P-adic constraint solving
Andreas Dolzmann, Thomas Sturm · 1999
We automatically check for the feasibility of arbitrary boolean combinations of linear parametric p-adic constraints using a quantier elimination method. This can be done uniformly for all p. We focus on the necessary simplication methods. Our method is implemented within the computer algebra system reduce. We illustrate the applicability of this implementation to non-trivial problems including the solution of systems of linear congruences over the integers. 1 Introduction It is well-known that linear parametric constraint solving over the reals has numerous important applications in science and engineering. The same holds for corresponding integer and mixed real-integer problems. In this article we consider analogue problems over p-adic numbers instead of real numbers. This also has important though less obvious applications, mainly in class eld theory and Diophantine analysis [Dub92]. One can, for instance, weaken the problem of nding integer solutions to a Diophantine ...