eval(RootSystem,ZZ,Root) -- evaluate the dual of a root at a fundamental weight

Synopsis

• Function: eval

• Usage:

  eval(R,i,r)

• Inputs:
  • R, an instance of the type RootSystem
  • i, an integer, the number of a weight
  • r, an instance of the type Root
• Outputs:
  • an integer, the dual of the root r evaluated at the i-th fundamental weight

Description

i1 : R=rootSystemA(2)

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

o1 : RootSystem

i2 : L=toList(positiveRoots(R))

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

o2 : List

i3 : eval(R,1,L#0)

o3 = 0

i4 : eval(R,1,L#1)

o4 = 1

i5 : eval(R,1,L#2)

o5 = 1