       # a simple algebraic system of 5 eqns second degree

• 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

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}]

```

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