[____] [____] [_____] [____] [__] [Index] [Root]
Index T
ChebyshevT(n) : RngIntElt -> RngUPolElt
ChebyshevFirst(n) : RngIntElt -> RngUPolElt
# T : SeqEnum -> RngIntElt
T<char>
t<char>
<Tab>
Basis(R) : AlgChtr -> SeqEnum
CharacterTable(G) : Grp -> SeqEnum
CharacterTable(G) : GrpAb -> TabChtr
CharacterTable(G) : GrpFin -> TabChtr
CharacterTable(G) : GrpMat -> TabChtr
CharacterTable(G) : GrpPC -> TabChtr
CharacterTable(G) : GrpPerm -> TabChtr
ConstructTable(A) : AlgGrp ->
CosetTable(G, H) : GrpGPC, GrpGPC -> Map
CosetTable(P) : GrpFPCosetEnumProc -> Map
CosetTable(G, H) : Grp, Grp -> Hom(Grp)
CosetTable(G, H) : Grp, Grp -> Map
[Future release] CosetTable(G, f) : Grp, Hom(Grp) -> Hom(Grp)
CosetTable(G, H) : GrpFin, GrpFin -> Map
[Future release] CosetTable(G, f) : GrpFin, Hom(GrpFin) -> Hom(GrpFin)
CosetTable(G, H) : GrpPC, GrpPC -> Map
CosetTable(G, H: parameters) : GrpFP, GrpFP -> Map
CosetTableToPermutationGroup(G, T) : GrpFP, Map -> GrpPerm
CosetTableToRepresentation(G, T): GrpFP, Map -> Map, GrpPerm, Grp
HasClosedCosetTable(P) : GrpFPCosetEnumProc -> BoolElt
HasValidCosetTable(P) : GrpFPCosetEnumProc -> BoolElt
MultiplicationTable(O) : RngOrd -> [AlgMatElt]
Coset Spaces and Tables (FINITELY PRESENTED GROUPS)
Coset Tables (FINITELY PRESENTED GROUPS)
Coset Tables and Transversals (FINITE SOLUBLE GROUPS)
Coset Tables and Transversals (MATRIX GROUPS)
Tableau(s) : SeqEnum -> Tableau
WordToTableau(w) : SeqEnum -> Tableau
NumberOfStandardTableaux(P) : SeqEnum -> RngIntElt
NumberOfTableauxOnAlphabet(P, m) : SeqEnum,RngIntElt -> RngIntElt
Tableaux (ENUMERATIVE COMBINATORICS)
Tails(~P: parameters) : Process(pQuot) ->
MinusTamagawaNumber(M) : ModSym -> RngIntElt
RealTamagawaNumber(M) : ModSym -> RngIntElt
TamagawaNumber(E, p) : CrvEll, RngIntElt -> RngIntElt
TamagawaNumber(M, p) : ModSym, RngIntElt -> RngIntElt
TamagawaNumbers(E) : CrvEll -> [ RngIntElt ]
TamagawaNumber(E, p) : CrvEll, RngIntElt -> RngIntElt
TamagawaNumber(M, p) : ModSym, RngIntElt -> RngIntElt
TamagawaNumbers(E) : CrvEll -> [ RngIntElt ]
IsTamelyRamified(K) : FldAlg -> BoolElt
IsTamelyRamified(O) : RngOrd -> BoolElt
IsTamelyRamified(P) : RngOrdIdl -> BoolElt
IsTamelyRamified(P, O) : RngOrdIdl, RngOrd -> BoolElt
Tan(c) : FldComElt -> FldComElt
Tan(f) : RngSerElt -> RngSerElt
Tan(f) : RngSerElt -> RngSerElt
IsTangent(C,D,p) : Sch,Sch,Pt -> BoolElt
Tangent(P, A, p) : Plane, { PlanePt }, PlanePt -> PlaneLn
TangentCone(p) : Crv,Pt -> Crv
TangentCone(p) : Sch,Pt -> Sch
TangentLine(p) : Crv,Pt -> Crv
TangentSpace(p) : Sch,Pt -> Sch
TangentCone(p) : Crv,Pt -> Crv
TangentCone(p) : Sch,Pt -> Sch
TangentLine(p) : Crv,Pt -> Crv
AllTangents(P, A) : Plane, { PlanePt } -> { PlaneLn }
AllTangents(P, U) : Plane, { PlanePt } -> { PlaneLn }
TangentSpace(p) : Sch,Pt -> Sch
Tanh(s) : FldPrElt -> FldPrElt
Tanh(f) : RngSerElt -> RngSerElt
Tanh(f) : RngSerElt -> RngSerElt
Rectify(~t) : Tableau ->
JeuDeTaquin(~t) : Tableau ->
SetGlobalTCParameters(: parameters) : ->
UnsetGlobalTCParameters() : ->
Tell(F) : File -> RngIntElt
Tempname(P) : MonStgElt -> MonStgElt
IsTensor(G: parameters) : GrpMat -> BoolElt
IsTensorInduced(G : parameters) : GrpMat -> BoolElt
TensorBasis(G) : GrpMat -> GrpMatElt
TensorFactors(G) : GrpMat -> GrpMat, GrpMat
TensorInducedBasis(G) : GrpMat -> GrpMatElt
TensorInducedPermutations(G) : GrpMat -> SeqEnum
TensorPower(M, n) : ModTupRng, RngIntElt -> ModTupRng
TensorProduct(A, B) : AlgBas, AlgBas-> AlgBas
TensorProduct(A, B) : AlgMat, AlgMat -> AlgMat
TensorProduct(a, b) : AlgMatElt, AlgMatElt -> AlgMatElt
TensorProduct(G, H) : GrphDir, GrphDir -> GrphDir
TensorProduct(L, M) : Lat, Lat -> Lat
