GrpFP -> GrpFP
Normaliser(e, f) : SubGrpLatElt, SubGrpLatElt -> SubGrpLatElt
Normalizer(L, K) : AlgLie, AlgLie -> AlgLie
Normalizer(G, H) : GrpAb, GrpAb -> GrpAb
Normalizer(G, H) : GrpFin, GrpFin -> GrpFin
[Future release] Normalizer(G, H) : GrpMat, GrpMat -> GrpMat
Normalizer(G, H) : GrpPC, GrpPC -> GrpPC
Normalizer(G, H) : GrpPerm, GrpPerm -> GrpPerm
SymmetricNormalizer(G) : GrpPerm -> GrpPerm
SystemNormalizer(G) : GrpPC -> GrpPC

Normalizing

AddNormalizingGenerator(~H, x) : GrpPerm, GrpPermElt ->
ExistsNormalisingCoset(P) : GrpFPCosetEnumProc -> BoolElt, GrpFPElt
IsSelfNormalising(G, H) : GrpGPC, GrpGPC -> BoolElt
IsSelfNormalizing(G, H) : GrpFin, GrpFin -> BoolElt
IsSelfNormalizing(G, H) : GrpPC, GrpPC -> BoolElt
IsSelfNormalizing(G, H) : GrpPerm, GrpPerm -> BoolElt
IsSelfNormalizing(G, H) : GrpFP, GrpFP -> BoolElt
SetNormalising( G, Normalising ) : GrpLie, BoolElt -> .

NormalLattice

NormalLattice(G) : GrpFin -> NormalLattice
NormalLattice(G) : GrpPC -> SubGrpLat
NormalLattice(G) : GrpPerm -> SubGrpLat

normals

Normal Subgroups and Complements (FINITE SOLUBLE GROUPS)

NormalStructure

GrpGPC_NormalStructure (Example H24E11)

NormalSubgroups

NormalSubgroups(G) : GrpFin -> [ Rec ]
NormalSubgroups(G) : GrpPC -> SeqEnum
NormalSubgroups(G) : GrpPerm -> [ Rec ]
NormalSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
GrpPerm_NormalSubgroups (Example H20E24)

NormEquation

NormEquation(K, y) : FldFin, FldFin -> BoolElt, FldFinElt
NormEquation(F, m) : FldQuad, RngIntElt -> BoolElt, SeqEnum
NormEquation(d, m) : RngIntElt, RngIntElt -> BoolElt, RngIntElt, RngIntElt
NormEquation(O, m) : RngOrd, RngIntElt -> BoolElt, [ RngOrdElt ]

NormModule

NormModule(S) : AlgQuatOrd -> ModTupRng
NormSpace(A) : AlgQuat -> ModTupFld

Norms

CorootNorms( RD ) : RootDtm -> [RngIntElt]
RootNorms( RD ) : RootDtm -> [RngIntElt]

NormsEtc

RngOrd_NormsEtc (Example H53E17)

NormSpace

NormModule(S) : AlgQuatOrd -> ModTupRng
NormSpace(A) : AlgQuat -> ModTupFld

not

Comparison (OVERVIEW)
not x : BoolElt -> BoolElt

notadj

e notadj f : GrphEdge, GrphEdge -> BoolElt
e notadj f : GrphEdge, GrphEdge -> BoolElt
u notadj v : GrphVert, GrphVert -> BoolElt
u notadj v : GrphVert, GrphVert -> BoolElt

notation

Notation (FREE MODULES)
Notation (SETS)
Notation for Database of Simple Groups (OVERVIEW)

notin

x notin L : ., RngLoc -> BoolElt
x notin y : AlgChtrElt, AlgChtrElt -> BoolElt
a notin A : AlgGenElt, AlgGen -> BoolElt
x notin R : AlgMatElt, AlgMat -> BoolElt
x notin A : AlgQuatElt, AlgQuat -> BoolElt
x notin S : Elt, Seq -> BoolElt
x notin R : Elt, Set -> BoolElt
g notin G : GrpAbElt, GrpAb -> BoolElt
g notin A : GrpAbGenElt, GrpAbGen -> BoolElt
w notin G : GrpAtcElt, GrpAtc -> BoolElt
g notin G : GrpFinElt, GrpFin -> BoolElt
g notin C : GrpFPElt, GrpFPCosElt -> BoolElt
g notin G : GrpGPCElt, GrpGPC -> BoolElt
u notin e : GrphVert, GrphEdge -> 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
w notin G : GrpRWSElt, GrpRWS -> BoolElt
g notin G : GrpSLPElt, GrpSLP -> BoolElt
p notin B : IncPt, IncBlk -> BoolElt
v notin V : ModTupFldElt, ModTupFld -> BoolElt
u notin C : ModTupRngElt, Code -> BoolElt
u notin C : ModTupRngElt, Code -> BoolElt
u notin M : ModTupRngElt, ModTupRng -> BoolElt
w notin M : MonRWSElt, MonRWS -> BoolElt
s notin t : MonStgElt, MonStgElt -> BoolElt
u notin H : GrpFPElt, GrpFP -> 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

