isRoot(RootSystem,Parabolic,Root) -- check whether a root is in the sub root system of the parabolic

Synopsis

• Function: isRoot

• Usage:

  isRoot(R,P,r)

• Inputs:
  • R, an instance of the type RootSystem,
  • P, an instance of the type Parabolic,
  • r, an instance of the type Root,
• Outputs:
  • a Boolean value, true if p is a root in the sub root system of R defined by P and false otherwise

Description

i1 : R=rootSystemE(6)

o1 = RootSystem{...8...}

o1 : RootSystem

i2 : P=parabolic(R,set{1,3})

o2 = set {1, 3}

o2 : Parabolic

i3 : r1=simpleRoot(R,1)

o3 = |  2 |
     |  0 |
     | -1 |
     |  0 |
     |  0 |
     |  0 |

       6
o3 : ZZ

i4 : r2=simpleRoot(R,2)

o4 = |  0 |
     |  2 |
     |  0 |
     | -1 |
     |  0 |
     |  0 |

       6
o4 : ZZ

i5 : isRoot(R,P,r1)

o5 = true

i6 : isRoot(R,P,r2)

o6 = false