Hecke

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Hecke

Computational number theory for everyone

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What is Hecke?

Hecke is a software package for computational algebraic number theory. It is written in julia and makes use of the computer algebra packages Nemo and AbstractAlgebra.

OSCAR

Hecke is part of the [OSCAR](https://www.oscar-system.org/) system, which covers, in addition to number theory, also commutative algebra, algebraic geometry, group theory and polyhedral geometry.

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

  • Quadratic and Hermitian forms and lattices

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},
}

Acknowledgement ​

Hecke is part of the OSCAR project and the development is supported by the Deutsche Forschungsgemeinschaft DFG within the Collaborative Research Center TRR 195.