%off echo,nat$
off echo$
out "rreducparautommodg6_51xCN6.r"$
write "rreducparautommodg6_51xCN6.r"$
operator b$
ON REVPRI$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "The generic automorphism phi of C x g_{5,1} as computed by calculautom6_51xC.red :"$
write "They fall into 4 kinds: "$
write "The first  kind (which contains the identity component) is: "$

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


write "The parameters are subject to the supplementary conditions :"$
condition11:=b(2,2)*( b(3,3)*b(1,1) - b(3,1)*b(1,3))$
write condition11,"neq 0"$


write "phi:=",phi;
on factor$
write "det(phi):=",det(phi);
write "condition11:=",condition11," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The generic derivation as computed by geneLplus.tex :
operator xi$

delta:=
mat((xi(1,1),xi(1,2),xi(1,3),xi(1,4),0,0),
(xi(2,1),xi(2,2),xi(1,4),xi(2,4),0,0),
(xi(3,1),xi(3,2),xi(3,3),-xi(2,1),0,0),
(xi(3,2),xi(4,2),-xi(1,2),xi(1,1)-xi(2,2)+xi(3,3),0,0),
(xi(5,1),xi(5,2),xi(5,3),xi(5,4),xi(1,1)+xi(3,3),xi(5,6)),
(xi(6,1),xi(6,2),xi(6,3),xi(6,4),0,xi(6,6)))$

write "generic derivation : delta:=",delta;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%The nonzero adjoint derivations
matrix adx1(6,6)$
adx1:=
sub({xi(1,1)=0,xi(1,2)=0,xi(1,3)=0,xi(1,4)=0,xi(2,1)=0,xi(2,2)=0,xi(2,4)=0,xi(3,1)=0,xi(3,2)=0,xi(3,3)=0,xi(4,2)=0,xi(5,1)=0,xi(5,2)=0,xi(5,3)=1,xi(5,4)=0,xi(5,6)=0,xi(6,1)=0,xi(6,2)=0,xi(6,3)=0,xi(6,4)=0,xi(6,6)=0}, delta)$
matrix adx2(6,6)$
adx2:=
sub({xi(1,1)=0,xi(1,2)=0,xi(1,3)=0,xi(1,4)=0,xi(2,1)=0,xi(2,2)=0,xi(2,4)=0,xi(3,1)=0,xi(3,2)=0,xi(3,3)=0,xi(4,2)=0,xi(5,1)=0,xi(5,2)=0,xi(5,3)=0,xi(5,4)=1,xi(5,6)=0,xi(6,1)=0,xi(6,2)=0,xi(6,3)=0,xi(6,4)=0,xi(6,6)=0}, delta)$
matrix adx3(6,6)$
adx3:=
sub({xi(1,1)=0,xi(1,2)=0,xi(1,3)=0,xi(1,4)=0,xi(2,1)=0,xi(2,2)=0,xi(2,4)=0,xi(3,1)=0,xi(3,2)=0,xi(3,3)=0,xi(4,2)=0,xi(5,1)=-1,xi(5,2)=0,xi(5,3)=0,xi(5,4)=0,xi(5,6)=0,xi(6,1)=0,xi(6,2)=0,xi(6,3)=0,xi(6,4)=0,xi(6,6)=0}, delta)$
matrix adx4(6,6)$
adx4:=
sub({xi(1,1)=0,xi(1,2)=0,xi(1,3)=0,xi(1,4)=0,xi(2,1)=0,xi(2,2)=0,xi(2,4)=0,xi(3,1)=0,xi(3,2)=0,xi(3,3)=0,xi(4,2)=0,xi(5,1)=0,xi(5,2)=-1,xi(5,3)=0,xi(5,4)=0,xi(5,6)=0,xi(6,1)=0,xi(6,2)=0,xi(6,3)=0,xi(6,4)=0,xi(6,6)=0}, delta)$
%matrix adx5(6,6)$
%adx5:=
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
on nat$
write adx1:=adx1$
write adx2:=adx2$
write adx3:=adx3$
write adx4:=adx4$
%write adx5:=adx5$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "The generic nilpotent derivation : the eigenvalues are 0"$
xi(3,3):=-xi(1,1)$
write "xi(3,3):=",xi(3,3)$
xi(6,6):=0$
write "xi(6,6):=",xi(6,6)$

write "And the matrix A:="$
mat((xi(1,1),xi(1,2),xi(1,3),xi(1,4)),
(xi(2,1),xi(2,2),xi(1,4),xi(2,4)),
(xi(3,1),xi(3,2),xi(3,3),-xi(2,1)),
(xi(3,2),xi(4,2),-xi(1,2),xi(1,1)-xi(2,2)+xi(3,3)));
write "is nilpotent."$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
M:=mat((xi(1,1),xi(1,2),xi(1,3),xi(1,4)),
(xi(2,1),xi(2,2),xi(1,4),xi(2,4)),
(xi(3,1),xi(3,2),xi(3,3),-xi(2,1)),
(xi(3,2),xi(4,2),-xi(1,2),xi(1,1)-xi(2,2)+xi(3,3)));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "we may suppose that A is an element of sp(4,C)+, that is:"$
xi(1,1):=0$
xi(2,1):=0$
xi(2,2):=0$
xi(3,1):=0$
xi(3,2):=0$
xi(4,2):=0$
write "xi(1,1):=",xi(1,1)$
write "xi(2,1):=",xi(2,1)$
write "xi(2,2):=",xi(2,2)$
write "xi(3,1):=",xi(3,1)$
write "xi(3,2):=",xi(3,2)$
write "xi(4,2):=",xi(4,2)$


for j:=1:4 do <<write "M**",j,":=",M**j>>;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

off nat$
off factor$
for j:=1:4 do <<write "Trace(M**",j,")/2:=",Trace(M**j)/2>>;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear M;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% by subtracting adjoints one then may suppose
xi(5,1):=0$
xi(5,2):=0$
xi(5,3):=0$
xi(5,4):=0$
write "By subtracting adjoints one then may suppose:"$
write "xi(5,1):=0,xi(5,2):=0,xi(5,3):=0,xi(5,4):=0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "delta:=",delta;
write "We denote this delta by the shortform"$
shortformdelta:=
{xi(1,2),xi(1,3),xi(1,4),SS,xi(2,4),SS,xi(5,6),SS,xi(6,1),xi(6,2),xi(6,3),xi(6,4)}$
paramindexeslist:=
{{1,2},{1,3},{1,4},{2,4},{5,6},{6,1},{6,2},{6,3},{6,4}}$

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

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

IF AUTOM=phi THEN  <<write "With the first kind automorphism one gets">>$
IF AUTOM=psi THEN  <<write "With the second kind automorphism one gets">>$
IF AUTOM=rho THEN  <<write "With the third kind automorphism one gets">>$
IF AUTOM=chi THEN  <<write "With the fourth kind automorphism one gets">>$

