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

Subindex: Pollard  ..  Polynomial


Pollard

   PollardRho(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]

PollardRho

   PollardRho(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]

Poly

   PolyMapKernel(f) : Map -> RngMPol
   PolyToSeries(s) : RngMPolElt -> RngPowAlgElt

poly

   Straight-line Polynomials (GALOIS THEORY OF NUMBER FIELDS)
   Using Newton Polygons to Find Roots of Polynomials over Series Rings (NEWTON POLYGONS)

poly bang

   AlgSym_poly bang (Example H146E4)

poly-fact

   RngLocA_poly-fact (Example H51E8)

Poly-Hensel

   RngLoc_Poly-Hensel (Example H47E19)

poly-ops

   Using Newton Polygons to Find Roots of Polynomials over Series Rings (NEWTON POLYGONS)

poly-ops-ex

   Newton_poly-ops-ex (Example H46E6)

poly_fact

   Polynomials over General Local Fields (GENERAL LOCAL FIELDS)

Polycyclic

   PolycyclicGroup< X | R > : List(Identifiers), List(GrpFPRel) -> GrpPC, Hom
   AbelianGroup< X | R > : List(Identifiers), List(GrpAbRel) -> GrpAb, Hom(GrpAb)
   Group< X | R > : List(Identifiers), List(GrpFPRel) -> GrpFP, Hom(Grp)
   IsPolycyclic(G : parameters) : GrpMat -> BoolElt
   IsPolycyclicByFinite(G : parameters) : GrpMat -> BoolElt
   PolycyclicGenerators(G) : GrpMat -> [ GrpPCElt ]
   PolycyclicGroup< x1, ..., xn | R : parameters > : List(Identifiers), List(GrpFPRel) -> GrpGPC, Map
   PolycyclicGroup< x1, ..., xn | R : parameters > : List(Identifiers), List(GrpFPRel) -> GrpPC, Map

polycyclic

   Introduction (POLYCYCLIC GROUPS)
   POLYCYCLIC GROUPS
   Polycyclic Groups and Polycyclic Presentations (POLYCYCLIC GROUPS)

polycyclic-groups

   Polycyclic Groups and Polycyclic Presentations (POLYCYCLIC GROUPS)

polycyclic-groups-introduction

   Introduction (POLYCYCLIC GROUPS)

PolycyclicGenerators

   PolycyclicGenerators(G) : GrpMat -> [ GrpPCElt ]

PolycyclicGroup

   PolycyclicGroup< X | R > : List(Identifiers), List(GrpFPRel) -> GrpPC, Hom
   AbelianGroup< X | R > : List(Identifiers), List(GrpAbRel) -> GrpAb, Hom(GrpAb)
   Group< X | R > : List(Identifiers), List(GrpFPRel) -> GrpFP, Hom(Grp)
   PolycyclicGroup< x1, ..., xn | R : parameters > : List(Identifiers), List(GrpFPRel) -> GrpGPC, Map
   PolycyclicGroup< x1, ..., xn | R : parameters > : List(Identifiers), List(GrpFPRel) -> GrpPC, Map
   GrpGPC_PolycyclicGroup (Example H72E2)
   GrpPC_PolycyclicGroup (Example H63E2)
   Grp_PolycyclicGroup (Example H57E5)

Polygon

   IsNewtonPolygonOf(N, f) : NwtnPgon, RngElt -> BoolElt
   IsPolygon(G) : Grph -> BoolElt
   NewtonPolygon(C) : Crv -> NwtnPgon
   NewtonPolygon(L) : RngDiffOpElt -> NwtnPgon, RingDiffOpElt
   NewtonPolygon(L, p) : RngDiffOpElt, PlcFunElt -> NwtnPgon, RingDiffOpElt
   NewtonPolygon(f) : RngMPolElt -> NwtnPgon
   NewtonPolygon(f) : RngUPolElt -> NwtnPgon
   NewtonPolygon(f) : RngUPolElt -> NwtnPgon
   NewtonPolygon(f, p) : RngUPolElt, PlcFunElt -> NwtnPgon
   NewtonPolygon(f, p) : RngUPolElt, RngOrdIdl -> NwtnPgon
   NewtonPolygon(V) : SeqEnum -> NwtnPgon
   PolygonGraph(n : parameters) : RngIntElt -> GrphUnd

polygon

   NEWTON POLYGONS
   Newton Polygons (DIFFERENTIAL RINGS)

