off echo,nat$
out "rcalculautom6_17.r"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
in "6nilp/6nilp.17"$
DIM:=6$

%for the invertible matrix (b(i,j)) i,j:=1:DIM to realize an isomorphism
%from g to g'
%one has to satisfy the following equations in "thelist":
%equations g-valued

for j:=1:DIM do y(j):= for k:=1:DIM sum b(k,j)*x(k)$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% donnees a priori

%for i:=1:3 do for j:=4:7 do <<b(i,j):=0 , b(j,i):=0>>$

%for i:=4:5 do for j:=6:7 do <<b(i,j):=0 , b(j,i):=0>>$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "we look for an automorphism of g_{6,17}"$
%relations de g_{6,17}

thelist:= {
{{1,2},y(1)*y(2)-  y(3)},
{{1,3},y(1)*y(3)-  y(4)},
{{1,4},y(1)*y(4)-  y(5)},
{{1,5},y(1)*y(5)-  y(6)},
{{1,6},y(1)*y(6)-  0},
{{2,3},y(2)*y(3)-  y(6)},
{{2,4},y(2)*y(4)-  0},
{{2,5},y(2)*y(5)-  0},
{{2,6},y(2)*y(6)-  0},
{{3,4},y(3)*y(4)-  0},
{{3,5},y(3)*y(5)-  0},
{{3,6},y(3)*y(6)-  0},
{{4,5},y(4)*y(5)-  0},
{{4,6},y(4)*y(6)-  0},
{{5,6},y(5)*y(6)-  0}
 }$

%collecting the scalar equations {i,j}|k obtained by projection on the x(k) k:=1:DIM

collect_eq :=
for i:=1:length(thelist) join  for j:=1:DIM
join {{{part(part(thelist,i),1),j} , V(j)*part(part(thelist,i),2)}}$

%COMMENT
write "nombre d'equations",length(collect_eq);
COMMENT
for k:=1:length(collect_eq) do
<<write {part(part(collect_eq,k),1), part(part(collect_eq,k),2)} >>$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "processus de resolution: phase 1"$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%on factor$
write "nombre d'equations",length(collect_eq);
write "collect_eq:=",collect_eq$

%for k:=1:length(collect_eq) do
%<<write {part(part(collect_eq,k),1), part(part(collect_eq,k),2)} >>$

matrix isom(DIM,DIM)$
for i:=1:DIM do for j:=1:DIM do isom(i,j):=b(i,j)$

%write "isom:=",isom$

%write "det(isom):=",det(isom)$

%matrix petitisom(3,3)$
%for i:=1:3 do for j:=1:3 do petitisom(i,j):=b(i,j)$
%on factor$
%write "det(petitisom):=",det(petitisom)$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
PROCEDURE OTEZERO(U)$  %enleve les 0 dans une liste
BEGIN$
LIST U$
RETURN FOR EACH A IN U JOIN IF A NEQ 0 THEN {A} ELSE {}$
END$


PROCEDURE distinct(U)$
BEGIN;INTEGER j;LIST UU$ j:=1;UU:={}$
S: IF U NEQ {} THEN    ZZZ:=PART(u,j)$
IF ZZZ MEMBER UU THEN <<GO TO P>> ELSE UU:= ZZZ. UU $
P: IF j<LENGTH(U) THEN <<j:=j+1,GO TO S>> ELSE <<RETURN REVERSE(UU)>>$
CLEAR ZZZ$
END$

PROCEDURE UNKNOWNSINLIST(U)$
BEGIN$ LIST U$
RETURN  IF U={} THEN U ELSE
        IF PART(PART(SOLVE(U),1),0) = LIST
          THEN FOR EACH A IN PART(SOLVE(U),1) COLLECT LHS A
        ELSE {LHS PART(SOLVE(U),1)} $
END$


PROCEDURE UNKNOWNSINEXPRESSION(U)$
BEGIN$
RETURN  IF NUMBERP U THEN {}  ELSE
        IF PART(PART(SOLVE(U),1),0) = LIST
          THEN FOR EACH A IN PART(SOLVE(U),1) COLLECT LHS A
        ELSE {LHS PART(SOLVE(U),1)} $
END$

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
PROCEDURE SELECTVAR(U)$
%with the b(i,j) as unknowns    %%%%%%%%% i,i from 1 to DIM
BEGIN$
integer i,j$
i:=1$ j:=1$
LI:=UNKNOWNSINEXPRESSION(U)$
S: IF b(i,j) MEMBER LI AND NUMBERP DF(U,b(i,j))
   THEN <<RETURN b(i,j), GO TO F>>
   ELSE
        IF j<DIM THEN <<j:=j+1, GO TO S>>
        ELSE IF i<DIM THEN <<i:=i+1,j:=0, GO TO S>>
             ELSE <<write "pas de selection possible de variable a coefficient independant des inconnues dans ", U, return 0>>$
F :
END$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
procedure calllet(U,V)$
let U=V$


PROCEDURE  resol(L)$
begin  integer k$
k:=1$
S:
  AA:=part(part(L,k),2)$
  If AA=0 then <<go to F>>$
  write "on resout l'equation " , PART(PART(L,k),1)," qui est  maintenant AA:=",AA$
  W:= SELECTVAR(AA)$
  if W=0 then <<go to F>>$
  write  "bonne inconnue W:=",w$
  WW:= RHS(part(solve(AA=0,W),1))$
  write "sa valeur doit etre WW:=",WW$
  calllet(W,WW)$
  F:
if k < length(L) then <<k:=k+1, go to S>>$
     clear AA,W,WW$
END$


resol(COLLECT_EQ)$


 WRITE "Automorphism equations to cancel (Reduce output) : \\", COLLECT_EQ$

% for i:=0:6 do for j:=0:6 do <<write "b(",i,",",j,"):=",b(i,j)>>$
% for i:=1:7 do for j:=1:7 do <<write "isom(",i,",",j,"):=",isom(i,j)>>$

write "resultats finaux"$
on factor$
write "collect_eq:=", collect_eq$
write "isom:=", isom$

write "det(isom):=",det(isom)$
%bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
write "phase2:"$
%{{{2,3},4},(b(2,2)*b(1,1) - b(2,1)*b(1,2))*b(1,2)},
 b(1,2):=0$
%det(isom):=(b(2,2)*b(1,1) - b(2,1)*b(1,2))**5*b(1,1)**6$
%{{{2,3},6}, (b(2,2) - b(1,1)**3)*b(2,2)*b(1,1)},
b(2,2) := b(1,1)**3$
%det(isom):=b(2,2)**5*b(1,1)**11$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

on factor$
%off factor$
collect_eq;
on factor$
write "isom:=",isom$
write "det(isom):=",det(isom)$
on nat$
write "isom:=",isom$
bye$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%