[____] [____] [_____] [____] [__] [Index] [Root]
Index P
d.eef P g : RngIntElt, RngIntElt, RngIntElt -> FldReElt
d.eef p g : RngIntElt, RngIntElt, RngIntElt -> FldReElt
d.e E fpg : RngIntElt, RngIntElt, RngIntElt -> FldReElt
d.e e fpg : RngIntElt, RngIntElt, RngIntElt -> FldReElt
d . eefpg : RngIntElt, RngIntElt, RngIntElt -> FldReElt
PolylogD(m, s) : FldPrElt -> FldPrElt
Counting p-groups (p-GROUPS)
Generating p-groups (p-GROUPS)
p-group Functions (MATRIX GROUPS)
p-GROUPS
p-Quotient (FINITELY PRESENTED GROUPS)
p-Quotients (Process Version) (FP GROUPS - ADVANCED FEATURES)
d . eefpg : RngIntElt, RngIntElt, RngIntElt -> FldReElt
Counting p-groups (p-GROUPS)
Generating p-groups (p-GROUPS)
p-group Functions (MATRIX GROUPS)
p-GROUPS
P
p
p-Quotient (FINITELY PRESENTED GROUPS)
p-Quotients (Process Version) (FP GROUPS - ADVANCED FEATURES)
Construction of p-Sylow Subgroups (GENERIC ABELIAN GROUPS)
FUNCTIONS, PROCEDURES AND PACKAGES
Packages (FUNCTIONS, PROCEDURES AND PACKAGES)
Func_PackageUserAttributes (Example H2E13)
SpherePackingBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
PadCode(C, n) : Code, RngIntElt -> Code
PadCode(C, n) : Code, RngIntElt -> Code
PadCode(C, n) : Code, RngIntElt -> Code
PadCode(C, n) : Code, RngIntElt -> Code
PrimeField(L) : FldLoc -> FldLoc
pAdicRing(L) : RngLoc -> RngLoc
pAdicField(L) : FldLoc -> FldLoc
PrimeRing(L) : RngLoc -> RngLoc
pAdicRing(L) : RngLoc -> RngLoc
pAdicEllipticLogarithm(P, p: parameters): PtEll, RngIntElt -> FldLocElt
pAdicEmbeddings(f, p) : ModFrmElt, RngIntElt -> List
pAdicRing(p, n) : RngIntElt, RngIntElt -> RngLoc
pAdicRing(p, n) : RngIntElt, RngIntElt -> RngLoc
pAdicRing(p, n) : RngIntElt, RngIntElt -> RngLoc
pAdicRing(p, n) : RngIntElt, RngIntElt -> RngLoc
p-ADIC RINGS AND FIELDS
pAdicEllipticLogarithm(P, p: parameters): PtEll, RngIntElt -> FldLocElt
pAdicEmbeddings(f, p) : ModFrmElt, RngIntElt -> List
PrimeField(L) : FldLoc -> FldLoc
pAdicRing(L) : RngLoc -> RngLoc
pAdicField(L) : FldLoc -> FldLoc
PrimeRing(L) : RngLoc -> RngLoc
pAdicRing(p, n) : RngIntElt, RngIntElt -> RngLoc
pAdicRing(p, n) : RngIntElt, RngIntElt -> RngLoc
PrimeField(L) : FldLoc -> FldLoc
pAdicRing(L) : RngLoc -> RngLoc
pAdicField(L) : FldLoc -> FldLoc
PrimeRing(L) : RngLoc -> RngLoc
pAdicRing(p, n) : RngIntElt, RngIntElt -> RngLoc
pAdicRing(p, n) : RngIntElt, RngIntElt -> RngLoc
PairReduce(L) : Lat -> Lat, AlgMatElt
PairReduce(X) : ModMatRngElt -> ModMatRngElt, AlgMatElt
PairReduceGram(F) : ModMatRngElt -> ModMatRngElt, AlgMatElt, RngIntElt
Pair Reduction (LATTICES)
Pair Reduction (LATTICES)
HeightPairing(P, Q: parameters) : PtEll, PtEll -> FldPrElt
HeightPairing(P, Q: Precision) : JacHypPt, JacHypPt -> FldPrElt
HeightPairingMatrix(S: Precision) : [JacHypPt] -> AlgMat
IntersectionPairing(x, y) : ModSymElt, ModSymElt -> FldRatElt
MonodromyPairing(P, Q) : ModSSElt, ModSSElt -> RngIntElt
TateLichtenbaumPairing(D1, D2, m) : DivFunElt, DivFunElt, RngIntElt -> RngElt
WeilPairing(P, Q, m) : JacHypPt, JacHypPt, RngIntElt -> RngElt
WeilPairing(P, Q, n) : PtEll, PtEll, RngIntElt -> RngElt
The Monodromy Pairing ({THE MODULE OF}{SUPERSINGULAR POINTS})
PairReduce(L) : Lat -> Lat, AlgMatElt
PairReduce(X) : ModMatRngElt -> ModMatRngElt, AlgMatElt
PairReduceGram(F) : ModMatRngElt -> ModMatRngElt, AlgMatElt, RngIntElt
PaleyGraph(q) : RngIntElt -> GrphUnd
PaleyTournament(q) : RngIntElt -> GrphDir
PaleyGraph(q) : RngIntElt -> GrphUnd
PaleyTournament(q) : RngIntElt -> GrphDir
IsStandardParabolicSubgroup( W, H ) : GrpCox -> GrpCox
StandardParabolicSubgroup( W, s ) : GrpCox, { } -> GrpCox
MaximalParabolics(C) : CosetGeom -> SetIndx
MaxParabolics(C) : CosetGeom -> SetIndx
MinParabolics(C) : CosetGeom -> SetIndx
AllParallelClasses(D) : Inc -> SeqEnum
HasParallelClass(D) : Inc -> BoolElt, { IncBlk }
IsParallel(P, l, m) : Plane, PlaneLn, PlaneLn -> BoolElt
IsParallelClass(D, B, C) : Inc, IncBlk, IncBlk -> BoolElt, { IncBlk }
ParallelClass(P, l) : Plane, PlaneLn -> { PlaneLn }
ParallelClasses(P) : PlaneAff -> { { PlaneLn } }
ParallelClass(P, l) : Plane, PlaneLn -> { PlaneLn }
ParallelClasses(P) : PlaneAff -> { { PlaneLn } }
HasParallelism(D: parameters) : Inc, RngIntElt -> BoolElt, { SetEnum }
IsParallelism(D, P) : Inc, SetEnum[SetEnum] -> BoolElt, RngIntElt
AllParallelisms(D) : Inc -> SeqEnum
UniformizingParameter(P) : PlcCrvElt -> FldFunRatMElt
UniformizingParameter(p) : Pt -> FldFunRatMElt
Intrinsics (OVERVIEW)
Options and Controls (FINITELY PRESENTED ALGEBRAS)
ExtraSpecialParameters(G) : GrpMat -> [RngIntElt, RngIntElt]
Parameters(D) : Dsgn -> Record
SetProcessParameters(~P: parameters) : GrpFPCosetEnumProc ->
Func_Parameters (Example H2E2)
Graph Colouring and Automorphism Group (GRAPHS)
Parametrization(X,C,p) : Sch, Crv, Pt -> MapIsoSch
Isomorphism(X,C,p) : Sch, Crv, Pt -> MapIsoSch
Parametrization(F, D) : FldFun, DivFunElt -> FldFunElt, [FldFunRatUElt]
Parametrization(P,C) : Prj, Crv -> MapSch
ParametrizationMatrix(C) : CrvCon -> ModMatRngElt
ParametrizationToPuiseux(T) : Tup -> SeqEnum
PuiseuxToParametrization(S) : RngSerElt -> Tup
ParametrizationMatrix(C) : CrvCon -> ModMatRngElt
ParametrizationToPuiseux(T) : Tup -> SeqEnum
CrvMod_Parametrized subgroup schemes (Example H89E3)
GetParent(SQP) : SQProc -> List
Parent(u) : AlgFPElt -> AlgFP
Parent(a) : AlgGenElt -> AlgGen
Parent(a) : AlgMatElt -> AlgMat
Parent(u) : GrpAbElt -> GrpAb
Parent(r) : GrpAbRel -> GrpAb
Parent(w) : GrpAtcElt -> GrpAtc
Parent(u) : GrpBrdElt -> GrpBrd
Parent(g) : GrpElt -> Grp
Parent(w) : GrpFPElt -> GrpFP
Parent(r) : GrpFPRel -> GrpFP
Parent(G) : GrpGPC -> PowStr
Parent(x) : GrpGPCElt -> GrpGPC
Parent(G) : GrpMatElt -> GrpMat
Parent(x) : GrpPCElt -> GrpPC
Parent(g) : GrpPermElt -> GrpPerm
Parent(w) : GrpRWSElt -> GrpRWS
Parent(u) : GrpSLPElt -> GrpSLP
Parent(m) : Map -> PowMap
Parent(f) : MapIsoSch -> PowIsoSch
Parent(x) : ModBrdtElt -> ModBrdt
Parent(V) : ModFld -> SetPow
Parent(u) : ModTupElt -> ModRng
Parent(u) : ModTupElt -> ModRng
Parent(w): ModTupRngElt -> ModTupRng
Parent(w): ModTupRngElt -> ModTupRng
Parent(w) : MonRWSElt -> MonRWS
Parent(P) : PtEll -> SetPtEll
Parent(R) : Rng -> Pow
Parent(r) : RngElt -> Rng
Parent(x) : RngLocElt -> RngLoc
Parent(S) : Seq -> Struct
Parent(R) : Set -> Struct
Parent(u) : SgpFPElt -> SgpFP
Parent(T) : Tup -> SetCart
ParentGraph(s) : GrphVert -> Grph
ParentGraph(S) : GrphVertSet -> Grph
ParentPlane(l) : PlaneLn -> Plane, PlanePtSet, PlaneLnSet
ParentPlane(L) : PlaneLnSet -> Plane, PlanePtSet, PlaneLnSet
ParentPlane(p) : PlanePt -> Plane, PlanePtSet, PlaneLnSet
ParentPlane(V) : PlanePtSet -> Plane, PlanePtSet, PlaneLnSet
ParentRing(N) : NwtnPgon -> Rng
Parent and Category (ALGEBRAIC FUNCTION FIELDS)
Parent and Category (ALGEBRAIC FUNCTION FIELDS)
Parent and Category (ALGEBRAIC FUNCTION FIELDS)
Parent and Category (ALGEBRAIC FUNCTION FIELDS)
Parent and Category (ALGEBRAIC FUNCTION FIELDS)
Parent and Category (ALGEBRAIC FUNCTION FIELDS)
Parent and Category (INTRODUCTION [BASIC RINGS])
Parent and Category (MULTIVARIATE POLYNOMIAL RINGS)
Parent and Category (ORDERS AND ALGEBRAIC FIELDS)
Parent and Category (POWER, LAURENT AND PUISEUX SERIES)
Parent and Category (UNIVARIATE POLYNOMIAL RINGS)
Parent and Category (VALUATION RINGS)
Retrieving the Plane from Points, Lines, Point-Sets and Line-Sets (FINITE PLANES)
Parent and Category (ALGEBRAIC FUNCTION FIELDS)
Parent and Category (ALGEBRAIC FUNCTION FIELDS)
Parent and Category (ALGEBRAIC FUNCTION FIELDS)
Parent and Category (ALGEBRAIC FUNCTION FIELDS)
Parent and Category (MULTIVARIATE POLYNOMIAL RINGS)
Parent and Category (ORDERS AND ALGEBRAIC FIELDS)
Parent and Category (POWER, LAURENT AND PUISEUX SERIES)
Parent and Category (UNIVARIATE POLYNOMIAL RINGS)
Parent and Category (VALUATION RINGS)
Type(r) : RngElt -> Cat
Parent and Category (INTRODUCTION [BASIC RINGS])
ParentGraph(s) : GrphVert -> Grph
ParentGraph(S) : GrphVertSet -> Grph
Expression (OVERVIEW)
Expression (OVERVIEW)
ParentPlane(l) : PlaneLn -> Plane, PlanePtSet, PlaneLnSet
ParentPlane(L) : PlaneLnSet -> Plane, PlanePtSet, PlaneLnSet
ParentPlane(p) : PlanePt -> Plane, PlanePtSet, PlaneLnSet
ParentPlane(V) : PlanePtSet -> Plane, PlanePtSet, PlaneLnSet
ParentRing(N) : NwtnPgon -> Rng
Parents of Maps (MAPPINGS)
ParityCheckMatrix(C) : Code -> ModMatFldElt
ParityCheckMatrix(C) : Code -> ModMatRngElt
SubfieldRepresentationParityCode(C, K) : Code, FldFin -> Code
ParityCheckMatrix(C) : Code -> ModMatFldElt
ParityCheckMatrix(C) : Code -> ModMatRngElt
Parsing Strings (INPUT AND OUTPUT)
ALGEBRAIC GEOMETRY (PART)
ALGEBRAS (PART)
BASIC RINGS (PART)
CODING THEORY AND CRYPTOGRAPHY (PART)
COMMUTATIVE ALGEBRA (PART)
CRYPTOGRAPHY (PART)
EXTENSION OF RINGS (PART)
FINITE INCIDENCE STRUCTURES (PART)
GROUPS (PART)
HOMOLOGICAL ALGEBRA (PART)
LATTICES AND QUADRATIC FORMS (PART)
LIE THEORY (PART)
LINEAR ALGEBRA AND MODULE THEORY (PART)
OPTIMIZATION (PART)
REPRESENTATION THEORY (PART)
SEMIGROUPS AND MONOIDS (PART)
SETS, SEQUENCES, AND MAPPINGS (PART)
THE MAGMA LANGUAGE (PART)
ContentAndPrimitivePart(f) : RngMPolElt -> RngIntElt, RngMPolElt
ContentAndPrimitivePart(p) : RngUPolElt -> RngIntElt, RngUPolElt
LRatioOddPart(M, j) : ModSym, RngIntElt -> FldRatElt
PrimitivePart(f) : RngMPolElt -> RngMPolElt
PrimitivePart(p) : RngUPolElt -> RngUPolElt
SquarefreePart(f) : RngMPolElt -> RngMPolElt
IsPartialRoot(f, c) : RngUPolElt, RngSerElt -> BoolElt
IsUniquePartialRoot(f, c) : RngUPolElt, RngSerElt -> BoolElt
PartialFactorization(S) : [ RngIntElt ] -> [ RngIntEltFact ]
PartialFractionDecomposition(f) : FldFunRatUElt -> [ <RngUPolElt, RngIntElt, RngUPolElt> ]
SquarefreePartialFractionDecomposition(f) : FldFunRatUElt -> [ <RngUPolElt, RngIntElt, RngUPolElt> ]
Creation of Partial Maps (MAPPINGS)
Partial Fraction Decomposition (RATIONAL FUNCTION FIELDS)
Partial Mappings (OVERVIEW)
Partial Fraction Decomposition (RATIONAL FUNCTION FIELDS)
Creation of Partial Maps (MAPPINGS)
RngInt_PartialFact (Example H38E8)
PartialFactorization(S) : [ RngIntElt ] -> [ RngIntEltFact ]
PartialFractionDecomposition(f) : FldFunRatUElt -> [ <RngUPolElt, RngIntElt, RngUPolElt> ]
FldFunRat_PartialFractionDecomposition (Example H44E3)
Partial Mappings (OVERVIEW)
ConjugatePartition(P) : SeqEnum -> SeqEnum
DistancePartition(u) : GrphVert -> [ { GrphVert } ]
DistancePartition(u) : GrphVert -> [ { GrphVert } ]
EquitablePartition(P, G) : { { GrphVert } }, GrphUnd -> { { GrphVert } }
IndexOfPartition(P) : SeqEnum -> RngIntElt
IsPartition(S) : SeqEnum -> BoolElt
IsPartitionRefined(G: parameters) : Grph -> BoolElt
MaximalPartition(G) : GrpPerm -> GSet
MinimalPartition(G: parameters) : GrpPerm -> GSet
OrbitsPartition(G) : GrphUnd -> [ { GrphVert } ]
Partition(S, p) : SeqEnum, RngIntElt -> SeqEnum(SeqEnum)
Partition(S, P) : SeqEnum, [RngIntElt] -> SeqEnum(SeqEnum)
PartitionCovers(P1, P2) : SeqEnum, SeqEnum -> BoolElt
RandomPartition(n) : RngIntElt -> SeqEnum
Action on a G-invariant Partition (PERMUTATION GROUPS)
Action on a G-invariant Partition (PERMUTATION GROUPS)
PartitionCovers(P1, P2) : SeqEnum, SeqEnum -> BoolElt
AllPartitions(G) : GrpPerm -> SetEnum
MinimalPartitions(G: parameters) : GrpPerm -> [ GSet ]
NumberOfPartitions(n) : RngIntElt -> RngIntElt
NumberOfPartitions(n) : RngIntElt -> RngIntElt
Partitions(n) : RngIntElt -> [ [ RngIntElt ] ]
Partitions(n) : RngIntElt -> [ [ RngIntElt ] ]
Partitions(n, k) : RngIntElt, RngIntElt -> [ [ RngIntElt ] ]
