isReduced(BasicList,WeylGroupElement) -- whether an Weyl group element can be multiplied by some simple reflections with length increasing at each step

Synopsis

• Function: isReduced

• Usage:

  isReduced(L,w)

• Inputs:
  • L, a basic list, of indices of simple reflections
  • w, an instance of the type WeylGroupElement,
• Outputs:
  • a Boolean value, true if the length of the product (on the left) of these simple reflections by w is the length of w plus their number, and false if not

Description

i1 : R=rootSystemA(3)

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

o1 : RootSystem

i2 : w=reduce(R,{1,2,1})

o2 = WeylGroupElement{RootSystem{...8...}, | -1 |}
                                           | -1 |
                                           |  3 |

o2 : WeylGroupElement

i3 : isReduced({2,3},w)

o3 = true

i4 : isReduced({1},w)

o4 = false