The power of Clifford or, geometric, algebra lies in its ability to represent geometric operations in a concise and elegant manner. Clifford algebras provide the natural generalizations of complex, dual numbers and quaternions into non-commutative multivectors. The paper demonstrates an algorithm for the computation of inverses of such numbers in a non-degenerate Clifford algebra of an arbitrary dimension. The algorithm is a variation of the Faddeev-LeVerrier-Souriau algorithm and is implemented in the open-source Computer Algebra System Maxima. Symbolic and numerical examples in different Clifford algebras are presented.

翻译：Clifford代数（或几何代数）的强大之处在于其能以简洁优雅的方式表示几何运算。Clifford代数将复数、对偶数和四元数自然推广为不可交换的多向量。本文提出一种算法，用于计算任意维非退化Clifford代数中此类数的逆。该算法是Faddeev-LeVerrier-Souriau算法的变体，并在开源计算机代数系统Maxima中实现。文中给出了不同Clifford代数下的符号与数值实例。