RestrictedPartitions(n, k, M) : RngIntElt, SetEnum -> [ [ RngIntElt ] ]
RestrictedPartitions(n, k, M) : RngIntElt, SetEnum -> [ [ RngIntElt ] ]
RestrictedPartitions(n, M) : RngIntElt, SetEnum -> [ [ RngIntElt ] ]
RestrictedPartitions(n, Q) : RngIntElt, SetEnum -> [ [ RngIntElt ] ]
Tableau_Partitions (Example H96E1)
Partitions (PARTITIONS, WORDS AND YOUNG TABLEAUX)
PascalTriangle(D) : Dsgn -> SeqEnum
PascalTriangle(D) : Dsgn -> SeqEnum
AllPassants(P, A) : Plane, { PlanePt } -> { PlaneLn }
ExternalLines(P, A) : Plane, { PlanePt } -> { PlaneLn }
AffinePatch(C,i) : Crv,RngIntElt -> SeqEnum
AffinePatch(X,p) : Sch,Pt -> Sch,Pt
AffinePatch(X,i) : Sch,RngIntElt -> Sch
CentredAffinePatch(S, p) : Sch, Pt -> Sch, MapSch
RestrictionToPatch(f,j) : MapSch,RngIntElt -> MapSch
RestrictionToPatch(f,i,j) : MapSch,RngIntElt,RngIntElt -> MapSch
MAGMA_PATH
BranchVertexPath(u,v) : GrphVert,GrphVert -> SeqEnum
DiameterPath(G) : Grph -> [GrphVert]
IsPath(G) : Grph -> BoolElt
PathGraph(p: parameters) : RngIntElt -> GrphUnd
PathTree(B, i) : AlgBas, RngIntElt -> ModRng
SetPath(s) : MonStgElt ->
VertexPath(u,v) : GrphSplVert,GrphSplVert -> SeqEnum,SeqEnum
VertexPath(u,v) : GrphVert,GrphVert -> SeqEnum
Connectedness, Paths and Circuits (GRAPHS)
Paths and Circuits in a Graph (GRAPHS)
Paths and Circuits in a Graph (GRAPHS)
PathGraph(p: parameters) : RngIntElt -> GrphUnd
PathTree(B, i) : AlgBas, RngIntElt -> ModRng
Groups (OVERVIEW)
Power-Conjugate Presentations (FINITE SOLUBLE GROUPS)
Transfer from GrpPC (FINITE SOLUBLE GROUPS)
Transfer to GrpPC (FINITE SOLUBLE GROUPS)
Power-Conjugate Presentations (FINITE SOLUBLE GROUPS)
GrpPC_pc-to-perm (Example H24E23)
GrpPC_pc_hom (Example H24E5)
GrpPC_pc_quotient (Example H24E19)
WeightClass(x) : GrpPCElt -> RngIntElt
PCClass(x) : GrpPCElt -> RngIntElt
pCentralSeries(G, p) : GrpFin, RngIntElt -> [ GrpFin ]
pCentralSeries(G, p) : GrpMat, RngIntElt -> [ GrpMat ]
pCentralSeries(G, p) : GrpPC, RngIntElt -> [GrpPC]
pCentralSeries(G, p) : GrpPerm, RngIntElt -> [ GrpPerm ]
pCentralSeries(G, p) : GrpFin, RngIntElt -> [ GrpFin ]
pCentralSeries(G, p) : GrpMat, RngIntElt -> [ GrpMat ]
pCentralSeries(G, p) : GrpPC, RngIntElt -> [GrpPC]
pCentralSeries(G, p) : GrpPerm, RngIntElt -> [ GrpPerm ]
PCExponents(G) : GrpGPC -> [RngIntElt]
PCGenerators(G) : GrpGPC -> {@ GrpGPCElt @}
Generators(G) : GrpGPC -> {@ GrpGPCElt @}
Generators(H, G) : GrpGPC, GrpGPC -> {@ GrpGPCElt @}
NumberOfGenerators(G) : GrpGPC -> RngIntElt
NumberOfPCGenerators(G) : GrpPC -> RngIntElt
NumberOfPCGenerators(P) : Process(pQuot) -> RngIntElt
PCGenerators(G) : GrpPC -> SetIndx
PCGroup(G) : Grp -> GrpPC, Hom(Grp)
PCGroup(A) : GrpAb -> GrpPC, Hom(Grp)
PCGroup(G) : GrpGPC -> GrpPC, Map
PCGroup(G) : GrpMat -> GrpPC, Map
PCGroup(G): GrpMat -> GrpPC, Map
PCGroup(G) : GrpPerm -> GrpPC, Map
PCGroup(Q : parameters ) : [RngIntElt] -> GrpPC
GrpPC_pcgroup (Example H24E22)
pClass(G) : GrpPC -> RngIntElt
pClass(P) : Process(pQuot) -> RngIntElt
MakePCMap(A, P, S) : Aff, Prj, SeqEnum ->
MakeProjectiveClosureMap(A, P, S) : Aff,Prj,SeqEnum ->
ProjectiveClosureMap(A) : Aff -> MapSch
pCore(G, p) : GrpAb, RngIntElt -> GrpAb
pCore(G, p) : GrpFin, RngIntElt -> GrpFin
pCore(G, p) : GrpMat, RngIntElt -> GrpMat
pCore(G, S) : GrpPC, { RngIntElt } -> GrpPC
pCore(G, S) : GrpPC, { RngIntElt } -> GrpPC
pCore(G, p) : GrpPerm, RngIntElt -> GrpPerm
pCover(G, F, p) : GrpFin, GrpFinFP, RngIntElt -> GrpFinFP
pCover(G, F, p) : GrpPerm, GrpFP, RngIntElt -> GrpFP
pCoveringGroup(~P) : Process(pQuot) ->
pCoveringGroup(~P) : Process(pQuot) ->
PCPrimes(G) : GrpPC -> [RngIntElt]
pElementaryAbelianNormalSubgroup(G, p) : GrpPerm, RngIntElt -> GrpPerm
pElementaryAbelianNormalSubgroup(G, p) : GrpPerm, RngIntElt -> GrpPerm
Pencil(P, p) : Plane, PlanePt -> { PlaneLn }
Creation from Pencils (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
GrphRes_pencil (Example H85E2)
IsNearlyPerfect(C) : Code -> BoolElt
IsPerfect(C) : Code -> BoolElt
IsPerfect(G) : GrpAb -> BoolElt
IsPerfect(G) : GrpFin -> BoolElt
IsPerfect(G) : GrpGPC -> BoolElt
IsPerfect(G) : GrpMat -> BoolElt
IsPerfect(G) : GrpPC -> BoolElt
IsPerfect(G) : GrpPerm -> BoolElt
PerfectGroupDatabase() : -> DB
PerfectSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
PerfectSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
RngInt_Perfect (Example H38E7)
PerfectGroupDatabase() : -> DB
PerfectSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
PerfectSubgroups(G: parameters) : GrpPerm -> [ rec< GrpPerm, RngIntElt, RngIntElt, GrpFP> ]
GrpData_perfgps (Example H22E5)
Database of Some Permutation Groups (OVERVIEW)
ClassicalPeriod(M, j, prec) : ModSym, RngIntElt, RngIntElt -> FldPrElt
PeriodMapping(M, prec) : ModSym, RngIntElt -> Map
RealPeriod(E: parameters) : CrvEll -> FldPRElt
The Period Map (MODULAR SYMBOLS)
The Period Map (MODULAR SYMBOLS)
PeriodMapping(M, prec) : ModSym, RngIntElt -> Map
Periods(M, prec) : ModSym, RngIntElt -> SeqEnum
Periods(E: parameters) : CrvEll -> [ FldPRElt ]
DualMatrixToPerm( W, M ) : GrpCox, AlgMatElt -> GrpPermElt
MatrixToPerm( W, M ) : GrpCox, AlgMatElt -> GrpPermElt
PermToMatrix( W, M ) : GrpCox, GrpPermElt -> AlgMatElt
PermToWord( W, p ) : GrpCox, GrpPermElt -> SeqEnum
WordToPerm( W, w ) : GrpCox, [] -> GrpPermElt
The Burnside Algorithm for General Groups (K[G]-MODULES AND GROUP REPRESENTATIONS)
Permutation Group Databases (DATABASES OF GROUPS)
Permutation Group Databases (DATABASES OF GROUPS)
Induced Permutation Representations (FP GROUPS - ADVANCED FEATURES)
PermToDualMatrix( W, M ) : GrpCox, GrpPermElt -> AlgMatElt
PermToMatrix( W, M ) : GrpCox, GrpPermElt -> AlgMatElt
PermToDualMatrix( W, M ) : GrpCox, GrpPermElt -> AlgMatElt
PermToMatrix( W, M ) : GrpCox, GrpPermElt -> AlgMatElt
PermToWord( W, p ) : GrpCox, GrpPermElt -> SeqEnum
CosetTableToPermutationGroup(G, T) : GrpFP, Map -> GrpPerm
IsProbablyPermutationPolynomial(p) : RngUPolElt -> BoolElt
Permutation(G, Q) : GrpPerm, [Elt] -> GrpPermElt
PermutationAutomorphism(A,g) : Sch,GrpPermElt -> IsoSch
PermutationCharacter(G, H) : Grp, Grp -> AlgChtrElt
PermutationCharacter(G, H) : GrpFin, GrpFin -> AlgChtrElt
PermutationCharacter(G, H) : GrpMat, GrpMat -> AlgChtrElt
PermutationCharacter(G) : GrpPerm -> AlgChtrElt
PermutationCharacter(G) : GrpPerm -> AlgChtrElt
PermutationCharacter(G) : GrpPerm -> AlgChtrElt
PermutationCharacter(G, H) : GrpPerm, GrpPerm -> AlgChtrElt
PermutationCode(u, G) : ModTupRngElt, GrpPerm -> Code
PermutationCode(u, G) : ModTupRngElt, GrpPerm -> Code
PermutationGroup(C) : Code -> GrpPerm, PowMap, Map
PermutationGroup(A) : GrpAb -> GrpPerm, Hom(Grp)
PermutationGroup(D, i: parameters): DB, RngIntElt -> GrpFP
PermutationGroup< n | L > : RngIntElt, List -> GrpPerm
PermutationGroup< X | L > : Set, List -> GrpPerm
PermutationGroup< X | L > : Set, List -> GrpPerm, Hom
PermutationModule(G, K) : Grp, Fld -> ModGrp
PermutationModule(G, K) : Grp, Fld -> ModGrp
PermutationModule(G, H, K) : Grp, Grp, Fld -> ModGrp
PermutationModule(G, H, R) : Grp, Grp, Rng -> ModGrp
PermutationModule(G, V) : Grp, ModTup -> ModGrp
PermutationModule(G, u) : Grp, ModTupElt -> ModGrp
PermutationModule(G, H, R) : GrpFin, GrpFin, Rng -> ModGrpFin
PermutationModule(G, H, R) : GrpMat, GrpMat, Rng -> ModGrp
PermutationModule(G, R) : GrpPerm, Rng -> ModGrp
PermutationModule(G, R) : GrpPerm, Rng -> ModGrpFin
PermutationRepresentation(A) : GrpAuto -> Map, GrpPerm, SetIndx
PermutationRepresentation(D, i: parameters): DB, RngIntElt -> Hom(Grp), GrpFP, GrpPerm
ReflectionPermutation( RD, r ) : RootDtm, RngIntElt -> []
Database of Some Permutation Groups (OVERVIEW)
Identification as a Permutation Group (PERMUTATION GROUPS)
Permutation Character (CHARACTERS OF FINITE GROUPS)
Permutation Group Actions on Polynomials (INVARIANT RINGS OF FINITE GROUPS)
PERMUTATION GROUPS
Permutation Modules (K[G]-MODULES AND GROUP REPRESENTATIONS)
Permutation Polynomials (FINITE FIELDS)
Permutation Polynomials (UNIVARIATE POLYNOMIAL RINGS)
Permutation Modules (K[G]-MODULES AND GROUP REPRESENTATIONS)
Permutation Polynomials (FINITE FIELDS)
Permutation Polynomials (UNIVARIATE POLYNOMIAL RINGS)
AlgFP_PermutationActionD8 (Example H75E3)
PermutationAutomorphism(A,g) : Sch,GrpPermElt -> IsoSch
PermutationCharacter(G, H) : Grp, Grp -> AlgChtrElt
PermutationCharacter(G, H) : GrpFin, GrpFin -> AlgChtrElt
PermutationCharacter(G, H) : GrpMat, GrpMat -> AlgChtrElt
PermutationCharacter(G) : GrpPerm -> AlgChtrElt
PermutationCharacter(G) : GrpPerm -> AlgChtrElt
PermutationCharacter(G) : GrpPerm -> AlgChtrElt
PermutationCharacter(G, H) : GrpPerm, GrpPerm -> AlgChtrElt
PermutationCode(u, G) : ModTupRngElt, GrpPerm -> Code
PermutationCode(u, G) : ModTupRngElt, GrpPerm -> Code
CodeFld_PermutationCode (Example H101E3)
CodeRng_PermutationCode (Example H102E3)
PermutationGroup(C) : Code -> GrpPerm, PowMap, Map
PermutationGroup(A) : GrpAb -> GrpPerm, Hom(Grp)
PermutationGroup(D, i: parameters): DB, RngIntElt -> GrpFP
PermutationGroup< n | L > : RngIntElt, List -> GrpPerm
PermutationGroup< X | L > : Set, List -> GrpPerm
PermutationGroup< X | L > : Set, List -> GrpPerm, Hom
PermutationModule(G, K) : Grp, Fld -> ModGrp
PermutationModule(G, K) : Grp, Fld -> ModGrp
PermutationModule(G, H, K) : Grp, Grp, Fld -> ModGrp
PermutationModule(G, H, R) : Grp, Grp, Rng -> ModGrp
PermutationModule(G, V) : Grp, ModTup -> ModGrp
PermutationModule(G, u) : Grp, ModTupElt -> ModGrp
PermutationModule(G, H, R) : GrpFin, GrpFin, Rng -> ModGrpFin
PermutationModule(G, H, R) : GrpMat, GrpMat, Rng -> ModGrp
PermutationModule(G, R) : GrpPerm, Rng -> ModGrp
PermutationModule(G, R) : GrpPerm, Rng -> ModGrpFin
ClassAction(A) : GrpAuto -> Map, GrpPerm, SetIndx
PermutationRepresentation(A) : GrpAuto -> Map, GrpPerm, SetIndx
PermutationRepresentation(D, i: parameters): DB, RngIntElt -> Hom(Grp), GrpFP, GrpPerm
NumberOfPermutations(n, k) : RngIntElt, RngIntElt -> RngIntElt
Permutations(S) : SetEnum -> SetEnum;
Permutations(S) : SetEnum -> SetEnum;
Permutations(S, k) : SetEnum, RngIntElt -> SetEnum;
Permutations(S, k) : SetEnum, RngIntElt -> SetEnum;
ReflectionPermutations( RD ) : RootDtm -> []
SimpleReflectionPermutations( RD ) : RootDtm -> []
TensorInducedPermutations(G) : GrpMat -> SeqEnum
GrpPerm_Permutations (Example H20E2)
Permutations (PERMUTATION GROUPS)
Database of Perfect Groups (DATABASES OF GROUPS)
pFundamentalUnits(O, p) : RngOrd, RngIntElt -> GrpAb, Map
pFundamentalUnits(O, p) : RngOrd, RngIntElt -> GrpAb, Map
PGammaL(arguments)
ProjectiveGammaLinearGroup(arguments)
ProjectiveGammaUnitaryGroup(arguments)
PGammaL(arguments)
ProjectiveGammaLinearGroup(arguments)
PGammaU(arguments)
ProjectiveGammaUnitaryGroup(arguments)
PGL(arguments)
ProjectiveGeneralLinearGroup(arguments)
ProjectiveGeneralOrthogonalGroup(n, q) : RngIntElt, RngIntElt -> GrpPerm, {@ ModTupFldElt @}
PGO(arguments)
ProjectiveGeneralOrthogonalGroupMinus(n, q) : RngIntElt, RngIntElt -> GrpPerm, {@ ModTupFldElt @}
PGOMinus(arguments)
ProjectiveGeneralOrthogonalGroupPlus(n, q) : RngIntElt, RngIntElt -> GrpPerm, {@ ModTupFldElt @}
PGOPlus(arguments)
PGroupStrong(G) : GrpMat -> GrpFP, Hom(Grp)
FPGroupStrong(G) : GrpPerm -> GrpFP, Hom(Grp)
NilpotentSection(SQP: parameter) : SQProc -> BoolElt, SQProc
NumberOfSubgroupsAbelianPGroup (A) : SeqEnum -> SeqEnum
OrderAutomorphismGroupAbelianPGroup (A) : SeqEnum -> RngIntElt
PGroupSection(SQP, p: parameter) : SQProc, RngIntElt -> BoolElt, SQProc
