%off echo,nat$
off echo$
out "rreducparautommodg6_54xCcase2N2.r"$
operator b$
ON REVPRI$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "The generic automorphism phi of C x g_{5,4} as computed by calculautom6_54xC.red :"$

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


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

delta:=
mat((xi(1,1),xi(1,2),0,0,0,0),
(xi(2,1),xi(2,2),0,0,0,0),
(xi(3,1),xi(3,2),xi(1,1)+xi(2,2),0,0,0),
(xi(4,1),xi(4,2),xi(3,2),2*xi(1,1)+xi(2,2),xi(1,2),xi(4,6)),
(xi(5,1),xi(5,2),- xi(3,1),xi(2,1),xi(1,1)+2*xi(2,2),xi(5,6)),
(xi(6,1),xi(6,2),0,0,0,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(2,1)=0,xi(2,2)=0,xi(3,1)=0,xi(3,2)=1,xi(4,1)=0,xi(4,2)=0,xi(4,6)=0,xi(5,1)=0,xi(5,2)=0,xi(5,6)=0,xi(6,1)=0,xi(6,2)=0,xi(6,6)=0}, delta)$
matrix adx2(6,6)$
adx2:=
sub({xi(1,1)=0,xi(1,2)=0,xi(2,1)=0,xi(2,2)=0,xi(3,1)=-1,xi(3,2)=0,xi(4,1)=0,xi(4,2)=0,xi(4,6)=0,xi(5,1)=0,xi(5,2)=0,xi(5,6)=0,xi(6,1)=0,xi(6,2)=0,xi(6,6)=0}, delta)$
matrix adx3(6,6)$
adx3:=
sub({xi(1,1)=0,xi(1,2)=0,xi(2,1)=0,xi(2,2)=0,xi(3,1)=0,xi(3,2)=0,xi(4,1)=-1,xi(4,2)=0,xi(4,6)=0,xi(5,1)=0,xi(5,2)=-1,xi(5,6)=0,xi(6,1)=0,xi(6,2)=0,xi(6,6)=0}, delta)$
%matrix adx4(6,6)$
%adx4:=
%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(6,6):=0$
write "xi(6,6):=",xi(6,6)$
write "And the matrix A:=(xi(1,1),xi(1,2)),(xi(2,1),xi(2,2)) is nilpotent"$
write "We hence get 2 cases acoording to whether A neq 0 or A=0."$
write "We consider here the case 2 where A = 0."$
xi(1,1):=0$
xi(1,2):=0$
xi(2,1):=0$
xi(2,2):=0$
write "xi(1,1):=0,xi(1,2):=1,xi(2,1):=0,xi(2,2):=0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% by subtracting adjoints one then may suppose
xi(3,1):=0$
xi(3,2):=0$
xi(4,1):=0$
write "by subtracting adjoints one then may suppose:"$
write "xi(3,1):=0,xi(3,2):=0,xi(4,1):=0"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "delta:=",delta;
write "We denote this delta by the shortform"$
shortformdelta:=
{xi(4,2),xi(4,6),SS,xi(5,1),xi(5,2),xi(5,6),SS,xi(6,1),xi(6,2)}$
paramindexeslist:=
{{4,2},{4,6},{5,1},{5,2},{5,6},{6,1},{6,2}}$

