rootCoefficients(RootSystem,Weight) -- the coefficients at the simple roots

Synopsis

• Function: rootCoefficients

• Usage:

  rootCoefficients(R,p)

• Inputs:
  • R, an instance of the type RootSystem,
  • p, an instance of the type Weight,
• Outputs:
  • a vector, whose components are the coefficients of p at the simple roots of R

Description

i1 : R=rootSystemE(6)

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

o1 : RootSystem

i2 : rootCoefficients(R,halfSumOfRoots(R))

o2 = |  8 |
     | 11 |
     | 15 |
     | 21 |
     | 15 |
     |  8 |

       6
o2 : QQ