scalarProduct(RootSystem,Weight,Weight) -- the scalar product of two weights

Synopsis

• Function: scalarProduct

• Usage:

  scalarProduct(R,u,v)

• Inputs:
  • R, an instance of the type RootSystem,
  • u, an instance of the type Weight, the first weight
  • v, an instance of the type Weight, the second weight
• Outputs:
  • a rational number, the scalar product of u and v

Description

i1 : R=rootSystemA(2)

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

o1 : RootSystem

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

o2 = | 1 |
     | 2 |

o2 : Weight

i3 : v=weight(R,{0,3})

o3 = | 0 |
     | 3 |

o3 : Weight

i4 : scalarProduct(R,u,v)

     5
o4 = -
     2

o4 : QQ