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))>>$
on factor$
write "det(AUTOM):=",det(AUTOM);
DELTAPRIMEMODADG:=M$
%on nat$
off nat$
write "DELTAPRIMEMODADG:=", M$
off nat$
CLEAR M$
%RETURN DELTAPRIMEMODADG$
END$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "************************************************************************"$
write "*******Suppose xi(1,2) = 0."$
write "*******Suppose xi(1,3) = 0."$
write "*******Suppose xi(1,4) = 0."$
write "*******Suppose xi(2,4) = 0."$
write "************************************************************************"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
xi(1,2):=0$
write "xi(1,2):=",xi(1,2)$
xi(1,3):=0$
write "xi(1,3):=",xi(1,3)$
xi(1,4):=0$
write "xi(1,4):=",xi(1,4)$
xi(2,4):=0$
write "xi(2,4):=",xi(2,4)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
on nat$
write "delta:=",delta$
off nat$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Take the following values:"$
b(1,3):=0$
b(1,2):=0$
b(4,2):=0$
b(3,2):=0$
write "b(1,3):=",b(1,3)$
write "b(1,2):=",b(1,2)$
write "b(3,2):=",b(3,2)$
write "b(4,2):=",b(4,2)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "****** Suppose xi(6,2) neq 0."$
write "Then we get deltaprime(6,2)=1 by taking:"$
%deltaprimemodg(6,2):=(b(6,6)*xi(6,2))/b(2,2)$
b(2,2):=(b(6,6)*xi(6,2))$
write "b(2,2):=",b(2,2)$


write "and we get deltaprime(6,1)=0 by taking:"$
%deltaprimemodg(6,1):=(b(6,6)*( - b(3,1)*xi(6,3) + b(3,3)*xi(6,1) + b(3,4)*xi(6,2
%)))/(b(3,3)*b(1,1))$
b(3,4):=-( - b(3,1)*xi(6,3) + b(3,3)*xi(6,1) )/(xi(6,2))$
write "b(3,4):=",b(3,4)$



write "and we get deltaprime(6,3)=0 by taking:"$
%deltaprimemodg(6,3):=(b(6,6)*(b(1,1)*xi(6,3) - b(1,4)*xi(6,2)))/(b(3,3)*b(1,1))$
b(1,4):=b(1,1)*xi(6,3) /xi(6,2)$
write "b(1,4):=",b(1,4)$


write "and we get deltaprime(6,4)=0 by taking:"$
comment
deltaprimemodg(6,4):=(b(6,6)*(b(3,1)*b(2,2)*b(1,4)*xi(6,3) + b(3,3)*b(2,2)*b(1,1
)*xi(6,4) - b(3,3)*b(2,2)*b(1,4)*xi(6,1) - b(3,3)*b(2,4)*b(1,1)*xi(6,2) - b(3,4)
*b(2,2)*b(1,1)*xi(6,3)))/(b(3,3)**2*b(1,1)**2)$

b(2,4):=(b(3,1)*b(2,2)*b(1,4)*xi(6,3) + b(3,3)*b(2,2)*b(1,1
)*xi(6,4) - b(3,3)*b(2,2)*b(1,4)*xi(6,1)
%- b(3,3)*b(2,4)*b(1,1)*xi(6,2)
- b(3,4)
*b(2,2)*b(1,1)*xi(6,3))/(b(3,3)*b(1,1)*xi(6,2))$
write "b(2,4):=",b(2,4)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence if xi(6,2) neq 0, we are reduced to :"$
write "(0,0,0,ss,0,ss,epsilon,ss,0,1,0,0}"$
write "where epsilon=xi(5,6)=0,1."$
write "*****************************************************************************"$
write "****** Suppose xi(6,2) = 0."$
xi(6,2):=0$
write "xi(6,2):=",xi(6,2)$
clear b(2,2),b(3,4),b(1,4),b(2,4)$
write "clear b(2,2),b(3,4),b(1,4),b(2,4)"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "****** Suppose xi(6,3) neq 0."$
write "Then we get deltaprime(6,3)=1 by taking:"$
%deltaprimemodg(6,3):=(b(6,6)*xi(6,3))/b(3,3)$
b(3,3):=(b(6,6)*xi(6,3))$
write "b(3,3):=",b(3,3)$

write "and we get deltaprime(6,1)=0 by taking:"$
%deltaprimemodg(6,1):=(b(6,6)*( - b(3,1)*xi(6,3) + b(3,3)*xi(6,1)))/(b(3,3)*b(1,1
%))$

b(3,1):=b(3,3)*xi(6,1)/xi(6,3)$
write "b(3,1):=",b(3,1)$



write "and we get deltaprime(6,4)=0 by taking:"$
%deltaprimemodg(6,4):=(b(6,6)*b(2,2)*(b(3,1)*b(1,4)*xi(6,3) + b(3,3)*b(1,1)*xi(6,
%4) - b(3,3)*b(1,4)*xi(6,1) - b(3,4)*b(1,1)*xi(6,3)))/(b(3,3)**2*b(1,1)**2)$

b(3,4):=(b(3,1)*b(1,4)*xi(6,3) + b(3,3)*b(1,1)*xi(6,
4) - b(3,3)*b(1,4)*xi(6,1) )/(b(1,1)*xi(6,3))$
write "b(3,4):=",b(3,4)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence if xi(6,2)=0 and xi(6,3) neq 0, we are reduced to :"$
write "(0,0,0,ss,0,ss,epsilon,ss,0,0,1,0}"$
write "where epsilon=xi(5,6)=0,1."$
write "*****************************************************************************"$
write "****** Suppose xi(6,2) = xi(6,3)= 0."$
xi(6,3):=0$
write "xi(6,3):=",xi(6,3)$
clear b(3,4),b(3,1),b(3,3)$
write "clear b(3,4),b(3,1),b(3,3)"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "****** Suppose xi(6,1) neq 0."$
write "Then we get deltaprime(6,1)=1 by taking:"$
%deltaprimemodg(6,1):=(b(6,6)*xi(6,1))/b(1,1)$
b(1,1):=(b(6,6)*xi(6,1))$
write "b(1,1):=",b(1,1)$


write "and we get deltaprime(6,4)=0 by taking:"$
%deltaprimemodg(6,4):=(b(6,6)*b(2,2)*(b(1,1)*xi(6,4) - b(1,4)*xi(6,1)))/(b(3,3)*b
%(1,1)**2)$
b(1,4):=b(1,1)*xi(6,4) /xi(6,1)$
write "b(1,4):=",b(1,4)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence if xi(6,2)=xi(6,3)= 0 and xi(6,1) neq 0, we are reduced to :"$
write "(0,0,0,ss,0,ss,epsilon,ss,1,0,0,0}"$
write "where epsilon=xi(5,6)=0,1."$
write "*****************************************************************************"$
write "*****************************************************************************"$
write "****** Suppose xi(6,2) = xi(6,3)=xi(6,1)= 0."$
xi(6,1):=0$
write "xi(6,1):=",xi(6,1)$
clear b(1,1),b(1,4)$
write "clear b(1,1),b(1,4)"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence if xi(6,2)=xi(6,3)= xi(6,1) = 0, we are reduced to :"$
write "if xi(5,6) neq 0 :"$
write "(0,0,0,ss,0,ss,1,ss,0,0,0,epsilon}"$
write "where epsilon=xi(6,4)=0,1."$
write "if xi(5,6) = 0 :"$
write "(0,0,0,ss,0,ss,0,ss,0,0,0,1}"$
write "*****************************************************************************"$
bye$




write "*****************************************************************************"$
write "Suppose xi(2,4) neq 0."$
write "*****************************************************************************"$
%if xi(2,4) neq 0
write "Then we get deltaprime(2,4)=1 by taking:"$
%deltaprimemodg(2,4):=(b(2,2)**2*xi(2,4))/(b(3,3)*b(1,1))$
b(3,3):=(b(2,2)**2*xi(2,4))/(b(1,1))$
write "b(3,3):=",b(3,3)$


write "and we get deltaprime(6,4)=0 by taking:"$
comment
deltaprimemodg(6,4):=(b(6,2)*b(3,3)*b(2,2)*b(1,1)*xi(2,4) + b(6,6)*b(3,1)*b(2,2)
*b(1,4)*xi(6,3) + b(6,6)*b(3,3)*b(2,2)*b(1,1)*xi(6,4) - b(6,6)*b(3,3)*b(2,2)*b(1
,4)*xi(6,1) - b(6,6)*b(3,3)*b(2,4)*b(1,1)*xi(6,2) - b(6,6)*b(3,4)*b(2,2)*b(1,1)*
xi(6,3))/(b(3,3)**2*b(1,1)**2)$
b(6,2):=-( b(6,6)*b(3,1)*b(2,2)
*b(1,4)*xi(6,3) + b(6,6)*b(3,3)*b(2,2)*b(1,1)*xi(6,4) - b(6,6)*b(3,3)*b(2,2)*b(1
,4)*xi(6,1) - b(6,6)*b(3,3)*b(2,4)*b(1,1)*xi(6,2) - b(6,6)*b(3,4)*b(2,2)*b(1,1)*
xi(6,3))/(b(3,3)*b(1,1)*b(2,2)*xi(2,4))$
write "b(6,2):=",b(6,2)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%if xi(6,2) neq 0
write "**** if xi(6,2) neq 0"$
write "we get deltaprime(6,2)=1 by taking:"$
%deltaprimemodg(6,2):=(b(6,6)*xi(6,2))/b(2,2)$
b(2,2):=(b(6,6)*xi(6,2))$
write "b(2,2):=",b(2,2)$

