[____] [____] [_____] [____] [__] [Index] [Root]
Index P
P
d . eefpg : RngIntElt, RngIntElt, RngIntElt -> FldReElt
p
Generating p-groups (SOLUBLE GROUPS)
p-Adics (LOCAL FIELDS)
p-group Functions (MATRIX GROUPS)
p-Quotients (FINITELY PRESENTED GROUPS)
d . eefpg : RngIntElt, RngIntElt, RngIntElt -> FldReElt
p-adic
p-Adics (LOCAL FIELDS)
p-group
Generating p-groups (SOLUBLE GROUPS)
p-group Functions (MATRIX GROUPS)
P-key
P
p-key
p
p-Quotient
p-Quotients (FINITELY PRESENTED GROUPS)
package
FUNCTIONS, PROCEDURES AND PACKAGES
Packages (FUNCTIONS, PROCEDURES AND PACKAGES)
pAdicField
pAdicField(p) : RngIntElt -> FldAdic
pAdicRing
pAdicRing(p) : RngIntElt -> RngAdic
pair
Pair Reduction (LATTICES)
pair-reduce
Pair Reduction (LATTICES)
PairReduce
PairReduce(L) : Lat -> Lat, AlgMatElt
PairReduce(X) : ModMatRngElt -> ModMatRngElt, AlgMatElt
PairReduceGram
PairReduceGram(F) : ModMatRngElt -> ModMatRngElt, AlgMatElt, RngIntElt
ParallelClass
ParallelClass(P, l) : Plane, PlaneLn -> { PlaneLn }
ParallelClasses
ParallelClasses(P) : AffPl -> { { PlaneLn } }
parameter
Intrinsics (OVERVIEW)
Options and Controls (FINITELY PRESENTED ALGEBRAS)
Parameters
Parameters(D) : Dsgn -> Record
Func_Parameters (Example H2E2)
Parent
Parent(u) : AlgFPElt -> AlgFP
Parent(a) : AlgGenElt -> AlgGen
Parent(a) : AlgMatElt -> AlgMat
Parent(u) : GrpAbElt -> GrpAb
Parent(r) : GrpAbRel -> GrpAb
Parent(u) : GrpBBElt -> GrpBB
Parent(g) : GrpElt -> Grp
Parent(u) : GrpFPElt -> GrpFP
Parent(r) : GrpFPRel -> GrpFP
Parent(G) : GrpMatElt -> GrpMat
Parent(G) : GrpPC -> PowerStructure
Parent(x) : GrpPCElt -> GrpPC
Parent(g) : GrpPermElt -> GrpPerm
Parent(V) : ModFld -> SetPow
Parent(u) : ModTupElt -> ModRng
Parent(w): ModTupFldElt -> ModTupFld
Parent(R) : Rng -> Pow
Parent(r) : RngElt -> Rng
Parent(S) : Seq -> Struct
Parent(R) : Set -> Struct
Parent(u) : SgpFPElt -> SgpFP
Parent(T) : Tup -> SetCart
parent
Category and Parent (FUNCTION FIELDS AND THEIR ORDERS)
Category and Parent (NUMBER FIELDS AND THEIR ORDERS)
Parent and Category (CYCLOTOMIC FIELDS)
Parent and Category (FUNCTION FIELDS AND THEIR ORDERS)
Parent and Category (INTRODUCTION [RINGS AND FIELDS])
Parent and Category (MULTIVARIATE POLYNOMIAL RINGS)
Parent and Category (NUMBER FIELDS AND THEIR ORDERS)
Parent and Category (POWER SERIES AND LAURENT SERIES)
Parent and Category (QUADRATIC FIELDS)
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-category
Parent and Category (CYCLOTOMIC FIELDS)
Parent and Category (FUNCTION FIELDS AND THEIR ORDERS)
Parent and Category (MULTIVARIATE POLYNOMIAL RINGS)
Parent and Category (NUMBER FIELDS AND THEIR ORDERS)
Parent and Category (POWER SERIES AND LAURENT SERIES)
Parent and Category (QUADRATIC FIELDS)
Parent and Category (UNIVARIATE POLYNOMIAL RINGS)
Parent and Category (VALUATION RINGS)
parent-type
Parent and Category (INTRODUCTION [RINGS AND FIELDS])
ParentGraph
ParentGraph(S) : GrphVertSet -> Grph
parentheses
Expression (OVERVIEW)
parenthesis
Expression (OVERVIEW)
ParentPlane
ParentPlane(V) : PlanePtSet -> Plane, PlanePtSet, PlaneLnSet
