Algorithmic properties of maximal orders in simple algebras over \(\mathbb{Q}\)

DOI10.1007/BF01272075zbMath0787.16002MaRDI QIDQ2366169

Lajos Rónyai

Publication date: 29 June 1993

Published in: Computational Complexity (Search for Journal in Brave)

zbMATH Keywords

algorithmmatrix algebraindexcentral simple algebracomplexity classskew-fieldlocal maximality of orders

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Symbolic computation and algebraic computation (68W30) Number-theoretic algorithms; complexity (11Y16) Algebraic number theory computations (11Y40) Computational aspects of associative rings (general theory) (16Z05) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05)

Related Items (12)

Orientations and the supersingular endomorphism ring problem ⋮ Lattice basis reduction for indefinite forms and an application ⋮ Splitting full matrix algebras over algebraic number fields. ⋮ Efficient decomposition of separable algebras. ⋮ Algorithms Based on *-Algebras, and Their Applications to Isomorphism of Polynomials with One Secret, Group Isomorphism, and Polynomial Identity Testing ⋮ Efficient decomposition of associative algebras over finite fields ⋮ Identifying the Matrix Ring: Algorithms for Quaternion Algebras and Quadratic Forms ⋮ Decompositions of algebras over \(\mathbb{R}\) and \(\mathbb{C}\) ⋮ Unnamed Item ⋮ A Lie algebra method for rational parametrization of Severi-Brauer surfaces. ⋮ Solvability of norm equations over cyclic number fields of prime degree ⋮ Finding maximal orders in semisimple algebras over \(\mathbb{Q}\)

Cites Work

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• An algorithm for computing modular forms on \(\Gamma_0(N)\)
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• CHARACTERIZATION OF BLOW-UP FOR A SEMILINEAR HEAT EQUATION WITH A CONVECTION TERM
• Zero divisors in quaternion algebras
• Polynomial Algorithms for Computing the Smith and Hermite Normal Forms of an Integer Matrix
• Computing Irreducible Representations of Finite Groups
• Systems of distinct representatives and linear algebra
• Sylvester's Identity and Multistep Integer-Preserving Gaussian Elimination

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