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

Synopsis

• Function: rootCoefficients

• Usage:

  rootCoefficients(R,r)

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

Description

i1 : R=rootSystemE(8)

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

o1 : RootSystem

i2 : r1=simpleRoot(R,1)

o2 = |  2 |
     |  0 |
     | -1 |
     |  0 |
     |  0 |
     |  0 |
     |  0 |
     |  0 |

o2 : Root

i3 : r2=simpleRoot(R,2)

o3 = |  0 |
     |  2 |
     |  0 |
     | -1 |
     |  0 |
     |  0 |
     |  0 |
     |  0 |

o3 : Root

i4 : rootCoefficients(R,r1+r2)

o4 = | 1 |
     | 1 |
     | 0 |
     | 0 |
     | 0 |
     | 0 |
     | 0 |
     | 0 |

       8
o4 : QQ