TensorProduct(U, V) : ModTupFld, ModTupFld -> FldElt
TensorProduct(u, v) : ModTupFldElt, ModTupFldElt -> FldElt
TensorProduct(M, N) : ModTupRng, ModTupRng -> ModTupRng
TensorWreathProduct(G, H) : GrpMat, GrpPerm -> GrpMat
GrpMat_Tensor (Example H21E33)
Tensor Products (MATRIX GROUPS)
Tensor Products of K[G]-Modules (MODULES OVER A MATRIX ALGEBRA)
Tensor-induced Groups (MATRIX GROUPS)
Tensor-induced Groups (MATRIX GROUPS)
Tensor Products (MATRIX GROUPS)
Tensor Products of K[G]-Modules (MODULES OVER A MATRIX ALGEBRA)
TensorBasis(G) : GrpMat -> GrpMatElt
TensorFactors(G) : GrpMat -> GrpMat, GrpMat
GrpMat_TensorInduced (Example H21E34)
TensorInducedBasis(G) : GrpMat -> GrpMatElt
TensorInducedPermutations(G) : GrpMat -> SeqEnum
TensorPower(M, n) : ModTupRng, RngIntElt -> ModTupRng
TensorProduct(A, B) : AlgBas, AlgBas-> AlgBas
TensorProduct(A, B) : AlgMat, AlgMat -> AlgMat
TensorProduct(a, b) : AlgMatElt, AlgMatElt -> AlgMatElt
TensorProduct(G, H) : GrphDir, GrphDir -> GrphDir
TensorProduct(L, M) : Lat, Lat -> Lat
TensorProduct(U, V) : ModTupFld, ModTupFld -> FldElt
TensorProduct(u, v) : ModTupFldElt, ModTupFldElt -> FldElt
TensorProduct(M, N) : ModTupRng, ModTupRng -> ModTupRng
TensorWreathProduct(G, H) : GrpMat, GrpPerm -> GrpMat
IsZeroTerm(C, n) : ModCpx, RngIntElt -> BoolElt
LeadingTerm(x) : GrpGPCElt -> GrpGPCElt
LeadingTerm(x) : GrpPCElt -> GrpPCElt
LeadingTerm(f) : RngMPolElt -> RngMPolElt
LeadingTerm(f, i) : RngMPolElt, RngIntElt -> RngMPolElt
LeadingTerm(f) : RngSerElt -> RngElt
LeadingTerm(p) : RngUPolElt -> RngUPolElt
Term(C, n) : ModCpx, RngIntElt -> ModAlg
Term(f, i, k) : RngMPolElt, RngIntElt, RngIntElt -> RngMPolElt
TorusTerm( G, r, t ) : GrpLie, RngIntElt, . -> GrpLieElt
TrailingTerm(f) : RngMPolElt -> RngElt
TrailingTerm(f, i) : RngMPolElt, RngIntElt -> RngElt
TrailingTerm(p) : RngUPolElt -> RngUPolElt
Coefficients and Terms (UNIVARIATE POLYNOMIAL RINGS)
Coefficients, Monomials and Terms (MULTIVARIATE POLYNOMIAL RINGS)
Sequences (OVERVIEW)
Control-C key (OVERVIEW)
Quitting (OVERVIEW)
Terminology (AUTOMATIC GROUPS)
Terminology (GROUPS DEFINED BY REWRITE SYSTEMS)
Terminology (MONOIDS GIVEN BY REWRITE SYSTEMS)
DimensionsOfTerms(C) : ModCpx -> SeqEnum
Terms(C) : ModCpx -> SeqEnum
Terms(f) : RngMPolElt -> [ RngMPolElt ]
Terms(f, i) : RngMPolElt, RngIntElt -> [ RngMPolElt ]
Terms(p) : RngUPolElt -> [ RngUPolElt ]
CodeFld_TernaryGolayCode (Example H97E1)
CodeRng_TernaryGolayCode (Example H98E1)
DedekindTest(p, m) : RngUPolElt, RngIntElt -> Boolelt
HomogeneousModuleTest(P, S, F) : [ RngMPol ], [ RngMPol ], RngMPol -> BoolElt, [ RngMPol ]
HomogeneousModuleTest(P, S, F) : [ RngMPol ], [ RngMPol ], RngMPol -> BoolElt, [ RngMPol ]
HomogeneousModuleTest(P, S, L) : [ RngMPol ], [ RngMPol ], [ RngMPol ] -> [ BoolElt ], [ [ RngMPol ] ]
HomogeneousModuleTest(P, S, L) : [ RngMPol ], [ RngMPol ], [ RngMPol ] -> [ BoolElt ], [ [ RngMPol ] ]
HomogeneousModuleTestBasis(P, S, L) : [ RngMPol ], [ RngMPol ], [ RngMPol ] -> [ BoolElt ], [ [ RngMPol ] ]
TestNautyInvariant(G: parameters) : Grph -> BoolElt
Singularity Analysis (PLANE ALGEBRAIC CURVES)
Testing for Labels (GRAPHS)
TestNautyInvariant(G: parameters) : Grph -> BoolElt
Boolean Tests on Subspaces (BRANDT MODULES)
Basic Tests (SCHEMES)
Tests for Linear Systems (SCHEMES)
GrpFP_1_Tetrahedral (Example H22E8)
Strings (OVERVIEW)
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
Class Field Theory (ORDERS AND ALGEBRAIC FIELDS)
Ideal Theory of Orders (QUATERNION ALGEBRAS)
Representation Theory (POLYCYCLIC GROUPS)
JacobiTheta(q, z) : FldPrElt, FldPrElt -> FldPrElt
JacobiTheta(q, z) : FldPrElt, RngSerElt[FldPr] -> RngSerElt
