Solving parametric linear systems

Algorithms in computer algebra are usually designed for a fixed set of domains. For example, algorithms over the domain of polynomials are not applicable to parameters because the inherent assumption that the indeterminate X bears no algebraic relation to other objects is violated.We propose to use a technique from model theory known as constraint programming to gain more flexibility, and we show how it can be applied to the Gaussian algorithm to be used for parametric systems. Our experiments suggest that in practice this leads to results comparable to the algorithm for parametric linear systems by Sit [9] -- at least if the parameters are sparse.