ParityCheckMatrix
ParityCheckMatrix(C) : Code -> ModMatFldElt
parsing
Parsing Strings (INPUT AND OUTPUT)
Part
ALGEBRAS (PART)
FINITE INCIDENCE STRUCTURES (PART)
GEOMETRY (PART)
MODULES AND LATTICES (PART)
RINGS AND FIELDS (PART)
SEMIGROUPS AND GROUPS (PART)
SETS, SEQUENCES, AND MAPPINGS (PART)
THE MAGMA LANGUAGE (PART)
partial
Creation of Partial Maps (MAPPINGS)
Partial Fraction Decomposition (RATIONAL FUNCTION FIELDS)
Partial Mappings (OVERVIEW)
partial-fraction
Partial Fraction Decomposition (RATIONAL FUNCTION FIELDS)
partial-mapping
Creation of Partial Maps (MAPPINGS)
PartialFractionDecomposition
PartialFractionDecomposition(f) : FldFunUElt -> [ <RngUPolElt, RngIntElt, RngUPolElt> ]
FldFun_PartialFractionDecomposition (Example H31E3)
PartialMap
Partial Mappings (OVERVIEW)
Partition
Partition(S, p) : SeqEnum, RngIntElt -> SeqEnum(SeqEnum)
partition
Action on a G-invariant Partition (PERMUTATION GROUPS)
partition-action
Action on a G-invariant Partition (PERMUTATION GROUPS)
Partitions
Partitions(n) : RngIntElt -> [ [ RngIntElt ] ]
Partitions(n) : RngIntElt -> [ [ RngIntElt ] ]
EnumComb_Partitions (Example H54E2)
partitions
Partitions (ENUMERATIVE COMBINATORICS)
PascalTriangle
PascalTriangle(D) : Dsgn -> SeqEnum
path
Connectedness, Paths and Circuits (GRAPHS)
PathGraph
PathGraph(p) : RngIntElt -> GrphUnd
pc
Groups (OVERVIEW)
PCClass
PCClass(x) : GrpPCElt -> RngIntElt
pCentralSeries
pCentralSeries(G, p) : GrpFin, RngIntElt -> [ GrpFin ]
pCentralSeries(G, p) : GrpMat, RngIntElt -> [ GrpMat ]
pCentralSeries(G, p) : GrpPC, RngIntElt -> [GrpPC]
pCentralSeries(G, p) : GrpPerm, RngIntElt -> [ GrpPerm ]
PCGenerators
PCGenerators(G) : GrpPC -> {@ GrpPCElt @}
PCGroup
PCGroup(G) : Grp -> GrpPC, Hom(Grp)
PCGroup(A) : GrpAb -> GrpPC, Hom(Grp)
PCGroup(G) : GrpPerm -> GrpPC, Map
PCGroup(Q : parameters ) : [RngIntElt] -> GrpPC
PolycyclicGenerators(G) : GrpMat -> [ GrpPCElt ]
pClass
pClass(G) : GrpPC -> RngIntElt
pClass(P) : Process(pQuot) -> RngIntElt
pCore
pCore(G, p) : GrpAb, RngIntElt -> GrpAb
pCore(G, p) : GrpFin, RngIntElt -> GrpFin
[Future release] pCore(G, p) : GrpMat, RngIntElt -> GrpMat
pCore(G, S) : GrpPC, { RngIntElt } -> GrpPC
pCore(G, p) : GrpPerm, RngIntElt -> GrpPerm
pCover
pCover(G, F, p) : GrpFin, GrpFinFP, RngIntElt -> GrpFinFP
pCover(G, F, p) : GrpPerm, GrpFP, RngIntElt -> GrpFP
pCoveringGroup
pCoveringGroup(~P) : Process(pQuot) ->
PCPrimes
PCPrimes(G) : GrpPC -> [RngIntElt]
Pencil
Pencil(P, p) : Plane, PlanePt -> { PlaneLn }
Perfect
RngInt_Perfect (Example H24E6)
perfect
Database of Finite Perfect Groups (OVERVIEW)
PerfectSubgroups
PerfectSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
perfgps
Database of Finite Perfect Groups (OVERVIEW)
pergps
Database of Some Permutation Groups (OVERVIEW)
Permutation
Permutation(G, Q) : GrpPerm, [Elt] -> GrpPermElt
permutation
Database of Some Permutation Groups (OVERVIEW)
Permutation Character (CHARACTERS OF FINITE GROUPS)
Permutation Group Actions on Polynomials (INVARIANT RINGS OF FINITE GROUPS)