NilpotentSection(SQP: parameter) : SQProc -> BoolElt, SQProc
PGroupStrong(G) : GrpMat -> GrpFP, Hom(Grp)
FPGroupStrong(G) : GrpPerm -> GrpFP, Hom(Grp)
PGU(arguments)
ProjectiveGeneralUnitaryGroup(arguments)
EulerPhi(n) : RngIntElt -> RngIntElt
EulerPhiInverse(m) : RngIntElt -> RngIntElt
FactoredEulerPhi(n) : RngIntElt -> RngIntEltFact
FactoredEulerPhiInverse(n) : RngIntElt -> RngIntEltFact
IsogenyMapPhi(I) : Map -> RngUPolElt
IsogenyMapPhiMulti(I) : Map -> RngUPolElt
PHom(M,N) : ModAlg, ModAlg -> ModMatFld
Pi(R) : FldPr -> FldPrElt
Hall pi-Subgroups and Sylow Systems (FINITE SOLUBLE GROUPS)
PicardNumber(O) : RngQuad -> RngIntElt
PicardGroup(O) : RngQuad -> GrpAb, Map
PicardNumber(O) : RngQuad -> RngIntElt
PicardGroup(O) : RngQuad -> GrpAb, Map
PicardNumber(O) : RngQuad -> RngIntElt
PicardGroup(O) : RngQuad -> GrpAb, Map
IsPrincipalIdealDomain(R) : Rng -> BoolElt
IsPID(R) : Rng -> BoolElt
Pipe(C, S) : MonStgElt, MonStgElt -> MonStgElt
IsPrincipalIdealRing(R) : Rng -> BoolElt
IsPIR(R) : Rng -> BoolElt
CurvePlace(P) : PlcFunElt -> PlcCrvElt
S ! P : PlcCrv, PlcFunElt -> PlcCrvElt
S ! I : PlcFun, RngFunOrdIdl -> PlcFunElt
FunctionFieldPlace(P) : PlcCrvElt -> PlcFunElt
IsWeierstrassPlace(P) : PlcCrvElt -> BoolElt
IsWeierstrassPlace(P) : PlcFunElt -> BoolElt
Place(C,m) : Crv,RngIntElt -> BoolElt,PlcCrvElt
Place(F, m) : FldFun, RngIntElt -> BoolElt, PlcFunElt
Place(F, m) : FldFun, RngIntElt -> PlcFunElt
Place(p) : Pt -> PlcCrvElt
Place(I) : RngFunOrdIdl -> PlcFunElt
Place(I) : RngOrdIdl -> PlcNumElt
Place(Q) : SeqEnum -> PlcCrvElt
RandomPlace(F, m) : FldFun, RngIntElt -> BoolElt, PlcFunElt
RandomPlace(F, m) : FldFun, RngIntElt -> BoolElt, PlcFunElt
Crv_place-equations (Example H84E13)
Places (ALGEBRAIC FUNCTION FIELDS)
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
Places(C) : Crv -> PlcCrv
Places(C,m) : Crv,RngIntElt -> SeqEnum
Places(F) : FldFun -> PlcFun
Places(F) : FldFun -> PlcFun
Places(F) : FldFun -> PlcFun
Places(F, m) : FldFun, RngIntElt -> SeqEnum[PlcFunElt]
Places(F, m) : FldFun, RngIntElt -> SeqEnum[PlcFunElt]
Places(F, m) : FldFun, RngIntElt -> SeqEnum[PlcFunElt]
Places(K) : FldNum -> PlcNum
Places(p) : Pt -> SeqEnum
WeierstrassPlaces(D) : DivCrvElt -> SeqEnum
WeierstrassPlaces(D) : DivFunElt -> [PlcFunElt]
WeierstrassPlaces(F) : FldFunG -> [PlcFunElt]
WeierstrassPlaces(F) : FldFunG -> [PlcFunElt]
Functions related to Places and Divisors (ALGEBRAIC FUNCTION FIELDS)
Places (PLANE ALGEBRAIC CURVES)
Places (PLANE ALGEBRAIC CURVES)
Sets of Places (PLANE ALGEBRAIC CURVES)
FldFunG_places (Example H53E17)
PlacticIntegerMonoid() : -> MonOrd
PlacticMonoid(O) : MonOrd -> MonOrd
Plactic Monoids (PARTITIONS, WORDS AND YOUNG TABLEAUX)
Plactic Monoids (PARTITIONS, WORDS AND YOUNG TABLEAUX)
PlacticIntegerMonoid() : -> MonOrd
PlacticMonoid(O) : MonOrd -> MonOrd
IsPlanar(G) : GraphUnd -> BoolElt, GrphUnd
Graph_Planarity (Example H97E15)
Planar Graphs (GRAPHS)
Combinatorial and Geometrical Structures (OVERVIEW)
AffineSpace(k,2) : Rng, RngIntElt -> Aff
FiniteAffinePlane(D) : Inc -> Plane, PlanePtSet, PlaneLnSet
FiniteAffinePlane(W) : ModFld -> PlaneAff
FiniteAffinePlane< v | X : parameters > : RngIntElt, List -> PlaneAff
FiniteAffinePlane(P, l) : PlaneProj, PlaneLn -> PlaneAff, PlanePtSet, PlaneLnSet, Map
FiniteProjectivePlane(D) : Inc -> Plane, PlanePtSet, PlaneLnSet
FiniteProjectivePlane(W) : ModTupFld -> PlaneProj
FiniteProjectivePlane< v | X : parameters > : RngIntElt, List -> PlaneProj
ParentPlane(l) : PlaneLn -> Plane, PlanePtSet, PlaneLnSet
ParentPlane(L) : PlaneLnSet -> Plane, PlanePtSet, PlaneLnSet
ParentPlane(p) : PlanePt -> Plane, PlanePtSet, PlaneLnSet
ParentPlane(V) : PlanePtSet -> Plane, PlanePtSet, PlaneLnSet
ProjectiveSpace(k,2) : Rng,RngIntElt -> Prj
UpperHalfPlaneWithCusps() : -> SpcHyp
FINITE PLANES
Genus and Singularities (PLANE ALGEBRAIC CURVES)
Planes (PLANE ALGEBRAIC CURVES)
The Upper Half Plane (SUBGROUPS OF PSL_2(R))
Genus and Singularities (PLANE ALGEBRAIC CURVES)
Crv_plane-points (Example H84E1)
Combinatorial and Geometrical Structures (OVERVIEW)
Combinatorial and Geometrical Structures (OVERVIEW)
Combinatorial and Geometrical Structures (OVERVIEW)
Combinatorial and Geometrical Structures (OVERVIEW)
Planes in Magma (FINITE PLANES)
Translation Planes (FINITE PLANES)
Planes in Magma (FINITE PLANES)
CrvEll_PlayWithPoints (Example H87E13)
PlotkinAsymptoticBound(K, delta) : FldFin, FldPrElt -> FldPrElt
PlotkinBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
PlotkinSum(C, D) : Code, Code -> Code
PlotkinSum(C1, C2) : Code, Code -> Code
PlotkinSum(C1, C2, C3: parameters) : Code, Code, Code -> Code
PlotkinAsymptoticBound(K, delta) : FldFin, FldPrElt -> FldPrElt
PlotkinBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
PlotkinSum(C, D) : Code, Code -> Code
PlotkinSum(C1, C2) : Code, Code -> Code
PlotkinSum(C1, C2, C3: parameters) : Code, Code, Code -> Code
GOPlus(arguments)
GeneralOrthogonalGroupPlus(arguments)
OmegaPlus(arguments)
PGOPlus(arguments)
PSOPlus(arguments)
ProjectiveOmegaPlus(arguments)
SpecialOrthogonalGroupPlus(arguments)
Operators (OVERVIEW)
Partial Mappings (OVERVIEW)
pmap< A -> B | x : -> e(x) > : Struct, Struct -> Map
pmap< A -> B | x : -> e(x), y : -> i(y) > : Struct, Struct -> Map
pmap< A -> B | x : -> e(x), y : -> i(y) > : Struct, Struct -> Map
pmap< A -> B | G > : Struct, Struct -> Map
pMaximalOrder(O, p) : RngOrd, RngIntElt -> RngOrd
pMaximalOrder(O, p) : RngOrd, RngIntElt -> RngOrd
pMinimalWeierstrassModel(C, p) : CrvHyp, RngIntElt -> CrvHyp, MapIsoSch
pMinimalWeierstrassModel(C, p) : CrvHyp, RngIntElt -> CrvHyp, MapIsoSch
pMinus1(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]
pMultiplicator(G, p) : GrpFin, RngIntElt -> [ RngIntElt ]
pMultiplicator(G, p) : GrpPerm, RngIntElt -> [ RngIntElt ]
pMultiplicatorRank(G) : GrpPC -> RngIntElt
pMultiplicatorRank(G) : GrpPC -> RngIntElt
pNormalModel(C, p) : CrvHyp, RngIntElt -> CrvHyp, MapIsoSch
pNormalModel(C, p) : CrvHyp, RngIntElt -> CrvHyp, MapIsoSch
PointSet(E, m) : CrvEll, Map -> SetPtEll
E(m) : CrvEll, Map -> SetPtEll
E(L) : CrvEll, Rng -> SetPtEll
BasePoint(G, i) : GrpMat, RngIntElt -> Elt
BasePoint(G, i) : GrpPerm, RngIntElt -> Elt
CollineationGroup(P) : Plane -> GrpPerm, GSet, GSet, PowMap, Map
EquivalentPoint(x) : SpcHypElt -> SpcHypElt, GrpPSL2Elt
HasNonsingularPoint(X) : Sch -> BoolElt,Pt
HasRationalPoint(C) : CrvCon -> BoolElt, Pt
IsBasePointFree(L) : LinSys -> BoolElt
IsDoublePoint(p) : Crv,Pt -> BoolElt
IsInflectionPoint(p) : Sch,Pt -> BoolElt,RngIntElt
IsPoint(C, S) : CrvHyp, SeqEnum -> BoolElt, PtHyp
IsPoint(N,p) : NwtnPgon,Tup -> BoolElt
IsPoint(H, x) : SetPtEll, RngElt -> BoolElt, PtEll
IsPoint(H, S) : SetPtEll, [ RngElt ] -> BoolElt, PtEll
IsPoint(K, S) : SrfKum, [RngElt] -> BoolElt, SrfKumPt
IsPointRegular(D) : IncNsp -> BoolElt, RngIntElt
IsPointTransitive(D) : Inc -> BoolElt
IsPointTransitive(P) : Plane -> BoolElt
Point(D, i) : Inc, RngIntElt -> IncPt
PointDegree(D, p) : Inc, IncPt -> RngIntElt
PointDegrees(D) : Inc -> [ RngIntElt ]
PointGraph(D) : Inc -> Grph
PointGraph(D) : Inc -> GrphUnd
PointGraph(P) : Plane -> GrphUnd;
PointGroup(D) : Inc -> GrpPerm, GSet
PointSet(D) : Inc -> IncPtSet
PointSet(P) : Plane -> PlanePtSet
ProjectionFromNonsingularPoint(X,p) : Sch,Pt -> Sch,MapSch,Sch
RationalPoint(C) : CrvCon -> Pt
RepresentativePoint(P) : PlcCrv -> Pt
X(L) : Sch,Rng -> SetPt
EltSeq(P): PtEll -> [ RngElt ]
Access Operations (ELLIPTIC CURVES)
Arithmetic (ELLIPTIC CURVES)
Associated Structures (ELLIPTIC CURVES)
Combinatorial and Geometrical Structures (OVERVIEW)
Creating Points and Blocks (INCIDENCE STRUCTURES AND DESIGNS)
Creation of Points (ELLIPTIC CURVES)
Creation of Points (MODULAR CURVES)
Creation Predicates (ELLIPTIC CURVES)
Finding Points (RATIONAL CURVES AND CONICS)
Operations on Points (ELLIPTIC CURVES)
Operations on Points and Blocks (INCIDENCE STRUCTURES AND DESIGNS)
Point Order (ELLIPTIC CURVES)
Points (PLANE ALGEBRAIC CURVES)
Predicates on Points (ELLIPTIC CURVES)
The Point-Set and Block-Set of an Incidence Structure (INCIDENCE STRUCTURES AND DESIGNS)
The Point-Set and Line-Set of a Plane (FINITE PLANES)
The Set of Points and Set of Lines (FINITE PLANES)
Using the Point-Set and Line-Set to Create Points and Lines (FINITE PLANES)
EltSeq(P): PtEll -> [ RngElt ]
Access Operations (ELLIPTIC CURVES)
Arithmetic (ELLIPTIC CURVES)
Creating Points and Blocks (INCIDENCE STRUCTURES AND DESIGNS)
The Point-Set and Block-Set of an Incidence Structure (INCIDENCE STRUCTURES AND DESIGNS)
Curve(P) : SetPtEll -> CrvEll
Associated Structures (ELLIPTIC CURVES)
Creation of Points (ELLIPTIC CURVES)
Creation of Points (MODULAR CURVES)
Creation Predicates (ELLIPTIC CURVES)
Finding Points (RATIONAL CURVES AND CONICS)
The Set of Points and Set of Lines (FINITE PLANES)
Using the Point-Set and Line-Set to Create Points and Lines (FINITE PLANES)
The Point-Set and Line-Set of a Plane (FINITE PLANES)
Point Order (ELLIPTIC CURVES)
Predicates on Points (ELLIPTIC CURVES)
ElementToSequence(P) : PtHyp -> SeqEnum
Access Operations (HYPERELLIPTIC CURVES)
Access Operations (HYPERELLIPTIC CURVES)
Access Operations (HYPERELLIPTIC CURVES)
ElementToSequence(P) : PtHyp -> SeqEnum
Access Operations (HYPERELLIPTIC CURVES)
Involution(P) : PtHyp -> PtHyp
Arithmetic of Points (HYPERELLIPTIC CURVES)
Point Counting (ELLIPTIC CURVES)
Creation of Points (HYPERELLIPTIC CURVES)
Enumeration and Counting Points (HYPERELLIPTIC CURVES)
Order of Points on the Jacobian (HYPERELLIPTIC CURVES)
Predicates on Points (HYPERELLIPTIC CURVES)
IsIdentity(P) : JacHypPt -> BoolElt
Booleans and Predicates for Points (HYPERELLIPTIC CURVES)
Predicates on Points (HYPERELLIPTIC CURVES)
Point Reduction (RATIONAL CURVES AND CONICS)
Rational Points and Group Structure (HYPERELLIPTIC CURVES)
CrvEll_PointArithmetic (Example H87E11)
PointDegree(D, p) : Inc, IncPt -> RngIntElt
PointDegrees(D) : Inc -> [ RngIntElt ]
CrvHyp_PointEnumeration (Example H88E6)
CrvCon_PointFinding (Example H86E8)
PointGraph(D) : Inc -> Grph
PointGraph(D) : Inc -> GrphUnd
PointGraph(P) : Plane -> GrphUnd;
AutomorphismGroup(P) : Plane -> GrpPerm, GSet, GSet, PowMap, Map
PointGroup(P) : Plane -> GrpPerm, GSet, GSet, PowMap, Map
CollineationGroup(P) : Plane -> GrpPerm, GSet, GSet, PowMap, Map
PointGroup(D) : Inc -> GrpPerm, GSet
CrvCon_PointReduction (Example H86E7)
BasePoints(L) : LinSys -> SeqEnum
BasePoints(f) : MapSch -> SetEnum
DefiningPoints(N) : NwtnPgon -> SeqEnum
EllipticPoints(G) : GrpPSL2, SpcHyp -> [SpcHypElt]
FixedPoints(g,H) : GrpPSL2Elt, SpcHyp -> SeqEnum
Flexes(C) : Sch -> SeqEnum
GoodBasePoints(G: parameters) : GrpMat -> []
HasPointsOverExtension(X) : Sch -> BoolElt
HasSingularPointsOverExtension(C) : Sch -> BoolElt
IntegralPoints(E) : CrvEll -> [ PtEll ], [ Tup ]
IntegralQuarticPoints(Q) : [ RngIntElt ] -> [ SeqEnum ]
IntegralQuarticPoints(Q, P) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]
ModuliPoints(X,E) : CrvMod, CrvEll -> SeqEnum
NumberOfPoints(D) : Inc -> RngInt
NumberOfPoints(P) : Plane -> RngIntElt
Points(C) : CrvHyp -> SetIndx
Points(C, x) : CrvHyp, RngElt -> SetIndx
Points(D) : Inc -> { IncPt }
Points(D) : IncGeom -> SetIndx
Points(J) : JacHyp -> SetIndx
Points(J, P) : JacHyp, SrfKumPt -> SetIndx
Points(P) : Plane -> { PlanePt }
Points(G) : SchGrpEll -> SetIndx
Points(H) : SetPtEll -> @ PtEll @
Points(H, x) : SetPtEll, RngElt -> [ PtEll ]
