*To*: mathgroup@smc.vnet.net*Subject*: [mg10488] a simple algebraic system of 5 eqns second degree*From*: "ns" <ns@ntua.gr>*Date*: Tue, 20 Jan 1998 02:22:40 -0500*Organization*: National Technical University of Athens, Greece

I tried to solve the following system in many PCs under Win95 The most powerful was a Pentium Pro 200, 32MB. Every time a message of running out of memory was coming up. Is this really a problem of memory or it has to do with Mathematica, since this system has at least one solution: (x,y,z,w,u)=(1,1,1,1,0) I would be greatful if someone could have an answer. f1[x_,y_,z_,w_,u_]:=-13 + u^2 + 4*u*w + w^2 + 4*x - 2*u*x + 18*x^2 - 4*u*y - 4*w*y + 8*y^2 - 2*(u + w + 7*x + y)*z + 4*z^2 f2[x_,y_,z_,w_,u_]:=-13 + u^2 + w^2 - 6*u*x - 4*w*x + 3*x^2 + 4*y + 18*x*y + 5*y^2 + 2*(u + w - x - 7*y)* f3[x_,y_,z_,w_,u_]:=-3 - u^2 + 4*u*w - w^2 + 2*(2 + 2*u - w + 7*x - y)*z - 10*z^2 f4[x_,y_,z_,w_,u_]:=-3 - u^2 + 4*w - 4*u*w - 8*w^2 + 2*w*x + 10*w*y + 2*(3*u + 2*x - 2*y)*z - 5*z^2 f5[x_,y_,z_,w_,u_]:=4*u - 8*u^2 - 4*u*w - w^2 + 2*u*x + 10*u*y + 2*(3*w + 2*x - 2*y)*z - 5*z^2 NSolve[{f1[x,y,z,w,u],f2[x,y,z,w,u],f3[x,y,z,w,u], f4[x,y,z,w,u],f5[x,y,z,w,u]}=={0,0,0,0,0} ,{x,y,z,w,u}]