%off echo,nat$
off echo$
out "rreducparautommodg6_17N2.r"$
operator b$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "The generic automorphism phi of g_{6,17} as computed by calculautom6_17.red :"$

phi:=
mat((b(1,1),0,0,0,0,0),(b(2,1),b(1,1)**3,0,0,0,0),(b(3,1),b(3,2),b(1,1)**4,0,0,0
),(b(4,1),b(4,2),b(3,2)*b(1,1),b(1,1)**5,0,0),(b(5,1),b(5,2),b(4,2)*b(1,1),b(3,2
)*b(1,1)**2,b(1,1)**6,0),(b(6,1),b(6,2),b(3,2)*b(2,1) - b(3,1)*b(1,1)**3 + b(5,2
)*b(1,1),(b(4,2) + b(2,1)*b(1,1)**2)*b(1,1)**2,b(3,2)*b(1,1)**3,b(1,1)**7))$


write "phi:=",phi;
on factor$
write "det(phi):=",det(phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The generic derivation as in (Cohomology tables section 4.1.2) :
operator xi$
delta:=
mat((xi(1,1),0,0,0,0,0),
    (xi(2,1),3*xi(1,1),0,0,0,0),
    (xi(3,1),xi(3,2),4*xi(1,1),0,0,0),
    (xi(4,1),xi(4,2),xi(3,2),5*xi(1,1),0,0),
    (xi(5,1),xi(5,2),xi(4,2),xi(3,2),6*xi(1,1),0),
    (xi(6,1),xi(6,2),-xi(3,1)+xi(5,2),xi(2,1)+xi(4,2),xi(3,2),7*xi(1,1)))$
write "generic derivation : delta:=",delta;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%The nonzero adjoint derivations
matrix adx1(6,6)$
adx1:=sub({xi(1,1)=0,xi(2,1)=0,xi(3,1)=0,xi(3,2)=1,xi(4,1)=0,xi(4,2)=0,xi(5,1)=0,xi(5,2)=0,xi(6,1)=0,xi(6,2)=0}, delta)$
matrix adx2(6,6)$
adx2:=sub({xi(1,1)=0,xi(2,1)=0,xi(3,1)=-1,xi(3,2)=0,xi(4,1)=0,xi(4,2)=0,xi(5,1)=0,xi(5,2)=0,xi(6,1)=0,xi(6,2)=0}, delta)$
matrix adx3(6,6)$
adx3:=sub({xi(1,1)=0,xi(2,1)=0,xi(3,1)=0,xi(3,2)=0,xi(4,1)=-1,xi(4,2)=0,xi(5,1)=0,xi(5,2)=0,xi(6,1)=0,xi(6,2)=-1}, delta)$
matrix adx4(6,6)$
adx4:=sub({xi(1,1)=0,xi(2,1)=0,xi(3,1)=0,xi(3,2)=0,xi(4,1)=0,xi(4,2)=0,xi(5,1)=-1,xi(5,2)=0,xi(6,1)=0,xi(6,2)=0}, delta)$
matrix adx5(6,6)$
adx5:=sub({xi(1,1)=0,xi(2,1)=0,xi(3,1)=0,xi(3,2)=0,xi(4,1)=0,xi(4,2)=0,xi(5,1)=0,xi(5,2)=0,xi(6,1)=-1,xi(6,2)=0}, delta)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
on nat$
write adx1:=adx1$
write adx2:=adx2$
write adx3:=adx3$
write adx4:=adx4$
write adx5:=adx5$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "The generic nilpotent derivation as in (Cohomology tables page 50) : the eigenvalues
are 0"$
xi(1,1):=0$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% by subtracting adjoints one then may suppose
xi(3,1):=0$
xi(3,2):=0$
xi(4,1):=0$
xi(5,1):=0$
xi(6,1):=0$
write "by subtracting adjoints one then may suppose xi(3,1)=xi(3,2)=xi(4,1)=xi(5,1)=xi(6,1)=0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "phi:=",phi;
on factor$
write "det(phi):=",det(phi);
write "delta:=",delta;
write "We denote this delta by the shortform"$
shortformdelta:=
{xi(2,1),SS,xi(4,2),SS,xi(5,2),SS,xi(6,2)}$
paramindexeslist:=
{ {2,1},{4,2},{5,2},{6,2}}$

write "shortformdelta:=", shortformdelta$
write "paramindexeslist:=",paramindexeslist$

