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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

RamificationIndex

RamificationIndex(p, P) : RngOrdIdl -> RngIntElt

Ranbig

Ranbig(n) : RngIntElt -> RngIntElt

Random

Random(R) : AlgMat -> AlgMatElt

Random(B) : Bool -> BoolElt

Random(C): Code -> ModTupFldElt

Random(F) : FldFin -> FldFinElt

Random(G) : GrpAb -> GrpAbElt

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

Random(G) : GrpPC -> GrpPCElt

Random(L): ModLat -> ModLatElt

Random(M) : ModRng -> ModRngElt

Random(V) : ModTupFld -> ModTupFldElt

Random(G: parameters) : GrpFin -> GrpFinElt

Random(G: parameters) : GrpMat -> GrpMatElt

Random(G: parameters) : GrpPerm -> GrpPermElt

Random(P) : Process -> GrpElt

Random(R) : Rng -> RngElt

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

Random(R) : RngIntRes -> RngIntResElt

Random(R) : SeqEnum -> Elt

Random(R) : SetIndx -> Elt

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

Random(L): SubGrpLat -> SubGrpLatElt

Random(S) : VertSet -> Vert

GrpMat_Random (Example H15E13)

Set_Random (Example H4E7)

random

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

RandomDigraph

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

RandomGraph

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

RandomProcess

RandomProcess(G) : Grp -> Process

RandomProcess(G) : Grp -> Process

RandomProcess(G) : GrpAb -> Process

RandomProcess(G) : GrpFin -> Process

RandomSchreier

RandomSchreier(G: parameters) : GrpMat ->

RandomSchreier(G: parameters) : GrpPerm : ->

GrpPerm_RandomSchreier (Example H14E22)

RandomTree

RandomTree(p) : RngIntElt -> GrphUnd

Rank

[Future release] Rank(F) : AlgMatElt -> RngIntElt

Rank(a) : ModMatElt -> RngIntElt

Rank(a) : ModMatRngElt -> RngIntElt

Rank(a) : ModMatRngElt -> RngIntElt

Rank(M) : ModTupRng -> RngIntElt

Rank(P) : RngDPol -> RngIntElt

Rank(Q) : RngQPol -> RngIntElt

Rank(P) : RngUPol -> RngIntElt

rank

Rank (MATRIX ALGEBRAS)

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 ]

RationalReconstruction

RationalReconstruction(s) : RngResElt -> BoolElt, FldRatElt

Rationals

Rationals() : Null -> FldRat

Re

Real(c) : FldComElt -> FldReElt

Reachable

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

Read

Read(F) : MonStgElt -> MonStgElt

Lang_Read (Example H1E1)

read

read identifier;

readi identifier;

readi

readi identifier;

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

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

recformat

recformat< L > : FieldnameList -> RecFormat

reconstruction

Rational Reconstruction (RATIONAL FIELD)

Record

Rec_Record (Example H7E2)

record

Creating a Record (RECORDS)

RECORDS

record-format

RECORDS

RecordAccess

Rec_RecordAccess (Example H7E3)

RecordFormat

Rec_RecordFormat (Example H7E1)

Recursion

Lang_Recursion (Example H1E15)

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)

Reduce

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

ReducedDiscriminant

ReducedDiscriminant(O) : RngOrd -> RngIntElt

ReduceGenerators

ReduceGenerators(~G) : GrpPerm ->

ReduceVector

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

Reduction

Reduction(f) : MagFormElt -> MagFormElt

Set_Reduction (Example H4E13)

reduction

Recursion, Reduction, and Iteration (SEQUENCES)

Reduction (SEQUENCES)

Reduction and Iteration over Sets (SETS)

reduction-iteration

Reduction and Iteration over Sets (SETS)

ReductionStep

ReductionStep(f) : MagFormElt -> MagFormElt

Reductum

Reductum(p) : RngDPolElt -> RngDPolElt

Reductum(f) : RngUPolElt -> RngUPolElt

Reed

Construction of Standard Linear Codes (ERROR-CORRECTING CODES)

ReedMullerCode

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

Code_ReedMullerCode (Example H40E5)

reference

Reference Arguments (MAGMA SEMANTICS)

reference-argument

Reference Arguments (MAGMA SEMANTICS)

regularity

Symmetry and Regularity Properties of Graphs (GRAPHS)

RegularSubgroups

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

Regulator

Regulator(K) : FldQuad -> RngIntElt

Regulator(O) : RngOrd -> FldReElt

related

Related Structures (CHARACTERS OF FINITE GROUPS)

Related Structures (CYCLOTOMIC FIELDS)

Related Structures (ELLIPTIC CURVES)

Related Structures (FINITE FIELDS)

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)

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(Q) : [ RngDPol ] -> RngDPol

