underBruhat(WeylGroupElement) -- Weyl group elements just under a given one for the Bruhat order

i1 : R=rootSystemA(3)

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

o1 : RootSystem

i2 : L=underBruhat(longestWeylGroupElement(R))

o2 = {{WeylGroupElement{RootSystem{...8...}, | -1 |}, |  2 |},
                                             | -2 |   | -1 |  
                                             |  1 |   |  0 |  
     ------------------------------------------------------------------------
     {WeylGroupElement{RootSystem{...8...}, | -2 |}, | -1 |},
                                            |  1 |   |  2 |  
                                            | -2 |   | -1 |  
     ------------------------------------------------------------------------
     {WeylGroupElement{RootSystem{...8...}, |  1 |}, |  0 |}}
                                            | -2 |   | -1 |
                                            | -1 |   |  2 |

o2 : List

i3 : apply(L,x->reducedDecomposition (x#0))

o3 = {{1, 2, 1, 3, 2}, {1, 2, 3, 2, 1}, {2, 1, 3, 2, 1}}

o3 : List