Points(K,[x1, x2, x3]) : SrfKum, [RngElt] -> SetIndx
PointsAtInfinity(C) : Crv -> SetEnum
PointsAtInfinity(C) : CrvHyp -> SetIndx
PointsAtInfinity(H) : SetPtEll -> @ PtEll @
PointsKnown(C) : CrvHyp -> BoolElt
PointsOverSplittingField(Z) : Clstr -> SetEnum
RationalPoints(C) : CrvCon -> SetIndx
RationalPoints(J, a, d) : JacHyp, RngUPolElt, RngIntElt -> SetIndx
RationalPoints(Z) : Sch -> SetEnum
RationalPoints(C) : Sch -> SetIndx
RationalPoints(X) : Sch -> SetIndx
RationalPoints(X) : Sch -> SetIndx
RationalPoints(X) : Sch -> SetIndx
RationalPoints(K, Q) : SrfKum, [RngElt] -> SetIndx
SIntegralDesbovesPoints(Q, S) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]
SIntegralLjunggrenPoints(Q, S) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]
SIntegralPoints(E, S) : CrvEll, SeqEnum -> [ PtEll ], [ Tup ]
SIntegralQuarticPoints(Q, S) : [ RngIntElt ], [ RngIntElt ] -> [ SeqEnum ]
SingularPoints(C) : Sch -> SetIndx
WeierstrassPlaces(D) : DivCrvElt -> SeqEnum
Arithmetic of Points (HYPERELLIPTIC CURVES)
Creation of Points on Curves (PLANE ALGEBRAIC CURVES)
Cusps and elliptic points of congruence subgroups (SUBGROUPS OF PSL_2(R))
Enumeration of Points (ELLIPTIC CURVES)
Maps and Points (SCHEMES)
Points of Subgroup Schemes (ELLIPTIC CURVES)
Points on Hyperelliptic Curves (HYPERELLIPTIC CURVES)
Points on the Jacobian (HYPERELLIPTIC CURVES)
Prelude to Points (SCHEMES)
Random Points (HYPERELLIPTIC CURVES)
Rational Points (SCHEMES)
Rational Points and Point Sets (SCHEMES)
The Fixed-point Space of a Module (K[G]-MODULES AND GROUP REPRESENTATIONS)
{THE MODULE OF}{SUPERSINGULAR POINTS}
Design_points-blocks (Example H98E2)
Points on the Jacobian (HYPERELLIPTIC CURVES)
Plane_points-lines (Example H99E2)
Creation of Points (HYPERELLIPTIC CURVES)
RationalPoints(J, P) : JacHyp, SrfKumPt -> SetIndx
Points on the Kummer Surface (HYPERELLIPTIC CURVES)
PointsAtInfinity(C) : Crv -> SetEnum
PointsAtInfinity(C) : CrvHyp -> SetIndx
PointsAtInfinity(H) : SetPtEll -> @ PtEll @
PointSet(E, m) : CrvEll, Map -> SetPtEll
E(m) : CrvEll, Map -> SetPtEll
E(L) : CrvEll, Rng -> SetPtEll
PointSet(D) : Inc -> IncPtSet
PointSet(P) : Plane -> PlanePtSet
X(L) : Sch,Rng -> SetPt
Associated Structures (ELLIPTIC CURVES)
Creation of Point Sets (ELLIPTIC CURVES)
Operations on Point Sets (ELLIPTIC CURVES)
Predicates on Point Sets (ELLIPTIC CURVES)
Associated Structures (ELLIPTIC CURVES)
PointSet(E, m) : CrvEll, Map -> SetPtEll
Creation of Point Sets (ELLIPTIC CURVES)
Predicates on Point Sets (ELLIPTIC CURVES)
CrvEll_PointSets (Example H87E10)
PointsKnown(C) : CrvHyp -> BoolElt
PointsOverSplittingField(Z) : Clstr -> SetEnum
Newton_pol-is (Example H54E7)
ComplexToPolar(c) : FldComElt -> FldReElt, FldReElt
PolarToComplex(m, a) : FldReElt, FldReElt -> FldComElt
PolarToComplex(m, a) : FldReElt, FldReElt -> FldComElt
Poles(a) : FldFunElt -> SeqEnum[PlcFunElt]
Poles(a) : FldFunElt -> [ PlcFunElt ]
Zeros(C,f) : DivCrv, FldFunElt -> SeqEnum
PollardRho(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]
PollardRho(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]
PolyMapKernel(f) : Map -> RngMPol
Operations on Polynomials which use Newton Polygons (NEWTON POLYGONS)
RngLoc_Poly-Hensel (Example H55E17)
RngPad_Poly-Hensel (Example H40E15)
Operations on Polynomials which use Newton Polygons (NEWTON POLYGONS)
Newton_poly-ops-ex (Example H54E6)
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)
PolycyclicGenerators(G) : GrpMat -> [ GrpPCElt ]
PolycyclicGroup< x_1, ..., x_n | R : parameters > : List(Identifiers), List(GrpFPRel) -> GrpGPC, Map
PolycyclicGroup< x_1, ..., x_n | R : parameters > : List(Identifiers), List(GrpFPRel) -> GrpPC, Map
Introduction (POLYCYCLIC GROUPS)
POLYCYCLIC GROUPS
Polycyclic Groups and Polycyclic Presentations (POLYCYCLIC GROUPS)
Polycyclic Groups and Polycyclic Presentations (POLYCYCLIC GROUPS)
Introduction (POLYCYCLIC GROUPS)
PolycyclicGenerators(G) : GrpMat -> [ GrpPCElt ]
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< x_1, ..., x_n | R : parameters > : List(Identifiers), List(GrpFPRel) -> GrpGPC, Map
PolycyclicGroup< x_1, ..., x_n | R : parameters > : List(Identifiers), List(GrpFPRel) -> GrpPC, Map
GrpGPC_PolycyclicGroup (Example H23E2)
GrpPC_PolycyclicGroup (Example H24E2)
Grp_PolycyclicGroup (Example H16E4)
IsPolygon(G) : Grph -> BoolElt
NewtonPolygon(C) : Crv -> NwtnPgon
NewtonPolygon(f) : RngMPolElt -> NwtnPgon
NewtonPolygon(f) : RngUPolElt -> NwtnPgon
NewtonPolygon(g) : RngUPolElt -> NwtnPgon
NewtonPolygon(g) : RngUPolElt -> NwtnPgon
NewtonPolygon(V) : SeqEnum -> NwtnPgon
PolygonGraph(p: parameters) : RngIntElt -> GrphUnd
NEWTON POLYGONS
PolygonGraph(p: parameters) : RngIntElt -> GrphUnd
DisplayPolygons(P,file) : SeqEnum, MonStgElt ->
Polylog(m, s) : FldPrElt -> FldPrElt
Polylog(m, f) : RngIntElt, RngSerElt -> RngSerElt
PolylogD(m, s) : FldPrElt -> FldPrElt
PolylogP(m, s) : FldPrElt -> FldPrElt
PolylogDold(m, s) : FldPrElt -> FldPrElt
PolylogP(m, s) : FldPrElt -> FldPrElt
PolylogD(m, s) : FldPrElt -> FldPrElt
PolylogDold(m, s) : FldPrElt -> FldPrElt
PolylogP(m, s) : FldPrElt -> FldPrElt
PolylogD(m, s) : FldPrElt -> FldPrElt
PolylogDold(m, s) : FldPrElt -> FldPrElt
PolylogP(m, s) : FldPrElt -> FldPrElt
PolylogD(m, s) : FldPrElt -> FldPrElt
PolyMapKernel(f) : Map -> RngMPol
AbsoluteCharacteristicPolynomial(a) : FldAlgElt -> RngUPolElt
AbsoluteMinimalPolynomial(a) : FldAlgElt -> RngUPolElt
AbsolutePolynomial(A) : FldAC ->
AtkinModularPolynomial(N) : RngIntElt -> RngMPolElt
BerlekampMassey(S) : SeqEnum -> RngUPolElt, RngIntElt
CharacteristicPolynomial(S) : SeqEnum -> RngUPolElt, RngIntElt
BernoulliPolynomial(n) : RngIntElt -> RngUPolElt
BernoulliPolynomial(n) : RngIntElt -> RngUPolElt
CanonicalModularPolynomial(N) : RngIntElt -> RngMPolElt
CharacteristicPolynomial(x) : AlgQuatElt -> RngUPolElt
CharacteristicPolynomial(a) : FldAlgElt -> RngUPolElt
CharacteristicPolynomial(a) : FldFinElt -> RngUPolElt
CharacteristicPolynomial(a, E) : FldFinElt, FldFin -> RngUPolElt
CharacteristicPolynomial(G) : GrphUnd -> RngUPolElt
CharacteristicPolynomial(a: parameters) : AlgMatElt -> RngUPolElt
CharacteristicPolynomial(g: parameters) : GrpMatElt -> RngPolElt
CharacteristicPolynomial(A: parameters) : Mtrx -> RngUPolElt
CheckPolynomial(C) : Code -> RngUPolElt
ChromaticPolynomial(G) : GrphUnd -> RngUPolElt
ClassicalModularPolynomial(N) : RngIntElt -> RngMPolElt
ConwayPolynomial(p, n) : RngIntElt, RngIntElt -> RngUPolElt
CyclotomicPolynomial(m) : RngIntElt -> RngUPolElt
DefiningPolynomial(C) : Crv -> RngMPolElt
DefiningPolynomial(E) : CrvEll -> RngMPolElt
DefiningPolynomial(F) : FldAlg -> RngUPolElt
DefiningPolynomial(F) : FldFin -> RngPolElt
DefiningPolynomial(F, E) : FldFin -> RngPolElt
DefiningPolynomial(F) : FldFun -> RngUPolElt
DefiningPolynomial(Q) : FldRat -> RngUPolElt
DefiningPolynomial(L) : RngLoc -> 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
EisensteinPolynomial(L) : RngLoc -> 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(A: parameters) : Mtrx -> [ <RngUPolElt, RngIntElt>]
FactoredMinimalPolynomial(A: parameter) : Mtrx -> [ <RngUPolElt, RngIntElt>]
GegenbauerPolynomial(n, m) : RngIntElt, RngElt ->RngUPolElt
GeneratorPolynomial(C) : Code -> RngUPolElt
HasPolynomial(N) : NwtnPgon -> BoolElt
HasPolynomialFactorization(R) : Rng -> BoolElt
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(M) : RngMPol -> RngUPolElt, RngIntElt
InertialPolynomial(L) : RngLoc -> RngUPolElt
IrreduciblePolynomial(F, m) : FldFin, RngIntElt -> RngPolElt
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
MinimalPolynomial(a) : AlgGenElt -> RngUPolElt
MinimalPolynomial(a) : AlgMatElt -> RngUPolElt
MinimalPolynomial(x) : AlgQuatElt -> RngUPolElt
MinimalPolynomial(a) : FldACElt -> RngPolElt
MinimalPolynomial(a) : FldAlgElt -> RngUPolElt
MinimalPolynomial(a) : FldFinElt -> RngPolElt
MinimalPolynomial(a, E) : FldFinElt, FldFin -> RngPolElt
MinimalPolynomial(q) : FldRatElt -> RngUPolElt
MinimalPolynomial(g) : GrpMatElt -> RngPolElt
MinimalPolynomial(A: parameter) : Mtrx -> RngUPolElt
MinimalPolynomial(n) : RngIntElt -> RngUPolElt
MinimalPolynomial(x) : RngLocElt -> RngUPolElt
MinimalPolynomial(f) : RngMPolResElt -> RngUPol
ModularPolynomial(M) : ModSS -> RngMPolElt
MultivariatePolynomial(P, f, i) : RngMPol, RngUPolElt, RngIntElt -> RngMPolElt
Polynomial(N) : NwtnPgon -> RngElt
Polynomial(R, f) : Rng, RngUPolElt -> RngUPolElt
Polynomial(R, Q) : Rng, [ RngElt] -> RngUPolElt
Polynomial(Q) : [ RngElt ] -> RngUPolElt
PolynomialAlgebra(R) : Rng -> RngUPol
PolynomialCoefficient(s, i) : RngPowLazElt, RngIntElt -> RngPowLazElt
PolynomialMap(L) : LinSys -> RngMPolElt
PolynomialRing(R, n) : Rng, RngIntElt -> 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, order) : Rng, RngIntElt, MonStgElt, ... -> RngMPol
PolynomialRing(R, n, order) : Rng, RngIntElt, MonStgElt, ... -> RngMPol
PolynomialRing(R, Q) : Rng, [ RngIntElt ] -> RngMPol
PolynomialRing(R) : RngInvar -> RngMPol
PolynomialSieve( T ) : Tup -> SeqEnum
PrimitivePolynomial(F, m) : FldFin, RngIntElt -> RngPolElt
RandomPrimePolynomial(R, d) : RngUPol, RngIntElt -> RngUPolElt
ReducedLegendrePolynomial(C) : CrvCon -> RngMPolElt, ModMatRngElt
SwinnertonDyerPolynomial(n) : RngIntElt -> RngUPolElt
TwoTorsionPolynomial(E) : CrvEll -> RngMPolElt
UnivariatePolynomial(f) : RngMPolElt -> RngUPolElt
WeberClassPolynomial(D) : RngIntElt -> RngUPolElt
WeberClassPolynomial(D) : RngIntElt -> RngUPolElt
Action on a Polynomial Ring (K[G]-MODULES AND GROUP REPRESENTATIONS)
Database of Galois Group Polynomials (OVERVIEW)
Minimal and Characteristic Polynomial (FINITE FIELDS)
Minimal Polynomial, Norm and Trace (ALGEBRAICALLY CLOSED FIELDS)
MULTIVARIATE POLYNOMIAL RINGS
Polynomials for Finite Fields (FINITE FIELDS)
Rings, Fields, and Algebras (OVERVIEW)
The Bernoulli Polynomial (UNIVARIATE POLYNOMIAL RINGS)
The Generator Polynomial (LINEAR CODES OVER FINITE FIELDS)
UNIVARIATE POLYNOMIAL RINGS
Action on a Polynomial Ring (K[G]-MODULES AND GROUP REPRESENTATIONS)
PolynomialRing(R) : Rng -> RngUPol
PolynomialAlgebra(R) : Rng -> RngUPol
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, Q) : Rng, [ RngIntElt ] -> RngMPol
PolynomialCoefficient(s, i) : RngPowLazElt, RngIntElt -> RngPowLazElt
PolynomialMap(L) : LinSys -> RngMPolElt
PolynomialRing(R) : Rng -> RngUPol
PolynomialAlgebra(R) : Rng -> RngUPol
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, Q) : Rng, [ RngIntElt ] -> RngMPol
PolynomialRing(R) : RngInvar -> RngMPol
AllIrreduciblePolynomials(F, m) : FldFin, RngIntElt -> { RngPolElt }
AlternateDefiningPolynomials(f) : MapSch -> SeqEnum
DefiningPolynomials(f) : MapSch -> SeqEnum
DefiningPolynomials(X) : Sch -> SeqEnum
FactoredDefiningPolynomials(f) : MapSch -> SeqEnum
FactoredInverseDefiningPolynomials(f) : MapSch -> SeqEnum
FactoredMinimalAndCharacteristicPolynomials(A: parameters) : Mtrx -> [<RngUPolElt, RngIntElt>], [<RngUPolElt, RngIntElt>]
HyperellipticPolynomials(C) : CrvHyp -> RngUPolElt, RngUPolElt
InverseDefiningPolynomials(f) : MapSch -> SeqEnum
MinimalAndCharacteristicPolynomials(A: parameter) : Mtrx -> RngUPolElt, RngUPolElt
NumberOfPrimePolynomials(q, d) : RngIntElt, RngIntElt -> RngIntElt
PrimePolynomials(R, d) : RngUPol, RngIntElt -> SeqEnum[ RngUPolElt ]
RngPol_Polynomials (Example H42E2)
Orthogonal Polynomials (UNIVARIATE POLYNOMIAL RINGS)
Permutation Polynomials (FINITE FIELDS)
