[____] [____] [_____] [____] [__] [Index] [Root]
Index R
R
r<char>
IsInRadical(f, I) : RngMPolElt, RngMPol -> BoolElt
IsRadical(I) : RngMPol -> BoolElt
IsRadical(I) : RngMPolRes -> BoolElt
JacobsonRadical(A) : AlgGen -> AlgGen
JacobsonRadical(M) : ModAlg -> ModAlg
JacobsonRadical(M) : ModRng -> ModRng
JacobsonRadical(e) : SubModLatElt -> SubModLatElt
NilRadical(L) : AlgLie -> AlgLie
ProbableRadicalDecomposition(I) : RngMPol -> [ RngMPol ]
Radical(G) : GrpFin -> GrpFin
Radical(G) : GrpPerm -> GrpPerm
SolvableRadical(G) : GrpPerm -> GrpPerm
Radical(I) : RngMPol -> RngMPol
RadicalDecomposition(I) : RngMPol -> [ RngMPol ]
RadicalDecomposition(I) : RngMPolRes -> [ RngMPolRes ]
RadicalExtension(F, d, a) : Rng, RngIntElt, RngElt -> FldAlg
RadicalQuotient(G) : GrpPerm -> GrpPerm, Hom(GrpPerm)
SolvableRadical(L) : AlgLie -> AlgLie
GB_Radical (Example H50E17)
GrpPerm_Radical (Example H20E27)
Radical (IDEAL THEORY AND GRÖBNER BASES)
Radical and Decomposition of Ideals (IDEAL THEORY AND GRÖBNER BASES)
The Soluble Radical and its Quotient (PERMUTATION GROUPS)
Radical and Decomposition of Ideals (IDEAL THEORY AND GRÖBNER BASES)
RadicalDecomposition(I) : RngMPol -> [ RngMPol ]
RadicalDecomposition(I) : RngMPolRes -> [ RngMPolRes ]
RadicalExtension(F, d, a) : Rng, RngIntElt, RngElt -> FldAlg
RadicalQuotient(G) : GrpPerm -> GrpPerm, Hom(GrpPerm)
CoveringRadius(C) : Code -> RngIntElt
CoveringRadius(L) : Lat -> FldRatElt
RamificationDegree(L) : RngLoc -> RngIntElt
RamificationDivisor(D) : DivCrvElt -> DivCrvElt
RamificationDivisor(F) : FldFunG -> DivFunElt
RamificationDivisor(D) : DivFunElt -> DivFunElt
RamificationField(p) : RngOrdIdl -> FldNum, Map
RamificationField(p, i) : RngOrdIdl -> FldNum, Map
RamificationGroup(p) : RngOrdIdl -> GrpPerm
RamificationGroup(p, i) : RngOrdIdl, RngIntElt -> GrpPerm
RamificationIndex(P) : PlcFunElt -> RngIntElt
RamificationIndex(I) : RngFunOrdIdl -> RngIntElt
RamificationIndex(I, p) : RngInt, RngIntElt -> RngIntElt
RamificationIndex(I) : RngOrdIdl -> RngIntElt
RngOrd_Ramification (Example H53E21)
RamificationDegree(L) : RngLoc -> RngIntElt
RamificationIndex(P) : PlcFunElt -> RngIntElt
RamificationIndex(I) : RngFunOrdIdl -> RngIntElt
RamificationIndex(I) : RngOrdIdl -> RngIntElt
RamificationDivisor(D) : DivCrvElt -> DivCrvElt
RamificationDivisor(F) : FldFunG -> DivFunElt
RamificationDivisor(D) : DivFunElt -> DivFunElt
RamificationField(p) : RngOrdIdl -> FldNum, Map
RamificationField(p, i) : RngOrdIdl -> FldNum, Map
RamificationGroup(p) : RngOrdIdl -> GrpPerm
RamificationGroup(p, i) : RngOrdIdl, RngIntElt -> GrpPerm
RamificationDegree(P) : PlcFunElt -> RngIntElt
RamificationIndex(P) : PlcFunElt -> RngIntElt
RamificationIndex(I) : RngFunOrdIdl -> RngIntElt
RamificationIndex(I, p) : RngInt, RngIntElt -> RngIntElt
RamificationIndex(I) : RngOrdIdl -> RngIntElt
IsRamified(P) : RngOrdIdl -> BoolElt
IsRamified(P, O) : RngOrdIdl, RngOrd -> BoolElt
IsTamelyRamified(K) : FldAlg -> BoolElt
IsTamelyRamified(O) : RngOrd -> BoolElt
IsTamelyRamified(P) : RngOrdIdl -> BoolElt
IsTamelyRamified(P, O) : RngOrdIdl, RngOrd -> BoolElt
IsTotallyRamified(P) : RngOrdIdl -> BoolElt
IsTotallyRamified(P, O) : RngOrdIdl, RngOrd -> BoolElt
IsWildlyRamified(K) : FldAlg -> BoolElt
IsWildlyRamified(O) : RngOrd -> BoolElt
IsWildlyRamified(P) : RngOrdIdl -> BoolElt
IsWildlyRamified(P, O) : RngOrdIdl, RngOrd -> BoolElt
RamifiedPrimes(A) : AlgQuat -> SeqEnum
TotallyRamifiedExtension(L, g) : RngLoc, RngUPolElt -> RngLoc
RngLoc_ramified-ext (Example H59E16)
RngPad_ramified-ext (Example H42E14)
AlgQuat_Ramified_Primes (Example H71E6)
RamifiedPrimes(A) : AlgQuat -> SeqEnum
RandomPlace(C,m) : Crv,RngIntElt -> BoolElt,PlcCrvElt
Place(C,m) : Crv,RngIntElt -> BoolElt,PlcCrvElt
Random(B) : AlgBas -> AlgBasElt
Random(A) : AlgGen -> AlgGenElt
Random(R) : AlgMat -> AlgMatElt
Random(B) : Bool -> BoolElt
Random(C): Code -> ModTupRngElt
Random(C): Code -> ModTupRngElt
Random(C) : CrvHyp -> PtHyp
Random(D) : DB -> CrvEll
Random(F, m) : FldAlg, RngIntElt -> FldAlgElt
Random(F) : FldFin -> FldFinElt
Random(F, m) : FldFun, RngIntElt -> FldFunElt
Random(G) : GrpAb -> GrpAbElt
Random(A) : GrpAbGen -> GrpAbGenElt
Random(G) : GrpAtc -> GrpAtcElt
Random(G, n) : GrpAtc, RngIntElt -> GrpAtcElt
Random(G) : GrpDrch -> GrpDrchElt
Random(G, m, n) : GrpFPElt, RngIntElt, RngIntElt -> GrpFPElt
Random(G) : GrpGPC -> GrpGPCElt
Random( G ) : GrpLie -> GrpLieElt
Random(G) : GrpPC -> GrpPCElt
Random(G,m) : GrpPSL2, RngIntElt -> GrpPSL2Elt
Random(G) : GrpRWS -> GrpRWSElt
Random(G, n) : GrpRWS, RngIntElt -> GrpRWSElt
Random(b) : IncBlk -> IncPt
Random(B) : IncBlkSet -> IncBlk
Random(P) : IncPtSet -> IncPt
Random(J) : JacHyp -> JacHypPt
Random(M) : ModRng -> ModRngElt
Random(M) : ModRng -> ModRngElt
Random(V) : ModTupFld -> ModTupFldElt
Random(M) : MonRWS -> MonRWSElt
Random(M, n) : MonRWS, RngIntElt -> MonRWSElt
Random(G: parameters) : GrpFin -> GrpFinElt
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 -> GrpFinElt
Random(P) : Process -> GrpMatElt
Random(P) : Process -> GrpPCElt
Random(P) : Process -> GrpPermElt
Random(P) : Process -> GrpSLPElt
Random(P) : Process -> GrpGPCElt
Random(R) : Rng -> RngElt
Random(O, m) : RngFunOrd, RngIntElt -> RngFunOrdElt
Random(R) : RngGal -> RngGalElt
Random(b) : RngIntElt -> RngIntElt
Random(b) : RngIntElt -> RngIntElt
Random(a, b) : RngIntElt, RngIntElt -> RngIntElt
Random(a, b) : RngIntElt, RngIntElt -> RngIntElt
Random(R) : RngIntRes -> RngIntResElt
Random(L) : RngLoc -> RngLocElt
Random(R) : SeqEnum -> Elt
Random(C) : SetCart -> Elt
Random(R) : SetIndx -> Elt
Random(H): SetPtEll -> PtEll
Random(S, m, n) : SgpFP, RngIntElt, RngIntElt -> SgpFPElt
Random(S) : Str -> Elt
Random(L) : SubFldLat -> SubFldLatElt
Random(L): SubGrpLat -> SubGrpLatElt
Random(L): SubModLat -> SubModLatElt
RandomBits(n) : RngIntElt -> RngIntElt
RandomConsecutiveBits(n, a, b) : RngIntElt, RngIntElt -> RngIntElt
RandomDigraph(p, r) : RngIntElt, FldReElt -> GrphDir
RandomGraph(D) : DB -> GrphUnd
RandomGraph(D, S) : DB, SeqEnum -> GrphUnd
RandomGraph(p, r) : RngIntElt, FldReElt -> GrphUnd
RandomLinearCode(K, n, k) : FldFin, RngIntElt, RngIntElt -> Code
RandomPlace(F, m) : FldFun, RngIntElt -> BoolElt, PlcFunElt
RandomPlace(F, m) : FldFun, RngIntElt -> BoolElt, PlcFunElt
RandomPrime(n: parameter) : RngIntElt -> RngIntElt
RandomPrime(n: parameter) : RngIntElt -> RngIntElt
RandomPrime(n, a, b, x: parameter) :RngIntElt, RngIntElt, RngIntElt -> BoolElt, RngIntElt
RandomPrime(n, a, b, x: parameter) :RngIntElt, RngIntElt, RngIntElt -> BoolElt, RngIntElt
RandomPrimePolynomial(R, d) : RngUPol, RngIntElt -> RngUPolElt
RandomProcess(G) : GrpAb -> Process
RandomProcess(G) : GrpFin -> Process
RandomProcess(G) : GrpMat -> Process
RandomProcess(G) : GrpPC -> Process
RandomProcess(G) : GrpPerm -> Process
RandomProcess(G) : GrpSLP -> Process
RandomProcess(G) : GrpGPC -> Process
RandomSchreier(G: parameters) : GrpMat ->
RandomSchreier(G: parameters) : GrpPerm : ->
RandomSequenceBlumBlumShub(b, t) : RngIntElt, RngIntElt -> SeqEnum
RandomSequenceBlumBlumShub(n, s, t) : RngIntElt, RngIntElt, RngIntElt -> SeqEnum
RandomSequenceRSA(b, t) : RngIntElt, RngIntElt -> SeqEnum
RandomSequenceRSA(n, e, s, t) : RngIntElt, RngIntElt, RngIntElt,RngIntElt -> SeqEnum
RandomSubcomplex(C,Q) : ModCpx, SeqEnum -> ModCpx, MapChn
RandomTree(p) : RngIntElt -> GrphUnd
Solution(C) : CrvCon -> Pt
GrpMat_Random (Example H21E13)
Set_Random (Example H7E8)
PSEUDO-RANDOM BIT SEQUENCES
Random Numbers (RING OF INTEGERS)
Random Object Generation (STATEMENTS AND EXPRESSIONS)
Random Points (HYPERELLIPTIC CURVES)
random{ e(x) : x in E | P(x) }
random{ e(x_1, ..., x_k) : x_1 in E_1,..., x_k in E_k | P(x_1, ..., x_k) }
Random Points (HYPERELLIPTIC CURVES)
Random Points (HYPERELLIPTIC CURVES)
RandomBits(n) : RngIntElt -> RngIntElt
RandomConsecutiveBits(n, a, b) : RngIntElt, RngIntElt -> RngIntElt
RandomDigraph(p, r) : RngIntElt, FldReElt -> GrphDir
RandomGraph(D) : DB -> GrphUnd
RandomGraph(D, S) : DB, SeqEnum -> GrphUnd
RandomGraph(p, r) : RngIntElt, FldReElt -> GrphUnd
RandomLinearCode(K, n, k) : FldFin, RngIntElt, RngIntElt -> Code
RandomPlace(C,m) : Crv,RngIntElt -> BoolElt,PlcCrvElt
Place(C,m) : Crv,RngIntElt -> BoolElt,PlcCrvElt
RandomPlace(F, m) : FldFun, RngIntElt -> BoolElt, PlcFunElt
RandomPlace(F, m) : FldFun, RngIntElt -> BoolElt, PlcFunElt
RandomPrime(n: parameter) : RngIntElt -> RngIntElt
RandomPrime(n: parameter) : RngIntElt -> RngIntElt
RandomPrime(n, a, b, x: parameter) :RngIntElt, RngIntElt, RngIntElt -> BoolElt, RngIntElt
RandomPrime(n, a, b, x: parameter) :RngIntElt, RngIntElt, RngIntElt -> BoolElt, RngIntElt
RandomPrimePolynomial(R, d) : RngUPol, RngIntElt -> RngUPolElt
RandomProcess(G) : GrpAb -> Process
RandomProcess(G) : GrpFin -> Process
RandomProcess(G) : GrpMat -> Process
RandomProcess(G) : GrpPC -> Process
RandomProcess(G) : GrpPerm -> Process
RandomProcess(G) : GrpSLP -> Process
RandomProcess(G) : GrpGPC -> Process
RandomSchreier(G: parameters) : GrpMat ->
RandomSchreier(G: parameters) : GrpPerm : ->
GrpPerm_RandomSchreier (Example H20E33)
