Extending Djokovićʼs lattice reduction algorithm to include isotropic lattices

Let k   be any field of characteristic not equaling 2. Djoković showed that every anisotropic k[x]k[x]-lattice has a reduced basis which enabled Gerstein to complete the classification of definite k[x]k[x]-lattices. This paper extends Djokovićʼs reduction algorithm to include the isotropic case.