Returns true if, and only if, the root system R is irreducible.
Returns true if, and only if, the root system R is a direct sum of a simple system and a toral system. This is equivalent to R having a connected Coxeter diagram.
Returns true if, and only if, the root system R is reduced.
Returns true if, and only if, the root system R is semisimple, i.e. its rank is equal to its dimension.
Returns true if, and only if, the root system R is crystallographic, i.e. its Cartan matrix is integral.
Returns true if, and only if, the root system R is simply laced, i.e. its Coxeter graph contains no labelled edges.
> R := RootSystem("A5 B2"); > IsIrreducible(R); false > IsSemisimple(R); true > IsCrystallographic(R); true > IsSimplyLaced(R); false