Builds
Hecke is a software package for algebraic number theory maintained by Claus Fieker and Tommy Hofmann. It is written in julia and is based on the computer algebra package Nemo.
- https://github.com/thofma/Hecke.jl (Source code)
- http://thofma.github.io/Hecke.jl/latest/ (Online documentation)
So far, Hecke provides the following features:
- Orders (including element and ideal arithmetic) in relative and absolute number fields
- Computation of maximal orders
- Verified residue computations of Dedekind zeta functions
- Factor base creation and relations search in number fields
- Lattice enumeration
- Sparse linear algebra
- Ray class groups and construction of class fields
- Class field theory
To use Hecke, a julia version of 0.6 or higher is necessary (the latest stable julia version will do). Please see http://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> Pkg.add("Hecke")Here is a quick example of using Hecke:
julia> using Hecke
...
Welcome to
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| | | | __/ (__| < __/
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Version 0.4.3 ...
... which comes with absolutely no warrant whatsoever
(c) 2015 by Claus Fieker and Tommy Hofmann
julia> Qx, x = PolynomialRing(FlintQQ, "x");
julia> f = x^3 + 2;
julia> K, a = NumberField(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]The online documentation can be found here: http://thofma.github.io/Hecke.jl/latest/
The documentation of the single functions can also be accessed at the julia prompt. Here is an example:
help?> signature
search: signature
----------------------------------------------------------------------------
signature(O::NfMaximalOrder) -> Tuple{Int, Int}
| Returns the signature of the ambient number field of \mathcal O.