Permutation Group Predicates (PERMUTATION GROUPS)
PERMUTATION GROUPS
Permutation Representations for Database of Finite Perfect Groups (OVERVIEW)
permutation-group
Permutation Group Predicates (PERMUTATION GROUPS)
permutation-representation
Permutation Representations for Database of Finite Perfect Groups (OVERVIEW)
PermutationActionD8
AlgFP_PermutationActionD8 (Example H52E3)
PermutationCharacter
PermutationCharacter(G, H) : GrpMat, GrpMat -> AlgChtrElt
PermutationCharacter(G) : GrpPerm -> AlgChtrElt
PermutationCharacter(G) : GrpPerm -> AlgChtrElt
PermutationCharacter(G) : GrpPerm -> AlgChtrElt
PermutationCode
PermutationCode(u, G) : ModTupFldElt, GrpPerm -> Code
Code_PermutationCode (Example H58E3)
PermutationGroup
PermutationGroup(C) : Code -> GrpPerm, PowMap, Map
PermutationGroup(A) : GrpAb -> GrpPerm, Hom(Grp)
PermutationGroup< X | L > : Set, List -> GrpPerm
PermutationGroup< X | L > : Set, List -> GrpPerm, Hom
PermutationModule
PermutationModule(G, H, R) : Grp, Grp, Rng -> ModGrp
PermutationModule(G, H, R) : Grp, Grp, Rng -> ModGrp
PermutationModule(G, H, R) : GrpFin, GrpFin, Rng -> ModGrpFin
PermutationModule(G, H, R) : GrpMat, GrpMat, Rng -> ModGrp
Permutations
Permutations(S) : SetEnum -> SetEnum;
Permutations(S) : SetEnum -> SetEnum;
GrpPerm_Permutations (Example H20E2)
pFundamentalUnits
pFundamentalUnits(O, p) : RngOrd, RngIntElt -> GrpAb, Map
PGammaL
ProjectiveGammaLinearGroup(arguments)
PGammaU
ProjectiveGammaUnitaryGroup(arguments)
PGL
ProjectiveGeneralLinearGroup(arguments)
PGO
PGO(arguments)
PGOMinus
PGOMinus(arguments)
PGOPlus
PGOPlus(arguments)
PGU
ProjectiveGeneralUnitaryGroup(arguments)
Pi
Pi(R) : FldPr -> FldPrElt
pi
Hall pi-Subgroups and Sylow Systems (SOLUBLE GROUPS)
Pipe
Pipe(C, S) : MonStgElt, MonStgElt -> MonStgElt
Plane
Combinatorial and Geometrical Structures (OVERVIEW)
plane
FINITE PLANES
PlaneLn
Combinatorial and Geometrical Structures (OVERVIEW)
PlaneLnSet
Combinatorial and Geometrical Structures (OVERVIEW)
PlanePt
Combinatorial and Geometrical Structures (OVERVIEW)
PlanePtSet
Combinatorial and Geometrical Structures (OVERVIEW)
planes
Planes in Magma (FINITE PLANES)
planes-in-magma
Planes in Magma (FINITE PLANES)
PlayWithPoints
Elcu_PlayWithPoints (Example H53E11)
PlotkinAsymptoticBound
PlotkinAsymptoticBound(K, delta) : FldFin, FldPrElt -> FldPrElt
PlotkinBound
PlotkinBound(K, n, d) : FldFin, RngIntElt, RngIntElt -> RngIntElt
PlotkinSum
PlotkinSum(C, D) : Code, Code -> Code
plus
Operators (OVERVIEW)
pmap
Partial Mappings (OVERVIEW)
pmap< A -> B | G > : Struct, Struct -> Map
pMaximalOrder
pMaximalOrder(O, p) : RngOrd, RngIntElt -> RngOrd
pMinus1
pMinus1(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]
pMultiplicator
pMultiplicator(G, p) : GrpFin, RngIntElt -> [ RngIntElt ]
pMultiplicator(G, p) : GrpPerm, RngIntElt -> [ RngIntElt ]
pMultiplicatorRank
pMultiplicatorRank(G) : GrpPC -> RngIntElt
pMultiplicatorRank(P) : Process(pgaProc) -> RngIntElt
Point
Point(D, i) : Inc, RngIntElt -> IncPt
point
Combinatorial and Geometrical Structures (OVERVIEW)
