Rank reduction processes for solving linear Diophantine systems and integer factorizations: a review (Q779712)

The authors first describe the class of integer ABS algorithms for solving linear Diophantine systems (see [\textit{J. Abaffy} et al., Numer. Math. 45, 361--376 (1984; Zbl 0535.65009)]). Then they review the class of integer ABS algorithms for solving integer systems of linear inequalities, rank-one changed problems, and generalized Rosser algorithms for solving systems of linear Diophantine equations. The new result of this article is to study a Wedderburn rank reduction process and its associated integer biconjugation process. As a byproduct the authors present new algorithms for integer matrix factorizations.