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

Index R


R-key

R

r-key

r<char>

R[G]

Construction of an R[G]-Module (GENERAL MODULES)

R[G]-module

Construction of an R[G]-Module (GENERAL MODULES)

Radical

Radical(G) : GrpFin -> GrpFin

Radical(G) : GrpPerm -> GrpPerm

Radical(I) : RngMPol -> RngMPol

RngMPol_Radical (Example H29E22)

radical

Radical and Primary Decomposition of Ideals (MULTIVARIATE POLYNOMIAL RINGS)

radical-decomposition

Radical and Primary Decomposition of Ideals (MULTIVARIATE POLYNOMIAL RINGS)

RadicalDecomposition

RadicalDecomposition(I) : RngMPol -> [ RngMPol ]

RadicalDecomposition(I) : RngMPolRes -> [ RngMPolRes ]

RadicalExtension

RadicalExtension(K, d, a) : FldNum, RngIntElt, FldNumElt -> FldNum

RadicalQuotient

RadicalQuotient(G) : GrpPerm -> GrpPerm, Hom(GrpPerm)

RamificationIndex

RamificationIndex(I) : RngFunOrdIdl -> RngIntElt

RamificationIndex(I) : RngOrdIdl -> RngIntElt

Random

Random(A) : AlgGen -> AlgGenElt

Random(R) : AlgMat -> AlgMatElt

Random(B) : Bool -> BoolElt

Random(C): Code -> ModTupFldElt

Random(E): CurveEll -> CurveEllPt

Random(F) : FldFin -> FldFinElt

Random(K, n) : FldFun, RngIntElt -> FldFunElt

Random(K, R) : FldNumElt, SeqEnum -> FldNumElt

Random(G, m, n) : GrpFPElt, RngIntElt, RngIntElt -> GrpFPElt

Random(b) : IncBlk -> IncPt

Random(B) : IncBlkSet -> IncBlk

Random(P) : IncPtSet -> IncPt

Random(M) : ModRng -> ModRngElt

Random(V) : ModTupFld -> ModTupFldElt

Random(G: parameters) : GrpMat -> GrpMatElt

Random(G: parameters) : GrpPerm -> GrpPermElt

Random(l) : PlaneLn -> PlanePt

Random(L) : PlaneLnSet -> PlaneLn

Random(V) : PlanePtSet -> PlanePt

Random(P) : Process -> GrpAbElt

Random(P) : Process -> GrpBBElt

Random(P) : Process -> GrpFinElt

Random(P) : Process -> GrpPCElt

Random(R) : Rng -> RngElt

Random(a, b) : RngIntElt, RngIntElt -> RngIntElt

Random(R) : RngIntRes -> RngIntResElt

Random(R) : SeqEnum -> Elt

Random(C) : SetCart -> Elt

Random(R) : SetIndx -> Elt

Random(S, m, n) : SgpFP, RngIntElt, RngIntElt -> SgpFPElt

Random(L): SubGrpLat -> SubGrpLatElt

Random(L): SubModLat -> SubModLatElt

GrpMat_Random (Example H21E13)

Set_Random (Example H7E8)

random

random{ e(x) : x in E | P(x) }

RandomBits

RandomBits(n) : RngIntElt -> RngIntElt

RandomConsecutiveBits

RandomConsecutiveBits(n, a, b) : RngIntElt, RngIntElt -> RngIntElt

RandomDigraph

RandomDigraph(p, r) : RngIntElt, FldReElt -> GrphDir

RandomGraph

RandomGraph(p, r) : RngIntElt, FldReElt -> GrphUnd

RandomLinearCode

RandomLinearCode(K, n, k) : FldFin, RngIntElt, RngIntElt -> Code

RandomProcess

RandomProcess(G) : GrpAb -> Process

RandomProcess(G) : GrpBB -> Process

RandomProcess(G) : GrpFin -> Process

RandomProcess(G) : GrpMat -> Process

RandomProcess(G) : GrpPC -> Process

RandomProcess(G) : GrpPerm -> Process

RandomSchreier

RandomSchreier(G: parameters) : GrpMat ->

RandomSchreier(G: parameters) : GrpPerm : ->

GrpPerm_RandomSchreier (Example H20E24)

