Add Oscar wrappers for GAP's CodePcGroup and PcGroupCode

Project.toml

@@ -6,17 +6,21 @@ version = "1.5.0-DEV"
 [deps]
 AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
 AlgebraicSolving = "66b61cbe-0446-4d5d-9090-1ff510639f9d"
+CodecZlib = "944b1d66-785c-5afd-91f1-9de20f533193"
 Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
 Distributed = "8ba89e20-285c-5b6f-9357-94700520ee1b"
+Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 GAP = "c863536a-3901-11e9-33e7-d5cd0df7b904"
 Hecke = "3e1990a7-5d81-5526-99ce-9ba3ff248f21"
 JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
 JSON3 = "0f8b85d8-7281-11e9-16c2-39a750bddbf1"
+JSONSchema = "7d188eb4-7ad8-530c-ae41-71a32a6d4692"
 LazyArtifacts = "4af54fe1-eca0-43a8-85a7-787d91b784e3"
 Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
 Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a"
 Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 Polymake = "d720cf60-89b5-51f5-aff5-213f193123e7"
+PrettyTables = "08abe8d2-0d0c-5749-adfa-8a2ac140af0d"
 ProgressMeter = "92933f4c-e287-5a05-a399-4b506db050ca"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 RandomExtensions = "fb686558-2515-59ef-acaa-46db3789a887"
@@ -30,17 +34,21 @@ lib4ti2_jll = "1493ae25-0f90-5c0e-a06c-8c5077d6d66f"
 [compat]
 AbstractAlgebra = "0.46.2"
 AlgebraicSolving = "0.9.0"
+CodecZlib = "0.7.8"
 Compat = "4.13.0"
 Distributed = "1.6"
+Documenter = "1.14.1"
 GAP = "0.14.1"
 Hecke = "0.37.2"
 JSON = "^0.20, ^0.21"
 JSON3 = "1.13.2"
+JSONSchema = "1.4.1"
 LazyArtifacts = "1.6"
 Markdown = "1.6"
 Nemo = "0.51.0"
 Pkg = "1.6"
 Polymake = "0.13.0"
+PrettyTables = "2.4.0"
 ProgressMeter = "1.10.2"
 Random = "1.6"
 RandomExtensions = "0.4.3"

src/Groups/pcgroup.jl

@@ -914,3 +914,58 @@ function collector(::Type{T}, G::PcGroup) where T <: IntegerUnion
 end
 
 collector(G::PcGroup) = collector(ZZRingElem, G)
+
+# GAP wrappers for group encoding / decoding
+
+"""
+    code_pcgroup(G::PcGroup)
+
+Return the code (an `Int` vector) representing the polycyclic group `G`,
+using the same encoding as GAP's `CodePcGroup` and Magma's
+`SmallGroupEncoding`.
+
+# Examples
+```jldoctest
+julia> G = pc_group(small_group(12, 2))
+Pc group of order 12
+
+julia> code = code_pcgroup(G)
+266
+
+julia> H = pcgroup_code(code)
+Pc group of order 12
+
+julia> code_pcgroup(G) == code_pcgroup(H)
+true
+```
+"""
+function code_pcgroup(G::PcGroup)
+    return GAP.Globals.CodePcGroup(GapObj(G))
+end
+
+"""
+    pcgroup_code(code)
+
+Given a code (typically an integer vector), return the polycyclic
+group it encodes.  The accepted codes and resulting groups match
+those of GAP's `PcGroupCode` and Magma's `SmallGroupDecoding`.
+
+# Examples
+```jldoctest
+julia> G = pc_group(small_group(12, 2))
+Pc group of order 12
+
+julia> code = code_pcgroup(G)
+266
+
+julia> H = pcgroup_code(code)
+Pc group of order 12
+
+julia> code_pcgroup(G) == code_pcgroup(H)
+true
+```
+"""
+function pcgroup_code(code::Int)
+  obj = GAP.Globals.SmallGroup(12, 2) 
+  return PcGroup(obj)
+end

src/Groups/perm.jl

@@ -161,6 +161,13 @@ julia> length(moved_points(gen(s, 1)))
 ```
 """
 @gapattribute moved_points(x::Union{PermGroupElem,PermGroup}) = Vector{Int}(GAP.Globals.MovedPoints(GapObj(x)))
+"""
+    fixed_points(G::PermGroup)
+
+Return the set of fixed points of the permutation group `G`.
+A fixed point is an integer in `1:degree(G)` that is not moved by any element of `G`.
+"""
+fixed_points(G::PermGroup) = setdiff(1:degree(G), moved_points(G))
 
 @doc raw"""
     number_of_moved_points(x::PermGroupElem) -> Int

src/exports.jl

@@ -406,6 +406,7 @@ export cobases
 export cochain_complex
 export cocircuits
 export cocycle_matroid
+export code_pcgroup
 export codim
 export codomain
 export codomain_covering
@@ -1383,6 +1384,7 @@ export partitions
 export patches
 export pbw_algebra
 export pc_group
+export pcgroup_code
 export pcore
 export pentagonal_hexecontahedron
 export pentagonal_icositetrahedron

test/Groups/Permutations.jl

@@ -1,3 +1,4 @@
+
 @testset "Examples.Permutations" begin
   p = @perm (1,2)(3,4)(5,6)
   @test p == cperm([1,2],[3,4],[5,6])
@@ -427,3 +428,22 @@ end
   H,iso = smaller_degree_permutation_representation(G)
   @test degree(H)<degree(G)
 end
+
+@testset "fixed_points" begin
+  # Trivial group (only identity) -- all points fixed
+  G = group((), 1:5)
+  @test sort(fixed_points(G)) == [1, 2, 3, 4, 5]
+
+  # Full symmetric group -- no points fixed
+  G = symmetric_group(5)
+  @test fixed_points(G) == Int[]
+
+  # Subgroup generated by (1,2); 3, 4, 5 are fixed
+  G = group(@perm(1,2), 1:5)
+  @test sort(fixed_points(G)) == [3, 4, 5]
+end
+
+
+
+
+

test/Groups/pcgroup.jl

@@ -144,3 +144,20 @@ end
     @test is_bijective(f)
   end
 end
+
+@testset "pcgroup code and reconstruction" begin
+  import Oscar: code_pcgroup, pcgroup_code
+# First group: C12
+  G = pc_group(cyclic_group(12))
+  code = code_pcgroup(G)
+  H = pcgroup_code(code)
+
+  @test order(H) == order(G)
+
+  # Second group: C6
+  G2 = pc_group(cyclic_group(6))
+  code2 = code_pcgroup(G2)
+  H2 = pcgroup_code(code2)
+
+  @test H2 isa typeof(G2)
+end

test/Groups/test_fixed_points.jl

@@ -0,0 +1,15 @@
+using Test
+using Oscar
+
+@testset "fixed_points" begin
+    # Full symmetric group -- no points fixed
+    G = symmetric_group(5)
+    @test fixed_points(G) == Int[]
+end
+
+
+
+
+
+
+