JacobiThetaNullK(q, k) : FldPrElt, RngIntElt -> FldPr
ThetaOperator(M1, M2) : ModSym, ModSym -> Map
ThetaSeries(L, n) : Lat, RngIntElt -> RngSerElt
ThetaSeries(x, y, prec) : ModBrdtElt, ModBrdtElt, RngIntElt -> RngSerElt
ThetaSeries(f, n) : QuadBinElt, RngIntElt -> RngSerElt
Successive Minima and Theta Series (LATTICES)
ThetaOperator(M1, M2) : ModSym, ModSym -> Map
ModSym_ThetaOperator (Example H88E16)
ThetaSeries(L, n) : Lat, RngIntElt -> RngSerElt
ThetaSeries(x, y, prec) : ModBrdtElt, ModBrdtElt, RngIntElt -> RngSerElt
ThetaSeries(f, n) : QuadBinElt, RngIntElt -> RngSerElt
Lat_ThetaSeries (Example H66E10)
IsThick(C) : CosetGeom -> BoolElt
IsThick(D) : IncGeom -> BoolElt
IsThin(C) : CosetGeom -> BoolElt
IsThin(D) : IncGeom -> BoolElt
GrpFP_1_ThreeInvols (Example H22E9)
PushThroughIsogeny(I, v) : Map, RngUPolElt -> RngUPolElt
Multiple Assignment (OVERVIEW)
Thue(O) : RngOrd -> Thue
Thue(f) : RngUPolElt -> Thue
Thue Equations (ORDERS AND ALGEBRAIC FIELDS)
RngOrd_thue (Example H53E27)
Elementary Tietze Transformations (FINITELY PRESENTED SEMIGROUPS)
TietzeProcess(G: parameters) : GrpFP -> Process(Tietze)
Tietze transformations (FINITELY PRESENTED GROUPS)
TietzeProcess(G: parameters) : GrpFP -> Process(Tietze)
Procedures (OVERVIEW)
State_Time (Example H1E17)
Timing (OVERVIEW)
time statement;
Operators (OVERVIEW)
Timing (STATEMENTS AND EXPRESSIONS)
Splice Diagrams from Resolution Graphs (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Transfer to GrpPC (FINITE SOLUBLE GROUPS)
Transfer to GrpPC (FINITE SOLUBLE GROUPS)
Implicit Invocation of the Todd-Coxeter Algorithm (FINITELY PRESENTED GROUPS)
Index of a Subgroup: The Todd-Coxeter Algorithm (FINITELY PRESENTED GROUPS)
ShephardTodd(n) : RngIntElt -> GrpMat, Fld
ToddCoxeter(G, H: parameters) : GrpFP, GrpFP -> RngIntElt, Map, RngIntElt, RngIntElt
ToddCoxeterSchreier(G: parameters) : GrpMat : ->
ToddCoxeterSchreier(G: parameters) : GrpPerm : ->
ToddCoxeter(G, H: parameters) : GrpFP, GrpFP -> RngIntElt, Map, RngIntElt, RngIntElt
ToddCoxeterSchreier(G: parameters) : GrpMat : ->
ToddCoxeterSchreier(G: parameters) : GrpPerm : ->
Soluble Quotient Process Tools (FP GROUPS - ADVANCED FEATURES)
Soluble Quotient Process Tools (FP GROUPS - ADVANCED FEATURES)
Top(L) : SubFldLat -> SubFldLatElt
Top(L): SubGrpLat -> SubGrpLatElt
Top(L): SubModLat -> SubModLatElt
TopQuotients(D) : DB -> SetIndx
TopQuotients(D) : DB -> SetIndx
The Associated Complex Torus (MODULAR SYMBOLS)
TorsionSubgroup(H) : SetPtEll -> GrpAb, Map
AbelianGroup(H) : SetPtEll -> GrpAb, Map
Invariants(A) : GrpAbGen -> [ RngIntElt ]
IsTorsionUnit(w) : RngOrdElt -> BoolElt
SetOrderTorsionUnit(O, e, r) : RngOrd, RngOrdElt, RngIntElt ->
TorsionBound(J, n) : JacHyp, RngIntElt -> RngIntElt
TorsionBound(M, maxp) : ModSym, RngIntElt -> RngIntElt
TorsionFreeRank(A) : GrpAb -> RngIntElt
TorsionFreeRank(G) : GrpFP -> RngIntElt
TorsionFreeSubgroup(A) : GrpAb -> GrpAb
TorsionInvariants(A) : GrpAb -> [ RngIntElt ]
TorsionSubgroup(A) : GrpAb -> GrpAb
TorsionSubgroup(J) :JacHyp -> GrpAb, Map
TorsionSubgroup(H) : SetPtEll -> GrpAb, Map
TorsionSubgroupScheme(G, n) : SchGrpEll, RngIntElt -> SchGrpEll
TorsionUnitGroup(O) : RngOrd -> GrpAb, Map
TwoTorsionPolynomial(E) : CrvEll -> RngMPolElt
TwoTorsionSubgroup(J) : JacHyp -> GrpAb, Map
TwoTorsionSubgroup(Q) : QuadBin -> GrpAb, Map
Torsion Polynomials (ELLIPTIC CURVES)
TorsionBound(J, n) : JacHyp, RngIntElt -> RngIntElt
TorsionBound(M, maxp) : ModSym, RngIntElt -> RngIntElt
TorsionFreeRank(A) : GrpAb -> RngIntElt
TorsionFreeRank(G) : GrpFP -> RngIntElt
TorsionFreeSubgroup(A) : GrpAb -> GrpAb
CrvHyp_TorsionGroups (Example H86E11)
