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https://github.com/thofma/Hecke.jl

Computational algebraic number theory
https://github.com/thofma/Hecke.jl

algebraic-number-theory class-field-theory computer-algebra discrete-mathematics julia math number-theory

Last synced: about 1 month ago
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Computational algebraic number theory

Host: GitHub
URL: https://github.com/thofma/Hecke.jl
Owner: thofma
License: other
Created: 2015-05-17T14:01:45.000Z (about 9 years ago)
Default Branch: master
Last Pushed: 2024-05-11T17:23:36.000Z (about 1 month ago)
Last Synced: 2024-05-12T17:34:27.813Z (about 1 month ago)
Topics: algebraic-number-theory, class-field-theory, computer-algebra, discrete-mathematics, julia, math, number-theory
Language: Julia
Homepage:
Size: 65.6 MB
Stars: 202
Watchers: 12
Forks: 57
Open Issues: 41
Metadata Files:
- Readme: README.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Citation: CITATION.bib

Lists

awesome-stars - thofma/Hecke.jl - Computational algebraic number theory (Julia)

README

        # Hecke

**Builds**

[![Docs dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://thofma.github.io/Hecke.jl/dev)

[![Docs stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://thofma.github.io/Hecke.jl/stable)

[![Build status](https://github.com/thofma/Hecke.jl/workflows/Run%20long%20tests/badge.svg?branch=master)](https://github.com/thofma/Hecke.jl/actions?query=workflow%3A%22Run-tests%22+branch%3Amaster)

[![Codecov](https://codecov.io/github/thofma/Hecke.jl/coverage.svg?branch=master&token=)](https://codecov.io/gh/thofma/Hecke.jl)

## About

Hecke is a software package for algebraic number theory maintained by Claus Fieker and Tommy Hofmann.

It is written in [julia](https://www.julialang.org) and is based on the computer algebra packages [Nemo](https://github.com/Nemocas/Nemo.jl) and [AbstractAlgebra](https://github.com/Nemocas/AbstractAlgebra.jl).

Hecke is part of the [OSCAR](https://www.oscar-system.org/) project and the development is supported by the Deutsche Forschungsgemeinschaft DFG within the Collaborative Research Center TRR 195.

-  (Source code)

-  (Online documentation)

So far, Hecke provides the following features:

  - Number fields (absolute, relative, simple and non-simple)

  - Orders and ideals in number fields

  - Class and unit group computations of orders

  - Lattice enumeration

  - Sparse linear algebra

  - Class field theory

  - Abelian groups

  - Associative algebras

  - Ideals and orders in (semisimple) associative algebras

  - Locally free class groups of orders in semisimple algebras

  - Quadratic and Hermitian forms and lattices

## Installation

To use Hecke, a julia version of 1.0 is necessary (the latest stable julia version will do).

Please see  for instructions on how to obtain julia for your system.

Once a suitable julia version is installed, use the following steps at the julia prompt to install Hecke:

```julia

julia> using Pkg

julia> Pkg.add("Hecke")

```

## Citing Hecke

If your research depends on computations done with Hecke, please consider giving us a formal citation:

- Claus Fieker, William Hart, Tommy Hofmann and Fredrik Johansson, [Nemo/Hecke: Computer Algebra and Number Theory Packages

  for the Julia Programming Language](https://doi.acm.org/10.1145/3087604.3087611). In: Proceedings of ISSAC '17, pages 157–164, New York, NY, USA, 2017. ACM.

```bib

@inproceedings{nemo,

    author = {Fieker, Claus and Hart, William and Hofmann, Tommy and Johansson, Fredrik},

     title = {Nemo/Hecke: Computer Algebra and Number Theory Packages for the Julia Programming Language},

 booktitle = {Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation},

    series = {ISSAC '17},

      year = {2017},

     pages = {157--164},

  numpages = {8},

       url = {https://doi.acm.org/10.1145/3087604.3087611},

       doi = {10.1145/3087604.3087611},

 publisher = {ACM},

   address = {New York, NY, USA},

}

```

## Quick start

Here is a quick example of using Hecke:

```julia

julia> using Hecke

Welcome to

    _    _           _

   | |  | |         | |

   | |__| | ___  ___| | _____

   |  __  |/ _ \/ __| |/ / _ \

   | |  | |  __/ (__|   <  __/

   |_|  |_|\___|\___|_|\_\___|

Version 0.22.8...

 ... which comes with absolutely no warranty whatsoever

(c) 2015-2024 by Claus Fieker, Tommy Hofmann and Carlo Sircana

julia> Qx, x = polynomial_ring(FlintQQ, "x");

julia> f = x^3 + 2;

julia> K, a = number_field(f, "a");

julia> O = maximal_order(K);

julia> O

Maximal order of Number field of degree 3 over QQ

with basis AbsSimpleNumFieldElem[1, a, a^2]

```

## Documentation

The online documentation can be found here:

- [stable](https://thofma.github.io/Hecke.jl/stable/)

- [dev](https://thofma.github.io/Hecke.jl/dev/)