Algorithmic applications of the corestriction of central simple algebras

07/14/2020

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by   Tímea Csahók, et al.

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Let L be a separable quadratic extension of either ℚ or 𝔽_q(t). We propose efficient algorithms for finding isomorphisms between quaternion algebras over L. Our techniques are based on computing maximal one-sided ideals of the corestriction of a central simple L-algebra. In order to obtain efficient algorithms in the characteristic 2 case, we propose an algorithm for finding nontrivial zeros of a regular quadratic form in four variables over 𝔽_2^k(t).