# Nemo/Hecke: Computer Algebra and Number Theory Packages for the Julia Programming Language

## TL;DR

This paper presents Nemo and Hecke, Julia packages for computer algebra and number theory, demonstrating high performance implementations using Julia's capabilities and interfacing with existing C/C++ libraries.

## Contribution

Introduction of Nemo and Hecke packages in Julia that achieve high performance for algebra and number theory computations without low-level language dependency.

## Key findings

- High performance generic algorithms implemented in Julia
- Effective wrapping of C/C++ libraries for specialized algorithms
- Demonstrated practical use cases and algorithm implementations

## Abstract

We introduce two new packages, Nemo and Hecke, written in the Julia programming language for computer algebra and number theory. We demonstrate that high performance generic algorithms can be implemented in Julia, without the need to resort to a low-level C implementation. For specialised algorithms, we use Julia's efficient native C interface to wrap existing C/C++ libraries such as Flint, Arb, Antic and Singular. We give examples of how to use Hecke and Nemo and discuss some algorithms that we have implemented to provide high performance basic arithmetic.