RandomTree

RandomTree(p) : RngIntElt -> GrphUnd

Rank

Dimension(L) : Lat -> RngIntElt

MordellWeilRank(E) : CurveEll -> RngIntElt

Rank(a) : AlgMatElt -> RngIntElt

Rank(F) : FldFun -> RngIntElt

Rank(a) : ModMatElt -> RngIntElt

Rank(a) : ModMatRngElt -> RngIntElt

Rank(X) : ModMatRngElt -> RngIntElt

Rank(M) : ModTupRng -> RngIntElt

Rank(P) : RngMPol -> RngIntElt

Rank(Q) : RngMPolRes -> RngIntElt

Rank(P) : RngUPol -> RngIntElt

RankBounds

MordellWeilRankBounds(E) : CurveEll -> RngIntElt, RngIntElt

rate

Upper Asymptotic Bounds on the Information Rate (ERROR-CORRECTING CODES)

rational

RATIONAL FIELD

RATIONAL FUNCTION FIELDS

Rings, Fields, and Algebras (OVERVIEW)

rational-function-field

RATIONAL FUNCTION FIELDS

RationalField

Rationals() : Null -> FldRat

RationalForm

RationalForm(a) : AlgMatElt -> AlgMatElt, AlgMatElt, [ RngUPolElt ]

RationalForm(g) : GrpMatElt -> AlgMatElt, AlgMatElt, [ RngUPolElt ]

RationalMap

RationalMap(E, F, i, t) : CurveEll, CurveEllPt -> Map

RationalPoints

RationalPoints(E) : CurveEll -> Set

RationalPoints(E) : CurveEllSubgroup -> Set

RationalPoints(E) : CurveEllSubscheme -> Set

RationalReconstruction

RationalReconstruction(s) : RngResElt -> BoolElt, FldRatElt

Rationals

Rationals() : Null -> FldRat

RayClassGroup

RayClassGroup( I ) : RngOrdIdl -> GrpAb, Map

Re

Real(c) : FldComElt -> FldReElt

Reachable

Reachable(u, v) : GrphVert, GrphVert -> BoolElt

Read

Read(F) : MonStgElt -> MonStgElt

IO_Read (Example H3E11)

read

read identifier;

readi identifier;

readi

readi identifier;

reading

Reading a Complete File (INPUT AND OUTPUT)

reading-file

Reading a Complete File (INPUT AND OUTPUT)

readinglabels

Reading Labels (GRAPHS)

Real

Real(c) : FldComElt -> FldReElt

real

REAL AND COMPLEX FIELDS

Real and Complex Valued Functions (NUMBER FIELDS AND THEIR ORDERS)

Rings, Fields, and Algebras (OVERVIEW)

real-complex

REAL AND COMPLEX FIELDS

Real and Complex Valued Functions (NUMBER FIELDS AND THEIR ORDERS)

RealField

RealField(p) : RngIntElt -> FldRe

rec

Aggregate (OVERVIEW)

rec< F | L > : RecFormat, FieldAssignmentList -> Rec

recformat

recformat< L > : FieldnameList -> RecFormat

reconstruction

Rational Reconstruction (RATIONAL FIELD)

Record

Rec_Record (Example H12E2)

record

Creating a Record (RECORDS)

RECORDS

record-format

RECORDS

RecordAccess

Rec_RecordAccess (Example H12E3)

RecordFormat

Rec_RecordFormat (Example H12E1)

Recursion

Func_Recursion (Example H2E1)

recursion

Recursion (OVERVIEW)

Recursion (SEQUENCES)

Recursion and forward (OVERVIEW)

Recursion and Mutual Recursion (MAGMA SEMANTICS)

Recursion, Reduction, and Iteration (SEQUENCES)

Recursive functions (OVERVIEW)

recursion-mutual

Recursion and Mutual Recursion (MAGMA SEMANTICS)

recursion-reduction-iteration

Recursion, Reduction, and Iteration (SEQUENCES)

redirecting

Redirecting Output (INPUT AND OUTPUT)

redirecting-output

Redirecting Output (INPUT AND OUTPUT)

Reduce

[Future release] Reduce(w, r) : GrpFPElt, GrpFPRel -> GrpFPElt

Reduce(H) : ModMatRng -> ModMatRng, Map

Reduce(O) : RngFunOrd -> RngFunOrd

Reduce(S) : [ RngMPolElt ] -> [ RngMPolElt ]

HMod_Reduce (Example H43E4)

reduce

Pair Reduction (LATTICES)

