Reflections

The root alpha acts on the root space via the reflection s_alpha; the coroot alpha^star acts on the coroot space via the coreflection s_alpha^star.

IsReflection( w ) : GrpCoxElt -> BoolElt, ., ., RngInt

Returns true if, and only if, w is a reflection, i.e., w is conjugate to a Coxeter generator. This function is only implemented for elements of finite groups. If w is a reflection, the root, coroot and root index are also returned.

Reflections( W ) : GrpFPCox -> GrpFPCoxElt

ReflectionWords( W ) : GrpFPCox -> GrpFPCoxElt

The sequence of reflections in the finite Coxeter group W.

Example GrpFPCox_Reflections (H83E10)

> W<a,b> := CoxeterGroup( GrpFPCox, "A2" );
> Reflections(W);
[ a, b, a * b * a, a, b, a * b * a ]
> IsReflection( a*b );
false