write "and we get deltaprime(6,1)=0 by taking:"$
comment
deltaprimemodg(6,1):=(b(6,6)*( - b(3,1)*xi(6,3) + b(3,3)*xi(6,1) + b(3,4)*xi(6,2
)))/(b(3,3)*b(1,1))$
b(3,4):=-( - b(3,1)*xi(6,3) + b(3,3)*xi(6,1) )/xi(6,2)$
write "b(3,4):=",b(3,4)$




write "and we get deltaprime(6,2)=0 by taking:"$
%deltaprimemodg(6,3):=(b(6,6)*(b(1,1)*xi(6,3) - b(1,4)*xi(6,2)))/(b(3,3)*b(1,1))$
b(1,4):=b(1,1)*xi(6,3)/xi(6,2)$
write "b(1,4):=",b(1,4)$


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%shortformdeltaprimemodadg:={0,0,0,ss,1,ss,b(6,6)*xi(6,2)**2*xi(5,6)*xi(2,4),ss,0,1,0,0}$
write "Hence if xi(2,4) neq 0 and xi(6,2) neq 0, we are reduced to :"$
%shortformdeltaprimemodadg:={0,0,0,ss,1,ss,epsilon,ss,0,1,0,0}$
write "(0,0,0,ss,1,ss,epsilon,ss,0,1,0,0}"$
write "where epsilon=xi(5,6)=0,1."$
write "*****************************************************************************"$
write "Suppose xi(6,2) = 0."$
xi(6,2):=0$
write "xi(6,2):=",xi(6,2)$
clear b(2,2),b(3,4),b(1,4)$
write "clear b(2,2),b(3,4),b(1,4)"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence if xi(2,4) neq 0 and xi(6,2) = 0, we are reduced to :"$
write "*** If xi(6,3) neq 0, "$
write "(0,0,0,ss,1,ss,epsilon,ss,0,0,1,0}"$
write "where epsilon=xi(5,6)=0,1."$

write "*** If xi(6,3) = 0, and if xi(5,6) neq 0 "$
write "(0,0,0,ss,1,ss,1,ss,epsilon,0,0,0}"$
write "where epsilon=xi(6,1)=0,1."$

write "*** If xi(6,3) = 0, and if xi(5,6) = 0 "$
write "(0,0,0,ss,1,ss,0,ss,1,0,0,0}."$
write "*****************************************************************************"$
bye$



write "hence we may suppose :"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
xi(1,3):=1$
xi(1,4):=0$
xi(6,3):=0$
write "xi(1,3):=",xi(1,3)$
write "xi(1,4):=",xi(1,4)$
write "xi(6,3):=",xi(6,3)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
xi(2,4):=0$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
on nat$
write "delta:=",delta$
off nat$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i:=1:6 do for j:=1:6 do <<clear b(i,j)>>$
write "for i:=1:6 do for j:=1:6 do <<clear b(i,j)>>"$
clear phi,psi,rho$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Now we use some fourth kind automorphism."$
%****** Suppose case 2.2 : b(3,2) = 0.$


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


condition22:=chi(3,4)*chi(1,2) - chi(3,2)*chi(1,4)$
off nat$
write "chi:=",chi;
on factor$
write "det(chi):=",det(chi);
write "condition22:=",condition22," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "We take:"$
%b(4,1):=0$
%b(1,4):=0$
%b(4,2):=0$
%b(4,4):=0$  %
%b(2,2):=0$
%b(2,3):=0$

%b(2,1):=0$
%b(2,4):=0$

write "b(4,1):=",b(4,1)$
write "b(1,4):=",b(1,4)$
write "b(4,2):=",b(4,2)$
write "b(4,4):=",b(4,4)$
write "b(2,2):=",b(2,2)$
write "b(2,3):=",b(2,3)$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,chi);
write "condition22:=",condition22," neq 0"$
bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Take:"$
b(3,1):=0$
b(3,2):=0$
b(4,2):=0$
%b(3,4):=0$
b(1,2):=0$
write "b(3,1):=",b(3,1)$
write "b(3,2):=",b(3,2)$
write "b(4,2):=",b(4,2)$
write "b(3,4):=",b(3,4)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Then we get deltaprime(1,2)=1 , deltaprime(1,3)=0, deltaprimemodg(1,4)=0 and"$
write "deltaprime(6,2)=0 by taking:"$

%deltaprimemodg(1,2):=(b(1,1)*xi(1,2))/b(2,2)$
b(2,2):=(b(1,1)*xi(1,2))$
write "b(2,2):=",b(2,2)$

%deltaprimemodg(1,3):=(b(1,1)**2*xi(1,3) + 2*b(1,2)*b(1,1)*xi(1,4) + b(1,2)**2*xi
%(2,4) - 2*b(1,4)*b(1,1)*xi(1,2))/(b(3,3)*b(1,1))$

b(1,4):=(b(1,1)**2*xi(1,3) + 2*b(1,2)*b(1,1)*xi(1,4) + b(1,2)**2*xi
(2,4))/ ( 2*b(1,1)*xi(1,2))$
write "b(1,4):=",b(1,4)$

%deltaprimemodg(1,4):=(b(2,2)*b(1,1)*xi(1,4) + b(2,2)*b(1,2)*xi(2,4) - b(2,4)*b(1
%,1)*xi(1,2))/(b(3,3)*b(1,1))$
b(2,4):=(b(2,2)*b(1,1)*xi(1,4) + b(2,2)*b(1,2)*xi(2,4))/(b(1,1)*xi(1,2))$
write "b(2,4):=",b(2,4)$

%deltaprimemodg(6,2):=(b(6,1)*b(1,1)*xi(1,2) + b(6,6)*b(1,1)*xi(6,2) - b(6,6)*b(1
%,2)*xi(6,1))/(b(2,2)*b(1,1))$

b(6,1):=-( b(6,6)*b(1,1)*xi(6,2) - b(6,6)*b(1
,2)*xi(6,1))/(xi(1,2)*b(1,1))$
write "b(6,1):=",b(6,1)$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Then one gets deltaprimemodg(6,3)=0 by taking:"$
comment
deltaprimemodg(6,3):=(2*b(6,2)*b(1,1)**3*xi(1,4)*xi(1,2) + 2*b(6,2)*b(1,2)*b(1,1
)**2*xi(2,4)*xi(1,2) - 2*b(6,4)*b(1,1)**3*xi(1,2)**2 - 2*b(6,6)*b(1,1)**3*xi(6,2
)*xi(1,3) + 2*b(6,6)*b(1,1)**3*xi(6,3)*xi(1,2) + b(6,6)*b(1,2)*b(1,1)**2*xi(6,1)
*xi(1,3) - 2*b(6,6)*b(1,2)*b(1,1)**2*xi(6,2)*xi(1,4) + 2*b(6,6)*b(1,2)*b(1,1)**2
*xi(6,4)*xi(1,2) - b(6,6)*b(1,2)**3*xi(6,1)*xi(2,4) - 2*b(6,6)*b(1,3)*b(1,1)**2*
xi(6,1)*xi(1,2))/(2*b(3,3)*b(1,1)**3*xi(1,2))$