off nat$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
PROCEDURE SHORTFORM(M0)$
BEGIN$
M:=M0$
WS:=  {M(2,1),SS,M(4,2),SS,M(5,2),SS,M(6,2)}$
RETURN WS$
END$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
PROCEDURE DELTAPRIMEMODADG(M0)$
BEGIN $
M:=M0$
M:=phi*M*phi**(-1)$
M:=M-M(3,2)*adx1 +M(3,1)*adx2 +M(4,1)*adx3 +M(5,1)*adx4 +M(6,1)*adx5$

write "shortformdeltaprimemodadg:=",shortform(M)$
for each U in paramindexeslist do <<write "deltaprimemodg(" ,part(U,1), ",", part(U,2), "):=" ,
                  M(part(U,1),part(U,2))>>$
write "det(phi):=",det(phi);
DELTAPRIMEMODADG:=M$
on nat$
write "DELTAPRIMEMODADG:=", M$
off nat$
CLEAR M$
%RETURN DELTAPRIMEMODADG$
END$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
DELTAPRIMEMODADG(delta);
%bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "********* Suppose that xi(2,1) =  0."$
xi(2,1):=0$
write "xi(2,1):=",xi(2,1)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "SUBSUBCASE I : **************** Suppose xi(4,2) NEQ 0"$
write "Then on may suppose xi(4,2):=1"$
xi(4,2):=1$
write "xi(4,2):=",xi(4,2)$
write "Then one keeps deltaprimemodg(4,2)=k by taking:"$
b(1,1):=sqrt(k)$
write "b(1,1):=",b(1,1)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
DELTAPRIMEMODADG(delta);
%bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "One gets deltaprimemodg(6,2)=0 by taking:"$
%deltaprimemodg(6,2):=((b(2,1) + sqrt(k)*xi(6,2)*k + b(2,1))*k)/sqrt(k)$
b(2,1) := - sqrt(k)*xi(6,2)*k/2$
write "b(2,1):=",b(2,1)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
DELTAPRIMEMODADG(delta);
%bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "If xi(5,2) neq 0"$
write "Then we get deltaprimemodg(5,2)=k  by taking for k"$
%deltaprimemodg(5,2):=(xi(5,2)*k**2)/sqrt(k)$
k:=(1/xi(5,2))**2$
write "k:=",k$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
DELTAPRIMEMODADG(delta);
%bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence, we are reduced to:"$
write "shortformdeltaprime ={0,SS,1,SS,epsilon,SS,0}"$
write "where epsilon=xi(5,2):= 0,1"$
%bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "SUBSUBCASE II : **************** Suppose xi(4,2) = 0"$
xi(4,2):=0$
write "xi(4,2):=",xi(4,2)$
clear b(1,1),b(2,1),k$
write "clear b(1,1),b(2,1),k"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
DELTAPRIMEMODADG(delta);
%bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%deltaprimemodg(5,2):=b(1,1)**3*xi(5,2)$
%deltaprimemodg(6,2):=b(1,1)**4*xi(6,2)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "If xi(5,2) neq 0"$
write "Then on may suppose xi(5,2):=1"$
xi(5,2):=1$
write "xi(5,2):=",xi(5,2)$
write "Then one keeps deltaprimemodg(5,2)=k by taking:"$
b(1,1):=(k)**(1/3)$
write "b(1,1):=",b(1,1)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
DELTAPRIMEMODADG(delta);
%bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Then  If xi(6,2) neq 0 we get deltaprimemodg(6,2)=k  by taking for k"$
%deltaprimemodg(6,2):=k**(1/3)*xi(6,2)*k$
k:=(1/xi(6,2))**3$
write "k:=",k$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
DELTAPRIMEMODADG(delta);
%bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence if xi(4,2)=0 and xi(5,2) neq 0"$
write "we are reduced to:"$
write "shortformdeltaprime ={0,SS,0,SS,1,SS,epsilon}"$
write "where epsilon=xi(6,2):= 0,1"$
%bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Finally if xi(4,2)=xi(5,2) neq 0"$
xi(5,2):=0$
write "xi(5,2):=",xi(5,2)$
clear b(1,1),k$
write "clear b(1,1),k"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
DELTAPRIMEMODADG(delta);
%bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "we are reduced to:"$
write "shortformdeltaprime ={0,SS,0,SS,0,SS,1}"$
bye$