PolygonGraph

   PolygonGraph(n : parameters) : RngIntElt -> GrphUnd

Polygons

   DisplayPolygons(P,file) : SeqEnum, MonStgElt ->

polyhedra

   Cones and Polyhedra (CONVEX POLYTOPES AND POLYHEDRA)
   CONVEX POLYTOPES AND POLYHEDRA
   Geometrical Properties of Cones and Polyhedra (TORIC VARIETIES)
   Polyhedra (CONVEX POLYTOPES AND POLYHEDRA)
   Polytopes, Cones and Polyhedra (CONVEX POLYTOPES AND POLYHEDRA)

Polyhedron

   ConeToPolyhedron(C) : TorCon -> TorPol
   EmptyPolyhedron(L) : TorLat -> TorPol
   FixedSubspaceToPolyhedron(G) : GrpMat -> TorPol
   HalfspaceToPolyhedron(v,h) : TorLatElt,FldRatElt -> TorPol
   HyperplaneToPolyhedron(v,h) : TorLatElt,FldRatElt -> TorPol
   Polyhedron(D) : DivTorElt -> TorPol
   Polyhedron(C) : TorCon -> TorPol
   Polyhedron(C,f,v) : TorCon,Map,TorLatElt -> TorPol
   Polyhedron(C,H,h) : TorCon,TorLatElt,FldRatElt -> TorPol
   PolyhedronInSublattice(P) : TorPol -> TorPol,Map,TorLatElt

PolyhedronInSublattice

   PolyhedronInSublattice(P) : TorPol -> TorPol,Map,TorLatElt

Polylog

   Polylog(m, s) : RngIntElt, FldComElt -> FldComElt
   Polylog(m, f) : RngIntElt, RngSerElt -> RngSerElt
   PolylogD(m, s) : RngIntElt, FldComElt -> FldComElt

PolylogD

   PolylogDold(m, s) : RngIntElt, FldComElt -> FldComElt
   PolylogP(m, s) : RngIntElt, FldComElt -> FldComElt
   PolylogD(m, s) : RngIntElt, FldComElt -> FldComElt

PolylogDold

   PolylogDold(m, s) : RngIntElt, FldComElt -> FldComElt
   PolylogP(m, s) : RngIntElt, FldComElt -> FldComElt
   PolylogD(m, s) : RngIntElt, FldComElt -> FldComElt

PolylogP

   PolylogDold(m, s) : RngIntElt, FldComElt -> FldComElt
   PolylogP(m, s) : RngIntElt, FldComElt -> FldComElt
   PolylogD(m, s) : RngIntElt, FldComElt -> FldComElt