RngDPol_RelationIdeal (Example H23E15)

RelationMatrix

RelationMatrix(O, B, n) : RngOrd, RngIntElt -> ModHomElt

Relations

Relations(A) : AlgFP -> [ Rel ]

Relations(A) : GrpAb -> [ Rel ]

Relations(G) : GrpFP -> [ GrpFPRel ]

Relations(S) : SgpFP -> [ Rel ]

GrpAb_Relations (Example H11E2)

GrpFP_Relations (Example H12E2)

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 ->

Rep

Rep(G) : GrpAb -> GrpAbElt

Representative(G) : GrpFin -> GrpFinElt

Representative(G) : GrpPC -> GrpPCElt

Representative(G) : GrpPerm -> GrpPermElt

Representative(R) : Rng -> RngElt

Representative(R) : SeqEnum -> Elt

Representative(R) : SetIndx -> Elt

Representative(S) : VertSet -> Vert

rep

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

repeat

The repeat statement (OVERVIEW)

Lang_repeat (Example H1E14)

Replace

GrpFP_Replace (Example H12E9)

ReplaceRelation

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

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

Represent

FldQuad_Represent (Example H26E5)

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 (RATIONAL FUNCTION FIELDS)

Representation (RESIDUE CLASS RINGS)

Representation (RING OF INTEGERS)

Representation (UNIVARIATE POLYNOMIAL RINGS)

Representation of Finite Fields (FINITE FIELDS)

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) : RngQPolElt -> AlgMatElt

Representative

Representative(G) : GrpFin -> GrpFinElt

Representative(G) : GrpPC -> GrpPCElt

Representative(G) : GrpPerm -> GrpPermElt

Representative(R) : Rng -> RngElt

Representative(R) : SeqEnum -> Elt

Representative(R) : SetIndx -> Elt

Representative(S) : VertSet -> Vert

RepUnits

RngInt_RepUnits (Example H19E5)

residue

Construction of Quadratic Residue Codes (ERROR-CORRECTING CODES)

RESIDUE CLASS RINGS

Rings, Fields, and Algebras (OVERVIEW)

residue-class

RESIDUE CLASS RINGS

ResidueClassRing

ResidueClassRing(m) : RngIntElt -> RngIntRes

restore

Saving and restoring Magma states (OVERVIEW)

restore "filename";

RestrictedPartitions

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

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(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) : RngDPolElt, RngDPolElt, RngIntElt -> RngDPolElt

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)

return

Return (OVERVIEW)

return-key

<Return>

Reverse

Reverse(~S) : SeqEnum ->

Reversion(f) : RngPowElt -> RngPowElt

Reversion

Reversion(f) : RngPowElt -> RngPowElt

RevertClass

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

Rewrite

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

GrpFP_Rewrite (Example H12E35)

rewriting

Rewriting (FINITELY PRESENTED GROUPS)

RHS

RHS(r) : Rel -> AlgFPElt

RHS(r) : Rel -> SgpFPElt

r[1] : GrpAbRel, RngIntElt -> GrpAbElt

r[1] : GrpFPRel, RngIntElt -> GrpFPElt

rideal

Constructor (OVERVIEW)

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

[Future release] 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

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 Rings (MATRIX ALGEBRAS)

Changing Rings (MATRIX GROUPS)

Changing Rings (UNIVARIATE POLYNOMIAL RINGS)

Changing the Coefficient Ring (GENERAL MODULES)

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

RModule

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

RModuleWithBasis

RModuleWithBasis(B) : [ModTupRngElt] -> ModTupRng

RngInt

Rings, Fields, and Algebras (OVERVIEW)

RngIntRes

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

Log, Order and Roots (FINITE FIELDS)

Roots (FINITE FIELDS)

Roots (UNIVARIATE POLYNOMIAL RINGS)

Square Root (POWER SERIES AND LAURENT SERIES)

RootOfUnity

RootOfUnity(n) : RngIntElt, FldCyc -> FldCycElt

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

Roots

Roots(f) : RngPolElt -> { < FldFinElt, RngIntElt> }

Roots(p) : RngUPolElt -> { < RngElt, RngIntElt> }

Roots(p) : RngUPolElt -> { FldComElt }

FldRe_Roots (Example H29E5)

roots

Roots (REAL AND COMPLEX FIELDS)

RootsNonExact

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

FldRe_RootsNonExact (Example H29E6)

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

Expression (OVERVIEW)

Rounding and Truncating (RATIONAL FIELD)

round-bracket

Expression (OVERVIEW)

Round2

FldNum_Round2 (Example H28E6)

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)

RowOps

HMod_RowOps (Example H35E5)

Rowops

KMod_Rowops (Example H33E14)

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(B) : [ModTupRngElt] -> ModTupRng


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