Another 6D Multivector Inverse Algorithm

A simple algorithm for the inverse of a non-singular 6D multivector is presented. It is indifferent to signature (including degeneracy). A simpler algorithm is unlikely. A 4D algorithm of the same form is also presented. The formulas here are unlike the grade-involution-based inverse algorithms from which they were derived; instead, they rescale the scalar component. This algorithm requires two fewer multivector multiplications than its antecedent. A general expression for an annihilating polynomial of any 6D self-reverse multivector is given, with coefficients formed solely from the scalar parts of powers of the multivector. Opportunities for optimization are analyzed, and a strategy is presented that can reduce the number of real multiplications required to form the inverse to fewer than are required to multiply two arbitrary multivectors. Python code is presented, with additional code and documentation available in a public repository (see Ref. [7]).