off nat;



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

%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;



%-------- samples of bracets ----------------------------------------

om(1)*xp(i1) * xm(j1)*om(1);


DELTA(I1,J1)*DELTA(1,I1)$

om(2)*xp(i1) * xm(j1)*om(2);


DELTA(I1,J1)*DELTA(2,I1)$


om(2)*xp(i1)*xp(i2) * xm(j1)*xm(j2)*om(2);


DELTA(2,I1)*( - K(I1,I2)*DELTA(I1,J2)*DELTA(I2,J1) + DELTA(I1,J1)*
DELTA(I2,J2)*DELTA(2,I2) + DELTA(I1,J2)*DELTA(I2,J1)*
DELTA(2,I2))$

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


2*DELTA(2,2)**3*(DELTA(2,2) - 1)$


%om(2)*xp(i1)*xp(i2)*xp(i3)*xp(i4)*xp(i5)*xp(i6)
%           *xm(j1)*xm(j2)*xm(j3)*xm(j4)*xm(j5)*xm(j6)*om(2);


shut bbrgen1;