PolyMapKernel

   PolyMapKernel(f) : Map -> RngMPol

Polynomial

   AbsoluteCharacteristicPolynomial(a) : FldAlgElt -> RngUPolElt
   AbsoluteCharacteristicPolynomial(a) : FldNumElt -> RngUPolElt
   AbsoluteMinimalPolynomial(a) : FldAlgElt -> RngUPolElt
   AbsoluteMinimalPolynomial(a) : FldFunElt -> RngUPolElt
   AbsoluteMinimalPolynomial(a) : FldNumElt -> RngUPolElt
   AbsolutePolynomial(A) : FldAC ->
   AdditivePolynomialFromRoots(x, P) : RngElt, PlcFunElt -> RngUPolTwstElt
   AtkinModularPolynomial(N) : RngIntElt -> RngMPolElt
   BerlekampMassey(S) : SeqEnum -> RngUPolElt, RngIntElt
   BernoulliPolynomial(n) : RngIntElt -> RngUPolElt
   BernoulliPolynomial(n) : RngIntElt -> RngUPolElt
   BooleanPolynomialRing(n) : RngIntElt -> RngMPolBool
   BooleanPolynomialRing(n, order) : RngIntElt, MonStgElt -> RngMPolBool
   BooleanPolynomialRing(B, Q) : RngMPolBool, [RngIntElt] -> RngMPolBoolElt
   CanonicalModularPolynomial(N) : RngIntElt -> RngMPolElt
   CharacteristicPolynomial(x) : AlgAssVOrdElt -> RngUPolElt
   CharacteristicPolynomial(x) : AlgQuatElt -> RngUPolElt
   CharacteristicPolynomial(a) : FldAlgElt -> RngUPolElt
   CharacteristicPolynomial(a) : FldFinElt -> RngUPolElt
   CharacteristicPolynomial(a, E) : FldFinElt, FldFin -> RngUPolElt
   CharacteristicPolynomial(a, R) : FldFunElt, Rng -> RngUPolElt
   CharacteristicPolynomial(a) : FldNumElt -> RngUPolElt
   CharacteristicPolynomial(G) : GrphUnd -> RngUPolElt
   CharacteristicPolynomial(phi) : MapModAbVar -> RngUPolElt
   CharacteristicPolynomial(a: parameters) : AlgMatElt -> RngUPolElt
   CharacteristicPolynomial(g: parameters) : GrpMatElt -> RngPolElt
   CharacteristicPolynomial(A: parameters) : Mtrx -> RngUPolElt
   CharacteristicPolynomial(x) : RngPadElt -> RngUPolElt
   CharacteristicPolynomial(x, R) : RngPadElt, RngPad -> RngUPolElt
   CharacteristicPolynomialFromTraces(traces) : [ Fld ] -> RngUPolElt
   CharacteristicPolynomialFromTraces(traces, d, q, i) : [ Fld ], RngIntElt, RngIntElt, RngIntElt -> RngUPolElt, RngUPolElt
   CheckPolynomial(C) : Code -> RngUPolElt
   CheckWeilPolynomial(f, q, h20) : RngUPolElt, RngIntElt, RngIntElt -> BoolElt
   ChevalleyOrderPolynomial(type, n: parameters) : MonStgElt, RngIntElt -> RngUPolElt
   ChromaticPolynomial(G) : GrphUnd -> RngUPolElt
   ClassicalModularPolynomial(N) : RngIntElt -> RngMPolElt
   ConwayPolynomial(p, n) : RngIntElt, RngIntElt -> RngUPolElt
   CyclotomicPolynomial(m) : RngIntElt -> RngUPolElt
   DefiningPolynomial(A) : ArtRep -> RngUPolElt
   DefiningPolynomial(C) : Crv -> RngMPolElt
   DefiningPolynomial(E) : CrvEll -> RngMPolElt
   DefiningPolynomial(F) : FldAlg -> RngUPolElt
   DefiningPolynomial(F) : FldFin -> RngUPolElt
   DefiningPolynomial(F, E) : FldFin -> RngUPolElt
   DefiningPolynomial(F) : FldFun -> RngUPolElt
   DefiningPolynomial(F) : FldNum -> RngUPolElt
   DefiningPolynomial(Q) : FldRat -> RngUPolElt
   DefiningPolynomial(L) : RngLocA -> RngUPolElt
   DefiningPolynomial(L) : RngPad -> RngUPolElt
   DefiningPolynomial(s) : RngPowAlgElt -> RngUPolElt
   DefiningPolynomial(E) : RngSerExt -> RngUPolElt
   DefiningPolynomial(C) : Sch -> RngMPolElt
   DefiningPolynomial(C) : Sch -> RngMPolElt
