Algorithm XXX: Computing the group of local dyadic square-classes the easy way

We propose a novel method for constructing a basis of the group of local square-classes of a dyadic completion of a number field. The described method has been implemented by the author in the computer algebra systems Magma and SageMath. It turned out to be substantially faster than the algorithm previously used. The paper presents the algorithm itself, together with a time comparison with the preexisting solution.