computed on Murrumesh (almost idle); First computation is much faster than second with memory consumption 10 times compared to before; Second comp. takes 1:30 h, mem consumption is almost factored by 1000. Additionally, below SINGULAR says "//used time: 4.14 sec". This takes actually about 10 min to determine. First computation: ************************************************************ > ring r = 0,(x(1),x(2),t(1),dx(1),dx(2),dt(1),u(1)),Dp; > matrix C[7][7] = 0,1,1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0; > matrix D[7][7] = 0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; > def S = nc_algebra(C,D); > setring S; > basering; // characteristic : 0 // number of vars : 7 // block 1 : ordering Dp // : names x(1) x(2) t(1) dx(1) dx(2) dt(1) u(1) // block 2 : ordering C // noncommutative relations: // dx(1)x(1)=x(1)*dx(1)+1 // dx(2)x(2)=x(2)*dx(2)+1 // dt(1)t(1)=t(1)*dt(1)+1 > ideal I = x(1)5*u(1)-5*x(1)4*x(2)*u(1)+10*x(1)3*x(2)2*u(1)-10*x(1)2*x(2)3*u(1)+5*x(1)*x(2)4*u(1)-x(2)5*u(1)-x(1)2*u(1)-2*x(1)*x(2)*u(1)-x(2)2*u(1)+t(1)*u(1),-5*x(1)4*dt(1)*u(1)+20*x(1)3*x(2)*dt(1)*u(1)-30*x(1)2*x(2)2*dt(1)*u(1)+20*x(1)*x(2)3*dt(1)*u(1)-5*x(2)4*dt(1)*u(1)+2*x(1)*dt(1)*u(1)+2*x(2)*dt(1)*u(1)+dx(1)*u(1),5*x(1)4*dt(1)*u(1)-20*x(1)3*x(2)*dt(1)*u(1)+30*x(1)2*x(2)2*dt(1)*u(1)-20*x(1)*x(2)3*dt(1)*u(1)+5*x(2)4*dt(1)*u(1)+2*x(1)*dt(1)*u(1)+2*x(2)*dt(1)*u(1)+dx(2)*u(1); > memory(0);memory(1);memory(2); 170344 659456 659456 > ideal J = eliminate(I,u(1)); > J; J[1]=0 > memory(0);memory(1);memory(2); 1621176 2242496 2242496 > listvar(all); // S [0] *ring // J [0] ideal, 1 generator(s) // I [0] ideal, 3 generator(s) // r [0] ring // D [0] matrix 7 x 7 // C [0] matrix 7 x 7 > kill S,r; > listvar(all); > memory(0);memory(1);memory(2); 1618856 2242496 2242496 > ************************************************************ Second computation: ************************************************************ > timer = 1; > ring r = 0,(x(1),x(2),t(1),dx(1),dx(2),dt(1),u(1)),Dp; > matrix C[7][7] = 0,1,1,1,1,1,1,0,0,1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0; > matrix D[7][7] = 0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0; > def S = nc_algebra(C,D); > setring S; > basering; // characteristic : 0 // number of vars : 7 // block 1 : ordering Dp // : names x(1) x(2) t(1) dx(1) dx(2) dt(1) u(1) // block 2 : ordering C // noncommutative relations: // dx(1)x(1)=x(1)*dx(1)+1 // dx(2)x(2)=x(2)*dx(2)+1 // dt(1)t(1)=t(1)*dt(1)+1 > ideal I = x(1)5*u(1)-5*x(1)4*x(2)*u(1)+10*x(1)3*x(2)2*u(1)-10*x(1)2*x(2)3*u(1)+5*x(1)*x(2)4*u(1)-x(2)5*u(1)-x(1)2*u(1)-2*x(1)*x(2)*u(1)-x(2)2*u(1)+t(1)*u(1),-5*x(1)4*dt(1)*u(1)+20*x(1)3*x(2)*dt(1)*u(1)-30*x(1)2*x(2)2*dt(1)*u(1)+20*x(1)*x(2)3*dt(1)*u(1)-5*x(2)4*dt(1)*u(1)+2*x(1)*dt(1)*u(1)+2*x(2)*dt(1)*u(1)+dx(1)*u(1),5*x(1)4*dt(1)*u(1)-20*x(1)3*x(2)*dt(1)*u(1)+30*x(1)2*x(2)2*dt(1)*u(1)-20*x(1)*x(2)3*dt(1)*u(1)+5*x(2)4*dt(1)*u(1)+2*x(1)*dt(1)*u(1)+2*x(2)*dt(1)*u(1)+dx(2)*u(1),-x(1)*x(2)*u(1)+x(1)*x(2); > ideal J = eliminate(I,u(1)); //used time: 4717.84 sec > memory(0);memory(1);memory(2); 1308915904 //used time: 4.14 sec 1329631232 1329631232 > listvar(all); // S [0] *ring // J [0] ideal, 60 generator(s) // I [0] ideal, 4 generator(s) // r [0] ring // D [0] matrix 7 x 7 // C [0] matrix 7 x 7 > kill J; > memory(0);memory(1);memory(2); 1307702232 1329631232 1329631232 > kill S,r; > listvar(all); > memory(0);memory(1);memory(2); 1307699920 1329631232 1329631232 > ************************************************************