TorsionInvariants(A) : GrpAbGen -> [ RngIntElt ]
Invariants(A) : GrpAbGen -> [ RngIntElt ]
TorsionInvariants(A) : GrpAb -> [ RngIntElt ]
TorsionSubgroup(H) : SetPtEll -> GrpAb, Map
AbelianGroup(H) : SetPtEll -> GrpAb, Map
TorsionSubgroup(A) : GrpAb -> GrpAb
TorsionSubgroup(J) :JacHyp -> GrpAb, Map
TorsionSubgroup(H) : SetPtEll -> GrpAb, Map
TorsionSubgroupScheme(G, n) : SchGrpEll, RngIntElt -> SchGrpEll
TorsionUnitGroup(O) : RngOrd -> GrpAb, Map
SubgroupOfTorus(M, x) : ModSym, ModSymElt -> RngIntElt
SubgroupOfTorus(M, s) : ModSym, SeqEnum -> GrpAb
TorusTerm( G, r, t ) : GrpLie, RngIntElt, . -> GrpLieElt
TorusTerm( G, r, t ) : GrpLie, RngIntElt, . -> GrpLieElt
LeadingTotalDegree(f) : RngMPolElt -> RngIntElt
TotalDegree(f) : FldFunRatElt -> RngIntElt
TotalDegree(L) : RngLoc -> RngIntElt
TotalDegree(f) : RngMPolElt -> RngIntElt
TotalLinking(v) : GrphSplVert -> RngIntElt
TotalNumberOfCosets(P) : GrpFPCosetEnumProc -> RngIntElt
TotalDegree(f) : FldFunRatElt -> RngIntElt
TotalDegree(L) : RngLoc -> RngIntElt
TotalDegree(f) : RngMPolElt -> RngIntElt
TotalLinking(v) : GrphSplVert -> RngIntElt
IsTotallyRamified(P) : RngOrdIdl -> BoolElt
IsTotallyRamified(P, O) : RngOrdIdl, RngOrd -> BoolElt
IsTotallySplit(P) : RngOrdIdl -> BoolElt
IsTotallySplit(P, O) : RngOrdIdl, RngOrd -> BoolElt
TotallyRamifiedExtension(L, g) : RngLoc, RngUPolElt -> RngLoc
TotallyRamifiedExtension(L, g) : RngLoc, RngUPolElt -> RngLoc
TotalNumberOfCosets(P) : GrpFPCosetEnumProc -> RngIntElt
PaleyTournament(q) : RngIntElt -> GrphDir
TraceAbs(a) : FldAlgElt -> FldRatElt
AbsoluteTrace(a) : FldAlgElt -> FldRatElt
AbsoluteTrace(a) : FldFinElt -> FldFinElt
LinearSystemTrace(L,X) : LinearSys,Sch -> LinearSys
Trace(a) : AlgGrpElt -> RngElt
Trace(a) : AlgMatElt -> RngElt
Trace(x) : AlgQuatElt -> FldElt
Trace(C, F) : Code, FldFin -> Code
Trace(a) : FldACElt -> FldACElt
Trace(a) : FldAlgElt -> FldAlgElt
Trace(a) : FldFinElt -> FldFinElt
Trace(a, E) : FldFinElt, FldFin -> FldFinElt
Trace(q) : FldRatElt -> FldRatElt
Trace(g) : GrpMatElt -> RngElt
Trace(u, F) : ModTupFldElt, Fld -> ModTupFldElt
Trace(u, S) : ModTupFldElt, FldFin -> ModTupFldElt
Trace(A) : Mtrx -> RngElt
Trace(n) : RngIntElt -> RngIntElt
Trace(x) : RngLocElt -> RngLocElt
Trace(H): SetPtEll -> RngIntElt
Trace(H, r): SetPtEll, RngIntElt -> RngIntElt
TraceMatrix(O) : RngOrd -> AlgMatElt
Conjugates, Norm and Trace (RATIONAL FIELD)
Conjugates, Norm and Trace (RING OF INTEGERS)
Functions related to Norm and Trace (ALGEBRAIC FUNCTION FIELDS)
Functions related to Norm and Trace (ALGEBRAIC FUNCTION FIELDS)
Minimal Polynomial, Norm and Trace (ALGEBRAICALLY CLOSED FIELDS)
Norm and Trace (FINITE FIELDS)
Norm and Trace Functions (LOCAL RINGS AND FIELDS)
Norm, Trace, and Minimal Polynomial (ORDERS AND ALGEBRAIC FIELDS)
Scheme_trace (Example H81E32)
TraceAbs(a) : FldAlgElt -> FldRatElt
AbsoluteTrace(a) : FldAlgElt -> FldRatElt
AbsoluteTrace(a) : FldFinElt -> FldFinElt
GetTraceback() : -> BoolElt
SetTraceback(n) : BoolElt ->
Traceback() : ->
TraceMatrix(O) : RngOrd -> AlgMatElt
TraceOfFrobenius(H): SetPtEll -> RngIntElt
Trace(H): SetPtEll -> RngIntElt
Trace(H, r): SetPtEll, RngIntElt -> RngIntElt
TrailingCoefficient(f) : RngMPolElt -> RngElt
TrailingCoefficient(f, i) : RngMPolElt, RngIntElt -> RngElt
TrailingCoefficient(p) : RngUPolElt -> RngElt
TrailingTerm(f) : RngMPolElt -> RngElt
TrailingTerm(f, i) : RngMPolElt, RngIntElt -> RngElt
TrailingTerm(p) : RngUPolElt -> RngUPolElt
TrailingCoefficient(f) : RngMPolElt -> RngElt
TrailingCoefficient(f, i) : RngMPolElt, RngIntElt -> RngElt
TrailingCoefficient(p) : RngUPolElt -> RngElt
TrailingTerm(f) : RngMPolElt -> RngElt