Creating Points and Blocks (INCIDENCE STRUCTURES AND DESIGNS)
Creation of Points (ELLIPTIC CURVES)
Operations on Points (ELLIPTIC CURVES)
Operations on Points and Blocks (INCIDENCE STRUCTURES AND DESIGNS)
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)
point-block
Creating Points and Blocks (INCIDENCE STRUCTURES AND DESIGNS)
point-block-set
The Point-Set and Block-Set of an Incidence Structure (INCIDENCE STRUCTURES AND DESIGNS)
point-line
The Set of Points and Set of Lines (FINITE PLANES)
Using the Point-Set and Line-Set to Create Points and Lines (FINITE PLANES)
point-line-set
The Point-Set and Line-Set of a Plane (FINITE PLANES)
PointDegree
PointDegree(D, p) : Inc, IncPt -> RngIntElt
PointDegrees
PointDegrees(D) : Inc -> [ RngIntElt ]
PointGraph
PointGraph(D) : Inc -> Grph
PointGraph(D) : Inc -> GrphUnd
PointGraph(P) : Plane -> GrphUnd;
PointGroup
CollineationGroup(P) : Plane -> GrpPerm, GSet, GSet, PowMap, Map
PointGroup(D) : Inc -> GrpPerm, GSet
Points
Points(D) : Inc -> { IncPt }
Points(P) : Plane -> { PlanePt }
points-blocks
Design_points-blocks (Example H56E2)
points-lines
Plane_points-lines (Example H57E2)
PointSet
PointSet(D) : Inc -> IncPtSet
PointSet(P) : Plane -> PlanePtSet
PolarToComplex
PolarToComplex(m, a) : FldReElt, FldReElt -> FldComElt
PollardRho
PollardRho(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]
polycyclic
Introduction (SOLUBLE GROUPS)
polycyclic-power-conjugate
Introduction (SOLUBLE GROUPS)
PolycyclicGenerators
PolycyclicGenerators(G) : GrpMat -> [ GrpPCElt ]
PolycyclicGroup
Group< X | R > : List(Identifiers), List(GrpFPRel) -> GrpFP, Hom(Grp)
PolycyclicGroup< x_1, ..., x_n | R : parameters > : List(Identifiers), List(GrpFPRel) -> GrpPC, Map
GrpPC_PolycyclicGroup (Example H19E1)
PolygonGraph
PolygonGraph(p) : RngIntElt -> GrphUnd
Polylog
Polylog(m, s) : FldPrElt -> FldPrElt
PolylogD
PolylogD(m, s) : FldPrElt -> FldPrElt
PolylogDold
PolylogD(m, s) : FldPrElt -> FldPrElt
PolylogP
PolylogD(m, s) : FldPrElt -> FldPrElt
PolyMapKernel
PolyMapKernel(f) : Map -> RngMPol
polynomial
Database of Galois Group Polynomials (OVERVIEW)
Minimal and Characteristic Polynomial (FINITE FIELDS)
MULTIVARIATE POLYNOMIAL RINGS
Polynomials for Finite Fields (FINITE FIELDS)
Rings, Fields, and Algebras (OVERVIEW)
UNIVARIATE POLYNOMIAL RINGS
PolynomialAlgebra
PolynomialAlgebra(P) : Rng -> RngUPol
PolynomialRing(R, n) : Rng, RngIntElt -> RngMPol
PolynomialRing(R, Q) : Rng, [ RngIntElt ] -> RngMPol
PolynomialRing
PolynomialAlgebra(P) : Rng -> RngUPol
PolynomialRing(R, n) : Rng, RngIntElt -> RngMPol
PolynomialRing(R, Q) : Rng, [ RngIntElt ] -> RngMPol
PolynomialRing(R) : RngInvar -> RngMPol
Polynomials
RngPol_Polynomials (Example H28E2)
POmega
ProjectiveOmega(arguments)
POmegaMinus
ProjectiveOmegaMinus(arguments)
POmegaPlus
ProjectiveOmegaPlus(arguments)
POpen
POpen(S, T) : MonStgElt, MonStgElt -> File
poset
Operations on Poset Elements (GROUPS)
Operations on Subgroup Class Posets (GROUPS)
The Poset of Subgroup Classes (GROUPS)
poset-element
