Ivanyos, Gábor and Lelkes, Á. D. and Rónyai, Lajos (2013) Improved algorithms for splitting full matrix algebras. JP JOURNAL OF ALGEBRA, NUMBER THEORY AND APPLICATIONS, 28 (2). pp. 141-156. ISSN 0972-5555
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Abstract
Let K be an algebraic number field of degree d and discriminant ∆ over Q. Let A be an associative algebra over K given by structure constants such that A ∼= Mn(K) holds for some positive integer n. Suppose that d, n and |∆| are bounded. In a previous paper a polynomial time ff-algorithm was given to construct explicitly an isomorphism A → Mn(K). Here we simplify and improve this algorithm in the cases n ≤ 43, K = Q, and n = 2, with K = Q(√−1) or K = Q(√−3). The improvements are based on work by Y. Kitaoka and R. Coulangeon on tensor products of lattices.
| Item Type: | Article |
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| Subjects: | Q Science / természettudomány > QA Mathematics / matematika Q Science / természettudomány > QA Mathematics / matematika > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány Q Science / természettudomány > QA Mathematics / matematika > QA76 Computer software / programozás |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 09 Aug 2024 09:53 |
| Last Modified: | 09 Aug 2024 09:53 |
| URI: | https://real.mtak.hu/id/eprint/202233 |
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