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WeylGroups :: isMinimalRepresentative(Parabolic,WeylGroupElement,Parabolic)

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

Synopsis

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 : Q=parabolic(R,set{2,3,4,5,6})

o3 = set {2, 3, 4, 5, 6}

o3 : Parabolic
i4 : w=minimalRepresentative ((P % (longestWeylGroupElement R)) % Q)

o4 = WeylGroupElement{RootSystem{...8...}, |  1  |}
                                           |  1  |
                                           |  1  |
                                           |  1  |
                                           |  1  |
                                           | -11 |

o4 : WeylGroupElement
i5 : isMinimalRepresentative(P,w,Q)

o5 = true