[ANN] New registered package Chevie

This to announce a new registered package Chevie dealing with various areas of representation theory.

Here is the README
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:

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 is the one package I use everyday, this and Oscar.jl are perhaps the most important packages in my workflow.

Thanks again for this!