First define the polynomial ring and two polynomials of .
The goal is to determine for which parameter values of , , and the generic linear equations and have solutions. Project the variety defined by and onto the parameter space.
Therefore, four regular systems encode this projection in the parameter space. The complement of cs should be those points that make the linear equations have no common solutions.
If you call Complement twice, you should retrieve the constructible set cs.
Semi-algebraic case
Verify compl = expected as set of points by Difference.