Move Weyl groups and root systems to src/ (#4399)

Co-authored-by: Felix Röhrich <[email protected]>

Author: lgoettgens

docs/doc.main

@@ -248,7 +248,7 @@
      "TropicalGeometry/tropicalization.md",
   ],
 
- "Noncommutative Algebra" => [
+  "Noncommutative Algebra" => [
     "NoncommutativeAlgebra/intro.md",
     "PBW-Algebras" => [
     "NoncommutativeAlgebra/PBWAlgebras/intro.md",
@@ -259,6 +259,14 @@
     "NoncommutativeAlgebra/free_associative_algebra.md",
   ],
 
+  "Lie Theory" => [
+    "LieTheory/intro.md",
+    "LieTheory/cartan_matrix.md",
+    "LieTheory/root_systems.md",
+    "LieTheory/weight_lattices.md",
+    "LieTheory/weyl_groups.md",
+  ],
+
   "Combinatorics" => [
     "Combinatorics/graphs.md",
     "Combinatorics/matroids.md",

experimental/LieAlgebras/docs/src/cartan_matrix.md docs/src/LieTheory/cartan_matrix.md

@@ -3,7 +3,7 @@ CurrentModule = Oscar
 DocTestSetup = Oscar.doctestsetup()
 ```
 
-# Cartan Matrices
+# Cartan matrices
 
 Cartan matrices can be constructed from a Cartan type, and are represented as a square `ZZMatrix`.
 

docs/src/LieTheory/intro.md

@@ -0,0 +1,26 @@
+```@meta
+CurrentModule = Oscar
+DocTestSetup = Oscar.doctestsetup()
+```
+
+# Introduction
+
+The Lie theory part of OSCAR provides functionality for handling
+- [Cartan matrices](@ref)
+- [Root systems](@ref)
+- [Weyl groups](@ref)
+- [Weight lattices](@ref)
+- more content can be found under `Experimental/LieAlgebras`
+
+It aims to provide the computational tools to work with the concepts defined in [Hum72](@cite) and [Bou02](@cite).
+
+## Contact
+
+Please direct questions about this part of OSCAR to the following people:
+* [Lars Göttgens](https://lgoe.li/)
+* [Max Horn](https://math.rptu.de/en/wgs/agag/people/head/prof-dr-max-horn).
+* [Felix Röhrich](https://www.art.rwth-aachen.de/cms/~xlgua)
+
+You can ask questions in the [OSCAR Slack](https://www.oscar-system.org/community/#slack).
+
+Alternatively, you can [raise an issue on github](https://www.oscar-system.org/community/#how-to-report-issues).

experimental/LieAlgebras/docs/src/root_systems.md docs/src/LieTheory/root_systems.md

@@ -34,6 +34,7 @@ weyl_group(::Vector{Tuple{Symbol,Int}})
 Basic group arithmetic like `*`, and `inv` are defined for `WeylGroupElem` objects.
 
 Using `(W::WeylGroup)(word::Vector{<:Integer})`, one can construct group elements from a word in the generators.
+Finite Weyl groups support iteration over all group elements (in an arbitrary order).
 
 ```@docs
 is_finite(::WeylGroup)
@@ -62,18 +63,6 @@ longest_element(::WeylGroup)
 ```
 
 
-## Conversion to other group types
-
-For many computations, it may be suitable to have a `WeylGroup` as a different kind of group object, to e.g. use functionality that is only available for that other type.
-
-The conversion functions come in pairs: one only creates an isomorphic group object, the other also computes the isomorphism.
-
-```@docs
-fp_group(::WeylGroup)
-isomorphism(::Type{FPGroup}, ::WeylGroup)
-```
-
-
 ## Reduced expressions
 
 ```@docs
@@ -89,4 +78,7 @@ reduced_expressions(::WeylGroupElem)
 
 
 ### Orbits
-TODO
+
+```@docs
+weyl_orbit(::WeightLatticeElem)
+```

experimental/LieAlgebras/docs/src/weight_lattices.md docs/src/LieTheory/weight_lattices.md

@@ -44,6 +44,8 @@ result = 0
     "src/InvariantTheory",
     "src/PolyhedralGeometry",
     "test/PolyhedralGeometry",
+    "src/LieTheory",
+    "test/LieTheory",
     "src/aliases.jl",
     "experimental/BasisLieHighestWeight",
     "experimental/ExperimentalTemplate",

experimental/LieAlgebras/docs/src/weyl_groups.md docs/src/LieTheory/weyl_groups.md

@@ -3,10 +3,9 @@ module BasisLieHighestWeight
 using ..Oscar
 using ..Oscar: IntegerUnion
 using ..Oscar: _is_weighted
+using ..Oscar: _root_system_type_string
 