The Reduced Form of a Matrix Module (THE MODULES Hom_(R)(M, N) AND End(M))

ReduceCharacters

ReduceCharacters(I, C) : [ AlgChtrElt ], [ AlgChtrElt ] -> [ AlgChtrElt ], [ AlgChtrElt ]

ReducedDiscriminant

ReducedDiscriminant(O) : RngOrd -> RngIntElt

ReducedForms

ReducedForms(D) : RngIntElt -> [ MagFormElt ]

ReduceGenerators

ReduceGenerators(~G) : GrpPerm ->

ReduceGroebnerBasis

ReduceGroebnerBasis(S) : [ RngMPolElt ] -> [ RngMPolElt ]

ReduceHom

HMod_ReduceHom (Example H43E5)

ReduceVector

ReduceVector(W, v) : ModTupRng, ModTupRngElt -> ModTupRngElt

Reduction

Reduction(f) : MagFormElt -> MagFormElt

Set_Reduction (Example H7E14)

reduction

Recursion, Reduction, and Iteration (SEQUENCES)

Reduction (SEQUENCES)

Reduction and Iteration over Sets (SETS)

Reduction of Matrices and Lattices (LATTICES)

reduction-iteration

Reduction and Iteration over Sets (SETS)

ReductionStep

ReductionStep(f) : MagFormElt -> MagFormElt

ReductionType

ReductionType(E, p) : CurveEll, RngIntElt -> MonStgElt

Reductum

Reductum(f) : RngMPolElt -> RngMPolElt

Reductum(f) : RngUPolElt -> RngUPolElt

ReedMullerCode

ReedMullerCode(r, m) : RngIntElt, RngIntElt -> Code

Code_ReedMullerCode (Example H58E5)

ReedSolomonCode

ReedSolomonCode(K, d, b) : FldFin, RngIntElt, RngIntElt -> Code

reference

Reference Arguments (MAGMA SEMANTICS)

reference-argument

Reference Arguments (MAGMA SEMANTICS)

Regexp

Regexp(R, S) : MonStgElt, MonStgElt -> BoolElt, MonStgElt, [ MonStgElt ]

IO_Regexp (Example H3E3)

regularity

Symmetry and Regularity Properties of Graphs (GRAPHS)

Transitivity Properties (FINITE PLANES)

Transitivity Properties (INCIDENCE STRUCTURES AND DESIGNS)

RegularRepresentation

RegularRepresentation(A : parameters) : AlgAss -> AlgMat, Map

RegularSubgroups

RegularSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]

Regulator

Regulator(E) : CurveEll -> FldPrElt

Regulator(K, M) : FldFun, AlgMatElt -> RngIntElt

Regulator(K) : FldQuad -> RngIntElt

Regulator(O) : RngOrd -> FldReElt

RegulatorLowerBound

RegulatorLowerBound(O) : RngOrd -> FldReElt

related

Related Functions (MATRIX GROUPS)

Related Functions (RING OF INTEGERS)

Related Operations on Matrix Groups (LATTICES)

Related Structures (CHARACTERS OF FINITE GROUPS)

Related Structures (CYCLOTOMIC FIELDS)

Related Structures (ELLIPTIC CURVES)

Related Structures (FINITE FIELDS)

Related Structures (FUNCTION FIELDS AND THEIR ORDERS)

Related Structures (INTRODUCTION [RINGS AND FIELDS])

Related Structures (NUMBER FIELDS AND THEIR ORDERS)

Related Structures (POWER SERIES AND LAURENT SERIES)

Related Structures (QUADRATIC FIELDS)

Related Structures (REAL AND COMPLEX FIELDS)

Related Structures (RESIDUE CLASS RINGS)

Related Structures (RING OF INTEGERS)

Related Structures (VALUATION RINGS)

The Construction of Related Structures (INCIDENCE STRUCTURES AND DESIGNS)

Design_related (Example H56E3)

relation

Creation and Manipulation of Relations (FINITELY PRESENTED GROUPS)

Editing Defining Relations (FINITELY PRESENTED ALGEBRAS)

Relation Ideals (MULTIVARIATE POLYNOMIAL RINGS)

Relations (ABELIAN GROUPS)

Relations (FINITELY PRESENTED SEMIGROUPS)

Specification of a Relation (FINITELY PRESENTED ALGEBRAS)

relation-modification

Editing Defining Relations (FINITELY PRESENTED ALGEBRAS)

