read "covariants.txt":

# The variables
protect(x,y,lambda,alpha):
X:=[x[0],x[1],x[2]]:
Y:=[y[0],y[1],y[2],y[3]]:
L:=[lambda[0],lambda[1],lambda[2]]:
A:=[alpha[0],alpha[1],alpha[2],alpha[3]]:

# The representant of Orbit Ii:
RepIi:=[
  2*x[1]*x[2],
  2*x[0]*x[2],
  2*x[0]*x[1],
  x[0]^2+x[1]^2+x[2]^2
]:

# Its covariants:
Phi:=`covariant/ListPhi`(RepIi,X,Y,L,A):
Delta:=`covariant/Discriminant`(RepIi,X):
eval(Phi);
Delta;

# Some interesting factorizations:
factor(Phi[9]);
factor(Phi[15]);