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

Subindex: RootOfUnity  ..  roots


RootOfUnity

   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

RootOperations

   GrpCox_RootOperations (Example H98E20)
   RootDtm_RootOperations (Example H97E22)
   RootSys_RootOperations (Example H96E14)

RootPermutation

   RootPermutation(phi) : Map -> GrpPermElt

RootPosition

   CorootPosition(G, v) : GrpLie, . -> (@@)
   RootPosition(G, v) : GrpLie, . -> (@@)
   RootPosition(W, v) : GrpMat, . -> (@@)
   RootPosition(W, v) : GrpPermCox, . -> (@@)
   RootPosition(R, v) : RootStr, . -> (@@)
   RootPosition(R, v) : RootSys, . -> (@@)

rootrefl

   Reflections (COXETER GROUPS)
   Reflections (GROUPS OF LIE TYPE)
   Reflections (REFLECTION GROUPS)
   Reflections (ROOT DATA)
   Reflections (ROOT SYSTEMS)

Roots

   AdditivePolynomialFromRoots(x, P) : RngElt, PlcFunElt -> RngUPolTwstElt
   AllRoots(a, n) : FldFinElt, RngIntElt -> SeqEnum
   AllSquareRoots(a) : RngIntResElt -> [ RngIntResElt ]
   GammaOrbitOnRoots(R,r) : RootDtm, RngIntElt -> GSetEnum
   GammaOrbitsOnRoots(R) : RootDtm -> SeqEnum[GSetEnum]
   HasAllRootsOnUnitCircle(f) : RngUPolElt -> BoolElt
   NumberOfPositiveRoots(C) : AlgMatElt -> RngIntElt
   NumberOfPositiveRoots(W) : GrpFPCox -> RngIntElt
   NumberOfPositiveRoots(G) : GrpLie -> RngIntElt
   NumberOfPositiveRoots(W) : GrpMat -> RngIntElt
   NumberOfPositiveRoots(W) : GrpPermCox -> RngIntElt
   NumberOfPositiveRoots(N) : MonStgElt -> .
   NumberOfPositiveRoots(R) : RootStr -> RngIntElt
   NumberOfPositiveRoots(R) : RootSys -> RngIntElt
   PositiveRoots(G) : GrpLie -> (@@)
   PositiveRoots(W) : GrpMat -> (@@)
   PositiveRoots(W) : GrpPermCox -> (@@)
   PositiveRoots(R) : RootStr -> (@@)
   PositiveRoots(R) : RootSys -> (@@)
   PositiveRootsPerm(U) : AlgQUE -> SeqEnum
   QuarticNumberOfRealRoots(q) : RngUPolElt -> RngUPolElt
   RelativeRoots(R) : RootDtm -> SetIndx
   Roots(G) : GrpLie -> (@@)
   Roots(W) : GrpMat -> (@@)
   Roots(W) : GrpPermCox -> (@@)
   Roots(f) : RngUPolElt -> [ < FldACElt, RngIntElt> ]
   Roots(f) : RngUPolElt -> [ < FldFinElt, RngIntElt> ]
   Roots(p) : RngUPolElt -> [ < RngElt, RngIntElt> ]
   Roots(p, S) : RngUPolElt -> [ < RngElt, RngIntElt> ]
   Roots(p) : RngUPolElt -> [ <FldComElt, RngIntElt> ]
   Roots(f) : RngUPolElt -> [ <RngPadElt, RngIntElt> ]
   Roots(f) : RngUPolElt -> [<RngSerElt, RngIntElt>]
   Roots(f, D) : RngUPolElt, DivFunElt -> SeqEnum[ FldFunElt ]
   Roots(f) : RngUPolElt[RngLocA] -> SeqEnum
   Roots(R) : RootStr -> (@@)
   Roots(R) : RootSys -> (@@)
   RootsAndCoroots(G) : GrpMat -> [RngIntElt], [ModTupRngElt], [ModTupRngElt]
   RootsInSplittingField(f) : RngUPolElt[FldFin] -> [<RngUPolElt, RngIntElt>], FldFin
   RootsNonExact(p) : RngUPolElt[FldRe] -> [ FldComElt ], [ FldComElt ]
   SimpleRoots(G) : GrpLie -> Mtrx
   SimpleRoots(W) : GrpMat -> Mtrx
   SimpleRoots(W) : GrpPermCox -> Mtrx
   SimpleRoots(R) : RootStr -> Mtrx
   SimpleRoots(R) : RootSys -> Mtrx
   SmallRoots(p, N, X) : RngUPolElt, RngElt, RngElt -> [RngElt]
   ValuationsOfRoots(f) : RngUPolElt -> SeqEnum[<FldRatElt, RngIntElt>]
   ValuationsOfRoots(f) : RngUPolElt -> [ < RngIntElt, RngIntElt > ]
   ValuationsOfRoots(f, p) : RngUPolElt, RngIntElt -> [ < RngIntElt, RngIntElt > ]
   FldRe_Roots (Example H25E5)

roots

   Functions returning Roots (p-ADIC RINGS AND THEIR EXTENSIONS)
   Hensel Lifting of Roots (p-ADIC RINGS AND THEIR EXTENSIONS)
   Roots (ALGEBRAICALLY CLOSED FIELDS)
   Roots (REAL AND COMPLEX FIELDS)
   Roots and Coroots (ROOT SYSTEMS)
   Roots of Elements (p-ADIC RINGS AND THEIR EXTENSIONS)
   Roots of Ideals (ALGEBRAIC FUNCTION FIELDS)
   Roots of Ideals (ORDERS AND ALGEBRAIC FIELDS)
   Roots of Polynomials (NEWTON POLYGONS)
   Roots of Polynomials (p-ADIC RINGS AND THEIR EXTENSIONS)
   Roots, Coroots and Reflections (COXETER GROUPS)
   Roots, Coroots and Weights (GROUPS OF LIE TYPE)
   Roots, Coroots and Weights (ROOT DATA)
   Simple and Positive Roots (ROOT DATA)
   Simple and Positive Roots (ROOT SYSTEMS)
   The Coxeter Group (ROOT SYSTEMS)

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

Version: V2.19 of Wed Apr 24 15:09:57 EST 2013