X notsubset R : { AlgMatElt } , AlgMat -> BoolElt
x notin R : AlgMatElt, AlgMat -> BoolElt
A notsubset B : AlgGen, AlgGen -> BoolElt
C notsubset D : Code, Code -> BoolElt
C notsubset D : Code, Code -> BoolElt
H notsubset G : GrpAb, GrpAb -> BoolElt
H notsubset A : GrpAbGen, GrpAbGen -> BoolElt
H notsubset G : GrpFin, GrpFin -> BoolElt
H notsubset G : GrpGPC, GrpGPC -> BoolElt
H notsubset G : GrpMat, GrpMat -> 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
H notsubset K : GrpFP, GrpFP -> 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 A : { GrpAbGenElt } , GrpAbGen -> BoolElt
S notsubset G : { GrpAtcElt }, GrpAtc -> BoolElt
S notsubset G : { GrpFinElt }, GrpFin -> BoolElt
S notsubset G : { GrpGPCElt } , GrpGPC -> BoolElt
S notsubset G : { GrpMatElt }, GrpMat -> BoolElt
S notsubset G : { GrpPCElt } , GrpPC -> BoolElt
S notsubset G : { GrpPermElt }, GrpPerm -> BoolElt
S notsubset G : { GrpRWSElt }, GrpRWS -> BoolElt
S notsubset G : { GrpSLPElt } , GrpSLP -> BoolElt
S notsubset B : { IncPt }, IncBlk -> BoolElt
S notsubset M : { MonRWSElt }, MonRWS -> BoolElt
S notsubset l : { PlanePt }, PlaneLn -> BoolElt

NPCGenerators

NPCGenerators(G) : GrpPC -> RngIntElt
NPCgens(G) : GrpPC -> RngIntElt
NumberOfPCGenerators(G) : GrpPC -> RngIntElt
NPCgens(G) : GrpPC -> RngIntElt

NPCgens

Ngens(G) : GrpGPC -> RngIntElt
NumberOfPCGenerators(G) : GrpGPC -> RngIntElt
NPCgens(G) : GrpGPC -> RngIntElt
NumberOfGenerators(G) : GrpGPC -> RngIntElt
NumberOfPCGenerators(G) : GrpGPC -> RngIntElt
NumberOfPCGenerators(G) : GrpPC -> RngIntElt
NPCgens(G) : GrpPC -> RngIntElt

Nrels

Nrels(G) : GrpAtc -> RngIntElt
NumberOfRelations(G) : GrpAtc -> RngIntElt
NumberOfRelations(G) : GrpRWS -> RngIntElt
NumberOfRelations(M) : MonRWS -> RngIntElt
NumberOfRelations(P) : Process(Tietze) -> RngIntElt

Nrows

Nrows(a) : AlgMatElt -> RngIntElt
NumberOfRows(a) : AlgMatElt -> RngIntElt
NumberOfRows(u) : ModTupFldElt -> RngIntElt
NumberOfRows(A) : Mtrx -> RngIntElt
NumberOfRows(t) : Tableau -> RngIntElt

Nsgens

Nsgens(G) : GrpMat -> RngIntElt
NumberOfStrongGenerators(G) : GrpMat -> RngIntElt
NumberOfStrongGenerators(G) : GrpPerm -> RngIntElt
NumberOfStrongGenerators(G, i) : GrpPerm, RngIntElt -> RngIntElt

NSrows

NSrows(t) : Tableau -> RngIntElt
NumberOfSkewRows(t) : Tableau -> RngIntElt

ntbg

BlumBlumShubModulus(b) : RngIntElt -> RngIntElt
Number Theoretic Bit Generators (PSEUDO-RANDOM BIT SEQUENCES)

