# 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:
• , 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