b(6,4):=(2*b(6,2)*b(1,1)**3*xi(1,4)*xi(1,2) + 2*b(6,2)*b(1,2)*b(1,1
)**2*xi(2,4)*xi(1,2)
%- 2*b(6,4)*b(1,1)**3*xi(1,2)**2
- 2*b(6,6)*b(1,1)**3*xi(6,2
)*xi(1,3) + 2*b(6,6)*b(1,1)**3*xi(6,3)*xi(1,2) + b(6,6)*b(1,2)*b(1,1)**2*xi(6,1)
*xi(1,3) - 2*b(6,6)*b(1,2)*b(1,1)**2*xi(6,2)*xi(1,4) + 2*b(6,6)*b(1,2)*b(1,1)**2
*xi(6,4)*xi(1,2) - b(6,6)*b(1,2)**3*xi(6,1)*xi(2,4) - 2*b(6,6)*b(1,3)*b(1,1)**2*
xi(6,1)*xi(1,2))/(2*b(1,1)**3*xi(1,2)**2)$
write "b(6,4):=",b(6,4)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "hence we may suppose :"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
xi(1,2):=1$
xi(1,3):=0$
xi(1,4):=0$
write "xi(1,2):=",xi(1,2)$
write "xi(1,3):=",xi(1,3)$
write "xi(1,4):=",xi(1,4)$
xi(6,3):=0$
xi(6,2):=0$
write "xi(6,2):=",xi(6,2)$
write "xi(6,3):=",xi(6,3)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "**** Suppose xi(2,4) = 0."$
xi(2,4):=0$
write "xi(2,4):=",xi(2,4)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence we are reduced to shortformdelta:={1,0,0,ss,0,ss,1,ss,epsilon,eta,0,0}"$
write "where epsilon=xi(6,1)=0,1 and eta=xi(6,2)=0,1 in the case xi(5,6) neq 0."$
write "If xi(5,6) = 0."$
write "Hence we are reduced to shortformdelta:={1,0,0,ss,0,ss,0,ss,1,epsilon,0,0}"$
write "where epsilon=xi(6,2)=0,1 in the case xi(6,1) neq 0."$
write "or to shortformdelta:={1,0,0,ss,0,ss,0,ss,0,1,0,0}"$
write "in the case xi(6,1) = 0."$
bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
comment
shortformdeltaprimemodadg:={1,0,0,ss,1,ss,
(b(1,1)**2*xi(5,6)*xi(2,4)*xi(1,2)**2)/b(6,6),ss,(b(6,6)*xi(6,1))/b(1,1),0,0,0}$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence we are reduced to shortformdelta:={1,0,0,ss,1,ss,1,ss,epsilon,0,0,0}"$
write "where epsilon=xi(6,1)=0,1 in the case xi(5,6) neq 0."$
write "If xi(5,6) = 0."$
write "Hence we are reduced to shortformdelta:={1,0,0,ss,1,ss,0,ss,1,0,0,0}"$
bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "hence we may suppose :"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
xi(1,2):=1$
xi(2,4):=1$
xi(1,4):=0$
write "xi(1,2):=",xi(1,2)$
write "xi(1,3):=",xi(1,3)$
write "xi(2,4):=",xi(2,4)$
xi(6,3):=0$
xi(6,2):=0$
xi(6,4):=0$
write "xi(6,3):=",xi(6,3)$
write "xi(6,2):=",xi(6,2)$
write "xi(6,4):=",xi(6,4)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i:=1:6 do for j:=1:6 do <<clear b(i,j)>>$
write "for i:=1:6 do for j:=1:6 do <<clear b(i,j)>>"$
clear phi,psi,rho$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Now we use some fourth kind automorphism."$
%****** Suppose case 2.2 : b(3,2) = 0.$


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


condition22:=chi(3,4)*chi(1,2) - chi(3,2)*chi(1,4)$
off nat$
write "chi:=",chi;
on factor$
write "det(chi):=",det(chi);
write "condition22:=",condition22," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "We take:"$
%b(4,1):=0$
%b(1,4):=0$
%b(4,2):=0$
%b(4,4):=0$  %
b(2,2):=0$
%b(2,3):=0$

b(2,1):=0$
%b(2,4):=0$

write "b(4,1):=",b(4,1)$
write "b(1,4):=",b(1,4)$
write "b(4,2):=",b(4,2)$
write "b(4,4):=",b(4,4)$
write "b(2,2):=",b(2,2)$
write "b(2,3):=",b(2,3)$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,chi);
write "condition22:=",condition22," neq 0"$
bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Take now:"$
b(3,4):=0$
write "b(3,4):=",b(3,4)$

%deltaprimemodg(2,2):=(b(1,1)*xi(2,2) - b(4,2)*xi(2,4))/b(1,1)$
b(4,2):=b(1,1)*xi(2,2)/xi(2,4)$
write "b(4,2):=",b(4,2)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence we may suppose xi(2,2)=0 as well."$
xi(2,2):=0$
write "xi(2,2):=",xi(2,2)$

write "Then we get deltaprimemodg(6,1)=deltaprime(6,2)=0 as well by taking:"$
%deltaprimemodg(6,1):=( - b(6,1)*xi(3,2) + b(6,2)*xi(2,4) - b(6,3)*xi(2,4) - b(6,
%3)*xi(3,2)**2 + b(6,4)*xi(3,2) + b(6,6)*xi(6,1))/b(1,1)$
b(6,2):=-( - b(6,1)*xi(3,2)
%+ b(6,2)*xi(2,4)
- b(6,3)*xi(2,4) - b(6,
3)*xi(3,2)**2 + b(6,4)*xi(3,2) + b(6,6)*xi(6,1))/xi(2,4)$

%deltaprimemodg(6,2):=(b(6,1) + b(6,3)*xi(3,2) - b(6,4) + b(6,6)*xi(6,2))/b(1,1)$
b(6,1):=-( b(6,3)*xi(3,2) - b(6,4) + b(6,6)*xi(6,2))$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence we can suppose xi(6,1)=xi(6,2)=0 as well:"$
xi(6,1):=0$
xi(6,2):=0$
write "xi(6,1):=",xi(6,1)$
write "xi(6,2):=",xi(6,2)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i:=1:6 do for j:=1:6 do <<clear b(i,j)>>$
write "for i:=1:6 do for j:=1:6 do <<clear b(i,j)>>"$
clear phi,psi,rho$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Now we use some fourth kind automorphism."$
%****** Suppose case 2.2 : b(3,2) = 0.$


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


condition22:=chi(3,4)*chi(1,2) - chi(3,2)*chi(1,4)$
off nat$
write "chi:=",chi;
on factor$
write "det(chi):=",det(chi);
write "condition22:=",condition22," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "We take:"$
b(4,1):=0$
b(1,4):=0$
b(4,2):=0$
b(2,2):=0$
b(2,3):=0$

write "b(4,1):=",b(4,1)$
write "b(1,4):=",b(1,4)$
write "b(4,2):=",b(4,2)$
write "b(2,2):=",b(2,2)$
write "b(2,3):=",b(2,3)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
on factor$
%off factor$
DELTAPRIMEMODADG(delta,chi);
write "condition22:=",condition22," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Then we get deltaprimemodg(2,4)=0 as well by taking:"$
%deltaprimemodg(2,4):=( - b(2,1) + b(2,4))**2/(b(4,3)*b(2,1))$
b(2,4) := b(2,1)$
write "b(2,4):=",b(2,4)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
on factor$
%off factor$
DELTAPRIMEMODADG(delta,chi);
write "condition22:=",condition22," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Then we get deltaprimemodg(1,2)=deltaprime(1,3)=0 by taking:"$
comment
deltaprimemodg(1,2):=( - ( - b(4,3)*xi(3,2) + b(4,4))**2*b(1,2))/(b(4,3)**2*b(2,
1))$
comment
deltaprimemodg(1,3):=(( - b(4,3)*xi(3,2) + b(4,4))**2*b(1,2)**2)/(b(4,3)**3*b(2,
1))$
b(4,4):=  b(4,3)*xi(3,2)$
write "b(4,4):=",b(4,4)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
on factor$
%off factor$
DELTAPRIMEMODADG(delta,chi);
write "condition22:=",condition22," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Then we also get deltaprimemodg(6,1)=deltaprime(6,2)=0 by taking:"$
%deltaprimemodg(6,1):=( - b(6,4) + b(6,1) + b(6,3)*xi(3,2))/b(1,2)$
b(6,4) := b(6,1) + b(6,3)*xi(3,2)$
write "b(6,4):=",b(6,4)$