Permutation Polynomials (UNIVARIATE POLYNOMIAL RINGS)
Polynomials (LOCAL RINGS AND FIELDS)
Polynomials (p-ADIC RINGS AND FIELDS)
Polynomials Associated with Newton Polygons (NEWTON POLYGONS)
Polynomials over series rings (POWER, LAURENT AND PUISEUX SERIES)
Special Families of Polynomials (UNIVARIATE POLYNOMIAL RINGS)
PolynomialSieve( T ) : Tup -> SeqEnum
POmega(arguments)
ProjectiveOmega(arguments)
ProjectiveOmegaMinus(arguments)
ProjectiveOmegaPlus(arguments)
POmegaMinus(arguments)
ProjectiveOmegaMinus(arguments)
POmegaPlus(arguments)
ProjectiveOmegaPlus(arguments)
IndentPop() : ->
POpen(S, T) : MonStgElt, MonStgElt -> File
NumPosRoots( W ) : GrpCox -> RngIntElt
NumberOfPositiveRoots( W ) : GrpCox -> RngIntElt
NumberOfPositiveRoots( G ) : GrpLie -> RngIntElt
NumberOfPositiveRoots( RD ) : RootDtm -> RngIntElt
Operations on Poset Elements (GROUPS)
Operations on Subgroup Class Posets (GROUPS)
The Poset of Subgroup Classes (GROUPS)
Operations on Poset Elements (GROUPS)
Operations on Subgroup Class Posets (GROUPS)
Position(s, t) : MonStgElt, MonStgElt -> RngIntElt
Index(s, t) : MonStgElt, MonStgElt -> RngIntElt
Index(S, x) : SeqEnum, Elt -> RngIntElt
Index(S, x) : SetIndx, Elt -> RngIntElt
RootPosition( W, v ) : GrpCox, . -> {@@}
RootPosition( G, v ) : GrpLie, . -> {@@}
RootPosition( RD, v ) : RootDtm, . -> {@@}
IdempotentPositions(B) : AlgBas -> SeqEnum
IsPositive(D) : DivCrvElt -> BoolElt
IsEffective(D) : DivCrvElt -> BoolElt
IsPositive( RD, r ) : RootDtm, RngIntElt -> BoolElt
IsPositiveDefinite(F) : ModMatRngElt -> BoolElt
IsPositiveSemiDefinite(F) : ModMatRngElt -> BoolElt
NumberOfPositiveRoots( W ) : GrpCox -> RngIntElt
NumberOfPositiveRoots( G ) : GrpLie -> RngIntElt
NumberOfPositiveRoots( RD ) : RootDtm -> RngIntElt
PositiveDefiniteForm(G) : GrpMat -> AlgMatElt
PositiveRoots( W ) : GrpCox -> {@@}
PositiveRoots( G ) : GrpLie -> {@@}
PositiveRoots( RD ) : RootDtm -> {@@}
PositiveSum(m, i) : Map, RngIntElt -> FldPrElt
Positive and Simple Roots (ROOT DATA FOR LIE THEORY)
Positive and Simple Roots (ROOT DATA FOR LIE THEORY)
PositiveCoroots( W ) : GrpCox -> {@@}
PositiveRoots( W ) : GrpCox -> {@@}
PositiveRoots( G ) : GrpLie -> {@@}
PositiveRoots( RD ) : RootDtm -> {@@}
PositiveDefiniteForm(G) : GrpMat -> AlgMatElt
Lat_PositiveDefiniteForm (Example H64E21)
PositiveCoroots( W ) : GrpCox -> {@@}
PositiveRoots( W ) : GrpCox -> {@@}
PositiveRoots( G ) : GrpLie -> {@@}
PositiveRoots( RD ) : RootDtm -> {@@}
PositiveSum(m, i) : Map, RngIntElt -> FldPrElt
CartesianPower(R, k) : Str, RngIntElt -> SetCart
ClassPowerCharacter(x, j) : AlgChtrElt, RngIntElt -> AlgChtrElt
DifferentiationSequence(x, n, a) : FldFunGElt, RngIntElt, FldFunGElt -> SeqEnum
IsPower(a, n) : FldACElt, RngIntElt -> BoolElt, FldACElt
IsPower(a, k) : FldAlgElt, RngIntElt -> BoolElt, FldAlgElt
IsPower(a, n) : FldFinElt, RngIntElt -> BoolElt, FldFinElt
IsPower(n) : RngIntElt -> BoolElt
IsPower(n, k) : RngIntElt -> BoolElt
IsPower(x, n) : RngLocElt, RngIntElt -> RngLocElt
IsPower(w, n) : RngOrdElt, RngIntElt -> BoolElt, RngOrdElt
IsPower(I, k) : RngOrdFracIdl, RngIntElt -> BoolElt, RngOrdFracIdl
IsPrimePower(n) : RngIntElt -> BoolElt, RngIntElt, RngIntElt
KeepPrimePower(SQP, p) : SQProc, RngIntElt -> SeqEnum
LazyPowerSeriesRing(C, n) : Rng, RngIntElt -> RngPowLaz
PowerFormalSet(R) : Struct -> PowSetIndx
PowerGroup(G) : GrpPC -> PowerGroup
PowerIndexedSet(R) : Struct -> PowSetIndx
PowerMap(G) : GrpAb -> Map
PowerMap(G) : GrpFin -> Map
PowerMap(G) : GrpMat -> Map
PowerMap(G) : GrpPC -> Map
PowerMap(G) : GrpPerm -> Map
PowerMultiset(R) : Struct -> PowSetMulti
PowerRelation(r, k: parameters) : FldPrElt, RngIntElt -> RngUPolElt
PowerResidueCode(K,n,p) : FldFin, RngIntElt, RngIntElt -> Code
PowerSequence(R) : Struct -> PowSeqEnum
PowerSeriesRing(R) : Rng -> RngSerPow
PowerSet(R) : Struct -> PowSetEnum
SetPowerPrinting(F, l) : FldFin, BoolElt ->
TensorPower(M, n) : ModGrp, RngIntElt -> ModGrp
f ^ n : QuadBinElt, RngIntElt -> QuadBinElt
qEigenform(M, prec) : ModSym, RngIntElt -> RngSerPowElt
qExpansion(f) : ModFrmElt -> RngSerPowElt
Operators (OVERVIEW)
Parents of Sets and Sequences (INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS])
Power Groups (POLYCYCLIC GROUPS)
Power Sequences (SEQUENCES)
Power Sets (SETS)
POWER, LAURENT AND PUISEUX SERIES
PowerGroup (FINITE SOLUBLE GROUPS)
Rings, Fields, and Algebras (OVERVIEW)
Power Groups (POLYCYCLIC GROUPS)
PowerGroup (FINITE SOLUBLE GROUPS)
Power Sequences (SEQUENCES)
Power Sets (SETS)
Parents of Sets and Sequences (INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS])
PowerFormalSet(R) : Struct -> PowSetIndx
PowerGroup(G) : GrpPC -> PowerGroup
GrpPC_PowerGroupTwo (Example H24E29)
PowerIndexedSet(R) : Struct -> PowSetIndx
AlgGrp_powering (Example H74E5)
PowerMap(G) : GrpAb -> Map
PowerMap(G) : GrpFin -> Map
PowerMap(G) : GrpMat -> Map
PowerMap(G) : GrpPC -> Map
PowerMap(G) : GrpPerm -> Map
PowerMultiset(R) : Struct -> PowSetMulti
PowerRelation(r, k: parameters) : FldPrElt, RngIntElt -> RngUPolElt
PowerResidueCode(K,n,p) : FldFin, RngIntElt, RngIntElt -> Code
PowerSequence(R) : Struct -> PowSeqEnum
Seq_PowerSequence (Example H8E2)
PowerSeries(M, prec) : ModSym, RngIntElt -> RngSerPowElt
qEigenform(M, prec) : ModSym, RngIntElt -> RngSerPowElt
qExpansion(f) : ModFrmElt -> RngSerPowElt
PowerSeriesRing(R) : Rng -> RngSerPow
PowerSet(R) : Struct -> PowSetEnum
Set_PowerSet (Example H7E6)
pPrimaryComponent(A, p) : GrpAb, RngIntElt -> GrpAb
pPrimaryInvariants(A, p) : GrpAb, RngIntElt -> [ RngIntElt ]
pPrimaryComponent(A, p) : GrpAb, RngIntElt -> GrpAb
pPrimaryInvariants(A, p) : GrpAb, RngIntElt -> [ RngIntElt ]
pQuotient(G, p, c) : GrpMat, RngIntElt, RngIntElt -> GrpPC, Map, SeqEnum, BoolElt
pQuotient(G, p, c) : GrpPerm, RngIntElt, RngIntElt -> GrpPC, Map, SeqEnum, BoolElt
pQuotient( F, p, c : parameters ) : GrpFP, RngIntElt, RngIntElt -> GrpPC, Map
pQuotient(G, p, c : parameters ) : GrpPC, RngIntElt, RngIntElt -> GrpPC, Map
pQuotient(F, p, c: parameters) : GrpFP, RngIntElt, RngIntElt -> GrpPC, Map
pQuotient(F, p, c: parameters) : GrpFP, RngIntElt, RngIntElt -> GrpPC, Map, SeqEnum , BoolElt
pQuotientProcess(F, p, c: parameters) : GrpFP, RngIntElt, RngIntElt -> Process
GrpFP_1_pQuotient1 (Example H19E20)
GrpFP_1_pQuotient2 (Example H19E21)
GrpFP_1_pQuotient3 (Example H19E22)
GrpFP_1_pQuotient4 (Example H19E23)
GrpFP_2_pQuotient5 (Example H32E9)
GrpFP_2_pQuotient6 (Example H32E10)
GrpFP_2_pQuotient7 (Example H32E11)
GrpFP_2_pQuotient8 (Example H32E12)
pQuotientProcess(F, p, c: parameters) : GrpFP, RngIntElt, RngIntElt -> Process
pRadical(O, p) : RngOrd, RngIntElt -> RngOrdIdl
ClassGroupPRank(F) : FldFunG -> RngIntElt
ClassGroupPRank(F) : FldFunG -> RngIntElt
pRank(P) : Plane -> RngIntElt
pRank(P, p) : Plane -> RngIntElt
pRanks(G) : GrpPC-> [ RngIntElt ]
Precision and Valuation (LOCAL RINGS AND FIELDS)
Precision and Valuation (p-ADIC RINGS AND FIELDS)
Precision and Valuation (LOCAL RINGS AND FIELDS)
Precision and Valuation (p-ADIC RINGS AND FIELDS)
Appendix A: Precedence (MAGMA SEMANTICS)
Appendix B: Reserved Words (MAGMA SEMANTICS)
AbsolutePrecision(x) : RngLocElt -> RngIntElt
AbsolutePrecision(f) : RngSerElt -> RngIntElt
ChangePrecision(L, r) : RngLoc, RngIntElt -> RngLoc
ChangePrecision(P, r) : RngLoc, RngIntElt -> RngLoc
ChangePrecision(x, m) : RngLocElt, RngIntElt -> RngLocElt
ExpandToPrecision(f, c, n) : RngUPolElt, RngSerPuisElt -> RngSerPuisElt
IsSinglePrecision(n) : RngIntElt -> BoolElt
Precision(R) : FldCom -> RngIntElt
Precision(s) : FldPrElt -> RngIntElt
Precision(r) : FldReElt -> RngIntElt
Precision(M) : ModFrm -> RngIntElt
Precision(L) : RngLoc -> RngIntElt
Precision(P) : RngLoc -> RngIntElt
Precision(x) : RngLocElt -> RngIntElt
Precision(R) : RngSer -> Rng
PrecisionBound(M : parameters) : ModFrm -> RngIntElt
PrintToPrecision(s, n) : RngPowLazElt, RngIntElt ->
RelativePrecision(x) : RngLocElt -> RngIntElt
RelativePrecision(f) : RngSerElt -> RngIntElt
SetKantPrecision(O, n) : RngOrd, RngIntElt ->
SetPrecision(M, prec) : ModFrm, RngIntElt ->
SuggestedPrecision(f) : RngUPolElt -> RngIntElt
SuggestedPrecision(f) : RngUPolElt -> RngIntElt
Fixed Precision Real Numbers (REAL AND COMPLEX FIELDS)
Free and Fixed Precision (POWER, LAURENT AND PUISEUX SERIES)
Precision (POWER, LAURENT AND PUISEUX SERIES)
Precision (POWER, LAURENT AND PUISEUX SERIES)
Precision (REAL AND COMPLEX FIELDS)
PrecisionBound(M : parameters) : ModFrm -> RngIntElt
Predicates on Elements (ALGEBRAIC FUNCTION FIELDS)
Predicates on Lazy Series (LAZY POWER SERIES RINGS)
Structure Predicates (ALGEBRAIC FUNCTION FIELDS)
Booleans (OVERVIEW)
Ideal Predicates (IDEAL THEORY AND GRÖBNER BASES)
Predicates (RING OF INTEGERS)
Predicates and Boolean Operations (INTRODUCTION [BASIC RINGS])
Predicates on Ring Elements (VALUATION RINGS)
Ring Predicates and Booleans (CHARACTERS OF FINITE GROUPS)
Ring Predicates and Booleans (FINITE FIELDS)
Ring Predicates and Booleans (GALOIS RINGS)
Ring Predicates and Booleans (RATIONAL FUNCTION FIELDS)
Ring Predicates and Booleans (RING OF INTEGERS)
Ring Predicates and Properties (ALGEBRAICALLY CLOSED FIELDS)
Predicates (CHAIN COMPLEXES)
AlgLie_Predicates (Example H76E9)
ModForm_Predicates (Example H93E10)
ModSS_Predicates (Example H92E6)
Basic Attributes (SUBGROUPS OF PSL_2(R))
Basic Attributes (SUBGROUPS OF PSL_2(R))
Basic Functions (SUBGROUPS OF PSL_2(R))
Creation Predicates (ELLIPTIC CURVES)
Creation Predicates (HYPERELLIPTIC CURVES)
Predicates (BASIC ALGEBRAS)
Predicates (CHAIN COMPLEXES)
Predicates (CLASS FIELD THEORY)
Predicates (FINITE SOLUBLE GROUPS)
Predicates (LIE ALGEBRAS)
Predicates (MATRICES)
Predicates (MODULAR FORMS)
Predicates (MODULES OVER AFFINE ALGEBRAS)
Predicates (MODULES OVER AFFINE ALGEBRAS)
Predicates (SPARSE MATRICES)
Predicates ({THE MODULE OF}{SUPERSINGULAR POINTS})
Predicates and Booleans on Lattices (LATTICES)
Predicates for Elements (FINITE SOLUBLE GROUPS)
Predicates for Subgroups (FINITE SOLUBLE GROUPS)
Predicates on Algebras (QUATERNION ALGEBRAS)
Predicates on Curve Models (ELLIPTIC CURVES)
Predicates on Curve Models (HYPERELLIPTIC CURVES)
Predicates on Elements (CYCLOTOMIC FIELDS)
Predicates on Elliptic Curves (ELLIPTIC CURVES)
Predicates on Point Sets (ELLIPTIC CURVES)
Predicates on Points (ELLIPTIC CURVES)
Predicates on Subgroup Schemes (ELLIPTIC CURVES)
Structure Predicates (ALGEBRAIC FUNCTION FIELDS)
Structure Predicates (ALGEBRAIC FUNCTION FIELDS)
Structure Predicates (ALGEBRAIC FUNCTION FIELDS)
Basic Attributes (SUBGROUPS OF PSL_2(R))
Basic Functions (SUBGROUPS OF PSL_2(R))
Predicates on Elements (ALGEBRAS)
PREFACE
PREFACE
AssignNamePrefix(A, S) : FldAC, MonStgElt ->
IsGlobalUnitWithPreimage(a) : FldFunElt -> BoolElt, GrpAbElt
IsGlobalUnitWithPreimage(a) : FldFunElt -> BoolElt, GrpAbElt
IsSUnitWithPreimage(a, S) : FldFunElt, SetEnum[PlcFunElt] -> BoolElt, GrpAbElt
IsUnitWithPreimage(a) : RngFunOrdElt -> BoolElt, GrpAbElt
PreimageIdeal(I) : RngMPolRes -> RngMPol
PreimageRing(I) : RngMPolRes -> RngMPol
PreimageRing(Q) : RngUPolRes -> RngUPol
Images and Preimages (MAPPINGS)
PreimageIdeal(I) : RngMPolRes -> RngMPol
PreimageRing(I) : RngMPolRes -> RngMPol
PreimageRing(Q) : RngUPolRes -> RngUPol
Gathering the Data (THE K3 DATABASE)
PreparataCode(m): RngIntElt, RngUPolElt -> Code
PreparataCode(m, h): RngIntElt, RngUPolElt -> Code
PreparataCode(m): RngIntElt, RngUPolElt -> Code
