scalarProduct(RootSystem,ZZ,Weight) -- the scalar product of a fundamental weight and a weight

Synopsis

• Function: scalarProduct

• Usage:

  scalarProduct(R,i,v)

• Inputs:
  • R, an instance of the type RootSystem,
  • i, an integer, the number of the fundamental weight
  • v, an instance of the type Weight, the other weight
• Outputs:
  • a rational number, the scalar product of the i-th fundamental weight with the weight v

Description

i1 : R=rootSystemA(2)

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

o1 : RootSystem

i2 : v=weight(R,{1,2})

o2 = | 1 |
     | 2 |

       2
o2 : ZZ

i3 : scalarProduct(R,1,v)

     2
o3 = -
     3

o3 : QQ