BlumBlumShub(b, t) : RngIntElt, RngIntElt -> SeqEnum
RandomSequenceBlumBlumShub(b, t) : RngIntElt, RngIntElt -> SeqEnum
RandomSequenceBlumBlumShub(n, s, t) : RngIntElt, RngIntElt, RngIntElt -> SeqEnum
RandomSequenceRSA(b, t) : RngIntElt, RngIntElt -> SeqEnum
RandomSequenceRSA(n, e, s, t) : RngIntElt, RngIntElt, RngIntElt,RngIntElt -> SeqEnum
RandomSubcomplex(C,Q) : ModCpx, SeqEnum -> ModCpx, MapChn
RandomTree(p) : RngIntElt -> GrphUnd
ColumnSubmatrixRange(A, i, j) : Mtrx, RngIntElt, RngIntElt -> Mtrx
ConductorRange(D) : DB -> RngIntElt, RngIntElt
RowSubmatrixRange(A, i, j) : Mtrx, RngIntElt, RngIntElt -> Mtrx
SubmatrixRange(A, i, j, r, s) : Mtrx, RngIntElt, RngIntElt, RngIntElt, RngIntElt -> Mtrx
Rank(L) : Lat -> RngIntElt
Dimension(L) : Lat -> RngIntElt
Dimension(M) : ModBrdt -> RngIntElt
NuclearRank(G) : GrpPC -> RngIntElt
Rank(a) : AlgMatElt -> RngIntElt
Rank(C) : CosetGeom -> RngIntElt
Rank(A) : FldAC -> RngIntElt
Rank(F) : FldFunRat -> RngIntElt
Rank( W ) : GrpCox -> RngIntElt
Rank( G ) : GrpLie -> RngIntElt
Rank(D) : IncGeom -> RngIntElt
Rank(a) : ModMatElt -> RngIntElt
Rank(a) : ModMatRngElt -> RngIntElt
Rank(M) : ModTupRng -> RngIntElt
Rank(A) : Mtrx -> RngIntElt
Rank(H: parameters) : SetPtEll -> RngIntElt
Rank(P) : RngMPol -> RngIntElt
Rank(Q) : RngMPolRes -> RngIntElt
Rank(P) : RngUPol -> RngIntElt
Rank( RD ) : RootDtm -> RngIntElt
RankBounds(H: parameters) : SetPtEll -> RngIntElt, RngIntElt
SemisimpleRank( G ) : GrpLie -> RngIntElt
TorsionFreeRank(A) : GrpAb -> RngIntElt
TorsionFreeRank(G) : GrpFP -> RngIntElt
UnitRank(O) : RngFunOrd -> RngIntElt
UnitRank(O) : RngOrd -> RngIntElt
UnitRank(O) : RngOrd -> RngIntElt
pMultiplicatorRank(G) : GrpPC -> RngIntElt
CrvEll_Rank (Example H85E17)
MordellWeilRankBounds(H: parameters) : SetPtEll -> RngIntElt, RngIntElt
RankBounds(H: parameters) : SetPtEll -> RngIntElt, RngIntElt
Rational Curves (RATIONAL CURVES AND CONICS)
CrvCon_rat_crv_parametrisation (Example H84E3)
InformationRate(C) : Code -> FldPrElt
InformationRate(C) : Code -> RngPrElt
Asymptotic Bounds on the Information Rate (LINEAR CODES OVER FINITE FIELDS)
Database of Rational Maximal Finite Matrix Groups (DATABASES OF GROUPS)
GrpData_ratgps1 (Example H34E5)
AbsoluteRationalScroll(k,N) : Rng,SeqEnum -> PrjScrl
FunctionField(R) : Rng -> FldFunRat
FunctionField(R, r) : Rng, RngIntElt -> FldFunRat
IsAmbientRationalFunction(A,f) : Sch,RngElt -> BoolElt
IsRationalCurve(X) : Sch -> BoolElt,CrvRat
IsRationalCurve(X) : Sch -> BoolElt,CrvRat
Points(C, x) : CrvHyp, RngElt -> SetIndx
Points(J) : JacHyp -> SetIndx
Points(J, P) : JacHyp, SrfKumPt -> SetIndx
Points(G) : SchGrpEll -> SetIndx
Points(H) : SetPtEll -> @ PtEll @
PrimaryRationalForm(a) : AlgMatElt -> AlgMatElt, AlgMatElt, [ <RngUPolElt, RngIntElt ]
PrimaryRationalForm(A) : Mtrx -> AlgMatElt, AlgMatElt, [ <RngUPolElt, RngIntElt ]
RationalCurve(X,f) : Sch,RngMPolElt -> CrvRat
RationalExtensionRepresentation(F) : FldFunG -> FldFun
RationalForm(a) : AlgMatElt -> AlgMatElt, AlgMatElt, [ RngUPolElt ]
RationalForm(A) : Mtrx -> Mtrx, AlgMatElt, [ RngUPolElt ]
RationalFunction(a) : FldFunGElt -> RngElt
RationalFunctions(P) : CrvPlcElt -> SeqEnum
RationalMap(i, t) : CrvEll, PtEll -> Map
RationalMapping(M) : ModSym -> Map
RationalMatrixGroupDatabase() : -> DB
RationalPoints(J, a, d) : JacHyp, RngUPolElt, RngIntElt -> SetIndx
RationalPoints(X) : Sch -> SetIndx
RationalPoints(K, Q) : SrfKum, [RngElt] -> SetIndx
RationalReconstruction(s) : RngResElt -> BoolElt, FldRatElt
Rationals() : Null -> FldRat
Projection Mappings (MODULAR SYMBOLS)
RATIONAL FIELD
RATIONAL FUNCTION FIELDS
Rings, Fields, and Algebras (OVERVIEW)
RATIONAL FUNCTION FIELDS
CrvCon_rational_curve (Example H84E1)
Curves over the Rationals (ELLIPTIC CURVES)
Heights and Height Pairing (ELLIPTIC CURVES)
Invariants of Rational Curves (ELLIPTIC CURVES)
Kodaira Symbols (ELLIPTIC CURVES)
Mordell--Weil Group (ELLIPTIC CURVES)
Periods and Elliptic Logarithms (ELLIPTIC CURVES)
Periods and Elliptic Logarithms (ELLIPTIC CURVES)
Mordell--Weil Group (ELLIPTIC CURVES)
Heights and Height Pairing (ELLIPTIC CURVES)
Kodaira Symbols (ELLIPTIC CURVES)
Invariants of Rational Curves (ELLIPTIC CURVES)
RationalCurve(X,f) : Sch,RngMPolElt -> CrvRat
RationalExtensionRepresentation(F) : FldFunG -> FldFun
RationalField() : Null -> FldRat
Rationals() : Null -> FldRat
RationalForm(a) : AlgMatElt -> AlgMatElt, AlgMatElt, [ RngUPolElt ]
RationalForm(A) : Mtrx -> Mtrx, AlgMatElt, [ RngUPolElt ]
RationalFunction(a) : FldFunGElt -> RngElt
RationalFunctionField(R) : Rng -> FldFunRat
FunctionField(R) : Rng -> FldFunRat
FunctionField(R, r) : Rng, RngIntElt -> FldFunRat
RationalFunctions(P) : CrvPlcElt -> SeqEnum
RationalMap(i, t) : CrvEll, PtEll -> Map
RationalMapping(M) : ModSym -> Map
RationalMatrixGroupDatabase() : -> DB
GrpMat_RationalMatrixGroupDatabase (Example H21E14)
RationalPoints(C, x) : CrvHyp, RngElt -> SetIndx
Points(C, x) : CrvHyp, RngElt -> SetIndx
Points(J) : JacHyp -> SetIndx
Points(J, P) : JacHyp, SrfKumPt -> SetIndx
Points(G) : SchGrpEll -> SetIndx
Points(H) : SetPtEll -> @ PtEll @
RationalPoints(J, a, d) : JacHyp, RngUPolElt, RngIntElt -> SetIndx
RationalPoints(X) : Sch -> SetIndx
RationalPoints(K, Q) : SrfKum, [RngElt] -> SetIndx
RationalReconstruction(s) : RngResElt -> BoolElt, FldRatElt
RationalField() : Null -> FldRat
Rationals() : Null -> FldRat
AbelianExtension(m) : Map -> FldAb
RayClassField(m) : Map -> FldAb
RayClassGroup(I) : RngOrdIdl -> GrpAb, Map
RayResidueRing(m) : RngOrdIdl -> GrpAb, Map
Ray Class Group (ORDERS AND ALGEBRAIC FIELDS)
Ray Class Group (ORDERS AND ALGEBRAIC FIELDS)
AbelianExtension(m) : Map -> FldAb
RayClassField(m) : Map -> FldAb
RayClassGroup(I) : RngOrdIdl -> GrpAb, Map
RayResidueRing(m) : RngOrdIdl -> GrpAb, Map
IsRC(C) : CosetGeom -> BoolElt
IsResiduallyConnected(C) : CosetGeom -> BoolElt
IsResiduallyConnected(D) : IncGeom -> BoolElt
GrpCox_RDFromCox (Example H36E4)
Re(c) : FldComElt -> FldReElt
Real(c) : FldComElt -> FldReElt
Reachable(u, v) : GrphVert, GrphVert -> BoolElt
Read(F) : MonStgElt -> MonStgElt
IO_Read (Example H3E11)
read identifier;
readi identifier;
readi identifier, prompt;
readi identifier;
Reading a Complete File (INPUT AND OUTPUT)
Reading a Complete File (INPUT AND OUTPUT)
Reading Labels (GRAPHS)
GetDefaultRealField() : Null -> FldPr
IsReal(x) : AlgChtrElt -> BoolElt
IsReal(c) : FldComElt -> BoolElt
IsReal(a) : FldCycElt -> BoolElt
Real(c) : FldComElt -> FldReElt
Real(z) : SpcHypElt -> FldPrElt
RealField() : Null -> FldPr
RealField(p) : RngIntElt -> FldRe
RealPeriod(E: parameters) : CrvEll -> FldPRElt
RealTamagawaNumber(M) : ModSym -> RngIntElt
RealVolume(M, prec) : ModSym, RngIntElt -> FldPrElt
SetDefaultRealField(R) : FldRe ->
REAL AND COMPLEX FIELDS
Real and Complex Valued Functions (ORDERS AND ALGEBRAIC FIELDS)
Rings, Fields, and Algebras (OVERVIEW)
REAL AND COMPLEX FIELDS
Real and Complex Valued Functions (ORDERS AND ALGEBRAIC FIELDS)
RealField() : Null -> FldPr
RealField(p) : RngIntElt -> FldRe
RealPeriod(E: parameters) : CrvEll -> FldPRElt
RealTamagawaNumber(M) : ModSym -> RngIntElt
Realtime() : -> FldReElt
Realtime(t) : FldReElt -> FldReElt
RealVolume(M, prec) : ModSym, RngIntElt -> FldPrElt
Aggregate (OVERVIEW)
rec< F | L > : RecFormat, FieldAssignmentList -> Rec
recformat< L > : FieldnameList -> RecFormat
Recognizing Classical Groups in their Natural Representation (MATRIX GROUPS)
RecognizeClassical( G : parameters): GrpMat -> BoolElt
RecognizeClassical( G : parameters): GrpMat -> BoolElt
GrpMat_RecognizeClassical (Example H21E30)
PseudoRandom_reconstruct-sequence (Example H99E1)
RationalReconstruction(s) : RngResElt -> BoolElt, FldRatElt
Rational Reconstruction (RATIONAL FIELD)
NumericalRecord(X) : VSrfK3 -> Rec
Rec_Record (Example H12E2)
Creating a Record (RECORDS)
RECORDS
RECORDS
Rec_RecordAccess (Example H12E3)
Rec_RecordFormat (Example H12E1)
Rectify(~t) : Tableau ->
JeuDeTaquin(~t) : Tableau ->
Func_Recursion (Example H2E1)
Recursion (OVERVIEW)
Recursion (SEQUENCES)
Recursion and forward (OVERVIEW)
Recursion and Mutual Recursion (MAGMA SEMANTICS)
Recursion, Reduction, and Iteration (SEQUENCES)
Recursive functions (OVERVIEW)
Recursion and Mutual Recursion (MAGMA SEMANTICS)
Recursion, Reduction, and Iteration (SEQUENCES)
Redirecting Output (INPUT AND OUTPUT)
Redirecting Output (INPUT AND OUTPUT)
CanRedoEnumeration(P) : GrpFPCosetEnumProc -> BoolElt
RedoEnumeration(~P: parameters) : GrpFPCosetEnumProc ->
RedoEnumeration(~P: parameters) : GrpFPCosetEnumProc ->
PairReduce(L) : Lat -> Lat, AlgMatElt
PairReduce(X) : ModMatRngElt -> ModMatRngElt, AlgMatElt
PairReduceGram(F) : ModMatRngElt -> ModMatRngElt, AlgMatElt, RngIntElt
Reduce( F, w ) : GrpFP, GrpFPElt -> GrpFPElt
Reduce(H) : ModMatRng -> ModMatRng, Map
Reduce(M) : ModOrd -> ModOrd, Map
Reduce(O) : RngFunOrd -> RngFunOrd
Reduce(S) : [ RngMPolElt ] -> [ RngMPolElt ]
ReduceCharacters(I, C) : [ AlgChtrElt ], [ AlgChtrElt ] -> [ AlgChtrElt ], [ AlgChtrElt ]
ReduceCurve(C) : CrvHyp -> CrvHyp
ReduceGenerators(~G) : GrpPerm ->
ReduceGenerators(G) : GrpFP -> GrpFP, Map
ReduceGroebnerBasis(S) : [ RngMPolElt ] -> [ RngMPolElt ]
