GAP package EDIM: The main purpose of the EDIM package is to publish an implementation of an algorithm (found by the package author) for computing prime parts of the elementary divisors of integer matrices (i.e., the diagonal entries of the Smith normal form). The programs are developed and already successfully used for large matrices (up to rank >12000) with moderate entries and many non-trivial elementary divisors which are products of some small primes. But they should be useful for other types of matrices as well. Among the other functions of the package are: An inversion algorithm for large rational matrices (using a p-adic method), a program for finding the largest elementary divisor of an integral matrix (particularly interesting when this is much smaller than the determinant) and implementations of some normal form algorithms described by Havas, Majewski, Matthews, Sterling (using LLL- or modular techniques).
Keywords for this software
References in zbMATH (referenced in 7 articles )
Showing results 1 to 7 of 7.
- Levandovskyy, Viktor; Schindelar, Kristina: Fraction-free algorithm for the computation of diagonal forms matrices over Ore domains using Gröbner bases (2012)
- Cao, Wei: Smith normal form of augmented degree matrix and its applications (2009)
- Borges-Quintana, M.; Borges-Trenard, M.A.; Martínez-Moro, E.: On the use of Gröbner bases for computing the structure of finite abelian groups (2005)
- Saunders, David; Wan, Zhendong: Smith normal form of dense integer matrices, fast algorithms into practice (2004)
- Lübeck, Frank: On the computation of elementary divisors of integer matrices (2002)
- Giesbrecht, Mark; Jacobson, Michael jun.; Storjohann, Arne: Algorithms for large integer matrix problems (2001)
- Lübeck, Frank: Small degree representations of finite Chevalley groups in defining characteristic. (2001)