reflect(RootSystem,BasicList,Root) -- apply to a root several reflections with respect to simple roots

Synopsis

• Function: reflect

• Usage:

  reflect(R,L,r)

• Inputs:
  • R, an instance of the type RootSystem,
  • L, a basic list,
  • r, an instance of the type Root,
• Outputs:
  • an instance of the type Weight, s_{L_0}...s_{L_{\#L-1}}(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,{1,2,3,4},r)

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

       4
o3 : ZZ