[____] [____] [_____] [____] [__] [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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