%deltaprimemodg(6,2):=( - ( - b(6,2) + b(6,3))*xi(2,4))/b(2,1)$
b(6,2) := b(6,3)$
write "b(6,2):=",b(6,2)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
on factor$
%off factor$
DELTAPRIMEMODADG(delta,chi);
write "condition22:=",condition22," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence the considered delta with xi(1,2)*xi(1,3)*(x(2,4)*xi(1,3)-xi(1,4)**2)"$
write "NEQ 0 is projectively equivalent to one with x(1,2)=xi(1,3)= 0 and" $
write  "x(2,4)*xi(1,3)-xi(1,4)**2 = 0."$
write "alternatively, we are reduced to the case where:"$
write "xi(1,2)=xi(1,3)=xi(1,4)=xi(2,1)xi(3,2)=0."$
bye$
%off echo,nat$
off echo$
out "rreducparautommodg6_51xCgeneralN4m.r"$
write "rreducparautommodg6_51xCgeneralN4m.r"$
operator b$
%ON REVPRI$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "The generic automorphism phi of C x g_{5,1} as computed by calculautom6_51xC.red :"$
write "They fall into 4 kinds: "$
write "The first  kind (which contains the identity component) is: "$

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


write "The parameters are subject to the supplementary conditions :"$
condition11:=b(2,2)*( b(3,3)*b(1,1) - b(3,1)*b(1,3))$
write condition11,"neq 0"$


write "phi:=",phi;
on factor$
write "det(phi):=",det(phi);
write "condition11:=",condition11," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The generic derivation as computed by geneLplus.tex :
operator xi$

delta:=
mat((xi(1,1),xi(1,2),xi(1,3),xi(1,4),0,0),
(xi(2,1),xi(2,2),xi(1,4),xi(2,4),0,0),
(xi(3,1),xi(3,2),xi(3,3),-xi(2,1),0,0),
(xi(3,2),xi(4,2),-xi(1,2),xi(1,1)-xi(2,2)+xi(3,3),0,0),
(xi(5,1),xi(5,2),xi(5,3),xi(5,4),xi(1,1)+xi(3,3),xi(5,6)),
(xi(6,1),xi(6,2),xi(6,3),xi(6,4),0,xi(6,6)))$

write "generic derivation : delta:=",delta;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%The nonzero adjoint derivations
matrix adx1(6,6)$
adx1:=
sub({xi(1,1)=0,xi(1,2)=0,xi(1,3)=0,xi(1,4)=0,xi(2,1)=0,xi(2,2)=0,xi(2,4)=0,xi(3,1)=0,xi(3,2)=0,xi(3,3)=0,xi(4,2)=0,xi(5,1)=0,xi(5,2)=0,xi(5,3)=1,xi(5,4)=0,xi(5,6)=0,xi(6,1)=0,xi(6,2)=0,xi(6,3)=0,xi(6,4)=0,xi(6,6)=0}, delta)$
matrix adx2(6,6)$
adx2:=
sub({xi(1,1)=0,xi(1,2)=0,xi(1,3)=0,xi(1,4)=0,xi(2,1)=0,xi(2,2)=0,xi(2,4)=0,xi(3,1)=0,xi(3,2)=0,xi(3,3)=0,xi(4,2)=0,xi(5,1)=0,xi(5,2)=0,xi(5,3)=0,xi(5,4)=1,xi(5,6)=0,xi(6,1)=0,xi(6,2)=0,xi(6,3)=0,xi(6,4)=0,xi(6,6)=0}, delta)$
matrix adx3(6,6)$
adx3:=
sub({xi(1,1)=0,xi(1,2)=0,xi(1,3)=0,xi(1,4)=0,xi(2,1)=0,xi(2,2)=0,xi(2,4)=0,xi(3,1)=0,xi(3,2)=0,xi(3,3)=0,xi(4,2)=0,xi(5,1)=-1,xi(5,2)=0,xi(5,3)=0,xi(5,4)=0,xi(5,6)=0,xi(6,1)=0,xi(6,2)=0,xi(6,3)=0,xi(6,4)=0,xi(6,6)=0}, delta)$
matrix adx4(6,6)$
adx4:=
sub({xi(1,1)=0,xi(1,2)=0,xi(1,3)=0,xi(1,4)=0,xi(2,1)=0,xi(2,2)=0,xi(2,4)=0,xi(3,1)=0,xi(3,2)=0,xi(3,3)=0,xi(4,2)=0,xi(5,1)=0,xi(5,2)=-1,xi(5,3)=0,xi(5,4)=0,xi(5,6)=0,xi(6,1)=0,xi(6,2)=0,xi(6,3)=0,xi(6,4)=0,xi(6,6)=0}, delta)$
%matrix adx5(6,6)$
%adx5:=
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
on nat$
write adx1:=adx1$
write adx2:=adx2$
write adx3:=adx3$
write adx4:=adx4$
%write adx5:=adx5$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%bye$
xi(1,1):=0$
xi(2,1):=0$
xi(2,2):=0$
xi(3,1):=0$
xi(3,2):=0$
xi(4,2):=0$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "The generic nilpotent derivation : the eigenvalues are 0"$
xi(3,3):=-xi(1,1)$
write "xi(3,3):=",xi(3,3)$
xi(6,6):=0$
write "xi(6,6):=",xi(6,6)$

write "And the matrix A:="$
mat((xi(1,1),xi(1,2),xi(1,3),xi(1,4)),
(xi(2,1),xi(2,2),xi(1,4),xi(2,4)),
(xi(3,1),xi(3,2),xi(3,3),-xi(2,1)),
(xi(3,2),xi(4,2),-xi(1,2),xi(1,1)-xi(2,2)+xi(3,3)));
write "is nilpotent."$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
M:=mat((xi(1,1),xi(1,2),xi(1,3),xi(1,4)),
(xi(2,1),xi(2,2),xi(1,4),xi(2,4)),
(xi(3,1),xi(3,2),xi(3,3),-xi(2,1)),
(xi(3,2),xi(4,2),-xi(1,2),xi(1,1)-xi(2,2)+xi(3,3)));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

off nat$
off factor$
for j:=1:4 do <<write "Trace(M**",j,")/2:=",Trace(M**j)/2>>;

write "************************************************************************"$
write "*******Suppose xi(1,2) = 0."$
xi(1,2):=0$
write "xi(1,2):=",xi(1,2)$
write "************************************************************************"$

for j:=1:4 do <<write "Trace(M**",j,")/2:=",Trace(M**j)/2>>;
for j:=1:4 do <<write "M**",j,":=",M**j>>;
MM:=M**2$
%M4:=M**4$
for j:=1:4 do for i:=1:4 do <<write "M**2(",i,",",j,"):=",MM(i,j)>>;
%for j:=1:4 do for i:=1:4 do <<write "M**4(",i,",",j,"):=",M4(i,j)>>;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "*****************************************"$

write "M:=",M$
for i:=1:4 do for j:=1:4 do <<write "xi(",i,",",j,"):=",M(i,j)>>;
off nat$
on factor$
for i:=1:4 do for j:=1:4 do <<write "M**2(",i,",",j,"):=",MM(i,j)>>;
for j:=1:4 do <<write "Trace(M**",j,")/2:=",Trace(M**j)/2>>;
for i:=1:4 do for j:=1:4 do <<write "M**2(",i,",",j,"):=",MM(i,j)>>;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear M;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% by subtracting adjoints one then may suppose
xi(5,1):=0$
xi(5,2):=0$
xi(5,3):=0$
xi(5,4):=0$
write "By subtracting adjoints one then may suppose:"$
write "xi(5,1):=0,xi(5,2):=0,xi(5,3):=0,xi(5,4):=0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
on nat$
write "delta:=",delta;
off nat$
write "We denote this delta by the shortform"$
shortformdelta:=
{xi(1,1),xi(1,2),xi(1,3),xi(1,4),SS,xi(2,2),SS,xi(4,2),SS,xi(5,6),SS,xi(6,1),xi(6,2),xi(6,3),xi(6,4)}$
paramindexeslist:=
{{1,1},{1,2},{1,3},{1,4},{2,1},{2,2},{2,4},{3,1},{3,2},{4,1},{4,2},{5,6},{6,1},{6,2},{6,3},{6,4}}$

