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Subindex: NPCGenerators  ..    Number




NPCGenerators

   NPCGenerators(G) : GrpPC -> RngIntElt

   NPCgens(G) : GrpPC -> RngIntElt

   NumberOfPCGenerators(G) : GrpPC -> RngIntElt


NPCgens

   Ngens(G) : GrpGPC -> RngIntElt

   NumberOfPCGenerators(G) : GrpGPC -> RngIntElt

   NPCgens(G) : GrpGPC -> RngIntElt

   NumberOfGenerators(G) : GrpGPC -> RngIntElt

   NumberOfPCGenerators(G) : GrpPC -> RngIntElt


Nqubits

   Nqubits(H) : HilbSpc -> RngIntElt

   NumberOfQubits(H) : HilbSpc -> RngIntElt


Nrels

   Nrels(G) : GrpRWS -> RngIntElt

   NumberOfRelations(G) : GrpRWS -> RngIntElt

   NumberOfRelations(M) : MonRWS -> RngIntElt

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


Nrows

   Nrows(phi) : MapModAbVar ->  RngIntElt

   NumberOfRows(a) : AlgMatElt -> RngIntElt

   NumberOfRows(u) : ModTupFldElt -> RngIntElt

   NumberOfRows(A) : Mtrx -> RngIntElt

   NumberOfRows(A) : MtrxSprs -> RngIntElt


Nsgens

   Nsgens(G) : GrpMat -> RngIntElt

   NumberOfStrongGenerators(G) : GrpMat -> RngIntElt

   NumberOfStrongGenerators(G) : GrpPerm -> RngIntElt

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


ntbg

   BlumBlumShubModulus(b) : RngIntElt -> RngIntElt

   Number Theoretic Bit Generators (PSEUDO-RANDOM BIT SEQUENCES)


Nth

   NthPrime(n) : RngIntElt -> RngIntElt


NthPrime

   NthPrime(n) : RngIntElt -> RngIntElt


nTorsionSubgroup

   nTorsionSubgroup(A, n) : ModAbVar, RngIntElt ->  ModAbVarSubGrp

   nTorsionSubgroup(G, n) : ModAbVarSubGrp, RngIntElt ->  ModAbVarSubGrp


Nuclear

   NuclearRank(G) : GrpPC -> RngIntElt


NuclearRank

   NuclearRank(G) : GrpPC -> RngIntElt


Null

   IsNull(G) : Grph -> BoolElt

   IsNull(G) : GrphMult -> BoolElt

   IsNull(S) : SeqEnum -> BoolElt

   IsNull(R) : SetEnum -> BoolElt

   JacobiThetaNullK(q, k) : FldReElt, RngIntElt -> FldReElt

   Kernel(a) : AlgMatElt -> ModTup

   Kernel(a) : ModMatElt -> ModTupFld

   Kernel(a) : ModMatRngElt -> ModTupRng

   NullGraph( : parameters) : -> GrphUnd

   NullspaceOfTranspose(X) : AlgMatVElt -> ModTupRng

   RowNullSpace(a) : AlgMatElt -> ModTup


null

   Sequences (OVERVIEW)

   Sets (OVERVIEW)


NullGraph

   NullGraph( : parameters) : -> GrphUnd


Nullity

   Nullity(phi) : MapModAbVar ->  RngIntElt


NullSpace

   NullSpace(a) : AlgMatElt -> ModTup

   Kernel(a) : AlgMatElt -> ModTup

   Kernel(a) : ModMatElt -> ModTupFld

   Kernel(a) : ModMatRngElt -> ModTupRng


Nullspace

   Nullspace(X) : AlgMatVElt -> ModTupRng

   Kernel(X) : AlgMatVElt -> ModTupRng

   Nullspace(A) : Mtrx -> ModTupRng

   Nullspace(A) : MtrxSprs -> ModTupRng

   NullspaceMatrix(A) : Mtrx -> ModTupRng

   NullspaceMatrix(A) : MtrxSprs -> Mtrx

   NullspaceOfTranspose(X) : AlgMatVElt -> ModTupRng

   NullspaceOfTranspose(A) : Mtrx -> ModTupRng

   NullspaceOfTranspose(A) : MtrxSprs -> ModTupRng

   RowNullSpace(a) : AlgMatElt -> ModTup

   Mat_Nullspace (Example H45E7)


