The dual quaternion algebra and its implementation in Asymptote language

The algebras of dual quaternions and screws are often opposed to geometric algebra. The purpose of this paper is to describe the algebra of dual quaternions and the algebra of screws, to give a number of examples of the use of dual quaternions to describe the screw motion of points, lines and planes in three-dimensional space. This algebra is very poorly covered in the literature, and the actively used principle of Kotelnikov-Study transfer is apparently forgotten. All calculations were performed using the Asymptote language. Structures were created that implement dual numbers, quaternions, and dual dual quaternions, as well as a set of computational tests to verify these structures.