Returns true if, and only if, the Coxeter group W is finite.
Returns true if, and only if, the Coxeter group W is affine
(Section Finite and Affine Coxeter Groups).
Returns true if, and only if, the Coxeter group W is hyperbolic
(Section Hyperbolic Groups).
Returns true if, and only if, the Coxeter group W is compact hyperbolic
(Section Hyperbolic Groups).
IsIrreducible(W) : GrpPermCox -> BoolElt
Returns true if, and only if, the Coxeter group W is
irreducible.
Returns true if, and only if, the permutation Coxeter group W is
semisimple,
i.e. its rank is equal to its dimension.
Returns true if, and only if, the permutation Coxeter group W is crystallographic, i.e. if the corresponding reflection representation is
defined over the integers.
IsSimplyLaced(W) : GrpFPCox -> BoolElt
Returns true if, and only if, the Coxeter group W is simply laced, i.e. its Coxeter graph has no labels.
> W := CoxeterGroup(GrpFPCox, HyperbolicCoxeterMatrix(22));
> IsFinite(W);
false
> IsAffine(W);
false
> IsHyperbolic(W);
true
> IsCompactHyperbolic(W);
false
> IsIrreducible(W);
true
> IsSimplyLaced(W);
true
> W := CoxeterGroup("A2 D4");
> IsIrreducible(W);
false
> IsSemisimple(W);
true
> IsCrystallographic(W);
true
> IsSimplyLaced(W);
true
V2.28, 13 July 2023