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)
