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Subindex: polytopes  ..  PositiveCoroots


polytopes

   Polytopes (CONVEX POLYTOPES AND POLYHEDRA)
   Polytopes, Cones and Polyhedra (CONVEX POLYTOPES AND POLYHEDRA)

polytopes-cones-polyhedra

   Polytopes, Cones and Polyhedra (CONVEX POLYTOPES AND POLYHEDRA)

PolyToSeries

   PolyToSeries(s) : RngMPolElt -> RngPowAlgElt

POmega

   POmega(arguments)
   ProjectiveOmega(arguments)
   ProjectiveOmegaMinus(arguments)
   ProjectiveOmegaPlus(arguments)

POmegaMinus

   POmegaMinus(arguments)
   ProjectiveOmegaMinus(arguments)

POmegaPlus

   POmegaPlus(arguments)
   ProjectiveOmegaPlus(arguments)

Pop

   IndentPop() : ->
   Pop(P) : StkPtnOrd ->

POpen

   POpen(C, T) : MonStgElt, MonStgElt -> File

Pos

   NumPosRoots(C) : AlgMatElt -> RngIntElt
   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

poset

   Operations on Poset Elements (GROUPS)
   Operations on Subgroup Class Posets (GROUPS)
   The Poset of Subgroup Classes (GROUPS)

poset-element

   Operations on Poset Elements (GROUPS)

poset-operation

   Operations on Subgroup Class Posets (GROUPS)

Position

   Position(s, t) : MonStgElt, MonStgElt -> RngIntElt
   Index(s, t) : MonStgElt, MonStgElt -> RngIntElt
   Index(S, x) : SeqEnum, Elt -> RngIntElt
   Index(S, x) : SetIndx, Elt -> RngIntElt
   PlaceEnumPosition(R) : PlcEnum -> [RngIntElt]
   RootPosition(G, v) : GrpLie, . -> (@@)
   RootPosition(W, v) : GrpMat, . -> (@@)
   RootPosition(W, v) : GrpPermCox, . -> (@@)
   RootPosition(R, v) : RootStr, . -> (@@)
   RootPosition(R, v) : RootSys, . -> (@@)

Positions

   IdempotentPositions(B) : AlgBas -> SeqEnum

Positive

   PositiveGammaOrbitsOnRoots(R) : RootDtm -> SeqEnum[GSetEnum]
   NegativeGammaOrbitsOnRoots(R) : RootDtm -> SeqEnum[GSetEnum]
   ZeroGammaOrbitsOnRoots(R) : RootDtm -> SeqEnum[GSetEnum]
   GammaOrbitsOnRoots(R) : RootDtm -> SeqEnum[GSetEnum]
   IsEffective(D) : DivCrvElt -> BoolElt
   IsPositive(W, r) : GrpPermCox, RngIntElt -> BoolElt
   IsPositive(R, r) : RootStr, RngIntElt -> BoolElt
   IsPositive(R, r) : RootSys, RngIntElt -> BoolElt
   IsPositiveDefinite(F) : ModMatRngElt -> BoolElt
   IsPositiveSemiDefinite(F) : ModMatRngElt -> BoolElt
   IsTotallyPositive(a) : FldNumElt -> BoolElt
   IsTotallyPositive(a) : RngOrdElt -> BoolElt
   MinimalElementConjugatingToPositive(x, s: parameters) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
   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
   PositiveConjugates(u: parameters) : GrpBrdElt -> SetIndx
   PositiveConjugatesProcess(u: parameters) : GrpBrdElt -> GrpBrdClassProc
   PositiveDefiniteForm(G) : GrpMat -> Mtrx
   PositiveDefiniteForm(L) : Lat -> AlgMatElt
   PositiveQuadrant(L) : TorLat -> TorCon
   PositiveRoots(G) : GrpLie -> (@@)
   PositiveRoots(W) : GrpMat -> (@@)
   PositiveRoots(W) : GrpPermCox -> (@@)
   PositiveRoots(R) : RootStr -> (@@)
   PositiveRoots(R) : RootSys -> (@@)
   PositiveRootsPerm(U) : AlgQUE -> SeqEnum
   PositiveSum(m, i) : Map, RngIntElt -> FldReElt
   RelativeRoots(R) : RootDtm -> SetIndx

positive

   Simple and Positive Roots (ROOT DATA)
   Simple and Positive Roots (ROOT SYSTEMS)
   The Coxeter Group (ROOT SYSTEMS)

positive-simple-roots

   Simple and Positive Roots (ROOT DATA)
   Simple and Positive Roots (ROOT SYSTEMS)
   The Coxeter Group (ROOT SYSTEMS)

PositiveConjugates

   PositiveConjugates(u: parameters) : GrpBrdElt -> SetIndx

PositiveConjugatesProcess

   PositiveConjugatesProcess(u: parameters) : GrpBrdElt -> GrpBrdClassProc

PositiveCoroots

   PositiveCoroots(G) : GrpLie -> (@@)
   PositiveRoots(G) : GrpLie -> (@@)
   PositiveRoots(W) : GrpMat -> (@@)
   PositiveRoots(W) : GrpPermCox -> (@@)
   PositiveRoots(R) : RootStr -> (@@)
   PositiveRoots(R) : RootSys -> (@@)

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