-using Oscar.LieAlgebras:
-  _root_system_type_string,
-  lie_algebra_simple_module_struct_consts_gap
+using Oscar.LieAlgebras: lie_algebra_simple_module_struct_consts_gap
 
 using AbstractAlgebra.PrettyPrinting
 

etc/test_formatting.jl

@@ -8,7 +8,7 @@ const expdir = joinpath(@__DIR__, "../experimental")
 const orderedpkgs = [
   "LieAlgebras",
   "BasisLieHighestWeight",   # needs code from LieAlgebras
-  "AlgebraicShifting", # Needs code form Lie Algebras (Weyl Groups specifically)
+  "AlgebraicShifting",       # Needs code from Lie Algebras (`isomorphism(PermGroup, ::WeylGroup)` specifically)
   "SetPartitions",
   "PartitionedPermutations", # needs code from SetPartitions
   "Schemes",

experimental/BasisLieHighestWeight/src/BasisLieHighestWeight.jl

@@ -1,5 +1,3 @@
-isdefined(Oscar, :word) || function word end
-
 include("Cohomology.jl")
 include("GaloisCohomology.jl")
 include("GrpExt.jl")

experimental/Experimental.jl

@@ -6,9 +6,6 @@
       "lie_algebra_homs.md",
       "modules.md",
       "module_homs.md",
-      "cartan_matrix.md",
-      "root_systems.md",
-      "weight_lattices.md",
-      "weyl_groups.md",
+      "weyl_groups_experimental.md",
    ],
 ]

experimental/GModule/src/GModule.jl

@@ -0,0 +1,20 @@
+```@meta
+CurrentModule = Oscar
+DocTestSetup = Oscar.doctestsetup()
+```
+
+# Weyl groups (experimental features)
+
+This page is an addition to the documentation of [Weyl groups](@ref) with the additional experimental features.
+
+
+## Conversion to other group types
+
+For many computations, it may be suitable to have a `WeylGroup` as a different kind of group object, to e.g. use functionality that is only available for that other type.
+
+The conversion functions come in pairs: one only creates an isomorphic group object, the other also computes the isomorphism.
+
+```@docs
+fp_group(::WeylGroup)
+isomorphism(::Type{FPGroup}, ::WeylGroup)
+```

experimental/LieAlgebras/docs/doc.main

@@ -1,10 +1,14 @@
-isdefined(Oscar, :word) || function word end
-
 module LieAlgebras
 
 using ..Oscar
 
-import Oscar: GAPWrap, IntegerUnion, MapHeader
+using Oscar:
+  _root_system_type_string,
+  _vec,
+  GAPWrap,
+  IntegerUnion,
+  MapHeader,
+  set_root_system_type!
 
 import Random
 
@@ -19,20 +23,19 @@ import ..Oscar:
   _is_exterior_power,
   _is_tensor_product,
   _iso_oscar_gap,
-  _vec,
   action,
-  add!,
-  addmul!,
   basis_matrix,
   basis,
   canonical_injection,
   canonical_injections,
   canonical_projection,
   canonical_projections,
+  cartan_matrix,
   center,
   centralizer,
   character,
   characteristic,
+  check_parent,
   coeff,
   coefficient_ring,
   coefficients,
@@ -41,15 +44,13 @@ import ..Oscar:
   derived_series,
   dim,
   direct_sum,
-  dot,
   dual,
   elem_type,
   expressify,
   exterior_power,
   fp_group,
   gen,
   gens,
-  height,
   hom,
   hom_direct_sum,
   hom_tensor,
@@ -59,8 +60,6 @@ import ..Oscar:
   induced_map_on_exterior_power,
   inv,
   is_abelian,
-  is_finite,
-  is_gen,
   is_isomorphism,
   is_nilpotent,
   is_perfect,
@@ -71,25 +70,17 @@ import ..Oscar:
   kernel,
   lower_central_series,
   matrix,
-  mul!,
-  neg!,
   normalizer,
   number_of_generators,
   ngens,
-  order,
   parent_type,
   permutation_group,
   rank,
-  root,
-  roots,
+  root_system,
   sub,
-  sub!,
   symbols,
   symmetric_power,
   tensor_product,
-  weyl_vector,
-  word,
-  zero!,
   zero_map,
   ⊕,
   ⊗
@@ -110,23 +101,12 @@ export _is_symmetric_power
 export _is_tensor_power
 export _is_tensor_product
 
-# Aliases
-function number_of_positive_roots end
-function number_of_roots end
-function number_of_simple_roots end
-
-@alias n_positive_roots number_of_positive_roots
-@alias n_roots number_of_roots
-@alias n_simple_roots number_of_simple_roots
-
 include("Types.jl")
 include("Combinatorics.jl")
 include("Util.jl")
 
-include("CartanMatrix.jl")
 include("CoxeterGroup.jl")
 include("RootSystem.jl")
-include("WeightLattice.jl")
 include("DynkinDiagram.jl")
 include("WeylGroup.jl")