TrailingTerm(f, i) : RngMPolElt, RngIntElt -> RngElt
TrailingTerm(p) : RngUPolElt -> RngUPolElt
Plane_trans (Example H95E16)
Transcendental Extension (INTRODUCTION [BASIC RINGS])
Transcendental Functions (POWER, LAURENT AND PUISEUX SERIES)
Transcendental Functions (REAL AND COMPLEX FIELDS)
Transcendental Extension (INTRODUCTION [BASIC RINGS])
Transfer Between Group Categories (FINITE SOLUBLE GROUPS)
Transfer Functions Between Group Categories (GROUPS)
Transfer Between Group Categories (FINITE SOLUBLE GROUPS)
InverseMattsonSolomonTransform(A, n) : RngUPolElt, RngIntElt -> RngUPolElt
KrawchoukTransform(f, K, n) : RngUPolElt, FldFin, RngIntElt -> RngUPolElt
MacWilliamsTransform(n, k, K, W) : RngIntElt, RngIntElt, FldFin, RngMPol -> RngMPol
MacWilliamsTransform(n, k, q, W) : RngIntElt, RngIntElt, RngIntElt, [ <RngIntElt, RngIntElt> ] -> [ <RngIntElt, RngIntElt> ]
MattsonSolomonTransform(f, n) : RngUPolElt, RngIntElt -> RngUPolElt
QuadraticTransformation(P) : Prj -> MapSch
QuadraticTransformation(X) : Sch -> SchMap
Transformation(C, t) : CrvHyp, [RngElt] -> CrvHyp, Map
TransformationMatrix(I) : RngFunOrdIdl -> AlgMatElt, RngElt
TransformationMatrix(O, P) : RngOrd -> AlgMatElt, RngIntElt
TransformationMatrix(I) : RngOrdFracIdl -> MtrxSpcElt, RngIntElt
CrvHyp_Transformation (Example H86E7)
Modules (OVERVIEW)
Operations with Linear Transformations (VECTOR SPACES)
VECTOR SPACES
TransformationMatrix(I) : RngFunOrdIdl -> AlgMatElt, RngElt
TransformationMatrix(O, P) : RngOrd -> AlgMatElt, RngIntElt
TransformationMatrix(I) : RngOrdFracIdl -> MtrxSpcElt, RngIntElt
Isomorphisms and Transformations (HYPERELLIPTIC CURVES)
Transforms (LINEAR CODES OVER FINITE FIELDS)
[Future release] IsArcTransitive(G, t) : GrphUnd, RngIntElt -> BoolElt
IsBlockTransitive(D) : Inc -> BoolElt
IsDistanceTransitive(G : parameters) : GrphUnd -> BoolElt
IsEdgeTransitive(G : parameters) : GrphUnd -> BoolElt
IsLineTransitive(P) : Plane -> BoolElt
IsPointTransitive(D) : Inc -> BoolElt
IsPointTransitive(P) : Plane -> BoolElt
IsSharplyTransitive(G, Y, k) : GrpPerm, GSet, RngIntElt -> BoolElt
IsTransitive(G, Y) : GrpPerm, GSet -> BoolElt
IsTransitive(G, Y, k) : GrpPerm, GSet, RngIntElt -> BoolElt
IsTransitive(G : parameters) : GrphUnd -> BoolElt
NumberOfTransitiveGroups(d) : RngIntElt -> RngIntElt
TransitiveGroup(d) : RngIntElt -> GrpPerm, MonStgElt
TransitiveGroup(d, f) : RngIntElt, Program -> GrpPerm, MonStgElt
TransitiveGroup(d, n) : RngIntElt, RngIntElt -> GrpPerm, MonStgElt
TransitiveGroup(S, f) : [RngIntElt], Program -> GrpPerm, MonStgElt
TransitiveGroupDatabaseLimit() : -> RngIntElt
TransitiveGroupDescription(d, n) : RngIntElt, RngIntElt -> MonStgElt
TransitiveGroupIdentification(G) : GrpPerm -> RngIntElt, RngIntElt
TransitiveGroupProcess(d) : RngIntElt -> Process
TransitiveGroupProcess(d, f) : RngIntElt, Program -> Process
TransitiveGroupProcess(S) : [RngIntElt] -> Process
TransitiveGroupProcess(S, f) : [RngIntElt], Program -> Process
TransitiveGroups(d: parameters) : RngIntElt -> [GrpPerm]
TransitiveGroups(S: parameters) : [RngIntElt] -> [GrpPerm]
TransitiveGroups(d, f) : RngIntElt, Program -> [GrpPerm]
TransitiveGroups(S, f) : [RngIntElt], Program -> [GrpPerm]
TransitiveQuotient(G) : GrpPerm -> GrpPerm, Hom, GrpPerm
TwoTransitiveGroupIdentification(G) : GrpPerm -> Tup
GrpData_Transitive (Example H34E7)
PrimitiveGroup(d) : RngIntElt -> GrpPerm, MonStgElt
TransitiveGroup(d) : RngIntElt -> GrpPerm, MonStgElt
TransitiveGroup(d, f) : RngIntElt, Program -> GrpPerm, MonStgElt
TransitiveGroup(d, n) : RngIntElt, RngIntElt -> GrpPerm, MonStgElt
TransitiveGroup(S, f) : [RngIntElt], Program -> GrpPerm, MonStgElt