ReduceVector(W, ~v) : ModTupRng, ModTupRngElt ->
ReduceVector(W, v) : ModTupRng, ModTupRngElt -> ModTupRngElt
ModRng_Reduce (Example H64E8)
Pair Reduction (LATTICES)
The Reduced Form of a Matrix Module (FREE MODULES)
ReduceCharacters(I, C) : [ AlgChtrElt ], [ AlgChtrElt ] -> [ AlgChtrElt ], [ AlgChtrElt ]
ReduceCurve(C) : CrvHyp -> CrvHyp
HasReducedPoint(C) : CrvCon -> BoolElt, Pt
HasPoint(C) : CrvCon -> BoolElt, Pt
HasReducedAffinePoint(C) : CrvCon -> BoolElt, Pt
IsReduced(s) : GrphSpl -> BoolElt
IsReduced(p) : Pt -> BoolElt
IsReduced(f) : QuadBinElt -> BoolElt
IsReduced(C) : Sch -> BoolElt
IsReduced(X) : Sch -> BoolElt
ReducedAffineSolution(C) : CrvCon -> BoolElt, Pt
ReducedBasis(S) : AlgQuatOrd -> SeqEnum
ReducedBasis(S: Precision) : [JacHypPt] -> SeqEnum, AlgMatElt
ReducedDiscriminant(O) : RngOrd -> RngIntElt
ReducedForm(C) : CrvCon -> RngMPolElt, ModMatRngElt
ReducedForms(Q) : QuadBin -> [ QuadBinElt ]
ReducedGramMatrix(S) : AlgQuatOrd -> AlgMat
ReducedMinimalWeierstrassModel(C) : CrvHyp -> CrvHyp, MapCrvHyp
ReducedModel(C) : CrvHyp -> CrvHyp, MapCrvHyp
ReducedOrbits(Q) : QuadBin -> [ {@ QuadBinElt @} ]
ReducedProjectiveSolution(C) : CrvCon -> Pt
ReducedScheme(X) : Sch -> Sch
Reduction(f) : QuadBinElt -> QuadBinElt
Finding a Reduced Solution (RATIONAL CURVES AND CONICS)
ReducedAffineSolution(C) : CrvCon -> BoolElt, Pt
ReducedBasis(S) : AlgQuatOrd -> SeqEnum
ReducedBasis(S: Precision) : [JacHypPt] -> SeqEnum, AlgMatElt
ReducedDiscriminant(O) : RngOrd -> RngIntElt
ReducedForm(C) : CrvCon -> RngMPolElt, ModMatRngElt
Reduction(f) : QuadBinElt -> QuadBinElt
ReducedForms(Q) : QuadBin -> [ QuadBinElt ]
ReducedGramMatrix(S) : AlgQuatOrd -> AlgMat
ReducedMinimalWeierstrassModel(C) : CrvHyp -> CrvHyp, MapCrvHyp
ReducedModel(C) : CrvHyp -> CrvHyp, MapCrvHyp
ReducedOrbits(Q) : QuadBin -> [ {@ QuadBinElt @} ]
ReducedProjectiveSolution(C) : CrvCon -> Pt
ReducedScheme(X) : Sch -> Sch
GrpFP_1_ReduceGeneratingSet (Example H22E56)
ReduceGenerators(~G) : GrpPerm ->
ReduceGenerators(G) : GrpFP -> GrpFP, Map
ReduceGroebnerBasis(S) : [ RngMPolElt ] -> [ RngMPolElt ]
ModRng_ReduceHom (Example H64E9)
ReduceVector(W, ~v) : ModTupRng, ModTupRngElt ->
ReduceVector(W, v) : ModTupRng, ModTupRngElt -> ModTupRngElt
IsReducible(C) : Sch -> BoolElt
IsReducible(X) : Sch -> BoolElt
Reducing Vectors Relative to a Subspace (VECTOR SPACES)
Reducing Vectors Relative to a Subspace (VECTOR SPACES)
DegreeReduction(G) : GrpPerm -> GrpPerm, Hom
[Future release] GeneralisedRowReduction( rho ) : GrpLie, Map -> Map
Reduction(D) : DivFunElt -> DivFunElt, RngIntElt, DivFunElt, FldFunElt
Reduction(L) : LinSys -> LinSys
Reduction(p: parameters) : Pt -> Pt
Reduction(f) : QuadBinElt -> QuadBinElt
Reduction(I) : RngQuadFracIdl -> RngQuadFracIdl
ReductionOrbit(f) : QuadBinElt -> SeqEnum[QuadBinElt]
ReductionStep(f) : QuadBinElt -> QuadBinElt
Set_Reduction (Example H7E14)
Recursion, Reduction, and Iteration (SEQUENCES)
Reduction (SEQUENCES)
Reduction and Iteration over Sets (SETS)
Reduction of Matrices and Lattices (LATTICES)
Reduction and Iteration over Sets (SETS)
ReductionOrbit(f) : QuadBinElt -> SeqEnum[QuadBinElt]
Reductions(f, p) : ModFrmElt, RngIntElt -> List
Reduced Permutation Actions (PERMUTATION GROUPS)
Reductions and Embeddings (MODULAR FORMS)
Reductions and Embeddings (MODULAR FORMS)
ModForm_ReductionsAndEmbeddings (Example H90E16)
ReductionStep(f) : QuadBinElt -> QuadBinElt
ReductiveRank( G ) : GrpLie -> RngIntElt
Rank( G ) : GrpLie -> RngIntElt
ReductiveRank( G ) : GrpLie -> RngIntElt
Rank( G ) : GrpLie -> RngIntElt
Reductum(f) : RngMPolElt -> RngMPolElt
Reductum(f, i) : RngMPolElt, RngIntElt -> RngMPolElt
Reductum(f) : RngUPolElt -> RngUPolElt
EliminateRedundancy(~P) : Process(pQuot) ->
AddRedundantGenerators(G, Q) : GrpSLP, [ GrpSLPElt ] -> GrpSLP
ReedMullerCode(r, m) : RngIntElt, RngIntElt -> Code
ReedSolomonCode(K, d, b) : FldFin, RngIntElt, RngIntElt -> Code
ReedSolomonCode(n, d) : RngIntElt, RngIntElt -> Code
Reed--Solomon and Justesen Codes (LINEAR CODES OVER FINITE FIELDS)
Reed--Solomon and Justesen Codes (LINEAR CODES OVER FINITE FIELDS)
ReedMullerCode(r, m) : RngIntElt, RngIntElt -> Code
CodeFld_ReedMullerCode (Example H97E7)
ReedSolomonCode(K, d, b) : FldFin, RngIntElt, RngIntElt -> Code
ReedSolomonCode(n, d) : RngIntElt, RngIntElt -> Code
CremonaReference(D, E) : CrvEll -> MonStgElt
Reference Arguments (MAGMA SEMANTICS)
Reference Arguments (MAGMA SEMANTICS)
RefineSection(G, M, N) : GrpPerm, GrpPerm, GrpPerm -> [ GrpPerm ]
RefineSection(G, M, N) : GrpPerm, GrpPerm, GrpPerm -> [ GrpPerm ]
ImprimitiveReflectionGroup(GrpFP,{ m, p, n}) : Cat, RngIntElt, RngIntElt, RngIntElt -> GrpFP
ImprimitiveReflectionGroup(GrpFP,{ m, p, n}) : Cat, RngIntElt, RngIntElt, RngIntElt -> GrpFP
ImprimitiveReflectionGroup(m, p, n) : RngIntElt, RngIntElt, RngIntElt -> GrpMat, Fld
IsReflectionSubgroup( W, H ) : GrpCox -> GrpCox
ReflectionGroup(M) : AlgMatElt -> GrpMat, Fld
ReflectionGroup( W ) : GrpCox -> GrpMat, Map
ReflectionMatrices( RD ) : RootDtm -> []
ReflectionMatrix( RD, r ) : RootDtm, RngIntElt -> []
ReflectionPermutation( RD, r ) : RootDtm, RngIntElt -> []
ReflectionPermutations( RD ) : RootDtm -> []
ReflectionSubgroup( W, s ) : GrpCox, [] -> GrpCox
ReflectionSubgroup( W, a ) : GrpCox, {} -> GrpCox
SimpleReflectionMatrices( RD ) : RootDtm -> []
SimpleReflectionPermutations( RD ) : RootDtm -> []
Imprimitive Unitary Reflection Groups (REFLECTION GROUPS)
Primitive Unitary Reflection Groups (REFLECTION GROUPS)
ReflectionGroup(M) : AlgMatElt -> GrpMat, Fld
ReflectionGroup( W ) : GrpCox -> GrpMat, Map
GrpCox_ReflectionGroups (Example H36E11)
CoreflectionMatrices( RD ) : RootDtm -> []
ReflectionMatrices( RD ) : RootDtm -> []
CoreflectionMatrix( RD, r ) : RootDtm, RngIntElt -> []
ReflectionMatrix( RD, r ) : RootDtm, RngIntElt -> []
ReflectionPermutation( RD, r ) : RootDtm, RngIntElt -> []
ReflectionPermutations( RD ) : RootDtm -> []
ReflectionSubgroup( W, s ) : GrpCox, [] -> GrpCox
ReflectionSubgroup( W, a ) : GrpCox, {} -> GrpCox
GrpCox_ReflectionSubgroups (Example H36E2)
Regexp(R, S) : MonStgElt, MonStgElt -> BoolElt, MonStgElt, [ MonStgElt ]
IO_Regexp (Example H3E3)
IsDistanceRegular(G) : GrphUnd -> BoolElt
IsLineRegular(D) : IncNsp -> BoolElt, RngIntElt
IsPointRegular(D) : IncNsp -> BoolElt, RngIntElt
IsRegular(a) : AlgGenElt -> BoolElt
IsRegular(G) : Grph -> BoolElt
IsRegular(s) : GrphSpl -> BoolElt
IsRegular(G, Y) : GrpPerm, GSet -> BoolElt
IsRegular(f) : MapSch -> BoolElt
RegularRepresentation(v) : AlgBasElt -> AlgMatElt
[Future release] RegularRepresentation( G ) : GrpLie -> Map
RegularRepresentation(A : parameters) : AlgAss -> AlgMat, Map
RegularSpliceDiagram(P) : PnclJac -> GrphSpl
RegularSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
RightRegularModule(B) : AlgBas -> ModAlg
StronglyRegularGraphsDatabase() : -> DB
Strongly Regular Graphs (GRAPHS)
Symmetry and Regularity Properties of Graphs (GRAPHS)
Transitivity Properties (FINITE PLANES)
RegularRepresentation(v) : AlgBasElt -> AlgMatElt
[Future release] RegularRepresentation( G ) : GrpLie -> Map
RegularRepresentation(A : parameters) : AlgAss -> AlgMat, Map
RegularSpliceDiagram(P) : PnclJac -> GrphSpl
RegularSubgroups(G: parameters) : GrpFin -> [ rec< Grp, RngIntElt, RngIntElt, GrpFP> ]
Regulator(O: parameters) : RngOrd -> FldPrElt
Regulator(H: parameters) : SetPtEll -> FldPrElt
Regulator(S: Precision) : [JacHypPt] -> FldPrElt
Regulator(O) : RngFunOrd -> RngIntElt
Regulator(S) : [ PtEll ] -> FldPrElt
RegulatorLowerBound(O) : RngOrd -> FldPrElt
RegulatorLowerBound(O) : RngOrd -> FldPrElt
ReidNumber(X) : VSrfK3 -> RngIntElt
FletcherNumber(X) : VSrfK3 -> RngIntElt
AltinokNumber(X) : VSrfK3 -> RngIntElt
AFRNumber(X) : VSrfK3 -> RngIntElt
ReidNumber(X) : VSrfK3 -> RngIntElt
FletcherNumber(X) : VSrfK3 -> RngIntElt
AltinokNumber(X) : VSrfK3 -> RngIntElt
AFRNumber(X) : VSrfK3 -> RngIntElt
PrintRelat(SQP : parameters) : SQProc ->
Factorization Related Functions (RING OF INTEGERS)
Other Related Structures (ALGEBRAIC FUNCTION FIELDS)
Other Related Structures (ALGEBRAIC FUNCTION FIELDS)
Related functions (IDEAL THEORY AND GRÖBNER BASES)
Related Functions (MATRIX GROUPS)
Related Operations on Matrix Groups (LATTICES)
Related Structures (ALGEBRAIC FUNCTION FIELDS)
Related Structures (ALGEBRAICALLY CLOSED FIELDS)
Related Structures (BINARY QUADRATIC FORMS)
Related Structures (CHARACTERS OF FINITE GROUPS)
Related structures (COXETER GROUPS)
Related Structures (CYCLOTOMIC FIELDS)
Related Structures (FINITE FIELDS)
Related Structures (GALOIS RINGS)
Related Structures (INTRODUCTION [BASIC RINGS])
Related Structures (ORDERS AND ALGEBRAIC FIELDS)
Related Structures (POWER, LAURENT AND PUISEUX SERIES)
Related Structures (REAL AND COMPLEX FIELDS)
Related Structures (RING OF INTEGERS)
Related structures (ROOT DATA FOR LIE THEORY)
Related Structures (VALUATION RINGS)
The Construction of Related Structures (INCIDENCE STRUCTURES AND DESIGNS)
Design_related (Example H94E3)
Related Structures (ALGEBRAIC FUNCTION FIELDS)
Related structures (ROOT DATA FOR LIE THEORY)
FldFunG_related-structures (Example H57E4)