PreparataCode(m, h): RngIntElt, RngUPolElt -> Code
Preprune(C) : ModCpx -> ModCpx
Preprune(C,n) : ModCpx, RngIntElt -> ModCpx
CompactPresentation(G) : GrpPC -> [RngIntElt]
IsIdenticalPresentation(G, H) : GrpGPC, GrpGPC -> BoolElt
IsIdenticalPresentation(G, H) : GrpPC, GrpPC -> BoolElt
NilpotentPresentation(G) : GrpGPC -> GrpGPC, Map
PresentationIsSmall(G) : GrpGPC -> BoolElt
PresentationLength(G) : GrpFP -> RngIntElt
PresentationLength(P) : Process(Tietze) -> RngIntElt
Simplify(~P : parameters) : Process(Tietze) ->
SpecialPresentation(G) : GrpPC -> GrpPC
StandardPresentation(G): GrpPC -> GrpPC, Map
Actions (COXETER GROUPS)
Braid Groups (COXETER GROUPS)
CompactPresentation (FINITE SOLUBLE GROUPS)
Conditioned Presentations (FINITE SOLUBLE GROUPS)
Constructing a Presentation for a Subgroup (FINITELY PRESENTED GROUPS)
Construction of a Quotient: Specification of a Presentation (FINITELY PRESENTED ALGEBRAS)
Conversion (COXETER GROUPS)
Creation (COXETER GROUPS)
Finitely Presented Coxeter Groups (COXETER GROUPS)
Generators and Relations (MATRIX GROUPS)
Isomorphism testing and Standard Presentations (p-GROUPS)
Operations on FP Coxeter Groups (COXETER GROUPS)
Operations on Words (COXETER GROUPS)
Presentation of Submodules (FREE MODULES)
Properties of a Polycyclic Presentation (POLYCYCLIC GROUPS)
Special Presentations (FINITE SOLUBLE GROUPS)
Specification of a Presentation (ABELIAN GROUPS)
Specification of a Presentation (FINITELY PRESENTED SEMIGROUPS)
Structuring Presentations (FINITELY PRESENTED ALGEBRAS)
The Presentation of Submodules (INTRODUCTION [LINEAR ALGEBRA AND MODULE THEORY])
Actions (COXETER GROUPS)
Braid Groups (COXETER GROUPS)
Conversion (COXETER GROUPS)
Creation (COXETER GROUPS)
Operations on Words (COXETER GROUPS)
Operations on FP Coxeter Groups (COXETER GROUPS)
Properties of a Polycyclic Presentation (POLYCYCLIC GROUPS)
PresentationIsSmall(G) : GrpGPC -> BoolElt
PresentationLength(G) : GrpFP -> RngIntElt
PresentationLength(P) : Process(Tietze) -> RngIntElt
Modifying Presentations (FP GROUPS - ADVANCED FEATURES)
More About Presentations (FINITE SOLUBLE GROUPS)
Power-Conjugate Presentations (FINITE SOLUBLE GROUPS)
Presentations (PERMUTATION GROUPS)
FINITELY PRESENTED ALGEBRAS
Finitely Presented Algebras (FINITELY PRESENTED ALGEBRAS)
FINITELY PRESENTED GROUPS
Finitely Presented Modules (FINITELY PRESENTED ALGEBRAS)
FINITELY PRESENTED SEMIGROUPS
FP GROUPS - ADVANCED FEATURES
Rings, Fields, and Algebras (OVERVIEW)
ClearPrevious() : ->
GetPreviousSize() : -> RngIntElt
PreviousPrime(n) : RngIntElt -> RngIntElt
SetPreviousSize(n) : RngIntElt ->
ShowPrevious() : ->
ShowPrevious(i) : RngIntElt ->
PrimeDivisors(n) : RngIntElt -> [RngIntElt]
Other Functions Relating to Primes (RING OF INTEGERS)
PreviousPrime(n) : RngIntElt -> RngIntElt
Primality (RING OF INTEGERS)
IsPrimary(I) : RngMPol -> BoolElt
IsPrimary(I) : RngMPolRes -> BoolElt
Primary(a) : RngQuadElt -> RngQuadElt
PrimaryAlgebra(R) : RngInvar -> RngMPol
PrimaryComponents(X) : Sch -> SeqEnum
PrimaryDecomposition(I) : RngMPol -> [ RngMPol ], [ RngMPol ]
PrimaryDecomposition(I) : RngMPolRes -> [ RngMPolRes ], [ RngMPolRes ]
PrimaryIdeal(R) : RngInvar -> RngMPol
PrimaryInvariantFactors(a) : AlgMatElt -> [ <RngUPolElt, RngIntElt ]
PrimaryInvariantFactors(A) : Mtrx -> [ <RngUPolElt, RngIntElt> ]
R`PrimaryInvariants
PrimaryInvariants(A) : GrpAb -> [ RngIntElt ]
PrimaryInvariants(R) : RngInvar -> [ RngMPolElt ]
PrimaryRationalForm(a) : AlgMatElt -> AlgMatElt, AlgMatElt, [ <RngUPolElt, RngIntElt ]
PrimaryRationalForm(A) : Mtrx -> AlgMatElt, AlgMatElt, [ <RngUPolElt, RngIntElt ]
Primary Decomposition (IDEAL THEORY AND GRÖBNER BASES)
Primary Invariants (INVARIANT RINGS OF FINITE GROUPS)
Primary Decomposition (IDEAL THEORY AND GRÖBNER BASES)
PrimaryAlgebra(R) : RngInvar -> RngMPol
PrimaryComponents(X) : Sch -> SeqEnum
PrimaryDecomposition(I) : RngMPol -> [ RngMPol ], [ RngMPol ]
PrimaryDecomposition(I) : RngMPolRes -> [ RngMPolRes ], [ RngMPolRes ]
GB_PrimaryDecomposition (Example H66E18)
PrimaryIdeal(R) : RngInvar -> RngMPol
PrimaryInvariantFactors(a) : AlgMatElt -> [ <RngUPolElt, RngIntElt ]
PrimaryInvariantFactors(A) : Mtrx -> [ <RngUPolElt, RngIntElt> ]
R`PrimaryInvariants
PrimaryInvariants(A) : GrpAb -> [ RngIntElt ]
PrimaryInvariants(R) : RngInvar -> [ RngMPolElt ]
PrimaryRationalForm(a) : AlgMatElt -> AlgMatElt, AlgMatElt, [ <RngUPolElt, RngIntElt ]
PrimaryRationalForm(A) : Mtrx -> AlgMatElt, AlgMatElt, [ <RngUPolElt, RngIntElt ]
DegreeOnePrimeIdeals(O, B) : RngOrd, RngIntElt -> [ RngOrdIdl ]
DifferentiationSequence(x, n, a) : FldFunGElt, RngIntElt, FldFunGElt -> SeqEnum
IsPrime(x) : RngElt -> BoolElt
IsPrime(I) : RngFunOrdIdl -> BoolElt
IsPrime(n) : RngIntElt -> BoolElt
IsPrime(n) : RngIntElt -> BoolElt
IsPrime(I) : RngMPol -> BoolElt
IsPrime(I) : RngMPolRes -> BoolElt
IsPrime(I) : RngOrdIdl -> BoolElt, RngOrdIdl
IsPrimePower(n) : RngIntElt -> BoolElt, RngIntElt, RngIntElt
IsProbablePrime(n: parameter) : RngIntElt -> BoolElt
KeepPrimePower(SQP, p) : SQProc, RngIntElt -> SeqEnum
NextPrime(n) : RngIntElt -> RngIntElt
NumberOfPrimePolynomials(q, d) : RngIntElt, RngIntElt -> RngIntElt
PreviousPrime(n) : RngIntElt -> RngIntElt
Prime(P) : FldLoc -> RngIntElt
Prime(M) : ModSS -> RngIntElt
Prime(L) : RngLoc -> RngIntElt
Prime(G) : SymGenLoc -> RngIntElt
PrimeBasis(n) : RngIntElt -> [RngIntElt]
PrimeBasis(n) : RngIntElt -> [RngIntElt]
PrimeBasis(n) : RngIntElt -> [RngIntElt]
PrimeComponents(X) : Sch -> SeqEnum
PrimeField(F) : Fld -> Fld
PrimeField(F) : FldFin -> FldFin
PrimeForm(Q, p) : QuadBin, RngIntElt -> QuadBinElt
PrimeIdeal(S,p) : AlgQuatOrd, RngIntElt -> AlgQuatOrd
PrimePolynomials(R, d) : RngUPol, RngIntElt -> SeqEnum[ RngUPolElt ]
PrimeRing(F) : FldFun -> Rng
PrimeRing(R) : Rng -> Rng
PrimeRing(L) : RngLoc -> RngLoc
pAdicRing(L) : RngLoc -> RngLoc
RandomPrime(n: parameter) : RngIntElt -> RngIntElt
RandomPrime(n: parameter) : RngIntElt -> RngIntElt
RandomPrime(n, a, b, x: parameter) :RngIntElt, RngIntElt, RngIntElt -> BoolElt, RngIntElt
RandomPrime(n, a, b, x: parameter) :RngIntElt, RngIntElt, RngIntElt -> BoolElt, RngIntElt
RandomPrimePolynomial(R, d) : RngUPol, RngIntElt -> RngUPolElt
PrimeDivisors(n) : RngIntElt -> [RngIntElt]
Primes and Primality Testing (RING OF INTEGERS)
PrimeDivisors(n) : RngIntElt -> [RngIntElt]
PrimeBasis(n) : RngIntElt -> [RngIntElt]
PrimeBasis(n) : RngIntElt -> [RngIntElt]
PrimeComponents(X) : Sch -> SeqEnum
PrimeDivisors(n) : RngIntElt -> [RngIntElt]
PrimeBasis(n) : RngIntElt -> [RngIntElt]
PrimeBasis(n) : RngIntElt -> [RngIntElt]
PrimeField(F) : Fld -> Fld
PrimeField(F) : FldFin -> FldFin
PrimeRing(F) : FldFun -> Rng
PrimeRing(L) : RngLoc -> RngLoc
PrimeForm(Q, p) : QuadBin, RngIntElt -> QuadBinElt
PrimeIdeal(S,p) : AlgQuatOrd, RngIntElt -> AlgQuatOrd
PrimePolynomials(R, d) : RngUPol, RngIntElt -> SeqEnum[ RngUPolElt ]
PrimePowerRepresentation(x, k, a) : FldFunGElt, RngIntElt, FldFunGElt -> SeqEnum
DifferentiationSequence(x, n, a) : FldFunGElt, RngIntElt, FldFunGElt -> SeqEnum
PrimeField(F) : FldFun -> Rng
PrimeRing(F) : FldFun -> Rng
PrimeRing(R) : Rng -> Rng
PrimeRing(L) : RngLoc -> RngLoc
AddPrimes(SQP, p): SQProc, RngIntElt ->
BadPrimes(C) : CrvCon -> SeqEnum
BadPrimes(E) : CrvEll -> [ RngIntElt ]
BadPrimes(C) : CrvHyp -> SeqEnum
BadPrimes(J) : JacHyp -> SeqEnum
ExtensionPrimes(D, Q) : DB, MonStgElt -> SetEnum
GModulePrimes(G, A) : GrpFP, GrpFP -> SetMulti
GModulePrimes(G, A, B) : GrpFP, GrpFP, GrpFP -> SetMulti
GModulePrimes(G, A) : GrpGPC, GrpGPC -> SetMulti
GModulePrimes(G, A, B) : GrpGPC, GrpGPC, GrpGPC -> SetMulti
GetPrimes(SQP) : SQProc -> SetEnum, BoolElt
Primes(SQP): SQProc ->
PrintPrimes(SQP) : SQProc ->
RamifiedPrimes(A) : AlgQuat -> SeqEnum
ReplacePrimes(SQP, m): SQProc, SetEnum ->
Calculating the Relevant Primes (FP GROUPS - ADVANCED FEATURES)
Relevant Primes (FP GROUPS - ADVANCED FEATURES)
Contpp(f) : RngMPolElt -> RngIntElt, RngMPolElt
ContentAndPrimitivePart(f) : RngMPolElt -> RngIntElt, RngMPolElt
ContentAndPrimitivePart(p) : RngUPolElt -> RngIntElt, RngUPolElt
IsPrimitive(a) : FldAlgElt -> BoolElt
IsPrimitive(a) : FldFinElt -> BoolElt
IsPrimitive(G) : GrphUnd -> BoolElt
IsPrimitive(G) : GrpPerm -> BoolElt
IsPrimitive(G, Y) : GrpPerm, GSet -> BoolElt
IsPrimitive(G: parameters) : GrpMat -> BoolElt
IsPrimitive(n, m) : RngIntElt, RngIntElt -> BoolElt
IsPrimitive(n) : RngIntResElt -> BoolElt
IsPrimitive(f) : RngUPolElt -> BoolElt
IsolIsPrimitive(n, p, i) : RngIntElt, RngIntElt, RngIntElt -> BoolElt
NonPrimitiveAlternantCode(n,m,r) : RngIntElt,RngIntElt,RngIntElt->Code
NumberOfTransitiveGroups(d) : RngIntElt -> RngIntElt
PrimitiveElement(F) : FldFin -> FldFinElt
PrimitiveElement(K) : FldNum -> FldNumElt
PrimitiveElement(R) : RngIntRes -> RngIntResElt
PrimitiveElement(I) : RngOrdIdl -> RngOrdElt
PrimitivePart(f) : RngMPolElt -> RngMPolElt
PrimitivePart(p) : RngUPolElt -> RngUPolElt
PrimitivePolynomial(F, m) : FldFin, RngIntElt -> RngPolElt
PrimitiveQuotient(G) : GrpPerm -> GrpPerm, Hom, GrpPerm
PrimitiveRoot(m) : RngIntElt -> RngIntElt
PrimitiveWreathProduct(G, H) : GrpPerm, GrpPerm -> GrpPerm
PrimitiveWreathProduct(Q) : [ GrpPerm ] -> GrpPerm
SetPrimitiveElement(F, x) : FldFin, FldFinElt ->
TransitiveGroup(d) : RngIntElt -> GrpPerm, MonStgElt
TransitiveGroup(d, f) : RngIntElt, Program -> GrpPerm, MonStgElt
TransitiveGroup(d, n) : RngIntElt, RngIntElt -> GrpPerm, MonStgElt
TransitiveGroup(S, f) : [RngIntElt], Program -> GrpPerm, MonStgElt
TransitiveGroupDatabaseLimit() : -> RngIntElt
TransitiveGroupDescription(d, n) : RngIntElt, RngIntElt -> MonStgElt
TransitiveGroupProcess(d) : RngIntElt -> Process
TransitiveGroupProcess(d, f) : RngIntElt, Program -> Process
TransitiveGroupProcess(S) : [RngIntElt] -> Process
TransitiveGroupProcess(S, f) : [RngIntElt], Program -> Process
TransitiveGroups(d: parameters) : RngIntElt -> [GrpPerm]
TransitiveGroups(S: parameters) : [RngIntElt] -> [GrpPerm]
TransitiveGroups(d, f) : RngIntElt, Program -> [GrpPerm]
TransitiveGroups(S, f) : [RngIntElt], Program -> [GrpPerm]
Contpp(f) : RngMPolElt -> RngIntElt, RngMPolElt
Content and Primitive Part (MULTIVARIATE POLYNOMIAL RINGS)
Finding Special Elements (ORDERS AND ALGEBRAIC FIELDS)
Primitive Unitary Reflection Groups (REFLECTION GROUPS)
Special Elements (FINITE FIELDS)
Primitive Unitary Reflection Groups (REFLECTION GROUPS)
PrimitiveElement(F) : FldFin -> FldFinElt
PrimitiveElement(K) : FldNum -> FldNumElt
PrimitiveElement(R) : RngIntRes -> RngIntResElt
PrimitiveElement(I) : RngOrdIdl -> RngOrdElt
PrimitiveGroup(d) : RngIntElt -> GrpPerm, MonStgElt
TransitiveGroup(d) : RngIntElt -> GrpPerm, MonStgElt
TransitiveGroup(d, f) : RngIntElt, Program -> GrpPerm, MonStgElt
TransitiveGroup(d, n) : RngIntElt, RngIntElt -> GrpPerm, MonStgElt
TransitiveGroup(S, f) : [RngIntElt], Program -> GrpPerm, MonStgElt
PrimitiveGroupDatabaseLimit() : -> RngIntElt
TransitiveGroupDatabaseLimit() : -> RngIntElt
PrimitiveGroupDescription(d, n) : RngIntElt, RngIntElt -> MonStgElt
TransitiveGroupDescription(d, n) : RngIntElt, RngIntElt -> MonStgElt
PrimitiveGroupProcess(d) : RngIntElt -> Process
TransitiveGroupProcess(d) : RngIntElt -> Process
TransitiveGroupProcess(d, f) : RngIntElt, Program -> Process
TransitiveGroupProcess(S) : [RngIntElt] -> Process
TransitiveGroupProcess(S, f) : [RngIntElt], Program -> Process
PrimitiveGroups(d: parameters) : RngIntElt -> [GrpPerm]