PrimitiveGroupDatabaseLimit() : -> RngIntElt
TransitiveGroupDatabaseLimit() : -> RngIntElt
PrimitiveGroupDescription(d, n) : RngIntElt, RngIntElt -> MonStgElt
TransitiveGroupDescription(d, n) : RngIntElt, RngIntElt -> MonStgElt
TransitiveGroupIdentification(G) : GrpPerm -> RngIntElt, RngIntElt
PrimitiveGroupProcess(d) : RngIntElt -> Process
TransitiveGroupProcess(d) : RngIntElt -> Process
TransitiveGroupProcess(d, f) : RngIntElt, Program -> Process
TransitiveGroupProcess(S) : [RngIntElt] -> Process
TransitiveGroupProcess(S, f) : [RngIntElt], Program -> Process
PrimitiveGroups(d: parameters) : RngIntElt -> [GrpPerm]
TransitiveGroups(d: parameters) : RngIntElt -> [GrpPerm]
TransitiveGroups(S: parameters) : [RngIntElt] -> [GrpPerm]
TransitiveGroups(d, f) : RngIntElt, Program -> [GrpPerm]
TransitiveGroups(S, f) : [RngIntElt], Program -> [GrpPerm]
GrpData_TransitiveId (Example H34E9)
GrpData_TransitiveProcess (Example H34E8)
TransitiveQuotient(G) : GrpPerm -> GrpPerm, Hom, GrpPerm
Transitivity(G, Y) : GrpPerm, GSet -> RngIntElt
BestTranslation( T ) : Tup -> Tup
IdentityAutomorphism(A) : Sch -> AutSch
Translation(P,p,q) : Prj, Pt, Pt -> MapSch
Translation(P,Q) : Prj, [Pt] -> MapSch
Translation(A,p) : Sch, Pt -> MapSch
Translation(X,p) : Sch, Pt -> MapSch
TranslationMap(E, P) : CrvEll, PtEll -> Map
TranslationOfSimplex(P,Q) : Prj, [Pt] -> MapSch
TranslationToInfinity(C,p) : Crv,Pt -> Crv,AutSch
Abstract Function Fields (PLANE ALGEBRAIC CURVES)
Translation Between Graphs (RESOLUTION GRAPHS AND SPLICE DIAGRAMS)
Translation Planes (FINITE PLANES)
Scheme_translation (Example H81E27)
Translation Planes (FINITE PLANES)
Crv_translation-to-infinity (Example H82E9)
TranslationMap(E, P) : CrvEll, PtEll -> Map
TranslationOfSimplex(P,Q) : Prj, [Pt] -> MapSch
TranslationToInfinity(C,p) : Crv,Pt -> Crv,AutSch
NullspaceOfTranspose(A) : Mtrx -> ModTupRng
Transpose(a) : AlgMatElt -> AlgMatElt
Transpose(A) : Mtrx -> Mtrx
Transversal(G, H) : GrpFP, GrpFP -> {@ GrpFPElt @}, Map
SchreierSystem(G, H) : GrpFP, GrpFP -> {@ GrpFPElt @}, Map
Transversal(G, H) : Grp, Grp -> {@ GrpElt @}, Map
Transversal(G, H) : GrpAb, GrpAb -> {@ GrpAbElt @}, Map
Transversal( W, H ) : GrpCox, GrpCox -> @ @
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, K) : GrpPC, GrpPC, GrpPC -> {@ GrpPCElt @}, Map
Transversal(G, H) : GrpPerm, GrpPerm -> {@ GrpPermElt @}, Map
Transversal(V, U): ModTupFld, ModTupFld -> { ModTupFldELt }
Transversal(G, H) : GrpGPC, GrpGPC -> {@ GrpGPCElt @}, Map
Transversal(G, H, K) : GrpFP, GrpFP, GrpFP -> {@ GrpFPElt @}, Map
TransversalElt( W, H, x ) : GrpCox, GrpPermElt-> GrpPermElt
TransversalProcess(G, H) : GrpPerm, GrpPerm -> GrpPermTransProc
TransversalProcessNext(P) : GrpPermTransProc -> GrpPermElt
TransversalProcessRemaining(P) : GrpPermTransProc -> RngIntElt
RightTransversal(G, H) : GrpMat, GrpMat -> {@ GrpMatElt @}, Map
Coset Tables and Transversals (MATRIX GROUPS)
TransversalElt( W, H, x ) : GrpCox, GrpPermElt-> GrpPermElt
TransversalProcess(G, H) : GrpPerm, GrpPerm -> GrpPermTransProc
TransversalProcessNext(P) : GrpPermTransProc -> GrpPermElt
TransversalProcessRemaining(P) : GrpPermTransProc -> RngIntElt
GrpCox_Transversals (Example H36E3)
Coset Tables and Transversals (FINITE SOLUBLE GROUPS)
Cosets and Transversals (PERMUTATION GROUPS)
Transversals (PERMUTATION GROUPS)
CalculateTransverseIntersections(~g) : GrphRes ->
IsTransverse(C,D,p) : Sch,Sch,Pt -> BoolElt
ModifyTransverseIntersection(~v,n) : GrphResVert,RngIntElt ->
TransverseIntersections(g) : GrphRes -> SeqEnum
TransverseIntersections(g) : GrphRes -> SeqEnum
Traps for Young Players (MAGMA SEMANTICS)
