isPositiveRoot(RootSystem,Weight) -- check whether a weight is a positive root

Synopsis

• Function: isPositiveRoot

• Usage:

  isPositiveRoot(R,p)

• Inputs:
  • R, an instance of the type RootSystem,
  • p, an instance of the type Weight,
• Outputs:
  • a Boolean value, true if p is a positive root in R and false otherwise

Description

i1 : R=rootSystemE(6)

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

o1 : RootSystem

i2 : p=halfSumOfRoots(R)

o2 = | 1 |
     | 1 |
     | 1 |
     | 1 |
     | 1 |
     | 1 |

       6
o2 : ZZ

i3 : isPositiveRoot(R,p)

o3 = false