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 facil...

The definition of morphological operators for colour images needs a total ordering between the colour points. A colour can be represented according to different algebraic structures, in particular in this paper we focus on real quaternions. The paper presents two main contributions. On the one hand, we have studied different alternatives to introduce the scalar part to obtain full colour quater...

The aim of this article is to introduce Pell–Padovan generalized quaternions. It also derives new properties associated with these and takes into account negative indices. Additionally, it presents generating function, Binet-like formula, Simson matrix representations, several summation properties.