Reduction of Smith Normal Form Transformation Matrices
2005 (English)In: Computing, ISSN 0010-485X, E-ISSN 1436-5057, Vol. 74, no 4, 377-388 p.Article in journal (Refereed) Published
Smith normal form computations are important in group theory, module theory and number theory. We consider the transformation matrices for the Smith normal form over the integers and give a presentation of arbitrary transformation matrices for this normal form. Our main contribution is an algorithm that replaces already computed transformation matrices by others with small entries. We combine methods from lattice basis reduction with a procedure to reduce the sum of the squared entries of both transformation matrices. This algorithm performs well even for matrices of large dimensions.
Place, publisher, year, edition, pages
Springer, 2005. Vol. 74, no 4, 377-388 p.
Smith normal form, transformation matrices, lattice basis reduction
IdentifiersURN: urn:nbn:se:umu:diva-83131DOI: 10.1007/s00607-004-0104-0OAI: oai:DiVA.org:umu-83131DiVA: diva2:665026