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

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

IF AUTOM=phi THEN  <<write "With the first kind automorphism one gets">>$
IF AUTOM=psi THEN  <<write "With the second kind automorphism one gets">>$
IF AUTOM=rho THEN  <<write "With the third kind automorphism one gets">>$

write "shortformdeltaprimemodadg:=",shortform(M)$
off factor$
on exp$
for each U in paramindexeslist do <<write "deltaprimemodg(" ,part(U,1), ",", part(U,2), "):=" ,
                  M(part(U,1),part(U,2))>>$
write "det(AUTOM):=",det(AUTOM);
%off factor$
DELTAPRIMEMODADG:=M$
%on nat$
off nat$
write "DELTAPRIMEMODADG:=", M$
off nat$
CLEAR M$
%RETURN DELTAPRIMEMODADG$
END$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Take the following values:"$
b(1,3):=0$
b(1,4):=0$
b(1,2):=0$
b(4,2):=0$
b(3,2):=0$
write "b(1,3):=",b(1,3)$
write "b(1,2):=",b(1,2)$
write "b(1,4):=",b(1,4)$
write "b(3,2):=",b(3,2)$
write "b(4,2):=",b(4,2)$
b(3,1):=0$
%deltaprimemodg(1,3):=(b(1,1)*xi(1,3))/b(3,3)$
b(3,3):=(b(1,1)*xi(1,3))$

%deltaprimemodg(1,4):=(b(2,2)*( - b(3,4)*xi(1,3) + b(3,3)*xi(1,4)))/b(3,3)**2$
b(3,4):= b(3,3)*xi(1,4)/xi(1,3)$

%deltaprimemodg(6,3):=(b(6,6)*xi(6,3) + b(6,2)*xi(1,4) + b(6,1)*xi(1,3))/(b(1,1)*
%xi(1,3))$
b(6,1):=-(b(6,6)*xi(6,3) + b(6,2)*xi(1,4) )/xi(1,3)$


xi(1,3):=1$
xi(1,4):=0$
xi(6,3):=0$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
xi(2,4):=0$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
on nat$
write "delta:=",delta$
off nat$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Now, we utilize a fourth kind automorphism."$
for i:=1:6 do for j:=1:6 do <<clear b(i,j)>>$
clear phi,psi$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%****** Suppose case 2.2 : b(3,2) = 0.$


chi:=
mat((( - ((b(4,4)*b(1,2) - b(4,2)*b(1,4))*b(2,1) - (b(2,4)*b(1,2) - b(2,2)*b(1,4
))*b(4,1)))/(b(4,3)*b(2,1) - b(4,1)*b(2,3)),b(1,2),(b(4,3)*b(2,4)*b(1,2) - b(4,3
)*b(2,2)*b(1,4) + b(4,2)*b(2,3)*b(1,4) - b(4,4)*b(2,3)*b(1,2))/(b(4,3)*b(2,1) -
b(4,1)*b(2,3)),b(1,4),0,0),(b(2,1),b(2,2),b(2,3),b(2,4),0,0),((b(4,2)*b(2,1) - b
(4,1)*b(2,2))/b(1,2),0,( - (b(4,3)*b(2,2) - b(4,2)*b(2,3)))/b(1,2),(b(4,3)*b(2,1
) - b(4,1)*b(2,3))/b(1,2),0,0),(b(4,1),b(4,2),b(4,3),b(4,4),0,0),(b(5,1),b(5,2),

b(5,3),b(5,4),b(4,4)*b(2,2) - b(4,2)*b(2,4) + b(4,3)*b(2,1) - b(4,1)*b(2,3),b(5,
6)),(b(6,1),b(6,2),b(6,3),b(6,4),0,b(6,6)))$


condition22:=(chi(3,4)*chi(1,2) - chi(3,2)*chi(1,4))*chi(1,2)$
off nat$
write "chi:=",chi;
on factor$
write "det(chi):=",det(chi);
write "condition22:=",condition22," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Take:"$
b(4,1):=0$
b(4,2):=0$%
%b(2,3):=0$

b(2,2):=0$

%b(2,4):=0$
%b(1,4):=0$
b(4,4):=0$ %

write "b(4,1):=",b(4,1)$
write "b(1,4):=",b(1,4)$
write "b(2,3):=",b(2,3)$
write "b(2,4):=",b(2,4)$
write "b(2,2):=",b(2,2)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,chi);
write "condition22:=",condition22," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
DELTAPRIMEMODADG(delta,phi);
write "condition11:=",condition11," neq 0"$
bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%deltaprimemodg(6,4):=( - b(6,6)*b(2,4)*xi(6,2) + b(6,6)*b(2,2)*xi(6,4) + b(6,2)*
%b(2,2)*xi(2,4))/b(1,1)**2$
b(6,2):=-( - b(6,6)*b(2,4)*xi(6,2) + b(6,6)*b(2,2)*xi(6,4) )/(b(2,2)*xi(2,4))$
%deltaprimemodg(2,4):=(b(2,2)**2*xi(2,4))/b(1,1)**2$
b(1,1):=b(2,2)*sqrt(xi(2,4))$
%deltaprimemodg(5,6):=(b(2,2)**2*xi(5,6)*xi(2,4))/b(6,6)$
b(6,6):=(b(2,2)**2*xi(5,6)*xi(2,4))$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
DELTAPRIMEMODADG(delta,phi);
write "condition11:=",condition11," neq 0"$
%bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
on nat$
write "delta:=",delta$
off nat$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Now, we utilize a fourth kind automorphism."$
for i:=1:6 do for j:=1:6 do <<clear b(i,j)>>$
clear phi,psi$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%****** Suppose case 2.2 : b(3,2) = 0.$


chi:=
mat((( - ((b(4,4)*b(1,2) - b(4,2)*b(1,4))*b(2,1) - (b(2,4)*b(1,2) - b(2,2)*b(1,4
))*b(4,1)))/(b(4,3)*b(2,1) - b(4,1)*b(2,3)),b(1,2),(b(4,3)*b(2,4)*b(1,2) - b(4,3
)*b(2,2)*b(1,4) + b(4,2)*b(2,3)*b(1,4) - b(4,4)*b(2,3)*b(1,2))/(b(4,3)*b(2,1) -
b(4,1)*b(2,3)),b(1,4),0,0),(b(2,1),b(2,2),b(2,3),b(2,4),0,0),((b(4,2)*b(2,1) - b
(4,1)*b(2,2))/b(1,2),0,( - (b(4,3)*b(2,2) - b(4,2)*b(2,3)))/b(1,2),(b(4,3)*b(2,1
) - b(4,1)*b(2,3))/b(1,2),0,0),(b(4,1),b(4,2),b(4,3),b(4,4),0,0),(b(5,1),b(5,2),

