WeylGroupDoubleCoset == WeylGroupDoubleCoset -- equality of double cosets

Operator: ==
Usage:

w1 == w2
Inputs:
- w1, an instance of the type WeylGroupDoubleCoset,
- w2, an instance of the type WeylGroupDoubleCoset,
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=P % (w % P)

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

o4 : WeylGroupDoubleCoset

i5 : w2=P % ((reduce(R,{4}) * w * reduce(R,{2,3})) % P)

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

i6 : w1==w2

o6 = true

Ways to use this method:

WeylGroupDoubleCoset == WeylGroupDoubleCoset -- equality of double cosets

The source of this document is in WeylGroups.m2:3509:0.