reflect(RootSystem,ZZ,Weight) -- apply to a weight the reflection with respect to a root

Synopsis

• Function: reflect

• Usage:

  reflect(R,i,p)

• Inputs:
  • R, an instance of the type RootSystem,
  • i, an integer,
  • p, an instance of the type Weight,
• Outputs:
  • an instance of the type Weight, s_i(p)

Description

i1 : R = rootSystemB(4)

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

o1 : RootSystem

i2 : p = halfSumOfRoots(R)

o2 = | 1 |
     | 1 |
     | 1 |
     | 1 |

       4
o2 : ZZ

i3 : reflect(R,4,p)

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

       4
o3 : ZZ