NullspaceMatrix

   KernelMatrix(A) : Mtrx -> ModTupRng

   NullspaceMatrix(A) : Mtrx -> ModTupRng

   NullspaceMatrix(A) : MtrxSprs -> Mtrx


NullspaceOfTranspose

   RowNullSpace(X) : AlgMatVElt -> ModTupRng

   NullspaceOfTranspose(X) : AlgMatVElt -> ModTupRng

   NullspaceOfTranspose(A) : Mtrx -> ModTupRng

   NullspaceOfTranspose(A) : MtrxSprs -> ModTupRng

   RowNullSpace(a) : AlgMatElt -> ModTup


Num

   NumExtraspecialPairs(R) : RootDtm -> SeqEnum

   NumberOfPositiveRoots(C) : AlgMatElt -> RngIntElt

   NumberOfPositiveRoots(W) : GrpFPCox -> RngIntElt

   NumberOfPositiveRoots(G) : GrpLie -> RngIntElt

   NumberOfPositiveRoots(W) : GrpMat -> RngIntElt

   NumberOfPositiveRoots(W) : GrpPermCox -> RngIntElt

   NumberOfPositiveRoots(N) : MonStgElt -> .

   NumberOfPositiveRoots(R) : RootStr -> RngIntElt

   NumberOfPositiveRoots(R) : RootSys -> RngIntElt


Number

   NumberOfGroups(D) : DB -> RngIntElt

   # D : DB -> RngIntElt

   # D : DB -> RngIntElt

   # D : DB -> RngIntElt

   # D : DB -> RngIntElt

   # D: DB -> RngIntElt

   BernoulliNumber(n) : RngIntElt -> FldRatElt

   BernoulliNumber(n) : RngIntElt -> FldRatElt

   BettiNumber(E, i) : CrvEll, RngIntElt -> RngIntElt

   BogomolovNumber(X) : GRFano -> FldRatElt

   ChromaticNumber(G) : GrphUnd -> RngIntElt

   ClassNumber(C) : Crv[FldFin] -> 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(W) : GrpFPCox -> SeqEnum

   CoxeterNumber(W) : GrpMat -> SeqEnum

   CoxeterNumber(W) : GrpPermCox -> GrpPermElt

   Dimension(C) : Code -> RngIntElt

   EulerianNumber(n, r) : RngIntElt, RngIntElt -> RngIntElt

   GaussNumber(n, v) : RngIntElt, RngElt -> RngElt

   GeneralizedFibonacciNumber(g0, g1, n) : RngIntElt, RngIntElt, RngIntElt							-> RngIntElt

   GeneralizedFibonacciNumber(g0, g1, n) : RngIntElt, RngIntElt, RngIntElt -> RngIntElt

   GeneratorNumber(w) : GrpFPElt -> RngIntElt

   HarmonicNumber(n) : RngIntElt -> FldRatElt

   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

   KostkaNumber(S, C) : SeqEnum[RngIntElt], SeqEnum[RngIntElt] -> RngIntElt

   MagicNumber(C) : GRCrvS -> RngIntElt

   MaximalNumberOfCosets(P) : GrpFPCosetEnumProc -> RngIntElt

   MinusTamagawaNumber(M) : ModSym -> RngIntElt

   NFaces(G) : GrphMultUnd -> RngIntElt

   NFaces(G) : GrphUnd -> RngIntElt

   Ngens(M) : ModDed -> RngIntElt

   NormalNumber(C) : GRCrvS -> RngIntElt

   Number(D,X) : DB,GRK3 -> RngIntElt,GRK3

   NumberField(A) : FldAb -> FldNum

   NumberField(F) : FldOrd -> FldNum

   NumberField(P) : PlcNumElt -> FldNum

   NumberField(O) : RngOrd -> FldNum

   NumberField(O) : RngQuad -> FldQuad

   NumberField(f) : RngUPolElt -> FldNum

   NumberField(e) : SubFldLatElt -> FldNum

   NumberField(s) : [ RngUPolElt ] -> FldNum

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

   NumberOfActionGenerators(L) : Lat -> RngIntElt

   NumberOfActionGenerators(M) : ModGrp -> RngIntElt

   NumberOfActionGenerators(M) : ModRng -> RngIntElt

   NumberOfAlgebraicGenerators(G) : GrpLie -> 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