Operations on Poset Elements (GROUPS)
poset-operation
Operations on Subgroup Class Posets (GROUPS)
Position
Index(s, t) : MonStgElt, MonStgElt -> RngIntElt
Index(S, x) : SeqEnum, Elt -> RngIntElt
Index(S, x) : SetIndx, Elt -> RngIntElt
PositiveDefiniteForm
PositiveDefiniteForm(G) : GrpMat -> AlgMatElt
Lat_PositiveDefiniteForm (Example H45E21)
PositiveSum
PositiveSum(m, i) : Map, RngIntElt -> FldPrElt
Power
f ^ n : MagFormElt, RngIntElt -> MagFormElt
power
Introduction (SOLUBLE GROUPS)
Operators (OVERVIEW)
Parents of Sets and Sequences (INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS])
Power Groups (SOLUBLE GROUPS)
Power Sequences (SEQUENCES)
POWER SERIES AND LAURENT SERIES
Power Sets (SETS)
PowerGroup (SOLUBLE GROUPS)
Rings, Fields, and Algebras (OVERVIEW)
power-group
Power Groups (SOLUBLE GROUPS)
PowerGroup (SOLUBLE GROUPS)
power-sequence
Power Sequences (SEQUENCES)
power-set
Power Sets (SETS)
power-set-sequence
Parents of Sets and Sequences (INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS])
PowerGroup
PowerGroup(G) : GrpPC -> PowerGroup
GrpPC_PowerGroup (Example H19E8)
PowerGroupTwo
GrpPC_PowerGroupTwo (Example H19E12)
PowerIndexedSet
PowerIndexedSet(R) : Struct -> PowSetIndx
powering
AlgGrp_powering (Example H50E5)
PowerMap
PowerMap(G) : GrpAb -> Map
PowerMap(G) : GrpFin -> Map
PowerMap(G) : GrpMat -> Map
PowerMap(G) : GrpPC -> Map
PowerMap(G) : GrpPerm -> Map
PowerMultiset
PowerMultiset(R) : Struct -> PowSetMulti
PowerRelation
PowerRelation(r, k: parameters) : FldPrElt, RngIntElt -> RngUPolElt
PowerSequence
PowerSequence(R) : Struct -> PowSeqEnum
Seq_PowerSequence (Example H8E2)
PowerSeriesAlgebra
PowerSeriesRing(R) : Rng -> AlgPowSer
PowerSeriesRing
PowerSeriesRing(R) : Rng -> AlgPowSer
PowerSet
PowerSet(R) : Struct -> PowSetEnum
Set_PowerSet (Example H7E6)
pPrimaryComponent
pPrimaryComponent(A, p) : GrpAb, RngIntElt -> GrpAb
pPrimaryInvariants
pPrimaryInvariants(A, p) : GrpAb, RngIntElt -> [ RngIntElt ]
pQuotient
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
pQuotient1
GrpFP_pQuotient1 (Example H16E27)
pQuotient2
GrpFP_pQuotient2 (Example H16E28)
pQuotient3
GrpFP_pQuotient3 (Example H16E29)
pQuotient4
GrpFP_pQuotient4 (Example H16E30)
pQuotient5
GrpFP_pQuotient5 (Example H16E31)
pQuotient6
GrpFP_pQuotient6 (Example H16E32)
pQuotient7
GrpFP_pQuotient7 (Example H16E33)
pQuotient8
GrpFP_pQuotient8 (Example H16E34)
pQuotientProcess
pQuotientProcess(F, p, c: parameters) : GrpFP, RngIntElt, RngIntElt -> Process
pRadical
pRadical(O, p) : RngOrd -> RngOrdIdl
pRank
pRank(P) : Plane -> RngIntElt
pRanks
pRanks(G) : GrpPC-> [ RngIntElt ]
Precision
Precision(R) : FldCom -> RngIntElt
Precision(r) : FldReElt -> RngIntElt
Precision(R) : RngSer -> Rng
precision
Changing Default Precision (POWER SERIES AND LAURENT SERIES)
Fixed Precision Real Numbers (REAL AND COMPLEX FIELDS)
Precision (LOCAL FIELDS)
Precision (POWER SERIES AND LAURENT SERIES)
Precision (POWER SERIES AND LAURENT SERIES)
Precision (REAL AND COMPLEX FIELDS)
predicate
Booleans (OVERVIEW)
