Properties of Root Systems

IsIrreducible(R) : RootSys -> BoolElt

Returns true if, and only if, the root system R is irreducible.

IsSemisimple(R) : RootSys-> BoolElt

Returns true if, and only if, the root system R is semisimple, i.e. its rank is equal to its dimension.

IsCrystallographic(R) : RootSys -> BoolElt

Returns true if, and only if, the root system R is crystallographic, i.e. its Cartan matrix is integral.

IsSimplyLaced(R) : RootSys-> BoolElt

Returns true if, and only if, the root system R is simply laced, i.e. its Coxeter graph contains no labelled edges.

Example RootSys_Properties (H79E8)

> R := RootSystem( "A5 B2" );
> IsIrreducible( R );
false
> IsSemisimple( R );
true
> IsCrystallographic( R );
true
> IsSimplyLaced( R );
false