   NumberOfColumns(A) : MtrxSprs -> RngIntElt

   NumberOfComponents(C) : SetCart -> RngIntElt

   NumberOfComponents(KS) : SymKod -> 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

   NumberOfExtensions(R, n) : RngPad, RngIntElt -> RngIntElt

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

   NumberOfGenerators(B) : AlgBas -> RngIntElt

   NumberOfGenerators(R) : AlgMat -> { AlgMatElt }

   NumberOfGenerators(C) : Code -> RngIntElt

   NumberOfGenerators(G) : Grp -> RngIntElt

   NumberOfGenerators(A) : GrpAb -> RngIntElt

   NumberOfGenerators(A) : GrpAbGen -> RngIntElt

   NumberOfGenerators(A) : GrpAutCrv -> RngIntElt

   NumberOfGenerators(A) : GrpAuto -> RngIntElt

   NumberOfGenerators(G) : GrpBB -> RngIntElt

   NumberOfGenerators(B) : GrpBrd -> RngIntElt

   NumberOfGenerators(G) : GrpFP -> RngIntElt

   NumberOfGenerators(G) : GrpGPC -> RngIntElt

   NumberOfGenerators(G) : GrpLie -> RngIntElt

   NumberOfGenerators(G) : GrpMat -> RngIntElt

   NumberOfGenerators(G) : GrpPC -> RngIntElt

   NumberOfGenerators(G) : GrpPerm -> RngIntElt

   NumberOfGenerators(G) : GrpRWS -> 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

   NumberOfGroups(D, o1, o2): DB, RngIntElt, RngIntElt -> RngIntElt, RngIntElt

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

   NumberOfInvariantForms(G) : GrpMat -> RngIntElt, RngIntElt

   NumberOfIrreducibleMatrixGroups(k, p) : RngIntElt, RngIntElt -> RngIntElt

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

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

   NumberOfLattices(D, d): DB, RngIntElt -> RngIntElt

   NumberOfLines(P) : Plane -> RngIntElt

   NumberOfMatrices(D, n) : DB, RngIntElt -> RngIntElt

   NumberOfMetacyclicPGroups (p, n): RngIntElt, RngIntElt -> SeqEnum

   NumberOfNewformClasses(M : parameters) : ModFrm  -> RngIntElt

   NumberOfNonZeroEntries(A) : Mtrx -> RngIntElt

   NumberOfNonZeroEntries(A) : MtrxSprs -> RngIntElt

   NumberOfPCGenerators(G) : GrpPC -> RngIntElt

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

   NumberOfPartitions(n) : RngIntElt -> RngIntElt

   NumberOfPartitions(n) : RngIntElt -> RngIntElt

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

   NumberOfPlacesOfDegreeOne(m, U) : DivFunElt, GrpAb -> RngIntElt

   NumberOfPlacesOfDegreeOneECFBound(C) : Crv -> RngIntElt

   NumberOfPlacesOfDegreeOneECFBound(F) : FldFun -> RngIntElt

   NumberOfPlacesOfDegreeOneOverExactConstantField(C) : Crv[FldFin] -> RngIntElt

   NumberOfPlacesOfDegreeOneOverExactConstantField(C, m) : Crv[FldFin], RngIntElt -> RngIntElt

   NumberOfPlacesOfDegreeOneOverExactConstantField(F) : FldFun -> RngIntElt

   NumberOfPlacesOfDegreeOneOverExactConstantField(F, m) : FldFun -> RngIntElt

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

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

   NumberOfPlacesOfDegreeOverExactConstantField(C, m) : Crv[FldFin], RngIntElt -> RngIntElt

