[____] [____] [_____] [____] [__] [Index] [Root]
Subindex: root .. Roots
Actions (COXETER GROUPS AS
PERMUTATION GROUPS)
Constants Associated with Root Data (ROOT DATA)
Constructing Root Data (ROOT DATA)
Constructing Root Systems (ROOT SYSTEMS)
Creating New Root Data from Old (ROOT DATA)
Creating New Root Systems from Old (ROOT SYSTEMS)
Operations and Properties for Root and Coroot indices (COXETER GROUPS AS
PERMUTATION GROUPS)
Operations and Properties for Root and Coroot indices (ROOT DATA)
Operations and Properties for Roots and Coroot Indices (ROOT SYSTEMS)
Operators on Root Data (ROOT DATA)
Operators on Root Systems (ROOT SYSTEMS)
Order and Roots (FINITE FIELDS)
Properties of Root Data (ROOT DATA)
Properties of Root Systems (ROOT SYSTEMS)
ROOT DATA
ROOT SYSTEMS
Roots (FINITE FIELDS)
Roots (UNIVARIATE POLYNOMIAL RINGS)
Roots, Coroots and Reflections (COXETER GROUPS AS
PERMUTATION GROUPS)
Square Root (POWER, LAURENT AND PUISEUX SERIES)
ROOT DATA
Roots, Coroots and Reflections (COXETER GROUPS AS
PERMUTATION GROUPS)
ROOT SYSTEMS
CorootAction( W ) : GrpPermCox -> Map
RootAction( W ) : GrpPermCox -> Map
GrpPermCox_RootArithmetic (Example H84E16)
RootDtm_RootArithmetic (Example H80E13)
RootSys_RootArithmetic (Example H79E13)
Isogeny (ROOT DATA)
RootDatum(L) : AlgLie -> RootDtm
RootDatum( C ) : AlgMatElt -> RootDtm
RootDatum( C ) : AlgMatElt -> RootDtm
RootDatum( A, B ) : AlgMatElt, AlgMatElt -> RootDtm
RootDatum( D ) : GrphDir -> RootDtm
RootDatum( G ) : GrpLie -> RootDtm
RootDatum( W ) : GrpMat -> RootDtm
RootDatum( W ) : GrpPermCox -> RootDtm
RootDatum( N ) : MonStgElt -> RootDtm
RootDatum( R ) : RootSys -> RootDtm
RootSystem(L) : AlgLie -> [ AlgLieElt ], [ AlgLieElt ], [ AlgLieElt ], AlgMatElt
AlgLie_RootDatum (Example H81E5)
Groups (OVERVIEW)
Definition of a Split Root Datum (ROOT DATA)
IsRootedTree(G) : GrphDir -> BoolElt, GrphVert
CorootGSet( W ) : GrpPermCox -> GSet
RootGSet( W ) : GrpPermCox -> GSet
CorootHeight( W, r ) : GrpPermCox, RngIntElt -> RngIntElt
RootHeight( W, r ) : GrpPermCox, RngIntElt -> RngIntElt
RootHeight( R, r ) : RootDtm, RngIntElt -> RngIntElt
RootHeight( R, r ) : RootSys, RngIntElt -> RngIntElt
CorootNorm( W, r ) : GrpPermCox, RngIntElt -> RngIntElt
RootNorm( W, r ) : GrpPermCox, RngIntElt -> RngIntElt
RootNorm( R, r ) : RootDtm, RngIntElt -> RngIntElt
RootNorm( R, r ) : RootSys, RngIntElt -> RngIntElt
CorootNorms( W ) : GrpPermCox -> [RngIntElt]
RootNorms( W ) : GrpPermCox -> [RngIntElt]
RootNorms( R ) : RootDtm -> [RngIntElt]
RootNorms( R ) : RootSys -> [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
GrpPermCox_RootOperations (Example H84E17)
RootDtm_RootOperations (Example H80E14)
RootSys_RootOperations (Example H79E14)
CorootPosition( G, v ) : GrpLie, . -> {@@}
RootPosition( G, v ) : GrpLie, . -> {@@}
RootPosition( W, v ) : GrpMat, . -> {@@}
RootPosition( W, v ) : GrpPermCox, . -> {@@}
RootPosition( R, v ) : RootDtm, . -> {@@}
RootPosition( R, v ) : RootSys, . -> {@@}
Reflections (COXETER GROUPS AS
PERMUTATION GROUPS)
Reflections (COXETER GROUPS)
Reflections (REFLECTION GROUPS)
Reflections (ROOT DATA)
Reflections (ROOT SYSTEMS)
AllRoots(a, n) : FldFinElt, RngIntElt -> SeqEnum
AllSquareRoots(a) : RngIntResElt -> [ RngIntResElt ]
NumberOfPositiveRoots( W ) : GrpFPCox -> RngIntElt
NumberOfPositiveRoots( G ) : GrpLie -> RngIntElt
NumberOfPositiveRoots( W ) : GrpMat -> RngIntElt
NumberOfPositiveRoots( W ) : GrpPermCox -> RngIntElt
NumberOfPositiveRoots( N ) : MonStgElt -> .
NumberOfPositiveRoots( R ) : RootDtm -> RngIntElt
NumberOfPositiveRoots( R ) : RootSys -> RngIntElt
PositiveRoots( G ) : GrpLie -> {@@}
PositiveRoots( W ) : GrpMat -> {@@}
PositiveRoots( W ) : GrpPermCox -> {@@}
PositiveRoots( R ) : RootDtm -> {@@}
PositiveRoots( R ) : RootSys -> {@@}
Roots( G ) : GrpLie -> {@@}
Roots( W ) : GrpMat -> {@@}
Roots( W ) : GrpPermCox -> {@@}
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(f) : RngUPolElt -> [ <RngLocElt, RngIntElt> ]
Roots(f) : RngUPolElt -> [<RngSerElt, RngIntElt>]
Roots(f, D) : RngUPolElt, DivFunElt -> SeqEnum[ FldFunElt ]
Roots( R ) : RootDtm -> {@@}
Roots( R ) : RootSys -> {@@}
RootsInSplittingField(f) : RngPolElt(FldFin) -> [<RngPolElt, RngIntElt>], FldFin
RootsNonExact(p) : RngUPolElt -> [ FldPrElt ], [ FldPrElt ]
SimpleRoots( W ) : GrpMat -> Mtrx
SimpleRoots( W ) : GrpPermCox -> Mtrx
SimpleRoots( R ) : RootDtm -> Mtrx
SimpleRoots( R ) : RootSys -> Mtrx
ValuationsOfRoots(f) : RngUPolElt -> SeqEnum[<FldRatElt, RngIntElt>]
FldRe_Roots (Example H40E6)
[____] [____] [_____] [____] [__] [Index] [Root]