Diophantine systems

On Solving Linear Diophantine Systems Using Generalized Rosser's Algorithm

Systems of quadratic diophantine inequalities

has a nonzero integer solution for every > 0. If some Qi is rational and is small enough then for x ∈ Zs the inequality |Qi(x)| < is equivalent to the equation Qi(x) = 0. Hence if all forms are rational then for sufficiently small the system (1.1) reduces to a system of equations. In this case W. Schmidt [10] proved the following result. Recall that the real pencil generated by the forms Q1, . ...

on solving linear diophantine systems using generalized rosser's algorithm

On Systems of Linear Diophantine Equations

Introduction Something happened to me recently I would wager has happened to many who read this note. Teaching a new topic, you cannot understand one of the proofs. Your first attempt to fill the gap fails. You look through your books for an answer. Next, you ask colleagues, go to the library, maybe even use the interlibrary loan. All in vain. Then it strikes you that, in fact, you cannot answe...

Optimal Systolic Algorithm for Diophantine Systems

We present a technique for finding a lower bound on the number of processors needed to achieve a given schedule of an algorithm represented as a dag for a Diophantine system. The application of this technique is illustrated with a tensor product computation. We then provide a time-minimal processor schedule that meets the computed processor lower bounds, including the one for tensor product. We...