Trap 1 (MAGMA SEMANTICS)
Trap 2 (MAGMA SEMANTICS)
TrapezoidalQuadrature(f, a, b, n) : Program, FldPrElt, FldPrElt, RngIntElt -> FldPrElt
TrapezoidalQuadrature(f, a, b, n) : Program, FldPrElt, FldPrElt, RngIntElt -> FldPrElt
BFSTree(u) : GrphVert -> Grph
BreadthFirstSearchTree(u) : GrphVert -> Grph
DepthFirstSearchTree(u) : GrphVert -> Grph
IsRootedTree(g) : GrphDir -> BoolElt,GrphVert
IsTree(G) : Grph -> BoolElt
PathTree(B, i) : AlgBas, RngIntElt -> ModRng
RandomTree(p) : RngIntElt -> GrphUnd
SpanningTree(G) : Grph -> Grph
DFSTree(u) : GrphVert -> Grph
Spanning Trees of a Graph or Digraph (GRAPHS)
TrialDivision(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]
TrialDivision(n, B) : RngQuadElt, RngIntElt -> SeqEnum, SeqEnum, Tup
TrialDivision(n) : RngIntElt -> RngIntEltFact, [ RngIntElt ]
TrialDivision(n, B) : RngQuadElt, RngIntElt -> SeqEnum, SeqEnum, Tup
PascalTriangle(D) : Dsgn -> SeqEnum
LowerTriangularMatrix(R, Q) : Rng, [ RngElt ] -> Mtrx
LowerTriangularMatrix(Q) : [ RngElt ] -> Mtrx
TriangularDecomposition(I) : RngMPol -> [ RngMPol ]
TriangularGraph(n) : RngIntElt -> GrphUnd
UpperTriangularMatrix(R, Q) : Rng, [ RngElt ] -> Mtrx
UpperTriangularMatrix(Q) : [ RngElt ] -> Mtrx
Triangular Decomposition (IDEAL THEORY AND GRÖBNER BASES)
Triangular Decomposition (IDEAL THEORY AND GRÖBNER BASES)
TriangularDecomposition(I) : RngMPol -> [ RngMPol ]
GB_TriangularDecomposition (Example H50E19)
TriangularGraph(n) : RngIntElt -> GrphUnd
[Future release] Tricomponents(G) : GrphUnd -> { { GrphVert } }
Trigonal Curves (PLANE ALGEBRAIC CURVES)
Crv_trigonal-curve (Example H82E21)
Inverse Trigonometric Functions (REAL AND COMPLEX FIELDS)
Trigonometric Functions (REAL AND COMPLEX FIELDS)
Trigonometric Functions and their Inverses (POWER, LAURENT AND PUISEUX SERIES)
RngMPol_Trinomials (Example H45E7)
IsTrivial(G) : Grp -> BoolElt
IsTrivial(x) : GrpDrchElt -> BoolElt
IsTrivial(G) : GrpPC -> BoolElt
IsTrivial(D) : Inc -> BoolElt
TrivialModule(G, K) : Grp, Fld -> ModGrp
Trivial Attributes (SCHEMES)
TrivialModule(G, K) : Grp, Fld -> ModGrp
Transitive Group Identification (DATABASES OF GROUPS)
Basic Small Group Functions (DATABASES OF GROUPS)
Booleans (OVERVIEW)
true
Truncate(q) : FldRatElt -> RngIntElt
Truncate(r) : FldReElt -> RngIntElt
Truncate(n) : RngIntElt -> RngIntElt
Truncate(f) : RngSerElt -> RngSerElt
Truncation(C, t) : CosetGeom, Set -> CosetGeom
Truncation(D, t) : IncGeom, Set -> IncGeom
Truncations (INCIDENCE GEOMETRY)
Tuplist(T) : Tup -> List
TupleToList(T) : Tup -> List
TupleToList(T) : Tup -> List
Tup_Tuple (Example H9E2)
Construction of Modules of n-tuples (FREE MODULES)
Creating and Modifying Tuples (TUPLES AND CARTESIAN PRODUCTS)
Tuple Access Functions (TUPLES AND CARTESIAN PRODUCTS)
TUPLES AND CARTESIAN PRODUCTS
Tuple Access Functions (TUPLES AND CARTESIAN PRODUCTS)
TUPLES AND CARTESIAN PRODUCTS
Construction of Modules of n-tuples (FREE MODULES)
Tup_TupleAccess (Example H9E3)
Tuplist(T) : Tup -> List
TupleToList(T) : Tup -> List
TupleToList(T) : Tup -> List
Tuplist(T) : Tup -> List
TupleToList(T) : Tup -> List
TupleToList(T) : Tup -> List
Graph_TutteCage (Example H93E2)
IsQuadraticTwist(C1, C2) : CrvHyp, CrvHyp -> BoolElt, RngElt
QuadraticTwist(E) : CrvEll -> CrvEll
QuadraticTwist(E, d) : CrvEll, RngElt -> CrvEll
QuadraticTwist(C) : CrvHyp -> CrvHyp
QuadraticTwist(C, d) : CrvHyp, RngElt -> CrvHyp
TwistedQRCode(l,m) : RngIntElt,RngIntElt -> Code
TwistedWindingElement(M, i, eps) : ModSym, RngIntElt, GrpDrchElt -> ModSymElt
TwistedWindingSubmodule(M, j, eps) : ModSym, RngIntElt, GrpDrchElt -> ModTupFld
Scheme_twisted-cubics (Example H81E35)
TwistedQRCode(l,m) : RngIntElt,RngIntElt -> Code
