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 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 (semisimple) 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.