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The Cartographer
About the Kannan-Bachem algorithm
October 22, 2024 Β· Declared Dead Β· π arXiv.org
"No code URL or promise found in abstract"
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Authors
Francis Sergeraert
arXiv ID
2411.02422
Category
cs.DS: Data Structures & Algorithms
Citations
0
Venue
arXiv.org
Last Checked
5 months ago
Abstract
The Smith reduction is a basic tool when analyzing integer matrices up to equivalence, and the Kannan-Bachem (KB) algorithm is the first polynomial algorithm computing such a reduction. Using this algorithm in complicated situations where the rank of the studied matrix is not maximal revealed an unexpected obstacle in the algorithm. This difficulty is described, analyzed, a simple solution is given to overcome it, finally leading to a general organization of the KB algorithm, simpler than the original one, efficient and having a general scope.
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