Abstract
We use complex vectors in geometrical reasoning, specifically automated theorem proving. The calculations are embedded in Clifford algebras, but commutative polynomial techniques can be used. Using the Gröbner basis package in the computer algebra package Maple, this approach is shown to have efficiency benefits in situations where distance and angle relations amongst geometrical entities predominate.
Acknowledgements
We thank the anonymous referees of the first draft of this paper for their helpful suggestions. We would also like to thank Desmond Fearnley-Sander for introducing us to the concept of automated theorem proving in geometry and many discussions over the years on that topic.
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Stokes, T., Bulmer, M. (2001). A Complex Change of Variables for Geometrical Reasoning. In: Richter-Gebert, J., Wang, D. (eds) Automated Deduction in Geometry. ADG 2000. Lecture Notes in Computer Science(), vol 2061. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45410-1_9
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DOI: https://doi.org/10.1007/3-540-45410-1_9
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