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

Synopsis

• Function: scalarProduct

• Usage:

  scalarProduct(R,i,j)

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

Description

i1 : R=rootSystemA(2)

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

o1 : RootSystem

i2 : scalarProduct(R,1,1)

     1
o2 = -
     3

o2 : QQ

i3 : scalarProduct(R,1,2)

     1
o3 = -
     6

o3 : QQ

i4 : scalarProduct(R,2,2)

     1
o4 = -
     3

o4 : QQ