Rule-Based Simplification in Vector-Product Spaces

Abstract. A vector-product space is a component-free representation of the common three-dimensional Cartesian vector space. The components of the vectors are invisible and formally inaccessible, although expressions for the components could be constructed. Expressions that have been built from the scalar and vector products can be simplified using a rule-based system. In order to develop and specify the system, an axiomatic system for a vector-product space is given. In addition, a brief description is given of an implementation in Aldor. The present work provides simplification functionality which overcomes difficulties encountered in earlier packages.