erou / LatticeGFH90.jl

LatticeGFH90.jl

A Julia/Nemo package to make lattices of compatibly embedded finite fields based on Hilbert's theorem 90 and Allombert's algorithm.

How to: install

The Julia packages

• Install Julia (preferably the last version, to avoid suprises...)
• Type ] to go in package mode (Backspace to quit)

(v1.1) pkg> add Nemo

(v1.1) pkg> add "https://github.com/erou/LatticeGFH90.jl"

julia> using Nemo, LatticeGFH90

• You're done!

Note: this has not been tested on a wide variety of systems, if you encounter a problem during install, please tell us!

Testing the package

A longer demo, with explanations, is available on Binder:

julia> make_zetas_conway(5)

julia> k3, x3 = FiniteField(5, 3, "x3")
(Finite field of degree 3 over F_5, x3)

julia> k6, x6 = FiniteField(5, 6, "x6")
(Finite field of degree 6 over F_5, x6)

julia> k12, x12 = FiniteField(5, 12, "x12")
(Finite field of degree 12 over F_5, x12)

julia> f = embed(k3, k6);

julia> g = embed(k6, k12);

julia> h = embed(k3, k12);

julia> x = rand(k3); g(f(x)) == h(x)
true

Benchmarks

Some benchmarks of the code are available in the folder benchmarks, together with a README file to explain what exactly is benchmarked.