TransitiveGroups(d: parameters) : RngIntElt -> [GrpPerm]
TransitiveGroups(S: parameters) : [RngIntElt] -> [GrpPerm]
TransitiveGroups(d, f) : RngIntElt, Program -> [GrpPerm]
TransitiveGroups(S, f) : [RngIntElt], Program -> [GrpPerm]
PrimitivePart(f) : RngMPolElt -> RngMPolElt
PrimitivePart(p) : RngUPolElt -> RngUPolElt
PrimitivePolynomial(F, m) : FldFin, RngIntElt -> RngPolElt
PrimitiveQuotient(G) : GrpPerm -> GrpPerm, Hom, GrpPerm
PrimitiveRoot(R) : RngIntRes -> RngIntResElt
PrimitiveElement(R) : RngIntRes -> RngIntResElt
PrimitiveRoot(m) : RngIntElt -> RngIntElt
GrpPerm_PrimitiveStructure (Example H20E26)
PrimitiveWreathProduct(G, H) : GrpPerm, GrpPerm -> GrpPerm
PrimitiveWreathProduct(Q) : [ GrpPerm ] -> GrpPerm
Primitivity Testing (MATRIX GROUPS)
PrincipalDivisor(a) : FldFunGElt -> DivFunElt
Divisor(a) : FldFunGElt -> DivFunElt
Id(R) : AlgChtr -> AlgChtrElt
IsPID(R) : Rng -> BoolElt
IsPIR(R) : Rng -> BoolElt
IsPrincipal(D) : DivCrvElt -> BoolElt,FldFunRatMElt
IsPrincipal(I) : RngFunOrdIdl -> BoolElt, FldFunElt
IsPrincipal(I) : RngMPol -> BoolElt, RngMPolElt
IsPrincipal(I) : RngOrdFracIdl -> BoolElt, FldOrdElt
IsPrincipalIdealRing(F) : FldAlg -> BoolElt
IsPrincipalIdealRing(O) : RngOrd -> BoolElt
PrincipalDivisor(Div,f) : DivCrv, FldFunElt -> DivCrvElt
PrincipalDivisorMap(F) : FldFun -> Map
PrincipalIdealMap(O) : RngFunOrd -> Map
Identity(R) : AlgChtr -> AlgChtrElt
One(R) : AlgChtr -> AlgChtrElt
PrincipalCharacter(G) : Grp -> AlgChtrElt
Id(R) : AlgChtr -> AlgChtrElt
PrincipalDivisor(a) : FldFunGElt -> DivFunElt
Divisor(a) : FldFunGElt -> DivFunElt
PrincipalDivisor(Div,f) : DivCrv, FldFunElt -> DivCrvElt
PrincipalDivisorMap(F) : FldFun -> Map
PrincipalIdealMap(O) : RngFunOrd -> Map
PrintCollector(SQP) : SQProc ->
PrintExtensions(SQP) : SQProc ->
PrintFile(F, x) : MonStgElt, Var ->
PrintFile(F, x, L) : MonStgElt, Var, MonStgElt ->
PrintFileMagma(F, x) : MonStgElt, Var ->
PrintModules(SQP) : SQProc ->
PrintPrimes(SQP) : SQProc ->
PrintProcess(SQP) : SQProc ->
PrintQuotient(SQP) : SQProc ->
PrintRelat(SQP) : SQProc ->
PrintSeries(SQP) : SQProc ->
PrintTermsOfDegree(s, l, n) : RngPowLazElt, RngIntElt, RngIntElt ->
PrintToPrecision(s, n) : RngPowLazElt, RngIntElt ->
SetPrintLevel(l) : MonStgElt ->
Access Functions (FP GROUPS - ADVANCED FEATURES)
Automatic Printing (INPUT AND OUTPUT)
Print Names (MULTIVARIATE POLYNOMIAL RINGS)
Printing (INPUT AND OUTPUT)
The print-Statement (INPUT AND OUTPUT)
The print statement (OVERVIEW)
print expression;
Access Functions (FP GROUPS - ADVANCED FEATURES)
PrintCollector(SQP) : SQProc ->
PrintExtensions(SQP) : SQProc ->
The printf and fprintf Statements (INPUT AND OUTPUT)
printf format, expression, ..., expression;
IO_printf (Example H3E4)
IO_printf (Example H3E6)
IO_printf2 (Example H3E5)
Write(F, x) : MonStgElt, Var ->
PrintFile(F, x) : MonStgElt, Var ->
PrintFile(F, x, L) : MonStgElt, Var, MonStgElt ->
PrintFileMagma(F, x) : MonStgElt, Var ->
SetKantPrinting(f) : BoolElt -> BoolElt
SetPowerPrinting(F, l) : FldFin, BoolElt ->
Printing to a File (INPUT AND OUTPUT)
Printing to a File (INPUT AND OUTPUT)
PrintModules(SQP) : SQProc ->
Generator Assignment (OVERVIEW)
PrintPrimes(SQP) : SQProc ->
PrintProcess(SQP) : SQProc ->
PrintQuotient(SQP) : SQProc ->
PrintRelat(SQP) : SQProc ->
PrintSeries(SQP) : SQProc ->
PrintTermsOfDegree(s, l, n) : RngPowLazElt, RngIntElt, RngIntElt ->
PrintToPrecision(s, n) : RngPowLazElt, RngIntElt ->
IsProbablyPrime(n: parameter) : RngIntElt -> BoolElt
IsProbablePrime(n: parameter) : RngIntElt -> BoolElt
ProbableRadicalDecomposition(I) : RngMPol -> [ RngMPol ]
ProbableRadicalDecomposition(I) : RngMPol -> [ RngMPol ]
IsProbablyPrime(n: parameter) : RngIntElt -> BoolElt
IsProbablePrime(n: parameter) : RngIntElt -> BoolElt
IsProbablyMaximal(G, H: parameters) : GrpPerm, GrpPerm -> BoolElt
IsProbablyPermutationPolynomial(p) : RngUPolElt -> BoolElt
IsProbablySupersingular(E) : CrvEll -> BoolElt
Procedure Expressions (OVERVIEW)
p := proc< x_1, ..., x_n: parameters | expression >;
Functions and Procedures (FUNCTIONS, PROCEDURES AND PACKAGES)
FUNCTIONS, PROCEDURES AND PACKAGES
Functions, Procedures, and Mappings (OVERVIEW)
Procedure Expressions (MAGMA SEMANTICS)
Procedures (FUNCTIONS, PROCEDURES AND PACKAGES)
Procedures (OVERVIEW)
p := procedure(x_1, ..., x_n: parameters) statements : ->
Procedure Expressions (MAGMA SEMANTICS)
Func_Procedures (Example H2E4)
AbsolutelyIrreducibleRepresentationProcessDelete( P) : SolRepProc ->
CentralExtensionProcess(G, U) : GrpPC, GrpPC -> Proc
CloseVectorsProcess(L, w, u) : Lat, ModTupRngElt, RngElt -> LatEnumProc
CosetEnumerationProcess(G, H: parameters) : GrpFP, GrpFP -> GrpFPCosetEnumProc
ExtensionProcess(G, M, F) : GrpFin, ModRng, GrpFinFP -> Process
ExtensionProcess(G, M, F) : GrpPerm, ModRng, GrpFP -> Process
IsolProcess() : -> Process
IsolProcessOfDegree(d) : . -> Process
IsolProcessOfDegreeField(d, p) : ., . -> Process
IsolProcessOfField(p) : . -> Process
LowIndexProcess(G, R : parameters) : GrpFP, RngIntElt -> Process(Lix)
PrintProcess(SQP) : SQProc ->
RandomProcess(G) : GrpAb -> Process
RandomProcess(G) : GrpFin -> Process
RandomProcess(G) : GrpGPC -> Process
RandomProcess(G) : GrpMat -> Process
RandomProcess(G) : GrpPC -> Process
RandomProcess(G) : GrpPerm -> Process
RandomProcess(G) : GrpSLP -> Process
SetProcessParameters(~P: parameters) : GrpFPCosetEnumProc ->
ShortVectorsProcess(L, u) : Lat, RngElt -> LatEnumProc
SmallGroupProcess(o: parameters) : RngIntElt -> Process
SmallGroupProcess(o, f: parameters) : RngIntElt, Program -> Process
SmallGroupProcess(S: parameters) : [RngIntElt] -> Process
SmallGroupProcess(S, f: parameters) : [RngIntElt], Program -> Process
SolubleQuotientProcess(F : parameters): GrpFP -> SQProc
TietzeProcess(G: parameters) : GrpFP -> Process(Tietze)
TransitiveGroupProcess(d) : RngIntElt -> Process
TransitiveGroupProcess(d, f) : RngIntElt, Program -> Process
TransitiveGroupProcess(S) : [RngIntElt] -> Process
TransitiveGroupProcess(S, f) : [RngIntElt], Program -> Process
TransversalProcess(G, H) : GrpPerm, GrpPerm -> GrpPermTransProc
TransversalProcessNext(P) : GrpPermTransProc -> GrpPermElt
TransversalProcessRemaining(P) : GrpPermTransProc -> RngIntElt
pQuotientProcess(F, p, c: parameters) : GrpFP, RngIntElt, RngIntElt -> Process
Calculation of Standard Sections (FP GROUPS - ADVANCED FEATURES)
Initialisation (FP GROUPS - ADVANCED FEATURES)
Miscellaneous Functions (FP GROUPS - ADVANCED FEATURES)
Processes (DATABASES OF GROUPS)
Processes (DATABASES OF GROUPS)
Processes (DATABASES OF GROUPS)
Short and Close Vector Processes (LATTICES)
Soluble Quotient Process Tools (FP GROUPS - ADVANCED FEATURES)
Soluble Quotient Processes (FP GROUPS - ADVANCED FEATURES)
The p-Quotient Process (FP GROUPS - ADVANCED FEATURES)
InnerProduct(u, v) : ModTupFldElt, ModTupFldElt -> FldElt
(u, v) : ModTupFldElt, ModTupFldElt -> FldElt
(u, v) : ModTupRngElt, ModTupRngElt -> RngElt
(u, v) : ModTupRngElt, ModTupRngElt : -> RngElt
(u, v) : ModTupRngElt, ModTupRngElt : -> RngElt
BasisProduct(A, i, j) : AlgGen, RngIntElt, RngIntElt -> AlgGenElt
CartesianProduct(G, H) : GrphDir, GrphDir -> GrphDir
CartesianProduct(R, S) : Str, ..., Str -> SetCart
DecomposeTensorProduct(D, w, x) : RootDtm, [ ], [ ] -> [ ModTupRngElt ], [ RngIntElt ]
DirectProduct(C, D) : Code, Code -> Code
DirectProduct(C, D) : Code, Code -> Code
DirectProduct(G, H) : Grp, Grp -> Grp
DirectProduct(G, H) : GrpFP, GrpFP -> GrpFP
DirectProduct(G, H) : GrpGPC, GrpGPC -> GrpGPC, [Map], [Map]
DirectProduct(G, H) : GrpMat, GrpMat -> GrpMat
DirectProduct(G, H) : GrpPC, GrpPC -> GrpPC, [Map], [Map]
DirectProduct(G, H) : GrpPerm, GrpPerm -> GrpPerm, [ Hom(Grp) ], [ Hom(Grp) ]
DirectProduct(A,B) : Prj,Prj -> PrjProd,SeqEnum
DirectProduct(A,B) : Sch,Sch -> Sch,SeqEnum
DirectProduct(R, S) : SgpFP, SgpFP -> SgpFP
DirectProduct(Q) : [ Grp ] -> Grp
DirectProduct(Q) : [ GrpFP ] -> GrpFP
DirectProduct(Q) : [ GrpMat ] -> GrpMat
DirectProduct(Q) : [ GrpPerm ] -> GrpPerm, [ Hom(Grp) ], [ Hom(Grp) ]
DirectProduct(Q) : [GrpPC] -> GrpPC, [ Map ], [ Map ]
FreeProduct(G, H) : GrpFP, GrpFP -> GrpFP
FreeProduct(R, S) : SgpFP, SgpFP -> SgpFP
FreeProduct(Q) : [ GrpFP ] -> GrpFP
InnerProduct(x, y) : AlgChtrElt, AlgChtrElt -> FldCycElt
InnerProduct(a, b) : AlgGenElt, AlgGenElt -> RngElt
InnerProduct(v, w) : LatElt, LatElt -> RngElt
InnerProduct(x,y) : ModBrdtElt, ModBrdtElt -> RngElt
InnerProductMatrix(L) : Lat -> AlgMatElt
InnerProductMatrix(M) : ModBrdt -> AlgMatElt
KroneckerProduct(A, B) : Mtrx, Mtrx -> Mtrx
LexProduct(G, H) : GrphDir, GrphDir -> GrphDir
PrimitiveWreathProduct(G, H) : GrpPerm, GrpPerm -> GrpPerm
PrimitiveWreathProduct(Q) : [ GrpPerm ] -> GrpPerm
ProductProjectiveSpace(k,N) : Rng,SeqEnum -> PrjScrl
ProductRepresentation(a) : FldFunGElt -> [FldFunGElt], [RngIntElt]
ProductRepresentation(Q, S) : [FldFunGElt], [RngIntElt] -> FldFunGElt
TensorProduct(A, B) : AlgBas, AlgBas-> AlgBas
TensorProduct(A, B) : AlgMat, AlgMat -> AlgMat
TensorProduct(a, b) : AlgMatElt, AlgMatElt -> AlgMatElt
TensorProduct(G, H) : GrphDir, GrphDir -> GrphDir
TensorProduct(L, M) : Lat, Lat -> Lat
TensorProduct(M, N) : ModGrp, ModGrp -> ModGrp
TensorProduct(U, V) : ModTupFld, ModTupFld -> FldElt
TensorProduct(u, v) : ModTupFldElt, ModTupFldElt -> FldElt
TensorWreathProduct(G, H) : GrpMat, GrpPerm -> GrpMat
WordProduct( F, w1, w2 ) : GrpFP, GrpFPElt, GrpFPElt -> GrpFPElt
WreathProduct(G, H) : GrpMat, GrpPerm -> GrpMat
WreathProduct(G, H) : GrpPC, GrpPC -> GrpPC
WreathProduct(G, H, f) : GrpPC, GrpPC, Map -> GrpPC
WreathProduct(G, H) : GrpPerm, GrpPerm -> GrpPerm, SeqEnum[Map], Map, Map
WreathProduct(Q) : [ GrpPerm ] -> GrpPerm
KSpace(K, n, F) : Fld, RngIntElt, Mtrx -> ModTupFld
Construction of a Vector Space with Inner Product Matrix (VECTOR SPACES)
Inner Products (FREE MODULES)
Operators (OVERVIEW)
Tensor Products (MATRIX GROUPS)
The Cartesian Product Constructors (SETS)
TUPLES AND CARTESIAN PRODUCTS
Unions and Products of Graphs (GRAPHS)
ProductProjectiveSpace(k,N) : Rng,SeqEnum -> PrjScrl
ProductRepresentation(a) : FldFunGElt -> [FldFunGElt], [RngIntElt]
ProductRepresentation(Q, S) : [FldFunGElt], [RngIntElt] -> FldFunGElt
BasisProducts(A) : AlgGen -> [[ AlgGenElt ]]
AlgMat_Products (Example H73E5)
GrpPerm_Products (Example H20E8)
Direct Products and Wreath Products (PERMUTATION GROUPS)
Tensor Products of K[G]-Modules (K[G]-MODULES AND GROUP REPRESENTATIONS)
Seq_Progression (Example H8E1)
Set_Progression (Example H7E5)
Sequences (OVERVIEW)
Sets (OVERVIEW)
The Arithmetic Progression Constructors (SEQUENCES)
The Arithmetic Progression Constructors (SETS)
Proj(R) : RngMPolRes -> Sch,Prj
ProjectiveSpace(R) : RngMPol -> Prj
Crv_proj-cl-commutes (Example H84E7)
Projection(X,Y) : Prj,Prj -> MapSch
Projection(X, Q) : Sch, Prj -> Sch, MapSch
ProjectionChains(X,DB) : VSrfK3,SeqEnum -> SeqEnum
ProjectionFromNonsingularPoint(X,p) : Sch,Pt -> Sch,MapSch,Sch
ProjectionChains(X,DB) : VSrfK3,SeqEnum -> SeqEnum
ProjectionFromNonsingularPoint(X,p) : Sch,Pt -> Sch,MapSch,Sch
CompactProjectiveResolution(M, n) : ModAlg, RngIntElt -> Tup
Curve(Div) : DivCrv -> Crv
Curve(D) : DivCrvElt -> Crv
Curve(F) : FldFun -> Crv
Curve(P) : PlcCrv -> Crv
Curve(P) : PlcCrvElt -> Crv
DimensionsOfProjectiveModules(B) : AlgBas -> SeqEnum
FactoredProjectiveOrder(a) : AlgMatElt -> [ <RngIntElt, RngIntElt> ]
FactoredProjectiveOrder(A) : AlgMatElt -> [ <RngIntElt, RngIntElt> ], RngElt
