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