RelationIdeal

RelationIdeal(R) : RngInvar -> RngMPol

RelationIdeal(Q) : [ RngMPol ] -> RngMPol

RngMPol_RelationIdeal (Example H29E19)

RelationMatrix

RelationMatrix(K, B) : FldNum, RngIntElt -> ModHomElt

Relations

Relations(A) : AlgFP -> [ Rel ]

Relations(A) : GrpAb -> [ Rel ]

Relations(G) : GrpFP -> [ GrpFPRel ]

Relations(R) : RngInvar -> [ RngMPolElt ]

Relations(S) : SgpFP -> [ Rel ]

GrpAb_Relations (Example H18E2)

GrpFP_Relations (Example H16E2)

RngInvar_Relations (Example H30E10)

relations

The Algebra of an Invariant Ring and Algebraic Relations (INVARIANT RINGS OF FINITE GROUPS)

RelativeField

RelativeField(K, L) : FldNum, FldNum -> FldNum

RelativePrecision

Precision(r) : FldReElt -> RngIntElt

RelativePrecision(a) : RngLocElt -> RngIntElt

RelativePrecision(f) : RngSerElt -> RngIntElt

release

Magma Updates (OVERVIEW)

remainder

Rings, Fields, and Algebras (OVERVIEW)

Remove

Remove(~S, i) : SeqEnum, RngIntElt ->

RemoveEdge

RemoveEdge(~G, i, j) : Grph, RngIntElt, RngIntElt ->

RemoveEdges

RemoveEdges(~G, S) : Grph, SeqEnum ->

RemoveIrreducibles

RemoveIrreducibles(I, C) : [ AlgChtrElt ], [ AlgChtrElt ] -> [ AlgChtrElt ], [ AlgChtrElt ]

RemoveVertex

RemoveVertex(~G, i) : Grph, RngIntElt ->

RemoveVertices

RemoveVertices(~G, S) : Grph, [RngIntElt] ->

Rep

Rep(G) : GrpAb -> GrpAbElt

Rep(G) : GrpBB -> GrpBBElt

Rep(C) : SetCart -> Elt

Representative(G) : GrpFin -> GrpFinElt

Representative(G) : GrpPC -> GrpPCElt

Representative(G) : GrpPerm -> GrpPermElt

Representative(b) : IncBlk -> IncPt

Representative(B) : IncBlkSet -> IncBlk

Representative(P) : IncPtSet -> IncPt

Representative(l) : PlaneLn -> PlanePt

Representative(L) : PlaneLnSet -> PlaneLn

Representative(V) : PlanePtSet -> PlanePt

Representative(R) : Rng -> RngElt

Representative(R) : SeqEnum -> Elt

Representative(R) : SetIndx -> Elt

rep

Writing Representations over Smaller Fields (MATRIX GROUPS)

rep{ e(x) : x in E | P(x) }

repeat

Indefinite Iteration (STATEMENTS AND EXPRESSIONS)

The repeat statement (OVERVIEW)

repeat statements until boolexpr : ->

State_repeat (Example H1E14)

repeat-statement

Indefinite Iteration (STATEMENTS AND EXPRESSIONS)

RepetitionCode

RepetitionCode(K, n) : FldFin, RngIntElt -> Code

Replace

GrpFP_Replace (Example H16E9)

ReplaceRelation

ReplaceRelation(G, s, r) : GrpFP, GrpFPRel, GrpFPRel -> GrpFP

ReplaceRelation(S, r_1, r_2) : SgpFP, Rel, Rel -> SgpFP

ReplicationNumber

ReplicationNumber(D) : Dsgn -> RngIntElt

Represent

FldQuad_Represent (Example H34E5)

Representation

Representation(M) : ModGrp -> Map(Hom)

representation

Modular Representations (GROUPS)

Permutation Representations for Database of Finite Perfect Groups (OVERVIEW)

Representation (MULTIVARIATE POLYNOMIAL RINGS)

Representation (QUADRATIC FIELDS)

Representation (RATIONAL FIELD)

Representation (RESIDUE CLASS RINGS)

Representation (RING OF INTEGERS)

Representation (UNIVARIATE POLYNOMIAL RINGS)

Representation of Finite Fields (FINITE FIELDS)

Representation of Strings (INPUT AND OUTPUT)

Representation Theory (ABELIAN GROUPS)

