isReduced(RootSystem,BasicList) -- whether a decomposition in simple reflections is reduced

• Function: isReduced

• Usage:

  isReduced(R,L)

• Inputs:
  • R, an instance of the type RootSystem,
  • L, a basic list, of indices of simple reflections
• Outputs:
  • a Boolean value, true if the length of the product of these simple reflections is indeed their number, and false if not

i1 : R=rootSystemF4

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

o1 : RootSystem

i2 : L=reducedDecomposition longestWeylGroupElement R

o2 = {1, 2, 1, 3, 2, 1, 3, 2, 3, 4, 3, 2, 1, 3, 2, 3, 4, 3, 2, 1, 3, 2, 3, 4}

o2 : List

i3 : isReduced(R,L)

o3 = true

i4 : L={1,1}

o4 = {1, 1}

o4 : List

i5 : isReduced(R,L)

o5 = false