Artifact e9eaaa7da7d73fe22bae0ee299e2da6e6b9e602df713e66ef8315d19072bd0f9:
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r37/packages/ncpoly/ncpoly.rlg
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2011-09-02 18:13:33
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— Some historical releases purely for archival purposes
git-svn-id: https://svn.code.sf.net/p/reduce-algebra/code/trunk/historical@1375 2bfe0521-f11c-4a00-b80e-6202646ff360 (user: arthurcnorman@users.sourceforge.net, size: 3569) [annotate] [blame] [check-ins using] [more...]
Mon Jan 4 00:02:48 MET 1999 REDUCE 3.7, 15-Jan-99 ... 1: 1: 2: 2: 2: 2: 2: 2: 2: 2: 2: 3: 3: nc_setup({k,n,NN,KK},{NN*n-n*NN=NN,KK*k-k*KK=KK},left); 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 - n + kk l_g:=nc_groebner ({p1,p2}); l_g := {k*nn - n*nn + n - nn + 1, k*kk + k - n + kk, n*nn*kk - n*kk - n + nn*kk - kk - 1} nc_preduce(p1+p2,l_g); 0 nc_divide (k*p1+p2,p1); {k,k*kk + k - n + kk} nc_divide (k*p1+p2,2*p1); {k,2*k*kk + 2*k - 2*n + 2*kk} nc_divide (2*k*k*p1 + k*p1 + p2,2*p1); 2 {2*k + k, 2*k*kk + 2*k - 2*n + 2*kk} nc_factorize (p1*p2); { - k*nn + n*nn - n + nn - 1, k*kk + k - n + kk} nc_setup({k,n,NN,KK},{NN*n-n*NN=NN,KK*k-k*KK=KK},right); nc_factorize (p1*p2); { - k*nn + n*nn - n + nn - 1, k*kk + k - n + kk} % applications to shift operators nc_setup({n,NN},{NN*n-n*NN=1},left); n*NN; n*nn nc_factorize(ws); {n,nn} nc_setup({n,NN},{NN*n-n*NN=1},right); n*NN; n*nn nc_factorize(ws); {n,nn} nc_setup({NN,n},{NN*n-n*NN=1},right); n*NN; nn*n - 1 nc_factorize(ws); {n,nn} nc_setup({NN,n},{NN*n-n*NN=1},left); n*NN; nn*n - 1 nc_factorize(ws); {n,nn} % Applications to partial differential equations nc_setup({x,Dx},{Dx*x-x*Dx=1}); p:= 2*Dx^2 + x* Dx^3 + 3*x*Dx + x^2*Dx^2 + 14 + 7*x*Dx; 2 2 3 2 p := x *dx + x*dx + 10*x*dx + 2*dx + 14 nc_factorize p; 2 {x*dx + 2,x*dx + dx + 7} right_factor(p,1); 2 2 3 2 x *dx + x*dx + 10*x*dx + 2*dx + 14 % no factor of degr 1 right_factor(p,2); 2 x*dx + dx + 7 left_factor(p,2); x*dx + 2 nc_setup({x,Dx},{Dx*x-x*Dx=1}); 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; 2 {x*dx + dx + 7, x, dx + 2} right_factor(q,1); dx + 2 right_factor(q,1,{x}); 2 2 2 3 2 2 x *dx + 2*x *dx + x*dx + 2*x*dx + 8*x*dx + 16*x + 2*dx + 4*dx % no such right factor right_factor(q,1,{dx}); dx + 2 % 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); 6 5 2 5 4 3 2 3 2 2 4 3 x *dx + x *dx + 12*x + 10*x *dx + 20*x + x *dx - x *dx + x*dx - x*dx 2 3 2 + 8*x*dx - 8*x*dx + 2*dx - 2*dx right_factor(q,dx^2); 4 2 x + dx - dx % some coefficient sports nc_setup({NN,n},{NN*n-n*NN=1},left); q:=(n*nn)^2; 2 2 q := nn *n - 3*nn*n + 1 nc_factorize q; {n, nn, n, nn} nc_preduce(q,{c1+c2*n + c3*nn + c4*n*nn}); 2 2 2 2 2 2 (c3 *c4)*nn + (2*c1*c3*c4 - 2*c2*c3 + c3*c4 )*nn + (c2 *c4)*n 2 2 2 + (2*c1*c2*c4 - 2*c2 *c3 - c2*c4 )*n + (c1 *c4 - 2*c1*c2*c3 + c2*c3*c4) nc_divide(q,n); 2 {nn *n - 3*nn,1} nc_cleanup; end; 4: 4: 4: 4: 4: 4: 4: 4: 4: Time for test: 47420 ms, plus GC time: 4670 ms 5: 5: Quitting Mon Jan 4 00:03:50 MET 1999