# Solving p-adic polynomial systems via iterative eigenvector algorithms

## TL;DR

This paper presents a method for solving 0-dimensional p-adic polynomial systems using iterative eigenvector algorithms, along with an improved eigenvalue/eigenvector computation for p-adic matrices.

## Contribution

It introduces an implementation of a polynomial system solver for p-adic systems and enhances an existing eigenvalue algorithm for p-adic matrices.

## Key findings

- Effective approximate solutions for p-adic polynomial systems.
- Improved eigenvalue and eigenvector computation for p-adic matrices.
- Enhanced algorithm performance in finite precision p-adic arithmetic.

## Abstract

In this article, we describe an implementation of a polynomial system solver to compute the approximate solutions of a 0-dimensional polynomial system with finite precision p-adic arithmetic. We also describe an improvement to an algorithm of Caruso, Roe, and Vaccon for calculating the eigenvalues and eigenvectors of a p-adic matrix.