AddRelation(G, g) : GrpFP, GrpFPElt -> GrpFP
AddRelation(G, g, i) : GrpFP, GrpFPElt, RngIntElt -> GrpFP
AddRelation(G, r) : GrpFP, GrpFPRel -> GrpFP
AddRelation(G, r, i) : GrpFP, GrpFPRel, RngIntElt -> GrpFP
AddRelation(S, r) : SgpFP, Rel -> SgpFP
DeleteRelation(G, g) : GrpFP, GrpFPElt -> GrpFP
DeleteRelation(G, r) : GrpFP, GrpFPRel -> GrpFP
DeleteRelation(G, i) : GrpFP, RngIntElt -> GrpFP
DeleteRelation(S, r) : SgpFP, Rel -> SgpFP
DeleteRelation(S, i) : SgpFP, RngIntElt -> SgpFP
LinearRelation(q: parameters) : [ FldPrElt ] -> [ RngIntElt ]
PowerRelation(r, k: parameters) : FldPrElt, RngIntElt -> RngUPolElt
RelationIdeal(R) : RngInvar -> RngMPol
RelationIdeal(Q) : [ RngMPol ] -> RngMPol
RelationMatrix(K, B) : FldNum, RngIntElt -> ModHomElt
RelationMatrix(O) : RngOrd -> ModHomElt
ReplaceRelation(G, s, r) : GrpFP, GrpFPRel, GrpFPRel -> GrpFP
ReplaceRelation(G, i, g) : GrpFP, RngIntElt, GrpFPElt -> GrpFP
ReplaceRelation(G, i, r) : GrpFP, RngIntElt, GrpFPRel -> GrpFP
ReplaceRelation(S, i, r) : SgpFP RngIntElt, Rel -> SgpFP
ReplaceRelation(S, r_1, r_2) : SgpFP, Rel, Rel -> SgpFP
Editing Defining Relations (FINITELY PRESENTED ALGEBRAS)
Relation Ideals (IDEAL THEORY AND GRÖBNER BASES)
Relations (ABELIAN GROUPS)
Relations (FINITELY PRESENTED GROUPS)
Relations (FINITELY PRESENTED SEMIGROUPS)
Specification of a Relation (FINITELY PRESENTED ALGEBRAS)
Editing Defining Relations (FINITELY PRESENTED ALGEBRAS)
RelationIdeal(R) : RngInvar -> RngMPol
RelationIdeal(Q) : [ RngMPol ] -> RngMPol
GB_RelationIdeal (Example H50E14)
RelationMatrix(K, B) : FldNum, RngIntElt -> ModHomElt
RelationMatrix(O) : RngOrd -> ModHomElt
CollectRelations(~P) : Process(pQuot) ->
NumberOfRelations(G) : GrpAtc -> RngIntElt
NumberOfRelations(G) : GrpRWS -> RngIntElt
NumberOfRelations(M) : MonRWS -> RngIntElt
NumberOfRelations(P) : Process(Tietze) -> RngIntElt
QuotientRelations(M) : ModMPol -> [ ModMPol ]
Relations(A) : AlgFP -> [ Rel ]
Relations(A) : GrpAb -> [ Rel ]
Relations(G) : GrpFP -> [ GrpFPRel ]
Relations(M, d, prec) : ModFrm, RngIntElt -> SeqEnum
Relations(G) : GrpAtc -> [GrpFPRel]
Relations(G) : GrpRWS -> [GrpFPRel]
Relations(M) : MonRWS -> [MonFPRel]
Relations(R) : RngInvar -> [ RngMPolElt ]
Relations(O) : RngOrd -> ModHomElt
Relations(L, R) : SeqEnum[ DiffFunElt ], Rng -> ModTupRng
Relations(L, R) : SeqEnum[ FldFunElt ], Rng -> ModTupRng
Relations(S) : SgpFP -> [ Rel ]
GrpAb_Relations (Example H28E2)
GrpAb_Relations (Example H28E4)
GrpFP_1_Relations (Example H22E4)
ModForm_Relations (Example H90E18)
RngInvar_Relations (Example H78E10)
Algebraic Relations (MODULAR FORMS)
Projection and Unprojection (THE K3 DATABASE)
Relations (SUBGROUPS OF PSL_2(R))
Relations between K3 Surfaces (THE K3 DATABASE)
The Algebra of an Invariant Ring and Algebraic Relations (INVARIANT RINGS OF FINITE GROUPS)
Relations (SUBGROUPS OF PSL_2(R))
RelativePrecision(s) : FldPrElt -> RngIntElt
Precision(s) : FldPrElt -> RngIntElt
RelativeField(F, L) : FldAlg, FldAlg -> FldAlg
RelativePrecision(x) : RngLocElt -> RngIntElt
RelativePrecision(f) : RngSerElt -> RngIntElt
RelativeField(F, L) : FldAlg, FldAlg -> FldAlg
RelativePrecision(s) : FldPrElt -> RngIntElt
Precision(s) : FldPrElt -> RngIntElt
RelativePrecision(x) : RngLocElt -> RngIntElt
RelativePrecision(f) : RngSerElt -> RngIntElt
AddRelator(~P, w) : GrpFPCosetEnumProc, GrpFPElt ->
Magma Updates (OVERVIEW)
Calculating the Relevant Primes (FP GROUPS - ADVANCED FEATURES)
Relevant Primes (FP GROUPS - ADVANCED FEATURES)
Calculating the Relevant Primes (FP GROUPS - ADVANCED FEATURES)
Relevant Primes (FP GROUPS - ADVANCED FEATURES)
ChineseRemainderTheorem(I1, L1, e1, L2) : RngOrdIdl, [RngIntElt], RngOrdElt, [RngIntElt] -> RngOrdElt
ClassRepresentative(I) : RngOrdFracIdl -> RngOrdFracIdl
CRT(I1, L1, e1, L2) : RngOrdIdl, [RngIntElt], RngOrdElt, [RngIntElt] -> RngOrdElt
ChineseRemainderTheorem(I, J, a, b) : RngInt, RngInt, RngIntElt, RngIntElt -> RngIntElt
ChineseRemainderTheorem(I1, I2, e1, e2) : RngOrdIdl, RngOrdIdl, RngOrdElt, RngOrdElt -> RngOrdElt
ChineseRemainderTheorem(X, N) : [RngIntElt], [RngIntElt] -> RngIntElt
PseudoRemainder(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
Rings, Fields, and Algebras (OVERVIEW)
TransversalProcessRemaining(P) : GrpPermTransProc -> RngIntElt
RemoveWeight(X,w) : VSrfK3,RngIntElt -> VSrfK3
AddWeight(X,w) : VSrfK3,RngIntElt -> VSrfK3
Remove(~S, i) : SeqEnum, RngIntElt ->
RemoveConstraint(L, n) : LP, RngIntElt ->
RemoveEdge(~G, i, j) : Grph, RngIntElt, RngIntElt ->
RemoveEdges(~G, S) : Grph, SeqEnum ->
RemoveIrreducibles(I, C) : [ AlgChtrElt ], [ AlgChtrElt ] -> [ AlgChtrElt ], [ AlgChtrElt ]
RemoveVertex(~G, i) : Grph, RngIntElt ->
RemoveVertices(~G, S) : Grph, [RngIntElt] ->
RemoveConstraint(L, n) : LP, RngIntElt ->
G -:= i, j : GrphUnd, { RngIntElt, RngIntElt } ->
RemoveEdge(~G, i, j) : Grph, RngIntElt, RngIntElt ->
RemoveEdges(~G, S) : Grph, SeqEnum ->
RemoveIrreducibles(I, C) : [ AlgChtrElt ], [ AlgChtrElt ] -> [ AlgChtrElt ], [ AlgChtrElt ]
G -:= i : Grph, RngIntElt ->
RemoveVertex(~G, i) : Grph, RngIntElt ->
RemoveVertices(~G, S) : Grph, [RngIntElt] ->
RemoveWeight(X,w) : VSrfK3,RngIntElt -> VSrfK3
AddWeight(X,w) : VSrfK3,RngIntElt -> VSrfK3
ExtractRep(~R, ~r) : SetEnum, Elt ->
Rep(G) : GrpAb -> GrpAbElt
Rep(G) : GrpSLP -> GrpSLPElt
Rep(C) : SetCart -> Elt
Representative(G) : GrpAtc -> GrpAtcElt
Representative(G) : GrpFin -> GrpFinElt
Representative(G) : GrpGPC -> GrpGPCElt
Representative(G) : GrpPC -> GrpPCElt
Representative(G) : GrpPerm -> GrpPermElt
Representative(G) : GrpRWS -> GrpRWSElt
Representative(b) : IncBlk -> IncPt
Representative(B) : IncBlkSet -> IncBlk
Representative(P) : IncPtSet -> IncPt
Representative(M) : MonRWS -> MonRWSElt
Representative(l) : PlaneLn -> PlanePt
Representative(L) : PlaneLnSet -> PlaneLn
Representative(V) : PlanePtSet -> PlanePt
Representative(R) : Rng -> RngElt
Representative(R) : SeqEnum -> Elt
Representative(R) : SetIndx -> Elt
Writing Representations over Subfields (MATRIX GROUPS)
rep{ e(x) : x in E | P(x) }
rep{ e(x_1, ..., x_k) : x_1 in E_1, ...,x_k in E_k | P(x_1, ..., x_k) }
Indefinite Iteration (STATEMENTS AND EXPRESSIONS)
The repeat statement (OVERVIEW)
repeat statements until boolexpr : ->
State_repeat (Example H1E14)
Indefinite Iteration (STATEMENTS AND EXPRESSIONS)
RepetitionCode(R, n) : FldFin, RngIntElt -> Code
RepetitionCode(R, n) : Rng, RngIntElt -> Code
RepetitionCode(R, n) : FldFin, RngIntElt -> Code
RepetitionCode(R, n) : Rng, RngIntElt -> Code
ReplacePrimes(SQP, m: IsComplete): SQProc, SetEnum ->
ReplaceRelation(G, s, r) : GrpFP, GrpFPRel, GrpFPRel -> GrpFP
ReplaceRelation(G, i, g) : GrpFP, RngIntElt, GrpFPElt -> GrpFP
ReplaceRelation(G, i, r) : GrpFP, RngIntElt, GrpFPRel -> GrpFP
ReplaceRelation(S, i, r) : SgpFP RngIntElt, Rel -> SgpFP
ReplaceRelation(S, r_1, r_2) : SgpFP, Rel, Rel -> SgpFP
GrpFP_2_Replace (Example H23E1)
ReplacePrimes(SQP, m: IsComplete): SQProc, SetEnum ->
ReplaceRelation(G, s, r) : GrpFP, GrpFPRel, GrpFPRel -> GrpFP
ReplaceRelation(G, i, g) : GrpFP, RngIntElt, GrpFPElt -> GrpFP
ReplaceRelation(G, i, r) : GrpFP, RngIntElt, GrpFPRel -> GrpFP
ReplaceRelation(S, i, r) : SgpFP RngIntElt, Rel -> SgpFP
ReplaceRelation(S, r_1, r_2) : SgpFP, Rel, Rel -> SgpFP
ReplicationNumber(D) : Dsgn -> RngIntElt
ReplicationNumber(D) : Dsgn -> RngIntElt
FldQuad_Represent (Example H54E4)
AbsoluteRepresentation(M) : GrpMat -> GrpMat
AbsoluteRepresentationMatrix(a) : FldAlgElt -> AlgMatElt
CartierRepresentation(F) : FldFunG -> AlgMatElt, SeqEnum[DiffFunElt]
ChangeRepresentationType(A, Rep) : AlgGrp, MonStgElt -> AlgGrp, Map
CosetTableToRepresentation(G, T): GrpFP, Map -> Map, GrpPerm, Grp
OptimizedRepresentation(F) : FldAlg -> FldAlg, map
OptimizedRepresentation(O) : RngOrd -> BoolElt, RngOrd, Map
PermutationRepresentation(A) : GrpAuto -> Map, GrpPerm, SetIndx
PermutationRepresentation(D, i: parameters): DB, RngIntElt -> Hom(Grp), GrpFP, GrpPerm
ProductRepresentation(a) : FldFunGElt -> [FldFunGElt], [RngIntElt]
ProductRepresentation(a) : RngFunOrdElt -> [RngElt], [RngIntElt]
ProductRepresentation(Q, S) : [FldFunGElt], [RngIntElt] -> FldFunGElt
RationalExtensionRepresentation(F) : FldFunG -> FldFun
RegularRepresentation(v) : AlgBasElt -> AlgMatElt
[Future release] RegularRepresentation( G ) : GrpLie -> Map
RegularRepresentation(A : parameters) : AlgAss -> AlgMat, Map
Representation(g) : GrpAbGenElt -> [RngIntElt]
Representation(M) : ModGrp -> Map(Hom)
Representation(S, g) : SeqEnum, GrpAbGenElt -> [RngIntElt], RngIntElt
RepresentationMatrix(a) : FldAlgElt -> AlgMatElt
RepresentationMatrix(a) : FldFunGElt -> AlgMatElt
RepresentationMatrix(a) : RngFunOrdElt -> AlgMatElt
RepresentationMatrix(f) : RngMPolResElt -> AlgMatElt
RepresentationNumber(f, n) : QuadBinElt, RngIntElt -> RngIntElt
RepresentationType(A) : AlgGrp -> MonStgElt
StandardRepresentation( G ) : GrpLie -> Map
SubfieldRepresentationCode(C, S) : Code, FldFin -> Code
SubfieldRepresentationParityCode(C, K) : Code, FldFin -> Code
UserRepresentation(g) : GrpAbGenElt -> [RngIntElt]
ModAlg_Representation (Example H76E10)
