There is functionality for working with dynamical systems over projective space in Sage. However, one of the areas lacking in functionality is the moduli space. We say two self-maps of projective space are equivalent if there is an element of the Projective Linear Group that conjugates one to the other. The following two algorithms should be implemented, in order to create more functionality in moduli space. The first algorithm would be that given two endomorphisms of projective space determine if they are conjugate. In other words, determine if they are in the same class in the moduli space. If they are, also return the PGL element that conjugates one to the other.The second algorithm would be that given an endomorphism of projective space to compute a reduced form. This conjugation would that makes the coefficients small. There is already an algorithm implemented to return the minimal model in terms of resultant, but the coefficients can be non-optimal. The simplest approach would be to reduce the binary form describing the fixed points or if the binary form describing the fixed points is not sufficiently nice then reduce the binary form for points of period n for some small n.

#### Student

Rebecca Lauren Miller

• Benh