Nuclear

NuclearRank(G) : GrpPC -> RngIntElt

NuclearRank

NuclearRank(G) : GrpPC -> RngIntElt

Null

IsNull(S) : SeqEnum -> BoolElt
IsNull(R) : SetEnum -> BoolElt
JacobiThetaNullK(q, k) : FldPrElt, RngIntElt -> FldPr
Kernel(a) : AlgMatElt -> ModTup
Kernel(a) : ModMatElt -> ModTupFld
Kernel(a) : ModMatRngElt -> ModTupRng
RowNullSpace(a) : AlgMatElt -> ModTup

null

Sequences (OVERVIEW)
Sets (OVERVIEW)

NullSpace

NullSpace(a) : AlgMatElt -> ModTup
Kernel(a) : AlgMatElt -> ModTup
Kernel(a) : ModMatElt -> ModTupFld
Kernel(a) : ModMatRngElt -> ModTupRng

Nullspace

Kernel(A) : Mtrx -> ModTupRng, Map
Nullspace(A) : Mtrx -> ModTupRng
NullspaceMatrix(A) : Mtrx -> ModTupRng
NullspaceOfTranspose(A) : Mtrx -> ModTupRng
Mat_Nullspace (Example H62E7)

NullspaceMatrix

KernelMatrix(A) : Mtrx -> ModTupRng
NullspaceMatrix(A) : Mtrx -> ModTupRng

NullspaceOfTranspose

NullspaceOfTranspose(A) : Mtrx -> ModTupRng

Num

NumPosRoots( W ) : GrpCox -> RngIntElt
NumberOfPositiveRoots( W ) : GrpCox -> RngIntElt
NumberOfPositiveRoots( G ) : GrpLie -> RngIntElt
NumberOfPositiveRoots( RD ) : RootDtm -> RngIntElt