ModSym_Representation (Example H88E9)
Associated Vector Space (MODULAR SYMBOLS)
Characters and Representations (GROUPS)
Representation (ALGEBRAICALLY CLOSED FIELDS)
Representation (MULTIVARIATE POLYNOMIAL RINGS)
Representation (QUADRATIC FIELDS)
Representation (RATIONAL FIELD)
Representation (RING OF INTEGERS)
Representation (RING OF INTEGERS)
Representation (UNIVARIATE POLYNOMIAL RINGS)
Representation of an Element (GENERIC ABELIAN GROUPS)
Representation of Finite Fields (FINITE FIELDS)
Representation of Series (POWER, LAURENT AND PUISEUX SERIES)
Representation of Strings (INPUT AND OUTPUT)
Representation Theory (ABELIAN GROUPS)
Representation Theory (FINITE SOLUBLE GROUPS)
Representation Theory (FINITELY PRESENTED GROUPS)
Representation Theory (GROUPS)
Representation Theory (MATRIX GROUPS)
Representation Theory (PERMUTATION GROUPS)
Representation Theory (POLYCYCLIC GROUPS)
The Representation Afforded by a K[G]-module (MODULES OVER A MATRIX ALGEBRA)
Representation Theory (POLYCYCLIC GROUPS)
ModSym_RepresentationConversion (Example H88E5)
RepresentationMatrix(a) : FldAlgElt -> AlgMatElt
RepresentationMatrix(a) : FldFunGElt -> AlgMatElt
RepresentationMatrix(a) : RngFunOrdElt -> AlgMatElt
RepresentationMatrix(f) : RngMPolResElt -> AlgMatElt
RepresentationNumber(f, n) : QuadBinElt, RngIntElt -> RngIntElt
AbsolutelyIrreducibleModules(G, k: parameters) : GrpPC, Rng -> List[GModule]
AbsolutelyIrreducibleRepresentations(G, k: parameters) : GrpPC, Rng -> List[Map]
IrreducibleRepresentations(G, k: parameters) : GrpPC, Rng -> List[Map]
NumberOfRepresentations(D, i): DB, RngIntElt -> RngIntElt
Matrix representations (GROUPS OF LIE TYPE)
Representations of an Automorphism Group (AUTOMORPHISM GROUPS OF GROUPS)
GrpFP_1_RepresentationTheory (Example H22E59)
GrpGPC_RepresentationTheory (Example H24E13)
RepresentationType(A) : AlgGrp -> MonStgElt
ChineseRemainderTheorem(I1, L1, e1, L2) : RngOrdIdl, [RngIntElt], RngOrdElt, [RngIntElt] -> RngOrdElt
ClassRepresentative(I) : RngOrdFracIdl -> RngOrdFracIdl
CRT(I1, L1, e1, L2) : RngOrdIdl, [RngIntElt], RngOrdElt, [RngIntElt] -> RngOrdElt
ClassRepresentative(G, x) : GrpAb, GrpAbElt -> GrpAbElt
ClassRepresentative(G, x) : GrpFin, GrpFinElt -> GrpFinElt
ClassRepresentative(G, x) : GrpMat, GrpMatElt -> GrpMatElt
ClassRepresentative(G, x) : GrpPC, GrpPCElt -> GrpPCElt
ClassRepresentative(G, x) : GrpPerm, GrpPermElt -> GrpPermElt
ClassRepresentative(I) : RngInt -> RngInt
Representative(G) : GrpAtc -> GrpAtcElt
Representative(G) : GrpFin -> GrpFinElt
Representative(G) : GrpGPC -> GrpGPCElt
Representative(G) : GrpPC -> GrpPCElt
Representative(G) : GrpPerm -> GrpPermElt
Representative(G) : GrpRWS -> GrpRWSElt
Representative(b) : IncBlk -> IncPt
Representative(B) : IncBlkSet -> IncBlk
Representative(P) : IncPtSet -> IncPt
Representative(M) : MonRWS -> MonRWSElt
Representative(l) : PlaneLn -> PlanePt
Representative(L) : PlaneLnSet -> PlaneLn
Representative(V) : PlanePtSet -> PlanePt
Representative(R) : Rng -> RngElt
Representative(L) : RngLoc -> RngLocElt
Representative(R) : SeqEnum -> Elt
Representative(R) : SetIndx -> Elt
Representative(G) : SymGen -> Lat
Representative(G) : SymGen -> Lat
Representative(G) : SymGenLoc -> Lat
RepresentativeCocycles (G, U, Ext, Hom) : GrpPC, GrpPC, [AlgMatElt], [AlgMatElt]-> [AlgMatElt]
RepresentativePoint(P) : PlcCrv -> Pt
RepresentativeCocycles (G, U, Ext, Hom) : GrpPC, GrpPC, [AlgMatElt], [AlgMatElt]-> [AlgMatElt]
RepresentativePoint(P) : PlcCrv -> Pt
CosetRepresentatives(G) : GrpPSL2 -> SeqEnum
CosetRepresentatives(FS) : SymFry -> SeqEnum
GenusRepresentatives(L) : Lat -> [ Lat ]
Representatives(G) : SymGen -> [ Lat ]
OrbitRepresentatives(G) : GrpPerm -> SeqEnum
GrpPC_Reps (Example H25E27)
RngInt_RepUnits (Example H40E6)
Argument Checking (FUNCTIONS, PROCEDURES AND PACKAGES)
require condition: print_args;
Func_require (Example H2E8)
requirege v, L;
requirerange v, L, U;
ResetMaximumMemoryUsage() : ->
ResetMaximumMemoryUsage() : ->
Residual(D, b) : Inc, IncBlk -> Inc
Residual(D, p) : Inc, IncPt -> Inc
SolubleResidual(G) : GrpFin -> GrpFin
SolubleResidual(G) : GrpMat -> GrpMat
SolubleResidual(G) : GrpPerm -> GrpPerm
IsRC(C) : CosetGeom -> BoolElt
IsResiduallyConnected(C) : CosetGeom -> BoolElt
IsResiduallyConnected(D) : IncGeom -> BoolElt
BiquadraticResidueSymbol(a, b) : RngQuadElt, RngQuadElt -> RngQuadElt
Degree(I) : RngFunOrdIdl -> RngIntElt
InertiaDegree(P) : PlcFunElt -> RngIntElt
PowerResidueCode(K,n,p) : FldFin, RngIntElt, RngIntElt -> Code
RayResidueRing(m) : RngOrdIdl -> GrpAb, Map
Residue(C, f) : CosetGeom, Set -> CosetGeom
Residue(d, P) : DiffFunElt, PlcFunElt -> RngElt
Residue(a,P) : DiffFunElt,PlcCrvElt -> RngElt
Residue(D, f) : IncGeom, Set -> IncGeom
ResidueClassField(P) : PlcFunElt -> Rng
ResidueClassField(R, I) : Rng, Rng -> Fld, Map
ResidueClassField(I) : RngFunOrdIdl -> Rng, Map
ResidueClassField(L) : RngLoc -> FldFin, Map
ResidueClassField(P) : RngLoc -> FldFin, Map
ResidueClassField(O, I) : RngOrd, RngOrdIdl -> FldFin, Map
ResidueClassRing(m) : RngIntElt -> RngIntRes
ResidueClassRing(Q) : RngIntEltFact -> RngIntRes
ResidueField(R) : RngGal -> RngIntElt
Quadratic Residue Codes and their Generalizations (LINEAR CODES OVER FINITE FIELDS)
Residue Class Fields (INTRODUCTION [BASIC RINGS])
Residue Class Rings (RING OF INTEGERS)
Rings, Fields, and Algebras (OVERVIEW)
Lcm(Q) : Seq(RngIntResElt) -> RngIntResElt
LCM(Q) : Seq(RngIntResElt) -> RngIntResElt
Residue Class Rings (RING OF INTEGERS)
Residue Class Fields (INTRODUCTION [BASIC RINGS])
InertiaDegree(I) : RngFunOrdIdl -> RngIntElt
ResidueClassDegree(I) : RngFunOrdIdl -> RngIntElt
Degree(I) : RngFunOrdIdl -> RngIntElt
InertiaDegree(P) : PlcFunElt -> RngIntElt
ResidueClassField(P) : PlcFunElt -> Rng
ResidueClassField(R, I) : Rng, Rng -> Fld, Map
ResidueClassField(I) : RngFunOrdIdl -> Rng, Map
ResidueClassField(L) : RngLoc -> FldFin, Map
ResidueClassField(P) : RngLoc -> FldFin, Map
ResidueClassField(O, I) : RngOrd, RngOrdIdl -> FldFin, Map
IntegerRing(m) : RngIntElt -> RngIntRes
Integers(m) : RngIntElt -> RngIntRes
RingOfIntegers(m) : RngIntElt -> RngIntRes
ResidueClassRing(m) : RngIntElt -> RngIntRes
ResidueClassRing(Q) : RngIntEltFact -> RngIntRes
ResidueField(R) : RngGal -> RngIntElt
Residues (INCIDENCE GEOMETRY)
Design_resol-parallel (Example H94E9)
CompactInjectiveResolution(M, n) : ModAlg, RngIntElt -> List, ModMatFldElt
CompactProjectiveResolution(M, n) : ModAlg, RngIntElt -> Tup
FreeResolution(M) : ModMPol -> [ ModMPol ]
FreeResolution(R) : RngInvar -> [ ModMPol ]
HasResolution(D) : Inc -> BoolElt, { SetEnum }, RngIntElt
HasResolution(D, lambda) : Inc, RngIntElt -> BoolElt, { SetEnum }
InjectiveResolution(M, n) : ModAlg, RngIntElt -> ModCpx, ModMatFldElt
IsResolution(D, P) : Inc, SetEnum[SetEnum] -> BoolElt, RngIntElt
MakeResolutionGraph(g,s,t) : GrphDir,SeqEnum,SeqEnum -> GrphRes
MakeResolutionGraph(N) : NewtonPgon -> GrphRes
MinimalFreeResolution(M) : ModMPol -> [ ModMPol ]
MinimalFreeResolution(M) : ModMPol -> [ ModMPol ]
ProjectiveResolution(M, n) : ModAlg, RngIntElt -> ModCpx, ModMatFldElt
ResolutionGraph(p) : Grm -> GrphRes
ResolutionGraph(v) : GrphResVert -> GrphRes
ResolutionGraph(P) : PnclJac -> GrphRes
ResolutionGraph(P,a,b) : PnclJac,RngElt,RngElt -> GrphRes
ResolutionGraph(C,p) : Sch,Pt -> GrphRes
ResolutionGraphVertex(g,i) : GrphRes,RngIntElt -> GrphResVert
Free Resolutions (MODULES OVER AFFINE ALGEBRAS)
Resolution Graphs (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Splice Diagrams from Resolution Graphs (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Resolution Graphs (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Splice Diagrams from Resolution Graphs (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
ResolutionGraph(p) : Grm -> GrphRes
ResolutionGraph(v) : GrphResVert -> GrphRes
ResolutionGraph(P) : PnclJac -> GrphRes
ResolutionGraph(P,a,b) : PnclJac,RngElt,RngElt -> GrphRes
ResolutionGraph(C,p) : Sch,Pt -> GrphRes
g ! i : GrphRes,RngIntElt -> GrphResVert
ResolutionGraphVertex(g,i) : GrphRes,RngIntElt -> GrphResVert
AllResolutions(D) : Inc -> SeqEnum
AllResolutions(D, lambda) : Inc, RngIntElt -> SeqEnum
Resolutions, Parallelisms and Parallel Classes (INCIDENCE STRUCTURES AND DESIGNS)
Saving and restoring Magma states (OVERVIEW)
restore "filename";
RestrictField(G, S) : GrpMat, FldFin -> GrpMat, Map
RestrictField(V, L) : ModTupFld, Fld -> ModTupFld, MapHom
SubfieldSubcode(C, S) : Code, FldFin -> Code, Map
IsRestrictedLieAlgebra(L) : AlgLie -> BoolElt
RestrictedPartitions(n, k, M) : RngIntElt, SetEnum -> [ [ RngIntElt ] ]
RestrictedPartitions(n, k, M) : RngIntElt, SetEnum -> [ [ RngIntElt ] ]
RestrictedPartitions(n, M) : RngIntElt, SetEnum -> [ [ RngIntElt ] ]
RestrictedPartitions(n, Q) : RngIntElt, SetEnum -> [ [ RngIntElt ] ]
RestrictedPartitions(n, k, M) : RngIntElt, SetEnum -> [ [ RngIntElt ] ]
RestrictedPartitions(n, k, M) : RngIntElt, SetEnum -> [ [ RngIntElt ] ]
RestrictedPartitions(n, M) : RngIntElt, SetEnum -> [ [ RngIntElt ] ]
RestrictedPartitions(n, Q) : RngIntElt, SetEnum -> [ [ RngIntElt ] ]
EnumComb_RestrictedPartitions (Example H92E3)