b(5,3),b(5,4),b(4,4)*b(2,2) - b(4,2)*b(2,4) + b(4,3)*b(2,1) - b(4,1)*b(2,3),b(5,
6)),(b(6,1),b(6,2),b(6,3),b(6,4),0,b(6,6)))$


condition22:=(chi(3,4)*chi(1,2) - chi(3,2)*chi(1,4))*chi(1,2)$
off nat$
write "chi:=",chi;
on factor$
write "det(chi):=",det(chi);
write "condition22:=",condition22," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Take:"$
b(4,1):=0$
b(4,2):=0$%
%b(2,3):=0$

b(2,2):=0$

%b(2,4):=0$
%b(1,4):=0$
b(4,4):=0$ %

write "b(4,1):=",b(4,1)$
write "b(1,4):=",b(1,4)$
write "b(2,3):=",b(2,3)$
write "b(2,4):=",b(2,4)$
write "b(2,2):=",b(2,2)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,chi);
write "condition22:=",condition22," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
on nat$
write "delta:=",delta$
off nat$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i:=1:6 do for j:=1:6 do <<clear b(i,j)>>$
clear phi$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "The generic automorphism phi of C x g_{5,1} as computed by calculautom6_51xC.red :"$
write "They fall into 4 kinds: "$
write "The first  kind (which contains the identity component) is: "$

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


write "The parameters are subject to the supplementary conditions :"$
condition11:=b(2,2)*( b(3,3)*b(1,1) - b(3,1)*b(1,3))$
write condition11,"neq 0"$


write "phi:=",phi;
on factor$
write "det(phi):=",det(phi);
write "condition11:=",condition11," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Take the following values:"$
b(1,3):=0$
b(1,4):=0$
b(1,2):=0$
b(4,2):=0$
b(3,2):=0$
write "b(1,3):=",b(1,3)$
write "b(1,2):=",b(1,2)$
write "b(1,4):=",b(1,4)$
write "b(3,2):=",b(3,2)$
write "b(4,2):=",b(4,2)$
b(3,1):=0$
b(6,1):=0$
b(3,3):=b(1,1)$
b(3,4):=0$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
DELTAPRIMEMODADG(delta,phi);
write "condition11:=",condition11," neq 0"$
bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%deltaprimemodg(6,4):=( - b(6,6)*b(2,4)*xi(6,2) + b(6,6)*b(2,2)*xi(6,4) + b(6,2)*
%b(2,2)*xi(2,4))/b(1,1)**2$
b(6,2):=-( - b(6,6)*b(2,4)*xi(6,2) + b(6,6)*b(2,2)*xi(6,4) )/(b(2,2)*xi(2,4))$
%deltaprimemodg(2,4):=(b(2,2)**2*xi(2,4))/b(1,1)**2$
b(1,1):=b(2,2)*sqrt(xi(2,4))$
%deltaprimemodg(5,6):=(b(2,2)**2*xi(5,6)*xi(2,4))/b(6,6)$
b(6,6):=(b(2,2)**2*xi(5,6)*xi(2,4))$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
DELTAPRIMEMODADG(delta,phi);
write "condition11:=",condition11," neq 0"$
bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
on nat$
write "delta:=",delta$
off nat$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Now, we utilize a fourth kind automorphism."$
for i:=1:6 do for j:=1:6 do <<clear b(i,j)>>$
clear phi,psi$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%****** Suppose case 2.2 : b(3,2) = 0.$


chi:=
mat((( - ((b(4,4)*b(1,2) - b(4,2)*b(1,4))*b(2,1) - (b(2,4)*b(1,2) - b(2,2)*b(1,4
))*b(4,1)))/(b(4,3)*b(2,1) - b(4,1)*b(2,3)),b(1,2),(b(4,3)*b(2,4)*b(1,2) - b(4,3
)*b(2,2)*b(1,4) + b(4,2)*b(2,3)*b(1,4) - b(4,4)*b(2,3)*b(1,2))/(b(4,3)*b(2,1) -
b(4,1)*b(2,3)),b(1,4),0,0),(b(2,1),b(2,2),b(2,3),b(2,4),0,0),((b(4,2)*b(2,1) - b
(4,1)*b(2,2))/b(1,2),0,( - (b(4,3)*b(2,2) - b(4,2)*b(2,3)))/b(1,2),(b(4,3)*b(2,1
) - b(4,1)*b(2,3))/b(1,2),0,0),(b(4,1),b(4,2),b(4,3),b(4,4),0,0),(b(5,1),b(5,2),

b(5,3),b(5,4),b(4,4)*b(2,2) - b(4,2)*b(2,4) + b(4,3)*b(2,1) - b(4,1)*b(2,3),b(5,
6)),(b(6,1),b(6,2),b(6,3),b(6,4),0,b(6,6)))$


condition22:=(chi(3,4)*chi(1,2) - chi(3,2)*chi(1,4))*chi(1,2)$
off nat$
write "chi:=",chi;
on factor$
write "det(chi):=",det(chi);
write "condition22:=",condition22," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Take:"$
b(4,1):=0$
b(4,2):=0$%
%b(2,3):=0$

b(2,2):=0$

%b(2,4):=0$
%b(1,4):=0$
b(4,4):=0$ %

write "b(4,1):=",b(4,1)$
write "b(1,4):=",b(1,4)$
write "b(2,3):=",b(2,3)$
write "b(2,4):=",b(2,4)$
write "b(2,2):=",b(2,2)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,chi);
write "condition22:=",condition22," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i:=1:6 do for j:=1:6 do <<clear b(i,j)>>$
write "for i:=1:6 do for j:=1:6 do <<clear b(i,j)>>"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Now we will use second kind automorphisms."$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear phi$
write "The second kind 1.2 is:"$

%**** Case 1.2 : suppose b(2,2) = 0.$


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


%The parameters are subject to the same conditions :$
%delta^(2,4)_(2,4) = delta^(1,3)_(1,3) neq 0$
%and delta^(2,4)_(2,4) + delta^(1,3)_(2,4) neq 0$
%That is :$
% - (b(3,2)*b(1,4) + b(3,1)*b(1,3) - b(3,3)*b(1,1) - b(3,4)*b(1,2)) neq 0$
%and b(3,3)*b(1,1) - b(3,1)*b(1,3) neq 0.$
condition12:=( b(3,3)*b(1,1) - b(3,1)*b(1,3))*b(2,4)$

write "psi:=",psi;
on factor$
write "det(psi):=",det(psi);
write "condition12:=",condition12," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Take :"$
b(3,2):=0$
b(1,2):=0$
b(1,4):=0$
b(4,4):=0$
b(3,4):=0$

