whoseReflection(WeylGroupElement) -- the positive root whose reflection is a given element of a Weyl group

Function: whoseReflection
Usage:

whoseReflection(w)
Inputs:
- w, an instance of the type WeylGroupElement,
Outputs:
- an instance of the type Root, the root whose corresponding reflection is w

Description

i1 : R=rootSystemD(5)

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

o1 : RootSystem

i2 : w=reduce(R,{3})

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

o2 : WeylGroupElement

i3 : if isReflection(w) then whoseReflection(w)

o3 = |  0 |
     | -1 |
     |  2 |
     | -1 |
     | -1 |

       5
o3 : ZZ

Caveat

If w is not a reflection, an error occurs.

Ways to use this method:

whoseReflection(WeylGroupElement) -- the positive root whose reflection is a given element of a Weyl group

The source of this document is in /__w/M2/M2/macaulay2-1.26.05+ds/M2/Macaulay2/packages/WeylGroups.m2:3295:0.