Representation Theory (GROUPS)

Representation Theory (MATRIX GROUPS)

Representation Theory (PERMUTATION GROUPS)

Representation Theory (SOLUBLE GROUPS)

RepresentationMatrix

RepresentationMatrix(a) : FldNumElt -> AlgMatElt

RepresentationMatrix(f) : RngMPolResElt -> AlgMatElt

RepresentationType

RepresentationType(A) : AlgGrp -> MonStgElt

Representative

Representative(G) : GrpFin -> GrpFinElt

Representative(G) : GrpPC -> GrpPCElt

Representative(G) : GrpPerm -> GrpPermElt

Representative(b) : IncBlk -> IncPt

Representative(B) : IncBlkSet -> IncBlk

Representative(P) : IncPtSet -> IncPt

Representative(l) : PlaneLn -> PlanePt

Representative(L) : PlaneLnSet -> PlaneLn

Representative(V) : PlanePtSet -> PlanePt

Representative(R) : Rng -> RngElt

Representative(R) : SeqEnum -> Elt

Representative(R) : SetIndx -> Elt

RepUnits

RngInt_RepUnits (Example H24E5)

require

Argument Checking (FUNCTIONS, PROCEDURES AND PACKAGES)

require condition: print_args;

Func_require (Example H2E7)

requirege

requirege v, L;

requirerange

requirerange v, L, U;

Residual

Residual(D, b) : Inc, IncBlk -> Inc

residue

Construction of Quadratic Residue Codes (ERROR-CORRECTING CODES)

RESIDUE CLASS RINGS

Residue Fields (INTRODUCTION [RINGS AND FIELDS])

Rings, Fields, and Algebras (OVERVIEW)

residue-class

RESIDUE CLASS RINGS

residue-field

Residue Fields (INTRODUCTION [RINGS AND FIELDS])

ResidueClassRing

ResidueClassRing(m) : RngIntElt -> RngIntRes

ResidueField

ResidueField(R, I) : Rng, Rng -> Fld, Map

ResidueField(O, I) : RngOrd, RngOrdIdl -> FldFin, Map

resolution

Free Resolutions (MODULES OVER AFFINE ALGEBRAS)

restore

Saving and restoring Magma states (OVERVIEW)

restore "filename";

RestrictedPartitions

RestrictedPartitions(n, Q) : RngIntElt, SeqEnum -> [ [ RngIntElt ] ]

RestrictedPartitions(n, Q) : RngIntElt, SetEnum -> [ [ RngIntElt ] ]

EnumComb_RestrictedPartitions (Example H54E3)

RestrictField

RestrictField(G, S) : GrpMat, FldFin -> GrpMat, Map

RestrictField(V, L) : ModTupFld, Fld -> ModTupFld, MapHom

RestrictField(V, L) : ModTupFld, Fld -> ModTupFld, MapHom

SubfieldSubcode(C, S) : Code, FldFin -> Code, Map

Restriction

Restriction(x, H) : AlgChtrElt, Grp -> AlgChtrElt

Restriction(D, S) : IncNsp, { Incpt } -> IncNsp

Restriction(M, H) : ModGrp, Grp -> ModGrp

restriction

Compatibility (SEQUENCES)

Compatibility (SETS)

Induction, Restriction, Extension (CHARACTERS OF FINITE GROUPS)

Introduction to Matrix Groups (MATRIX GROUPS)

Restrictions on Sets and Sequences (INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS])

Resultant

Resultant(f, g, i) : RngMPolElt, RngMPolElt, RngIntElt -> RngMPolElt

Resultant(p, q) : RngUPolElt, RngUPolElt -> RngElt

resultant

Resultant and Discriminant (MULTIVARIATE POLYNOMIAL RINGS)

Resultant and Discriminant (UNIVARIATE POLYNOMIAL RINGS)

resultant-discriminant

Resultant and Discriminant (MULTIVARIATE POLYNOMIAL RINGS)

Resultant and Discriminant (UNIVARIATE POLYNOMIAL RINGS)

Retrieve

Retrieve(x) : CopElt -> Elt

retrieve

Retrieve (COPRODUCTS)

return

Return (OVERVIEW)

return-key

<Return>

Reverse

Reverse(~S) : SeqEnum ->

Reversion(f) : RngPowElt -> RngPowElt

Reversion

Reversion(f) : RngPowElt -> RngPowElt

RevertClass

RevertClass(~P) : Process(pQuot) ->

Rewind

Rewind(F) : File ->

Rewrite

Rewrite(G, H : parameters) : GrpFP, GrpFP -> GrpFP

GrpFP_Rewrite (Example H16E35)

rewriting

Rewriting (FINITELY PRESENTED GROUPS)