Number

NumberOfGroups(D) : DB -> RngIntElt
# D : DB -> RngIntElt
# D : DB -> RngIntElt
# D : DB -> RngIntElt
# D : DB -> RngIntElt
# D : DB -> RngIntElt
NumberOfLattices(D) : DB -> RngIntElt
# D: DB -> RngIntElt
AFRNumber(X) : VSrfK3 -> RngIntElt
FletcherNumber(X) : VSrfK3 -> RngIntElt
AltinokNumber(X) : VSrfK3 -> RngIntElt
BernoulliNumber(n) : RngIntElt -> FldRatElt
BernoulliNumber(n) : RngIntElt -> RngIntElt
ChromaticNumber(G) : GrphUnd -> RngIntElt
ClassNumber(F) : FldFun -> RngIntElt
ClassNumber(F) : FldFun -> RngIntElt
ClassNumber(K) : FldQuad -> RngIntElt
ClassNumber(Q: parameters) : QuadBin -> RngIntElt
ClassNumber(O: parameters) : RngOrd -> RngIntElt
ClassNumber(O) : RngFunOrd -> RngIntElt
ClassNumberApproximation(F, e) : FldFun, FldPrElt -> FldReElt
ClassNumberApproximationBound(q, g, e) : RngIntElt, RngIntElt, -> RngIntElt
CliqueNumber(G: parameters) : GrphUnd -> RngIntElt
ConnectionNumber(D, p, B) : Inc, IncPt, IncBlk -> RngIntElt
CoxeterNumber( G ) : GrpCox -> GrpPermElt
CoxeterNumber( W ) : GrpCox -> GrpPermElt
Dimension(C) : Code -> RngIntElt
EulerianNumber(n, r) : RngIntElt, RngIntElt -> RngIntElt
GeneralizedFibonacciNumber(g0, g1, n) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
GeneralizedFibonacciNumber(g0, g1, n) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt
GeneratorNumber(w) : GrpFPElt -> RngIntElt
HarmonicNumber(n) : RngIntElt -> RngIntElt
HirschNumber(G) : GrpGPC -> RngIntElt
IdentificationNumber(D, i): DB, RngIntElt -> RngIntElt
IndependenceNumber(G: parameters) : GrphUnd -> RngIntElt
IntersectionNumber(D, i, j) : Dsgn, RngIntElt, RngIntElt -> RngIntElt
IntersectionNumber(C,D,p) : Sch,Sch,Pt -> RngIntElt
IsolNumberOfDegreeField(n, p) : RngIntElt, RngIntElt -> RngIntElt
KissingNumber(L) : Lat -> RngElt
MaximalNumberOfCosets(P) : GrpFPCosetEnumProc -> RngIntElt
MinusTamagawaNumber(M) : ModSym -> RngIntElt
Ngens(A) : GrpAuto -> RngIntElt
Ngens(M) : ModOrd -> RngIntElt
Number(X) : VSrfK3 -> RngIntElt
NumberField(F) : FldOrd -> FldNum
NumberField(s) : [ RngUPolElt ] -> FldNum
NumberField(O) : RngOrd -> FldNum
NumberField(O) : RngQuad -> FldQuad
NumberField(f) : RngUPolElt -> FldNum
NumberField(e) : SubFldLatElt -> FldNum
NumberOfActionGenerators(L) : Lat -> RngIntElt
NumberOfActionGenerators(M) : ModTupRng -> RngIntElt
NumberOfAntisymmetricForms(G) : GrpMat -> RngIntElt
NumberOfBlocks(D) : Inc -> RngIntElt
NumberOfClasses(D) : DB -> RngIntElt
NumberOfClasses(G) : GrpAb -> RngIntElt
NumberOfClasses(G) : GrpFin -> RngIntElt
NumberOfClasses(G) : GrpMat -> RngIntElt
NumberOfClasses(G) : GrpPC -> RngIntElt
NumberOfClasses(G) : GrpPerm -> RngIntElt
NumberOfColumns(a) : AlgMatElt -> RngIntElt
NumberOfColumns(u) : ModTupFldElt -> RngIntElt
NumberOfColumns(A) : Mtrx -> RngIntElt
NumberOfComponents(C) : SetCart -> RngIntElt
NumberOfConstantWords(C, i) : Code, RngIntElt -> RngIntElt
NumberOfConstraints(L) : LP -> RngIntElt
NumberOfCoordinates(X) : Sch -> RngIntElt
NumberOfCurves(D, N) : DB, RngIntElt -> RngIntElt
NumberOfCurves(D, N, i) : DB, RngIntElt, RngIntElt -> RngIntElt
NumberOfDivisors(n) : RngIntElt -> RngIntElt
NumberOfFixedSpaces (x, s) : GrpMatElt, RngIntElt -> RngIntElt
NumberOfGenerators(B) : AlgBas -> RngIntElt
NumberOfGenerators(A) : AlgFP -> RngIntElt
NumberOfGenerators(R) : AlgMat -> { AlgMatElt }
NumberOfGenerators(C) : Code -> RngIntElt
NumberOfGenerators(G) : Grp -> RngIntElt
NumberOfGenerators(A) : GrpAb -> RngIntElt
NumberOfGenerators(A) : GrpAbGen -> RngIntElt
NumberOfGenerators(G) : GrpAtc -> RngIntElt
NumberOfGenerators(G) : GrpFP -> RngIntElt
NumberOfGenerators(G) : GrpGPC -> RngIntElt
NumberOfPCGenerators(G) : GrpGPC -> RngIntElt
NumberOfGenerators(G) : GrpMat -> RngIntElt
