%off nat;

procedure delta(ii,jj);begin if ii eq jj then return 1 else return 0; end;


DELTA


%k:=mat((2,-1),(-1,2));
%k:=mat((2,-2),(-1,2));
k:=mat((2,-1),(-2,2));


     [2   -1]
K := [      ]
     [-2  2 ]


%k(1,1):=2;
%k(2,2):=2;
noncom om;


noncom xp;


noncom xm;


noncom h;




for all ii,jj let xp(ii)*om(jj) = 0;


*** XP declared operator 

*** OM declared operator 


%-------- commutation rules ----------------------------------------
for all ii,jj let xp(ii)*xm(jj) = xm(jj)*xp(ii) + delta(ii,jj)*h(ii);


*** XM declared operator 

for all ii,jj let  xp(jj)*h(ii) = h(ii)*xp(jj) - k(jj,ii)*xp(jj);


*** H declared operator 

for all ii,jj let  h(ii)*xm(jj) = xm(jj)*h(ii) - k(jj,ii)*xm(jj);



%-------- highest vector rules ----------------------------------------

for all ii,jj let xp(ii)*om(jj) = 0;


for all ii,jj let om(jj)*xm(ii) = 0;



for all ii,jj let h(ii)*om(jj) = delta(jj,ii)*om(jj);


for all ii let om(ii)*om(ii) = 1;





LP:=AP1*xp(1) + AP2*xp(2);


LP := XP(2)*AP2 + XP(1)*AP1

LM:=AM1*xm(1) + AM2*xm(2);


LM := XM(2)*AM2 + XM(1)*AM1



INVMP:=1 - LP + LP**2;


              2    2                                          2    2
INVMP := XP(2) *AP2  + XP(2)*XP(1)*AP1*AP2 - XP(2)*AP2 + XP(1) *AP1

          + XP(1)*XP(2)*AP1*AP2 - XP(1)*AP1 + 1

MM:=1 + LM + LM**2;


           2    2                                          2    2
MM := XM(2) *AM2  + XM(2)*XM(1)*AM1*AM2 + XM(2)*AM2 + XM(1) *AM1

       + XM(1)*XM(2)*AM1*AM2 + XM(1)*AM1 + 1



GG1:=OM(1)*INVMP*MM*OM(1);


GG1 := AP1*AP2*AM1*AM2 - AP1*AM1 + 1

GG2:=OM(2)*INVMP*MM*OM(2);


GG2 := 2*AP1*AP2*AM1*AM2 - AP2*AM2 + 1





xm(kk)*xm(ll);


XM(KK)*XM(LL)

xp(ii)*xp(jj)*xm(kk)*xm(ll)*om(pp);


0


om(pp)*xp(ii)*xp(jj)*xm(kk)*xm(ll)*om(pp);


0


om(pp)*xp(ii)*xm(kk)*xm(ll)*om(pp);


0


om(pp)*xp(rr)*xp(ii)*xp(jj)*xm(kk)*xm(ll)*om(pp);


0



om(1)*xp(1)*xm(1)*om(1);


1

om(1)*xp(2)*xm(2)*om(1);


0


%------------------------------------------------
for ii:=1:2 do
for jj:=1:2 do 
<< R:=om(1)*xp(ii)*xm(jj)*om(1);
IF R NEQ 0 THEN write(ii,",",jj,"r:=",R); >>;


1,1r:=1


for ii:=1:2 do
for jj:=1:2 do 
<< R:=om(2)*xp(ii)*xm(jj)*om(2);
IF R NEQ 0 THEN write(ii,",",jj,"r:=",R); >>;


2,2r:=1


for ii:=1:2 do
for jj:=1:2 do
for kk:=1:2 do
for ll:=1:2 do 
<< R:=om(1)*xp(ii)*xp(jj)*xm(kk)*xm(ll)*om(1);
IF R NEQ 0 THEN write(ii,",",jj,",",kk,",",ll,"r:=",R); >>;


1,2,2,1r:=1



for ii:=1:2 do
for jj:=1:2 do
for kk:=1:2 do
for ll:=1:2 do 
<< R:=om(2)*xp(ii)*xp(jj)*xm(kk)*xm(ll)*om(2);
IF R NEQ 0 THEN write(ii,",",jj,",",kk,",",ll,"r:=",R); >>;


2,1,1,2r:=2


for i1:=1:2 do
for i2:=1:2 do
for i3:=1:2 do
for j1:=1:2 do 
for j2:=1:2 do
for j3:=1:2 do 
<< R:=om(1)*xp(i1)*xp(i2)*xp(i3)*xm(j1)*xm(j2)*xm(j3)*om(1);
IF R NEQ 0 THEN write(i1,i2,i3,j1,j2,j3," r:= ",R); >>;


121121 r:= 1


for i1:=1:2 do
for i2:=1:2 do
for i3:=1:2 do
for j1:=1:2 do 
for j2:=1:2 do
for j3:=1:2 do 
<< R:=om(2)*xp(i1)*xp(i2)*xp(i3)*xm(j1)*xm(j2)*xm(j3)*om(2);
IF R NEQ 0 THEN write(i1,i2,i3,j1,j2,j3," r:= ",R); >>;


211112 r:= 4


for i1:=1:2 do
for i2:=1:2 do
for i3:=1:2 do
for i4:=1:2 do 
for j1:=1:2 do 
for j2:=1:2 do
for j3:=1:2 do 
for j4:=1:2 do 

<< R:=om(1)*xp(i1)*xp(i2)*xp(i3)*xp(i4)
           *xm(j1)*xm(j2)*xm(j3)*xm(j4)*om(1);

IF R NEQ 0 THEN write(i1,i2,i3,i4,j1,j2,j3,j4," r:= ",R); >>;



for i1:=1:2 do
for i2:=1:2 do
for i3:=1:2 do
for i4:=1:2 do 
for j1:=1:2 do 
for j2:=1:2 do
for j3:=1:2 do 
for j4:=1:2 do 

<< R:=om(2)*xp(i1)*xp(i2)*xp(i3)*xp(i4)*
            xm(j1)*xm(j2)*xm(j3)*xm(j4)*om(2);

IF R NEQ 0 THEN write(i1,i2,i3,i4,j1,j2,j3,j4," r:= ",R); >>;


21122112 r:= 4


for i1:=1:2 do
for i2:=1:2 do
for i3:=1:2 do
for i4:=1:2 do 
for i5:=1:2 do 
for j1:=1:2 do 
for j2:=1:2 do
for j3:=1:2 do 
for j4:=1:2 do 
for j5:=1:2 do 

<< R:=om(1)*xp(i1)*xp(i2)*xp(i3)*xp(i4)*xp(i5)
           *xm(j1)*xm(j2)*xm(j3)*xm(j4)*xm(j5)*om(1);

IF R NEQ 0 THEN write(i1,i2,i3,i4,i5,j1,j2,j3,j4,j5," r:= ",R); >>;



for i1:=1:2 do
for i2:=1:2 do
for i3:=1:2 do
for i4:=1:2 do 
for i5:=1:2 do 
for j1:=1:2 do 
for j2:=1:2 do
for j3:=1:2 do 
for j4:=1:2 do 
for j5:=1:2 do 

<< R:=om(2)*xp(i1)*xp(i2)*xp(i3)*xp(i4)*xp(i5)
           *xm(j1)*xm(j2)*xm(j3)*xm(j4)*xm(j5)*om(2);

IF R NEQ 0 THEN write(i1,i2,i3,i4,i5,j1,j2,j3,j4,j5," r:= ",R); >>;



shut bbr2;