Chevie.jl

This is my attempt to port the Chevie package from GAP3 to Julia. I started this project at the end of 2018 and it is still in flux so some function names or interfaces may still change. Pull requests and issues are welcome.

I have implemented the GAP functionality (infrastructure) needed to make Chevie work. I have already registered most of this infrastructure as separate packages; the following packages are loaded and re-exported so that their functionality is automatically available when you use Chevie. In other words, Chevie is a meta-package for the following packages:

  • (univariate) LaurentPolynomials (and rational fractions)

  • (multivariate) PuiseuxPolynomials (and rational fractions when there are no fractional exponents)

  • CyclotomicNumbers(elements of cyclotomic fields)

  • ModuleElts (elements of a free module over some ring)

  • Combinat (combinatorics and some basic number theory)

  • PermGroups (permutations, groups, permutations groups. It contains the modules Perms and Groups which could be separate packages)

  • SignedPerms (signed permutations)

  • MatInt (Integer matrices and lattices)

  • CycPols (cyclotomic polynomials)

  • GenLinearAlgebra (linear algebra on any field/ring)

  • FinitePosets (finite posets)

  • FiniteFields (finite fields)

  • GroupPresentations (presentations of groups, and groups defined by generators and relations)

  • UsingMerge (Automatically compose several packages) Have a look at the documentation of the above packages to see how to use their features. I have implemented some other infrastructure which currently resides in Chevie but may eventually become separate packages:

  • factorizing polynomials over finite fields (module FFfac)

  • factorizing polynomials over the rationals (module Fact)

  • Number fields which are subfields of the Cyclotomics (module Nf)

For permutation groups I have often replaced GAP's sophisticated algorithms with naive but easy-to-write methods suitable only for small groups (sufficient for the rest of the package but perhaps not for your needs). Otherwise the infrastructure code is often competitive with GAP, despite using much less code (often 100 lines of Julia replace 1000 lines of C); and I am sure it could be optimised better than I did. Comments on code and design are welcome. For functions that are too inefficient or difficult to implement (such as character tables of arbitrary groups), Chevie uses the GAP package as an extension. This means that if you have the GAP package installed, Chevie will automatically call GAP4 to implement these functions. The code in this package is often 10 times faster than the equivalent GAP3 Chevie code (after the maddeningly long compilation time on the first run --- Julia's TTFP).

The Chevie package currently contains about 95% of the GAP3/Chevie functionality, ported from Gap3. If you are a user of GAP3/Chevie, the gap function can help you to find the equivalent functionality in Chevie.jl to a Gap3 function: it takes a string and gives you Julia translations of functions in Gap3 that match that string.

julia> gap("words")
CharRepresentationWords  =>  traces_words_mats
CoxeterWords(W[,l])      =>  word.(Ref(W),elements(W[,l]))
GarsideWords             =>  elements

You can then access online help for the functions you have found.

The port to Julia is not complete in the sense that 80% of the code is the data library from Chevie, which was automatically ported by a transpiler so its code is "strange". When the need to maintain the GAP3 and Julia versions simultaneously subsides, I will do a proper translation of the data library, which should give an additional speed boost.

This package requires julia 1.9 or later.