b(3,3):=0$

b(1,1):=0$
b(6,1):=0$
write "b(1,1):=",b(1,1)$
write "b(1,2):=",b(1,2)$
write "b(1,4):=",b(1,4)$
write "b(3,2):=",b(3,2)$
write "b(3,3):=",b(3,3)$
write "b(3,4):=",b(3,4)$
write "b(4,4):=",b(4,4)$
write "b(6,1):=",b(6,1)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
DELTAPRIMEMODADG(delta,psi);
write "condition12:=",condition12," neq 0"$
bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%deltaprimemodg(6,4):=(b(6,4)*b(2,4)*xi(4,2))/(b(3,1)*b(1,3))$
b(6,4):=b(3,1)*b(1,3)/(b(2,4)*xi(4,2))$
write "b(6,4):=",b(6,4)$
%det(AUTOM):= - b(6,6)*b(3,1)**3*b(1,3)**3$
%condition12:= - b(3,1)*b(2,4)*b(1,3) neq 0$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
DELTAPRIMEMODADG(delta,psi);
write "condition12:=",condition12," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
DELTAPRIMEMODADG(delta,phi);
write "condition11:=",condition11," neq 0"$
bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Then we get deltaprime(1,3):=1 and deltaprime(1,4):=0 by taking:"$
%deltaprimemodg(1,3):=(b(1,1)*xi(1,3))/b(3,3)$
b(3,3):=(b(1,1)*xi(1,3))$
write "b(3,3):=",b(3,3)$
%deltaprimemodg(1,4):=(b(2,2)*( - b(3,4)*xi(1,3) + b(3,3)*xi(1,4)))/b(3,3)**2$
b(3,4):= b(3,3)*xi(1,4)/xi(1,3)$
write "b(3,4):=",b(3,4)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
DELTAPRIMEMODADG(delta,phi);
write "condition11:=",condition11," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence one may suppose :"$
xi(1,3):=1$
xi(1,4):=0$
write "xi(1,3):=",xi(1,3)$
write "xi(1,4):=",xi(1,4)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
DELTAPRIMEMODADG(delta,phi);
write "condition11:=",condition11," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Then we get deltaprime(1,1):=0 and deltaprime(2,2):=0 by taking:"$
%deltaprimemodg(1,1):=( - b(3,1) + b(1,1)*xi(1,1))/b(1,1)$
b(3,1) := b(1,1)*xi(1,1)$
write "b(3,1):=",b(3,1)$


%deltaprimemodg(2,2):=(b(2,4)*xi(4,2) + b(2,2)*xi(2,2))/b(2,2)$
b(2,4):=-b(2,2)*xi(2,2)/(xi(4,2))$
write "b(2,4):=",b(2,4)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
DELTAPRIMEMODADG(delta,phi);
write "condition11:=",condition11," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence one may suppose :"$
xi(1,1):=0$
xi(2,2):=0$
write "xi(1,1):=",xi(1,1)$
write "xi(2,2):=",xi(2,2)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
DELTAPRIMEMODADG(delta,phi);
write "condition11:=",condition11," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Then we get deltaprime(6,2):=0 and deltaprime(6,3):=0 by taking:"$
%deltaprimemodg(6,2):=(b(6,6)*xi(6,2) + b(6,4)*xi(4,2))/b(2,2)$
b(6,4):=-b(6,6)*xi(6,2) /xi(4,2)$
write "b(6,4):=",b(6,4)$

%deltaprimemodg(6,3):=(b(6,6)*xi(6,3) + b(6,1))/b(1,1)$
b(6,1):=-b(6,6)*xi(6,3)$
write "b(6,1):=",b(6,1)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
DELTAPRIMEMODADG(delta,phi);
write "condition11:=",condition11," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence one may suppose :"$
xi(6,2):=0$
xi(6,3):=0$
write "xi(6,2):=",xi(6,2)$
write "xi(6,3):=",xi(6,3)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
DELTAPRIMEMODADG(delta,phi);
write "condition11:=",condition11," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
comment
shortformdeltaprimemodadg:={0,
1,
0,
ss,
0,
ss,
ss,
(b(1,1)**2*xi(4,2))/b(2,2)**2,
ss,
(b(1,1)**2*xi(5,6))/b(6,6),
ss,
(b(6,6)*xi(6,1))/b(1,1),
0,
0,
(b(6,6)*b(2,2)*xi(6,4))/b(1,1)**2}$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence we are reduced to the case where :"$
on nat$
write "delta:=",delta$
off nat$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for i:=1:6 do for j:=1:6 do <<clear b(i,j)>>$
write "for i:=1:6 do for j:=1:6 do <<clear b(i,j)>>"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Now we will use second kind automorphisms."$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear phi$
write "The second kind 1.2 is:"$

%**** Case 1.2 : suppose b(2,2) = 0.$


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


%The parameters are subject to the same conditions :$
%delta^(2,4)_(2,4) = delta^(1,3)_(1,3) neq 0$
%and delta^(2,4)_(2,4) + delta^(1,3)_(2,4) neq 0$
%That is :$
% - (b(3,2)*b(1,4) + b(3,1)*b(1,3) - b(3,3)*b(1,1) - b(3,4)*b(1,2)) neq 0$
%and b(3,3)*b(1,1) - b(3,1)*b(1,3) neq 0.$
condition12:=( b(3,3)*b(1,1) - b(3,1)*b(1,3))*b(2,4)$

write "psi:=",psi;
on factor$
write "det(psi):=",det(psi);
write "condition12:=",condition12," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Take :"$
b(3,2):=0$
b(1,2):=0$
b(1,4):=0$
b(4,4):=0$
b(3,4):=0$

b(3,3):=0$

b(1,1):=0$
b(6,1):=0$
write "b(1,1):=",b(1,1)$
write "b(1,2):=",b(1,2)$
write "b(1,4):=",b(1,4)$
write "b(3,2):=",b(3,2)$
write "b(3,3):=",b(3,3)$
write "b(3,4):=",b(3,4)$
write "b(4,4):=",b(4,4)$
write "b(6,1):=",b(6,1)$
%deltaprimemodg(6,4):=(b(6,4)*b(2,4)*xi(4,2))/(b(3,1)*b(1,3))$
b(6,4):=b(3,1)*b(1,3)/(b(2,4)*xi(4,2))$
write "b(6,4):=",b(6,4)$
%det(AUTOM):= - b(6,6)*b(3,1)**3*b(1,3)**3$
%condition12:= - b(3,1)*b(2,4)*b(1,3) neq 0$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
DELTAPRIMEMODADG(delta,psi);
write "condition12:=",condition12," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence we are reduced to the case xi(1,2)=xi(1,3)=xi(1,4)=0."$
bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
on nat$
write "delta:=",delta$
off nat$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Now, we utilize a fourth kind automorphism."$
for i:=1:6 do for j:=1:6 do <<clear b(i,j)>>$
clear phi,psi$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%****** Suppose case 2.2 : b(3,2) = 0.$


chi:=
mat((( - ((b(4,4)*b(1,2) - b(4,2)*b(1,4))*b(2,1) - (b(2,4)*b(1,2) - b(2,2)*b(1,4
))*b(4,1)))/(b(4,3)*b(2,1) - b(4,1)*b(2,3)),b(1,2),(b(4,3)*b(2,4)*b(1,2) - b(4,3
)*b(2,2)*b(1,4) + b(4,2)*b(2,3)*b(1,4) - b(4,4)*b(2,3)*b(1,2))/(b(4,3)*b(2,1) -
b(4,1)*b(2,3)),b(1,4),0,0),(b(2,1),b(2,2),b(2,3),b(2,4),0,0),((b(4,2)*b(2,1) - b
(4,1)*b(2,2))/b(1,2),0,( - (b(4,3)*b(2,2) - b(4,2)*b(2,3)))/b(1,2),(b(4,3)*b(2,1
) - b(4,1)*b(2,3))/b(1,2),0,0),(b(4,1),b(4,2),b(4,3),b(4,4),0,0),(b(5,1),b(5,2),

b(5,3),b(5,4),b(4,4)*b(2,2) - b(4,2)*b(2,4) + b(4,3)*b(2,1) - b(4,1)*b(2,3),b(5,
6)),(b(6,1),b(6,2),b(6,3),b(6,4),0,b(6,6)))$


condition22:=(chi(3,4)*chi(1,2) - chi(3,2)*chi(1,4))*chi(1,2)$
off nat$
write "chi:=",chi;
on factor$
write "det(chi):=",det(chi);
write "condition22:=",condition22," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Take:"$
b(4,1):=0$
b(2,3):=0$

b(2,2):=0$

b(2,4):=0$
b(1,4):=0$

write "b(4,1):=",b(4,1)$
write "b(1,4):=",b(1,4)$
write "b(2,3):=",b(2,3)$
write "b(2,4):=",b(2,4)$
write "b(2,2):=",b(2,2)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%on factor$
off factor$
DELTAPRIMEMODADG(delta,chi);
write "condition22:=",condition22," neq 0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%