Ideal Predicates (MULTIVARIATE POLYNOMIAL RINGS)
Predicates (RING OF INTEGERS)
Predicates and Boolean Operations (INTRODUCTION [RINGS AND FIELDS])
Predicates on Elements (QUADRATIC FIELDS)
Predicates on Ring Elements (VALUATION RINGS)
Ring Predicates and Booleans (CHARACTERS OF FINITE GROUPS)
Ring Predicates and Booleans (FINITE FIELDS)
Ring Predicates and Booleans (RATIONAL FUNCTION FIELDS)
Ring Predicates and Booleans (RESIDUE CLASS RINGS)
Predicates
AlgLie_Predicates (Example H49E7)
predicates
Predicates (LIE ALGEBRAS)
Predicates (MODULES OVER AFFINE ALGEBRAS)
Predicates (MODULES OVER AFFINE ALGEBRAS)
preds
Predicates on Elements (ALGEBRAS)
Preface
PREFACE
preimage
Images and Preimages (MAPPINGS)
PreimageIdeal
PreimageIdeal(I) : RngMPolRes -> RngMPol
PreimageRing
PreimageRing(I) : RngMPolRes -> RngMPol
PreimageRing(Q) : RngUPolRes -> RngUPol
presentation
CompactPresentation (SOLUBLE GROUPS)
Conditioned Presentations (SOLUBLE GROUPS)
Constructing a Presentation for a Subgroup (FINITELY PRESENTED GROUPS)
Construction of a Quotient: Specification of a Presentation (FINITELY PRESENTED ALGEBRAS)
Construction of a Quotient: Specification of a Presentation (FINITELY PRESENTED GROUPS)
Presentation of Submodules (GENERAL MODULES)
Specification of a Presentation (ABELIAN GROUPS)
Specification of a Presentation (FINITELY PRESENTED SEMIGROUPS)
Standard Presentation Algorithm (SOLUBLE GROUPS)
Structuring Presentations (FINITELY PRESENTED ALGEBRAS)
The Presentation of Submodules (INTRODUCTION [MODULES AND LATTICES])
presentation-quotient
Construction of a Quotient: Specification of a Presentation (FINITELY PRESENTED GROUPS)
presented
FINITELY PRESENTED ALGEBRAS
Finitely Presented Algebras (FINITELY PRESENTED ALGEBRAS)
FINITELY PRESENTED GROUPS
Finitely Presented Modules (FINITELY PRESENTED ALGEBRAS)
FINITELY PRESENTED SEMIGROUPS
Rings, Fields, and Algebras (OVERVIEW)
The Finitely Presented Group Associated with a Permutation Group (PERMUTATION GROUPS)
previous
Other Functions Relating to Primes (RING OF INTEGERS)
PreviousPrime
PreviousPrime(n) : RngIntElt -> RngIntElt
primality
Primality (RING OF INTEGERS)
Primary
Primary(a) : FldQuadElt -> FldQuadElt
primary
Primary Invariants (INVARIANT RINGS OF FINITE GROUPS)
PrimaryDecomposition
PrimaryDecomposition(I) : RngMPol -> [ RngMPol ], [ RngMPol ]
PrimaryDecomposition(I) : RngMPolRes -> [ RngMPolRes ], [ RngMPolRes ]
RngMPol_PrimaryDecomposition (Example H29E23)
PrimaryInvariantFactors
PrimaryInvariantFactors(a) : AlgMatElt -> [ <RngUPolElt, RngIntElt ]
PrimaryInvariantFactors(g) : GrpMatElt -> [ <RngUPolElt, RngIntElt> ]
PrimaryInvariants
R`PrimaryInvariants
PrimaryInvariants(A) : GrpAb -> [ RngIntElt ]
PrimaryInvariants(R) : RngInvar -> [ RngMPolElt ]
PrimaryRationalForm
PrimaryRationalForm(a) : AlgMatElt -> AlgMatElt, AlgMatElt, [ <RngUPolElt, RngIntElt ]
PrimaryRationalForm(g) : GrpMatElt -> AlgMatElt, AlgMatElt, [ <RngUPolElt, RngIntElt> ]
Prime
Prime(R) : FldLoc -> RngIntElt
prime
Primes and Primality Testing (RING OF INTEGERS)