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

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

   NumberOfPoints(D) : Inc -> RngInt

   NumberOfPoints(P) : Plane -> RngIntElt

   NumberOfPointsAtInfinity(C) : CrvHyp -> RngIntElt

   NumberOfPointsOnSurface(E, e) : CrvEll, RngIntElt -> RngIntElt

   NumberOfPositiveRoots(C) : AlgMatElt -> RngIntElt

   NumberOfPositiveRoots(W) : GrpFPCox -> RngIntElt

   NumberOfPositiveRoots(G) : GrpLie -> RngIntElt

   NumberOfPositiveRoots(W) : GrpMat -> RngIntElt

   NumberOfPositiveRoots(W) : GrpPermCox -> RngIntElt

   NumberOfPositiveRoots(N) : MonStgElt -> .

   NumberOfPositiveRoots(R) : RootStr -> RngIntElt

   NumberOfPositiveRoots(R) : RootSys -> RngIntElt

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

   NumberOfPrimitiveGroups(d) : RngIntElt -> RngIntElt

   NumberOfProjectives(B) : AlgBas -> RngIntElt

   NumberOfPunctures(C): CrvPln -> RngIntElt

   NumberOfQubits(H) : HilbSpc -> RngIntElt

   NumberOfRationalPoints(A) : ModAbVar ->  RngIntElt, RngIntElt

   NumberOfRelations(G) : GrpRWS -> RngIntElt

   NumberOfRelations(M) : MonRWS -> RngIntElt

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

   NumberOfRelationsRequired(P) : NFSProc -> RngIntElt

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

   NumberOfRows(a) : AlgMatElt -> RngIntElt

   NumberOfRows(u) : ModTupFldElt -> RngIntElt

   NumberOfRows(A) : Mtrx -> RngIntElt

   NumberOfRows(A) : MtrxSprs -> RngIntElt

   NumberOfRows(t) : Tbl -> RngIntElt

   NumberOfSkewRows(t) : Tbl -> RngIntElt

   NumberOfSmallGroups(o) : RngIntElt -> RngIntElt

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

   NumberOfStandardTableaux(P) : SeqEnum -> RngIntElt

   NumberOfStandardTableauxOnWeight(n) : RngIntElt -> RngIntElt

   NumberOfStrings(B) : GrpBrd -> 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

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

   PicardGroup(O) : RngQuad -> GrpAb, Map

   PseudoDimension(C) : Code -> RngIntElt

   QuarticNumberOfRealRoots(q) : RngUPolElt -> RngUPolElt

   Rank(W) : GrpFPCox -> RngIntElt

   Rank(W) : GrpMat -> RngIntElt

   Rank(W) : GrpPermCox -> RngIntElt

   RealTamagawaNumber(M) : ModSym -> RngIntElt

   ReplicationNumber(D) : Dsgn -> RngIntElt

   RepresentationNumber(f, n) : QuadBinElt, RngIntElt -> RngIntElt

   RootNumber(E) : CrvEll -> RngIntElt

   RootNumber(E) : CrvEll -> RngIntElt

   RootNumber(E) : CrvEll -> RngIntElt

   RootNumber(E, p) : CrvEll, RngIntElt  -> RngIntElt

   RootNumber(E, P) : CrvEll, RngOrdIdl -> RngIntElt

   SClassNumber(S) : SetEnum[PlcFunElt] -> RngIntElt

   TamagawaNumber(E, p) : CrvEll, RngIntElt -> RngIntElt

   TamagawaNumber(A) : ModAbVar ->  RngIntElt, RngIntElt, BoolElt

   TamagawaNumber(A, p) : ModAbVar, RngIntElt ->  RngIntElt, RngIntElt, BoolElt

   TamagawaNumber(M, p) : ModSym, RngIntElt -> RngIntElt

   TotalNumberOfCosets(P) : GrpFPCosetEnumProc -> RngIntElt




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