If K is a field, and f,g are endomorphisms of \mathbb{P}^N(K), for N > 1, a topic of interest is computing the conjugating set that takes f to g. The method employed by Sage, the fixed point algorithm, for computing these conjugating sets is a naive search that tries all possible mappings from specific subsets of the fixed points and their pre-images of one endomorphism, to those of the other. In this paper, we propose two algorithms that improve upon this fixed point method by restricting the number of mappings to search through.

This restriction comes from the fact that the conjugation action preserves the characteristic polynomial of the multiplier matrices of fixed points. Even simple implementations of these improved algorithms are shown to work significantly better in low dimensions, and we demonstrate that this difference in performance will grow as dimension increases.

Alexander would like to thank his faculty sponsor Benjamin Hutz for their support of this project.