Merge pull request #32 from kalmarek/total_rewrite

Total rewrite of the package:
 * Drop the dependency on `AbstractAlgebra.Perm`: we ship our own `Perm{T}` which is defined   inside `PermutationGroups.Perms` module. Notable changes from the `AA` version:
   - `AbstractPermutation` interface (testable!) which the new `Perm` follows
   - `Perm` caches its inverse (so that second and later calls to `inv` are essentially free!)
   - and tries very hard to make sure that there will be at most one inverse perm (that is unless you copy it explicitly).
   - caching usually is problematic with multithreading, but the new `Perm` tries to stay thread-safe 
   - due to the usage of `@atomic`s `Perm` is now a `mutable struct`, so creating a `Perm` requires two allocations (julia-1.9): one for the storage of images, second for the `Perm` object.
 * Rewrite `StabilizerChain` to use the recursive formulation and rewrite `schreier_sims` accordingly
 * New, rather fast iteration over leafs of the `StabilizerChain` tree (i.e. group elements)
 * switch to using `Transversal` by default. This is justified by benchmarks; If you want to use `SchreierTransversal` (e.g. because you run out of memory) you may do so by defining `PermGroup(SchreierTransversal, gens)`
 * By default `Perm`s use `UInt16` as storage; This applies to `perm"(1,2,3)"` macro as well. Again, you may change this by calling `PermGroup(Perm{UInt}.(gens))`; For "normal" usage `UInt32` should be more than enough though. 

 * Major breaking changes:
  - non-constant `degree` in a permutation group (in particular `degree(one(perm)) == 1`)
  - all `Perm`s are compatible (i.e. embedded in `Sym(∞)`)
  - `Permutation`s implement Group interface; `Perm`s don't.

If you use just external interface it is likely that this release won't be breaking for you.

Project.toml

@@ -1,23 +1,21 @@
 name = "PermutationGroups"
 uuid = "8bc5a954-2dfc-11e9-10e6-cd969bffa420"
 authors = ["Marek Kaluba <kalmar@amu.edu.pl>", "tweisser <tillmann.weisser@web.de>"]
-version = "0.3.4"
+version = "0.4.0"
 
 [deps]
-AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
 GroupsCore = "d5909c97-4eac-4ecc-a3dc-fdd0858a4120"
-Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 
 [compat]
-AbstractAlgebra = "0.22 - 0.31"
 GroupsCore = "0.4"
 julia = "1.6"
 
 [extras]
+AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Test", "Random", "BenchmarkTools"]
+test = ["Test", "Random", "BenchmarkTools", "AbstractAlgebra"]

src/Perms/Perms.jl

@@ -0,0 +1,18 @@
+module Perms
+
+using GroupsCore
+export AbstractPermutation, Perm, cycles, degree, permtype, @perm_str
+
+include("cycle_decomposition.jl")
+
+# abstract definitions
+include("abstract_perm.jl")
+include("arithmetic.jl")
+include("misc.jl")
+
+include("utils.jl")
+
+# concrete implementations
+include("perm_images.jl")
+include("macro_perm.jl")
+end