   DefiningPolynomial(X) : Sch -> RngMPolElt
   DefiningPolynomial(K) : SrfKum -> RngMPolElt
   DefiningSubschemePolynomial(G) : SchGrpEll -> RngUPolElt
   DivisionPolynomial(E, n) : CrvEll, RngIntElt -> RngUPolElt, RngUPolElt, RngUPolElt
   EhrhartPolynomial(P) : TorPol -> [RngUPolElt]
   ElementarySymmetricPolynomial(P, k) : RngMPol, RngIntElt -> RngMPolElt
   ElementarySymmetricPolynomial(P, k) : RngMPol, RngIntElt -> RngMPolElt
   EvaluatePolynomial(C, a, b, c) : CrvHyp, RngElt, RngElt, RngElt -> RngElt
   ExistsConwayPolynomial(p, n) : RngIntElt, RngIntElt -> BoolElt, RngUPolElt
   FactoredCharacteristicPolynomial(phi) : MapModAbVar -> RngUPolElt
   FactoredCharacteristicPolynomial(A: parameters) : Mtrx -> [ <RngUPolElt, RngIntElt>]
   FactoredHeckePolynomial(A, n) : ModAbVar, RngIntElt -> RngUPolElt
   FactoredMinimalPolynomial(A: parameters) : Mtrx -> [ <RngUPolElt, RngIntElt>]
   FactorisationToPolynomial(f) : [Tup] -> BoolElt
   FrobeniusPolynomial(A, P) : ModAbVar, RngOrdIdl -> RngUPolElt
   FrobeniusPolynomial(A : parameters) : ModAbVar -> RngUPolElt
   FrobeniusPolynomial(A, p : parameters) : ModAbVar, RngIntElt -> RngUPolElt
   GegenbauerPolynomial(n, m) : RngIntElt, RngElt ->RngUPolElt
   GeneratorPolynomial(C) : Code -> RngUPolElt
   HasPolynomial(N) : NwtnPgon -> BoolElt
   HasPolynomialFactorization(R) : Rng -> BoolElt
   HeckePolynomial(A, n) : ModAbVar, RngIntElt -> RngUPolElt
   HeckePolynomial(M, n) : ModSym, RngIntElt -> RngUPolResElt
   HeckePolynomial(M, n : parameters) : ModFrm, RngIntElt -> RngUPolElt
   HermitePolynomial(n) : RngIntElt -> RngUPolElt
   HilbertClassPolynomial(D) : RngIntElt -> RngUPolElt
   HilbertClassPolynomial(D) : RngIntElt -> RngUPolElt
   HilbertPolynomial(D) : DivTor -> [RngUPolElt]
   HilbertPolynomial(I) : ModMPol -> RngUPolElt, RngIntElt
   HilbertPolynomial(I) : RngMPol -> RngUPolElt, RngIntElt
   HilbertPolynomialOfCurve(g,m) : RngIntElt,RngIntElt -> RngUPolElt
   HyperellipticCurveFromShiodaInvariants(JI) : SeqEnum[FldFin] -> CrvHyp, GrpPerm
   HyperellipticPolynomial(A) : AnHcJac -> RngUPolElt
   IndicialPolynomial(L, p) : RngDiffOpElt, PlcFunElt -> RngElt
   IrreducibleLowTermGF2Polynomial(n) : RngIntElt -> RngUPolElt
   IrreduciblePolynomial(F, n) : FldFin, RngIntElt -> RngUPolElt
   IrreducibleSparseGF2Polynomial(n) : RngIntElt -> RngUPolElt
   IsPolynomial(s) : RngPowAlgElt -> BoolElt, RngMPolElt
   IsProbablyPermutationPolynomial(p) : RngUPolElt -> BoolElt
   IsRegular(f) : MapSch -> BoolElt
   KrawchoukPolynomial(K, n, k) : FldFin, RngIntElt, RngIntElt -> RngUPolElt
   LaguerrePolynomial(n) : RngIntElt -> RngUPolElt
   LegendrePolynomial(C) : CrvCon -> RngMPolElt, ModMatRngElt
   LegendrePolynomial(n) : RngIntElt -> RngUPolElt
   LocalPolynomialRing(K, n) : Rng, RngIntElt -> RngMPolLoc
   LocalPolynomialRing(K, n, order) : Rng, RngIntElt, MonStgElt, ... -> RngMPolLoc
   LocalPolynomialRing(K, n, T) : Rng, RngIntElt, Tup -> RngMPolLoc
   MinimalHeckePolynomial(A, n) : ModAbVar, RngIntElt -> RngUPolElt
   MinimalPolynomial(x) : AlgAssVOrdElt -> RngUPolElt
   MinimalPolynomial(f) : AlgFPElt -> RngUPol
   MinimalPolynomial(a) : AlgGenElt -> RngUPolElt
