Computing preimages of points and curves under polynomial maps

TL;DR

This paper introduces two algorithms for computing preimages of points and curves under polynomial maps, providing an efficient method for inversion and an abstract framework for iteratively computing polynomial automorphism inverses.

Contribution

The paper presents novel algorithms for preimage computation under polynomial endomorphisms and an abstract setting for iteratively inverting polynomial automorphisms.

Findings

Efficient algorithms for preimages of points and curves.

Framework for iterative inversion of polynomial automorphisms.

Application to polynomial endomorphism inverse computation.

Abstract

In this paper, we give two algorithms to compute preimages of curves under polynomial endomorphisms. In particular, this gives an efficient way of computing preimages of points. Furthermore, we explain the abstract setting under which one can iteratively compute the inverse of a polynomial automorphism.