Parallelism in Hermite and Smith normal forms

Overview & Synopsis

The Smith and Hermite normal forms play an important role in various fields of investigations. In many applications it is crucial to compute the Smith or Hermite normal form of an integral matrix. A construction of a special sequence of integral matrices based on the twin primes is presented. We suggest that this construction could show a method how to obtain a lower bound for triangular unimodular matrices in the terms of elementary operations. We also define a class of parallel networks for the computation of a gcd of n numbers. An analogy of the zero-one principle for comparison networks is derived for the gcd networks.