21 FUNDAMENTAL ALGORITHMS FOR NONLINEAR PRODUCTS
In the previous chapter, we looked at how to implement the linear products in geometric algebra. The linearity of these products allowed us to implement them using linear algebra or through a simple double loop. However, there are other operations in geometric algebra that are nonlinear (such as inverse, meet, join, and factorization). These cannot be implemented in the same way.
In this chapter, we discuss the implementation of such nonlinear geometric algebra operations. The nonlinearity results in more complex algorithms, still reasonably efficient but typically an order of magnitude more time-consuming than linear operations.
We give algorithms for the inverse, for exponentiation, for testing ...