We present an algorithm for computing a Smith form with multipliers of a regular matrix polynomial over a field. This algorithm differs from previous ones in that it computes a local Smith form for each irreducible factor in the determinant separately and then combines them into a global Smith form, whereas other algorithms apply a sequence of unimodular row and column operations to the origina...

Loop transformations have been shown to be very useful in parallelising compilation and regular array design. This paper provides a solution to the open problem of automatic rewriting loop nests for non-unimodular loop transformations. We present an algorithm that rewrites a loop nest under any non-singular (unimodular or non-unimodular) transformation in a mechanical manner. The algorithm work...

A recursive construction is provided for sequence sets which possess good Hamming Distance and low Peak-to-Average Power Ratio (PAR) under any Local Unitary Unimodular Transform. We identify a subset of these sequences that map to binary indicators for linear and nonlinear Factor Graphs, after application of subspace Walsh-Hadamard Transforms. Finally we investigate the quantum PARl measure of ...

This paper describes unimodular probing { a new technique that has been used to solve a class of dynamic scheduling problems. In benchmarks a unimodular probing algorithm has outperformed two well-established approaches: backtrack search with local consistency and spe-cialised heuristics, and mixed integer programming (MIP). The problems amenable to unimodular probing involve disjunctive constr...

We discuss sharpness in the Hausdorff Young theorem for unimodular groups. First the functions on unimodular locally compact groups for which equality holds in the Hausdorff Young theorem are determined. Then it is shown that the Hausdorff Young theorem is not sharp on any unimodular group which contains the real Une as a direct summand, or any unimodular group which contains an Abelian normal ...

7 We first characterize submatrices of a unimodular integral matrix. We then prove that if n entries of an 8 n× n partial integral matrix are prescribed and these n entries do not constitute a row or a column, then this 9 matrix can be completed to a unimodular matrix. Consequently an n× n partial integral matrix with n− 1 10 prescribed entries can always be completed to a unimodular matrix. 11...

Let ∇ be a meromorphic connection on a vector bundle over a compact Riemann surface Γ. An automorphism σ : Γ → Γ is called a symmetry of ∇ if the pull-back bundle and the pull-back connection can be identified with ∇. We study the symmetries by means of what we call the Fano Group; and, under the hypothesis that ∇ has a unimodular reductive Galois group, we relate the differential Galois group,...

Rauzy fractals are compact sets with fractal boundary that can be associated with any unimodular Pisot irreducible substitution. These fractals can be defined as the Hausdorff limit of a sequence of compact planar sets, where each set is the projection of a finite union of faces of unit cubes. We exploit this combinatorial definition to prove the connectedness of the fractal associated with any...