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

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 |

       8
o2 : ZZ

i3 : r2=simpleRoot(R,2)

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

       8
o3 : ZZ

i4 : rootCoefficients(R,r1+r2)

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

       8
o4 : QQ

The source of this document is in WeylGroups.m2:2553:0.