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));
k(1,1):=2;


K(1,1) := 2$

k(2,2):=2;


K(2,2) := 2$

noncom om;


noncom xp;


noncom xm;


noncom h;




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



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


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


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;


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

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


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



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


GG1 :=  - K(1,2)*AP1*AP2*AM1*AM2 - AP1*AM1 + 1$

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


GG2 :=  - K(2,1)*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:= - K(1,2)$



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:= - K(2,1)$


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(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:= K(1,2)*(K(2,1) + 1)$

122221 r:= 2*K(1,2)*(K(1,2) + 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:= 2*K(2,1)*(K(2,1) + 1)$

212212 r:= K(2,1)*(K(1,2) + 1)$


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); >>;


12111121 r:= 2*K(1,2)*( - K(2,1)**2 - 3*K(2,1) - 2)$

12121221 r:=  - 2*K(1,2)*(K(2,1)*K(1,2) + K(2,1) + K(1,2) + 1)$

12122121 r:=  - 2*K(1,2)*(K(2,1)*K(1,2) + K(2,1) + K(1,2) + 1)$

12211221 r:= 2*K(1,2)*( - 2*K(2,1)*K(1,2) - 2*K(2,1) - K(1,2) - 1)$

12212121 r:=  - 2*K(1,2)*(K(2,1)*K(1,2) + K(2,1) + K(1,2) + 1)$

12222221 r:= 6*K(1,2)*( - K(1,2)**2 - 3*K(1,2) - 2)$


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); >>;


21111112 r:= 6*K(2,1)*( - K(2,1)**2 - 3*K(2,1) - 2)$

21121212 r:=  - 2*K(2,1)*(K(2,1)*K(1,2) + K(2,1) + K(1,2) + 1)$

21122112 r:= 2*K(2,1)*( - 2*K(2,1)*K(1,2) - K(2,1) - 2*K(1,2) - 1)$

21211212 r:=  - 2*K(2,1)*(K(2,1)*K(1,2) + K(2,1) + K(1,2) + 1)$

21212112 r:=  - 2*K(2,1)*(K(2,1)*K(1,2) + K(2,1) + K(1,2) + 1)$

21222212 r:= 2*K(2,1)*( - K(1,2)**2 - 3*K(1,2) - 2)$


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); >>;


