%off echo,nat$
off echo$
out "rreducparautom6_4N4.r"$
operator b$



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The generic automorphism of g_{6,4} as in (art ijac1 section5) :
phi:=mat((b(1,1),0,0,0,0,0),
         (0,b(2,2),0,0,0,0),
         (b(3,1),b(3,2),b(3,3),0,0,0),
         (b(4,1),b(4,2),0,b(2,2)*b(1,1),0,0),
         (b(5,1),b(5,2),b(5,3), -b(4,1)*b(2,2), b(2,2)**2*b(1,1), 0),
         (b(6,1),b(6,2),b(6,3), b(3,2)*b(1,1), 0, b(3,3)*b(1,1)))$


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The generic nilpotent derivation as in (Cohomology tables page 116) : the eigenvalues
% are 0
operator xi$
delta:=
mat((0,0,0,0,0,0),
    (0,0,0,0,0,0),
    (xi(3,1),xi(3,2),0,0,0,0),
    (xi(4,1),xi(4,2),0,0,0,0),
    (xi(5,1),xi(5,2),xi(5,3),-xi(4,1),0,0),
    (xi(6,1),xi(6,2),xi(6,3),xi(3,2),0,0))$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "The nonzero ajoints are delta(4,1), delta(5,2), delta(6,1), and delta(4,2)-delta(6,3)"$
write "Hence delta(4,2) and delta(6,3) are adjoint related"$
% by subtracting adjoints one then may suppose
xi(4,1):=0$
xi(6,1):=0$
xi(5,2):=0$
xi(4,2):=0$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


write "phi:=",phi;
write "det(phi):=",det(phi);
write "delta:=",delta;
write "We denote this delta by the shortform"$
shortformdelta:={xi(3,1),xi(3,2),SS,xi(5,1),xi(5,3),SS,xi(6,2),xi(6,3)}$
paramindexeslist:={{3,1},{3,2},{5,1},{5,3},{6,2},{6,3}}$

write "shortformdelta:=", shortformdelta$
%bye$

off nat$

Matrix deltaprime(6,6)$
deltaprime:=phi*delta*phi**(-1)$
write "deltaprime:=phi*delta*phi**(-1)"$

shortformdeltaprime:= for each U in shortformdelta collect
  if U = ss then U else deltaprime(part(U,1),part(U,2))$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%case under consideration here  for reduction by automorphism
write "******* Suppose xi(3,1) = 0 and xi(3,2) = 0 and xi(5,3)=0"$
xi(3,1):=0$
xi(3,2):=0$
xi(5,3):=0$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "phi*delta*phi**(-1):=",phi*delta*phi**(-1);


for each U in paramindexeslist do  <<write "deltaprime(" ,part(U,1), ",", part(U,2), "):=" ,           deltaprime(part(U,1),part(U,2))>>$

bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%