Skip to content

thofma/Hecke.jl

master
Switch branches/tags

Name already in use

A tag already exists with the provided branch name. Many Git commands accept both tag and branch names, so creating this branch may cause unexpected behavior. Are you sure you want to create this branch?
Code

Files

Permalink
Failed to load latest commit information.
Type
Name
Latest commit message
Commit time
March 2, 2023 23:52
August 18, 2021 17:46
January 9, 2021 11:43
November 7, 2020 13:52
May 18, 2015 10:20
March 28, 2023 08:51
March 2, 2023 23:52
February 24, 2023 08:57
March 6, 2021 14:55
November 12, 2015 23:50

Hecke

Builds

Docs dev Docs stable Build status Codecov

About

Hecke is a software package for algebraic number theory maintained by Claus Fieker, Tommy Hofmann and Carlo Sircana. It is written in julia and is based on the computer algebra packages Nemo and AbstractAlgebra. Hecke is part of the OSCAR project and the development is supported by the Deutsche Forschungsgemeinschaft DFG within the Collaborative Research Center TRR 195.

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 (semsimple) associative algebras
  • Locally free class groups of orders in semisimple algebras

Installation

To use Hecke, a julia version of 1.0 is necessary (the latest stable julia version will do). Please see https://julialang.org/downloads/ 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> using Pkg
julia> Pkg.add("Hecke")

Citing Hecke

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

@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> using Hecke
...

Welcome to

  _    _           _
 | |  | |         | |
 | |__| | ___  ___| | _____
 |  __  |/ _ \/ __| |/ / _ \
 | |  | |  __/ (__|   <  __/
 |_|  |_|\___|\___|_|\_\___|

Version 0.10.12...
 ... which comes with absolutely no warrant whatsoever
(c) 2015-2019 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 over Rational Field with defining polynomial x^3 + 2
with basis [1,a,a^2]

Documentation

The online documentation can be found here: