First, define the polynomial ring and two polynomials of .
Using the GeneralConstruct command and adding one inequality, you can build a constructible set. Using the polynomials and for defining inequations, the two constructible sets cs1 and cs2 are different.
The intersection of cs1 and cs2 is a new constructible set cs.
Check the result in another way.
The results are as desired.
Consider now the semi-algebraic case:
Verify the results