1211111121 r:= 6*K(1,2)*(K(2,1)**3 + 6*K(2,1)**2 + 11*K(2,1) + 6)$

1211211221 r:= 4*K(1,2)*(K(2,1)**2*K(1,2) + K(2,1)**2 + 3*K(2,1)*K(1,
2) + 3*K(2,1) + 2*K(1,2) + 2)$

1211212121 r:= 4*K(1,2)*(K(2,1)**2*K(1,2) + K(2,1)**2 + 3*K(2,1)*K(1,
2) + 3*K(2,1) + 2*K(1,2) + 2)$

1211221121 r:= 2*K(1,2)*(3*K(2,1)**2*K(1,2) + 2*K(2,1)**2 + 9*K(2,1)*
K(1,2) + 6*K(2,1) + 6*K(1,2) + 4)$

1212111221 r:= 8*K(1,2)*(K(2,1)**2*K(1,2) + K(2,1)**2 + 2*K(2,1)*K(1,
2) + 2*K(2,1) + K(1,2) + 1)$

1212112121 r:= 2*K(1,2)*(3*K(2,1)**2*K(1,2) + 3*K(2,1)**2 + 7*K(2,1)*
K(1,2) + 7*K(2,1) + 4*K(1,2) + 4)$

1212121121 r:= 4*K(1,2)*(K(2,1)**2*K(1,2) + K(2,1)**2 + 3*K(2,1)*K(1,
2) + 3*K(2,1) + 2*K(1,2) + 2)$

1212212221 r:= 6*K(1,2)*(K(2,1)*K(1,2)**2 + 3*K(2,1)*K(1,2) + 2*K(2,1
) + K(1,2)**2 + 3*K(1,2) + 2)$

1212221221 r:= 4*K(1,2)*(2*K(2,1)*K(1,2)**2 + 5*K(2,1)*K(1,2) + 3*K(2
,1) + 2*K(1,2)**2 + 5*K(1,2) + 3)$

1212222121 r:= 4*K(1,2)*(2*K(2,1)*K(1,2)**2 + 5*K(2,1)*K(1,2) + 3*K(2
,1) + 2*K(1,2)**2 + 5*K(1,2) + 3)$

1221111221 r:= 8*K(1,2)*(2*K(2,1)**2*K(1,2) + 2*K(2,1)**2 + 3*K(2,1)*
K(1,2) + 3*K(2,1) + K(1,2) + 1)$

1221112121 r:= 8*K(1,2)*(K(2,1)**2*K(1,2) + K(2,1)**2 + 2*K(2,1)*K(1,
2) + 2*K(2,1) + K(1,2) + 1)$

1221121121 r:= 4*K(1,2)*(K(2,1)**2*K(1,2) + K(2,1)**2 + 3*K(2,1)*K(1,
2) + 3*K(2,1) + 2*K(1,2) + 2)$

1221212221 r:= 6*K(1,2)*(2*K(2,1)*K(1,2)**2 + 6*K(2,1)*K(1,2) + 4*K(2
,1) + K(1,2)**2 + 3*K(1,2) + 2)$

1221221221 r:= 4*K(1,2)*(3*K(2,1)*K(1,2)**2 + 8*K(2,1)*K(1,2) + 5*K(2
,1) + 2*K(1,2)**2 + 5*K(1,2) + 3)$

1221222121 r:= 4*K(1,2)*(2*K(2,1)*K(1,2)**2 + 5*K(2,1)*K(1,2) + 3*K(2
,1) + 2*K(1,2)**2 + 5*K(1,2) + 3)$

1222112221 r:= 6*K(1,2)*(3*K(2,1)*K(1,2)**2 + 9*K(2,1)*K(1,2) + 6*K(2
,1) + K(1,2)**2 + 3*K(1,2) + 2)$

1222121221 r:= 6*K(1,2)*(2*K(2,1)*K(1,2)**2 + 6*K(2,1)*K(1,2) + 4*K(2
,1) + K(1,2)**2 + 3*K(1,2) + 2)$

1222122121 r:= 6*K(1,2)*(K(2,1)*K(1,2)**2 + 3*K(2,1)*K(1,2) + 2*K(2,1
) + K(1,2)**2 + 3*K(1,2) + 2)$

1222222221 r:= 24*K(1,2)*(K(1,2)**3 + 6*K(1,2)**2 + 11*K(1,2) + 6)$


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); >>;


2111111112 r:= 24*K(2,1)*(K(2,1)**3 + 6*K(2,1)**2 + 11*K(2,1) + 6)$

2111211212 r:= 6*K(2,1)*(K(2,1)**2*K(1,2) + K(2,1)**2 + 3*K(2,1)*K(1,
2) + 3*K(2,1) + 2*K(1,2) + 2)$

2111212112 r:= 6*K(2,1)*(2*K(2,1)**2*K(1,2) + K(2,1)**2 + 6*K(2,1)*K(
1,2) + 3*K(2,1) + 4*K(1,2) + 2)$

2111221112 r:= 6*K(2,1)*(3*K(2,1)**2*K(1,2) + K(2,1)**2 + 9*K(2,1)*K(
1,2) + 3*K(2,1) + 6*K(1,2) + 2)$

2112111212 r:= 4*K(2,1)*(2*K(2,1)**2*K(1,2) + 2*K(2,1)**2 + 5*K(2,1)*
K(1,2) + 5*K(2,1) + 3*K(1,2) + 3)$

2112112112 r:= 4*K(2,1)*(3*K(2,1)**2*K(1,2) + 2*K(2,1)**2 + 8*K(2,1)*
K(1,2) + 5*K(2,1) + 5*K(1,2) + 3)$

2112121112 r:= 6*K(2,1)*(2*K(2,1)**2*K(1,2) + K(2,1)**2 + 6*K(2,1)*K(
1,2) + 3*K(2,1) + 4*K(1,2) + 2)$

2112212212 r:= 4*K(2,1)*(K(2,1)*K(1,2)**2 + 3*K(2,1)*K(1,2) + 2*K(2,1
) + K(1,2)**2 + 3*K(1,2) + 2)$

2112221212 r:= 8*K(2,1)*(K(2,1)*K(1,2)**2 + 2*K(2,1)*K(1,2) + K(2,1) 
+ K(1,2)**2 + 2*K(1,2) + 1)$

2112222112 r:= 8*K(2,1)*(2*K(2,1)*K(1,2)**2 + 3*K(2,1)*K(1,2) + K(2,1
) + 2*K(1,2)**2 + 3*K(1,2) + 1)$

2121111212 r:= 4*K(2,1)*(2*K(2,1)**2*K(1,2) + 2*K(2,1)**2 + 5*K(2,1)*
K(1,2) + 5*K(2,1) + 3*K(1,2) + 3)$

2121112112 r:= 4*K(2,1)*(2*K(2,1)**2*K(1,2) + 2*K(2,1)**2 + 5*K(2,1)*
K(1,2) + 5*K(2,1) + 3*K(1,2) + 3)$

2121121112 r:= 6*K(2,1)*(K(2,1)**2*K(1,2) + K(2,1)**2 + 3*K(2,1)*K(1,
2) + 3*K(2,1) + 2*K(1,2) + 2)$

2121212212 r:= 4*K(2,1)*(K(2,1)*K(1,2)**2 + 3*K(2,1)*K(1,2) + 2*K(2,1
) + K(1,2)**2 + 3*K(1,2) + 2)$

2121221212 r:= 2*K(2,1)*(3*K(2,1)*K(1,2)**2 + 7*K(2,1)*K(1,2) + 4*K(2
,1) + 3*K(1,2)**2 + 7*K(1,2) + 4)$

2121222112 r:= 8*K(2,1)*(K(2,1)*K(1,2)**2 + 2*K(2,1)*K(1,2) + K(2,1) 
+ K(1,2)**2 + 2*K(1,2) + 1)$

2122112212 r:= 2*K(2,1)*(3*K(2,1)*K(1,2)**2 + 9*K(2,1)*K(1,2) + 6*K(2
,1) + 2*K(1,2)**2 + 6*K(1,2) + 4)$

2122121212 r:= 4*K(2,1)*(K(2,1)*K(1,2)**2 + 3*K(2,1)*K(1,2) + 2*K(2,1
) + K(1,2)**2 + 3*K(1,2) + 2)$

2122122112 r:= 4*K(2,1)*(K(2,1)*K(1,2)**2 + 3*K(2,1)*K(1,2) + 2*K(2,1
) + K(1,2)**2 + 3*K(1,2) + 2)$

2122222212 r:= 6*K(2,1)*(K(1,2)**3 + 6*K(1,2)**2 + 11*K(1,2) + 6)$


shut bbr3;