FiniteProjectivePlane(D) : Inc -> Plane, PlanePtSet, PlaneLnSet
FiniteProjectivePlane(W) : ModTupFld -> PlaneProj
FiniteProjectivePlane< v | X : parameters > : RngIntElt, List -> PlaneProj
IsOrdinaryProjective(X) : Sch -> BoolElt
IsOrdinaryProjectiveSpace(X) : Sch -> BoolElt
IsProjective(C) : Code -> BoolElt
IsProjective(M) : ModAlg -> BoolElt, SeqEnum
IsProjective(X) : Sch -> BoolElt
IsProjectiveSpace(X) : Sch -> BoolElt
MakeProjectiveClosureMap(A, P, S) : Aff,Prj,SeqEnum ->
PGO(arguments)
PGOMinus(arguments)
PGOPlus(arguments)
PSO(arguments)
PSOMinus(arguments)
PSOPlus(arguments)
ProductProjectiveSpace(k,N) : Rng,SeqEnum -> PrjScrl
ProjectiveClosure(f) : MapSch -> MapSch
ProjectiveClosure(A): Sch -> Sch
ProjectiveClosure(C) : Sch -> Sch
ProjectiveClosure(X) : Sch -> Sch
ProjectiveClosureMap(A) : Aff -> MapSch
ProjectiveCover(M) : ModAlg -> ModAlg, ModMatFldElt, SeqEnum[ModMatFldElt], SeqEnum[ModMatFldElt], SeqEnum[RngIntElt]
ProjectiveCurve(F) : FldFun -> Crv
ProjectiveEmbedding(P) : PlaneAff -> PlaneProj, PlanePtSet, PlaneLnSet, Map
ProjectiveGammaLinearGroup(arguments)
ProjectiveGammaUnitaryGroup(arguments)
ProjectiveGeneralLinearGroup(arguments)
ProjectiveGeneralUnitaryGroup(arguments)
ProjectiveModule(B, i) : AlgBas, RngIntElt -> ModRng
ProjectiveModule(B, S) : AlgBas, SeqEnum[RngIntElt] -> ModAlg, SeqEnum, SeqEnum
ProjectiveOmega(arguments)
ProjectiveOmegaMinus(arguments)
ProjectiveOmegaPlus(arguments)
ProjectiveOrder(a) : AlgMatElt -> RngIntElt
ProjectiveOrder(A) : AlgMatElt -> RngIntElt, RngElt
ProjectiveResolution(M, n) : ModAlg, RngIntElt -> ModCpx, ModMatFldElt
ProjectiveSigmaLinearGroup(arguments)
ProjectiveSigmaSymplecticGroup(arguments)
ProjectiveSigmaUnitaryGroup(arguments)
ProjectiveSpace(k,2) : Rng,RngIntElt -> Prj
ProjectiveSpace(k,n) : Rng,RngIntElt -> Prj
ProjectiveSpace(R) : RngMPol -> Prj
ProjectiveSpecialLinearGroup(arguments)
ProjectiveSpecialUnitaryGroup(arguments)
ProjectiveSuzukiGroup(arguments)
ProjectiveSymplecticGroup(arguments)
Combinatorial and Geometrical Structures (OVERVIEW)
Indecomposable Projective Modules (BASIC ALGEBRAS)
Projective Automorphisms (SCHEMES)
Projective Covers (BASIC ALGEBRAS)
The Connection between Projective and Affine Planes (FINITE PLANES)
The Connection between Projective and Affine Planes (FINITE PLANES)
Scheme_projective-automorphism-group (Example H83E26)
Projective Automorphisms (SCHEMES)
Scheme_projective-closure (Example H83E10)
Projective Covers (BASIC ALGEBRAS)
ProjectiveClosure(f) : MapSch -> MapSch
ProjectiveClosure(A): Sch -> Sch
ProjectiveClosure(C) : Sch -> Sch
ProjectiveClosure(X) : Sch -> Sch
PCMap(A) : Aff -> MapSch
ProjectiveClosureMap(A) : Aff -> MapSch
ProjectiveCover(M) : ModAlg -> ModAlg, ModMatFldElt, SeqEnum[ModMatFldElt], SeqEnum[ModMatFldElt], SeqEnum[RngIntElt]
ProjectiveCurve(Div) : DivCrv -> Crv
Curve(Div) : DivCrv -> Crv
Curve(D) : DivCrvElt -> Crv
Curve(F) : FldFun -> Crv
Curve(P) : PlcCrv -> Crv
Curve(P) : PlcCrvElt -> Crv
ProjectiveCurve(F) : FldFun -> Crv
ProjectiveEmbedding(P) : PlaneAff -> PlaneProj, PlanePtSet, PlaneLnSet, Map
PGammaL(arguments)
ProjectiveGammaLinearGroup(arguments)
PGammaU(arguments)
ProjectiveGammaUnitaryGroup(arguments)
PGL(arguments)
ProjectiveGeneralLinearGroup(arguments)
ProjectiveGeneralOrthogonalGroup(n, q) : RngIntElt, RngIntElt -> GrpPerm, {@ ModTupFldElt @}
PGO(arguments)
ProjectiveGeneralOrthogonalGroupMinus(n, q) : RngIntElt, RngIntElt -> GrpPerm, {@ ModTupFldElt @}
PGOMinus(arguments)
ProjectiveGeneralOrthogonalGroupPlus(n, q) : RngIntElt, RngIntElt -> GrpPerm, {@ ModTupFldElt @}
PGOPlus(arguments)
PGU(arguments)
ProjectiveGeneralUnitaryGroup(arguments)
ProjectiveModule(B, i) : AlgBas, RngIntElt -> ModRng
ProjectiveModule(B, S) : AlgBas, SeqEnum[RngIntElt] -> ModAlg, SeqEnum, SeqEnum
POmega(arguments)
ProjectiveOmega(arguments)
POmegaMinus(arguments)
ProjectiveOmegaMinus(arguments)
POmegaPlus(arguments)
ProjectiveOmegaPlus(arguments)
ProjectiveOrder(a) : AlgMatElt -> RngIntElt
ProjectiveOrder(A) : AlgMatElt -> RngIntElt, RngElt
ProjectivePlane(k) : Rng -> Prj
ProjectiveSpace(k,2) : Rng,RngIntElt -> Prj
ProjectiveResolution(M, n) : ModAlg, RngIntElt -> ModCpx, ModMatFldElt
NumberOfProjectives(A) : AlgBas -> RngIntElt
PSigmaL(arguments)
ProjectiveSigmaLinearGroup(arguments)
PSigmaSp(arguments)
ProjectiveSigmaSymplecticGroup(arguments)
PSigmaU(arguments)
ProjectiveSigmaUnitaryGroup(arguments)
ProjectivePlane(k) : Rng -> Prj
ProjectiveSpace(k,2) : Rng,RngIntElt -> Prj
ProjectiveSpace(k,n) : Rng,RngIntElt -> Prj
ProjectiveSpace(R) : RngMPol -> Prj
PSL(arguments)
ProjectiveSpecialLinearGroup(arguments)
ProjectiveSpecialOrthogonalGroup(n, q) : RngIntElt, RngIntElt -> GrpPerm, {@ ModTupFldElt @}
PSO(arguments)
ProjectiveSpecialOrthogonalGroupMinus(n, q) : RngIntElt, RngIntElt -> GrpPerm, {@ ModTupFldElt @}
PSOMinus(arguments)
ProjectiveSpecialOrthogonalGroupPlus(n, q) : RngIntElt, RngIntElt -> GrpPerm, {@ ModTupFldElt @}
PSOPlus(arguments)
PSU(arguments)
ProjectiveSpecialUnitaryGroup(arguments)
PSz(arguments)
ProjectiveSuzukiGroup(arguments)
PSp(arguments)
ProjectiveSymplecticGroup(arguments)
Projectivity(A,M) : Aff,Mtrx -> MapAutSch
Scheme_projectivity (Example H83E25)
Combinatorial and Geometrical Structures (OVERVIEW)
GetIgnorePrompt() : -> BoolElt
SetIgnorePrompt(b) : BoolElt ->
SetPrompt(s) : MonStgElt ->
Prompt (OVERVIEW)
HasPRoot(L) : RngLoc -> BoolElt
Properties (LOCAL RINGS AND FIELDS)
Properties (p-ADIC RINGS AND FIELDS)
Properties (LOCAL RINGS AND FIELDS)
Properties (p-ADIC RINGS AND FIELDS)
IsProper(I) : RngMPol -> BoolElt
IsProper(I) : RngMPolRes -> BoolElt
IsProperChainMap(f) : MapChn -> BoolElt
The Number Field Sieve (RING OF INTEGERS)
ModForm_Properties (Example H93E11)
ModSS_Properties (Example H92E4)
RootDtm_Properties (Example H33E8)
Abstract Properties of a Group (PERMUTATION GROUPS)
Basic Group Properties (FINITE SOLUBLE GROUPS)
Basic Group Properties (p-GROUPS)
Basic Invariants of a Matrix Group (MATRIX GROUPS)
Determinant and Other Properties (MATRICES)
Elementary Properties of a Subgroup (PERMUTATION GROUPS)
Elementary Properties of Subgroups (MATRIX GROUPS)
Geometrical Properties (SCHEMES)
Minimal and Characteristic Polynomials and Eigenvalues (MATRICES)
Properties (COXETER GROUPS)
Properties (MODULAR FORMS)
Properties (PARTITIONS, WORDS AND YOUNG TABLEAUX)
Properties ({THE MODULE OF}{SUPERSINGULAR POINTS})
Properties of a Polycyclic Presentation (POLYCYCLIC GROUPS)
Properties of AG--Codes (LINEAR CODES OVER FINITE FIELDS)
Properties of Elements (FINITE SOLUBLE GROUPS)
Properties of Incidence Geometries and Coset Geometries (INCIDENCE GEOMETRY)
Properties of Invariant Rings (INVARIANT RINGS OF FINITE GROUPS)
Properties of Lattices (LATTICES)
Properties of Module Elements (MODULES OVER A MATRIX ALGEBRA)
Properties of Root Data (ROOT DATA FOR LIE THEORY)
Properties of Subgroups (FINITE SOLUBLE GROUPS)
Properties of Vectors (FREE MODULES)
Properties of Root Data (ROOT DATA FOR LIE THEORY)
Elementary Properties of a Subgroup (PERMUTATION GROUPS)
Properties of Groups of Lie type (GROUPS OF LIE TYPE)
Properties (ALGEBRAICALLY CLOSED FIELDS)
IsProportional(X, k) : Mtrx, RngIntElt -> BoolElt, Tup
Prune(A) : FldAC ->
Prune(~S) : List ->
Prune(S) : List -> List
Prune(C) : ModCpx -> ModCpx
Prune(C,n) : ModCpx, RngIngElt -> ModCpx
Prune(~S) : SeqEnum ->
Prune(~T) : Tup ->
Prune(T) : Tup -> Tup
pSelmerGroup(O, p, S) : RngOrd O, prime p, { RngOrdIdl } -> G, m
pSelmerGroup(O, p, S) : RngOrd O, prime p, { RngOrdIdl } -> G, m
PseudoAdd(P1, P2, P3) : SrfKumPt, SrfKumPt, SrfKumPt -> SrfKumPt
PseudoAddMultiple(P1, P2, P3, n) : SrfKumPt, SrfKumPt, SrfKumPt, RngIntElt -> SrfKumPt
PseudoBasis(M) : ModDed -> SeqEnum
PseudoRemainder(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
PSEUDO-RANDOM BIT SEQUENCES
PSEUDO-RANDOM BIT SEQUENCES
PseudoAdd(P1, P2, P3) : SrfKumPt, SrfKumPt, SrfKumPt -> SrfKumPt
PseudoAddMultiple(P1, P2, P3, n) : SrfKumPt, SrfKumPt, SrfKumPt, RngIntElt -> SrfKumPt
PseudoBasis(M) : ModDed -> SeqEnum
PseudoRemainder(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
IsogenyMapPsi(I) : Map -> RngUPolElt
IsogenyMapPsiMulti(I) : Map -> RngUPolElt
IsogenyMapPsiSquared(I) : Map -> RngUPolElt
LogDerivative(s) : FldPrElt -> FldPrElt
PSigmaL(arguments)
ProjectiveSigmaLinearGroup(arguments)
ProjectiveSigmaSymplecticGroup(arguments)
ProjectiveSigmaUnitaryGroup(arguments)
PSigmaL(arguments)
ProjectiveSigmaLinearGroup(arguments)
PSigmaSp(arguments)
ProjectiveSigmaSymplecticGroup(arguments)
PSigmaU(arguments)
ProjectiveSigmaUnitaryGroup(arguments)
PSL(arguments)
ProjectiveSpecialLinearGroup(arguments)
PSL2(R) : Rng -> GrpPSL2
ProjectiveSpecialOrthogonalGroup(n, q) : RngIntElt, RngIntElt -> GrpPerm, {@ ModTupFldElt @}
PSO(arguments)
ProjectiveSpecialOrthogonalGroupMinus(n, q) : RngIntElt, RngIntElt -> GrpPerm, {@ ModTupFldElt @}
PSOMinus(arguments)
ProjectiveSpecialOrthogonalGroupPlus(n, q) : RngIntElt, RngIntElt -> GrpPerm, {@ ModTupFldElt @}
PSOPlus(arguments)
PSp(arguments)
ProjectiveSymplecticGroup(arguments)
PSU(arguments)
ProjectiveSpecialUnitaryGroup(arguments)
GrpAbGen_pSylowComputation (Example H17E5)
PSz(arguments)
ProjectiveSuzukiGroup(arguments)
Tests for Points and Faces (NEWTON POLYGONS)
Design_pts-blks-ops (Example H98E8)
DuvalPuiseuxExpansion(f, n) : RngUPolElt, RngIntElt -> SeqEnum
ParametrizationToPuiseux(T) : Tup -> SeqEnum
PuiseuxExpansion(f, n) : RngUPolElt, RngIntElt -> SeqEnum[RngSerPuisElt]
PuiseuxExponents(p) : RngSerElt -> SeqEnum
PuiseuxExponentsCommon(p, q) : RngSerElt, RngSerElt -> SeqEnum
PuiseuxSeriesRing(R) : Rng -> RngSerPuis
PuiseuxToParametrization(S) : RngSerElt -> Tup
FldAC_Puiseux (Example H52E3)
Puiseux Series (POWER, LAURENT AND PUISEUX SERIES)
PuiseuxExpansion(f, n) : RngUPolElt, RngIntElt -> SeqEnum[RngSerPuisElt]
PuiseuxExponents(p) : RngSerElt -> SeqEnum
PuiseuxExponentsCommon(p, q) : RngSerElt, RngSerElt -> SeqEnum
PuiseuxSeriesRing(R) : Rng -> RngSerPuis
PuiseuxToParametrization(S) : RngSerElt -> Tup
Pull-Back of an Element (GENERIC ABELIAN GROUPS)
Pullback(f,P) : MapIsoSch, PtHyp -> PtHyp
P @@ f : PtHyp, MapIsoSch -> PtHyp
Pullback(f,L) : AmbProjMap,LinSys -> LinSys
Pullback(f, N) : Map, ModGrp -> GrpFP
Pullback(N, f1, M1, f2, M2) : ModAlg, ModMatFldElt, ModAlg, ModMatFldElt, ModAlg -> ModAlg, ModMatFldElt, ModMatFldElt
PunctureCode(C, i) : Code, RngIntElt -> Code
PunctureCode(C, i) : Code, RngIntElt -> Code
PunctureCode(C, S) : Code, { RngIntElt } -> Code
PunctureCode(C, S) : Code, { RngIntElt } -> Code
PunctureCode(C, i) : Code, RngIntElt -> Code
PunctureCode(C, i) : Code, RngIntElt -> Code
PunctureCode(C, S) : Code, { RngIntElt } -> Code
PunctureCode(C, S) : Code, { RngIntElt } -> Code
NumberOfPunctures(C): Crv -> RngIntElt
PureBraidGroup( W ) : GrpCox -> GrpFP, Map
PureBraidGroup( F ) : GrpFP -> GrpFP, Map
PureLattice(L) : Lat -> Lat
PureBraidGroup( W ) : GrpCox -> GrpFP, Map
PureBraidGroup( F ) : GrpFP -> GrpFP, Map
PureLattice(L) : Lat -> Lat
IndentPush() : ->
PushThroughIsogeny(I, v) : Map, RngUPolElt -> RngUPolElt
Pushout(M, f1, N1, f2, N2) : ModAlg, ModMatFldElt, ModAlg, ModMatFldElt, ModAlg -> ModAlg, ModMatFldElt, ModMatFldElt
PushThroughIsogeny(I, v) : Map, RngUPolElt -> RngUPolElt
Put(F, S) : File, MonStgElt ->
Puts(F, S) : File, MonStgElt ->
[____] [____] [_____] [____] [__] [Index] [Root]