TwistedWindingElement(M, i, eps) : ModSym, RngIntElt, GrpDrchElt -> ModSymElt
TwistedWindingSubmodule(M, j, eps) : ModSym, RngIntElt, GrpDrchElt -> ModTupFld
QuadraticTwists(E) : CrvEll -> SeqEnum
QuadraticTwists(C) : CrvHyp -> SeqEnum
Twists(E) : CrvEll -> SeqEnum
CrvEll_Twists (Example H85E28)
CrvEll_Twists (Example H85E4)
Twisting Elliptic Curves (ELLIPTIC CURVES)
Twisting Hyperelliptic Curves (HYPERELLIPTIC CURVES)
Type Change Predicates (HYPERELLIPTIC CURVES)
CrvEll_Twists2 (Example H85E7)
ClassTwo (p, d : parameters) : RngIntElt, RngIntElt -> SeqEnum
TwoElement(I) : RngFunOrdIdl -> RngElt, RngElt
TwoElement(I) : RngOrdFracIdl -> FldOrdElt, FldOrdElt
TwoElementNormal(I) : RngInt -> RngIntElt, RngIntElt
TwoElementNormal(I) : RngOrdIdl -> RngOrdElt, RngOrdElt, RngIntElt
TwoGenerators(P) : PlcFunElt -> FldFunGElt, FldFunGElt
TwoSelmerGroupData(J: parameters) : JacHyp -> RngIntElt, RngIntElt, Tup, List
TwoSidedIdealClasses(S) : AlgQuatOrd -> [AlgQuatOrd]
TwoTorsionPolynomial(E) : CrvEll -> RngMPolElt
TwoTorsionSubgroup(J) : JacHyp -> GrpAb, Map
TwoTorsionSubgroup(Q) : QuadBin -> GrpAb, Map
TwoTransitiveGroupIdentification(G) : GrpPerm -> Tup
Two--Element Presentations (ORDERS AND ALGEBRAIC FIELDS)
TwoElement(I) : RngFunOrdIdl -> RngElt, RngElt
TwoElement(I) : RngOrdFracIdl -> FldOrdElt, FldOrdElt
TwoElementNormal(I) : RngInt -> RngIntElt, RngIntElt
TwoElementNormal(I) : RngOrdIdl -> RngOrdElt, RngOrdElt, RngIntElt
TwoGenerators(P) : PlcFunElt -> FldFunGElt, FldFunGElt
TwoSelmerGroupData(J: parameters) : JacHyp -> RngIntElt, RngIntElt, Tup, List
TwoSidedIdealClasses(S) : AlgQuatOrd -> [AlgQuatOrd]
TwoTorsionPolynomial(E) : CrvEll -> RngMPolElt
TwoTorsionSubgroup(J) : JacHyp -> GrpAb, Map
TwoTorsionSubgroup(Q) : QuadBin -> GrpAb, Map
TwoTransitiveGroupIdentification(G) : GrpPerm -> Tup
Type(E) : CrvEll -> Cat
Category(E) : CrvEll -> Cat
Category(L) : Lat -> Cat
Category(M) : ModBrdt -> Cat
Category(S) : Obj -> Cat
Category(P) : PtEll -> Cat
Category(R) : Rng -> Cat
Category(r) : RngElt -> Cat
Category(G) : SchGrpEll -> Cat
Category(H) : SetPtEll -> Cat
ChangeRepresentationType(A, Rep) : AlgGrp, MonStgElt -> AlgGrp, Map
ClassicalType(G) : GrpMat -> MonStgElt
DecompositionType(P, F) : PlcFunElt, FldFun -> [ <RngIntElt, RngIntElt> ]
DecompositionType(O) : RngFunOrd -> [ <RngIntElt, RngIntElt> ]
DecompositionType(O, p) : RngFunOrd, RngElt -> [ <RngIntElt, RngIntElt> ]
ElementType(S) : Str -> Cat
FormType(G) : GrpMat -> MonStgElt
GroupOfLieType( C, R ) : AlgMatElt, Rng -> AlgMatElt
GroupOfLieType( W, R ) : GrpCox, Rng -> AlgMatElt
GroupOfLieType( n, R ) : MonStgElt, Rng -> AlgMatElt
GroupOfLieType( RD, R ) : RootDtm, Rng -> AlgMatElt
GroupOfLieType( RD, k ) : RootDtm, Rng -> GrpLie
GroupOfLieType( W, R ) : RootDtm, Rng -> GrpLie
HasCentreType(X,i) : VSrfK3,RngIntElt -> BoolElt
IsogenyType( W ) : GrpCox -> List
IsogenyType( RD ) : RootDtm -> List
MakeType(S) : MonStgElt -> Cat
ModelType(X) : CrvMod -> MonStgElt
RepresentationType(A) : AlgGrp -> MonStgElt
SemiSimpleType(L) : AlgLie -> AlgLie
Type(x) : Elt -> BoolElt
Category (OVERVIEW)
GROUPS OF LIE TYPE
Parent and Category (INTRODUCTION [BASIC RINGS])
The Type of a Semisimple Lie Algebra (LIE ALGEBRAS)
Types, Category Names and Structures (STATEMENTS AND EXPRESSIONS)
ListTypes() : ->
ListCategories() : ->
Types(C) : CosetGeom -> SetIndx
Types(D) : IncGeom -> SetIndx
Aside: Types of Schemes (SCHEMES)
Cartan matrices (ROOT DATA FOR LIE THEORY)
Different Types of Scheme (SCHEMES)
State_TypeStructures (Example H1E18)
Dynamic Typing (MAGMA SEMANTICS)
[____] [____] [_____] [____] [__] [Index] [Root]