Quaternica: a Package for Manipulating Expressions Involving Quaternions

Quaternions are well suited to describe and combine rotations in the usual 3D euclidian space. Therefore, an increasing interest has been shown especially by engineers for symbolically computing with quaternions. Quaternica is a Mathematica package designed to give the ability to perform manipulations on symbolic expressions involving quaternions. The features of this package include some facilities already available in the non-commutative algebra package NCAlgebra written by J.W. Helton and R.L. Miller on computing with symbols with a non-commutative product. What is new and original in Quaternica is that it deals with three diierent ways to represent a quaternion, as a symbol by itself, as a pair of its scalar (real) part and its 3-dimensional vector part, and as a list of its four real coordinates. This feature is of particular importance for practical applications because the user can keep its expressions as compact as possible (avoiding the introduction of the four coordinates as long as they are not explicitly needed). Quaternica also provides facilities for manipulating the 3 dimensional vectors (and expressions involving the scalar and cross products) that can appear in quaternions and that are very important for their geometric meaning. The main functionalities of Quaternica are described and some details about implementation are given. A sample session demonstrate the use of the package.