substitution_nonlinsolve_parts7jul2016.py

def _extract_main_soln(sol, soln_imageset):
            """separate the Complements, Intersections, ImageSet lambda expr
            and it's base_set.
            """
            # if there is union, then need to check
            # complement, intersection, Imageset
            # order should not be changed.
            if isinstance(sol, Complement):
                # extract solution and complement
                complements[sym] = sol.args[1]
                sol = sol.args[0]
                # complement will be added at the end
            if isinstance(sol, Intersection):
                # Interval will be at 0th index always
                if sol.args[0] != Interval(-oo, oo):
                    # sometimes solveset returns soln
                    # with intersection S.Reals, to confirm that
                    # soln is in domain=S.Reals
                    intersections[sym] = sol.args[0]
                sol = sol.args[1]
            # after intersection and complement Imageset should
            # be checked.
            if isinstance(sol, ImageSet):
                soln_imagest = sol
                sol = FiniteSet(sol.lamda.expr)
                soln_imageset[sol] = soln_imagest

            # if there is union of Imageset in soln
            # no testcase is written for this if block
            if isinstance(sol, Union):
                sol_args = sol.args
                sol = []
                # put FiniteSet, ImageSet in the soln list.
                for sol_arg2 in sol_args:
                    if isinstance(sol_arg2, FiniteSet):
                        list_finiteset = list(
                            [sol_1 for sol_1 in sol_arg2])
                        sol += list_finiteset
                    else:
                        # ImageSet or Intersection or complement
                        # append them directly
                        sol.append(sol_arg2)

            return sol, soln_imageset
        # end of def _extract_main_soln