positiveRoots(RootSystem,Parabolic) -- the set of all positive roots in a parabolic sugroups

Synopsis

• Function: positiveRoots

• Usage:

  positiveRoots(R,P)

• Inputs:
  • R, an instance of the type RootSystem,
  • P, an instance of the type Parabolic,
• Outputs:
  • a set, of all positive roots of R that are written as sums of roots corresponding to reflexions in P

Description

i1 : R=rootSystemA(4)

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

o1 : RootSystem

i2 : P=parabolic(R,set{1,2})

o2 = set {1, 2}

o2 : Parabolic

i3 : positiveRoots(R,P)

o3 = set {|  1 |, |  2 |, | -1 |}
          |  1 |  | -1 |  |  2 |
          | -1 |  |  0 |  | -1 |
          |  0 |  |  0 |  |  0 |

o3 : Set