RestrictField(G, S) : GrpMat, FldFin -> GrpMat, Map
RestrictField(V, L) : ModTupFld, Fld -> ModTupFld, MapHom
SubfieldSubcode(C, S) : Code, FldFin -> Code, Map
Restriction(x, H) : AlgChtrElt, Grp -> AlgChtrElt
Restriction(D, S) : IncNsp, { Incpt } -> IncNsp
Restriction(f,X,Y) : MapSch,Sch,Sch -> MapSch
Restriction(M, H) : ModGrp, Grp -> ModGrp
RestrictionToPatch(f,j) : MapSch,RngIntElt -> MapSch
RestrictionToPatch(f,i,j) : MapSch,RngIntElt,RngIntElt -> MapSch
WeilRestriction(E, n) : FldFun, RngIntElt -> FldFun, UserProgram
Compatibility (SEQUENCES)
Compatibility (SETS)
Induction and Restriction (MODULES OVER A MATRIX ALGEBRA)
Induction, Restriction, Extension (CHARACTERS OF FINITE GROUPS)
Introduction to Matrix Groups (MATRIX GROUPS)
Restrictions on Sets and Sequences (INTRODUCTION [SETS, SEQUENCES, AND MAPPINGS])
Explicit Restrictions (SCHEMES)
Geometrical Restrictions (SCHEMES)
RestrictionToPatch(f,j) : MapSch,RngIntElt -> MapSch
RestrictionToPatch(f,i,j) : MapSch,RngIntElt,RngIntElt -> MapSch
Resultant(f, g, i) : RngMPolElt, RngMPolElt, RngIntElt -> RngMPolElt
Resultant(f, g) : RngUPolElt, RngUPolElt -> RngElt
Resultant and Discriminant (UNIVARIATE POLYNOMIAL RINGS)
Resultants and Discriminants (MULTIVARIATE POLYNOMIAL RINGS)
Resultant and Discriminant (UNIVARIATE POLYNOMIAL RINGS)
Resultants and Discriminants (MULTIVARIATE POLYNOMIAL RINGS)
ResumeEnumeration(~P: parameters) : GrpFPCosetEnumProc ->
ResumeEnumeration(~P: parameters) : GrpFPCosetEnumProc ->
Retrieve(x) : CopElt -> Elt
Retrieve (COPRODUCTS)
Return (OVERVIEW)
<Return>
IsReverseLatticeWord(w) : SeqEnum -> BoolElt
Reverse(~S) : SeqEnum ->
ReverseFilling(P1) : SeqEnum -> Tableau
ReverseFilling(P1, P2) : SeqEnum,SeqEnum -> Tableau
Reversion(f) : RngSerElt -> RngSerElt
ReverseFilling(P1) : SeqEnum -> Tableau
ReverseFilling(P1, P2) : SeqEnum,SeqEnum -> Tableau
Reverse(f) : RngSerElt -> RngSerElt
Reversion(f) : RngSerElt -> RngSerElt
Composition and Reversion (POWER, LAURENT AND PUISEUX SERIES)
RevertClass(~P) : Process(pQuot) ->
RevertClass(~P) : Process(pQuot) ->
Rewind(F) : File ->
Rewrite(G, H : parameters) : GrpFP, GrpFP -> GrpFP, Map
GrpFP_1_Rewrite (Example H22E35)
GROUPS DEFINED BY REWRITE SYSTEMS
MONOIDS GIVEN BY REWRITE SYSTEMS
Rewrite Group Predicates (GROUPS DEFINED BY REWRITE SYSTEMS)
Rewrite Monoid Predicates (MONOIDS GIVEN BY REWRITE SYSTEMS)
Rewrite Group Predicates (GROUPS DEFINED BY REWRITE SYSTEMS)
Rewrite Monoid Predicates (MONOIDS GIVEN BY REWRITE SYSTEMS)
GROUPS DEFINED BY REWRITE SYSTEMS
MONOIDS GIVEN BY REWRITE SYSTEMS
Rewriting (FINITELY PRESENTED GROUPS)
ReynoldsOperator(f, G) : RngMPolElt, GrpMat -> RngMPolElt
ReynoldsOperator(f, G) : RngMPolElt, GrpMat -> RngMPolElt
DickmanRho(u) : FldPrElt -> FldReElt;
PollardRho(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]
RHS(r) : Rel -> AlgFPElt
RHS(r) : Rel -> SgpFPElt
r[2] : GrpAbRel, RngIntElt -> GrpAbElt
r[2] : GrpFPRel, RngIntElt -> GrpFPElt
IsLittleWoodRichardsonSkew(t) : Tableau -> BoolElt
Constructor (OVERVIEW)
RightIdeal(S,X) : AlgQuatOrd, [AlgQuatOrdElt] -> AlgQuatOrd
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
RiemannRochSpace(D) : DivCrvElt -> ModTupFld,Map
RiemannRochSpace(D) : DivFunElt -> ModFld, Map
Riemann--Roch Spaces (PLANE ALGEBRAIC CURVES)
Riemann--Roch Spaces (PLANE ALGEBRAIC CURVES)
RiemannRochSpace(D) : DivCrvElt -> ModTupFld,Map
RiemannRochSpace(D) : DivFunElt -> ModFld, Map
RightAction(M) : ModTupRng -> AlgMat
Action(M) : ModTupRng -> AlgMat
ActionGenerator(M, i) : ModTupRng, RngIntElt -> AlgMatElt
CohomologyRightModuleGenerators(P, Q, CQ) : Tup, Tup, Tup -> Tup
IsRightIdeal(S) : AlgGrpSub -> BoolElt
IsRightIsomorphic(I,J) : AlgQuatOrd, AlgQuatOrd -> BoolElt, Map, AlgQuatElt
MaximalLeftIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
MinimalLeftIdeals(A : parameters) : AlgGen -> [ AlgGen ], BoolElt
RightAnnihilator(A, B) : AlgAss, AlgAss -> AlgAss, AlgAss
RightAnnihilator(S) : AlgGrpSub -> AlgGrpSub
RightCosetSpace(P) : GrpFPCosetEnumProc -> GrpFPCos
RightCosetSpace(G, H: parameters) : GrpFP, GrpFP -> GrpFPCos
RightDescentSet( W, w ) : GrpCox, GrpPermElt -> {}
RightExactExtension(C) : ModCpx -> ModCpx
RightIdeal(S,X) : AlgQuatOrd, [AlgQuatOrdElt] -> AlgQuatOrd
RightIdealClasses(S) : AlgQuatOrd -> [AlgQuatOrd]
RightIsomorphism(I,J) : AlgQuatOrd, AlgQuatOrd -> Map, AlgQuatElt
RightOrder(I) : AlgQuatOrd -> AlgQuatOrd
RightRegularModule(B) : AlgBas -> ModAlg
RightString( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
RightStringLength( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
RightZeroExtension(C) : ModCpx -> ModCpx
Transversal(G, H) : Grp, Grp -> {@ GrpElt @}, Map
Transversal(G, H) : GrpAb, GrpAb -> {@ GrpAbElt @}, Map
Transversal(G, H) : GrpFP, GrpFP -> {@ GrpFPElt @}, Map
Transversal(P) : GrpFPCosetEnumProc -> {@ GrpFPElt @}, Map
Transversal(G, H) : GrpMat, GrpMat -> {@ GrpMatElt @}, Map
Transversal(G, H) : GrpPC, GrpPC -> {@ GrpPCElt @}, Map
Transversal(G, H) : GrpPerm, GrpPerm -> {@ GrpPermElt @}, Map
Transversal(G, H) : GrpGPC, GrpGPC -> {@ GrpGPCElt @}, Map
RightAction(M) : ModTupRng -> AlgMat
Action(M) : ModTupRng -> AlgMat
RightActionGenerator(M, i) : ModTupRng, RngIntElt -> AlgMatElt
ActionGenerator(M, i) : ModTupRng, RngIntElt -> AlgMatElt
RightAnnihilator(A, B) : AlgAss, AlgAss -> AlgAss, AlgAss
RightAnnihilator(S) : AlgGrpSub -> AlgGrpSub
LeftCosetSpace(P) : GrpFPCosetEnumProc -> GrpFPCos
RightCosetSpace(P) : GrpFPCosetEnumProc -> GrpFPCos
RightCosetSpace(G, H: parameters) : GrpFP, GrpFP -> GrpFPCos
RightDescentSet( W, w ) : GrpCox, GrpPermElt -> {}
RightExactExtension(C) : ModCpx -> ModCpx
rideal<S | X> : AlgQuatOrd, [AlgQuatOrdElt] -> AlgQuatOrd
RightIdeal(S,X) : AlgQuatOrd, [AlgQuatOrdElt] -> AlgQuatOrd
RightIdealClasses(S) : AlgQuatOrd -> [AlgQuatOrd]
RightIsomorphism(I,J) : AlgQuatOrd, AlgQuatOrd -> Map, AlgQuatElt
RightOrder(I) : AlgQuatOrd -> AlgQuatOrd
RightRegularModule(B) : AlgBas -> ModAlg
RightString( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
LieConstant_q( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
RightStringLength( RD, r, s ) : RootDtm, RngIntElt, RngIntElt -> RngIntElt
RightTransversal(G, H) : Grp, Grp -> {@ GrpElt @}, Map
Transversal(G, H) : Grp, Grp -> {@ GrpElt @}, Map
Transversal(G, H) : GrpAb, GrpAb -> {@ GrpAbElt @}, Map
Transversal(G, H) : GrpFP, GrpFP -> {@ GrpFPElt @}, Map
Transversal(P) : GrpFPCosetEnumProc -> {@ GrpFPElt @}, Map
Transversal(G, H) : GrpMat, GrpMat -> {@ GrpMatElt @}, Map
Transversal(G, H) : GrpPC, GrpPC -> {@ GrpPCElt @}, Map
Transversal(G, H) : GrpPerm, GrpPerm -> {@ GrpPermElt @}, Map
Transversal(G, H) : GrpGPC, GrpGPC -> {@ GrpGPCElt @}, Map
RightZeroExtension(C) : ModCpx -> ModCpx
AbsoluteQuotientRing(A) : FldAC -> RngUPolRes
AbsoluteAffineAlgebra(A) : FldAC -> RngUPolRes
AffineAlgebra(A) : FldAC -> RngMPolRes
BaseField(A) : AlgQuat -> Fld
BaseField(J) : JacHyp -> Fld
CoefficientRing(J) : JacHyp -> Rng
BaseField(C) : Sch -> Fld
CoefficientRing(C) : Sch -> Fld
BaseField(K) : SrfKum -> Fld
CoefficientRing(K) : SrfKum -> Rng
BaseRing(B) : AlgBas -> Rng
BaseRing(R) : AlgMat -> Rng
BaseRing(S) : AlgQuatOrd -> Rng
BaseRing(E) : CrvEll -> Rng
BaseRing(F) : Fld -> Rng
CoefficientRing(F) : FldFun -> Rng
BaseRing(F) : FldFunRat -> Rng
BaseRing( G ) : GrpLie -> Rng
BaseRing(G) : GrpPSL2 -> Rng
BaseRing(L) : Lat -> Rng
BaseRing(M) : ModBrdt -> Rng
BaseRing(M) : ModOrd -> Rng
BaseRing(A) : Mtrx -> Rng
BaseRing(F) : RngFunOrd -> Rng
BaseRing(P) : RngMPol -> Rng
BaseRing(O) : RngOrd -> Rng
BaseRing(R) : RngSer -> Rng
BaseRing(P) : RngUPol -> Rng
BaseRing(C) : Sch -> Rng
BaseField(C) : Sch -> Fld
BaseRing(X) : Sch -> Rng
BaseRing(G) : SchGrpEll -> Rng
CentreOfEndomorphismRing(G) : GrpMat -> AlgMat
ChangeRing(A, S) : AlgGen, Rng -> AlgGen, Map
ChangeRing(A, S, f) : AlgGen, Rng, Map -> AlgGen, Map
ChangeRing(A, S) : AlgMat, Rng -> AlgMat, Map
ChangeRing(A, S, f) : AlgMat, Rng, Map -> AlgMat, Map
ChangeRing(E, K) : CrvEll, Rng -> CrvEll
ChangeRing(G, S) : GrpMat, Rng -> GrpMat, Map
ChangeRing(G, S, f) : GrpMat, Rng, Map -> GrpMat, Map
ChangeRing(L, S) : Lat, Rng -> Lat, Map
ChangeRing(M, S) : ModRng, Rng -> ModRng, Map
ChangeRing(M, S) : ModRng, Rng -> ModRng, Map
ChangeRing(M, S, f) : ModRng, Rng, Map -> ModRng, Map
ChangeRing(M, S, f) : ModRng, Rng, Map -> ModRng, Map
ChangeRing(A, R) : Mtrx, Ring -> Mtrx
ChangeRing(I, S) : RngMPol, Rng -> RngMPol
ChangeRing(P, S) : RngMPol, Rng -> RngMPol
ChangeRing(P, S) : RngUPol, Rng -> RngUPol, Map
ChangeRing(P, S, f) : RngUPol, Rng, Map -> RngUPol, Map
ChangeRing(C, K) : Sch, Rng -> Sch
ClassFunctionSpace(G) : Grp -> AlgChtr
CoefficientRing(A) : Alg -> Rng
CoefficientRing(A) : AlgGen -> Rng
CoefficientRing(G) : GrpMat -> Rng
CoefficientRing(M) : ModMPol -> ModMPol
CoefficientRing(M) : ModTupRng -> Rng
CoefficientRing(M) : ModTupRng -> Rng
CoefficientRing(R) : RngInvar -> Grp
CoefficientRing(Q) : RngMPolRes -> Rng
CoefficientRing(X) : Sch -> Fld
CohomologyRingGenerators(P) : Tup -> Tup
Completion(P, n) : RngOrdIdl, RngIntElt -> RngLoc, Map
CoordinateRing(L) : Lat -> RngInt
