Splitting quaternion algebras over quadratic number fields

2016/06/03 by Kutas, Péter
#FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA) #Symbolic Computation (cs.SC)

paper · doi:10.48550/arxiv.1606.01053

Abstract

We propose an algorithm for finding zero divisors in quaternion algebras over quadratic number fields, or equivalently, solving homogeneous quadratic equations in three variables over ℚ(√(d)) where d is a square-free integer. The algorithm is randomized and runs in polynomial time if one is allowed to call oracles for factoring integers.

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