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

Function: isMinimalRepresentative
Usage:

minimalRepresentative(w,P)
Inputs:
- w, an instance of the type WeylGroupElement,
- P, an instance of the type Parabolic,
Outputs:
- a Boolean value, true if w is the representative of minimal length of a left 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 ((longestWeylGroupElement R) % P)

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

o3 : WeylGroupElement

i4 : isMinimalRepresentative(w,P)

o4 = true

Caveat

This function is less efficient than the corresponding function for right cosets.

Ways to use this method:

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

The source of this document is in WeylGroups.m2:3751:0.