A theory on extending algorithms for parametric problems

Given certain algorithms for certain problems, these algorithms can be incorporated in a lift, solve, and lower sequence to form algorithms for solving parametric versions of the problems. In the first phase of the sequence the parametric problem is lifted to an extended ordered field where it becomes a single nonparametric problem. Second, the original algorithm is run in the extended order field to solve the single problem. Finally, this solution to the single problem is lowered to the original ordered field to obtain a parametric solution to the original parametric problem.