@@ -1,249 +1,249 @@ -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) +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)