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

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

IF AUTOM=phi THEN  <<write "With the first kind automorphism one gets">>$
IF AUTOM=psi THEN  <<write "With the second 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))>>$
write "det(AUTOM):=",det(AUTOM);
DELTAPRIMEMODADG:=M$
on nat$
write "DELTAPRIMEMODADG:=", M$
off nat$
CLEAR M$
%RETURN DELTAPRIMEMODADG$
END$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "*************************** SUBCASE 2 : ***************************************"$
write "************ Suppose xi(6,1) and xi(6,2)  simultaneously zero.**************"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
xi(6,1):=0$
write "xi(6,1):=",xi(6,1)$
xi(6,2):=0$
write "xi(6,2):=",xi(6,2)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
on factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "************************ SUBSUBCASE 2.1 : ************************************"$
write "************ Suppose xi(4,6) and xi(5,6)  not simultaneously zero.**************"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Then one may suppose  xi(4,6)=1 and xi(5,6)=0."$
write "In fact there exists then a bijective linear map of C^2 to C^2 sending"$
write "the nonzero vector (xi(4,6),xi(5,6)) on the vector (1,0)."$
write "If we take moreover b(6,6) equal to the determinant of that linear map, we get"$
write "deltaprime(4,6):=1, deltaprime(5,6):=0."$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
xi(4,6):=1$
write "xi(4,6):=",xi(4,6)$
xi(5,6):=0$
write "xi(5,6):=",xi(5,6)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
on  factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Then to keep deltaprime(4,6)=k and deltaprime(5,6)=0 one has to take:"$
%deltaprimemodg(4,6):=(b(1,1)*( - b(2,1)*b(1,2) + b(2,2)*b(1,1)))/b(6,6)$

%deltaprimemodg(5,6):=(b(2,1)*( - b(2,1)*b(1,2) + b(2,2)*b(1,1)))/b(6,6)$
b(2,1):=0$
b(2,2):=k*b(6,6)/b(1,1)**2$
write "b(2,1):=",b(2,1)$
write "b(2,2):=",b(2,2)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Then one gets deltaprime(4,2)=0 by taking :"$
comment
deltaprimemodg(4,2):=(b(6,1)*b(1,2)*b(1,1) - b(6,2)*b(1,1)**2 + b(6,6)*b(1,1)**2
*xi(4,2) + b(6,6)*b(1,2)*b(1,1)*xi(5,2) - b(6,6)*b(1,2)**2*xi(5,1))/b(6,6)$

b(6,2):=(b(6,1)*b(1,2)*b(1,1)                 + b(6,6)*b(1,1)**2
*xi(4,2) + b(6,6)*b(1,2)*b(1,1)*xi(5,2) - b(6,6)*b(1,2)**2*xi(5,1))/b(1,1)**2$
write "b(6,2):=",b(6,2)$


write "and one gets deltaprime(5,2)=0 by taking :"$
comment
deltaprimemodg(5,2):=(k*(b(6,1)*b(1,1) + b(6,6)*b(1,1)*xi(5,2) - 2*b(6,6)*b(1,2)
*xi(5,1)))/b(1,1)**2$