NumberOfGenerators(G) : GrpPC -> RngIntElt
NumberOfGenerators(G) : GrpPerm -> RngIntElt
NumberOfGenerators(G) : GrpRWS -> RngIntElt
NumberOfGenerators(G) : GrpSLP -> RngIntElt
NumberOfGenerators(M) : ModTupFld -> RngIntElt
NumberOfGenerators(M) : MonRWS -> RngIntElt
NumberOfGenerators(P) : Process(Tietze) -> RngIntElt
NumberOfGenerators(H) : SetPtEll -> RngIntElt
NumberOfGenerators(H) : SetPtEll -> RngIntElt
NumberOfGenerators(S) : SgpFP -> RngIntElt
NumberOfGradings(X) : Sch -> RngIntElt
NumberOfGraphs(D) : DB -> RngIntElt
NumberOfGraphs(D, S) : DB, SeqEnum -> RngIntElt
NumberOfGroups(D, d) : DB, RngIntElt -> RngIntElt
NumberOfGroups(D, d) : DB, RngIntElt -> RngIntElt
NumberOfGroups(D, o) : DB, RngIntElt -> RngIntElt
NumberOfInclusions(e, f) : SubGrpLatElt, SubGrpLatElt -> RngIntElt
NumberOfInvariantForms(G) : GrpMat -> RngIntElt, RngIntElt
NumberOfIsogenyClasses(D, N) : DB, RngIntElt -> RngIntElt
NumberOfLattices(D, N): DB, MonStgElt -> RngIntElt
NumberOfLattices(D, d): DB, RngIntElt -> RngIntElt
NumberOfLines(P) : Plane -> RngIntElt
NumberOfNewformClasses(M : parameters) : ModFrm -> RngIntElt
NumberOfPCGenerators(G) : GrpPC -> RngIntElt
NumberOfPCGenerators(P) : Process(pQuot) -> RngIntElt
NumberOfPartitions(n) : RngIntElt -> RngIntElt
NumberOfPartitions(n) : RngIntElt -> RngIntElt
NumberOfPermutations(n, k) : RngIntElt, RngIntElt -> RngIntElt
NumberOfPlaces(F, m) : FldFun, RngIntElt -> RngIntElt
NumberOfPlaces(F, m) : FldFun, RngIntElt -> RngIntElt
NumberOfPlacesOfDegreeOne(F) : FldFun -> RngIntElt
NumberOfPlacesOfDegreeOne(F, m) : FldFun, RngIntElt -> RngIntElt
NumberOfPlacesOfDegreeOne(F, m) : FldFun, RngIntElt -> RngIntElt
NumberOfPlacesOfDegreeOneBound(F) : FldFun -> RngIntElt
NumberOfPlacesOfDegreeOneBound(F, m) : FldFun, RngIntElt -> RngIntElt
NumberOfPoints(D) : Inc -> RngInt
NumberOfPoints(P) : Plane -> RngIntElt
NumberOfPositiveRoots( W ) : GrpCox -> RngIntElt
NumberOfPositiveRoots( G ) : GrpLie -> RngIntElt
NumberOfPositiveRoots( RD ) : RootDtm -> RngIntElt
NumberOfPrimePolynomials(q, d) : RngIntElt, RngIntElt -> RngIntElt
NumberOfProjectives(A) : AlgBas -> RngIntElt
NumberOfPunctures(C): Crv -> RngIntElt
NumberOfRelations(G) : GrpAtc -> RngIntElt
NumberOfRelations(G) : GrpRWS -> RngIntElt
NumberOfRelations(M) : MonRWS -> RngIntElt
NumberOfRelations(P) : Process(Tietze) -> RngIntElt
NumberOfRepresentations(D, i): DB, RngIntElt -> RngIntElt
NumberOfRows(a) : AlgMatElt -> RngIntElt
NumberOfRows(u) : ModTupFldElt -> RngIntElt
NumberOfRows(A) : Mtrx -> RngIntElt
NumberOfRows(t) : Tableau -> RngIntElt
NumberOfSkewRows(t) : Tableau -> RngIntElt
NumberOfSmallGroups(o) : RngIntElt -> RngIntElt
NumberOfSmoothDivisors(n, m, P) : RngIntElt, RngIntElt, SeqEnum[RngElt] -> RngElt
NumberOfStandardTableaux(P) : SeqEnum -> RngIntElt
NumberOfStrongGenerators(G) : GrpMat -> RngIntElt
NumberOfStrongGenerators(G) : GrpPerm -> RngIntElt
NumberOfStrongGenerators(G, i) : GrpPerm, RngIntElt -> RngIntElt
NumberOfSubgroupsAbelianPGroup (A) : SeqEnum -> SeqEnum
NumberOfSymmetricForms(G) : GrpMat -> RngIntElt
NumberOfTableauxOnAlphabet(P, m) : SeqEnum,RngIntElt -> RngIntElt
NumberOfTransitiveGroups(d) : RngIntElt -> RngIntElt
NumberOfVariables(L) : LP -> RngIntElt
NumberOfWords(C, w) : Code, RngIntElt -> RngIntElt
PicardGroup(O) : RngQuad -> GrpAb, Map
RealTamagawaNumber(M) : ModSym -> RngIntElt
ReplicationNumber(D) : Dsgn -> RngIntElt
RepresentationNumber(f, n) : QuadBinElt, RngIntElt -> RngIntElt
SClassNumber(S) : SetEnum[PlcFunElt] -> RngIntElt
TamagawaNumber(E, p) : CrvEll, RngIntElt -> RngIntElt
TamagawaNumber(M, p) : ModSym, RngIntElt -> RngIntElt
TotalNumberOfCosets(P) : GrpFPCosetEnumProc -> RngIntElt

