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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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