b(6,1):=-(             b(6,6)*b(1,1)*xi(5,2) - 2*b(6,6)*b(1,2)
*xi(5,1))/b(1,1)$
write "b(6,1):=",b(6,1)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
comment
shortformdeltaprimemodadg:={0,
k,
ss,
(b(6,6)**2*xi(5,1)*k**2)/b(1,1)**4,
0,
0,
ss,
0,
0}$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence, we are reduced in the subsubcase 2.1. under consideration to:"$
write "shortformdeltaprime ={0,1,SS,epsilon,0,0,SS,0,0}"$
write "where epsilon=xi(5,1) =0,1."$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "************************ SUBSUBCASE 2.2 : ************************************"$
write "************ Suppose xi(4,6) and xi(5,6)  simultaneously zero.**************"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
xi(4,6):=0$
write "xi(4,6):=",xi(4,6)$
xi(5,6):=0$
write "xi(5,6):=",xi(5,6)$
clear b(6,1),b(6,2),b(2,1),b(2,2)$
write "clear b(6,1),b(6,2),b(2,1),b(2,2)"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "*** Suppose now  xi(4,2) NEQ 0."$
write "Then one may suppose  xi(4,2) =1 :"$
xi(4,2):=1$
write "xi(4,2):=",xi(4,2)$
write "Then to keep deltaprime(4,2)=k one  takes:"$
%deltaprimemodg(4,2):=b(1,1)**2*xi(4,2) + b(1,2)*b(1,1)*xi(5,2) - b(1,2)**2*xi(5,1)$
b(1,1):=sqrt(k)$
b(1,2):=0$
write "b(1,1):=",b(1,1)$
write "b(1,2):=",b(1,2)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Then one gets deltaprime(5,2)=0 by taking :"$
%deltaprimemodg(5,2):=(k*(2*b(2,1) + b(2,2)*xi(5,2)))/sqrt(k)$
b(2,1):=- b(2,2)*xi(5,2)/2$
write "b(2,1):=",b(2,1)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
comment
shortformdeltaprimemodadg:={k,
0,
ss,
(b(2,2)**2*(4*xi(5,1) + xi(5,2)**2))/4,
0,
0,
ss,
0,
0}$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence, we are reduced in the subsubcase 2.2. and if xi(4,2) neq 0 to:"$
write "shortformdeltaprime ={1,0,SS,epsilon,0,0,SS,0,0}."$
write "where epsilon=xi(5,1) =0,1."$
write "However, recall that we dismiss all direct products by Cx_7."$
write "Hence we discard the cases in which xi(4,6)=xi(5,6)=xi(6,1)=xi(6,2)=0."$
write "The foregoing  cases for xi(4,2) neq 0 are thus to be dismissed."$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "*** We suppose now  xi(4,2) = 0."$
xi(4,2):=0$
write "xi(4,2):=",xi(4,2)$
clear b(1,1),b(1,2),b(2,1)$
write "clear b(1,1),b(1,2),b(2,1)"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Then one keeps deltaprime(4,2)=0 by taking :"$
%deltaprimemodg(4,2):=b(1,2)*(b(1,1)*xi(5,2) - b(1,2)*xi(5,1))$
b(1,2):=0$
write "b(1,2):=",b(1,2)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Then if xi(5,2) neq 0, one may suppose xi(5,2):=1."$
xi(5,2):=1$
write "xi(5,2):=",xi(5,2)$
write "Then one keeps deltaprime(5,2)=k and we gets deltaprime(5,1):=0 by taking :"$
%deltaprimemodg(5,1):=b(2,2)*( - b(2,1)*xi(5,2) + b(2,2)*xi(5,1))$
b(2,1):=- b(2,2)*xi(5,1)/xi(5,2)$
write "b(2,1):=",b(2,1)$

%deltaprimemodg(5,2):=b(2,2)*b(1,1)*xi(5,2)$
b(2,2):=k/b(1,1)$
write "b(2,2):=",b(2,2)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
comment
shortformdeltaprimemodadg:={0,
0,
ss,
(2*xi(5,1)*k**2)/b(1,1)**2,
k,
0,
ss,
0,
0}$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence, we are reduced in the subsubcase 2.2. and if xi(4,2)= 0 and xi(5,2) neq 0 to:"$
write "shortformdeltaprime ={0,0,SS,epsilon,1,0,SS,0,0}."$
write "where epsilon=xi(5,1) =0,1."$
write "However, recall that we dismiss all direct products by Cx_7."$
write "Hence we discard the cases in which xi(4,6)=xi(5,6)=xi(6,1)=xi(6,2)=0."$
write "The foregoing  cases for xi(5,2) neq 0 are thus to be dismissed."$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Finally, if xi(5,2) = 0, one has :"$
xi(5,2):=0$
write "xi(5,2):=",xi(5,2)$
clear b(2,1),b(2,2)$
write "clear b(2,1),b(2,2)"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Then as we suppose delta neq 0 , we have xi(5,1) neq 0, hence we may suppose "$
xi(5,1):=1$
write "xi(5,1):=",xi(5,1)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
off factor$
DELTAPRIMEMODADG(delta,phi);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "Hence, we are reduced in the subsubcase 2.2. and if xi(4,2)= xi(5,2) = 0 to:"$
write "shortformdeltaprime ={0,0,SS,1,0,0,SS,0,0}."$
write "However, recall that we dismiss all direct products by Cx_7."$
write "Hence we discard the cases in which xi(4,6)=xi(5,6)=xi(6,1)=xi(6,2)=0."$
write "The foregoing  case is thus to be dismissed."$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


bye$