number

Q as a Number Field (RING OF INTEGERS)
Rings, Fields, and Algebras (OVERVIEW)

number-field-like

Q as a Number Field (RING OF INTEGERS)

NumberField

NumberField(F) : FldOrd -> FldNum
NumberField(s) : [ RngUPolElt ] -> FldNum
NumberField(O) : RngOrd -> FldNum
NumberField(O) : RngQuad -> FldQuad
NumberField(f) : RngUPolElt -> FldNum
NumberField(e) : SubFldLatElt -> FldNum

Numbering

NumberingMap(G) : GrpAb -> Map
NumberingMap(G) : GrpFin -> Map
NumberingMap(G) : GrpMat -> Map
NumberingMap(G) : GrpPC -> Map
NumberingMap(G) : GrpPerm -> Map

NumberingMap

NumberingMap(G) : GrpAb -> Map
NumberingMap(G) : GrpFin -> Map
NumberingMap(G) : GrpMat -> Map
NumberingMap(G) : GrpPC -> Map
NumberingMap(G) : GrpPerm -> Map

NumberOfActionGenerators

Nagens(L) : Lat -> RngIntElt
NumberOfActionGenerators(L) : Lat -> RngIntElt
NumberOfActionGenerators(M) : ModTupRng -> RngIntElt

NumberOfAntisymmetricForms

NumberOfAntisymmetricForms(G) : GrpMat -> RngIntElt

NumberOfBlocks

# B : IncBlkSet -> RngIntElt
NumberOfBlocks(D) : Inc -> RngIntElt

NumberOfClasses

NumberOfClasses(D) : DB -> RngIntElt
NumberOfClasses(G) : GrpAb -> RngIntElt
NumberOfClasses(G) : GrpFin -> RngIntElt
NumberOfClasses(G) : GrpMat -> RngIntElt
NumberOfClasses(G) : GrpPC -> RngIntElt
NumberOfClasses(G) : GrpPerm -> RngIntElt

NumberOfColumns

Ncols(a) : AlgMatElt -> RngIntElt
NumberOfColumns(a) : AlgMatElt -> RngIntElt
NumberOfColumns(u) : ModTupFldElt -> RngIntElt
NumberOfColumns(A) : Mtrx -> RngIntElt

NumberOfComponents

NumberOfComponents(C) : SetCart -> RngIntElt

NumberOfConstantWords

NumberOfConstantWords(C, i) : Code, RngIntElt -> RngIntElt

NumberOfConstraints

NumberOfConstraints(L) : LP -> RngIntElt

NumberOfCoordinates

Length(X) : Sch -> RngIntElt
NumberOfCoordinates(X) : Sch -> RngIntElt

NumberOfCurves

NumberOfCurves(D) : DB -> RngIntElt
# D : DB -> RngIntElt
NumberOfCurves(D, N) : DB, RngIntElt -> RngIntElt
NumberOfCurves(D, N, i) : DB, RngIntElt, RngIntElt -> RngIntElt

NumberOfDivisors

NumberOfDivisors(n) : RngIntElt -> RngIntElt

NumberOfFixedSpaces

NumberOfFixedSpaces (x, s) : GrpMatElt, RngIntElt -> RngIntElt

NumberOfGenerators

NumberOfGenerators(C) : Code -> RngIntElt
Dimension(C) : Code -> RngIntElt
Ngens(A) : GrpAuto -> RngIntElt
Ngens(M) : ModOrd -> RngIntElt
NumberOfGenerators(B) : AlgBas -> RngIntElt
NumberOfGenerators(A) : AlgFP -> RngIntElt
NumberOfGenerators(R) : AlgMat -> { AlgMatElt }
NumberOfGenerators(C) : Code -> RngIntElt
NumberOfGenerators(G) : Grp -> RngIntElt
NumberOfGenerators(A) : GrpAb -> RngIntElt
NumberOfGenerators(A) : GrpAbGen -> RngIntElt
NumberOfGenerators(G) : GrpAtc -> RngIntElt
NumberOfGenerators(G) : GrpFP -> RngIntElt
NumberOfGenerators(G) : GrpGPC -> RngIntElt
NumberOfGenerators(G) : GrpMat -> RngIntElt
NumberOfGenerators(G) : GrpPC -> RngIntElt
NumberOfGenerators(G) : GrpPerm -> RngIntElt
NumberOfGenerators(G) : GrpRWS -> RngIntElt
NumberOfGenerators(G) : GrpSLP -> RngIntElt
NumberOfGenerators(M) : ModTupFld -> RngIntElt
NumberOfGenerators(M) : MonRWS -> RngIntElt
NumberOfGenerators(P) : Process(Tietze) -> RngIntElt
NumberOfGenerators(H) : SetPtEll -> RngIntElt
NumberOfGenerators(H) : SetPtEll -> RngIntElt
NumberOfGenerators(S) : SgpFP -> RngIntElt

NumberOfGradings

NGrad(X) : Sch -> RngIntElt
NumberOfGradings(X) : Sch -> RngIntElt

NumberOfGraphs

NumberOfGraphs(D) : DB -> RngIntElt
NumberOfGraphs(D, S) : DB, SeqEnum -> RngIntElt

