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A
canonical form for positive definite matrices
Mathieu Dutour Sikirić, Anna Haensch, John Voight and Wessel P.J. van Woerden |
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Vol. 4 (2020), No. 1, 179–195
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Abstract |
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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 , but it is practical and more efficient than canonical forms based on Minkowski reduction. |
Keywords
canonical form, quadratic form, positive definite matrix,
lattice isomorphism, graph isomorphism
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Mathematical Subject Classification 2010
Primary: 11H55, 11H56, 15A21
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Milestones
Received: 28 February 2020
Accepted: 29 April 2020
Published: 29 December 2020
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Authors |
| Mathieu Dutour Sikirić | |
| Institut Rudjer Bošković Zagreb Croatia |
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| Anna Haensch | |
| Department of Mathematics and
Computer Science Duquesne University Pittsburgh, PA United States |
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| John Voight | |
| Department of Mathematics Dartmouth College Hanover, NH United States |
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| Wessel P.J. van Woerden | |
| Centrum Wiskunde & Informatica
(CWI) Amsterdam Netherlands |
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