A canonical form for positive definite matrices

Dutour Sikirić, Mathieu; Haensch, Anna; Voight, John; van Woerden, Wessel

doi:10.2140/obs.2020.4.179

M. Dutour Sikirić (Mathieu), A. Haensch (Anna), J. Voight (John) and W.P.J. van Woerden (Wessel)

2020-12-29

A canonical form for positive definite matrices

Presented at the 14th Algorithmic Number Theory Symposium (June 2020), Virtual, Online

We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software. The algorithm runs in a number of arithmetic operations that is exponential in the dimension n, but it is practical and more efficient than canonical forms based on Minkowski reduction.

Additional Metadata
Keywords	Canonical form, Quadratic form, Positive definite matrix, Lattice isomorphism, Graph isomorphism
Persistent URL	doi.org/10.2140/obs.2020.4.179
Series	The Open Book Series
Conference	14th Algorithmic Number Theory Symposium
Organisation	Cryptology
Citation APA Style AAA Style APA Style Cell Style Chicago Style Harvard Style IEEE Style MLA Style Nature Style Vancouver Style American-Institute-of-Physics Style Council-of-Science-Editors Style BibTex Format Endnote Format RIS Format CSL Format DOIs only Format	Dutour Sikirić, M., Haensch, A., Voight, J., & van Woerden, W. (2020). A canonical form for positive definite matrices. In Proceedings of the 14th Algorithmic Number Theory Symposium, ANTS-XIV (pp. 179–195). doi:10.2140/obs.2020.4.179

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