NumberOfGroups

NumberOfGroups(D) : DB -> RngIntElt
# D : DB -> RngIntElt
# D : DB -> RngIntElt
# D : DB -> RngIntElt
NumberOfGroups(D, d) : DB, RngIntElt -> RngIntElt
NumberOfGroups(D, d) : DB, RngIntElt -> RngIntElt
NumberOfGroups(D, o) : DB, RngIntElt -> RngIntElt

NumberOfInclusions

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

NumberOfInvariantForms

NumberOfInvariantForms(G) : GrpMat -> RngIntElt, RngIntElt

NumberOfIsogenyClasses

NumberOfIsogenyClasses(D, N) : DB, RngIntElt -> RngIntElt

NumberOfLattices

NumberOfGroups(D) : DB -> RngIntElt
NumberOfLattices(D) : DB -> RngIntElt
# D : DB -> RngIntElt
# D : DB -> RngIntElt
# D: DB -> RngIntElt
NumberOfGroups(D, d) : DB, RngIntElt -> RngIntElt
NumberOfGroups(D, d) : DB, RngIntElt -> RngIntElt
NumberOfLattices(D, N): DB, MonStgElt -> RngIntElt
NumberOfLattices(D, d): DB, RngIntElt -> RngIntElt

NumberOfLines

# L : PlaneLnSet -> RngIntElt
NumberOfLines(P) : Plane -> RngIntElt

NumberOfNewformClasses

NumberOfNewformClasses(M : parameters) : ModFrm -> RngIntElt

NumberOfPartitions

NumberOfPartitions(n) : RngIntElt -> RngIntElt
NumberOfPartitions(n) : RngIntElt -> RngIntElt

NumberOfPCGenerators

Ngens(G) : GrpGPC -> RngIntElt
NumberOfPCGenerators(G) : GrpGPC -> RngIntElt
NPCgens(G) : GrpGPC -> RngIntElt
NumberOfGenerators(G) : GrpGPC -> RngIntElt
NumberOfPCGenerators(G) : GrpPC -> RngIntElt
NumberOfPCGenerators(P) : Process(pQuot) -> RngIntElt

NumberOfPermutations

NumberOfPermutations(n, k) : RngIntElt, RngIntElt -> RngIntElt

NumberOfPlaces

NumberOfPlaces(F, m) : FldFun, RngIntElt -> RngIntElt
NumberOfPlaces(F, m) : FldFun, RngIntElt -> RngIntElt

NumberOfPlacesOfDegreeOne

NumberOfPlacesOfDegreeOne(F) : FldFun -> RngIntElt
NumberOfPlacesOfDegreeOne(F, m) : FldFun, RngIntElt -> RngIntElt
NumberOfPlacesOfDegreeOne(F, m) : FldFun, RngIntElt -> RngIntElt

NumberOfPlacesOfDegreeOneBound

NumberOfPlacesOfDegreeOneBound(F) : FldFun -> RngIntElt
NumberOfPlacesOfDegreeOneBound(F, m) : FldFun, RngIntElt -> RngIntElt

NumberOfPoints

# P : IncPtSet -> RngIntElt
NumberOfPoints(D) : Inc -> RngInt
NumberOfPoints(P) : Plane -> RngIntElt

NumberOfPositiveRoots

NumPosRoots( W ) : GrpCox -> RngIntElt
NumberOfPositiveRoots( W ) : GrpCox -> RngIntElt
NumberOfPositiveRoots( G ) : GrpLie -> RngIntElt
NumberOfPositiveRoots( RD ) : RootDtm -> RngIntElt

NumberOfPrimePolynomials

NumberOfPrimePolynomials(q, d) : RngIntElt, RngIntElt -> RngIntElt

NumberOfPrimitiveGroups

NumberOfPrimitiveGroups(d) : RngIntElt -> RngIntElt
NumberOfTransitiveGroups(d) : RngIntElt -> RngIntElt

NumberOfProjectives

NumberOfProjectives(A) : AlgBas -> RngIntElt

NumberOfPunctures

NumberOfPunctures(C): Crv -> RngIntElt

NumberOfRelations

Nrels(G) : GrpAtc -> RngIntElt
NumberOfRelations(G) : GrpAtc -> RngIntElt
NumberOfRelations(G) : GrpRWS -> RngIntElt
NumberOfRelations(M) : MonRWS -> RngIntElt
NumberOfRelations(P) : Process(Tietze) -> RngIntElt