CoordinateRing(A) : Sch -> Rng
CoordinateRing(C) : Sch -> Rng
CoordinateRing(A) : Sch -> RngMPol
CoordinateRing(X) : Sch -> RngMPol
DimensionOfCentreOfEndomorphismRing(G) : GrpMat -> RngIntElt
DimensionOfEndomorphismRing(G) : GrpMat -> RngIntElt
EndomorphismRing(G) : GrpMat -> AlgMat
GaloisRing(q, d) : RngIntElt, RngIntElt -> RngGal
GaloisRing(p, a, d) : RngIntElt, RngIntElt, RngIntElt -> RngGal
GaloisRing(p, a, D) : RngIntElt, RngIntElt, RngUPol -> RngGal
GaloisRing(q, D) : RngIntElt, RngUPol -> RngGal
HeckeEigenvalueRing(M : parameters) : ModSym -> Rng, Map
InertiaRing(L) : RngLoc -> RngLoc
IntegerRing(F) : FldFunRat -> RngPol
IntegerRing(L) : FldLoc -> RngLoc
RingOfIntegers(L) : FldLoc -> RngLoc
IntegerRing(P) : FldLoc -> RngLoc
RingOfIntegers(P) : FldLoc -> RngLoc
IntegerRing() : Null -> RngInt
RingOfIntegers(Q) : Fldrat -> RngInt
InvariantRing(G) : GrpMat -> RngInvar
IsDivisionRing(R) : Rng -> BoolElt
IsEuclideanRing(R) : Rng -> BoolElt
IsPIR(R) : Rng -> BoolElt
IsPrincipalIdealRing(F) : FldAlg -> BoolElt
IsPrincipalIdealRing(O) : RngOrd -> BoolElt
IsRingOfAllModularForms(M) : ModFrm -> BoolElt
LaurentSeriesRing(R) : Rng -> RngSerLaur
LocalRing(p, f, n) : RngIntElt, RngIntElt, RngIntElt -> RngLoc
LocalRing(p, f, g, n) : RngIntElt, RngIntElt, RngUPolElt, RngIntElt -> RngLoc
LocalRing(p, g, n) : RngIntElt, RngUPolElt, RngIntElt -> RngLoc
LocalRing(L, f, n) : RngLoc, RngIntElt -> RngLoc
LocalRing(L, g, n) : RngLoc, RngUPolElt, RngIntElt -> RngLoc
LocalRing(P, prec) : RngOrdIdl, RngIntElt -> RngLoc, Map
MatrixAlgebra(S, n) : Rng, RngIntElt -> AlgMat
MatrixAlgebra<S, n | L> : Rng, RngIntElt, List -> AlgMat
MaximalOrder(F) : FldAlg -> RngOrd
Integers(F) : FldAlg -> RngOrd
MaximalOrder(F) : FldQuad -> RngQuad
RingOfIntegers(F) : FldQuad -> RngQuad
MaximalOrder(Q) : FldRat -> RngInt
Integers() : Null -> RngInt
RingOfIntegers(Q) : FldRat -> RngInt
MultiplicatorRing(I) : RngFunOrdIdl -> RngFunOrd
MultiplicatorRing(I) : RngOrdFracIdl -> Rng
OriginalRing(Q) : RngMPolRes -> Rng
ParentRing(N) : NwtnPgon -> Rng
PolynomialAlgebra(R) : Rng -> RngUPol
PolynomialRing(E) : CrvEll -> RngMPol, Map
PolynomialRing(R, n) : Rng, RngIntElt -> RngMPol
PolynomialRing(R, n) : Rng, RngIntElt -> RngMPol
PolynomialRing(R, n, order) : Rng, RngIntElt, MonStgElt, ... -> RngMPol
PolynomialRing(R, n, order) : Rng, RngIntElt, MonStgElt, ... -> RngMPol
PolynomialRing(R, Q) : Rng, [ RngIntElt ] -> RngMPol
PolynomialRing(R) : RngInvar -> RngMPol
PowerSeriesRing(R) : Rng -> RngSerPow
PreimageRing(I) : RngMPolRes -> RngMPol
PreimageRing(Q) : RngUPolRes -> RngUPol
PrimeRing(F) : FldFun -> Rng
PrimeRing(R) : Rng -> Rng
PrimeRing(F) : RngFunOrd -> Rng
PrimeRing(L) : RngLoc -> RngLoc
pAdicRing(L) : RngLoc -> RngLoc
PuiseuxSeriesRing(R) : Rng -> RngSerPuis
RayResidueRing(m) : RngOrdIdl -> GrpAb, Map
ResidueClassRing(m) : RngIntElt -> RngIntRes
Integers(m) : RngIntElt -> RngIntRes
RingOfIntegers(m) : RngIntElt -> RngIntRes
ResidueClassRing(Q) : RngIntEltFact -> RngIntRes
Integers(Q) : RngIntEltFact -> RngIntRes
Ring(P) : SetPt -> Rng
Ring(H) : SetPtEll -> Rng
ValuationRing(F) : FldFun -> RngVal
ValuationRing(F, f) : FldFun, RngUPolElt -> RngVal
ValuationRing(F) : FldFunRat -> RngVal
ValuationRing(F, f) : FldFunRat -> RngVal
ValuationRing(Q, p) : FldRat, RngIntElt -> RngVal
pAdicRing(p, n) : RngIntElt, RngIntElt -> RngLoc
pAdicRing(p, n) : RngIntElt, RngIntElt -> RngLoc
Accessing an Algebra (FINITELY PRESENTED ALGEBRAS)
Action on a Polynomial Ring (MODULES OVER A MATRIX ALGEBRA)
Base Ring and Base Change (LATTICES)
Between Ring and Field (LOCAL RINGS AND FIELDS)
Between Ring and Field (p-ADIC RINGS AND FIELDS)
Changing Coefficient Ring (IDEAL THEORY AND GRÖBNER BASES)
Changing Coefficient Ring (MULTIVARIATE POLYNOMIAL RINGS)
Changing Ring (MATRICES)
Changing Rings (ALGEBRAS)
Changing Rings (MATRIX ALGEBRAS)
Changing Rings (MATRIX GROUPS)
Changing Rings (UNIVARIATE POLYNOMIAL RINGS)
Changing the Coefficient Ring (FREE MODULES)
Changing the Coefficient Ring (MODULES OVER A MATRIX ALGEBRA)
Creation of Invariant Rings (INVARIANT RINGS OF FINITE GROUPS)
GALOIS RINGS
INVARIANT RINGS OF FINITE GROUPS
p-adic Rings (p-ADIC RINGS AND FIELDS)
Quotient Rings (ORDERS AND ALGEBRAIC FIELDS)
Rings, Fields, and Algebras (OVERVIEW)
Structure Creation (CHARACTERS OF FINITE GROUPS)
Structure Operations (CHARACTERS OF FINITE GROUPS)
The Endomorphsim Ring (FREE MODULES)
Between Ring and Field (LOCAL RINGS AND FIELDS)
Between Ring and Field (p-ADIC RINGS AND FIELDS)
Rings, Fields, and Algebras (OVERVIEW)
Accessing an Algebra (FINITELY PRESENTED ALGEBRAS)
RingOfIntegers(F) : FldFunRat -> RngPol
IntegerRing(F) : FldFunRat -> RngPol
IntegerRing(L) : FldLoc -> RngLoc
IntegerRing(P) : FldLoc -> RngLoc
IntegerRing() : Null -> RngInt
MaximalOrder(F) : FldAlg -> RngOrd
MaximalOrder(F) : FldQuad -> RngQuad
MaximalOrder(Q) : FldRat -> RngInt
ResidueClassRing(m) : RngIntElt -> RngIntRes
Creation of Polynomial Rings (IDEAL THEORY AND GRÖBNER BASES)
Local Rings (LOCAL RINGS AND FIELDS)
Polynomial Rings and Polynomials (MULTIVARIATE POLYNOMIAL RINGS)
Residue Class Rings (RING OF INTEGERS)
Rings, Fields, and Algebras (OVERVIEW)
RMatrixSpace(R, m, n) : Rng, RngIntElt, RngIntElt -> ModMatRng
RMatrixSpace(R, m, n) : Rng, RngIntElt, RngIntElt -> ModMatRng
RMatrixSpaceWithBasis(Q) : [ ModMatRngElt ] -> ModMatRng
RMatrixSpaceWithBasis(Q) : [ModTupRngElt] -> ModMatRng
RMatrixSpace(R, m, n) : Rng, RngIntElt, RngIntElt -> ModMatRng
RMatrixSpace(R, m, n) : Rng, RngIntElt, RngIntElt -> ModMatRng
RMatrixSpaceWithBasis(Q) : [ ModMatRngElt ] -> ModMatRng
RMatrixSpaceWithBasis(Q) : [ModTupRngElt] -> ModMatRng
RModule(A) : AlgMat -> ModTupRng
RModule(Q) : [ AlgMatElt ] -> ModTupRng
RModuleWithBasis(Q) : [ModRngElt] -> ModTupRng
RSpace(R, n) : Rng, RngIntElt -> ModTupRng
RSpaceWithBasis(Q) : [ModTupRngElt] -> ModTupRng
RModuleWithBasis(Q) : [ModRngElt] -> ModTupRng
Rings, Fields, and Algebras (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
Rings, Fields, and Algebras (OVERVIEW)
RiemannRochSpace(D) : DivCrvElt -> ModTupFld,Map
RiemannRochSpace(D) : DivFunElt -> ModFld, Map
Riemann--Roch Spaces (PLANE ALGEBRAIC CURVES)
RombergQuadrature(f, a, b: parameters) : Program, FldPrElt, FldPrElt -> FldPrElt
RombergQuadrature(f, a, b: parameters) : Program, FldPrElt, FldPrElt -> FldPrElt
MAGMA_LIBRARY_ROOT
HasRoot(p) : RngUPolElt -> BoolElt, RngElt
HasRoot(g) : RngUPolElt -> BoolElt, RngLocElt
HasRoot(g) : RngUPolElt -> BoolElt, RngLocElt
HasRoot(f) : RngUPolElt -> BoolElt, RngSerElt
HasRoot(p, S) : RngUPolElt, Rng -> BoolElt, RngElt
HighestRoot( RD ) : RootDtm -> .
HighestShortRoot( RD ) : RootDtm -> .
IsLongRoot( RD, r ) : RootDtm, RngIntElt -> BoolElt
IsPartialRoot(f, c) : RngUPolElt, RngSerElt -> BoolElt
IsRoot(v) : GrphVert -> BoolElt
IsShortRoot( RD, r ) : RootDtm, RngIntElt -> BoolElt
IsUniquePartialRoot(f, c) : RngUPolElt, RngSerElt -> BoolElt
PrimitiveElement(R) : RngIntRes -> RngIntResElt
PrimitiveRoot(m) : RngIntElt -> RngIntElt
Root(a, n) : FldACElt, RngIntElt -> FldACElt
Root(a, n) : FldFinElt, RngIntElt -> FldFinElt
Root(r, n) : FldReElt, RngIntElt -> FldReElt
Root( W, r ) : GrpCox, RngIntElt -> {@@}
Root(g) : GrphDir -> GrphVert
Root( G, r ) : GrpLie, RngIntElt -> {@@}
Root(x, n) : RngLocElt, RngIntElt -> RngLocElt
Root(a, n) : RngOrdElt -> RngOrdElt
Root(I, k) : RngOrdFracIdl, RngIntElt -> RngOrdFracIdl
Root( RD, r ) : RootDtm, RngIntElt -> {@@}
RootAction( W ) : GrpCox -> Map
RootAction( F ) : GrpFP -> Map
RootDatum( C ) : AlgMatElt -> RootDtm
RootDatum( A, B ) : AlgMatElt, AlgMatElt -> RootDtm
RootDatum( F ) : GrpCox -> RootDtm
RootDatum( W ) : GrpCox -> RootDtm
RootDatum( G ) : GrpLie -> RootDtm
RootDatum( t ) : MonStgElt -> RootDtm
RootGSet( W ) : GrpCox -> GSet
RootHeight( RD, r ) : RootDtm, RngIntElt -> RngIntElt
RootNorm( RD, r ) : RootDtm, RngIntElt -> RngIntElt
RootNorms( RD ) : RootDtm -> [RngIntElt]
RootOfUnity(n) : RngIntElt -> FldCycElt
RootOfUnity(n, A) : RngIntElt, FldAC -> FldACElt
RootOfUnity(n, K) : RngIntElt, FldCyc -> FldCycElt
RootOfUnity(n, K) : RngIntElt, FldFin -> FldFinElt
RootOfUnity(n, Q) : RngIntElt, FldRat -> FldRatElt
RootPosition( W, v ) : GrpCox, . -> {@@}
RootPosition( G, v ) : GrpLie, . -> {@@}
RootPosition( RD, v ) : RootDtm, . -> {@@}
RootSide(v) : GrphVert -> GrphVert
RootSpace( W ) : GrpCox -> .
RootSpace( RD ) : RootDtm -> .
RootSubdatum( RD, s ) : RootDtm, SeqEnum -> RootDtm
RootSubdatum( RD, a ) : RootDtm, SetEnum -> RootDtm
RootSystem(L) : AlgLie -> [ AlgLieElt ], [ AlgLieElt ], [ AlgLieElt ], [[]]
RootSystemMatrix(t, n) : MonStgElt, RngIntElt -> AlgMatElt
RootVertex(s) : GrphSpl -> GrphSplVert
SetLibraryRoot(s) : MonStgElt ->
Sqrt(a) : RngIntResElt -> RngIntResElt
Sqrt(a) : RngOrdElt -> RngOrdElt
SquareRoot(a) : FldACElt -> FldACElt
SquareRoot(c) : FldComElt -> FldComElt
SquareRoot(a) : FldFinElt -> FldFinElt
SquareRoot(x) : RngLocElt -> RngLocElt
SquareRoot(I) : RngOrdFracIdl -> RngOrdFracIdl
SquareRoot(f) : RngSerElt -> RngSerElt
WordOnRoot( W, r, w ) : GrpCox, RngIntElt, . -> RngIntElt
WordOnRootSpace( W, v, w ) : GrpCox, ., . -> .
