REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ...
nc_setup({k,n,NN,KK},{NN*n-n*NN=NN,KK*k-k*KK=KK},left);
***** 0=nn invalid as commutator relation
p1 := (n-k+1)*NN - (n+1);
p1 := - k*nn + n*nn - n + nn - 1
p2 := (k+1)*KK -(n-k);
p2 := k*kk + k + kk - n
l_g:=nc_groebner ({p1,p2});
***** Vdpinit: vdpvars not set
nc_preduce(p1+p2,l_g);
***** Vdpinit: vdpvars not set
nc_divide (k*p1+p2,p1);
***** Vdpinit: vdpvars not set
nc_divide (k*p1+p2,2*p1);
***** Vdpinit: vdpvars not set
nc_divide (2*k*k*p1 + k*p1 + p2,2*p1);
***** Vdpinit: vdpvars not set
nc_factorize (p1*p2);
***** Vdpinit: vdpvars not set
nc_setup({k,n,NN,KK},{NN*n-n*NN=NN,KK*k-k*KK=KK},right);
***** invalid as rule list
nc_factorize (p1*p2);
***** Vdpinit: vdpvars not set
% applications to shift operators
nc_setup({n,NN},{NN*n-n*NN=1},left);
***** invalid as rule list
n*NN;
n*nn
nc_factorize(ws);
***** Vdpinit: vdpvars not set
nc_setup({n,NN},{NN*n-n*NN=1},right);
***** invalid as rule list
n*NN;
n*nn
nc_factorize(ws);
***** Vdpinit: vdpvars not set
nc_setup({NN,n},{NN*n-n*NN=1},right);
***** invalid as rule list
n*NN;
n*nn
nc_factorize(ws);
***** Vdpinit: vdpvars not set
nc_setup({NN,n},{NN*n-n*NN=1},left);
***** invalid as rule list
n*NN;
n*nn
nc_factorize(ws);
***** Vdpinit: vdpvars not set
% Applications to partial differential equations
nc_setup({x,Dx},{Dx*x-x*Dx=1});
***** invalid as rule list
p:= 2*Dx^2 + x* Dx^3 + 3*x*Dx + x^2*Dx^2 + 14 + 7*x*Dx;
3 2 2 2
p := dx *x + dx *x + 2*dx + 10*dx*x + 14
nc_factorize p;
***** Vdpinit: vdpvars not set
right_factor(p,1);
***** Vdpinit: vdpvars not set
% no factor of degr 1
right_factor(p,2);
***** Vdpinit: vdpvars not set
left_factor(p,2);
***** Vdpinit: vdpvars not set
nc_setup({x,Dx},{Dx*x-x*Dx=1});
***** invalid as rule list
q := x**2*dx**2 + 2*x**2*dx + x*dx**3 + 2*x*dx**2
+ 8*x*dx + 16*x + 2*dx**2 + 4*dx$
nc_factorize q;
***** Vdpinit: vdpvars not set
right_factor(q,1);
***** Vdpinit: vdpvars not set
right_factor(q,1,{x});
***** Vdpinit: vdpvars not set
% no such right factor
right_factor(q,1,{dx});
***** Vdpinit: vdpvars not set
% looking for factor with degree bound for an individual variable
q := x**6*dx + x**5*dx**2 + 12*x**5 + 10*x**4*dx + 20*x**3
+ x**2*dx**3 - x**2*dx**2 + x*dx**4 - x*dx**3 + 8*x*dx**2
- 8*x*dx + 2*dx**3 - 2*dx**2$
right_factor(q,dx);
***** Vdpinit: vdpvars not set
right_factor(q,dx^2);
***** Vdpinit: vdpvars not set
% some coefficient sports
nc_setup({NN,n},{NN*n-n*NN=1},left);
***** invalid as rule list
q:=(n*nn)^2;
2 2
q := n *nn
nc_factorize q;
***** Vdpinit: vdpvars not set
nc_preduce(q,{c1+c2*n + c3*nn + c4*n*nn});
***** Vdpinit: vdpvars not set
nc_divide(q,n);
***** Vdpinit: vdpvars not set
nc_cleanup;
***** invalid as rule list
end;
(TIME: ncpoly 90 90)