reflect(RootSystem,ZZ,Root) -- apply to a root the reflection with respect to a simple root

Synopsis

• Function: reflect

• Usage:

  reflect(R,i,r)

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

Description

i1 : R = rootSystemB(4)

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

o1 : RootSystem

i2 : r = simpleRoot(R,3)

o2 = |  0 |
     | -1 |
     |  2 |
     | -2 |

       4
o2 : ZZ

i3 : reflect(R,4,r)

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

       4
o3 : ZZ