Subindex: <B><B>Coreflection</B> .. Coroots</B>

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Subindex: Coreflection .. Coroots

Coreflection

   CoreflectionGroup( W ) : GrpPermCox -> GrpMat, Map
   ReflectionGroup( W ) : GrpPermCox -> GrpMat, Map
   ReflectionMatrices( W ) : GrpPermCox -> []
   ReflectionMatrices( R ) : RootDtm -> []
   ReflectionMatrices( R ) : RootSys -> []
   ReflectionMatrix( W, r ) : GrpPermCox, RngIntElt -> []
   ReflectionMatrix( R, r ) : RootDtm, RngIntElt -> []
   ReflectionMatrix( R, r ) : RootSys, RngIntElt -> []
   SimpleReflectionMatrices( W ) : GrpPermCox -> []
   SimpleReflectionMatrices( R ) : RootDtm -> []
   SimpleReflectionMatrices( R ) : RootSys -> []

CoreflectionGroup

CoreflectionGroup( W ) : GrpPermCox -> GrpMat, Map
ReflectionGroup( W ) : GrpPermCox -> GrpMat, Map

CoreflectionMatrices

   CoreflectionMatrices( W ) : GrpPermCox -> []
   ReflectionMatrices( W ) : GrpPermCox -> []
   ReflectionMatrices( R ) : RootDtm -> []
   ReflectionMatrices( R ) : RootSys -> []

CoreflectionMatrix

   CoreflectionMatrix( W, r ) : GrpPermCox, RngIntElt -> []
   ReflectionMatrix( W, r ) : GrpPermCox, RngIntElt -> []
   ReflectionMatrix( R, r ) : RootDtm, RngIntElt -> []
   ReflectionMatrix( R, r ) : RootSys, RngIntElt -> []

Coroot

   Coroot( G, r ) : GrpLie, RngIntElt -> {@@}
   Root( G, r ) : GrpLie, RngIntElt -> {@@}
   Root( W, r ) : GrpMat, RngIntElt -> {@@}
   Root( W, r ) : GrpPermCox, RngIntElt -> {@@}
   Root( R, r ) : RootDtm, RngIntElt -> {@@}
   Root( R, r ) : RootSys, RngIntElt -> {@@}
   RootAction( W ) : GrpPermCox -> Map
   RootGSet( W ) : GrpPermCox -> GSet
   RootHeight( W, r ) : GrpPermCox, RngIntElt -> RngIntElt
   RootHeight( R, r ) : RootDtm, RngIntElt -> RngIntElt
   RootHeight( R, r ) : RootSys, RngIntElt -> RngIntElt
   RootNorm( W, r ) : GrpPermCox, RngIntElt -> RngIntElt
   RootNorm( R, r ) : RootDtm, RngIntElt -> RngIntElt
   RootNorm( R, r ) : RootSys, RngIntElt -> RngIntElt
   RootNorms( W ) : GrpPermCox -> [RngIntElt]
   RootNorms( R ) : RootDtm -> [RngIntElt]
   RootNorms( R ) : RootSys -> [RngIntElt]
   RootPosition( G, v ) : GrpLie, . -> {@@}
   RootPosition( W, v ) : GrpMat, . -> {@@}
   RootPosition( W, v ) : GrpPermCox, . -> {@@}
   RootPosition( R, v ) : RootDtm, . -> {@@}
   RootPosition( R, v ) : RootSys, . -> {@@}
   RootSpace( W ) : GrpMat -> Lat
   RootSpace( W ) : GrpPermCox -> .
   RootSpace( R ) : RootDtm -> Lat
   RootSpace( R ) : RootSys -> ModTupFld

coroot

   Actions (COXETER GROUPS AS PERMUTATION GROUPS)
   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)

CorootAction

   CorootAction( W ) : GrpPermCox -> Map
   RootAction( W ) : GrpPermCox -> Map
   GrpPermCox_CorootAction (Example H84E23)

CorootGSet

CorootGSet( W ) : GrpPermCox -> GSet
RootGSet( W ) : GrpPermCox -> GSet

CorootHeight

   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

   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

   CorootNorms( W ) : GrpPermCox -> [RngIntElt]
   RootNorms( W ) : GrpPermCox -> [RngIntElt]
   RootNorms( R ) : RootDtm -> [RngIntElt]
   RootNorms( R ) : RootSys -> [RngIntElt]

CorootPosition

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

Coroots

   PositiveCoroots( G ) : GrpLie -> {@@}
   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( R ) : RootDtm -> {@@}
   Roots( R ) : RootSys -> {@@}
   SimpleRoots( W ) : GrpMat -> Mtrx
   SimpleRoots( W ) : GrpPermCox -> Mtrx
   SimpleRoots( R ) : RootDtm -> Mtrx
   SimpleRoots( R ) : RootSys -> Mtrx

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