FundamentalCoweights( W ) : GrpCox -> SeqEnum
Accessing the root datum (COXETER GROUPS)
Actions on roots and coroots (COXETER GROUPS)
Classification of root data (ROOT DATA FOR LIE THEORY)
Constants associated with crystallographic root data (ROOT DATA FOR LIE THEORY)
Creating new root data from old (ROOT DATA FOR LIE THEORY)
Creating root data (ROOT DATA FOR LIE THEORY)
Log, Order and Roots (FINITE FIELDS)
Operations (COXETER GROUPS)
Operations and properties for (co)roots (ROOT DATA FOR LIE THEORY)
Operators on root data (ROOT DATA FOR LIE THEORY)
Properties (COXETER GROUPS)
Properties of root data (ROOT DATA FOR LIE THEORY)
ROOT DATA FOR LIE THEORY
Root Systems (LIE ALGEBRAS)
Root Systems (REFLECTION GROUPS)
Roots (FINITE FIELDS)
Roots (UNIVARIATE POLYNOMIAL RINGS)
Roots, coroots and weights (COXETER GROUPS)
Square Root (POWER, LAURENT AND PUISEUX SERIES)
FundamentalCoweights( W ) : GrpCox -> SeqEnum
Accessing the root datum (COXETER GROUPS)
ROOT DATA FOR LIE THEORY
Operations (COXETER GROUPS)
Properties (COXETER GROUPS)
FundamentalCoweights( W ) : GrpCox -> SeqEnum
Roots, coroots and weights (COXETER GROUPS)
Root Systems (LIE ALGEBRAS)
Root Systems (REFLECTION GROUPS)
CorootAction( W ) : GrpCox -> Map
RootAction( W ) : GrpCox -> Map
RootAction( F ) : GrpFP -> Map
RootDtm_RootArithmetic (Example H35E12)
RootDatum( C ) : AlgMatElt -> RootDtm
RootDatum( A, B ) : AlgMatElt, AlgMatElt -> RootDtm
RootDatum( F ) : GrpCox -> RootDtm
RootDatum( W ) : GrpCox -> RootDtm
RootDatum( G ) : GrpLie -> RootDtm
RootDatum( t ) : MonStgElt -> RootDtm
Groups (OVERVIEW)
IsRootedTree(g) : GrphDir -> BoolElt,GrphVert
CorootGSet( W ) : GrpCox -> GSet
RootGSet( W ) : GrpCox -> GSet
CorootHeight( RD, r ) : RootDtm, RngIntElt -> RngIntElt
RootHeight( RD, r ) : RootDtm, RngIntElt -> RngIntElt
CorootNorm( RD, r ) : RootDtm, RngIntElt -> RngIntElt
RootNorm( RD, r ) : RootDtm, RngIntElt -> RngIntElt
CorootNorms( RD ) : RootDtm -> [RngIntElt]
RootNorms( RD ) : RootDtm -> [RngIntElt]
RootOfUnity(n) : RngIntElt -> FldCycElt
RootOfUnity(n, A) : RngIntElt, FldAC -> FldACElt
RootOfUnity(n, K) : RngIntElt, FldCyc -> FldCycElt
RootOfUnity(n, K) : RngIntElt, FldFin -> FldFinElt
RootOfUnity(n, Q) : RngIntElt, FldRat -> FldRatElt
RootDtm_RootOperations (Example H35E13)
CorootPosition( W, v ) : GrpCox, . -> {@@}
RootPosition( W, v ) : GrpCox, . -> {@@}
RootPosition( G, v ) : GrpLie, . -> {@@}
RootPosition( RD, v ) : RootDtm, . -> {@@}
AllRoots(a, n) : FldFinElt, RngIntElt -> SeqEnum
AllSquareRoots(a) : RngIntResElt -> [ RngIntResElt ]
NumberOfPositiveRoots( W ) : GrpCox -> RngIntElt
NumberOfPositiveRoots( G ) : GrpLie -> RngIntElt
NumberOfPositiveRoots( RD ) : RootDtm -> RngIntElt
PositiveRoots( W ) : GrpCox -> {@@}
PositiveRoots( G ) : GrpLie -> {@@}
PositiveRoots( RD ) : RootDtm -> {@@}
Roots( W ) : GrpCox -> {@@}
Roots( G ) : GrpLie -> {@@}
Roots(f) : RngPolElt -> [ < FldACElt, RngIntElt> ]
Roots(f) : RngPolElt -> [ < FldFinElt, RngIntElt> ]
Roots(p) : RngUPolElt -> [ < RngElt, RngIntElt> ]
Roots(p, S) : RngUPolElt -> [ < RngElt, RngIntElt> ]
Roots(p) : RngUPolElt -> [ <FldComElt, RngIntElt> ]
Roots(g) : RngUPolElt -> [ <RngLocElt, RngIntElt> ]
Roots(g) : RngUPolElt -> [ <RngLocElt, RngIntElt> ]
Roots(f) : RngUPolElt -> [<RngSerElt, RngIntElt>]
Roots(f, D) : RngUPolElt, DivFunElt -> SeqEnum[ FldFunElt ]
Roots( RD ) : RootDtm -> {@@}
RootsInSplittingField(f) : RngPolElt(FldFin) -> [<RngPolElt, RngIntElt>], FldFin
RootsNonExact(p) : RngUPolElt -> [ FldPrElt ], [ FldPrElt ]
SimpleRoots( W ) : GrpCox -> Mtrx
SimpleRoots( RD ) : RootDtm -> Mtrx
ValuationsOfRoots(g) : RngUPolElt -> SeqEnum[<FldRatElt, RngIntElt>]
ValuationsOfRoots(g) : RngUPolElt -> SeqEnum[<FldRatElt, RngIntElt>]
FldRe_Roots (Example H43E5)
Functions returning roots (LOCAL RINGS AND FIELDS)
Functions returning roots (p-ADIC RINGS AND FIELDS)
Hensel Lifting of Roots (LOCAL RINGS AND FIELDS)
Hensel Lifting of Roots (p-ADIC RINGS AND FIELDS)
Positive and simple roots (ROOT DATA FOR LIE THEORY)
Roots (ALGEBRAICALLY CLOSED FIELDS)
Roots (REAL AND COMPLEX FIELDS)
Roots of Elements (LOCAL RINGS AND FIELDS)
Roots of Elements (p-ADIC RINGS AND FIELDS)
Roots of Ideals (ORDERS AND ALGEBRAIC FIELDS)
Roots of Polynomials (LOCAL RINGS AND FIELDS)
Roots of Polynomials (NEWTON POLYGONS)
Roots of Polynomials (p-ADIC RINGS AND FIELDS)
Roots, coroots and weights (COXETER GROUPS)
Roots, coroots and weights (ROOT DATA FOR LIE THEORY)
Roots, coroots and weights (ROOT DATA FOR LIE THEORY)
Functions returning roots (LOCAL RINGS AND FIELDS)
Functions returning roots (p-ADIC RINGS AND FIELDS)
Newton_roots-ex (Example H58E10)
RootDtm_RootsCoroots (Example H35E9)
RootSide(v) : GrphVert -> GrphVert
RootsInSplittingField(f) : RngPolElt(FldFin) -> [<RngPolElt, RngIntElt>], FldFin
RootsNonExact(p) : RngUPolElt -> [ FldPrElt ], [ FldPrElt ]
FldRe_RootsNonExact (Example H43E6)
CorootSpace( W ) : GrpCox -> .
RootSpace( W ) : GrpCox -> .
RootSpace( RD ) : RootDtm -> .
RootDtm_RootSubdata (Example H35E16)
RootSubdatum( RD, s ) : RootDtm, SeqEnum -> RootDtm
RootSubdatum( RD, a ) : RootDtm, SetEnum -> RootDtm
RootSystem(L) : AlgLie -> [ AlgLieElt ], [ AlgLieElt ], [ AlgLieElt ], [[]]
AlgLie_RootSystem (Example H75E2)
RootSystemMatrix(t, n) : MonStgElt, RngIntElt -> AlgMatElt
RootVertex(s) : GrphSpl -> GrphSplVert
Rotate(~u, k) : ModTupElt, RngIntElt ->
Rotate(u, k) : ModTupElt, RngIntElt -> ModTupElt
Rotate(~u, k) : ModTupFldElt, RngIntElt ->
Rotate(u, k) : ModTupFldElt, RngIntElt -> ModTupFldElt
Rotate(~u, k) : ModTupRngElt, RngIntElt ->
Rotate(~u, k) : ModTupRngElt, RngIntElt ->
Rotate(u, k) : ModTupRngElt, RngIntElt -> ModTupRngElt
Rotate(u, k) : ModTupRngElt, RngIntElt -> ModTupRngElt
Rotate(~S, p) : SeqEnum, RngIntElt ->
RotateWord(u, n) : GrpFPElt, RngIntElt -> GrpFPElt
RotateWord(u, n) : SgpFPElt, RngIntElt -> SgpFPElt
RotateWord(u, n) : GrpFPElt, RngIntElt -> GrpFPElt
RotateWord(u, n) : SgpFPElt, RngIntElt -> SgpFPElt
Round(q) : FldRatElt -> RngIntElt
Round(r) : FldReElt -> FldReElt
Round(n) : RngIntElt -> RngIntElt
Round(p) : RngUPolElt -> RngUPolElt
Expression (OVERVIEW)
Rounding and Truncating (RATIONAL FIELD)
Expression (OVERVIEW)
RngOrd_Round2 (Example H53E6)
Rounding (REAL AND COMPLEX FIELDS)
Functions, Procedures, and Mappings (OVERVIEW)
AddRow(~a, u, i, j) : AlgMatElt, RngElt, RngIntElt, RngIntElt ->
AddRow(A, c, i, j) : Mtrx, RngElt, RngIntElt, RngIntElt -> Mtrx
FirstRowEntry(t, i) : Tableau,RngIntElt -> RngIntElt
[Future release] GeneralisedRowReduction( rho ) : GrpLie, Map -> Map
HadamardRowDesign(H, i) : AlgMatElt, RngIntElt -> Dsgn
Image(a) : AlgMatElt -> ModTup
LastRowEntry(t, i) : Tableau,RngIntElt -> RngIntElt
LiftNonsplitExtensionRow (SQP, p, l) : SQProc, RngIntElt, RngIntElt -> RngIntElt, SQProc
LiftSplitExtensionRow (SQP): SQProc -> RngIntElt, SQProc
MultiplyRow(~a, u, j) : AlgMatElt, RngElt, RngIntElt ->
MultiplyRow(A, c, i) : Mtrx, RngElt, RngIntElt -> Mtrx
Row(t, i) : Tableau -> SeqEnum
RowInsert(~t, i) : Tableau,RngIntElt ->
RowInsert(~t, w) : Tableau,SeqEnum ->
RowNullSpace(a) : AlgMatElt -> ModTup
RowSkewLength(t, i) : Tableau,RngIntElt -> RngIntElt
RowSubmatrix(A, i) : Mtrx, RngIntElt -> Mtrx
RowSubmatrix(A, i, k) : Mtrx, RngIntElt, RngIntElt -> Mtrx
RowSubmatrixRange(A, i, j) : Mtrx, RngIntElt, RngIntElt -> Mtrx
Word(t) : Tableau -> SeqEnum
Row and Column Operations (MATRICES)
Row and Column Operations (MATRIX ALGEBRAS)
Row and Column Operations (MATRICES)
Row and Column Operations (MATRIX ALGEBRAS)
Mat_RowColumnOps (Example H62E6)
RowInsert(~t, i) : Tableau,RngIntElt ->
RowInsert(~t, w) : Tableau,SeqEnum ->
RowLength(t, i) : Tableau,RngIntElt -> RngIntElt
LastRowEntry(t, i) : Tableau,RngIntElt -> RngIntElt
RowNullSpace(a) : AlgMatElt -> ModTup
Nrows(a) : AlgMatElt -> RngIntElt
NumberOfRows(a) : AlgMatElt -> RngIntElt
NumberOfRows(u) : ModTupFldElt -> RngIntElt
NumberOfRows(A) : Mtrx -> RngIntElt
NumberOfRows(t) : Tableau -> RngIntElt
NumberOfSkewRows(t) : Tableau -> RngIntElt
Rows(t) : Tableau -> SeqEnum
SetRows(n) : RngIntElt ->
SwapRows(~a, i, j) : AlgMatElt, RngIntElt, RngIntElt ->
SwapRows(A, i, j) : Mtrx, RngIntElt, RngIntElt -> Mtrx
RowSkewLength(t, i) : Tableau,RngIntElt -> RngIntElt
RowSpace(a) : AlgMatElt -> ModTup
Image(a) : AlgMatElt -> ModTup
RowSubmatrix(A, i) : Mtrx, RngIntElt -> Mtrx
RowSubmatrix(A, i, k) : Mtrx, RngIntElt, RngIntElt -> Mtrx
RowSubmatrixRange(A, i, j) : Mtrx, RngIntElt, RngIntElt -> Mtrx
RowWord(t) : Tableau -> SeqEnum
Word(t) : Tableau -> SeqEnum
RandomSequenceRSA(b, t) : RngIntElt, RngIntElt -> SeqEnum
RandomSequenceRSA(n, e, s, t) : RngIntElt, RngIntElt, RngIntElt,RngIntElt -> SeqEnum
PseudoRandom_rsa_stats (Example H99E2)
RSAModulus(b) : RngIntElt -> RngIntElt, RngIntElt
RSAModulus(b, e) : RngIntElt, RngIntElt -> RngIntElt
RESOLUTION GRAPHS AND SPLICE DIAGRAMS
RSpaceWithBasis(Q) : [ModTupRngElt] -> ModTupRng
RModuleWithBasis(Q) : [ModRngElt] -> ModTupRng
RSpace(C) : Code -> ModTupRng
RSpace(C) : Code -> ModTupRng
RSpace(C) : Code -> ModTupRng
RSpace(G) : GrpMat -> ModTupRng
RSpace(R, n) : Rng, RngIntElt -> ModTupRng
RSpace(R, n, F) : Rng, RngIntElt, Mtrx -> ModTupRng
RSpaceWithBasis(Q) : [ModTupRngElt] -> ModTupRng
RModuleWithBasis(Q) : [ModRngElt] -> ModTupRng
Rules for Maps (MAPPINGS)
RuledSurface(k,n) : Rng,RngIntElt -> PrjScrl
RuledSurface(k,n) : Rng,RngIntElt -> PrjScrl
RuledSurface(k,a,b) : Rng,RngIntElt,RngIntElt -> PrjScrl
RuledSurface(k,n) : Rng,RngIntElt -> PrjScrl
RuledSurface(k,n) : Rng,RngIntElt -> PrjScrl
RuledSurface(k,a,b) : Rng,RngIntElt,RngIntElt -> PrjScrl
GB_RungeKutta2 (Example H50E3)
RWSGroup(Q: parameters) : GrpFP -> GrpRWS
GrpRWS_RWSGroup (Example H30E1)
RWSMonoid(Q: parameters) : MonFP -> MonRWS
MonRWS_RWSMonoid (Example H18E1)
[____] [____] [_____] [____] [__] [Index] [Root]