ReynoldsOperator

ReynoldsOperator(f, G) : RngMPolElt, GrpMat -> RngMPolElt

RHS

RHS(r) : Rel -> AlgFPElt

RHS(r) : Rel -> SgpFPElt

r[1] : GrpAbRel, RngIntElt -> GrpAbElt

r[1] : GrpFPRel, RngIntElt -> GrpFPElt

rideal

Constructor (OVERVIEW)

rideal< cat : A | L> : Cat, AlgGrp, List -> AlgGrp, Map

rideal<A | L_1, ..., L_r> : AlgFP, AlgFPElt, ..., AlgFPElt -> AlgFP

rideal< A | L > : AlgGen, List -> AlgGen, Map

rideal<R | L> : AlgMat, List -> AlgMatIdeal

rideal<G | L_1, ..., L_r> : SgpFP, SgpFPElt, ..., SgpFPElt -> SgpFPIdl

RightAction

Action(M) : ModTupRng -> AlgMat

RightActionGenerator

ActionGenerator(M, i) : ModTupRng, RngIntElt -> AlgMatElt

RightAnnihilator

RightAnnihilator(A, B) : AlgAss, AlgAss -> AlgAss, AlgAss

RightAnnihilator(S) : AlgGrpSub -> AlgGrpSub

RightCosetSpace

RightCosetSpace(G, H: parameters) : GrpFP, GrpFP -> GrpFPCos

RightRing

Ring(M) : ModTupRng -> Rng

RightTransversal

Transversal(G, H) : Grp, Grp -> {@ GrpElt @}, Map

Transversal(G, H) : GrpAb, GrpAb -> {@ GrpAbElt @}, Map

Transversal(G, H) : GrpFP, GrpFP -> {@ GrpFPElt @}, Map

Transversal(G, H) : GrpMat, GrpMat -> {@ GrpMatElt @}, Map

Transversal(G, H) : GrpPC, GrpPC -> {@ GrpPCElt @}, Map

Transversal(G, H) : GrpPerm, GrpPerm -> {@ GrpPermElt @}, Map

Ring

Ring(M) : ModTupRng -> Rng

ring

Accessing an Algebra (FINITELY PRESENTED ALGEBRAS)

Change Ground Ring (ELLIPTIC CURVES)

Changing Coefficient Ring (MULTIVARIATE POLYNOMIAL RINGS)

Changing Rings (ALGEBRAS)

Changing Rings (MATRIX ALGEBRAS)

Changing Rings (MATRIX GROUPS)

Changing Rings (UNIVARIATE POLYNOMIAL RINGS)

Changing the Coefficient Ring (GENERAL MODULES)

Creation of Invariant Rings (INVARIANT RINGS OF FINITE GROUPS)

INVARIANT RINGS OF FINITE GROUPS

Quotient Rings (NUMBER FIELDS AND THEIR ORDERS)

Rings, Fields, and Algebras (OVERVIEW)

Structure Creation (CHARACTERS OF FINITE GROUPS)

Structure Operations (CHARACTERS OF FINITE GROUPS)

ring-field-algebra

Rings, Fields, and Algebras (OVERVIEW)

ring-monoid

Accessing an Algebra (FINITELY PRESENTED ALGEBRAS)

rings

Rings, Fields, and Algebras (OVERVIEW)

RMatrixSpace

RMatrixSpace(R, m, n) : Rng, RngIntElt, RngIntElt -> ModMatRng

RMatrixSpaceWithBasis

RMatrixSpaceWithBasis(Q) : [ ModMatRngElt ] -> ModMatRng

RModule

RModule(R, n) : Rng, RngIntElt -> ModTupRng

RModuleWithBasis

RModuleWithBasis(Q) : [ModTupRngElt] -> ModTupRng

RngInt

Rings, Fields, and Algebras (OVERVIEW)

RngIntRes

Rings, Fields, and Algebras (OVERVIEW)

RngInvar

Rings, Fields, and Algebras (OVERVIEW)

RngMPol

Rings, Fields, and Algebras (OVERVIEW)

