isMinimalRepresentative(Parabolic,WeylGroupElement) -- check whether an element of a Weyl group is the minimal representative of a right coset

Function: isMinimalRepresentative
Usage:

minimalRepresentative(P,w)
Inputs:
- P, an instance of the type Parabolic,
- w, an instance of the type WeylGroupElement,
Outputs:
- a Boolean value, true if w is the representative of minimal length of a right coset, and false otherwise

Description

i1 : R=rootSystemE(6)

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

o1 : RootSystem

i2 : P=parabolic(R,set{1,2,3,4,5})

o2 = set {1, 2, 3, 4, 5}

o2 : Parabolic

i3 : w=minimalRepresentative (P % (longestWeylGroupElement R))

o3 = WeylGroupElement{RootSystem{...8...}, |  1  |}
                                           |  1  |
                                           |  1  |
                                           |  1  |
                                           |  1  |
                                           | -11 |

o3 : WeylGroupElement

i4 : isMinimalRepresentative(P,w)

o4 = true

Ways to use this method:

isMinimalRepresentative(Parabolic,WeylGroupElement) -- check whether an element of a Weyl group is the minimal representative of a right coset

The source of this document is in WeylGroups.m2:3772:0.