reflection(RootSystem,Root) -- the reflection with respect to a root

Synopsis

Function: reflection
Usage:

reflection(R,r)
Inputs:
- R, an instance of the type RootSystem
- r, an instance of the type Root
Outputs:
- an instance of the type WeylGroupElement, the reflection with respect to r

Description

i1 : R=rootSystemE(8)

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

o1 : RootSystem

i2 : r=addRoots(R,simpleRoot(R,1),simpleRoot(R,3))

o2 = |  1 |
     |  0 |
     |  1 |
     | -1 |
     |  0 |
     |  0 |
     |  0 |
     |  0 |

o2 : Root

i3 : reflection(R,r)

o3 = WeylGroupElement{RootSystem{...8...}, | -1 |}
                                           |  1 |
                                           | -1 |
                                           |  3 |
                                           |  1 |
                                           |  1 |
                                           |  1 |
                                           |  1 |

o3 : WeylGroupElement