[sci.math] solution to system of quadratic equations

heath@cs.jhu.edu (David Heath) (01/11/91)

Say I have a set of variables X={x1,x2,...xn} and a set of equations of the 
form:

xi^2 +xj^2 - xk^2 - xl^2 = 0	(quadratic in four vars)

xi^2 +xj^2 - xk^2 - xl^2 >=0	(quadratic in four vars, inequality)

xi + cxj^2 + d = 0		(quadratic in one, linear in another)

xi + exj = 0			(linear, two vars)

xi <= xj			(linear, two vars, inequality)

c, d, e are just constants.

I want to know if there is a real solution (not necessarily algebraic).
I do not want to know what the solution is, just if there is one.
Is this problem in NP? I know that it is NP-hard. 

Any information is appreciated.

Thanks
-dave heath
heath@cs.jhu.edu