### Abstract

We formalize the theory of homogeneous linear diophantine equations,
focusing on two main results: (1) an abstract characterization of
minimal complete sets of solutions, and (2) an algorithm computing
them. Both, the characterization and the algorithm are based on
previous work by Huet. Our starting point is a simple but inefficient
variant of Huet's lexicographic algorithm incorporating improved
bounds due to Clausen and Fortenbacher. We proceed by proving its
soundness and completeness. Finally, we employ code equations to
obtain a reasonably efficient implementation. Thus, we provide a
formally verified solver for homogeneous linear diophantine equations.

GNU Lesser General Public License (LGPL)### Topics

### Theories of Diophantine_Eqns_Lin_Hom

- List_Vector
- Linear_Diophantine_Equations
- Sorted_Wrt
- Minimize_Wrt
- Simple_Algorithm
- Algorithm
- Solver_Code