   MinimalPolynomial(a) : AlgMatElt -> RngUPolElt
   MinimalPolynomial(x) : AlgQuatElt -> RngUPolElt
   MinimalPolynomial(a) : FldACElt -> RngUPolElt
   MinimalPolynomial(a) : FldAlgElt -> RngUPolElt
   MinimalPolynomial(a) : FldFinElt -> RngUPolElt
   MinimalPolynomial(a, E) : FldFinElt, FldFin -> RngUPolElt
   MinimalPolynomial(a, R) : FldFunElt, Rng -> RngUPolElt
   MinimalPolynomial(a) : FldNumElt -> RngUPolElt
   MinimalPolynomial(q) : FldRatElt -> RngUPolElt
   MinimalPolynomial(g) : GrpMatElt -> RngPolElt
   MinimalPolynomial(phi) : MapModAbVar -> RngUPolElt
   MinimalPolynomial(A: parameters) : Mtrx -> RngUPolElt
   MinimalPolynomial(s) : RngDiffElt -> RngUPolElt
   MinimalPolynomial(n) : RngIntElt -> RngUPolElt
   MinimalPolynomial(f) : RngMPolResElt -> RngUPol
   MinimalPolynomial(x) : RngPadElt -> RngUPolElt
   MinimalPolynomial(x, R) : RngPadElt, RngPad -> RngUPolElt
   MultivariatePolynomial(P, f, i) : RngMPol, RngUPolElt, RngIntElt -> RngMPolElt
   NewtonPolynomial(F) : NwtnPgonFace -> RngUPolElt
   Polynomial(N) : NwtnPgon -> RngElt
   Polynomial(R, f) : Rng, RngUPolElt -> RngUPolElt
   Polynomial(R, Q) : Rng, [ RngElt] -> RngUPolElt
   Polynomial(G) : RngUPolTwstElt -> RngUPolElt
   Polynomial(Q) : [ RngElt ] -> RngUPolElt
   Polynomial(C, M) : [RngElt], [RngMPolElt] -> RngMPolElt
   PolynomialAlgebra(R) : Rng -> RngUPol
   PolynomialCoefficient(s, i) : RngPowLazElt, RngIntElt -> RngPowLazElt
   PolynomialMap(L) : LinearSys -> RngMPolElt
   PolynomialRing(model) : ModelG1 -> RngMPol
   PolynomialRing(R, n) : Rng, RngIntElt -> RngMPol
   PolynomialRing(R, n) : Rng, RngIntElt -> RngMPol
   PolynomialRing(R, n, order) : Rng, RngIntElt, MonStgElt, ... -> RngMPol
   PolynomialRing(R, n, order) : Rng, RngIntElt, MonStgElt, ... -> RngMPol
   PolynomialRing(R, n, T) : Rng, RngIntElt, Tup -> RngMPol
   PolynomialRing(R, Q) : Rng, [ RngIntElt ] -> RngMPol
   PolynomialRing(R) : RngInvar -> RngMPol
   PolynomialSieve(F, m, J0, J1,MaxAlpha) : RngMPolElt, RngIntElt, RngIntElt, RngIntElt, FldReElt -> List
   PowerPolynomial(f,n) : RngUPolElt, RngIntElt -> RngUPolElt
   PrimitivePolynomial(F, m) : FldFin, RngIntElt -> RngUPolElt
   QuadraticFormPolynomial(V) : ModTupRng -> RngPolElt
   RandomIrreduciblePolynomial(F, n) : FldFin, RngIntElt -> RngUPolElt
   RandomPrimePolynomial(R, d) : RngUPol, RngIntElt -> RngUPolElt
   ReciprocalPolynomial(f) : RngUPolElt -> RngUPolElt
   ReducedLegendrePolynomial(C) : CrvCon -> RngMPolElt, ModMatRngElt
   SupersingularPolynomial(p) : RngIntElt -> RngUPolElt
   SwinnertonDyerPolynomial(n) : RngIntElt -> RngUPolElt
   TwoTorsionPolynomial(E) : CrvEll -> RngMPolElt
   UnivariatePolynomial(f) : RngMPolElt -> RngUPolElt
   WeberClassPolynomial(D) : RngIntElt -> RngUPolElt
   WeberClassPolynomial(D) : RngIntElt -> RngUPolElt, FldFunRatUElt
   WeberToHilbertClassPolynomial(f,D) : RngUPolElt, RngIntElt -> RngUPolElt
   WeilPolynomialOverFieldExtension(f, deg) : RngUPolElt, RngIntElt -> RngUPolElt
   WeilPolynomialToRankBound(f, q) : RngUPolElt, RngIntElt -> RngIntElt

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

Version: V2.19 of Mon Dec 17 14:40:36 EST 2012