PrimeBasis
PrimeBasis(n) : RngIntElt -> [RngIntElt]
PrimeBasis(n) : RngIntElt -> [RngIntElt]
PrimeDivisors
PrimeBasis(n) : RngIntElt -> [RngIntElt]
PrimeBasis(n) : RngIntElt -> [RngIntElt]
PrimeField
PrimeField(F) : Fld -> Fld
PrimeField(F) : FldFin -> FldFin
PrimeForm
PrimeForm(B, p) : MagForm, RngIntElt -> MagFormElt
PrimeRing
PrimeRing(R) : Rng -> Rng
primitive
Database of Primitive Groups (OVERVIEW)
Finding Special Elements (NUMBER FIELDS AND THEIR ORDERS)
Natural Actions for Primitive Groups (PERMUTATION GROUPS)
Special Elements (FINITE FIELDS)
PrimitiveElement
PrimitiveElement(F) : FldFin -> FldFinElt
PrimitiveElement(K) : FldNum -> FldNumElt
PrimitiveElement(R) : RngIntRes -> RngIntResElt
PrimitiveElement(I) : RngOrdIdl -> RngOrdElt
PrimitiveGroup
TransitiveGroup(d) : RngIntElt -> GrpPerm, MonStgElt
TransitiveGroup(d, n) : RngIntElt, RngIntElt -> GrpPerm, MonStgElt
PrimitiveGroupDatabaseLimit
TransitiveGroupDatabaseLimit() : -> RngIntElt
PrimitiveGroupDescription
TransitiveGroupDescription(d, n) : RngIntElt, RngIntElt -> MonStgElt
PrimitiveGroupProcess
TransitiveGroupProcess(d) : RngIntElt -> Process
PrimitiveGroups
TransitiveGroups(d: parameters) : RngIntElt -> [GrpPerm]
PrimitivePart
PrimitivePart(f) : RngMPolElt -> RngMPolElt
PrimitivePart(p) : RngUPolElt -> RngUPolElt
PrimitivePolynomial
PrimitivePolynomial(F, m) : FldFin, RngIntElt -> RngPolElt
PrimitiveRoot
PrimitiveElement(R) : RngIntRes -> RngIntResElt
PrimitiveRoot(m) : RngIntElt -> RngIntElt
PrimitiveStructure
GrpPerm_PrimitiveStructure (Example H20E18)
PrimitiveWreathProduct
PrimitiveWreathProduct(G, H) : GrpPerm, GrpPerm -> GrpPerm
primitivity
Primitivity Testing (MATRIX GROUPS)
PrincipalCharacter
Id(R) : AlgChtr -> AlgChtrElt
print
Automatic Printing (INPUT AND OUTPUT)
Print Names (MULTIVARIATE POLYNOMIAL RINGS)
Printing (INPUT AND OUTPUT)
The print statement (OVERVIEW)
The print-Statement (INPUT AND OUTPUT)
print expression;
printf
The printf and fprintf Statements (INPUT AND OUTPUT)
printf format, expression, ..., expression;
IO_printf (Example H3E4)
IO_printf (Example H3E6)
printf2
IO_printf2 (Example H3E5)
PrintFile
PrintFile(F, x) : MonStgElt, Var ->
PrintFileMagma
PrintFileMagma(F, x) : MonStgElt, Var ->
printing
Printing to a File (INPUT AND OUTPUT)
printing-file
Printing to a File (INPUT AND OUTPUT)
printname
Generator Assignment (OVERVIEW)
prmgps
Database of Primitive Groups (OVERVIEW)
ProbableRadicalDecomposition
ProbableRadicalDecomposition(I) : RngMPol -> [ RngMPol ]
proc
Procedure Expressions (OVERVIEW)
p := proc< x_1, ..., x_n: parameters | expression >;
procedure
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-expression
Procedure Expressions (MAGMA SEMANTICS)
Procedures
Func_Procedures (Example H2E3)
process
Processes (GROUPS)
Processes (PERMUTATION GROUPS)
Short and Close Vector Processes (LATTICES)
The p-Quotient Process (FINITELY PRESENTED GROUPS)
product
Operators (OVERVIEW)
Tensor Products (MATRIX GROUPS)
The Cartesian Product Constructors (SETS)
