WeylGroupLeftCoset == WeylGroupLeftCoset -- equality of left cosets

Operator: ==
Usage:

w1 == w2
Inputs:
- w1, an instance of the type WeylGroupLeftCoset,
- w2, an instance of the type WeylGroupLeftCoset,
Outputs:
- a Boolean value, true if w1 and w2 belong to the same quotient and coincide, and false otherwise

Description

i1 : R=rootSystemD(5)

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

o1 : RootSystem

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

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

o2 : Parabolic

i3 : w=longestWeylGroupElement R

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

o3 : WeylGroupElement

i4 : w1=w % P

o4 = WeylGroupLeftCoset{set {2, 3, 4, 5}, WeylGroupElement{RootSystem{...8...}, | -7 |}}
                                                                                |  1 |
                                                                                |  1 |
                                                                                |  1 |
                                                                                |  1 |

o4 : WeylGroupLeftCoset

i5 : w2=(w * reduce(R,{2,3})) % P

o5 = WeylGroupLeftCoset{set {2, 3, 4, 5}, WeylGroupElement{RootSystem{...8...}, | -7 |}}
                                                                                |  1 |
                                                                                |  1 |
                                                                                |  1 |
                                                                                |  1 |

o5 : WeylGroupLeftCoset

i6 : w1==w2

o6 = true

Ways to use this method:

WeylGroupLeftCoset == WeylGroupLeftCoset -- equality of left cosets

The source of this document is in WeylGroups.m2:3424:0.