NumberOfRepresentations

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

NumberOfRows

Nrows(a) : AlgMatElt -> RngIntElt
NumberOfRows(a) : AlgMatElt -> RngIntElt
NumberOfRows(u) : ModTupFldElt -> RngIntElt
NumberOfRows(A) : Mtrx -> RngIntElt
NumberOfRows(t) : Tableau -> RngIntElt

NumberOfSkewRows

NSrows(t) : Tableau -> RngIntElt
NumberOfSkewRows(t) : Tableau -> RngIntElt

NumberOfSmallGroups

NumberOfSmallGroups(o) : RngIntElt -> RngIntElt

NumberOfSmoothDivisors

NumberOfSmoothDivisors(n, m, P) : RngIntElt, RngIntElt, SeqEnum[RngElt] -> RngElt

NumberOfStandardTableaux

NumberOfStandardTableaux(P) : SeqEnum -> RngIntElt

NumberOfStrongGenerators

Nsgens(G) : GrpMat -> RngIntElt
NumberOfStrongGenerators(G) : GrpMat -> RngIntElt
NumberOfStrongGenerators(G) : GrpPerm -> RngIntElt
NumberOfStrongGenerators(G, i) : GrpPerm, RngIntElt -> RngIntElt

NumberOfSubgroupsAbelianPGroup

NumberOfSubgroupsAbelianPGroup (A) : SeqEnum -> SeqEnum

NumberOfSymmetricForms

NumberOfSymmetricForms(G) : GrpMat -> RngIntElt

NumberOfTableauxOnAlphabet

NumberOfTableauxOnAlphabet(P, m) : SeqEnum,RngIntElt -> RngIntElt

NumberOfTransitiveGroups

NumberOfPrimitiveGroups(d) : RngIntElt -> RngIntElt
NumberOfTransitiveGroups(d) : RngIntElt -> RngIntElt

NumberOfVariables

NumberOfVariables(L) : LP -> RngIntElt

NumberOfWords

NumberOfWords(C, w) : Code, RngIntElt -> RngIntElt

Numbers

ExtensionNumbers(D, Q, p, r) : DB, MonStgElt, RngIntElt, RngIntElt -> SetEnum
GapNumbers(D) : DivCrvElt -> SeqEnum
GapNumbers(D) : DivFunElt -> SeqEnum[RngIntElt]
GapNumbers(D, P) : DivFunElt, PlcFunElt -> SeqEnum[RngIntElt]
GapNumbers(F) : PlcFunElt -> SeqEnum[RngIntElt]
GapNumbers(F, P) : PlcFunElt -> SeqEnum[RngIntElt]
GapNumbers(p) : Pt -> SeqEnum
LinkingNumbers(s) : GrphSpl -> SeqEnum
TamagawaNumbers(E) : CrvEll -> [ RngIntElt ]

Numerator

HilbertNumerator(X) : VSrfK3 -> RngUPolElt
Numerator(D) : DivFunElt -> DivFunElt
Numerator(a, O) : FldFunElt, RngFunOrd -> RngFunOrdElt
Numerator(f) : FldFunRatElt -> RngElt
Numerator(q) : FldRatElt -> RngIntElt

numerator

Numerator and Denominator (RATIONAL FIELD)
Numerator, Denominator and Degree (RATIONAL FUNCTION FIELDS)
FldRat_numerator (Example H41E3)

numerator-denominator

Numerator and Denominator (RATIONAL FIELD)

numerator-denominator-degree

Numerator, Denominator and Degree (RATIONAL FUNCTION FIELDS)

Numerical

NumericalRecord(X) : VSrfK3 -> Rec

numerical

Basic Numerical Invariants (LINEAR CODES OVER FINITE FIELDS)
Numerical Data Associated to a Graph (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Numerical Functions (REAL AND COMPLEX FIELDS)
Numerical Functions of Splice Diagrams (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)

numerical-data

Numerical Data Associated to a Graph (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Numerical Functions of Splice Diagrams (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)

numerical-invariants

Basic Numerical Invariants (LINEAR CODES OVER FINITE FIELDS)

NumericalRecord

NumericalRecord(X) : VSrfK3 -> Rec

NumPosRoots

NumPosRoots( W ) : GrpCox -> RngIntElt
NumberOfPositiveRoots( W ) : GrpCox -> RngIntElt
NumberOfPositiveRoots( G ) : GrpLie -> RngIntElt
NumberOfPositiveRoots( RD ) : RootDtm -> RngIntElt

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