Computing nearby non-trivial Smith forms

Computing Hermite and Smith normal forms of triangular integer matrices

This paper considers the problem of transforming a triangular integer input matrix to canonical Hermite and Smith normal form. We provide algorithms and prove deterministic running times for both transformation problems that are optimal in the matrix dimension. The algorithms are easily implemented, assume standard integer arithmetic, and admit excellent performance in practice. The results pre...

Near Optimal Algorithms for Computing Smith Normal Forms of Integer

We present new algorithms for computing Smith normal forms of matrices over the integers and over the integers modulo d. For the case of matrices over Z Z d, we present an algorithm that computes the Smith form S of an A 2 Z Z nm d in only O(n ?1 m) operations from Z Z d. Here, is the exponent for matrix multiplication over rings: two n n matrices over a ring R can be multiplied in O(n) operati...

Enhancing Usability of Non-Trivial Online Forms through Modellling

Trivial Stable Structures with Non-trivial Reducts

We offer a new viewpoint on some of the generic structures constructed using Hrushovski’s predimensions and show that they are natural reducts of quite straightforward trivial, one-based stable structures. 2000 Mathematics Subject Classification: 03C45.

Some Non-trivial Cocycles

For each locally compact non-compact c-compact Abelian group G whose dual is an I-group and each compact Abelian group ,?J such that there is a one-to-one continous homomorphism from G onto a dense subgroup of Z, we show the existence of cocycles on Z whose associated unitary representations of G have purely singular continuous spectrum, as well as the existence of cocycles on Z whose associate...