Four non-linear equations in Four variables

Hey,

I have four equations of the form:

x^2 + y^2 + z^2 + A1*x + B1*y + C1*z - D1*R + E1=0

Similarly, I have three more equations (with "1" replaced in above equation by 2,3,4)

I need to get x,y,z and R in terms of (A1,B1,C1,D1,E1....A4,B4,C4,D4,E4).

Any help in this regard will be greatly appreciated. Thanks.

[Walter Roberson]

solve(). And wait, and wait, and wait...

[Walter Roberson]

I had to kill my solver after it chewed through 6 Gb of working memory.

Can you place constraints on the ranges for x, y, z, R ? For example, the constraint of them being non-negative would cut down the solution possibilities a fair bit.

[manish sharma]

I am sorry. I did not noticed your reply Walter. We can put the following constraints:

0 < x, y, z < 500 and R>=0

Thanks for your efforts.

[Walter Roberson]

Processing is taking a fair while.

What is it that your equations represent? It looks like some kind of conic ?

[Walter Roberson]

I worked iterative, finding x, then y; but finding z chewed up more than an hour of CPU time on my machine before I killed it (I needed the CPU back.)