RngPad

Rings, Fields, and Algebras (OVERVIEW)

RngUPol

Rings, Fields, and Algebras (OVERVIEW)

RngUPolRes

Rings, Fields, and Algebras (OVERVIEW)

RngVal

Rings, Fields, and Algebras (OVERVIEW)

Root

Root(a, n) : FldFinElt, RngIntElt -> FldFinElt

Root(f, n) : FldLocElt, RngIntElt -> FldLocElt

Root(r, n) : FldReElt, RngIntElt -> FldReElt

Root(a, n) : RngOrdElt -> RngOrdElt

root

Log, Order and Roots (FINITE FIELDS)

Root Systems (LIE ALGEBRAS)

Roots (FINITE FIELDS)

Roots (UNIVARIATE POLYNOMIAL RINGS)

Square Root (POWER SERIES AND LAURENT SERIES)

root-system

Root Systems (LIE ALGEBRAS)

RootOfUnity

RootOfUnity(n) : RngIntElt, FldCyc -> FldCycElt

RootOfUnity(n, K) : RngIntElt, FldFin -> FldFinElt

RootOfUnity(n, Q) : RngIntElt, FldRat -> FldRatElt

Roots

Roots(K) : FldFun -> [ FldPowElt ]

Roots(f) : RngPolElt -> [ < FldFinElt, RngIntElt> ]

Roots(p) : RngUPolElt -> [ < RngElt, RngIntElt> ]

Roots(p) : RngUPolElt -> [ <FldComElt, RngIntElt> ]

FldRe_Roots (Example H37E5)

roots

Roots (REAL AND COMPLEX FIELDS)

RootsNonExact

RootsNonExact(p) : RngUPolElt -> [ FldPrElt ], [ FldPrElt ]

FldRe_RootsNonExact (Example H37E6)

RootSystem

RootSystem(L) : AlgLie -> [ AlgLieElt ], [ AlgLieElt ], [ AlgLieElt ], [[]]

AlgLie_RootSystem (Example H49E2)

Rotate

Rotate(u, k) : ModTupElt, RngIntElt -> ModTupElt

Rotate(u, k) : ModTupFldElt, RngIntElt -> ModTupFldElt

Rotate(u, k) : ModTupFldElt, RngIntElt -> ModTupFldElt

Rotate(~S, p) : SeqEnum, RngIntElt ->

RotateWord

RotateWord(u, n) : GrpFPElt, RngIntElt -> GrpFPElt

RotateWord(u, n) : SgpFPElt, RngIntElt -> SgpFPElt

Round

Round(q) : FldRatElt -> RngIntElt

Round(r) : FldReElt -> FldReElt

Round(n) : RngIntElt -> RngIntElt

Round(p) : RngUPolElt -> RngUPolElt

round

Expression (OVERVIEW)

Rounding and Truncating (RATIONAL FIELD)

round-bracket

Expression (OVERVIEW)

Round2

FldNum_Round2 (Example H36E6)

rounding

Rounding (REAL AND COMPLEX FIELDS)

routine

Functions, Procedures, and Mappings (OVERVIEW)

row

Row and Column Operations (MATRIX ALGEBRAS)

Row and Column Operations (THE MODULES Hom_(R)(M, N) AND End(M))

Row and Column Operations (VECTOR SPACES)

row-column

Row and Column Operations (MATRIX ALGEBRAS)

Row and Column Operations (THE MODULES Hom_(R)(M, N) AND End(M))

Row and Column Operations (VECTOR SPACES)

RowNullSpace

RowNullSpace(a) : AlgMatElt -> ModTup

RowNullSpace(a) : ModMatElt -> ModTupFld

RowNullSpace(a) : ModMatRngElt -> ModTupRng

RowOps

HMod_RowOps (Example H43E9)

Rowops

KMod_Rowops (Example H41E14)

RowSpace

Image(a) : AlgMatElt -> ModTup

Image(a) : ModMatElt -> ModTupFld

Image(a) : ModMatRngElt -> ModTupRng

RSpace

RModule(R, n) : Rng, RngIntElt -> ModTupRng

RSpace(G) : GrpMat -> ModTupRng

RSpaceWithBasis

RModuleWithBasis(Q) : [ModTupRngElt] -> ModTupRng

rule

Rules for Maps (MAPPINGS)

RungeKutta2

RngMPol_RungeKutta2 (Example H29E11)


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