TUPLES AND CARTESIAN PRODUCTS
Unions and Products of Graphs (GRAPHS)
Products
AlgMat_Products (Example H51E5)
Progression
Seq_Progression (Example H8E1)
Set_Progression (Example H7E5)
progression
Sequences (OVERVIEW)
Sets (OVERVIEW)
The Arithmetic Progression Constructors (SEQUENCES)
The Arithmetic Progression Constructors (SETS)
projective
Combinatorial and Geometrical Structures (OVERVIEW)
The Connection between Projective and Affine Planes (FINITE PLANES)
projective-affine
The Connection between Projective and Affine Planes (FINITE PLANES)
ProjectiveEmbedding
ProjectiveEmbedding(P) : AffPl -> ProjPl, Map
ProjectiveGammaLinearGroup
ProjectiveGammaLinearGroup(arguments)
ProjectiveGammaUnitaryGroup
ProjectiveGammaUnitaryGroup(arguments)
ProjectiveGeneralLinearGroup
ProjectiveGeneralLinearGroup(arguments)
ProjectiveGeneralOrthogonalGroup
PGO(arguments)
ProjectiveGeneralOrthogonalGroupMinus
PGOMinus(arguments)
ProjectiveGeneralOrthogonalGroupPlus
PGOPlus(arguments)
ProjectiveGeneralUnitaryGroup
ProjectiveGeneralUnitaryGroup(arguments)
ProjectiveOmega
ProjectiveOmega(arguments)
ProjectiveOmegaMinus
ProjectiveOmegaMinus(arguments)
ProjectiveOmegaPlus
ProjectiveOmegaPlus(arguments)
ProjectiveOrder
ProjectiveOrder(a) : AlgMatElt -> RngIntElt
ProjectivePlane
ProjectivePlane(D) : Inc -> Plane, PlanePtSet, PlaneLnSet
ProjectivePlane< v | X : parameters > : RngIntElt, List -> ProjPl
ProjectiveSigmaLinearGroup
ProjectiveSigmaLinearGroup(arguments)
ProjectiveSigmaSymplecticGroup
ProjectiveSigmaSymplecticGroup(arguments)
ProjectiveSigmaUnitaryGroup
ProjectiveSigmaUnitaryGroup(arguments)
ProjectiveSpecialLinearGroup
ProjectiveSpecialLinearGroup(arguments)
ProjectiveSpecialOrthogonalGroup
PSO(arguments)
ProjectiveSpecialOrthogonalGroupMinus
PSOMinus(arguments)
ProjectiveSpecialOrthogonalGroupPlus
PSOPlus(arguments)
ProjectiveSpecialUnitaryGroup
ProjectiveSpecialUnitaryGroup(arguments)
ProjectiveSuzukiGroup
ProjectiveSuzukiGroup(arguments)
ProjectiveSymplecticGroup
ProjectiveSymplecticGroup(arguments)
ProjPl
Combinatorial and Geometrical Structures (OVERVIEW)
prompt
Prompt (OVERVIEW)
properties
Properties of Invariant Rings (INVARIANT RINGS OF FINITE GROUPS)
Prune
Prune(S) : List -> List
Prune(~S) : SeqEnum -> Elt
PseudoRemainder
PseudoRemainder(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
Psi
LogDerivative(s) : FldPrElt -> FldPrElt
PSigmaL
ProjectiveSigmaLinearGroup(arguments)
PSigmaSp
ProjectiveSigmaSymplecticGroup(arguments)
PSigmaU
ProjectiveSigmaUnitaryGroup(arguments)
PSL
ProjectiveSpecialLinearGroup(arguments)
PSO
PSO(arguments)
PSOMinus
PSOMinus(arguments)
PSOPlus
PSOPlus(arguments)
PSp
ProjectiveSymplecticGroup(arguments)
PSU
ProjectiveSpecialUnitaryGroup(arguments)
PSz
ProjectiveSuzukiGroup(arguments)
pts-blks-ops
Design_pts-blks-ops (Example H56E8)
PunctureCode
PunctureCode(C, i) : Code, RngIntElt -> Code
PureLattice
PureLattice(L) : Lat -> Lat
Put
Put(F, S) : File, MonStgElt ->
Puts
Puts(F, S) : File, MonStgElt ->
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