eval(RootSystem,Weight,Root) -- evaluate the dual of a root at a Weight

• Function: eval

• Usage:

  eval(R,v,r)

• Inputs:
  • R, an instance of the type RootSystem,
  • v, an instance of the type Weight,
  • r, an instance of the type Root,
• Outputs:
  • an integer, the dual of the root r evaluated at the weight v

i1 : R=rootSystemA(2)

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

o1 : RootSystem

i2 : L=toList(positiveRoots(R))

o2 = {| -1 |, | 1 |, |  2 |}
      |  2 |  | 1 |  | -1 |

o2 : List

i3 : v=weight(R,{1,2})

o3 = | 1 |
     | 2 |

       2
o3 : ZZ

i4 : eval(R,v,L#0)

o4 = 2

i5 : eval(R,v,L#1)

o5 = 3

i6 : eval(R,v,L#2)

o6 = 1